Finite Group Databasebeta

← C3×#186814 #72271644

Subgroups — C3×#186814 #72271644

Order 1536.

7152 conjugacy classes of subgroups.

The subgroup lattice has 1718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#62811C211yesmaximal, characteristic
2C3×#20591C211yesmaximal, characteristic, complemented
3C3×#17587C212yesmaximal, complemented
4C2×C3×#1504C212yesmaximal, complemented
5C3×#13956C211yesmaximal, characteristic, complemented
6C3×#8455C214yesmaximal, complemented
7C3×#8453C214yesmaximal, complemented
8#186814C311yesmaximal, characteristic, direct product factor, Sylow
9C2×C3×#585C411yescharacteristic, complemented
10C23×C3×#41C2211yescharacteristic
11C3×#3489—22no—
12C3×#3489—22no—
13C3×#3488—22no—
14C3×#3488—22no—
15C3×#3487C412yescomplemented
16C3×#3486C2212yes—
17C3×#3485—22no—
18C3×#3485C412yescomplemented
19C3×#3484—22no—
20C3×#3484C2212yes—
21C3×D4×#41—24no—
22C3×D4×#41—24no—
23C3×#3449—22no—
24C3×#3449C412yescomplemented
25C2×C3×#525—22no—
26C2×C3×#525C2212yes—
27C3×#3428C411yescharacteristic, complemented
28C2×C3×#413—22no—
29C2×C3×#407C2212yescomplemented
30C2×C3×#386—22no—
31C2×C3×#381C2211yescharacteristic, complemented
32C22×C3×#95C2211yescharacteristic, complemented
33C3×#1785—22no—
34C3×#1784C2212yescomplemented
35C3×#1783C2212yescomplemented
36C3×#1516—24no—
37C3×#1511—22no—
38C3×#1510—22no—
39C3×#1504—24no—
40C3×#1504C2218yescomplemented
41C3×#1504C2218yescomplemented
42C2×C3×#328—22no—
43C2×C3×#327—22no—
44C3×#1446C2212yescomplemented
45C3×#1438C2212yescomplemented
46C3×C22⋊#95—22no—
47#62811C2×C311yescharacteristic
48#20591C2×C311yescharacteristic, complemented
49#17587C2×C312yescomplemented
50C2×#1504C2×C312yescomplemented
51#13956C2×C311yescharacteristic, complemented
52#8455C2×C314yescomplemented
53#8453C2×C314yescomplemented
54C3×#585—48no—
55C2×C3×2−1+4—22no—
56C2×C3×2−1+4C2×C412yescomplemented
57C2×C3×H(5,𝔽2)—22no—
58C2×C3×H(5,𝔽2)—22no—
59C2×C3×H(5,𝔽2)C2×C412yescomplemented
60C22×C3×#41—24no—
61C22×C3×#41—22no—
62C22×C3×#41—22no—
63C22×C3×#41—22no—
64C22×C3×#41—22no—
65C22×C3×#41—22no—
66C22×C3×#41—48no—
67C22×C3×#41C2×C412yes—
68C22×C3×#41C2×C411yescharacteristic
69C22×C3×#41C2×C411yescharacteristic
70C22×C3×#41C2×C411yescharacteristic
71C22×C3×#41C2×C411yescharacteristic
72C22×C3×#41D412yes—
73C22×C3×#41D412yes—
74C23×C3×Q8C2311yescharacteristic
75C23×C3×D4D412yes—
76C23×C3×D4C2311yescharacteristic
77C24×C3×C4—21no—
78C24×C3×C4D412yes—
79C24×C3×C4C2311yescharacteristic
80C22×C3×M16—22no—
81C3×#550—24no—
82C3×#550—24no—
83C3×D4×Q8—24no—
84C3×D4×Q8—24no—
85C3×#548—24no—
86C3×#548—24no—
87C3×#548—24no—
88C3×#548—24no—
89C3×#547—28no—
90C3×#547—28no—
91C3×#547—24no—
92C3×#547—24no—
93C3×#546—28no—
94C3×#546—28no—
95C3×#546—28no—
96C3×#546—28no—
97C3×#546—24no—
98C3×#546—24no—
99C3×#546—24no—
100C3×#546—24no—
101C3×D42—28no—
102C3×D42—28no—
103C3×D42—24no—
104C3×D42—24no—
105C3×#537—24no—
106C3×#537—24no—
107C3×#537—22no—
108C3×#537—22no—
109C3×#536—24no—
110C3×#536—22no—
111C3×#536—24no—
112C3×#536C2×C414yescomplemented
113C3×#535—24no—
114C3×#535—24no—
115C3×#535—22no—
116C3×#535C2×C414yescomplemented
117C3×#534—24no—
118C3×#534—24no—
119C3×#534—24no—
120C3×#532—28no—
121C3×#532—24no—
122C3×#525—24no—
123C3×#525—24no—
124C3×#525—24no—
125C3×#525—24no—
126C3×#525—28no—
127C3×#525—24no—
128C3×#525—24no—
129C3×#525—22no—
130C3×#525—24no—
131C3×#525—22no—
132C3×#525—22no—
133C3×#525—22no—
134C3×#525—24no—
135C3×#525C2×C414yes—
136C3×#525D414yes—
137C3×#525D414yes—
138C3×#525C2314yes—
139C2×C3×#123—24no—
140C2×C3×#123—22no—
141C2×C3×C22⋊Q8—22no—
142C2×C3×C22⋊Q8—22no—
143C2×C3×C22⋊Q8D412yes—
144C2×C3×C22⋊Q8D412yes—
145C2×C3×#121—22no—
146C2×C3×#121—22no—
147C2×C3×#121D412yes—
148C2×C3×#121D412yes—
149C2×C3×#120—24no—
150C2×C3×#120—22no—
151C3×#520—22no—
152C3×#520—22no—
153C3×#519C2×C412yescomplemented
154C3×#518—22no—
155C3×#518C2×C412yescomplemented
156C3×C4×#41—24no—
157C2×C3×C4×D4—24no—
158C2×C3×C4×D4—24no—
159C2×C3×C4×D4—22no—
160C2×C3×C4×D4—22no—
161C2×C3×#117—22no—
162C2×C3×#117C2×C412yes—
163C22×C3×C22⋊C4—21no—
164C22×C3×C22⋊C4—24no—
165C3×#413—48no—
166C2×C3×#101—24no—
167C2×C3×#100—24no—
168C3×#407—22no—
169C3×#407—22no—
170C3×#407—22no—
171C3×#407C2314yes—
172C2×C3×C22⋊C8—22no—
173C2×C3×C22⋊C8—22no—
174C3×#386—48no—
175C3×#381—22no—
176C3×#381—22no—
177C2×C3×#95—22no—
178C2×C3×#95—22no—
179C2×C3×#95—21no—
180C2×C3×#95—21no—
181C2×C3×#95—24no—
182C2×C3×#95C2312yes—
183C2×C3×#95C2312yes—
184C3×#328—28no—
185C3×#328—28no—
186C3×#327—28no—
187C3×#327—28no—
188C2×#585C3×C411yescharacteristic, complemented
189C23×#41C22×C311yescharacteristic
190#3489—22no—
191#3489—22no—
192#3488—22no—
193#3488—22no—
194#3487C3×C412yescomplemented
195#3486C22×C312yes—
196#3485—22no—
197#3485C3×C412yescomplemented
198#3484—22no—
199#3484C22×C312yes—
200D4×#41—24no—
201D4×#41—24no—
202#3449—22no—
203#3449C3×C412yescomplemented
204C2×#525—22no—
205C2×#525C22×C312yes—
206#3428C3×C411yescharacteristic, complemented
207C2×#413—22no—
208C2×#407C22×C312yescomplemented
209C2×#386—22no—
210C2×#381C22×C311yescharacteristic, complemented
211C22×#95C22×C311yescharacteristic, complemented
212#1785—22no—
213#1784C22×C312yescomplemented
214#1783C22×C312yescomplemented
215#1516—24no—
216#1511—22no—
217#1510—22no—
218#1504—24no—
219#1504C22×C318yescomplemented
220#1504C22×C318yescomplemented
221C2×#328—22no—
222C2×#327—22no—
223#1446C22×C312yescomplemented
224#1438C22×C312yescomplemented
225C22⋊#95—22no—
226C25×C3C2×D412yes—
227C25×C3C2×D411yescharacteristic
228C3×2−1+4—48no—
229C3×2−1+4—416no—
230C3×H(5,𝔽2)—48no—
231C3×H(5,𝔽2)—48no—
232C3×H(5,𝔽2)—416no—
233C3×H(5,𝔽2)—48no—
234C2×C3×#41—24no—
235C2×C3×#41—24no—
236C2×C3×#41—28no—
237C2×C3×#41—24no—
238C2×C3×#41—28no—
239C2×C3×#41—28no—
240C2×C3×#41—24no—
241C2×C3×#41—22no—
242C2×C3×#41—22no—
243C2×C3×#41—22no—
244C2×C3×#41—22no—
245C2×C3×#41—22no—
246C2×C3×#41—22no—
247C2×C3×#41—22no—
248C2×C3×#41—22no—
249C2×C3×#41—22no—
250C2×C3×#41—24no—
251C2×C3×#41—22no—
252C2×C3×#41—24no—
253C2×C3×#41—24no—
254C2×C3×#41—24no—
255C2×C3×#41—24no—
256C2×C3×#41—44no—
257C2×C3×#41—44no—
258C2×C3×#41—44no—
259C2×C3×#41—44no—
260C2×C3×#41—44no—
261C2×C3×#41—44no—
262C2×C3×#41—48no—
263C2×C3×#41—48no—
264C2×C3×#41—48no—
265C2×C3×#41—416no—
266C2×C3×#41—416no—
267C2×C3×#41—416no—
268C2×C3×#41—416no—
269C2×C3×#41—432no—
270C2×C3×#41C22⋊C414yescomplemented
271C2×C3×#41C22×C414yes—
272C22×C3×Q8—22no—
273C22×C3×Q8—24no—
274C22×C3×Q8—22no—
275C22×C3×Q8—22no—
276C22×C3×Q8—44no—
277C22×C3×Q8C22⋊C412yescomplemented
278C22×C3×Q8C22×C411yescharacteristic
279C22×C3×Q8C22×C411yescharacteristic
280C22×C3×Q8C2×D412yes—
281C22×C3×D4—22no—
282C22×C3×D4—28no—
283C22×C3×D4—24no—
284C22×C3×D4—22no—
285C22×C3×D4—24no—
286C22×C3×D4—24no—
287C22×C3×D4—24no—
288C22×C3×D4—24no—
289C22×C3×D4—22no—
290C22×C3×D4—22no—
291C22×C3×D4—28no—
292C22×C3×D4—24no—
293C22×C3×D4—22no—
294C22×C3×D4—22no—
295C22×C3×D4—44no—
296C22×C3×D4—44no—
297C22×C3×D4C22⋊C412yes—
298C22×C3×D4C22⋊C412yes—
299C22×C3×D4C22⋊C412yes—
300C22×C3×D4C22⋊C412yes—
301C22×C3×D4C22⋊C412yescomplemented
302C22×C3×D4C22×C411yescharacteristic
303C22×C3×D4C22×C411yescharacteristic
304C22×C3×D4C2×D412yes—
305C23×C3×C4—24no—
306C23×C3×C4—22no—
307C23×C3×C4—22no—
308C23×C3×C4—22no—
309C23×C3×C4—22no—
310C23×C3×C4—22no—
311C23×C3×C4—22no—
312C23×C3×C4—22no—
313C23×C3×C4—44no—
314C23×C3×C4—44no—
315C23×C3×C4—44no—
316C23×C3×C4—44no—
317C23×C3×C4—42no—
318C23×C3×C4—44no—
319C23×C3×C4—82no—
320C23×C3×C4C22⋊C412yes—
321C23×C3×C4C22⋊C412yes—
322C23×C3×C4C22⋊C412yes—
323C23×C3×C4C22⋊C412yes—
324C23×C3×C4C22×C411yescharacteristic
325C23×C3×C4C22×C411yescharacteristic
326C23×C3×C4C2×D412yes—
327C23×C3×C4C2×D411yescharacteristic
328C23×C3×C4C2×D411yescharacteristic
329C23×C3×C4C2×D412yes—
330C23×C3×C4C2×D412yes—
331C23×C3×C4C2×D412yes—
332C23×C3×C4C2×D412yes—
333C23×C3×C4C2×D411yescharacteristic
334C23×C3×C4C2411yescharacteristic
335C2×C3×M16—24no—
336C2×C3×M16—42no—
337C2×C3×M16—48no—
338C22×C3×C8—42no—
339C3×C4⋊Q8—28no—
340C3×C4⋊Q8—24no—
341C3×#127—28no—
342C3×#127—24no—
343C3×#124—28no—
344C3×#124—28no—
345C3×#124—24no—
346C3×#124—24no—
347C3×#123—28no—
348C3×#123—28no—
349C3×#123—28no—
350C3×#123—28no—
351C3×#123—28no—
352C3×#123—24no—
353C3×#123—28no—
354C3×#123—24no—
355C3×#123—24no—
356C3×#123—24no—
357C3×C22⋊Q8—24no—
358C3×C22⋊Q8—24no—
359C3×C22⋊Q8—24no—
360C3×C22⋊Q8—24no—
361C3×C22⋊Q8—24no—
362C3×C22⋊Q8—24no—
363C3×C22⋊Q8—28no—
364C3×C22⋊Q8—28no—
365C3×C22⋊Q8—22no—
366C3×C22⋊Q8—22no—
367C3×C22⋊Q8—22no—
368C3×C22⋊Q8—22no—
369C3×C22⋊Q8—24no—
370C3×C22⋊Q8—24no—
371C3×C22⋊Q8C22⋊C414yescomplemented
372C3×C22⋊Q8C22⋊C414yescomplemented
373C3×C22⋊Q8C2×D414yes—
374C3×C22⋊Q8C2×D414yes—
375C3×#121—24no—
376C3×#121—24no—
377C3×#121—24no—
378C3×#121—24no—
379C3×#121—24no—
380C3×#121—24no—
381C3×#121—28no—
382C3×#121—28no—
383C3×#121—28no—
384C3×#121—28no—
385C3×#121—28no—
386C3×#121—28no—
387C3×#121—28no—
388C3×#121—28no—
389C3×#121—22no—
390C3×#121—22no—
391C3×#121—22no—
392C3×#121—22no—
393C3×#121—24no—
394C3×#121—24no—
395C3×#121C22⋊C414yescomplemented
396C3×#121C22⋊C414yescomplemented
397C3×#121C2×D414yes—
398C3×#121C2×D414yes—
399C3×#120—28no—
400C3×#120—28no—
401C3×#120—28no—
402C3×#120—28no—
403C3×#120—28no—
404C3×#120—28no—
405C3×#120—24no—
406C3×#120—24no—
407C3×#120—24no—
408C3×#120—24no—
409C3×C4×Q8—24no—
410C3×C4×Q8—24no—
411C3×C4×D4—28no—
412C3×C4×D4—28no—
413C3×C4×D4—28no—
414C3×C4×D4—28no—
415C3×C4×D4—28no—
416C3×C4×D4—28no—
417C3×C4×D4—28no—
418C3×C4×D4—28no—
419C3×C4×D4—24no—
420C3×C4×D4—24no—
421C3×C4×D4—24no—
422C3×C4×D4—24no—
423C3×C4×D4—24no—
424C3×C4×D4—24no—
425C3×C4×D4—24no—
426C3×C4×D4—24no—
427C3×C4×D4—24no—
428C3×C4×D4—24no—
429C3×#117—24no—
430C3×#117—24no—
431C3×#117—22no—
432C3×#117—24no—
433C3×#117—22no—
434C3×#117C22⋊C414yescomplemented
435C3×#117C22×C414yes—
436C2×C3×C4⋊C4—22no—
437C2×C3×C4⋊C4—22no—
438C2×C3×C4⋊C4—24no—
439C2×C3×C4⋊C4—24no—
440C2×C3×C4⋊C4—22no—
441C2×C3×C4⋊C4—22no—
442C2×C3×C4⋊C4C22⋊C412yescomplemented
443C2×C3×C4⋊C4C22⋊C412yescomplemented
444C2×C3×C22⋊C4—24no—
445C2×C3×C22⋊C4—24no—
446C2×C3×C22⋊C4—24no—
447C2×C3×C22⋊C4—24no—
448C2×C3×C22⋊C4—24no—
449C2×C3×C22⋊C4—22no—
450C2×C3×C22⋊C4—22no—
451C2×C3×C22⋊C4—22no—
452C2×C3×C22⋊C4—22no—
453C2×C3×C22⋊C4—22no—
454C2×C3×C22⋊C4—48no—
455C2×C3×C22⋊C4—48no—
456C2×C3×C22⋊C4—44no—
457C2×C3×C22⋊C4—42no—
458C2×C3×C22⋊C4—84no—
459C2×C3×C42—24no—
460C2×C3×C42—22no—
461C3×#101—48no—
462C3×#100—48no—
463C3×C22⋊C8—24no—
464C3×C22⋊C8—24no—
465C3×C22⋊C8—42no—
466C3×C22⋊C8—42no—
467C3×#95—24no—
468C3×#95—24no—
469C3×#95—48no—
470C3×#95—41no—
471C3×#95—41no—
472C3×#95—41no—
473C3×#95—41no—
474#585—48no—
475C2×2−1+4—22no—
476C2×2−1+4C2×C3×C412yescomplemented
477C2×H(5,𝔽2)—22no—
478C2×H(5,𝔽2)—22no—
479C2×H(5,𝔽2)C2×C3×C412yescomplemented
480C22×#41—24no—
481C22×#41—22no—
482C22×#41—22no—
483C22×#41—22no—
484C22×#41—22no—
485C22×#41—22no—
486C22×#41—48no—
487C22×#41C2×C3×C412yes—
488C22×#41C2×C3×C411yescharacteristic
489C22×#41C2×C3×C411yescharacteristic
490C22×#41C2×C3×C411yescharacteristic
491C22×#41C2×C3×C411yescharacteristic
492C22×#41C3×D412yes—
493C22×#41C3×D412yes—
494C23×Q8C23×C311yescharacteristic
495C23×D4C3×D412yes—
496C23×D4C23×C311yescharacteristic
497C24×C4—21no—
498C24×C4C3×D412yes—
499C24×C4C23×C311yescharacteristic
500C22×M16—22no—
501#550—24no—
502#550—24no—
503D4×Q8—24no—
504D4×Q8—24no—
505#548—24no—
506#548—24no—
507#548—24no—
508#548—24no—
509#547—28no—
510#547—28no—
511#547—24no—
512#547—24no—
513#546—28no—
514#546—28no—
515#546—28no—
516#546—28no—
517#546—24no—
518#546—24no—
519#546—24no—
520#546—24no—
521D42—28no—
522D42—28no—
523D42—24no—
524D42—24no—
525#537—24no—
526#537—24no—
527#537—22no—
528#537—22no—
529#536—24no—
530#536—22no—
531#536—24no—
532#536C2×C3×C414yescomplemented
533#535—24no—
534#535—24no—
535#535—22no—
536#535C2×C3×C414yescomplemented
537#534—24no—
538#534—24no—
539#534—24no—
540#532—28no—
541#532—24no—
542#525—24no—
543#525—24no—
544#525—24no—
545#525—24no—
546#525—28no—
547#525—24no—
548#525—24no—
549#525—22no—
550#525—24no—
551#525—22no—
552#525—22no—
553#525—22no—
554#525—24no—
555#525C2×C3×C414yes—
556#525C3×D414yes—
557#525C3×D414yes—
558#525C23×C314yes—
559C2×#123—24no—
560C2×#123—22no—
561C2×C22⋊Q8—22no—
562C2×C22⋊Q8—22no—
563C2×C22⋊Q8C3×D412yes—
564C2×C22⋊Q8C3×D412yes—
565C2×#121—22no—
566C2×#121—22no—
567C2×#121C3×D412yes—
568C2×#121C3×D412yes—
569C2×#120—24no—
570C2×#120—22no—
571#520—22no—
572#520—22no—
573#519C2×C3×C412yescomplemented
574#518—22no—
575#518C2×C3×C412yescomplemented
576C4×#41—24no—
577C2×C4×D4—24no—
578C2×C4×D4—24no—
579C2×C4×D4—22no—
580C2×C4×D4—22no—
581C2×#117—22no—
582C2×#117C2×C3×C412yes—
583C22×C22⋊C4—21no—
584C22×C22⋊C4—24no—
585#413—48no—
586C2×#101—24no—
587C2×#100—24no—
588#407—22no—
589#407—22no—
590#407—22no—
591#407C23×C314yes—
592C2×C22⋊C8—22no—
593C2×C22⋊C8—22no—
594#386—48no—
595#381—22no—
596#381—22no—
597C2×#95—22no—
598C2×#95—22no—
599C2×#95—21no—
600C2×#95—21no—
601C2×#95—24no—
602C2×#95C23×C312yes—
603C2×#95C23×C312yes—
604#328—28no—
605#328—28no—
606#327—28no—
607#327—28no—
608C24×C3—24no—
609C24×C3—24no—
610C24×C3—24no—
611C24×C3—22no—
612C24×C3—22no—
613C24×C3—22no—
614C24×C3—41no—
615C24×C3—42no—
616C24×C3—41no—
617C24×C3—42no—
618C24×C3—42no—
619C24×C3—44no—
620C24×C3—42no—
621C24×C3C2×C22⋊C412yes—
622C24×C3C2×C22⋊C411yescharacteristic
623C24×C3C2×C22⋊C412yes—
624C24×C3C2×C22⋊C411yescharacteristic
625C24×C3#12012yes—
626C24×C3#12012yes—
627C24×C3C22×D411yescharacteristic
628C3×#41—216no—
629C3×#41—216no—
630C3×#41—416no—
631C3×#41—416no—
632C3×#41—416no—
633C3×#41—416no—
634C3×#41—416no—
635C3×#41—48no—
636C3×#41—48no—
637C3×#41—48no—
638C3×#41—416no—
639C3×#41—48no—
640C3×#41—48no—
641C3×#41—48no—
642C3×#41—48no—
643C3×#41—48no—
644C3×#41—48no—
645C3×#41—416no—
646C3×#41—432no—
647C3×#41—48no—
648C3×#41—48no—
649C3×#41—416no—
650C3×#41—48no—
651C2×C3×Q8—24no—
652C2×C3×Q8—22no—
653C2×C3×Q8—22no—
654C2×C3×Q8—24no—
655C2×C3×Q8—22no—
656C2×C3×Q8—24no—
657C2×C3×Q8—24no—
658C2×C3×Q8—42no—
659C2×C3×Q8—42no—
660C2×C3×Q8—48no—
661C2×C3×Q8—44no—
662C2×C3×Q8—48no—
663C2×C3×Q8—48no—
664C2×C3×Q8—416no—
665C2×C3×Q8C2×C22⋊C414yes—
666C2×C3×D4—24no—
667C2×C3×D4—24no—
668C2×C3×D4—24no—
669C2×C3×D4—28no—
670C2×C3×D4—24no—
671C2×C3×D4—24no—
672C2×C3×D4—24no—
673C2×C3×D4—24no—
674C2×C3×D4—24no—
675C2×C3×D4—24no—
676C2×C3×D4—24no—
677C2×C3×D4—24no—
678C2×C3×D4—24no—
679C2×C3×D4—24no—
680C2×C3×D4—24no—
681C2×C3×D4—24no—
682C2×C3×D4—28no—
683C2×C3×D4—28no—
684C2×C3×D4—24no—
685C2×C3×D4—24no—
686C2×C3×D4—22no—
687C2×C3×D4—22no—
688C2×C3×D4—24no—
689C2×C3×D4—22no—
690C2×C3×D4—24no—
691C2×C3×D4—42no—
692C2×C3×D4—42no—
693C2×C3×D4—42no—
694C2×C3×D4—42no—
695C2×C3×D4—44no—
696C2×C3×D4—48no—
697C2×C3×D4—416no—
698C2×C3×D4—416no—
699C2×C3×D4—48no—
700C2×C3×D4—48no—
701C2×C3×D4—416no—
702C2×C3×D4—432no—
703C2×C3×D4—48no—
704C2×C3×D4—48no—
705C2×C3×D4—48no—
706C2×C3×D4—84no—
707C2×C3×D4—82no—
708C2×C3×D4—82no—
709C2×C3×D4—88no—
710C2×C3×D4—84no—
711C2×C3×D4—84no—
712C2×C3×D4#9918yes—
713C2×C3×D4C2×C22⋊C414yes—
714C22×C3×C4—24no—
715C22×C3×C4—24no—
716C22×C3×C4—24no—
717C22×C3×C4—22no—
718C22×C3×C4—22no—
719C22×C3×C4—24no—
720C22×C3×C4—24no—
721C22×C3×C4—28no—
722C22×C3×C4—22no—
723C22×C3×C4—22no—
724C22×C3×C4—22no—
725C22×C3×C4—24no—
726C22×C3×C4—24no—
727C22×C3×C4—24no—
728C22×C3×C4—22no—
729C22×C3×C4—22no—
730C22×C3×C4—24no—
731C22×C3×C4—22no—
732C22×C3×C4—22no—
733C22×C3×C4—24no—
734C22×C3×C4—22no—
735C22×C3×C4—22no—
736C22×C3×C4—22no—
737C22×C3×C4—22no—
738C22×C3×C4—24no—
739C22×C3×C4—24no—
740C22×C3×C4—24no—
741C22×C3×C4—42no—
742C22×C3×C4—42no—
743C22×C3×C4—42no—
744C22×C3×C4—42no—
745C22×C3×C4—42no—
746C22×C3×C4—42no—
747C22×C3×C4—42no—
748C22×C3×C4—42no—
749C22×C3×C4—44no—
750C22×C3×C4—44no—
751C22×C3×C4—44no—
752C22×C3×C4—44no—
753C22×C3×C4—42no—
754C22×C3×C4—48no—
755C22×C3×C4—48no—
756C22×C3×C4—48no—
757C22×C3×C4—48no—
758C22×C3×C4—416no—
759C22×C3×C4—48no—
760C22×C3×C4—44no—
761C22×C3×C4—44no—
762C22×C3×C4—42no—
763C22×C3×C4—48no—
764C22×C3×C4—42no—
765C22×C3×C4—44no—
766C22×C3×C4—44no—
767C22×C3×C4—42no—
768C22×C3×C4—42no—
769C22×C3×C4—42no—
770C22×C3×C4—816no—
771C22×C3×C4—84no—
772C22×C3×C4—84no—
773C22×C3×C4C2×C22⋊C412yes—
774C22×C3×C4C2×C22⋊C412yes—
775C22×C3×C4C2×C22⋊C412yes—
776C22×C3×C4C2×C22⋊C411yescharacteristic
777C22×C3×C4C2×C22⋊C411yescharacteristic
778C22×C3×C4C2×C22⋊C412yes—
779C22×C3×C4C2×C22⋊C412yes—
780C22×C3×C4C2×C22⋊C412yes—
781C22×C3×C4#12012yes—
782C22×C3×C4#12012yes—
783C22×C3×C4#12012yes—
784C22×C3×C4#12012yes—
785C22×C3×C4#12011yescharacteristic
786C22×C3×C4#12011yescharacteristic
787C22×C3×C4#12011yescharacteristic
788C22×C3×C4#12011yescharacteristic
789C22×C3×C4C23×C411yescharacteristic
790C22×C3×C4C22×D411yescharacteristic
791C22×C3×C4C22×D412yes—
792C22×C3×C4C22×D412yes—
793C3×M16—48no—
794C3×M16—84no—
795C2×C3×C8—44no—
796C2×C3×C8—84no—
797C3×C4⋊C4—24no—
798C3×C4⋊C4—24no—
799C3×C4⋊C4—28no—
800C3×C4⋊C4—28no—
801C3×C4⋊C4—24no—
802C3×C4⋊C4—24no—
803C3×C4⋊C4—24no—
804C3×C4⋊C4—24no—
805C3×C4⋊C4—22no—
806C3×C4⋊C4—22no—
807C3×C4⋊C4C2×C22⋊C414yes—
808C3×C4⋊C4C2×C22⋊C414yes—
809C3×C22⋊C4—28no—
810C3×C22⋊C4—28no—
811C3×C22⋊C4—28no—
812C3×C22⋊C4—28no—
813C3×C22⋊C4—28no—
814C3×C22⋊C4—24no—
815C3×C22⋊C4—24no—
816C3×C22⋊C4—24no—
817C3×C22⋊C4—24no—
818C3×C22⋊C4—24no—
819C3×C22⋊C4—24no—
820C3×C22⋊C4—24no—
821C3×C22⋊C4—24no—
822C3×C22⋊C4—24no—
823C3×C22⋊C4—24no—
824C3×C22⋊C4—816no—
825C3×C22⋊C4—84no—
826C3×C42—28no—
827C3×C42—24no—
828C3×C42—24no—
829C25C2×C3×D412yes—
830C25C2×C3×D411yescharacteristic
8312−1+4—48no—
8322−1+4—416no—
833H(5,𝔽2)—48no—
834H(5,𝔽2)—48no—
835H(5,𝔽2)—416no—
836H(5,𝔽2)—48no—
837C2×#41—24no—
838C2×#41—24no—
839C2×#41—28no—
840C2×#41—24no—
841C2×#41—28no—
842C2×#41—28no—
843C2×#41—24no—
844C2×#41—22no—
845C2×#41—22no—
846C2×#41—22no—
847C2×#41—22no—
848C2×#41—24no—
849C2×#41—22no—
850C2×#41—22no—
851C2×#41—22no—
852C2×#41—22no—
853C2×#41—22no—
854C2×#41—22no—
855C2×#41—24no—
856C2×#41—24no—
857C2×#41—24no—
858C2×#41—24no—
859C2×#41—44no—
860C2×#41—44no—
861C2×#41—44no—
862C2×#41—44no—
863C2×#41—44no—
864C2×#41—44no—
865C2×#41—48no—
866C2×#41—48no—
867C2×#41—48no—
868C2×#41—416no—
869C2×#41—416no—
870C2×#41—416no—
871C2×#41—416no—
872C2×#41—432no—
873C2×#41C3×C22⋊C414yescomplemented
874C2×#41C22×C3×C414yes—
875C22×Q8—22no—
876C22×Q8—24no—
877C22×Q8—22no—
878C22×Q8—22no—
879C22×Q8—44no—
880C22×Q8C3×C22⋊C412yescomplemented
881C22×Q8C22×C3×C411yescharacteristic
882C22×Q8C22×C3×C411yescharacteristic
883C22×Q8C2×C3×D412yes—
884C22×D4—22no—
885C22×D4—28no—
886C22×D4—24no—
887C22×D4—22no—
888C22×D4—24no—
889C22×D4—24no—
890C22×D4—24no—
891C22×D4—24no—
892C22×D4—22no—
893C22×D4—22no—
894C22×D4—28no—
895C22×D4—24no—
896C22×D4—22no—
897C22×D4—22no—
898C22×D4—44no—
899C22×D4—44no—
900C22×D4C3×C22⋊C412yes—
901C22×D4C3×C22⋊C412yes—
902C22×D4C3×C22⋊C412yes—
903C22×D4C3×C22⋊C412yes—
904C22×D4C3×C22⋊C412yescomplemented
905C22×D4C22×C3×C411yescharacteristic
906C22×D4C22×C3×C411yescharacteristic
907C22×D4C2×C3×D412yes—
908C23×C4—24no—
909C23×C4—22no—
910C23×C4—22no—
911C23×C4—22no—
912C23×C4—22no—
913C23×C4—22no—
914C23×C4—22no—
915C23×C4—22no—
916C23×C4—44no—
917C23×C4—44no—
918C23×C4—44no—
919C23×C4—44no—
920C23×C4—42no—
921C23×C4—44no—
922C23×C4—82no—
923C23×C4C3×C22⋊C412yes—
924C23×C4C3×C22⋊C412yes—
925C23×C4C3×C22⋊C412yes—
926C23×C4C3×C22⋊C412yes—
927C23×C4C22×C3×C411yescharacteristic
928C23×C4C22×C3×C411yescharacteristic
929C23×C4C2×C3×D412yes—
930C23×C4C2×C3×D411yescharacteristic
931C23×C4C2×C3×D411yescharacteristic
932C23×C4C2×C3×D412yes—
933C23×C4C2×C3×D412yes—
934C23×C4C2×C3×D412yes—
935C23×C4C2×C3×D412yes—
936C23×C4C2×C3×D411yescharacteristic
937C23×C4C24×C311yescharacteristic
938C2×M16—24no—
939C2×M16—42no—
940C2×M16—48no—
941C22×C8—42no—
942C4⋊Q8—28no—
943C4⋊Q8—24no—
944#127—28no—
945#127—24no—
946#124—28no—
947#124—28no—
948#124—24no—
949#124—24no—
950#123—28no—
951#123—28no—
952#123—28no—
953#123—28no—
954#123—28no—
955#123—24no—
956#123—28no—
957#123—24no—
958#123—24no—
959#123—24no—
960C22⋊Q8—24no—
961C22⋊Q8—24no—
962C22⋊Q8—24no—
963C22⋊Q8—24no—
964C22⋊Q8—24no—
965C22⋊Q8—24no—
966C22⋊Q8—28no—
967C22⋊Q8—28no—
968C22⋊Q8—22no—
969C22⋊Q8—22no—
970C22⋊Q8—22no—
971C22⋊Q8—22no—
972C22⋊Q8—24no—
973C22⋊Q8—24no—
974C22⋊Q8C3×C22⋊C414yescomplemented
975C22⋊Q8C3×C22⋊C414yescomplemented
976C22⋊Q8C2×C3×D414yes—
977C22⋊Q8C2×C3×D414yes—
978#121—24no—
979#121—24no—
980#121—24no—
981#121—24no—
982#121—24no—
983#121—24no—
984#121—28no—
985#121—28no—
986#121—28no—
987#121—28no—
988#121—28no—
989#121—28no—
990#121—28no—
991#121—28no—
992#121—22no—
993#121—22no—
994#121—22no—
995#121—22no—
996#121—24no—
997#121—24no—
998#121C3×C22⋊C414yescomplemented
999#121C3×C22⋊C414yescomplemented
1000#121C2×C3×D414yes—
1001#121C2×C3×D414yes—
1002#120—28no—
1003#120—28no—
1004#120—28no—
1005#120—28no—
1006#120—28no—
1007#120—28no—
1008#120—24no—
1009#120—24no—
1010#120—24no—
1011#120—24no—
1012C4×Q8—24no—
1013C4×Q8—24no—
1014C4×D4—28no—
1015C4×D4—28no—
1016C4×D4—28no—
1017C4×D4—28no—
1018C4×D4—28no—
1019C4×D4—28no—
1020C4×D4—28no—
1021C4×D4—28no—
1022C4×D4—24no—
1023C4×D4—24no—
1024C4×D4—24no—
1025C4×D4—24no—
1026C4×D4—24no—
1027C4×D4—24no—
1028C4×D4—24no—
1029C4×D4—24no—
1030C4×D4—24no—
1031C4×D4—24no—
1032#117—24no—
1033#117—24no—
1034#117—22no—
1035#117—24no—
1036#117—22no—
1037#117C3×C22⋊C414yescomplemented
1038#117C22×C3×C414yes—
1039C2×C4⋊C4—22no—
1040C2×C4⋊C4—22no—
1041C2×C4⋊C4—24no—
1042C2×C4⋊C4—24no—
1043C2×C4⋊C4—22no—
1044C2×C4⋊C4—22no—
1045C2×C4⋊C4C3×C22⋊C412yescomplemented
1046C2×C4⋊C4C3×C22⋊C412yescomplemented
1047C2×C22⋊C4—24no—
1048C2×C22⋊C4—24no—
1049C2×C22⋊C4—24no—
1050C2×C22⋊C4—24no—
1051C2×C22⋊C4—24no—
1052C2×C22⋊C4—22no—
1053C2×C22⋊C4—22no—
1054C2×C22⋊C4—22no—
1055C2×C22⋊C4—22no—
1056C2×C22⋊C4—22no—
1057C2×C22⋊C4—48no—
1058C2×C22⋊C4—48no—
1059C2×C22⋊C4—44no—
1060C2×C22⋊C4—42no—
1061C2×C22⋊C4—84no—
1062C2×C42—24no—
1063C2×C42—22no—
1064#101—48no—
1065#100—48no—
1066C22⋊C8—24no—
1067C22⋊C8—24no—
1068C22⋊C8—42no—
1069C22⋊C8—42no—
1070#95—24no—
1071#95—24no—
1072#95—48no—
1073#95—41no—
1074#95—41no—
1075#95—41no—
1076#95—41no—
1077C23×C3—22no—
1078C23×C3—22no—
1079C23×C3—21no—
1080C23×C3—21no—
1081C23×C3—22no—
1082C23×C3—24no—
1083C23×C3—22no—
1084C23×C3—22no—
1085C23×C3—22no—
1086C23×C3—24no—
1087C23×C3—24no—
1088C23×C3—22no—
1089C23×C3—22no—
1090C23×C3—22no—
1091C23×C3—24no—
1092C23×C3—22no—
1093C23×C3—42no—
1094C23×C3—41no—
1095C23×C3—41no—
1096C23×C3—41no—
1097C23×C3—41no—
1098C23×C3—42no—
1099C23×C3—44no—
1100C23×C3—44no—
1101C23×C3—48no—
1102C23×C3—48no—
1103C23×C3—42no—
1104C23×C3—42no—
1105C23×C3—42no—
1106C23×C3—42no—
1107C23×C3—48no—
1108C23×C3—48no—
1109C23×C3—48no—
1110C23×C3—44no—
1111C23×C3—42no—
1112C23×C3—42no—
1113C23×C3—44no—
1114C23×C3—82no—
1115C23×C3—82no—
1116C23×C3—82no—
1117C23×C3—82no—
1118C23×C3—84no—
1119C23×C3—84no—
1120C23×C3—84no—
1121C23×C3—84no—
1122C23×C3#37912yes—
1123C23×C3#37912yes—
1124C23×C3C2×#9914yes—
1125C23×C3C2×#9914yes—
1126C23×C3C22×C22⋊C411yescharacteristic
1127C23×C3C2×#12011yescharacteristic
1128C23×C3C2×#12011yescharacteristic
1129C3×Q8—28no—
1130C3×Q8—48no—
1131C3×Q8—44no—
1132C3×Q8—44no—
1133C3×Q8—44no—
1134C3×Q8—48no—
1135C3×D4—28no—
1136C3×D4—216no—
1137C3×D4—48no—
1138C3×D4—48no—
1139C3×D4—44no—
1140C3×D4—44no—
1141C3×D4—44no—
1142C3×D4—48no—
1143C3×D4—48no—
1144C3×D4—416no—
1145C3×D4—48no—
1146C3×D4—48no—
1147C3×D4—44no—
1148C3×D4—44no—
1149C3×D4—48no—
1150C3×D4—48no—
1151C3×D4—84no—
1152C3×D4—84no—
1153C3×D4—88no—
1154C3×D4—88no—
1155C2×C3×C4—28no—
1156C2×C3×C4—28no—
1157C2×C3×C4—22no—
1158C2×C3×C4—22no—
1159C2×C3×C4—22no—
1160C2×C3×C4—22no—
1161C2×C3×C4—22no—
1162C2×C3×C4—22no—
1163C2×C3×C4—24no—
1164C2×C3×C4—24no—
1165C2×C3×C4—24no—
1166C2×C3×C4—24no—
1167C2×C3×C4—22no—
1168C2×C3×C4—22no—
1169C2×C3×C4—24no—
1170C2×C3×C4—24no—
1171C2×C3×C4—24no—
1172C2×C3×C4—22no—
1173C2×C3×C4—41no—
1174C2×C3×C4—41no—
1175C2×C3×C4—41no—
1176C2×C3×C4—41no—
1177C2×C3×C4—42no—
1178C2×C3×C4—42no—
1179C2×C3×C4—42no—
1180C2×C3×C4—42no—
1181C2×C3×C4—42no—
1182C2×C3×C4—42no—
1183C2×C3×C4—44no—
1184C2×C3×C4—44no—
1185C2×C3×C4—44no—
1186C2×C3×C4—44no—
1187C2×C3×C4—44no—
1188C2×C3×C4—44no—
1189C2×C3×C4—44no—
1190C2×C3×C4—48no—
1191C2×C3×C4—44no—
1192C2×C3×C4—48no—
1193C2×C3×C4—416no—
1194C2×C3×C4—48no—
1195C2×C3×C4—44no—
1196C2×C3×C4—48no—
1197C2×C3×C4—44no—
1198C2×C3×C4—82no—
1199C2×C3×C4—82no—
1200C2×C3×C4—84no—
1201C2×C3×C4—84no—
1202C2×C3×C4—84no—
1203C2×C3×C4—82no—
1204C2×C3×C4—816no—
1205C2×C3×C4—82no—
1206C2×C3×C4—84no—
1207C2×C3×C4—82no—
1208C2×C3×C4—84no—
1209C2×C3×C4—82no—
1210C2×C3×C4—82no—
1211C2×C3×C4#37911yescharacteristic
1212C2×C3×C4#37911yescharacteristic
1213C2×C3×C4#37911yescharacteristic
1214C2×C3×C4#37911yescharacteristic
1215C2×C3×C4C2×#9914yes—
1216C2×C3×C4C22×C22⋊C412yes—
1217C2×C3×C4C2×#12012yes—
1218C3×C8—84no—
1219C24—24no—
1220C24—24no—
1221C24—24no—
1222C24—22no—
1223C24—22no—
1224C24—22no—
1225C24—42no—
1226C24—41no—
1227C24—41no—
1228C24—42no—
1229C24—44no—
1230C24—42no—
1231C24—42no—
1232C24C2×C3×C22⋊C412yes—
1233C24C2×C3×C22⋊C411yescharacteristic
1234C24C2×C3×C22⋊C412yes—
1235C24C2×C3×C22⋊C411yescharacteristic
1236C24C3×#12012yes—
1237C24C3×#12012yes—
1238C24C22×C3×D411yescharacteristic
1239#41—216no—
1240#41—216no—
1241#41—416no—
1242#41—416no—
1243#41—416no—
1244#41—416no—
1245#41—416no—
1246#41—48no—
1247#41—48no—
1248#41—48no—
1249#41—416no—
1250#41—48no—
1251#41—48no—
1252#41—48no—
1253#41—48no—
1254#41—48no—
1255#41—48no—
1256#41—416no—
1257#41—432no—
1258#41—48no—
1259#41—48no—
1260#41—416no—
1261#41—48no—
1262C2×Q8—24no—
1263C2×Q8—22no—
1264C2×Q8—24no—
1265C2×Q8—24no—
1266C2×Q8—22no—
1267C2×Q8—22no—
1268C2×Q8—24no—
1269C2×Q8—42no—
1270C2×Q8—42no—
1271C2×Q8—48no—
1272C2×Q8—44no—
1273C2×Q8—48no—
1274C2×Q8—48no—
1275C2×Q8—416no—
1276C2×Q8C2×C3×C22⋊C414yes—
1277C2×D4—24no—
1278C2×D4—24no—
1279C2×D4—24no—
1280C2×D4—28no—
1281C2×D4—24no—
1282C2×D4—24no—
1283C2×D4—24no—
1284C2×D4—24no—
1285C2×D4—24no—
1286C2×D4—24no—
1287C2×D4—24no—
1288C2×D4—24no—
1289C2×D4—24no—
1290C2×D4—24no—
1291C2×D4—24no—
1292C2×D4—24no—
1293C2×D4—28no—
1294C2×D4—28no—
1295C2×D4—24no—
1296C2×D4—24no—
1297C2×D4—22no—
1298C2×D4—24no—
1299C2×D4—22no—
1300C2×D4—22no—
1301C2×D4—24no—
1302C2×D4—42no—
1303C2×D4—42no—
1304C2×D4—42no—
1305C2×D4—42no—
1306C2×D4—44no—
1307C2×D4—48no—
1308C2×D4—416no—
1309C2×D4—416no—
1310C2×D4—48no—
1311C2×D4—48no—
1312C2×D4—416no—
1313C2×D4—432no—
1314C2×D4—48no—
1315C2×D4—48no—
1316C2×D4—48no—
1317C2×D4—84no—
1318C2×D4—82no—
1319C2×D4—82no—
1320C2×D4—88no—
1321C2×D4—84no—
1322C2×D4—84no—
1323C2×D4C3×#9918yes—
1324C2×D4C2×C3×C22⋊C414yes—
1325C22×C4—24no—
1326C22×C4—24no—
1327C22×C4—24no—
1328C22×C4—22no—
1329C22×C4—22no—
1330C22×C4—24no—
1331C22×C4—24no—
1332C22×C4—28no—
1333C22×C4—22no—
1334C22×C4—24no—
1335C22×C4—22no—
1336C22×C4—22no—
1337C22×C4—24no—
1338C22×C4—24no—
1339C22×C4—22no—
1340C22×C4—22no—
1341C22×C4—22no—
1342C22×C4—22no—
1343C22×C4—24no—
1344C22×C4—22no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—22no—
1348C22×C4—24no—
1349C22×C4—24no—
1350C22×C4—24no—
1351C22×C4—24no—
1352C22×C4—42no—
1353C22×C4—42no—
1354C22×C4—42no—
1355C22×C4—42no—
1356C22×C4—42no—
1357C22×C4—42no—
1358C22×C4—42no—
1359C22×C4—42no—
1360C22×C4—44no—
1361C22×C4—44no—
1362C22×C4—44no—
1363C22×C4—44no—
1364C22×C4—42no—
1365C22×C4—48no—
1366C22×C4—48no—
1367C22×C4—48no—
1368C22×C4—48no—
1369C22×C4—416no—
1370C22×C4—48no—
1371C22×C4—44no—
1372C22×C4—44no—
1373C22×C4—42no—
1374C22×C4—48no—
1375C22×C4—42no—
1376C22×C4—44no—
1377C22×C4—44no—
1378C22×C4—42no—
1379C22×C4—42no—
1380C22×C4—42no—
1381C22×C4—816no—
1382C22×C4—84no—
1383C22×C4—84no—
1384C22×C4C2×C3×C22⋊C412yes—
1385C22×C4C2×C3×C22⋊C411yescharacteristic
1386C22×C4C2×C3×C22⋊C411yescharacteristic
1387C22×C4C2×C3×C22⋊C412yes—
1388C22×C4C2×C3×C22⋊C412yes—
1389C22×C4C2×C3×C22⋊C412yes—
1390C22×C4C2×C3×C22⋊C412yes—
1391C22×C4C2×C3×C22⋊C412yes—
1392C22×C4C3×#12012yes—
1393C22×C4C3×#12012yes—
1394C22×C4C3×#12011yescharacteristic
1395C22×C4C3×#12011yescharacteristic
1396C22×C4C3×#12011yescharacteristic
1397C22×C4C3×#12011yescharacteristic
1398C22×C4C3×#12012yes—
1399C22×C4C3×#12012yes—
1400C22×C4C23×C3×C411yescharacteristic
1401C22×C4C22×C3×D411yescharacteristic
1402C22×C4C22×C3×D412yes—
1403C22×C4C22×C3×D412yes—
1404M16—48no—
1405M16—84no—
1406C2×C8—44no—
1407C2×C8—84no—
1408C4⋊C4—24no—
1409C4⋊C4—24no—
1410C4⋊C4—28no—
1411C4⋊C4—28no—
1412C4⋊C4—24no—
1413C4⋊C4—24no—
1414C4⋊C4—22no—
1415C4⋊C4—22no—
1416C4⋊C4—24no—
1417C4⋊C4—24no—
1418C4⋊C4C2×C3×C22⋊C414yes—
1419C4⋊C4C2×C3×C22⋊C414yes—
1420C22⋊C4—28no—
1421C22⋊C4—28no—
1422C22⋊C4—28no—
1423C22⋊C4—28no—
1424C22⋊C4—28no—
1425C22⋊C4—24no—
1426C22⋊C4—24no—
1427C22⋊C4—24no—
1428C22⋊C4—24no—
1429C22⋊C4—24no—
1430C22⋊C4—24no—
1431C22⋊C4—24no—
1432C22⋊C4—24no—
1433C22⋊C4—24no—
1434C22⋊C4—24no—
1435C22⋊C4—816no—
1436C22⋊C4—84no—
1437C42—28no—
1438C42—24no—
1439C42—24no—
1440C22×C3—24no—
1441C22×C3—24no—
1442C22×C3—21no—
1443C22×C3—21no—
1444C22×C3—21no—
1445C22×C3—22no—
1446C22×C3—21no—
1447C22×C3—21no—
1448C22×C3—22no—
1449C22×C3—21no—
1450C22×C3—24no—
1451C22×C3—22no—
1452C22×C3—22no—
1453C22×C3—22no—
1454C22×C3—44no—
1455C22×C3—44no—
1456C22×C3—48no—
1457C22×C3—44no—
1458C22×C3—44no—
1459C22×C3—44no—
1460C22×C3—44no—
1461C22×C3—42no—
1462C22×C3—42no—
1463C22×C3—42no—
1464C22×C3—44no—
1465C22×C3—44no—
1466C22×C3—42no—
1467C22×C3—44no—
1468C22×C3—42no—
1469C22×C3—82no—
1470C22×C3—84no—
1471C22×C3—88no—
1472C22×C3—84no—
1473C22×C3—82no—
1474C22×C3—164no—
1475C22×C3—168no—
1476C22×C3#178114yes—
1477C22×C3C2×#37911yescharacteristic
1478C22×C3C22×#9912yes—
1479C22×C3#301812yes—
1480C22×C3#302111yescharacteristic
1481C22×C3#302211yescharacteristic
1482C3×C4—22no—
1483C3×C4—21no—
1484C3×C4—21no—
1485C3×C4—21no—
1486C3×C4—21no—
1487C3×C4—22no—
1488C3×C4—24no—
1489C3×C4—42no—
1490C3×C4—44no—
1491C3×C4—44no—
1492C3×C4—44no—
1493C3×C4—84no—
1494C3×C4—162no—
1495C23—22no—
1496C23—22no—
1497C23—21no—
1498C23—21no—
1499C23—22no—
1500C23—24no—
1501C23—24no—
1502C23—24no—
1503C23—22no—
1504C23—22no—
1505C23—22no—
1506C23—22no—
1507C23—22no—
1508C23—22no—
1509C23—24no—
1510C23—22no—
1511C23—42no—
1512C23—41no—
1513C23—41no—
1514C23—41no—
1515C23—41no—
1516C23—42no—
1517C23—44no—
1518C23—44no—
1519C23—48no—
1520C23—48no—
1521C23—42no—
1522C23—42no—
1523C23—42no—
1524C23—42no—
1525C23—48no—
1526C23—48no—
1527C23—48no—
1528C23—44no—
1529C23—42no—
1530C23—42no—
1531C23—44no—
1532C23—82no—
1533C23—82no—
1534C23—82no—
1535C23—82no—
1536C23—84no—
1537C23—84no—
1538C23—84no—
1539C23—84no—
1540C23C3×#37912yes—
1541C23C3×#37912yes—
1542C23C2×C3×#9914yes—
1543C23C2×C3×#9914yes—
1544C23C22×C3×C22⋊C411yescharacteristic
1545C23C2×C3×#12011yescharacteristic
1546C23C2×C3×#12011yescharacteristic
1547Q8—28no—
1548Q8—48no—
1549Q8—44no—
1550Q8—44no—
1551Q8—48no—
1552Q8—44no—
1553D4—28no—
1554D4—216no—
1555D4—48no—
1556D4—48no—
1557D4—44no—
1558D4—44no—
1559D4—48no—
1560D4—44no—
1561D4—48no—
1562D4—416no—
1563D4—48no—
1564D4—48no—
1565D4—48no—
1566D4—48no—
1567D4—44no—
1568D4—44no—
1569D4—84no—
1570D4—84no—
1571D4—88no—
1572D4—88no—
1573C2×C4—28no—
1574C2×C4—28no—
1575C2×C4—22no—
1576C2×C4—22no—
1577C2×C4—22no—
1578C2×C4—22no—
1579C2×C4—22no—
1580C2×C4—24no—
1581C2×C4—24no—
1582C2×C4—24no—
1583C2×C4—24no—
1584C2×C4—22no—
1585C2×C4—22no—
1586C2×C4—22no—
1587C2×C4—24no—
1588C2×C4—24no—
1589C2×C4—24no—
1590C2×C4—22no—
1591C2×C4—41no—
1592C2×C4—41no—
1593C2×C4—41no—
1594C2×C4—41no—
1595C2×C4—42no—
1596C2×C4—42no—
1597C2×C4—42no—
1598C2×C4—42no—
1599C2×C4—42no—
1600C2×C4—42no—
1601C2×C4—44no—
1602C2×C4—44no—
1603C2×C4—44no—
1604C2×C4—44no—
1605C2×C4—44no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—48no—
1609C2×C4—44no—
1610C2×C4—416no—
1611C2×C4—48no—
1612C2×C4—48no—
1613C2×C4—44no—
1614C2×C4—48no—
1615C2×C4—44no—
1616C2×C4—82no—
1617C2×C4—82no—
1618C2×C4—84no—
1619C2×C4—84no—
1620C2×C4—84no—
1621C2×C4—82no—
1622C2×C4—816no—
1623C2×C4—82no—
1624C2×C4—84no—
1625C2×C4—82no—
1626C2×C4—84no—
1627C2×C4—82no—
1628C2×C4—82no—
1629C2×C4C3×#37911yescharacteristic
1630C2×C4C3×#37911yescharacteristic
1631C2×C4C3×#37911yescharacteristic
1632C2×C4C3×#37911yescharacteristic
1633C2×C4C2×C3×#9914yes—
1634C2×C4C22×C3×C22⋊C412yes—
1635C2×C4C2×C3×#12012yes—
1636C8—84no—
1637C2×C3—21no—
1638C2×C3—22no—
1639C2×C3—22no—
1640C2×C3—21no—
1641C2×C3—24no—
1642C2×C3—42no—
1643C2×C3—44no—
1644C2×C3—82no—
1645C2×C3—84no—
1646C2×C3C2×#178111yescharacteristic
1647C2×C3#2061511yescharacteristic
1648C2×C3#2061811yescharacteristic
1649C22—24no—
1650C22—24no—
1651C22—21no—
1652C22—21no—
1653C22—21no—
1654C22—22no—
1655C22—21no—
1656C22—21no—
1657C22—22no—
1658C22—21no—
1659C22—24no—
1660C22—22no—
1661C22—22no—
1662C22—22no—
1663C22—44no—
1664C22—44no—
1665C22—48no—
1666C22—44no—
1667C22—44no—
1668C22—44no—
1669C22—44no—
1670C22—42no—
1671C22—42no—
1672C22—42no—
1673C22—44no—
1674C22—44no—
1675C22—42no—
1676C22—44no—
1677C22—42no—
1678C22—82no—
1679C22—84no—
1680C22—88no—
1681C22—84no—
1682C22—82no—
1683C22—164no—
1684C22—168no—
1685C22C3×#178114yes—
1686C22C2×C3×#37911yescharacteristic
1687C22C22×C3×#9912yes—
1688C22C3×#301812yes—
1689C22C3×#302111yescharacteristic
1690C22C3×#302211yescharacteristic
1691C4—22no—
1692C4—21no—
1693C4—21no—
1694C4—21no—
1695C4—21no—
1696C4—24no—
1697C4—22no—
1698C4—42no—
1699C4—44no—
1700C4—44no—
1701C4—44no—
1702C4—84no—
1703C4—162no—
1704C3#18681411yescharacteristic, direct product factor, Sylow
1705C2—21no—
1706C2—22no—
1707C2—22no—
1708C2—21no—
1709C2—24no—
1710C2—42no—
1711C2—44no—
1712C2—82no—
1713C2—84no—
1714C2C2×C3×#178111yescharacteristic
1715C2C3×#2061511yescharacteristic
1716C2C3×#2061811yescharacteristic
subgroupG/H
center, socleC22×C3C2×#379
commutatorC22×C4C23×C3×C4
Frattini, cosocleC23×C4C24×C3
prime radicalC3×#62811C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C3 ◁ C24×C3×C4 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#20591C2semidirect
3. C3×#17587C2semidirect
4. C2×C3×#1504C2semidirect
5. C3×#13956C2semidirect
6. C3×#8455C2semidirect
7. C3×#8453C2semidirect
8. #186814C3direct (N × H)
9. C2×C3×#585C4semidirect
15. C3×#3487C4semidirect
18. C3×#3485C4semidirect
24. C3×#3449C4semidirect
27. C3×#3428C4semidirect
29. C2×C3×#407C22semidirect
31. C2×C3×#381C22semidirect
32. C22×C3×#95C22semidirect
34. C3×#1784C22semidirect
35. C3×#1783C22semidirect
40. C3×#1504C22semidirect
41. C3×#1504C22semidirect
44. C3×#1446C22semidirect
45. C3×#1438C22semidirect
48. #20591C2×C3semidirect
49. #17587C2×C3semidirect
50. C2×#1504C2×C3semidirect
51. #13956C2×C3semidirect
52. #8455C2×C3semidirect
53. #8453C2×C3semidirect
56. C2×C3×2−1+4C2×C4semidirect
59. C2×C3×H(5,𝔽2)C2×C4semidirect
112. C3×#536C2×C4semidirect
116. C3×#535C2×C4semidirect
153. C3×#519C2×C4semidirect
155. C3×#518C2×C4semidirect
188. C2×#585C3×C4semidirect
194. #3487C3×C4semidirect
197. #3485C3×C4semidirect
203. #3449C3×C4semidirect
206. #3428C3×C4semidirect
208. C2×#407C22×C3semidirect
210. C2×#381C22×C3semidirect
211. C22×#95C22×C3semidirect
213. #1784C22×C3semidirect
214. #1783C22×C3semidirect
219. #1504C22×C3semidirect
220. #1504C22×C3semidirect
223. #1446C22×C3semidirect
224. #1438C22×C3semidirect
270. C2×C3×#41C22⋊C4semidirect
277. C22×C3×Q8C22⋊C4semidirect
301. C22×C3×D4C22⋊C4semidirect
371. C3×C22⋊Q8C22⋊C4semidirect
372. C3×C22⋊Q8C22⋊C4semidirect
395. C3×#121C22⋊C4semidirect
396. C3×#121C22⋊C4semidirect
434. C3×#117C22⋊C4semidirect
442. C2×C3×C4⋊C4C22⋊C4semidirect
443. C2×C3×C4⋊C4C22⋊C4semidirect
476. C2×2−1+4C2×C3×C4semidirect
479. C2×H(5,𝔽2)C2×C3×C4semidirect
532. #536C2×C3×C4semidirect
536. #535C2×C3×C4semidirect
573. #519C2×C3×C4semidirect
575. #518C2×C3×C4semidirect
873. C2×#41C3×C22⋊C4semidirect
880. C22×Q8C3×C22⋊C4semidirect
904. C22×D4C3×C22⋊C4semidirect
974. C22⋊Q8C3×C22⋊C4semidirect
975. C22⋊Q8C3×C22⋊C4semidirect
998. #121C3×C22⋊C4semidirect
999. #121C3×C22⋊C4semidirect
1037. #117C3×C22⋊C4semidirect
1045. C2×C4⋊C4C3×C22⋊C4semidirect
1046. C2×C4⋊C4C3×C22⋊C4semidirect
1704. C3#186814direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#628112
C3×#205912
C3×#175872
C2×C3×#15042
C3×#139562
C3×#84552
C3×#84532
#1868143