Finite Group Databasebeta

← C3×#30447 #10649054

Subgroups — C3×#30447 #10649054

Order 768.

1268 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#493C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×C3×#449C211yesmaximal, characteristic, complemented
5C3×#2431C211yesmaximal, characteristic, complemented
6C3×#2428C211yesmaximal, characteristic, complemented
7C3×#2054C211yesmaximal, characteristic, complemented
8C3×#2041C211yesmaximal, characteristic, complemented
9C3×#2014C211yesmaximal, characteristic, complemented
10C3×#2012C211yesmaximal, characteristic, complemented
11C3×#1999C211yesmaximal, characteristic, complemented
12C3×#1999C211yesmaximal, characteristic, complemented
13C3×#1933C211yesmaximal, characteristic, complemented
14C3×#1923C211yesmaximal, characteristic, complemented
15C3×#1879C211yesmaximal, characteristic, complemented
16#30447C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C22×C3×D8C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C22×C3×D8C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#127C2211yescharacteristic
25C2×C3×#127C2211yescharacteristic
26C2×C3×#124C2211yescharacteristic
27C2×C3×#121—21no—
28C2×C3×#121C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×C4×D4C2211yescharacteristic
32C3×#493—24no—
33C3×#463—24no—
34C3×#449—24no—
35C3×#449—24no—
36C2×C3×C4⋊C8C2211yescharacteristic
37C2×C3×#103C2211yescharacteristic
38C2×C3×#103C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C2×C3×#102C2211yescharacteristic
42C2×C3×#102C2211yescharacteristic
43C2×C3×#102C2211yescharacteristic
44C2×C3×#102C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2211yescharacteristic
47C2×C3×C4×C8C2211yescharacteristic
48C3×#394—21no—
49C3×#392—21no—
50C3×#392—21no—
51C3×#392—21no—
52C3×#391C2211yescharacteristic
53C3×#390C2211yescharacteristic
54C3×#390C2211yescharacteristic
55C3×#389C2211yescharacteristic
56C3×#386—21no—
57C3×#386—21no—
58C3×#386—21no—
59C3×C4×C22⋊C4C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C3×#336C2211yescharacteristic
63C3×#336C2211yescharacteristic
64C2×#493C2×C311yescharacteristic, complemented
65C2×#463C2×C311yescharacteristic, complemented
66C2×#449C2×C311yescharacteristic, complemented
67C2×#449C2×C311yescharacteristic, complemented
68#2431C2×C311yescharacteristic, complemented
69#2428C2×C311yescharacteristic, complemented
70#2054C2×C311yescharacteristic, complemented
71#2041C2×C311yescharacteristic, complemented
72#2014C2×C311yescharacteristic, complemented
73#2012C2×C311yescharacteristic, complemented
74#1999C2×C311yescharacteristic, complemented
75#1999C2×C311yescharacteristic, complemented
76#1933C2×C311yescharacteristic, complemented
77#1923C2×C311yescharacteristic, complemented
78#1879C2×C311yescharacteristic, complemented
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4—21no—
87C22×C3×D4—21no—
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4—21no—
92C22×C3×D4—21no—
93C22×C3×D4—21no—
94C22×C3×D4C2311yescharacteristic
95C22×C3×D4C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C22×C3×D4C2311yescharacteristic
98C23×C3×C4—21no—
99C23×C3×C4—21no—
100C23×C3×C4C2311yescharacteristic
101C2×C3×SD16—22no—
102C2×C3×SD16—22no—
103C2×C3×SD16—22no—
104C2×C3×SD16—41no—
105C2×C3×SD16—41no—
106C2×C3×SD16—41no—
107C2×C3×D8—22no—
108C2×C3×D8—22no—
109C2×C3×D8—22no—
110C2×C3×D8—22no—
111C2×C3×D8—22no—
112C2×C3×D8—41no—
113C2×C3×D8—41no—
114C2×C3×D8—41no—
115C2×C3×D8—41no—
116C2×C3×D8—41no—
117C2×C3×D8—41no—
118C2×C3×D8D414yescomplemented
119C22×C3×C8C2311yescharacteristic
120C22×C3×C8C2311yescharacteristic
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C3×#127—22no—
124C3×#127—22no—
125C3×#127—41no—
126C3×#127—41no—
127C3×#124—22no—
128C3×#124—41no—
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—44no—
132C3×#121—41no—
133C3×#121—41no—
134C3×#121—41no—
135C3×#121—41no—
136C3×C4×D4—22no—
137C3×C4×D4—41no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4C2311yescharacteristic
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—21no—
144C2×C3×C22⋊C4—21no—
145C2×C3×C22⋊C4—21no—
146C2×C3×C22⋊C4—21no—
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—21no—
152C2×C3×C22⋊C4D411yescharacteristic
153C2×C3×C22⋊C4D411yescharacteristic
154C2×C3×C42C2311yescharacteristic
155C2×C3×C42C2311yescharacteristic
156C3×C4⋊C8—22no—
157C3×#103—22no—
158C3×#103D414yescomplemented
159C3×#102—22no—
160C3×#102—22no—
161C3×#102—22no—
162C3×#102—41no—
163C3×#102—41no—
164C3×#102—41no—
165C3×C22⋊C8—22no—
166C3×C22⋊C8—22no—
167C3×C4×C8—22no—
168C3×#95—21no—
169C3×#95—21no—
170C3×#95—21no—
171C3×#95D411yescharacteristic
172C3×#95D411yescharacteristic
173C22×#41C22×C311yescharacteristic
174C22×SD16C22×C311yescharacteristic
175C22×SD16C22×C311yescharacteristic
176C22×D8C22×C311yescharacteristic
177C22×D8C22×C311yescharacteristic
178C22×D8C22×C311yescharacteristic
179C22×D8C22×C311yescharacteristic
180C2×#127C22×C311yescharacteristic
181C2×#127C22×C311yescharacteristic
182C2×#124C22×C311yescharacteristic
183C2×#121—21no—
184C2×#121C22×C311yescharacteristic
185C2×#121C22×C311yescharacteristic
186C2×#121C22×C311yescharacteristic
187C2×C4×D4C22×C311yescharacteristic
188#493—24no—
189#463—24no—
190#449—24no—
191#449—24no—
192C2×C4⋊C8C22×C311yescharacteristic
193C2×#103C22×C311yescharacteristic
194C2×#103C22×C311yescharacteristic
195C2×#102C22×C311yescharacteristic
196C2×#102C22×C311yescharacteristic
197C2×#102C22×C311yescharacteristic
198C2×#102C22×C311yescharacteristic
199C2×#102C22×C311yescharacteristic
200C2×#102C22×C311yescharacteristic
201C2×C22⋊C8C22×C311yescharacteristic
202C2×C22⋊C8C22×C311yescharacteristic
203C2×C4×C8C22×C311yescharacteristic
204#394—21no—
205#392—21no—
206#392—21no—
207#392—21no—
208#391C22×C311yescharacteristic
209#390C22×C311yescharacteristic
210#390C22×C311yescharacteristic
211#389C22×C311yescharacteristic
212#386—21no—
213#386—21no—
214#386—21no—
215C4×C22⋊C4C22×C311yescharacteristic
216#340C22×C311yescharacteristic
217#340C22×C311yescharacteristic
218#336C22×C311yescharacteristic
219#336C22×C311yescharacteristic
220C24×C3—21no—
221C24×C3—21no—
222C24×C3—21no—
223C24×C3—21no—
224C24×C3C2×D411yescharacteristic
225C3×#41—44no—
226C3×#41—44no—
227C3×#41—44no—
228C3×#41—44no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8—21no—
232C2×C3×Q8—21no—
233C2×C3×Q8—21no—
234C2×C3×Q8C2×D412yes—
235C2×C3×D4—21no—
236C2×C3×D4—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—42no—
258C2×C3×D4—42no—
259C2×C3×D4—42no—
260C2×C3×D4—42no—
261C2×C3×D4—42no—
262C2×C3×D4—42no—
263C2×C3×D4—42no—
264C2×C3×D4—42no—
265C2×C3×D4—42no—
266C2×C3×D4—42no—
267C2×C3×D4—42no—
268C2×C3×D4—42no—
269C2×C3×D4—42no—
270C2×C3×D4—42no—
271C2×C3×D4—42no—
272C2×C3×D4—42no—
273C2×C3×D4—81no—
274C2×C3×D4—81no—
275C2×C3×D4—81no—
276C2×C3×D4—81no—
277C2×C3×D4—81no—
278C2×C3×D4—81no—
279C2×C3×D4—81no—
280C2×C3×D4—81no—
281C2×C3×D4C2×D412yes—
282C2×C3×D4C2×D412yes—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—42no—
294C22×C3×C4—42no—
295C22×C3×C4—42no—
296C22×C3×C4—42no—
297C22×C3×C4—42no—
298C22×C3×C4—81no—
299C22×C3×C4C2×D411yescharacteristic
300C22×C3×C4C2×D411yescharacteristic
301C22×C3×C4C2×D411yescharacteristic
302C22×C3×C4C2×D411yescharacteristic
303C22×C3×C4C2×D411yescharacteristic
304C22×C3×C4C2411yescharacteristic
305C3×SD16—44no—
306C3×SD16—44no—
307C3×D8—44no—
308C3×D8—44no—
309C3×D8—44no—
310C3×D8—44no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8C2×D412yes—
322C2×C3×C8C2×D412yes—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—42no—
329C3×C4⋊C4C2×D412yes—
330C3×C22⋊C4—22no—
331C3×C22⋊C4—22no—
332C3×C22⋊C4—42no—
333C3×C22⋊C4—42no—
334C3×C22⋊C4—42no—
335C3×C22⋊C4—42no—
336C3×C22⋊C4—42no—
337C3×C22⋊C4—42no—
338C3×C22⋊C4—42no—
339C3×C22⋊C4—81no—
340C3×C22⋊C4—81no—
341C3×C22⋊C4—81no—
342C3×C42—21no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—41no—
349C2×#41—41no—
350C2×#41—41no—
351C2×#41—41no—
352C22×Q8C23×C311yescharacteristic
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—21no—
356C22×D4—21no—
357C22×D4—21no—
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4C23×C311yescharacteristic
362C22×D4C23×C311yescharacteristic
363C22×D4C23×C311yescharacteristic
364C22×D4C23×C311yescharacteristic
365C23×C4—21no—
366C23×C4—21no—
367C23×C4C23×C311yescharacteristic
368C2×SD16—22no—
369C2×SD16—22no—
370C2×SD16—22no—
371C2×SD16—41no—
372C2×SD16—41no—
373C2×SD16—41no—
374C2×D8—22no—
375C2×D8—22no—
376C2×D8—22no—
377C2×D8—22no—
378C2×D8—22no—
379C2×D8—41no—
380C2×D8—41no—
381C2×D8—41no—
382C2×D8—41no—
383C2×D8—41no—
384C2×D8—41no—
385C2×D8C3×D414yescomplemented
386C22×C8C23×C311yescharacteristic
387C22×C8C23×C311yescharacteristic
388C22×C8C23×C311yescharacteristic
389C22×C8C23×C311yescharacteristic
390#127—22no—
391#127—22no—
392#127—41no—
393#127—41no—
394#124—22no—
395#124—41no—
396#121—22no—
397#121—22no—
398#121—44no—
399#121—41no—
400#121—41no—
401#121—41no—
402#121—41no—
403C4×D4—22no—
404C4×D4—41no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4C23×C311yescharacteristic
407C2×C4⋊C4C23×C311yescharacteristic
408C2×C4⋊C4C23×C311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4C3×D411yescharacteristic
420C2×C22⋊C4C3×D411yescharacteristic
421C2×C42C23×C311yescharacteristic
422C2×C42C23×C311yescharacteristic
423C4⋊C8—22no—
424#103—22no—
425#103C3×D414yescomplemented
426#102—22no—
427#102—22no—
428#102—22no—
429#102—41no—
430#102—41no—
431#102—41no—
432C22⋊C8—22no—
433C22⋊C8—22no—
434C4×C8—22no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95C3×D411yescharacteristic
439#95C3×D411yescharacteristic
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—21no—
443C23×C3—21no—
444C23×C3—22no—
445C23×C3—21no—
446C23×C3—21no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—41no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—41no—
455C23×C3—41no—
456C23×C3—41no—
457C23×C3—41no—
458C23×C3—41no—
459C23×C3—41no—
460C23×C3—41no—
461C23×C3—41no—
462C23×C3—41no—
463C23×C3—41no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3C22×D411yescharacteristic
476C3×Q8—22no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8—41no—
480C3×D4—22no—
481C3×D4—22no—
482C3×D4—22no—
483C3×D4—22no—
484C3×D4—48no—
485C3×D4—41no—
486C3×D4—41no—
487C3×D4—41no—
488C3×D4—41no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—41no—
494C3×D4—41no—
495C3×D4—41no—
496C3×D4—41no—
497C3×D4—84no—
498C3×D4—84no—
499C3×D4—84no—
500C3×D4—84no—
501C3×D4—84no—
502C3×D4—84no—
503C3×D4—84no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—22no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—48no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—84no—
535C2×C3×C4#13512yes—
536C2×C3×C4AGL(1,ℤ/8)12yes—
537C2×C3×C4C22×D411yescharacteristic
538C2×C3×C4C22×D411yescharacteristic
539C2×C3×C4H(5,𝔽2)11yescharacteristic
540C2×C3×C4H(5,𝔽2)11yescharacteristic
541C2×C3×C4H(5,𝔽2)11yescharacteristic
542C2×C3×C4H(5,𝔽2)11yescharacteristic
543C3×C8—22no—
544C3×C8—22no—
545C3×C8—41no—
546C3×C8—41no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24C2×C3×D411yescharacteristic
552#41—44no—
553#41—44no—
554#41—44no—
555#41—44no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8C2×C3×D412yes—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—42no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—81no—
601C2×D4—81no—
602C2×D4—81no—
603C2×D4—81no—
604C2×D4—81no—
605C2×D4—81no—
606C2×D4—81no—
607C2×D4—81no—
608C2×D4C2×C3×D412yes—
609C2×D4C2×C3×D412yes—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—81no—
626C22×C4C2×C3×D411yescharacteristic
627C22×C4C2×C3×D411yescharacteristic
628C22×C4C2×C3×D411yescharacteristic
629C22×C4C2×C3×D411yescharacteristic
630C22×C4C2×C3×D411yescharacteristic
631C22×C4C24×C311yescharacteristic
632SD16—44no—
633SD16—44no—
634D8—44no—
635D8—44no—
636D8—44no—
637D8—44no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8C2×C3×D412yes—
649C2×C8C2×C3×D412yes—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4C2×C3×D412yes—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4—81no—
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C22×C3—42no—
674C22×C3—41no—
675C22×C3—42no—
676C22×C3—41no—
677C22×C3—41no—
678C22×C3—41no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—81no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3—81no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—81no—
706C22×C3—81no—
707C22×C3—81no—
708C22×C3#53511yescharacteristic
709C22×C3D4211yescharacteristic
710C22×C3D4211yescharacteristic
711C22×C3C2×#13511yescharacteristic
712C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
713C22×C3#57611yescharacteristic
714C22×C3#57611yescharacteristic
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—41no—
718C3×C4—42no—
719C3×C4—41no—
720C3×C4—42no—
721C3×C4—41no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4#53411yescharacteristic
725C3×C4#53511yescharacteristic
726C3×C4D4211yescharacteristic
727C3×C4#56011yescharacteristic
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23C22×C3×D411yescharacteristic
764Q8—22no—
765Q8—22no—
766Q8—41no—
767Q8—41no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—84no—
786D4—84no—
787D4—84no—
788D4—84no—
789D4—84no—
790D4—84no—
791D4—84no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—48no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—84no—
823C2×C4C3×#13512yes—
824C2×C4C3×AGL(1,ℤ/8)12yes—
825C2×C4C22×C3×D411yescharacteristic
826C2×C4C22×C3×D411yescharacteristic
827C2×C4C3×H(5,𝔽2)11yescharacteristic
828C2×C4C3×H(5,𝔽2)11yescharacteristic
829C2×C4C3×H(5,𝔽2)11yescharacteristic
830C2×C4C3×H(5,𝔽2)11yescharacteristic
831C8—22no—
832C8—22no—
833C8—41no—
834C8—41no—
835C2×C3—81no—
836C2×C3—82no—
837C2×C3—82no—
838C2×C3—161no—
839C2×C3—161no—
840C2×C3#266911yescharacteristic
841C2×C3#320711yescharacteristic
842C2×C3#322011yescharacteristic
843C2×C3#326411yescharacteristic
844C2×C3#327411yescharacteristic
845C2×C3#328011yescharacteristic
846C2×C3#328711yescharacteristic
847C22—42no—
848C22—41no—
849C22—42no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—42no—
858C22—41no—
859C22—41no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22C3×#53511yescharacteristic
883C22C3×D4211yescharacteristic
884C22C3×D4211yescharacteristic
885C22C2×C3×#13511yescharacteristic
886C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
887C22C3×#57611yescharacteristic
888C22C3×#57611yescharacteristic
889C4—22no—
890C4—22no—
891C4—41no—
892C4—42no—
893C4—41no—
894C4—42no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4C3×#53411yescharacteristic
899C4C3×#53511yescharacteristic
900C4C3×D4211yescharacteristic
901C4C3×#56011yescharacteristic
902C3#3044711yescharacteristic, direct product factor, Sylow
903C2—81no—
904C2—82no—
905C2—82no—
906C2—161no—
907C2—161no—
908C2C3×#266911yescharacteristic
909C2C3×#320711yescharacteristic
910C2C3×#322011yescharacteristic
911C2C3×#326411yescharacteristic
912C2C3×#327411yescharacteristic
913C2C3×#328011yescharacteristic
914C2C3×#328711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#493C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#449C2semidirect
4. C2×C3×#449C2semidirect
5. C3×#2431C2semidirect
6. C3×#2428C2semidirect
7. C3×#2054C2semidirect
8. C3×#2041C2semidirect
9. C3×#2014C2semidirect
10. C3×#2012C2semidirect
11. C3×#1999C2semidirect
12. C3×#1999C2semidirect
13. C3×#1933C2semidirect
14. C3×#1923C2semidirect
15. C3×#1879C2semidirect
16. #30447C3direct (N × H)
64. C2×#493C2×C3semidirect
65. C2×#463C2×C3semidirect
66. C2×#449C2×C3semidirect
67. C2×#449C2×C3semidirect
68. #2431C2×C3semidirect
69. #2428C2×C3semidirect
70. #2054C2×C3semidirect
71. #2041C2×C3semidirect
72. #2014C2×C3semidirect
73. #2012C2×C3semidirect
74. #1999C2×C3semidirect
75. #1999C2×C3semidirect
76. #1933C2×C3semidirect
77. #1923C2×C3semidirect
78. #1879C2×C3semidirect
118. C2×C3×D8D4semidirect
158. C3×#103D4semidirect
385. C2×D8C3×D4semidirect
425. #103C3×D4semidirect
902. C3#30447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4932
C2×C3×#4632
C2×C3×#4492
C3×#24312
C3×#24282
C3×#20542
C3×#20412
C3×#20142
C3×#20122
C3×#19992
C3×#19332
C3×#19232
C3×#18792
#304473