Finite Group Databasebeta

← C3×#29601 #10648208

Subgroups — C3×#29601 #10648208

Order 768.

1462 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#525C211yesmaximal, characteristic
2C2×C3×#485C211yesmaximal, characteristic, complemented
3C2×C3×#452C211yesmaximal, characteristic, complemented
4C3×#2848C211yesmaximal, characteristic, complemented
5C3×#2036C211yesmaximal, characteristic, complemented
6C3×#2035C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8C3×#2033C211yesmaximal, characteristic, complemented
9C3×#2001C211yesmaximal, characteristic, complemented
10C3×#2001C211yesmaximal, characteristic, complemented
11C3×#2000C211yesmaximal, characteristic, complemented
12C3×#2000C211yesmaximal, characteristic, complemented
13C3×#1825C211yesmaximal, characteristic, complemented
14C3×#1788C211yesmaximal, characteristic, complemented
15C3×#1779C211yesmaximal, characteristic, complemented
16#29601C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×#41C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C22×C3×SD16C2211yescharacteristic, complemented
21C3×#525—24no—
22C3×#525—24no—
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×#121C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C2×C3×#120—21no—
32C2×C3×C4×D4—21no—
33C2×C3×C4×D4—21no—
34C2×C3×#117C2211yescharacteristic
35C3×#485—24no—
36C3×#452—24no—
37C2×C3×#107C2211yescharacteristic, complemented
38C2×C3×#106C2211yescharacteristic, complemented
39C2×C3×#103C2211yescharacteristic, complemented
40C2×C3×#103C2211yescharacteristic, complemented
41C2×C3×#103C2211yescharacteristic, complemented
42C2×C3×#103C2211yescharacteristic, complemented
43C2×C3×#103C2211yescharacteristic, complemented
44C2×C3×#102C2211yescharacteristic, complemented
45C2×C3×#102C2211yescharacteristic, complemented
46C2×C3×#102C2211yescharacteristic, complemented
47C2×C3×C22⋊C8C2211yescharacteristic
48C2×C3×C22⋊C8C2211yescharacteristic
49C2×C3×C22⋊C8C2211yescharacteristic
50C2×C3×C22⋊C8C2211yescharacteristic
51C2×C3×C22⋊C8C2211yescharacteristic
52C2×C3×C22⋊C8C2211yescharacteristic
53C3×#385—21no—
54C3×#385—21no—
55C3×#385—21no—
56C3×#380C2211yescharacteristic
57C3×#380C2211yescharacteristic
58C3×#380C2211yescharacteristic
59C3×#379—21no—
60C3×#340C2211yescharacteristic, complemented
61C3×#340C2211yescharacteristic, complemented
62C3×#340C2211yescharacteristic, complemented
63C3×#340C2211yescharacteristic, complemented
64C2×#525C2×C311yescharacteristic
65C2×#485C2×C311yescharacteristic, complemented
66C2×#452C2×C311yescharacteristic, complemented
67#2848C2×C311yescharacteristic, complemented
68#2036C2×C311yescharacteristic, complemented
69#2035C2×C311yescharacteristic, complemented
70#2034C2×C311yescharacteristic, complemented
71#2033C2×C311yescharacteristic, complemented
72#2001C2×C311yescharacteristic, complemented
73#2001C2×C311yescharacteristic, complemented
74#2000C2×C311yescharacteristic, complemented
75#2000C2×C311yescharacteristic, complemented
76#1825C2×C311yescharacteristic, complemented
77#1788C2×C311yescharacteristic, complemented
78#1779C2×C311yescharacteristic, complemented
79C25×C3D411yescharacteristic
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C2×C3×#41—41no—
84C2×C3×#41—41no—
85C2×C3×#41D414yes—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4—21no—
90C22×C3×D4—21no—
91C22×C3×D4C2311yescharacteristic
92C23×C3×C4—22no—
93C23×C3×C4—22no—
94C23×C3×C4—21no—
95C23×C3×C4—41no—
96C23×C3×C4—41no—
97C23×C3×C4—41no—
98C23×C3×C4—41no—
99C23×C3×C4D411yescharacteristic
100C23×C3×C4D411yescharacteristic
101C23×C3×C4D411yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C2×C3×Q16—22no—
106C2×C3×Q16—41no—
107C2×C3×Q16—41no—
108C2×C3×SD16—22no—
109C2×C3×SD16—41no—
110C2×C3×SD16—41no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×#123—28no—
116C3×C22⋊Q8—22no—
117C3×C22⋊Q8—22no—
118C3×C22⋊Q8—22no—
119C3×C22⋊Q8—22no—
120C3×C22⋊Q8—22no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—41no—
123C3×C22⋊Q8—41no—
124C3×C22⋊Q8—41no—
125C3×C22⋊Q8—41no—
126C3×#121—22no—
127C3×#121—22no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#120—28no—
131C3×C4×D4—28no—
132C3×C4×D4—28no—
133C3×#117—22no—
134C3×#117D414yes—
135C2×C3×C4⋊C4—21no—
136C2×C3×C4⋊C4—21no—
137C2×C3×C4⋊C4—21no—
138C2×C3×C4⋊C4—21no—
139C2×C3×C4⋊C4—21no—
140C2×C3×C4⋊C4C2311yescharacteristic
141C2×C3×C4⋊C4C2311yescharacteristic
142C2×C3×C4⋊C4C2311yescharacteristic
143C2×C3×C4⋊C4C2311yescharacteristic
144C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C42—21no—
157C3×#107—22no—
158C3×#106—22no—
159C3×#103—22no—
160C3×#103—22no—
161C3×#103—22no—
162C3×#103—41no—
163C3×#103—41no—
164C3×#102—22no—
165C3×#102—41no—
166C3×#102—41no—
167C3×C22⋊C8—22no—
168C3×C22⋊C8—22no—
169C3×C22⋊C8—41no—
170C3×C22⋊C8—41no—
171C3×C22⋊C8—41no—
172C3×C22⋊C8—41no—
173C3×#95—21no—
174C3×#95—21no—
175C3×#95—21no—
176C22×#41C22×C311yescharacteristic
177C24×C4C22×C311yescharacteristic
178C22×Q16C22×C311yescharacteristic, complemented
179C22×SD16C22×C311yescharacteristic, complemented
180#525—24no—
181#525—24no—
182C2×#123—21no—
183C2×C22⋊Q8C22×C311yescharacteristic
184C2×C22⋊Q8C22×C311yescharacteristic
185C2×C22⋊Q8C22×C311yescharacteristic
186C2×C22⋊Q8C22×C311yescharacteristic
187C2×C22⋊Q8C22×C311yescharacteristic
188C2×#121C22×C311yescharacteristic
189C2×#121C22×C311yescharacteristic
190C2×#120—21no—
191C2×C4×D4—21no—
192C2×C4×D4—21no—
193C2×#117C22×C311yescharacteristic
194#485—24no—
195#452—24no—
196C2×#107C22×C311yescharacteristic, complemented
197C2×#106C22×C311yescharacteristic, complemented
198C2×#103C22×C311yescharacteristic, complemented
199C2×#103C22×C311yescharacteristic, complemented
200C2×#103C22×C311yescharacteristic, complemented
201C2×#103C22×C311yescharacteristic, complemented
202C2×#103C22×C311yescharacteristic, complemented
203C2×#102C22×C311yescharacteristic, complemented
204C2×#102C22×C311yescharacteristic, complemented
205C2×#102C22×C311yescharacteristic, complemented
206C2×C22⋊C8C22×C311yescharacteristic
207C2×C22⋊C8C22×C311yescharacteristic
208C2×C22⋊C8C22×C311yescharacteristic
209C2×C22⋊C8C22×C311yescharacteristic
210C2×C22⋊C8C22×C311yescharacteristic
211C2×C22⋊C8C22×C311yescharacteristic
212#385—21no—
213#385—21no—
214#385—21no—
215#380C22×C311yescharacteristic
216#380C22×C311yescharacteristic
217#380C22×C311yescharacteristic
218#379—21no—
219#340C22×C311yescharacteristic, complemented
220#340C22×C311yescharacteristic, complemented
221#340C22×C311yescharacteristic, complemented
222#340C22×C311yescharacteristic, complemented
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—21no—
227C24×C3—41no—
228C24×C3—41no—
229C24×C3—41no—
230C24×C3—41no—
231C24×C3C2×D411yescharacteristic
232C24×C3C2×D411yescharacteristic
233C24×C3C2×D411yescharacteristic
234C3×#41—44no—
235C3×#41—44no—
236C3×#41—44no—
237C3×#41—44no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8C2×D412yes—
250C2×C3×D4—24no—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—21no—
254C2×C3×D4—21no—
255C2×C3×D4—21no—
256C2×C3×D4—21no—
257C2×C3×D4—21no—
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×D4C2×D412yes—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—22no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—24no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
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—41no—
293C22×C3×C4—41no—
294C22×C3×C4—41no—
295C22×C3×C4—41no—
296C22×C3×C4—41no—
297C22×C3×C4—41no—
298C22×C3×C4—44no—
299C22×C3×C4—44no—
300C22×C3×C4—44no—
301C22×C3×C4—44no—
302C22×C3×C4—42no—
303C22×C3×C4—42no—
304C22×C3×C4C2×D411yescharacteristic
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4C2411yescharacteristic
310C3×Q16—44no—
311C3×SD16—44no—
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×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C3×C4⋊C4—24no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—42no—
335C3×C4⋊C4—42no—
336C3×C4⋊C4—42no—
337C3×C4⋊C4C2×D412yes—
338C3×C4⋊C4C2×D412yes—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—24no—
341C3×C22⋊C4—24no—
342C3×C22⋊C4—24no—
343C3×C22⋊C4—24no—
344C3×C22⋊C4—42no—
345C3×C22⋊C4—42no—
346C3×C22⋊C4—42no—
347C3×C22⋊C4—42no—
348C3×C22⋊C4—42no—
349C3×C22⋊C4—42no—
350C3×C42—24no—
351C25C3×D411yescharacteristic
352C2×#41—22no—
353C2×#41—41no—
354C2×#41—41no—
355C2×#41—41no—
356C2×#41—41no—
357C2×#41C3×D414yes—
358C22×Q8C23×C311yescharacteristic
359C22×Q8C23×C311yescharacteristic
360C22×D4—21no—
361C22×D4—21no—
362C22×D4—21no—
363C22×D4C23×C311yescharacteristic
364C23×C4—21no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—41no—
368C23×C4—41no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4C3×D411yescharacteristic
372C23×C4C3×D411yescharacteristic
373C23×C4C3×D411yescharacteristic
374C23×C4C23×C311yescharacteristic
375C23×C4C23×C311yescharacteristic
376C23×C4C23×C311yescharacteristic
377C2×Q16—22no—
378C2×Q16—41no—
379C2×Q16—41no—
380C2×SD16—22no—
381C2×SD16—41no—
382C2×SD16—41no—
383C22×C8C23×C311yescharacteristic
384C22×C8C23×C311yescharacteristic
385C22×C8C23×C311yescharacteristic
386C22×C8C23×C311yescharacteristic
387#123—28no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—41no—
395C22⋊Q8—41no—
396C22⋊Q8—41no—
397C22⋊Q8—41no—
398#121—22no—
399#121—22no—
400#121—22no—
401#121—22no—
402#120—28no—
403C4×D4—28no—
404C4×D4—28no—
405#117—22no—
406#117C3×D414yes—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4C23×C311yescharacteristic
413C2×C4⋊C4C23×C311yescharacteristic
414C2×C4⋊C4C23×C311yescharacteristic
415C2×C4⋊C4C23×C311yescharacteristic
416C2×C4⋊C4C23×C311yescharacteristic
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C42—21no—
429#107—22no—
430#106—22no—
431#103—22no—
432#103—22no—
433#103—22no—
434#103—41no—
435#103—41no—
436#102—22no—
437#102—41no—
438#102—41no—
439C22⋊C8—22no—
440C22⋊C8—22no—
441C22⋊C8—41no—
442C22⋊C8—41no—
443C22⋊C8—41no—
444C22⋊C8—41no—
445#95—21no—
446#95—21no—
447#95—21no—
448C23×C3—21no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—22no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3—44no—
472C23×C3—44no—
473C23×C3—44no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3#12012yes—
481C23×C3#13512yes—
482C23×C3#13712yes—
483C23×C3C22×D411yescharacteristic
484C3×Q8—22no—
485C3×Q8—22no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×D4—22no—
493C3×D4—22no—
494C3×D4—48no—
495C3×D4—48no—
496C3×D4—48no—
497C3×D4—41no—
498C3×D4—41no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—22no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—44no—
515C2×C3×C4—44no—
516C2×C3×C4—48no—
517C2×C3×C4—44no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
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—41no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4#12012yes—
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4H(5,𝔽2)11yescharacteristic
548C2×C3×C4H(5,𝔽2)11yescharacteristic
549C2×C3×C4H(5,𝔽2)11yescharacteristic
550C2×C3×C4H(5,𝔽2)11yescharacteristic
551C3×C8—41no—
552C3×C8—41no—
553C3×C8—41no—
554C3×C8—41no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—21no—
559C24—41no—
560C24—41no—
561C24—41no—
562C24—41no—
563C24C2×C3×D411yescharacteristic
564C24C2×C3×D411yescharacteristic
565C24C2×C3×D411yescharacteristic
566#41—44no—
567#41—44no—
568#41—44no—
569#41—44no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C2×C3×D412yes—
582C2×D4—24no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4C2×C3×D412yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
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—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4C2×C3×D411yescharacteristic
637C22×C4C2×C3×D411yescharacteristic
638C22×C4C2×C3×D411yescharacteristic
639C22×C4C2×C3×D412yes—
640C22×C4C2×C3×D412yes—
641C22×C4C24×C311yescharacteristic
642Q16—44no—
643SD16—44no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4C2×C3×D412yes—
670C4⋊C4C2×C3×D412yes—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—24no—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C42—24no—
683C22×C3—22no—
684C22×C3—22no—
685C22×C3—22no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—22no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—416no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—81no—
709C22×C3—81no—
710C22×C3—81no—
711C22×C3—81no—
712C22×C3C2×#12011yescharacteristic
713C22×C3#53411yescharacteristic
714C22×C3#53411yescharacteristic
715C22×C3C2×#13511yescharacteristic
716C22×C3C2×#13711yescharacteristic
717C22×C3#57511yescharacteristic
718C22×C3#57511yescharacteristic
719C3×C4—22no—
720C3×C4—41no—
721C3×C4—41no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—81no—
726C3×C4—81no—
727C3×C4—81no—
728C3×C4—81no—
729C3×C4#53411yescharacteristic
730C3×C4#53411yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4#53511yescharacteristic
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23C3×#12012yes—
766C23C3×#13512yes—
767C23C3×#13712yes—
768C23C22×C3×D411yescharacteristic
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776Q8—41no—
777D4—22no—
778D4—22no—
779D4—48no—
780D4—48no—
781D4—48no—
782D4—41no—
783D4—41no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—48no—
802C2×C4—44no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
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—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4C3×#12012yes—
830C2×C4C22×C3×D411yescharacteristic
831C2×C4C22×C3×D411yescharacteristic
832C2×C4C3×H(5,𝔽2)11yescharacteristic
833C2×C4C3×H(5,𝔽2)11yescharacteristic
834C2×C4C3×H(5,𝔽2)11yescharacteristic
835C2×C4C3×H(5,𝔽2)11yescharacteristic
836C8—41no—
837C8—41no—
838C8—41no—
839C8—41no—
840C2×C3—42no—
841C2×C3—42no—
842C2×C3—42no—
843C2×C3—82no—
844C2×C3#261311yescharacteristic
845C2×C3#300211yescharacteristic
846C2×C3#300711yescharacteristic
847C2×C3#319011yescharacteristic
848C2×C3#319111yescharacteristic
849C2×C3#319611yescharacteristic
850C2×C3#319711yescharacteristic
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—416no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22C2×C3×#12011yescharacteristic
881C22C3×#53411yescharacteristic
882C22C3×#53411yescharacteristic
883C22C2×C3×#13511yescharacteristic
884C22C2×C3×#13711yescharacteristic
885C22C3×#57511yescharacteristic
886C22C3×#57511yescharacteristic
887C4—22no—
888C4—42no—
889C4—42no—
890C4—41no—
891C4—41no—
892C4—42no—
893C4—81no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4C3×#53411yescharacteristic
898C4C3×#53411yescharacteristic
899C4C3×#53511yescharacteristic
900C4C3×#53511yescharacteristic
901C3#2960111yescharacteristic, direct product factor, Sylow
902C2—42no—
903C2—42no—
904C2—42no—
905C2—82no—
906C2C3×#261311yescharacteristic
907C2C3×#300211yescharacteristic
908C2C3×#300711yescharacteristic
909C2C3×#319011yescharacteristic
910C2C3×#319111yescharacteristic
911C2C3×#319611yescharacteristic
912C2C3×#319711yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#485C2semidirect
3. C2×C3×#452C2semidirect
4. C3×#2848C2semidirect
5. C3×#2036C2semidirect
6. C3×#2035C2semidirect
7. C3×#2034C2semidirect
8. C3×#2033C2semidirect
9. C3×#2001C2semidirect
10. C3×#2001C2semidirect
11. C3×#2000C2semidirect
12. C3×#2000C2semidirect
13. C3×#1825C2semidirect
14. C3×#1788C2semidirect
15. C3×#1779C2semidirect
16. #29601C3direct (N × H)
19. C22×C3×Q16C22semidirect
20. C22×C3×SD16C22semidirect
37. C2×C3×#107C22semidirect
38. C2×C3×#106C22semidirect
39. C2×C3×#103C22semidirect
40. C2×C3×#103C22semidirect
41. C2×C3×#103C22semidirect
42. C2×C3×#103C22semidirect
43. C2×C3×#103C22semidirect
44. C2×C3×#102C22semidirect
45. C2×C3×#102C22semidirect
46. C2×C3×#102C22semidirect
60. C3×#340C22semidirect
61. C3×#340C22semidirect
62. C3×#340C22semidirect
63. C3×#340C22semidirect
65. C2×#485C2×C3semidirect
66. C2×#452C2×C3semidirect
67. #2848C2×C3semidirect
68. #2036C2×C3semidirect
69. #2035C2×C3semidirect
70. #2034C2×C3semidirect
71. #2033C2×C3semidirect
72. #2001C2×C3semidirect
73. #2001C2×C3semidirect
74. #2000C2×C3semidirect
75. #2000C2×C3semidirect
76. #1825C2×C3semidirect
77. #1788C2×C3semidirect
78. #1779C2×C3semidirect
178. C22×Q16C22×C3semidirect
179. C22×SD16C22×C3semidirect
196. C2×#107C22×C3semidirect
197. C2×#106C22×C3semidirect
198. C2×#103C22×C3semidirect
199. C2×#103C22×C3semidirect
200. C2×#103C22×C3semidirect
201. C2×#103C22×C3semidirect
202. C2×#103C22×C3semidirect
203. C2×#102C22×C3semidirect
204. C2×#102C22×C3semidirect
205. C2×#102C22×C3semidirect
219. #340C22×C3semidirect
220. #340C22×C3semidirect
221. #340C22×C3semidirect
222. #340C22×C3semidirect
901. C3#29601direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5252
C2×C3×#4852
C2×C3×#4522
C3×#28482
C3×#20362
C3×#20352
C3×#20342
C3×#20332
C3×#20012
C3×#20002
C3×#18252
C3×#17882
C3×#17792
#296013