Finite Group Databasebeta

← C3×#81140 #11870578

Subgroups — C3×#81140 #11870578

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 747 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5691C211yesmaximal, characteristic, complemented
2C3×C4×#237C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5016C211yesmaximal, characteristic, complemented
6C3×#4885C211yesmaximal, characteristic, complemented
7C3×#4873C211yesmaximal, characteristic, complemented
8C3×#4868C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4845C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4783C211yesmaximal, characteristic, complemented
13C3×#4781C211yesmaximal, characteristic
14C3×#4758C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#81140C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×C4×Dic3—21no—
26C2×C3×Dic12C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#898—21no—
29C3×#897C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#894—21no—
32C3×#893—21no—
33C3×#893C2211yescharacteristic
34C3×#892—21no—
35C3×#892C2211yescharacteristic
36C3×#887C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#67⋊C4—21no—
39C3×#877—21no—
40C3×#875C2211yescharacteristic
41C3×C42×D3C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#810C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5691C2×C311yescharacteristic, complemented
64C4×#237C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—31no—
68C3×#478—21no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#464—31no—
72C3×#463—31no—
73C3×#452—31no—
74C3×#449—31no—
75C3×C4×Q16—31no—
76C3×C4×SD16—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#431—31no—
80#5063C2×C311yescharacteristic, complemented
81#5016C2×C311yescharacteristic, complemented
82#4885C2×C311yescharacteristic, complemented
83#4873C2×C311yescharacteristic, complemented
84#4868C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4845C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4783C2×C311yescharacteristic, complemented
89#4781C2×C311yescharacteristic
90#4758C2×C311yescharacteristic, complemented
91#4756C2×C311yescharacteristic, complemented
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C3×#237—22no—
98C3×#237—22no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116C3×#217—21no—
117C3×#214—22no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×Dic12—22no—
140C3×#204—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×Q16—31no—
145C2×C3×SD16—31no—
146C2×C3×SD16—31no—
147C2×C3×D8—31no—
148C3×#126—61no—
149C3×#125—21no—
150C3×#125C2×D311yescharacteristic
151C3×#125C22×C311yescharacteristic
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C3×C4×D4—61no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C22×C311yescharacteristic
167C3×#117—31no—
168C3×#117—61no—
169C3×#117—61no—
170C2×C3×C42—31no—
171C2×C3×C42—61no—
172D4×Dic3C22×C311yescharacteristic
173C2×#214C22×C311yescharacteristic
174C2×#213C22×C311yescharacteristic
175C4×#67—21no—
176C2×C4×Dic3—21no—
177C2×Dic12C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179#898—21no—
180#897C22×C311yescharacteristic
181#895C22×C311yescharacteristic
182#894—21no—
183#893—21no—
184#893C22×C311yescharacteristic
185#892—21no—
186#892C22×C311yescharacteristic
187#887C22×C311yescharacteristic
188#887C22×C311yescharacteristic
189#67⋊C4—21no—
190#877—21no—
191#875C22×C311yescharacteristic
192C42×D3C22×C311yescharacteristic
193C4×Dic6C22×C311yescharacteristic
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C22×C311yescharacteristic
198C3×#106—21no—
199C3×#106—31no—
200C3×#106C2×D311yescharacteristic
201C3×#106C22×C311yescharacteristic
202C3×C4⋊C8—21no—
203C3×C4⋊C8—31no—
204C3×C4⋊C8C2×D311yescharacteristic
205C3×C4⋊C8C22×C311yescharacteristic
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#102—21no—
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic
215C3×#102C2×D311yescharacteristic
216C3×#102C22×C311yescharacteristic
217C3×#102C22×C311yescharacteristic
218C3×C22⋊C8—31no—
219C3×C22⋊C8—31no—
220C3×C4×C8—31no—
221C3×C4×C8—31no—
222#821C22×C311yescharacteristic
223(C2×D3)⋊C8C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225#816C22×C311yescharacteristic
226C8×Dic3C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#810C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—42no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C3×#67—24no—
248C2×C3×Dic3—24no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—22no—
262C3×C4×D3—41no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6#4112yes—
268C32×C8—21no—
269C32×C8—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—31no—
273C4×#41—31no—
274#485—31no—
275#482—31no—
276#479—31no—
277#478C3×D311yescharacteristic, complemented
278#464—31no—
279#463—31no—
280#452—31no—
281#449—31no—
282C4×Q16—31no—
283C4×SD16—31no—
284C4×SD16—31no—
285C4×D8—31no—
286#431—31no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—31no—
293C2×C3×D4—61no—
294C2×C3×D4—61no—
295C2×C3×D4C22×D311yescharacteristic
296C2×C3×D4C23×C311yescharacteristic
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—31no—
301C22×C3×C4—31no—
302C22×C3×C4—41no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309#237—22no—
310#237—22no—
311C2×D12—21no—
312C2×D12C23×C311yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3C3×D411yescharacteristic
315C2×C4×D3C3×D411yescharacteristic
316C2×C4×D3C23×C311yescharacteristic
317C2×Dic6C23×C311yescharacteristic
318C2×Dic6C23×C311yescharacteristic
319C3×Q16—62no—
320C3×SD16—62no—
321C3×SD16—62no—
322C3×D8—62no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C22×D311yescharacteristic
329C2×C3×C8C23×C311yescharacteristic
330C2×C3×C8C23×C311yescharacteristic
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—41no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C23×C311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C22⋊C4—21no—
352C3×C22⋊C4—21no—
353C3×C22⋊C4—41no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C42—21no—
362C3×C42—31no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—61no—
366C3×C42—61no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42C22×D311yescharacteristic
370C3×C42C23×C311yescharacteristic
371#217—21no—
372#214—22no—
373#213—22no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3C23×C311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3C3×D411yescharacteristic
390C4×Dic3C3×D411yescharacteristic
391C4×Dic3C23×C311yescharacteristic
392C2×C3⋊C8C23×C311yescharacteristic
393C2×C3⋊C8C23×C311yescharacteristic
394Dic12—22no—
395#204—22no—
396C22×C32—22no—
397C22×C32—41no—
398C22×C32—41no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—21no—
401C2×C3×D3—21no—
402C2×C3×D3—21no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4C2×#4111yescharacteristic
412C32×C4C2×#4111yescharacteristic
413C3×Dic3—22no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3#13512yes—
419C2×#41—31no—
420C2×Q16—31no—
421C2×SD16—31no—
422C2×SD16—31no—
423C2×D8—31no—
424#126—61no—
425#125C2×C3×D311yescharacteristic
426#124—31no—
427#123—61no—
428C22⋊Q8—31no—
429#121—31no—
430C4×Q8—31no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—61no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4C2×C3×D311yescharacteristic
439#117—31no—
440#117—61no—
441#117—61no—
442C2×C42—31no—
443C2×C42—61no—
444#107—31no—
445#107C2×C3×D311yescharacteristic
446#106—31no—
447#106C2×C3×D311yescharacteristic
448C4⋊C8—31no—
449C4⋊C8C2×C3×D311yescharacteristic
450#103—31no—
451#103—31no—
452#103—31no—
453#103—31no—
454#102—31no—
455#102—31no—
456#102C2×C3×D311yescharacteristic
457#102C2×C3×D311yescharacteristic
458C22⋊C8—31no—
459C22⋊C8—31no—
460C4×C8—31no—
461C4×C8—31no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—31no—
465C23×C3—41no—
466C23×C3—61no—
467C22×D3—21no—
468C22×D3C2×C3×D411yescharacteristic
469C3×Q8—32no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×Q8—61no—
473C3×D4—21no—
474C3×D4—21no—
475C3×D4—22no—
476C3×D4—41no—
477C3×D4—64no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—122no—
481C3×D4#23912yes—
482C3×D4C3×#4112yes—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—42no—
499C2×C3×C4—42no—
500C2×C3×C4—62no—
501C2×C3×C4—64no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—82no—
508C2×C3×C4—121no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C2×C3×D411yescharacteristic
514C2×C3×C4C2×C3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C24×C311yescharacteristic
517#67—24no—
518C2×Dic3—24no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—42no—
523C2×Dic3C2×C3×D411yescharacteristic
524C2×Dic3C2×C3×D411yescharacteristic
525C2×Dic3C2×C3×D411yescharacteristic
526D12—21no—
527D12—21no—
528D12—42no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—22no—
532C4×D3—41no—
533C4×D3—42no—
534Dic6—21no—
535Dic6—21no—
536Dic6—21no—
537Dic6C3×#4112yes—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—21no—
542C3×C8—41no—
543C3×C8—41no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C2×C32—42no—
549C2×C32#52511yescharacteristic
550C2×C32C2×#13511yescharacteristic
551C2×C32#57511yescharacteristic
552C3×D3—41no—
553C3×D3—81no—
554#41—62no—
555#41—62no—
556C2×Q8—31no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4C22×C3×D311yescharacteristic
562C22×C4—21no—
563C22×C4—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569Q16—62no—
570SD16—62no—
571SD16—62no—
572D8—62no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8C22×C3×D311yescharacteristic
576C2×C8C22×C3×D311yescharacteristic
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—31no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4C22×C3×D311yescharacteristic
585C4⋊C4C22×C3×D311yescharacteristic
586C4⋊C4C22×C3×D311yescharacteristic
587C22⋊C4—21no—
588C22⋊C4—61no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C42—31no—
596C42—31no—
597C42—31no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C42C22×C3×D311yescharacteristic
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—21no—
606C22×C3—42no—
607C22×C3—41no—
608C22×C3—41no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—81no—
615C22×C3—81no—
616C22×C3—121no—
617C22×C3—121no—
618C22×C3—121no—
619C22×C3C2×D3×D411yescharacteristic
620C22×C3C22×C3×D411yescharacteristic
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—41no—
625C2×D3—41no—
626C2×D3—41no—
627C3×C4—21no—
628C3×C4—21no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—32no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—62no—
645C3×C4—81no—
646C3×C4—81no—
647C3×C4—81no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23911yescharacteristic
651C3×C4D3×#4111yescharacteristic
652C3×C4C2×C3×#4111yescharacteristic
653C3×C4C2×C3×#4111yescharacteristic
654Dic3—21no—
655Dic3—22no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3C3×#13512yes—
660C32#310211yescharacteristic, complemented, Sylow
661C23—21no—
662C23—31no—
663C23—61no—
664Q8—32no—
665Q8—61no—
666Q8—61no—
667Q8—61no—
668D4—21no—
669D4—64no—
670D4—61no—
671D4—61no—
672D4—122no—
673D4C3×#23912yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—31no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—42no—
681C2×C4—62no—
682C2×C4—64no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—121no—
689C2×C4—122no—
690C2×C4—122no—
691C2×C4C3×D3×D411yescharacteristic
692C2×C4C3×D3×D411yescharacteristic
693C2×C4C23×C3×D311yescharacteristic
694C8—21no—
695C8—21no—
696C8—61no—
697C8—61no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—42no—
702C2×C3—42no—
703C2×C3—82no—
704C2×C3—121no—
705C2×C3—241no—
706C2×C3#562711yescharacteristic
707C2×C3D3×#13511yescharacteristic
708C2×C3#577311yescharacteristic
709C2×C3C3×#52511yescharacteristic
710C2×C3C2×C3×#13511yescharacteristic
711C2×C3C3×#57511yescharacteristic
712D3—41no—
713D3—81no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—121no—
721C22—121no—
722C22—121no—
723C22C2×C3×D3×D411yescharacteristic
724C4—21no—
725C4—21no—
726C4—32no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—61no—
731C4—61no—
732C4—62no—
733C4—121no—
734C4—121no—
735C4C2×C3×#23911yescharacteristic
736C4C3×D3×#4111yescharacteristic
737C3—21no—
738C3#8114011yescharacteristic, direct product factor
739C3C3×#310211yescharacteristic, complemented
740C2—42no—
741C2—121no—
742C2—241no—
743C2C3×#562711yescharacteristic
744C2C3×D3×#13511yescharacteristic
745C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
prime radicalC3×#4781C2
hypercenterC3×#478D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#478

Complements

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

NH ≅ G/Ntype
1. C3×#5691C2semidirect
2. C3×C4×#237C2semidirect
3. C32×#478C2semidirect
4. C3×#5063C2semidirect
5. C3×#5016C2semidirect
6. C3×#4885C2semidirect
7. C3×#4873C2semidirect
8. C3×#4868C2semidirect
9. C3×#4852C2semidirect
10. C3×#4845C2semidirect
11. C3×#4833C2semidirect
12. C3×#4783C2semidirect
14. C3×#4758C2semidirect
15. C3×#4756C2semidirect
17. #81140C3direct (N × H)
63. #5691C2×C3semidirect
64. C4×#237C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5063C2×C3semidirect
81. #5016C2×C3semidirect
82. #4885C2×C3semidirect
83. #4873C2×C3semidirect
84. #4868C2×C3semidirect
85. #4852C2×C3semidirect
86. #4845C2×C3semidirect
87. #4833C2×C3semidirect
88. #4783C2×C3semidirect
90. #4758C2×C3semidirect
91. #4756C2×C3semidirect
277. #478C3×D3semidirect
660. C32#3102semidirect
738. C3#81140direct (N × H)
739. C3C3×#3102semidirect

Maximal subgroups

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

subgroupindex
C3×#56912
C3×C4×#2372
C32×#4782
C3×#50632
C3×#50162
C3×#48852
C3×#48732
C3×#48682
C3×#48522
C3×#48452
C3×#48332
C3×#47832
C3×#47812
C3×#47582
C3×#47562
C3×#31023
#811403