Finite Group Databasebeta

← C3×#81204 #11870584

Subgroups — C3×#81204 #11870584

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5691C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5028C211yesmaximal, characteristic, complemented
6C3×#4888C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4866C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4833C211yesmaximal, characteristic, complemented
12C3×#4810C211yesmaximal, characteristic
13C3×#4808C211yesmaximal, characteristic, complemented
14C3×#4790C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3102—31nomaximal
17#81204C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×#204C2211yescharacteristic
26C3×#898—21no—
27C3×#897C2211yescharacteristic
28C3×#895C2211yescharacteristic
29C3×#894—21no—
30C3×#893—21no—
31C3×#893—21no—
32C3×#893C2211yescharacteristic
33C3×#893C2211yescharacteristic
34C3×#892—21no—
35C3×#892—21no—
36C3×#892C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#875C2211yescharacteristic
39C3×C4×D12—21no—
40C3×C4×D12C2211yescharacteristic
41C3×C42×D3—21no—
42C3×C42×D3C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×C8×Dic3C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#529—31no—
62C3×C4×#41—31no—
63#5691C2×C311yescharacteristic, complemented
64C4×#239C2×C311yescharacteristic, complemented
65C3×#485—31no—
66C3×#482—31no—
67C3×#479—21no—
68C3×#479D311yescharacteristic, complemented
69C3×#479C2×C311yescharacteristic, complemented
70C3×#478—31no—
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#5066C2×C311yescharacteristic, complemented
81#5028C2×C311yescharacteristic, complemented
82#4888C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4866C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4844C2×C311yescharacteristic, complemented
87#4833C2×C311yescharacteristic, complemented
88#4810C2×C311yescharacteristic
89#4808C2×C311yescharacteristic, complemented
90#4790C2×C311yescharacteristic, complemented
91#4788C2×C311yescharacteristic, complemented
92C2×C32×Q8C2311yescharacteristic
93C3×#239—22no—
94C3×#239—22no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C32×C8C2311yescharacteristic
108C2×C32×C8C2311yescharacteristic
109C32×C4⋊C4—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115C32×C42—21no—
116C32×C42C2311yescharacteristic
117C3×#216—22no—
118C3×#215—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×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—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×D24—22no—
140C3×#204—22no—
141#3102—31noSylow
142C2×C3×#41—31no—
143C2×#239C22×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—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8—31no—
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×Q8C22×C311yescharacteristic
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4—61no—
167C3×#117—31no—
168C3×#117—61no—
169C3×#117—61no—
170C2×C3×C42—31no—
171C2×C3×C42—61no—
172Q8×Dic3C22×C311yescharacteristic
173C2×#216C22×C311yescharacteristic
174C2×#215C22×C311yescharacteristic
175C2×D24C22×C311yescharacteristic
176C2×#204C22×C311yescharacteristic
177#898—21no—
178#897C22×C311yescharacteristic
179#895C22×C311yescharacteristic
180#894—21no—
181#893—21no—
182#893—21no—
183#893C22×C311yescharacteristic
184#893C22×C311yescharacteristic
185#892—21no—
186#892—21no—
187#892C22×C311yescharacteristic
188#887C22×C311yescharacteristic
189#875C22×C311yescharacteristic
190C4×D12—21no—
191C4×D12C22×C311yescharacteristic
192C42×D3—21no—
193C42×D3C22×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—21no—
207C3×#103—21no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212C3×#103C22×C311yescharacteristic
213C3×#103C22×C311yescharacteristic
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
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#809C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×Q8—21no—
239C32×Q8#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—24no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—42no—
257C3×D12#4112yes—
258C3×C4×D3—24no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—22no—
262C3×C4×D3—41no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
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#479C3×D311yescharacteristic, complemented
277#478—31no—
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—21no—
290C2×C3×Q8—31no—
291C2×C3×Q8C22×D311yescharacteristic
292C2×C3×Q8C23×C311yescharacteristic
293C2×C3×D4—31no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—61no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304#239—22no—
305#239—22no—
306C2×D12—21no—
307C2×D12—21no—
308C2×D12C23×C311yescharacteristic
309C2×D12C23×C311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—21no—
313C2×C4×D3—21no—
314C2×C4×D3C3×D411yescharacteristic
315C2×C4×D3C3×D411yescharacteristic
316C2×C4×D3C23×C311yescharacteristic
317C2×Dic6C23×C311yescharacteristic
318C3×Q16—62no—
319C3×SD16—62no—
320C3×SD16—62no—
321C3×D8—62no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C2×C3×C8C22×D311yescharacteristic
327C2×C3×C8C22×D311yescharacteristic
328C2×C3×C8C23×C311yescharacteristic
329C2×C3×C8C23×C311yescharacteristic
330C3×C4⋊C4—21no—
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—21no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—41no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C23×C311yescharacteristic
350C3×C4⋊C4C23×C311yescharacteristic
351C3×C4⋊C4C23×C311yescharacteristic
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
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×C42—21no—
361C3×C42—21no—
362C3×C42—21no—
363C3×C42—31no—
364C3×C42—31no—
365C3×C42—31no—
366C3×C42—41no—
367C3×C42—61no—
368C3×C42—61no—
369C3×C42—61no—
370C3×C42C22×D311yescharacteristic
371C3×C42C23×C311yescharacteristic
372#216—22no—
373#215—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—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3C23×C311yescharacteristic
385Dic3⋊C4—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
394D24—22no—
395#204—22no—
396C22×C32C22×D411yescharacteristic
397C2×C3×D3—21no—
398C2×C3×D3—22no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—22no—
407C32×C4—21no—
408C32×C4—21no—
409C32×C4—41no—
410C32×C4—41no—
411C32×C4—41no—
412C32×C4C2×#4111yescharacteristic
413C32×C4C2×#4111yescharacteristic
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×Q8C2×C3×D311yescharacteristic
433C4×D4—31no—
434C4×D4—31no—
435C4×D4—31no—
436C4×D4—61no—
437C4×D4—61no—
438C4×D4—61no—
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#103C2×C3×D311yescharacteristic
453#103C2×C3×D311yescharacteristic
454#102—31no—
455#102—31no—
456#102—31no—
457#102—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C4×C8—31no—
461C4×C8—31no—
462C23×C3—31no—
463C23×C3—61no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3C2×C3×D411yescharacteristic
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—22no—
471C3×Q8—41no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×Q8#23912yes—
475C3×Q8C3×#4112yes—
476C3×D4—32no—
477C3×D4—64no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—122no—
482C2×C3×C4—21no—
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—21no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—31no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
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—121no—
507C2×C3×C4—122no—
508C2×C3×C4—122no—
509C2×C3×C4—122no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×C3×D411yescharacteristic
513C2×C3×C4C2×C3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C24×C311yescharacteristic
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3C2×C3×D411yescharacteristic
519C2×Dic3C2×C3×D411yescharacteristic
520C2×Dic3C2×C3×D411yescharacteristic
521D12—24no—
522D12—21no—
523D12—21no—
524D12—21no—
525D12—42no—
526D12C3×#4112yes—
527C4×D3—24no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—22no—
531C4×D3—41no—
532C4×D3—42no—
533C4×D3—42no—
534C4×D3—42no—
535Dic6—21no—
536Dic6—21no—
537C3×C8—21no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—21no—
541C3×C8—41no—
542C3×C8—41no—
543C3×C8—61no—
544C3×C8—61no—
545C3⋊C8—21no—
546C3⋊C8—21no—
547C2×C32#52511yescharacteristic
548C2×C32C2×#13511yescharacteristic
549C2×C32#57511yescharacteristic
550C3×D3—41no—
551C3×D3—42no—
552C3×D3—81no—
553#41—62no—
554#41—62no—
555C2×Q8—31no—
556C2×Q8C22×C3×D311yescharacteristic
557C2×D4—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—61no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568Q16—62no—
569SD16—62no—
570SD16—62no—
571D8—62no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8C22×C3×D311yescharacteristic
575C2×C8C22×C3×D311yescharacteristic
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—31no—
580C4⋊C4—61no—
581C4⋊C4—61no—
582C4⋊C4—61no—
583C4⋊C4C22×C3×D311yescharacteristic
584C4⋊C4C22×C3×D311yescharacteristic
585C4⋊C4C22×C3×D311yescharacteristic
586C22⋊C4—61no—
587C22⋊C4—61no—
588C22⋊C4—61no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C42—21no—
595C42—31no—
596C42—31no—
597C42—31no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42C22×C3×D311yescharacteristic
602C22×C3—21no—
603C22×C3—61no—
604C22×C3—61no—
605C22×C3—62no—
606C22×C3—61no—
607C22×C3—121no—
608C22×C3—121no—
609C22×C3—121no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3C2×D3×D411yescharacteristic
613C22×C3C22×C3×D411yescharacteristic
614C2×D3—21no—
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—22no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C2×D3—41no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—21no—
626C3×C4—21no—
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—21no—
630C3×C4—21no—
631C3×C4—32no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—42no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—81no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4C2×#23911yescharacteristic
649C3×C4D3×#4111yescharacteristic
650C3×C4C2×C3×#4111yescharacteristic
651C3×C4C2×C3×#4111yescharacteristic
652Dic3—21no—
653Dic3—21no—
654Dic3—41no—
655Dic3—41no—
656Dic3C3×#13512yes—
657C32#310211yescharacteristic, complemented, Sylow
658C23—31no—
659C23—61no—
660C23—61no—
661Q8—21no—
662Q8—61no—
663Q8—61no—
664Q8C3×#23912yes—
665D4—32no—
666D4—64no—
667D4—61no—
668D4—61no—
669D4—61no—
670D4—122no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—31no—
678C2×C4—62no—
679C2×C4—64no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—121no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—122no—
688C2×C4C3×D3×D411yescharacteristic
689C2×C4C3×D3×D411yescharacteristic
690C2×C4C23×C3×D311yescharacteristic
691C8—21no—
692C8—21no—
693C8—61no—
694C8—61no—
695C2×C3—21no—
696C2×C3—21no—
697C2×C3—21no—
698C2×C3—121no—
699C2×C3—122no—
700C2×C3—241no—
701C2×C3#562711yescharacteristic
702C2×C3D3×#13511yescharacteristic
703C2×C3#577711yescharacteristic
704C2×C3C3×#52511yescharacteristic
705C2×C3C2×C3×#13511yescharacteristic
706C2×C3C3×#57511yescharacteristic
707D3—41no—
708D3—42no—
709D3—81no—
710C22—61no—
711C22—61no—
712C22—62no—
713C22—61no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22C2×C3×D3×D411yescharacteristic
720C4—21no—
721C4—21no—
722C4—22no—
723C4—32no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—61no—
728C4—61no—
729C4—121no—
730C4—121no—
731C4C2×C3×#23911yescharacteristic
732C4C3×D3×#4111yescharacteristic
733C3—21no—
734C3#8120411yescharacteristic, direct product factor
735C3C3×#310211yescharacteristic, complemented
736C2—121no—
737C2—122no—
738C2—241no—
739C2C3×#562711yescharacteristic
740C2C3×D3×#13511yescharacteristic
741C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
prime radicalC3×#4810C2
hypercenterC3×#479D3
hypocenterC3C3×#3102
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#479

Complements

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

NH ≅ G/Ntype
1. C3×#5691C2semidirect
2. C3×C4×#239C2semidirect
3. C32×#479C2semidirect
4. C3×#5066C2semidirect
5. C3×#5028C2semidirect
6. C3×#4888C2semidirect
7. C3×#4872C2semidirect
8. C3×#4866C2semidirect
9. C3×#4852C2semidirect
10. C3×#4844C2semidirect
11. C3×#4833C2semidirect
13. C3×#4808C2semidirect
14. C3×#4790C2semidirect
15. C3×#4788C2semidirect
17. #81204C3direct (N × H)
63. #5691C2×C3semidirect
64. C4×#239C2×C3semidirect
68. C3×#479D3semidirect
69. C3×#479C2×C3semidirect
80. #5066C2×C3semidirect
81. #5028C2×C3semidirect
82. #4888C2×C3semidirect
83. #4872C2×C3semidirect
84. #4866C2×C3semidirect
85. #4852C2×C3semidirect
86. #4844C2×C3semidirect
87. #4833C2×C3semidirect
89. #4808C2×C3semidirect
90. #4790C2×C3semidirect
91. #4788C2×C3semidirect
276. #479C3×D3semidirect
657. C32#3102semidirect
734. C3#81204direct (N × H)
735. 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×#2392
C32×#4792
C3×#50662
C3×#50282
C3×#48882
C3×#48722
C3×#48662
C3×#48522
C3×#48442
C3×#48332
C3×#48102
C3×#48082
C3×#47902
C3×#47882
C3×#31023
#812043