Finite Group Databasebeta

← C3×#81144 #11872271

Subgroups — C3×#81144 #11872271

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5697C211yesmaximal, characteristic, complemented
2C3×#5546C211yesmaximal, characteristic, complemented
3C32×#478C211yesmaximal, characteristic, complemented
4C3×#5063C211yesmaximal, characteristic, complemented
5C3×#5015C211yesmaximal, characteristic, complemented
6C3×#4889C211yesmaximal, characteristic, complemented
7C3×#4882C211yesmaximal, characteristic, complemented
8C3×#4863C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4848C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4785C211yesmaximal, characteristic, complemented
13C3×#4781C211yesmaximal, characteristic, complemented
14C3×#4781C211yesmaximal, characteristic, complemented
15C3×#4756C211yesmaximal, characteristic, complemented
16C3×#3119—31nomaximal
17#81144C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×Dic3⋊C4—21no—
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C3×#895—21no—
29C3×#895—21no—
30C3×#895C2211yescharacteristic
31C3×#895C2211yescharacteristic
32C3×#894—21no—
33C3×#894—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×D3×C4⋊C4C2211yescharacteristic
37C3×#887C2211yescharacteristic
38C3×#67⋊C4—21no—
39C3×#877—21no—
40C3×#874C2211yescharacteristic
41C3×#872C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#102C2211yescharacteristic
47C32×#102C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#810C2211yescharacteristic
55C3×#810C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#540—31no—
62C3×#520—31no—
63#5697C2×C311yescharacteristic, complemented
64#5546C2×C311yescharacteristic, complemented
65C3×#481—31no—
66C3×#480—31no—
67C3×#479—31no—
68C3×#478—21no—
69C3×#478D311yescharacteristic, complemented
70C3×#478C2×C311yescharacteristic, complemented
71C3×#460—31no—
72C3×#459—31no—
73C3×#449—31no—
74C3×#449—31no—
75C3×#442—31no—
76C3×#440—31no—
77C3×C4×SD16—31no—
78C3×C4×D8—31no—
79C3×#433—31no—
80#5063C2×C311yescharacteristic, complemented
81#5015C2×C311yescharacteristic, complemented
82#4889C2×C311yescharacteristic, complemented
83#4882C2×C311yescharacteristic, complemented
84#4863C2×C311yescharacteristic, complemented
85#4852C2×C311yescharacteristic, complemented
86#4848C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4785C2×C311yescharacteristic, complemented
89#4781C2×C311yescharacteristic, complemented
90#4781C2×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×D12—21no—
101C2×C3×D12—21no—
102C2×C3×D12—21no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C22⋊C4—21no—
118C32×C42C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×#204—22no—
141#3119—31noSylow
142C2×C3×#41—31no—
143C2×#237C22×C311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C2×C3×D8—31no—
147C2×C3×D8—31no—
148C3×#127—31no—
149C3×#125—21no—
150C3×#125C2×D311yescharacteristic
151C3×#125C22×C311yescharacteristic
152C3×#123—61no—
153C3×#123—61no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#121—61no—
158C3×C4×Q8—31no—
159C3×C4×Q8—31no—
160C3×C4×D4—21no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165C3×C4×D4—61no—
166C3×C4×D4C2×D311yescharacteristic
167C3×C4×D4C22×C311yescharacteristic
168C3×#117—31no—
169C3×#117—61no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—61no—
172D4×Dic3C22×C311yescharacteristic
173C2×#213C22×C311yescharacteristic
174C2×#213C22×C311yescharacteristic
175C4×#67—21no—
176C2×Dic3⋊C4—21no—
177C2×#204C22×C311yescharacteristic
178C2×#204C22×C311yescharacteristic
179#895—21no—
180#895—21no—
181#895C22×C311yescharacteristic
182#895C22×C311yescharacteristic
183#894—21no—
184#894—21no—
185#893C22×C311yescharacteristic
186#893C22×C311yescharacteristic
187D3×C4⋊C4C22×C311yescharacteristic
188#887C22×C311yescharacteristic
189#67⋊C4—21no—
190#877—21no—
191#874C22×C311yescharacteristic
192#872C22×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×#102—21no—
209C3×#102—21no—
210C3×#102—31no—
211C3×#102—31no—
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×#97—31no—
221C3×C4×C8—31no—
222#821C22×C311yescharacteristic
223#821C22×C311yescharacteristic
224(C2×D3)⋊C8C22×C311yescharacteristic
225(C2×D3)⋊C8C22×C311yescharacteristic
226#815C22×C311yescharacteristic
227C8×Dic3C22×C311yescharacteristic
228#810C22×C311yescharacteristic
229#810C22×C311yescharacteristic
230#809C22×C311yescharacteristic
231#809C22×C311yescharacteristic
232#808C22×C311yescharacteristic
233#807C22×C311yescharacteristic
234C4⋊(C3⋊C8)C22×C311yescharacteristic
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C3×#67—24no—
249C2×C3×Dic3—24no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—81no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—81no—
261C3×D12—81no—
262C3×D12—81no—
263C3×D12—81no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×Dic6—21no—
270C3×Dic6#4112yes—
271C32×C8—21no—
272C32×C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—31no—
276#520—31no—
277#481—31no—
278#480—31no—
279#479—31no—
280#478C3×D311yescharacteristic, complemented
281#460—31no—
282#459—31no—
283#449—31no—
284#449—31no—
285#442—31no—
286#440—31no—
287C4×SD16—31no—
288C4×D8—31no—
289#433—31no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C23×C311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—41no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C2×#67—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315#237—22no—
316#237—22no—
317C2×D12—21no—
318C2×D12—21no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12C23×C311yescharacteristic
322C2×D12C23×C311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3C23×C311yescharacteristic
327C2×Dic6C23×C311yescharacteristic
328C3×SD16—62no—
329C3×SD16—62no—
330C3×D8—62no—
331C3×D8—62no—
332C2×C3×C8—21no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C2×C3×C8C23×C311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—21no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—41no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C23×C311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—41no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—21no—
372C3×C42—31no—
373C3×C42—61no—
374C3×C42—61no—
375C3×C42C22×D311yescharacteristic
376C3×C42C23×C311yescharacteristic
377#217—21no—
378#213—22no—
379#213—22no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4C3×D411yescharacteristic
385(C2×D3)⋊C4C3×D411yescharacteristic
386C4⋊Dic3C23×C311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4C3×D411yescharacteristic
391Dic3⋊C4C3×D411yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397#204—22no—
398#204—22no—
399C22×C32—22no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—21no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—31no—
426C2×SD16—31no—
427C2×D8—31no—
428C2×D8—31no—
429#127—31no—
430#125C2×C3×D311yescharacteristic
431#123—61no—
432#123—61no—
433#121—31no—
434#121—31no—
435#121—61no—
436#121—61no—
437C4×Q8—31no—
438C4×Q8—31no—
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—61no—
443C4×D4—61no—
444C4×D4C2×C3×D311yescharacteristic
445#117—31no—
446#117—61no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—61no—
449#107—31no—
450#107C2×C3×D311yescharacteristic
451#106—31no—
452#106C2×C3×D311yescharacteristic
453C4⋊C8—31no—
454C4⋊C8C2×C3×D311yescharacteristic
455#103—31no—
456#103—31no—
457#102—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102C2×C3×D311yescharacteristic
462#102C2×C3×D311yescharacteristic
463C22⋊C8—31no—
464C22⋊C8—31no—
465#97—31no—
466C4×C8—31no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—41no—
471C23×C3—61no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×C3×D411yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—41no—
482C3×D4—64no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—241no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C3×D4#23912yes—
492C3×D4C3×#4112yes—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—64no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—81no—
514C2×C3×C4—81no—
515C2×C3×C4—82no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4—241no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C2×C3×D411yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C24×C311yescharacteristic
526#67—24no—
527C2×Dic3—24no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—81no—
531C2×Dic3C2×C3×D411yescharacteristic
532C2×Dic3C2×C3×D411yescharacteristic
533C2×Dic3C2×C3×D411yescharacteristic
534D12—21no—
535D12—21no—
536D12—21no—
537D12—21no—
538D12—81no—
539D12—81no—
540D12—81no—
541D12—81no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—81no—
547Dic6—21no—
548Dic6C3×#4112yes—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—41no—
554C3×C8—41no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C2×C32—42no—
560C2×C32#52511yescharacteristic
561C2×C32#57611yescharacteristic
562C2×C32#57711yescharacteristic
563C3×D3—41no—
564C3×D3—81no—
565C3×D3—81no—
566#41—62no—
567#41—62no—
568C2×Q8—31no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C2×D4C22×C3×D311yescharacteristic
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—61no—
584SD16—62no—
585SD16—62no—
586D8—62no—
587D8—62no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8C22×C3×D311yescharacteristic
591C2×C8C22×C3×D311yescharacteristic
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4C22×C3×D311yescharacteristic
601C4⋊C4C22×C3×D311yescharacteristic
602C4⋊C4C22×C3×D311yescharacteristic
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42C22×C3×D311yescharacteristic
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×C3×D411yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—62no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—81no—
666C3×C4—121no—
667C3×C4C2×#23911yescharacteristic
668C3×C4D3×#4111yescharacteristic
669C3×C4C2×C3×#4111yescharacteristic
670C3×C4C2×C3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—22no—
674Dic3—21no—
675Dic3—41no—
676C32#311911yescharacteristic, complemented, Sylow
677C23—21no—
678C23—31no—
679C23—61no—
680C23—61no—
681Q8—32no—
682Q8—61no—
683D4—21no—
684D4—64no—
685D4—61no—
686D4—61no—
687D4—61no—
688D4—61no—
689D4—241no—
690D4—241no—
691D4—241no—
692D4—241no—
693D4C3×#23912yes—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—64no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—81no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—241no—
709C2×C4—241no—
710C2×C4C3×D3×D411yescharacteristic
711C2×C4C3×D3×D411yescharacteristic
712C2×C4C23×C3×D311yescharacteristic
713C8—21no—
714C8—21no—
715C8—61no—
716C8—61no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—121no—
724C2×C3—241no—
725C2×C3—241no—
726C2×C3#562711yescharacteristic
727C2×C3#577011yescharacteristic
728C2×C3#577411yescharacteristic
729C2×C3C3×#52511yescharacteristic
730C2×C3C3×#57611yescharacteristic
731C2×C3C3×#57711yescharacteristic
732D3—41no—
733D3—81no—
734D3—81no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22C2×C3×D3×D411yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—62no—
757C4—121no—
758C4C2×C3×#23911yescharacteristic
759C4C3×D3×#4111yescharacteristic
760C3—21no—
761C3#8114411yescharacteristic, direct product factor
762C3C3×#311911yescharacteristic, complemented
763C2—42no—
764C2—121no—
765C2—241no—
766C2—241no—
767C2C3×#562711yescharacteristic
768C2C3×#577011yescharacteristic
769C2C3×#577411yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#478C2
socleC22×C32C22×D4
hypercenterC3×#478D3
hypocenterC3C3×#3119
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×#5697C2semidirect
2. C3×#5546C2semidirect
3. C32×#478C2semidirect
4. C3×#5063C2semidirect
5. C3×#5015C2semidirect
6. C3×#4889C2semidirect
7. C3×#4882C2semidirect
8. C3×#4863C2semidirect
9. C3×#4852C2semidirect
10. C3×#4848C2semidirect
11. C3×#4840C2semidirect
12. C3×#4785C2semidirect
13. C3×#4781C2semidirect
14. C3×#4781C2semidirect
15. C3×#4756C2semidirect
17. #81144C3direct (N × H)
63. #5697C2×C3semidirect
64. #5546C2×C3semidirect
69. C3×#478D3semidirect
70. C3×#478C2×C3semidirect
80. #5063C2×C3semidirect
81. #5015C2×C3semidirect
82. #4889C2×C3semidirect
83. #4882C2×C3semidirect
84. #4863C2×C3semidirect
85. #4852C2×C3semidirect
86. #4848C2×C3semidirect
87. #4840C2×C3semidirect
88. #4785C2×C3semidirect
89. #4781C2×C3semidirect
90. #4781C2×C3semidirect
91. #4756C2×C3semidirect
280. #478C3×D3semidirect
676. C32#3119semidirect
761. C3#81144direct (N × H)
762. C3C3×#3119semidirect

Maximal subgroups

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

subgroupindex
C3×#56972
C3×#55462
C32×#4782
C3×#50632
C3×#50152
C3×#48892
C3×#48822
C3×#48632
C3×#48522
C3×#48482
C3×#48402
C3×#47852
C3×#47812
C3×#47562
C3×#31193
#811443