Finite Group Databasebeta

← C3×#81208 #11872277

Subgroups — C3×#81208 #11872277

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5697C211yesmaximal, characteristic, complemented
2C3×#5574C211yesmaximal, characteristic, complemented
3C32×#479C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5C3×#5027C211yesmaximal, characteristic, complemented
6C3×#4882C211yesmaximal, characteristic, complemented
7C3×#4872C211yesmaximal, characteristic, complemented
8C3×#4869C211yesmaximal, characteristic, complemented
9C3×#4863C211yesmaximal, characteristic, complemented
10C3×#4843C211yesmaximal, characteristic, complemented
11C3×#4840C211yesmaximal, characteristic, complemented
12C3×#4817C211yesmaximal, characteristic, complemented
13C3×#4810C211yesmaximal, characteristic, complemented
14C3×#4810C211yesmaximal, characteristic, complemented
15C3×#4788C211yesmaximal, characteristic, complemented
16C3×#3119—31nomaximal
17#81208C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C32×#125C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C3×#895—21no—
27C3×#895—21no—
28C3×#895C2211yescharacteristic
29C3×#895C2211yescharacteristic
30C3×#894—21no—
31C3×#894—21no—
32C3×#893—21no—
33C3×#893C2211yescharacteristic
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×D3×C4⋊C4—21no—
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#874C2211yescharacteristic
39C3×C4×D12—21no—
40C3×C4×D12C2211yescharacteristic
41C3×#872—21no—
42C3×#872C2211yescharacteristic
43C32×#107C2211yescharacteristic
44C32×#106C2211yescharacteristic
45C32×C4⋊C8C2211yescharacteristic
46C32×#103C2211yescharacteristic
47C32×#103C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×#809C2211yescharacteristic
55C3×#809C2211yescharacteristic
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic
58C3×#808C2211yescharacteristic
59C3×#807C2211yescharacteristic
60C3×C4⋊(C3⋊C8)C2211yescharacteristic
61C3×#540—31no—
62C3×#520—31no—
63#5697C2×C311yescharacteristic, complemented
64#5574C2×C311yescharacteristic, complemented
65C3×#481—31no—
66C3×#480—31no—
67C3×#479—21no—
68C3×#479D311yescharacteristic, complemented
69C3×#479C2×C311yescharacteristic, complemented
70C3×#478—31no—
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#5066C2×C311yescharacteristic, complemented
81#5027C2×C311yescharacteristic, complemented
82#4882C2×C311yescharacteristic, complemented
83#4872C2×C311yescharacteristic, complemented
84#4869C2×C311yescharacteristic, complemented
85#4863C2×C311yescharacteristic, complemented
86#4843C2×C311yescharacteristic, complemented
87#4840C2×C311yescharacteristic, complemented
88#4817C2×C311yescharacteristic, complemented
89#4810C2×C311yescharacteristic, complemented
90#4810C2×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×D12—21no—
98C2×C3×D12—21no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4—21no—
113C32×C4⋊C4—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117C32×C4⋊C4C2311yescharacteristic
118C32×C42—21no—
119C32×C42C2311yescharacteristic
120C3×#215—22no—
121C3×#215—22no—
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×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4D411yescharacteristic
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×D24—22no—
141#3119—31noSylow
142C2×C3×#41—31no—
143C2×#239C22×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—21no—
159C3×C4×Q8—31no—
160C3×C4×Q8C2×D311yescharacteristic
161C3×C4×Q8C22×C311yescharacteristic
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C3×C4×D4—31no—
166C3×C4×D4—61no—
167C3×C4×D4—61no—
168C3×#117—31no—
169C3×#117—61no—
170C2×C3×C4⋊C4—31no—
171C2×C3×C4⋊C4—61no—
172Q8×Dic3C22×C311yescharacteristic
173C2×#215C22×C311yescharacteristic
174C2×#215C22×C311yescharacteristic
175C2×D24C22×C311yescharacteristic
176C2×D24C22×C311yescharacteristic
177#895—21no—
178#895—21no—
179#895C22×C311yescharacteristic
180#895C22×C311yescharacteristic
181#894—21no—
182#894—21no—
183#893—21no—
184#893C22×C311yescharacteristic
185#893C22×C311yescharacteristic
186#893C22×C311yescharacteristic
187D3×C4⋊C4—21no—
188D3×C4⋊C4C22×C311yescharacteristic
189#874C22×C311yescharacteristic
190C4×D12—21no—
191C4×D12C22×C311yescharacteristic
192#872—21no—
193#872C22×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×#103C2×D311yescharacteristic
209C3×#103C2×D311yescharacteristic
210C3×#103C22×C311yescharacteristic
211C3×#103C22×C311yescharacteristic
212C3×#102—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
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#809C22×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×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
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—21no—
257C3×D12—21no—
258C3×D12—81no—
259C3×D12—81no—
260C3×D12—81no—
261C3×D12—81no—
262C3×D12#4112yes—
263C3×C4×D3—24no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
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#479C3×D311yescharacteristic, complemented
280#478—31no—
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—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C23×C311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4—61no—
310#239—22no—
311#239—22no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12C23×C311yescharacteristic
318C2×D12C23×C311yescharacteristic
319C2×D12C23×C311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3C23×C311yescharacteristic
327C3×SD16—62no—
328C3×SD16—62no—
329C3×D8—62no—
330C3×D8—62no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8C22×D311yescharacteristic
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C23×C311yescharacteristic
338C2×C3×C8C23×C311yescharacteristic
339C3×C4⋊C4—21no—
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—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—41no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—41no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C23×C311yescharacteristic
360C3×C4⋊C4C23×C311yescharacteristic
361C3×C4⋊C4C23×C311yescharacteristic
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—21no—
371C3×C42—21no—
372C3×C42—21no—
373C3×C42—31no—
374C3×C42—41no—
375C3×C42—61no—
376C3×C42C22×D311yescharacteristic
377C3×C42C23×C311yescharacteristic
378#215—22no—
379#215—22no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4C3×D411yescharacteristic
387(C2×D3)⋊C4C3×D411yescharacteristic
388C4⋊Dic3—21no—
389C4⋊Dic3C23×C311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4C3×D411yescharacteristic
392Dic3⋊C4C3×D411yescharacteristic
393C4×Dic3—21no—
394C4×Dic3C23×C311yescharacteristic
395C2×C3⋊C8C23×C311yescharacteristic
396C2×C3⋊C8C23×C311yescharacteristic
397D24—22no—
398D24—22no—
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
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—22no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
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×Q8C2×C3×D311yescharacteristic
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
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#103C2×C3×D311yescharacteristic
456#103C2×C3×D311yescharacteristic
457#102—31no—
458#102—31no—
459#102—31no—
460#102—31no—
461#102—31no—
462#102—31no—
463C22⋊C8—31no—
464C22⋊C8—31no—
465#97—31no—
466C4×C8—31no—
467C23×C3—31no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3C2×C3×D411yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8#23912yes—
480C3×Q8C3×#4112yes—
481C3×D4—32no—
482C3×D4—64no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—241no—
489C3×D4—241no—
490C3×D4—241no—
491C3×D4—241no—
492C2×C3×C4—21no—
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—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—64no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4—241no—
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C2×C3×D411yescharacteristic
522C2×C3×C4C2×C3×D411yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524C2×C3×C4C24×C311yescharacteristic
525C2×Dic3—21no—
526C2×Dic3C2×C3×D411yescharacteristic
527C2×Dic3C2×C3×D411yescharacteristic
528C2×Dic3C2×C3×D411yescharacteristic
529D12—24no—
530D12—21no—
531D12—21no—
532D12—21no—
533D12—21no—
534D12—21no—
535D12—81no—
536D12—81no—
537D12—81no—
538D12—81no—
539D12C3×#4112yes—
540C4×D3—24no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—81no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—41no—
553C3×C8—41no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C2×C32#52511yescharacteristic
559C2×C32#57611yescharacteristic
560C2×C32#57711yescharacteristic
561C3×D3—41no—
562C3×D3—42no—
563C3×D3—81no—
564C3×D3—81no—
565#41—62no—
566#41—62no—
567C2×Q8C22×C3×D311yescharacteristic
568C2×D4—31no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—61no—
575C2×D4—61no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—61no—
583SD16—62no—
584SD16—62no—
585D8—62no—
586D8—62no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8C22×C3×D311yescharacteristic
590C2×C8C22×C3×D311yescharacteristic
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4C22×C3×D311yescharacteristic
600C4⋊C4C22×C3×D311yescharacteristic
601C4⋊C4C22×C3×D311yescharacteristic
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C42—21no—
611C42—31no—
612C42—61no—
613C42C22×C3×D311yescharacteristic
614C22×C3—21no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—62no—
618C22×C3—61no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×C3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—21no—
632C2×D3—22no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—61no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4C2×#23911yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4C2×C3×#4111yescharacteristic
668C3×C4C2×C3×#4111yescharacteristic
669Dic3—21no—
670Dic3—21no—
671Dic3—21no—
672Dic3—41no—
673C32#311911yescharacteristic, complemented, Sylow
674C23—31no—
675C23—61no—
676C23—61no—
677C23—61no—
678Q8—21no—
679Q8C3×#23912yes—
680D4—32no—
681D4—64no—
682D4—61no—
683D4—61no—
684D4—61no—
685D4—61no—
686D4—61no—
687D4—241no—
688D4—241no—
689D4—241no—
690D4—241no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—64no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—241no—
703C2×C4—241no—
704C2×C4—241no—
705C2×C4—241no—
706C2×C4—241no—
707C2×C4C3×D3×D411yescharacteristic
708C2×C4C3×D3×D411yescharacteristic
709C2×C4C23×C3×D311yescharacteristic
710C8—21no—
711C8—21no—
712C8—61no—
713C8—61no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—121no—
718C2×C3—122no—
719C2×C3—241no—
720C2×C3—241no—
721C2×C3#562711yescharacteristic
722C2×C3#576911yescharacteristic
723C2×C3#577811yescharacteristic
724C2×C3C3×#52511yescharacteristic
725C2×C3C3×#57611yescharacteristic
726C2×C3C3×#57711yescharacteristic
727D3—41no—
728D3—42no—
729D3—81no—
730D3—81no—
731C22—61no—
732C22—61no—
733C22—62no—
734C22—61no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22C2×C3×D3×D411yescharacteristic
744C4—21no—
745C4—21no—
746C4—22no—
747C4—41no—
748C4—41no—
749C4—41no—
750C4—61no—
751C4—61no—
752C4—61no—
753C4—121no—
754C4C2×C3×#23911yescharacteristic
755C4C3×D3×#4111yescharacteristic
756C3—21no—
757C3#8120811yescharacteristic, direct product factor
758C3C3×#311911yescharacteristic, complemented
759C2—121no—
760C2—122no—
761C2—241no—
762C2—241no—
763C2C3×#562711yescharacteristic
764C2C3×#576911yescharacteristic
765C2C3×#577811yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#479C2
socleC22×C32C22×D4
hypercenterC3×#479D3
hypocenterC3C3×#3119
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×#5697C2semidirect
2. C3×#5574C2semidirect
3. C32×#479C2semidirect
4. C3×#5066C2semidirect
5. C3×#5027C2semidirect
6. C3×#4882C2semidirect
7. C3×#4872C2semidirect
8. C3×#4869C2semidirect
9. C3×#4863C2semidirect
10. C3×#4843C2semidirect
11. C3×#4840C2semidirect
12. C3×#4817C2semidirect
13. C3×#4810C2semidirect
14. C3×#4810C2semidirect
15. C3×#4788C2semidirect
17. #81208C3direct (N × H)
63. #5697C2×C3semidirect
64. #5574C2×C3semidirect
68. C3×#479D3semidirect
69. C3×#479C2×C3semidirect
80. #5066C2×C3semidirect
81. #5027C2×C3semidirect
82. #4882C2×C3semidirect
83. #4872C2×C3semidirect
84. #4869C2×C3semidirect
85. #4863C2×C3semidirect
86. #4843C2×C3semidirect
87. #4840C2×C3semidirect
88. #4817C2×C3semidirect
89. #4810C2×C3semidirect
90. #4810C2×C3semidirect
91. #4788C2×C3semidirect
279. #479C3×D3semidirect
673. C32#3119semidirect
757. C3#81208direct (N × H)
758. 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×#55742
C32×#4792
C3×#50662
C3×#50272
C3×#48822
C3×#48722
C3×#48692
C3×#48632
C3×#48432
C3×#48402
C3×#48172
C3×#48102
C3×#47882
C3×#31193
#812083