Finite Group Databasebeta

← #13177317

Subgroups — #13177317

Order 1728.

2316 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic, complemented
2C2×C3⋊D3×#67C211yesmaximal, characteristic, complemented
3#11723970C211yesmaximal, characteristic, complemented
4C2×C3×#3752C211yesmaximal, characteristic, complemented
5#11723635C211yesmaximal, characteristic, complemented
6#11723634C211yesmaximal, characteristic, complemented
7#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
8#11723540C211yesmaximal, characteristic, complemented
9D3×#3752C211yesmaximal, characteristic, complemented
10#11723514C211yesmaximal, characteristic, complemented
11#11723513C211yesmaximal, characteristic, complemented
12#11723506C211yesmaximal, characteristic, complemented
13#11723476C211yesmaximal, characteristic, complemented
14#11723474C211yesmaximal, characteristic, complemented
15#11723392C211yesmaximal, characteristic, complemented
16#10596300—31nomaximal
17#10595065—34nomaximal
18C23×C3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C2×#6312C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C32×#235—24no—
26C2×C32×D12C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28C2×C32×C4×D3C2211yescharacteristic, complemented
29C2×C32×Dic6C2211yescharacteristic, complemented
30C3⋊D3×#67—24no—
31C2×#6292C2211yescharacteristic
32C2×#6291C2211yescharacteristic, complemented
33C2×#6290C2211yescharacteristic
34C2×#6290C2211yescharacteristic
35C2×#6290C2211yescharacteristic, complemented
36C2×Dic3×C3⋊D3C2211yescharacteristic
37C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
38#88864C2211yescharacteristic, complemented
39#88859C2211yescharacteristic, complemented
40#88859C2211yescharacteristic, complemented
41#88857C2211yescharacteristic, complemented
42#88857C2211yescharacteristic, complemented
43C3×#3752C2211yescharacteristic
44C3×#3752C2211yescharacteristic
45C3×#3752C2211yescharacteristic, complemented
46C3×#3752C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88804C2211yescharacteristic, complemented
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55C2×C32×#41—31no—
56C2×D4×C3⋊D3—31no—
57C2×C3×#235D314yescomplemented
58C2×D3×#67—34no—
59#64156—31no—
60#64155—31no—
61#64148—31no—
62#64148—31no—
63#64146—31no—
64#64146—31no—
65D4×C3⋊Dic3—31no—
66#64139—31no—
67#64138—31no—
68#64138—31no—
69#64138—34no—
70#64138—64no—
71C4×#638—31no—
72C2×#3752—31no—
73C2×#3752D311yescharacteristic, complemented
74C2×C3×(C2×D3)⋊C4—34no—
75#63978—34no—
76#63976—34no—
77Dic3×#67—34no—
78#63922—34no—
79D3×(C2×D3)⋊C4—34no—
80#63907—34no—
81#63906—34no—
82#63905—34no—
83#63887—34no—
84#63885—34no—
85#63879—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)C2311yescharacteristic
88C22×C3×C3⋊D3—22no—
89C22×C3×C3⋊D3—22no—
90C22×C3×C3⋊D3—41no—
91C22×C3×C3⋊D3C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3—41no—
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101#6312—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
105C2×C3×C3⋊Dic3—41no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C32×#67—22no—
109C32×#67D414yescomplemented
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×D12—22no—
113C32×C4×D3—22no—
114C32×C4×D3—22no—
115C32×Dic6—22no—
116#6292—22no—
117#6291—41no—
118#6290—22no—
119#6290—22no—
120#6290—41no—
121Dic3×C3⋊D3—22no—
122D3×C3⋊Dic3—41no—
123#5829—94no—
124#5490—91no—
125C23×C3⋊D3—31no—
126C23×C3⋊D3C2×D311yescharacteristic
127C23×C3×D3—34no—
128C22×D32—34no—
129C32×#41—64no—
130C2×C32×Q8—31no—
131C2×C32×D4—31no—
132C2×C32×D4—31no—
133C2×C32×D4—31no—
134C22×C32×C4—24no—
135C22×C32×C4—31no—
136C22×C32×C4—31no—
137C22×C32×C4C2×D314yescomplemented
138C22×C32×C4C2×D311yescharacteristic, complemented
139C2×#638—31no—
140C2×#638—34no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—64no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3C2×D311yescharacteristic, complemented
148D4×C3⋊D3—64no—
149C2×C4⋊(C3⋊D3)—31no—
150C2×C4×C3⋊D3—31no—
151C2×C3×#67C2×D314yes—
152C2×C3×#67C2×D314yescomplemented
153C22×C3×Dic3—34no—
154C3×#235—216no—
155C2×C3×D12C2×D314yescomplemented
156C2×C3×C4×D3C2×D314yescomplemented
157C2×C3×C4×D3C2×D314yescomplemented
158C2×C3×Dic6C2×D314yescomplemented
159D3×#67—616no—
160C2×#626—34no—
161C2×#626—34no—
162C2×#625—34no—
163C2×#625—34no—
164C2×#625—34no—
165C2×D3×Dic3—34no—
166C2×D3×Dic3—34no—
167#3757—31no—
168#3757—34no—
169#3757—31no—
170#3757—31no—
171#3757—64no—
172#3752—31no—
173#3752—31no—
174#3752—31no—
175#3752—31no—
176#3752—34no—
177#3752—34no—
178#3752—31no—
179#3752—64no—
180#3752—64no—
181#3752C2×D311yescharacteristic
182#3752C2×D311yescharacteristic
183#3752C2×D311yescharacteristic, complemented
184#3752C2×D311yescharacteristic, complemented
185C4⋊(C3⋊Dic3)—31no—
186#3750—31no—
187#3750—31no—
188#3750—34no—
189#3750—34no—
190#3750—31no—
191#3750—64no—
192#3750—64no—
193C4×C3⋊Dic3—31no—
194C3×(C2×D3)⋊C4—34no—
195C3×(C2×D3)⋊C4—34no—
196C3×(C2×D3)⋊C4—34no—
197C3×(C2×D3)⋊C4—34no—
198Dic3⋊Dic3—34no—
199Dic3⋊Dic3—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203(C2×D3)⋊Dic3—34no—
204(C2×D3)⋊Dic3—34no—
205Dic32—34no—
206C22×C33—21no—
207C22×C33—21no—
208C22×C33C2×D412yes—
209C22×C33C2411yescharacteristic
210C2×C3⋊(C3⋊D3)—21no—
211C2×C3⋊(C3⋊D3)—21no—
212C2×C3⋊(C3⋊D3)—21no—
213C2×C3×C3⋊D3—21no—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3—21no—
217C2×C3×C3⋊D3—21no—
218C2×C3×C3⋊D3—44no—
219C2×C3×C3⋊D3#4112yescomplemented
220C2×C32×D3—21no—
221C2×C32×D3—21no—
222C2×C32×D3—21no—
223C2×C32×D3—21no—
224C2×C32×D3—21no—
225C2×C32×D3C2×D412yes—
226D3×C3⋊D3—44no—
227C33×C4—21no—
228C33×C4—21no—
229C3⋊(C3⋊Dic3)—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3—21no—
234C32×Dic3—21no—
235C32×Dic3C2×D412yes—
236C2×C3×#41—34no—
237C22×#67—91no—
238C2×D3×D4—94no—
239C2×#235C3⋊D311yescharacteristic, complemented
240C2×C3×C22⋊C4—91no—
241#953—91no—
242#947—94no—
243#946—94no—
244#939—94no—
245#939—94no—
246#937—94no—
247#937—94no—
248D4×Dic3—94no—
249#930—94no—
250#930—91no—
251#929—94no—
252#929—94no—
253#929—91no—
254#929—184no—
255C4×#67—94no—
256C4×#67—91no—
257C2×(C2×D3)⋊C4—34no—
258C2×(C2×D3)⋊C4—94no—
259#885—91no—
260#884—91no—
261#884—91no—
262#883—91no—
263#882—91no—
264#67⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32—24no—
268C23×C32—31no—
269C23×C32—31no—
270C23×C32C22×D314yes—
271C23×C32C22×D311yescharacteristic
272C22×C3⋊D3—22no—
273C22×C3⋊D3—22no—
274C22×C3⋊D3—31no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—41no—
277C22×C3⋊D3—64no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—62no—
280C22×C3⋊D3—121no—
281C22×C3⋊D3C22×D311yescharacteristic
282C22×C3⋊D3C22×D311yescharacteristic
283C22×C3×D3—34no—
284C22×C3×D3—34no—
285C22×C3×D3—68no—
286C22×C3×D3—68no—
287C22×C3×D3—124no—
288C22×C3×D3C22×D314yes—
289C22×C3×D3C22×D314yes—
290C2×D32—68no—
291C2×D32—68no—
292C2×D32—124no—
293C32×Q8—62no—
294C32×D4—34no—
295C32×D4—62no—
296C32×D4—62no—
297C2×C32×C4—22no—
298C2×C32×C4—24no—
299C2×C32×C4—24no—
300C2×C32×C4—28no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—48no—
304C2×C32×C4—62no—
305C2×C32×C4—62no—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D314yes—
308C2×C32×C4C22×D311yescharacteristic
309C2×C32×C4C22×D311yescharacteristic
310#638—62no—
311#638—62no—
312#638—62no—
313#638—68no—
314#638—128no—
315#638—121no—
316#638—121no—
317C2×C3⋊Dic3—31no—
318C2×C3⋊Dic3—31no—
319C2×C3⋊Dic3—31no—
320C2×C3⋊Dic3—34no—
321C2×C3⋊Dic3—34no—
322C2×C3⋊Dic3—34no—
323C2×C3⋊Dic3—41no—
324C2×C3⋊Dic3—64no—
325C2×C3⋊Dic3—64no—
326C2×C3⋊Dic3—64no—
327C2×C3⋊Dic3—121no—
328C2×C3⋊Dic3C22×D311yescharacteristic
329C2×C3⋊Dic3C22×D311yescharacteristic
330C4⋊(C3⋊D3)—62no—
331C4×C3⋊D3—62no—
332C3×#67—28no—
333C3×#67#67116yescomplemented
334C2×C3×Dic3—34no—
335C2×C3×Dic3—34no—
336C2×C3×Dic3—124no—
337C2×C3×Dic3C22×D314yes—
338C2×C3×Dic3C22×D314yes—
339C3×D12—28no—
340C3×C4×D3—28no—
341C3×C4×D3—28no—
342C3×Dic6—28no—
343#626—68no—
344#626—124no—
345#625—68no—
346#625—68no—
347#625—124no—
348D3×Dic3—68no—
349D3×Dic3—124no—
350#546—271noSylow
351C2×C33—22no—
352C2×C33C22×D411yescharacteristic
353C2×C33C2×#4111yescharacteristic
354C2×C33H(5,𝔽2)11yescharacteristic
355C3⋊(C3⋊D3)—41no—
356C3×C3⋊D3—22no—
357C3×C3⋊D3—41no—
358C32×D3—22no—
359C32×D3—41no—
360C24×C3—91no—
361C23×D3—34no—
362C23×D3—94no—
363C23×D3—91no—
364C3×#41—616no—
365C2×C3×Q8—34no—
366C2×C3×D4—34no—
367C2×C3×D4—34no—
368C2×C3×D4—34no—
369C22×C3×C4—24no—
370C22×C3×C4—34no—
371C22×C3×C4—34no—
372C22×C3×C4—91no—
373C22×C3×C4D3214yescomplemented
374C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
375C2×#67—94no—
376C2×#67—94no—
377C2×#67—94no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—94no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—184no—
386C2×#67—184no—
387C2×#67C2×C3⋊D311yescharacteristic
388C2×#67C2×C3⋊D311yescharacteristic, complemented
389C22×Dic3—34no—
390C22×Dic3—94no—
391C22×Dic3—91no—
392D3×D4—1816no—
393#235—24no—
394C2×D12—94no—
395C2×D12—91no—
396C2×D12C2×C3⋊D311yescharacteristic, complemented
397C2×C4×D3—94no—
398C2×C4×D3—91no—
399C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
400C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
401C2×Dic6C2×C3⋊D311yescharacteristic, complemented
402C3×C22⋊C4—91no—
403C3×C22⋊C4—91no—
404C3×C22⋊C4—91no—
405C3×C22⋊C4—91no—
406#217—94no—
407#217—94no—
408#217—94no—
409#217—91no—
410#217—91no—
411#217—91no—
412#217—184no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—34no—
417(C2×D3)⋊C4—94no—
418(C2×D3)⋊C4—94no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—91no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—94no—
423(C2×D3)⋊C4—94no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—184no—
428(C2×D3)⋊C4—184no—
429C4⋊Dic3—94no—
430C4⋊Dic3—91no—
431Dic3⋊C4—94no—
432Dic3⋊C4—94no—
433Dic3⋊C4—94no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—184no—
438Dic3⋊C4—184no—
439C4×Dic3—94no—
440C4×Dic3—91no—
441C22×C32—21no—
442C22×C32—21no—
443C22×C32—24no—
444C22×C32—28no—
445C22×C32—24no—
446C22×C32—24no—
447C22×C32—32no—
448C22×C32—44no—
449C22×C32—44no—
450C22×C32—61no—
451C22×C32—61no—
452C22×C32—61no—
453C22×C32—61no—
454C22×C32—61no—
455C22×C32D3×D412yes—
456C22×C32C2×#6718yes—
457C22×C32C23×D314yes—
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—21no—
460C2×C3⋊D3—21no—
461C2×C3⋊D3—21no—
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—44no—
465C2×C3⋊D3—61no—
466C2×C3⋊D3—61no—
467C2×C3⋊D3—61no—
468C2×C3⋊D3—64no—
469C2×C3⋊D3—64no—
470C2×C3⋊D3—64no—
471C2×C3⋊D3—124no—
472C2×C3⋊D3—124no—
473C2×C3⋊D3—124no—
474C2×C3⋊D3—124no—
475C2×C3⋊D3#23512yescomplemented
476C2×C3×D3—24no—
477C2×C3×D3—24no—
478C2×C3×D3—24no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—38no—
482C2×C3×D3—64no—
483C2×C3×D3—64no—
484C2×C3×D3—64no—
485C2×C3×D3—64no—
486C2×C3×D3—64no—
487C2×C3×D3—1216no—
488C2×C3×D3C2×#6718yes—
489D32—1216no—
490C32×C4—21no—
491C32×C4—21no—
492C32×C4—24no—
493C32×C4—24no—
494C32×C4—32no—
495C32×C4—44no—
496C32×C4—44no—
497C32×C4—61no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—61no—
501C3⋊Dic3—61no—
502C3⋊Dic3—61no—
503C3⋊Dic3—64no—
504C3⋊Dic3—64no—
505C3⋊Dic3—64no—
506C3⋊Dic3—124no—
507C3⋊Dic3—124no—
508C3⋊Dic3—124no—
509C3×Dic3—24no—
510C3×Dic3—64no—
511C3×Dic3—64no—
512C3×Dic3C2×#6718yes—
513C2×#41—31no—
514C22×D4—271no—
515#124—271no—
516#123—271no—
517#123—271no—
518C22⋊Q8—271no—
519#121—271no—
520#121—271no—
521#121—271no—
522#120—271no—
523#120—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C22⋊C4—91no—
527C2×C22⋊C4—271no—
528C33#54611yescharacteristic, complemented, Sylow
529C23×C3—24no—
530C23×C3—34no—
531C23×C3—34no—
532C23×C3—91no—
533C23×C3—91no—
534C23×C3—182no—
535C23×C3—182no—
536C23×C3—361no—
537C23×C3C2×D3214yes—
538C23×C3C22×C3⋊D311yescharacteristic
539C22×D3—34no—
540C22×D3—34no—
541C22×D3—68no—
542C22×D3—68no—
543C22×D3—94no—
544C22×D3—91no—
545C22×D3—124no—
546C22×D3—184no—
547C22×D3—182no—
548C22×D3—188no—
549C22×D3—188no—
550C22×D3—182no—
551C22×D3—361no—
552C22×D3—364no—
553C22×D3C22×C3⋊D311yescharacteristic
554C22×D3C22×C3⋊D311yescharacteristic
555C3×Q8—68no—
556C3×D4—316no—
557C3×D4—68no—
558C3×D4—68no—
559C2×C3×C4—28no—
560C2×C3×C4—22no—
561C2×C3×C4—24no—
562C2×C3×C4—24no—
563C2×C3×C4—34no—
564C2×C3×C4—34no—
565C2×C3×C4—48no—
566C2×C3×C4—68no—
567C2×C3×C4—68no—
568C2×C3×C4—91no—
569C2×C3×C4—91no—
570C2×C3×C4—361no—
571C2×C3×C4C2×D3214yes—
572C2×C3×C4C2×D3214yes—
573C2×C3×C4C22×C3⋊D311yescharacteristic
574C2×C3×C4C22×C3⋊D311yescharacteristic
575#67—22no—
576#67—182no—
577#67—188no—
578#67—188no—
579#67—188no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—368no—
584#67—364no—
585#67—361no—
586#67—364no—
587#67#63814yescomplemented
588C2×Dic3—34no—
589C2×Dic3—34no—
590C2×Dic3—94no—
591C2×Dic3—94no—
592C2×Dic3—94no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—124no—
597C2×Dic3—184no—
598C2×Dic3—184no—
599C2×Dic3—184no—
600C2×Dic3—182no—
601C2×Dic3—364no—
602C2×Dic3C22×C3⋊D311yescharacteristic
603C2×Dic3C22×C3⋊D311yescharacteristic
604D12—22no—
605D12—188no—
606D12—361no—
607C4×D3—22no—
608C4×D3—22no—
609C4×D3—188no—
610C4×D3—361no—
611Dic6—22no—
612C2×C32—22no—
613C2×C32—24no—
614C2×C32—24no—
615C2×C32—24no—
616C2×C32—28no—
617C2×C32—48no—
618C2×C32—62no—
619C2×C32—121no—
620C2×C32C2×#23511yescharacteristic
621C2×C32C2×D3×D411yescharacteristic
622C2×C32#100411yescharacteristic
623C2×C32D3×#4114yes—
624C2×C32#100914yes—
625C2×C32C22×#6714yes—
626C3⋊D3—22no—
627C3⋊D3—41no—
628C3⋊D3—121no—
629C3⋊D3—124no—
630C3⋊D3—244no—
631C3×D3—28no—
632C3×D3—44no—
633C3×D3—68no—
634C3×D3—124no—
635C24—91no—
636C24—271no—
637#41—64no—
638C2×Q8—31no—
639C2×D4—31no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—271no—
643C2×D4—271no—
644C2×D4—271no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—544no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4D3×C3⋊D311yescharacteristic, complemented
655C4⋊C4—271no—
656C4⋊C4—271no—
657C4⋊C4—271no—
658C4⋊C4—271no—
659C22⋊C4—91no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—91no—
663C22⋊C4—271no—
664C22⋊C4—271no—
665C22⋊C4—271no—
666C22⋊C4—271no—
667C22⋊C4—271no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C42—271no—
672C22×C3—24no—
673C22×C3—24no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—28no—
678C22×C3—38no—
679C22×C3—44no—
680C22×C3—44no—
681C22×C3—64no—
682C22×C3—64no—
683C22×C3—64no—
684C22×C3—64no—
685C22×C3—64no—
686C22×C3—92no—
687C22×C3—181no—
688C22×C3—181no—
689C22×C3—181no—
690C22×C3—181no—
691C22×C3—181no—
692C22×C3—364no—
693C22×C3D3×#6718yes—
694C22×C3C2×#63812yes—
695C22×C3C22×D3214yes—
696C22×C3C23×C3⋊D311yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—38no—
703C2×D3—64no—
704C2×D3—64no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—64no—
708C2×D3—1216no—
709C2×D3—184no—
710C2×D3—184no—
711C2×D3—184no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—364no—
716C2×D3—364no—
717C2×D3—364no—
718C2×D3—364no—
719C2×D3—3616no—
720C2×D3C2×#63812yes—
721C3×C4—24no—
722C3×C4—24no—
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—38no—
726C3×C4—44no—
727C3×C4—44no—
728C3×C4—64no—
729C3×C4—181no—
730C3×C4—181no—
731Dic3—21no—
732Dic3—64no—
733Dic3—64no—
734Dic3—184no—
735Dic3—184no—
736Dic3—184no—
737Dic3—181no—
738Dic3—181no—
739Dic3—181no—
740Dic3—364no—
741Dic3—364no—
742Dic3—364no—
743Dic3C2×#63812yes—
744C32—24no—
745C32#549011yescharacteristic, complemented
746C32#582914yescomplemented
747C23—31no—
748C23—31no—
749C23—91no—
750C23—91no—
751C23—182no—
752C23—182no—
753C23—271no—
754C23—361no—
755C23—542no—
756C23—542no—
757C23—1081no—
758C23C2×D3×C3⋊D311yescharacteristic
759Q8—62no—
760D4—34no—
761D4—62no—
762D4—62no—
763D4—542no—
764D4—542no—
765D4—542no—
766D4—542no—
767D4—1081no—
768D4—1081no—
769C2×C4—22no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—62no—
773C2×C4—62no—
774C2×C4—91no—
775C2×C4—91no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—361no—
780C2×C4—542no—
781C2×C4—1081no—
782C2×C4C2×D3×C3⋊D311yescharacteristic
783C2×C4C2×D3×C3⋊D311yescharacteristic
784C2×C3—22no—
785C2×C3—28no—
786C2×C3—24no—
787C2×C3—24no—
788C2×C3—24no—
789C2×C3—48no—
790C2×C3—68no—
791C2×C3—124no—
792C2×C3—182no—
793C2×C3—361no—
794C2×C3D3×#23514yes—
795C2×C3#6430714yes—
796C2×C3C2×D3×#6714yes—
797C2×C3#41×C3⋊D311yescharacteristic
798C2×C3#6436611yescharacteristic
799C2×C3C22×#63811yescharacteristic
800D3—22no—
801D3—41no—
802D3—68no—
803D3—124no—
804D3—361no—
805D3—364no—
806D3—724no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—92no—
816C22—181no—
817C22—181no—
818C22—181no—
819C22—181no—
820C22—181no—
821C22—364no—
822C22—541no—
823C22—541no—
824C22—541no—
825C22—1084no—
826C22D3×#63812yes—
827C22C22×D3×C3⋊D311yescharacteristic
828C4—21no—
829C4—21no—
830C4—32no—
831C4—61no—
832C4—181no—
833C4—181no—
834C4—541no—
835C4—541no—
836C4—541no—
837C3—24no—
838C3#1059506514yescomplemented
839C3#1059630011yescharacteristic, complemented
840C2—22no—
841C2—62no—
842C2—121no—
843C2—182no—
844C2—361no—
845C2—1081no—
846C2C3⋊D3×#23511yescharacteristic
847C2#1172458011yescharacteristic
848C2C2×D3×#63811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC22×C33×C4C22
hypercenterC22×C4D3×C3⋊D3
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#235C2semidirect
2. C2×C3⋊D3×#67C2semidirect
3. #11723970C2semidirect
4. C2×C3×#3752C2semidirect
5. #11723635C2semidirect
6. #11723634C2semidirect
7. #67×C3⋊Dic3C2semidirect
8. #11723540C2semidirect
9. D3×#3752C2semidirect
10. #11723514C2semidirect
11. #11723513C2semidirect
12. #11723506C2semidirect
13. #11723476C2semidirect
14. #11723474C2semidirect
15. #11723392C2semidirect
20. C22×C33×C4C22semidirect
22. C22×C3×C3⋊Dic3C22semidirect
24. C2×C32×#67C22semidirect
26. C2×C32×D12C22semidirect
27. C2×C32×C4×D3C22semidirect
28. C2×C32×C4×D3C22semidirect
29. C2×C32×Dic6C22semidirect
32. C2×#6291C22semidirect
35. C2×#6290C22semidirect
37. C2×D3×C3⋊Dic3C22semidirect
38. #88864C22semidirect
39. #88859C22semidirect
40. #88859C22semidirect
41. #88857C22semidirect
42. #88857C22semidirect
45. C3×#3752C22semidirect
46. C3×#3752C22semidirect
47. #88807C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88804C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
57. C2×C3×#235D3semidirect
73. C2×#3752D3semidirect
109. C32×#67D4semidirect
137. C22×C32×C4C2×D3semidirect
138. C22×C32×C4C2×D3semidirect
147. C22×C3⋊Dic3C2×D3semidirect
152. C2×C3×#67C2×D3semidirect
155. C2×C3×D12C2×D3semidirect
156. C2×C3×C4×D3C2×D3semidirect
157. C2×C3×C4×D3C2×D3semidirect
158. C2×C3×Dic6C2×D3semidirect
183. #3752C2×D3semidirect
184. #3752C2×D3semidirect
219. C2×C3×C3⋊D3#41semidirect
239. C2×#235C3⋊D3semidirect
333. C3×#67#67semidirect
373. C22×C3×C4D32semidirect
374. C22×C3×C4C2×C3⋊D3semidirect
388. C2×#67C2×C3⋊D3semidirect
396. C2×D12C2×C3⋊D3semidirect
399. C2×C4×D3C2×C3⋊D3semidirect
400. C2×C4×D3C2×C3⋊D3semidirect
401. C2×Dic6C2×C3⋊D3semidirect
475. C2×C3⋊D3#235semidirect
528. C33#546semidirect
587. #67#638semidirect
654. C22×C4D3×C3⋊D3semidirect
745. C32#5490semidirect
746. C32#5829semidirect
838. C3#10595065semidirect
839. C3#10596300semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C2×C3⋊D3×#672
#117239702
C2×C3×#37522
#117236352
#117236342
#67×C3⋊Dic32
#117235402
D3×#37522
#117235142
#117235132
#117235062
#117234762
#117234742
#117233922
#105963003
#105950653