Finite Group Databasebeta

← #13149371

Subgroups — #13149371

Order 1728.

824 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721752C211yesmaximal, characteristic, complemented
2C9×#898C211yesmaximal, characteristic, complemented
3C3×#63457C211yesmaximal, characteristic, complemented
4#11721049C211yesmaximal, characteristic, complemented
5#11721049C211yesmaximal, characteristic, complemented
6#11721048C211yesmaximal, characteristic, complemented
7#11721042C211yesmaximal, characteristic, complemented
8#11721031C211yesmaximal, characteristic, complemented
9#11721007C211yesmaximal, characteristic, complemented
10#11721002C211yesmaximal, characteristic, complemented
11#11720982C211yesmaximal, characteristic, complemented
12#11720981C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14#11720948C211yesmaximal, characteristic, complemented
15#11720946C211yesmaximal, characteristic, complemented
16#10594660—31nomaximal
17#10589806—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C3×D36C2211yescharacteristic
22C2×C3×D36C2211yescharacteristic
23C2×C3×D36C2211yescharacteristic, complemented
24C2×C3×C4×D9C2211yescharacteristic, complemented
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6192C2211yescharacteristic
28C2×#6192C2211yescharacteristic
29C2×(C3⋊D9)⋊C4C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C9×C4⋊C4C2211yescharacteristic, complemented
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34#88534C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36C9×(C2×D3)⋊C4C2211yescharacteristic
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
41C9×C4⋊Dic3C2211yescharacteristic, complemented
42C9×Dic3⋊C4C2211yescharacteristic, complemented
43C4×C9×Dic3C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47(C2×D9)⋊Dic3C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51Dic3⋊Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64105—31no—
54C3×#898D311yescharacteristic
55C3×#895—31no—
56#63922—31no—
57#63922—31no—
58#63921—31no—
59#63916—31no—
60#63913—31no—
61#63905—31no—
62#63904—31no—
63#63885—31no—
64#63884—31no—
65#63880—31no—
66#63860—31no—
67#63858—31no—
68C9×#126—31no—
69#63460—31no—
70#63458—31no—
71#63458—61no—
72#63457—31no—
73#63457D311yescharacteristic, complemented
74#63456—31no—
75#63455—31no—
76#63447—31no—
77#63446—31no—
78#63445—31no—
79#63444—31no—
80#63444—31no—
81C22⋊C4×D9—31no—
82#63437—31no—
83C4×D36—31no—
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×C3×C4×C9C2311yescharacteristic
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C4×C3⋊D9—41no—
99#6226—41no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C3×D36—41no—
105C3×D36—41no—
106C3×D36—41no—
107C3×C4×D9—41no—
108#6194—41no—
109#6194—41no—
110#6192—22no—
111#6192—22no—
112(C3⋊D9)⋊C4—41no—
113Dic3×D9—41no—
114#5704—91no—
115#5613—91no—
116C22×D32—31no—
117C2×C4×C3⋊D3—31no—
118C2×#634—31no—
119C2×C3×D12—31no—
120C2×C3×D12—31no—
121C2×C3×D12—31no—
122C2×C3×C4×D3—31no—
123C2×#626—31no—
124C2×#626—31no—
125C2×#625—31no—
126C2×#625—31no—
127C2×#624—31no—
128C2×D3×Dic3—31no—
129C23×D9—31no—
130C32×C4⋊C4C2×D311yescharacteristic
131#3752—31no—
132#3752—31no—
133#3750—31no—
134#3750—31no—
135C3×(C2×D3)⋊C4—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×(C2×D3)⋊C4C2×D311yescharacteristic
140C3×C4⋊Dic3C2×D311yescharacteristic
141C3×Dic3⋊C4C2×D311yescharacteristic
142C3×C4×Dic3C2×D311yescharacteristic
143Dic3⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×D36—31no—
155C2×D36—31no—
156C2×D36C2×D311yescharacteristic
157C2×D36C2×D311yescharacteristic
158C2×D36C2×D311yescharacteristic, complemented
159C2×C4×D9—31no—
160C2×C4×D9—31no—
161C2×C4×D9—31no—
162C2×C4×D9—61no—
163C2×C4×D9C2×D311yescharacteristic, complemented
164C2×Dic18—31no—
165C2×Dic18—61no—
166C9×C4⋊C4—21no—
167C9×C4⋊C4—31no—
168C9×C4⋊C4—31no—
169C9×C4⋊C4C2×D311yescharacteristic, complemented
170C9×C22⋊C4—31no—
171C9×C22⋊C4—31no—
172C9×C22⋊C4—31no—
173C42×C9—31no—
174#3676—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179(C2×D9)⋊C4—31no—
180(C2×D9)⋊C4—31no—
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—61no—
184(C2×D9)⋊C4—61no—
185(C2×D9)⋊C4C2×D311yescharacteristic
186(C2×D9)⋊C4C2×D311yescharacteristic, complemented
187C4⋊Dic9—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—61no—
191Dic9⋊C4—61no—
192C4×Dic9—31no—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9#4112yes—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C2×C3×D9—21no—
205C2×C3×D9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209D3×D9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3×C4×C9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C3⋊Dic9—21no—
216C9×Dic3—21no—
217C9×Dic3—21no—
218C9×Dic3—21no—
219C3×Dic9—21no—
220C3×#126—31no—
221C3×#121—91no—
222#939—91no—
223#938—91no—
224#937—91no—
225#937—91no—
226#936—91no—
227#935—91no—
228#929—91no—
229C4×#67—91no—
230#898—91no—
231#898D911yescharacteristic, complemented
232#896—91no—
233#896—91no—
234#896—181no—
235#895—31no—
236#895—91no—
237#894—91no—
238#893—91no—
239#885—91no—
240#885—91no—
241#884—91no—
242#883—91no—
243#882—91no—
244#882—91no—
245#67⋊C4—91no—
246D3×C22⋊C4—91no—
247D3×C22⋊C4—91no—
248#879—91no—
249#875—91no—
250C4×D12—91no—
251C22×C3⋊D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—31no—
255C22×C3×D3C22×D311yescharacteristic
256C2×D32—62no—
257C2×D32—121no—
258C2×D32—121no—
259C2×C32×C4C22×D311yescharacteristic
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C4×C3⋊D3—121no—
266#634—121no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271C3×D12—121no—
272C3×D12—121no—
273C3×D12—121no—
274C3×C4×D3—121no—
275#626—62no—
276#626—62no—
277#625—121no—
278#625—121no—
279#624—121no—
280D3×Dic3—121no—
281C23×C9—31no—
282C22×D9—31no—
283C22×D9—61no—
284C22×D9—62no—
285C22×D9—121no—
286C22×D9—121no—
287C22×D9C22×D311yescharacteristic
288C22×D9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290C2×C4×C9—21no—
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—31no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9C22×D311yescharacteristic
297C2×C4×C9C22×D311yescharacteristic
298C2×C4×C9C22×D311yescharacteristic
299#611—121no—
300#611—121no—
301C2×Dic9—31no—
302C2×Dic9—31no—
303C2×Dic9—31no—
304C2×Dic9—61no—
305C2×Dic9—61no—
306C2×Dic9—61no—
307C2×Dic9C22×D311yescharacteristic
308D36—41no—
309D36—41no—
310D36—41no—
311D36—62no—
312D36—62no—
313C4×D9—41no—
314C4×D9—121no—
315C4×D9—121no—
316C4×D9—122no—
317C4×D9—121no—
318Dic18—121no—
319Dic18—122no—
320#538—271noSylow
321C2×C3×C9C2×#4111yescharacteristic
322C2×C3×C9H(5,𝔽2)11yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C3⋊D9—22no—
325D3×C9—41no—
326C3×D9—41no—
327C3×D9—41no—
328C3×D9—41no—
329C23×D3—91no—
330C23×D3—91no—
331C2×C3×D4—91no—
332C2×C3×D4—91no—
333C2×C3×D4—91no—
334C22×C3×C4—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C22×Dic3—91no—
342C2×D12—31no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—91no—
346C2×D12—91no—
347C2×C4×D3—31no—
348C2×C4×D3—91no—
349C2×C4×D3—91no—
350C2×C4×D3—91no—
351C2×C4×D3—91no—
352C2×C4×D3—91no—
353C2×C4×D3—181no—
354C2×Dic6—91no—
355C2×Dic6—91no—
356C2×Dic6—181no—
357C3×C4⋊C4—21no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4C2×D911yescharacteristic, complemented
361C3×C4⋊C4D3211yescharacteristic
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—91no—
366C3×C22⋊C4—91no—
367C3×C42—31no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—91no—
373#217—91no—
374#217—91no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—91no—
378(C2×D3)⋊C4—91no—
379(C2×D3)⋊C4—91no—
380(C2×D3)⋊C4—91no—
381(C2×D3)⋊C4—91no—
382(C2×D3)⋊C4—91no—
383(C2×D3)⋊C4—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—91no—
388(C2×D3)⋊C4—181no—
389(C2×D3)⋊C4—181no—
390(C2×D3)⋊C4C2×D911yescharacteristic
391(C2×D3)⋊C4C2×D911yescharacteristic
392(C2×D3)⋊C4C2×D911yescharacteristic
393C4⋊Dic3—91no—
394C4⋊Dic3C2×D911yescharacteristic, complemented
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—181no—
401Dic3⋊C4—181no—
402Dic3⋊C4C2×D911yescharacteristic, complemented
403C4×Dic3—91no—
404C4×Dic3—91no—
405C4×Dic3C2×D911yescharacteristic, complemented
406C22×C32C23×D311yescharacteristic
407C2×C3⋊D3—32no—
408C2×C3⋊D3—61no—
409C2×C3⋊D3—61no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—61no—
414C2×C3×D3—61no—
415C2×C3×D3—61no—
416C2×C3×D3—61no—
417C2×C3×D3—61no—
418C2×C3×D3—61no—
419C2×C3×D3—61no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422D32—124no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—21no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—61no—
433C22×C9—21no—
434C22×C9—61no—
435C22×C9—61no—
436C22×C9—61no—
437C22×C9C23×D311yescharacteristic
438C2×D9—21no—
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C2×D9—32no—
448C2×D9—62no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—121no—
452C2×D9—121no—
453C2×D9—124no—
454C4×C9—21no—
455C4×C9—21no—
456C4×C9—21no—
457C4×C9—41no—
458C4×C9—41no—
459C4×C9—41no—
460C4×C9—61no—
461C4×C9—61no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—62no—
465Dic9—61no—
466Dic9—61no—
467Dic9—61no—
468Dic9—121no—
469Dic9—121no—
470#126—31no—
471#126—271no—
472#124—271no—
473#124—271no—
474#123—271no—
475#123—271no—
476C22⋊Q8—271no—
477#121—91no—
478#121—271no—
479#121—271no—
480#120—271no—
481#120—271no—
482C4×D4—271no—
483C4×D4—271no—
484C2×C22⋊C4—271no—
485C3×C9#53811yescharacteristic, complemented, Sylow
486C23×C3—31no—
487C23×C3—91no—
488C23×C3—91no—
489C23×C3—91no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—91no—
494C22×D3—91no—
495C22×D3—181no—
496C22×D3—182no—
497C22×D3—182no—
498C22×D3—361no—
499C22×D3—361no—
500C22×D3—361no—
501C22×D3—361no—
502C22×D3C22×D911yescharacteristic
503C3×D4—361no—
504C3×D4—361no—
505C3×D4—361no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—91no—
513C2×C3×C4—361no—
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C22×D911yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519C2×C3×C4C2×D3211yescharacteristic
520#67—182no—
521#67—182no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526C2×Dic3—31no—
527C2×Dic3—91no—
528C2×Dic3—91no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—181no—
534C2×Dic3—181no—
535C2×Dic3—181no—
536C2×Dic3—361no—
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540D12—121no—
541D12—121no—
542D12—121no—
543D12—182no—
544D12—182no—
545C4×D3—121no—
546C4×D3—361no—
547C4×D3—361no—
548C4×D3—361no—
549C4×D3—361no—
550C4×D3—362no—
551C4×D3—361no—
552Dic6—361no—
553Dic6—361no—
554Dic6—362no—
555C2×C32D3×#4111yescharacteristic
556C2×C32#100911yescharacteristic
557C2×C32#100911yescharacteristic
558C3⋊D3—62no—
559C3×D3—41no—
560C3×D3—121no—
561C3×D3—121no—
562C3×D3—121no—
563C2×C9—21no—
564C2×C9—21no—
565C2×C9—21no—
566C2×C9—121no—
567C2×C9#100411yescharacteristic
568C2×C9#100411yescharacteristic
569C2×C9D3×#4111yescharacteristic
570D9—41no—
571D9—41no—
572D9—41no—
573D9—62no—
574D9—122no—
575C24—271no—
576C2×Q8—271no—
577C2×D4—91no—
578C2×D4—91no—
579C2×D4—91no—
580C2×D4—271no—
581C2×D4—271no—
582C2×D4—271no—
583C2×D4—271no—
584C22×C4—91no—
585C22×C4—271no—
586C22×C4—271no—
587C22×C4—271no—
588C4⋊C4—31no—
589C4⋊C4—31no—
590C4⋊C4—271no—
591C4⋊C4—271no—
592C4⋊C4—271no—
593C4⋊C4D3×D911yescharacteristic, complemented
594C22⋊C4—31no—
595C22⋊C4—31no—
596C22⋊C4—31no—
597C22⋊C4—91no—
598C22⋊C4—91no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C42—31no—
609C42—271no—
610C22×C3—21no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—61no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3—181no—
620C22×C3—181no—
621C22×C3—181no—
622C22×C3—181no—
623C22×C3C23×D911yescharacteristic
624C22×C3C22×D3211yescharacteristic
625C2×D3—21no—
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—92no—
638C2×D3—92no—
639C2×D3—182no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—181no—
644C2×D3—361no—
645C2×D3—361no—
646C2×D3—364no—
647C2×D3—364no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—61no—
660C3×C4—181no—
661Dic3—21no—
662Dic3—21no—
663Dic3—21no—
664Dic3—61no—
665Dic3—182no—
666Dic3—181no—
667Dic3—181no—
668Dic3—181no—
669Dic3—181no—
670Dic3—181no—
671Dic3—181no—
672Dic3—361no—
673Dic3—361no—
674C32#570411yescharacteristic
675C9—21no—
676C9#561311yescharacteristic, complemented
677C23—31no—
678C23—91no—
679C23—91no—
680C23—91no—
681C23—271no—
682C23—542no—
683C23—1081no—
684C23—1081no—
685Q8—1081no—
686D4—361no—
687D4—361no—
688D4—361no—
689D4—542no—
690D4—542no—
691D4—1081no—
692D4—1081no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—91no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—271no—
700C2×C4—361no—
701C2×C4—1081no—
702C2×C4—1081no—
703C2×C4—1081no—
704C2×C4C2×D3×D911yescharacteristic
705C2×C4C2×D3×D911yescharacteristic
706C2×C4C2×D3×D911yescharacteristic
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—21no—
710C2×C3—121no—
711C2×C3—361no—
712C2×C3—361no—
713C2×C3—361no—
714C2×C3#41×D911yescharacteristic
715C2×C3#6371511yescharacteristic
716C2×C3#6371511yescharacteristic
717C2×C3#6430711yescharacteristic
718C2×C3#6431411yescharacteristic
719C2×C3#6431911yescharacteristic
720D3—41no—
721D3—121no—
722D3—121no—
723D3—121no—
724D3—182no—
725D3—182no—
726D3—362no—
727C22—61no—
728C22—61no—
729C22—61no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—181no—
736C22—181no—
737C22—181no—
738C22—181no—
739C22—272no—
740C22—541no—
741C22—541no—
742C22—1084no—
743C22C22×D3×D911yescharacteristic
744C4—21no—
745C4—21no—
746C4—21no—
747C4—61no—
748C4—61no—
749C4—61no—
750C4—181no—
751C4—541no—
752C4—541no—
753C4—541no—
754C3—21no—
755C3#1058980611yescharacteristic, complemented
756C3#1059466011yescharacteristic
757C2—121no—
758C2—361no—
759C2—361no—
760C2—361no—
761C2—542no—
762C2#1172247711yescharacteristic
763C2#1172250111yescharacteristic
764C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721752C2semidirect
2. C9×#898C2semidirect
3. C3×#63457C2semidirect
4. #11721049C2semidirect
5. #11721049C2semidirect
6. #11721048C2semidirect
7. #11721042C2semidirect
8. #11721031C2semidirect
9. #11721007C2semidirect
10. #11721002C2semidirect
11. #11720982C2semidirect
12. #11720981C2semidirect
13. #11720977C2semidirect
14. #11720948C2semidirect
15. #11720946C2semidirect
20. C2×#6226C22semidirect
23. C2×C3×D36C22semidirect
24. C2×C3×C4×D9C22semidirect
30. C2×Dic3×D9C22semidirect
31. C3×C9×C4⋊C4C22semidirect
34. #88534C22semidirect
35. #88534C22semidirect
40. C3×(C2×D9)⋊C4C22semidirect
41. C9×C4⋊Dic3C22semidirect
42. C9×Dic3⋊C4C22semidirect
43. C4×C9×Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. Dic3⋊Dic9C22semidirect
52. Dic3×Dic9C22semidirect
73. #63457D3semidirect
158. C2×D36C2×D3semidirect
163. C2×C4×D9C2×D3semidirect
169. C9×C4⋊C4C2×D3semidirect
186. (C2×D9)⋊C4C2×D3semidirect
231. #898D9semidirect
360. C3×C4⋊C4C2×D9semidirect
394. C4⋊Dic3C2×D9semidirect
402. Dic3⋊C4C2×D9semidirect
405. C4×Dic3C2×D9semidirect
485. C3×C9#538semidirect
593. C4⋊C4D3×D9semidirect
676. C9#5613semidirect
755. C3#10589806semidirect

Maximal subgroups

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

subgroupindex
#117217522
C9×#8982
C3×#634572
#117210492
#117210482
#117210422
#117210312
#117210072
#117210022
#117209822
#117209812
#117209772
#117209482
#117209462
#105946603
#105898063