Finite Group Databasebeta

← #13147729

Subgroups — #13147729

Order 1728.

810 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721713C211yesmaximal, characteristic, complemented
2C4×C9×D12C211yesmaximal, characteristic, complemented
3C3×#63437C211yesmaximal, characteristic, complemented
4#11721050C211yesmaximal, characteristic, complemented
5#11721049C211yesmaximal, characteristic, complemented
6D3×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
7#11721035C211yesmaximal, characteristic, complemented
8#11721034C211yesmaximal, characteristic, complemented
9#11721032C211yesmaximal, characteristic, complemented
10#11721018C211yesmaximal, characteristic, complemented
11#11721016C211yesmaximal, characteristic, complemented
12#11720988C211yesmaximal, characteristic, complemented
13#11720982C211yesmaximal, characteristic, complemented
14#11720976C211yesmaximal, characteristic, complemented
15#11720946C211yesmaximal, characteristic, complemented
16#10594012—31nomaximal
17#10589662—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C9×D12C2211yescharacteristic
20C2×C4×D3×C9C2211yescharacteristic
21C2×C4×D3×C9C2211yescharacteristic, complemented
22C2×C3×D36C2211yescharacteristic
23C2×C3×Dic18C2211yescharacteristic, complemented
24C2×#6195C2211yescharacteristic
25C2×#6194C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic, complemented
28C2×D3×Dic9C2211yescharacteristic
29C2×#6192C2211yescharacteristic
30C2×Dic3×D9C2211yescharacteristic, complemented
31C3×C42×C9C2211yescharacteristic, complemented
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34#88536C2211yescharacteristic
35#88534C2211yescharacteristic, complemented
36#88534C2211yescharacteristic, complemented
37#88534C2211yescharacteristic, complemented
38C9×(C2×D3)⋊C4C2211yescharacteristic
39C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C3×(C2×D9)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic
42C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C9×C4⋊Dic3C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48(C2×D9)⋊Dic3C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64085—31no—
54C3×#875—31no—
55C3×C4×D12D311yescharacteristic
56#63922—31no—
57#63922—31no—
58D3×(C2×D3)⋊C4—31no—
59#63907—31no—
60#63906—31no—
61#63905—31no—
62#63890—31no—
63#63887—31no—
64#63885—31no—
65#63885—31no—
66#63879—31no—
67#63858—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63499—31no—
71#63492—31no—
72#63491—31no—
73C4×#611—31no—
74C2×(C2×D9)⋊C4—31no—
75#63460—31no—
76#63456—31no—
77#63447—31no—
78#63446—31no—
79#63444—31no—
80#63440—31no—
81#63438—31no—
82#63438—61no—
83#63437D311yescharacteristic, complemented
84C22×C3⋊D9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
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
98C2×C9×Dic3C2311yescharacteristic
99C2×C9×Dic3C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C9×D12—22no—
103C4×D3×C9—41no—
104C4×D3×C9—41no—
105C3×D36—41no—
106C3×Dic18—41no—
107#6195—41no—
108#6194—22no—
109#6194—41no—
110#6194—41no—
111D3×Dic9—41no—
112#6192—41no—
113Dic3×D9—41no—
114#5678—91no—
115#5560—91no—
116C22×D32—31no—
117C2×C3×D12—31no—
118C2×C3×D12C2×D311yescharacteristic
119C2×C3×C4×D3C2×D311yescharacteristic
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×C3×Dic6—31no—
122C2×#626—31no—
123C2×#626—31no—
124C2×#625—31no—
125C2×#625—31no—
126C2×#625—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C23×D9—31no—
130C32×C42C2×D311yescharacteristic
131#3752—31no—
132#3752—31no—
133#3752—31no—
134#3750—31no—
135#3750—31no—
136#3750—31no—
137C3×(C2×D3)⋊C4—31no—
138C3×(C2×D3)⋊C4—31no—
139C3×(C2×D3)⋊C4—31no—
140C3×(C2×D3)⋊C4—31no—
141C3×(C2×D3)⋊C4C2×D311yescharacteristic
142C3×(C2×D3)⋊C4C2×D311yescharacteristic
143C3×C4⋊Dic3C2×D311yescharacteristic
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146#3722—31no—
147(C2×D3)⋊Dic3—31no—
148(C2×D3)⋊Dic3—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152C2×D4×C9—31no—
153C22×C4×C9—31no—
154C22×C4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—31no—
159C22×Dic9—31no—
160C2×D36—31no—
161C2×D36C2×D311yescharacteristic
162C2×C4×D9—31no—
163C2×Dic18C2×D311yescharacteristic, complemented
164C9×C4⋊C4—31no—
165C9×C22⋊C4—31no—
166C9×C22⋊C4—31no—
167C42×C9—21no—
168C42×C9C2×D311yescharacteristic, complemented
169#3676—31no—
170#3676—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4—31no—
174(C2×D9)⋊C4—31no—
175(C2×D9)⋊C4—31no—
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—61no—
178(C2×D9)⋊C4—61no—
179(C2×D9)⋊C4—61no—
180(C2×D9)⋊C4C2×D311yescharacteristic
181(C2×D9)⋊C4C2×D311yescharacteristic
182(C2×D9)⋊C4C2×D311yescharacteristic, complemented
183(C2×D9)⋊C4C2×D311yescharacteristic, complemented
184C4⋊Dic9—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—61no—
190Dic9⋊C4—61no—
191Dic9⋊C4—61no—
192C4×Dic9—31no—
193C22×C3×C9C2411yescharacteristic
194C2×C3⋊D9—21no—
195C2×C3⋊D9—21no—
196C2×C3⋊D9—21no—
197C2×D3×C9—21no—
198C2×D3×C9—21no—
199C2×D3×C9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9#4112yes—
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—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#124—91no—
221C3×C4×D4—31no—
222#947—91no—
223#946—91no—
224#939—91no—
225#939—91no—
226#937—91no—
227#937—91no—
228#930—91no—
229#929—91no—
230C4×#67—91no—
231C2×(C2×D3)⋊C4—91no—
232#898—91no—
233#894—91no—
234#886—91no—
235#885—91no—
236#884—91no—
237#884—91no—
238#884—91no—
239#883—91no—
240#882—91no—
241#882—91no—
242#67⋊C4—91no—
243D3×C22⋊C4—91no—
244#879—91no—
245#878—91no—
246#876—91no—
247#876—91no—
248#876—181no—
249#875—31no—
250C4×D12D911yescharacteristic, complemented
251C22×C3⋊D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3C22×D311yescharacteristic
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—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—31no—
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C3×D12—22no—
270C3×D12—121no—
271C3×C4×D3—41no—
272C3×C4×D3—41no—
273C3×Dic6—121no—
274#626—121no—
275#626—121no—
276#625—62no—
277#625—121no—
278#625—121no—
279D3×Dic3—121no—
280D3×Dic3—121no—
281C23×C9—31no—
282C23×C9—31no—
283C22×D9—31no—
284C22×D9—61no—
285C22×D9—62no—
286C22×D9—121no—
287C22×D9—121no—
288C22×D9C22×D311yescharacteristic
289C22×D9C22×D311yescharacteristic
290D4×C9—62no—
291C2×C4×C9—21no—
292C2×C4×C9—21no—
293C2×C4×C9—21no—
294C2×C4×C9—31no—
295C2×C4×C9—31no—
296C2×C4×C9—121no—
297C2×C4×C9—121no—
298C2×C4×C9C22×D311yescharacteristic
299C2×C4×C9C22×D311yescharacteristic
300C2×C4×C9C22×D311yescharacteristic
301#611—62no—
302#611—121no—
303#611—121no—
304#611—121no—
305C2×Dic9—31no—
306C2×Dic9—31no—
307C2×Dic9—31no—
308C2×Dic9—61no—
309C2×Dic9—61no—
310C2×Dic9—61no—
311C2×Dic9—121no—
312C2×Dic9C22×D311yescharacteristic
313C2×Dic9C22×D311yescharacteristic
314D36—41no—
315D36—121no—
316C4×D9—121no—
317Dic18—41no—
318#538—271noSylow
319C2×C3×C9C2×#4111yescharacteristic
320C2×C3×C9H(5,𝔽2)11yescharacteristic
321C2×C3×C9H(5,𝔽2)11yescharacteristic
322C3⋊D9—41no—
323D3×C9—22no—
324D3×C9—41no—
325C3×D9—41no—
326C3×D9—41no—
327C23×D3—91no—
328C23×D3—91no—
329C2×C3×Q8—91no—
330C2×C3×D4—31no—
331C2×C3×D4—91no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C2×#67—91no—
335C2×#67—91no—
336C2×#67—91no—
337C2×#67—91no—
338C2×#67—91no—
339C2×#67—91no—
340C2×#67—91no—
341C2×#67—91no—
342C22×Dic3—91no—
343C22×Dic3—91no—
344C2×D12—31no—
345C2×D12—91no—
346C2×D12—91no—
347C2×D12C2×D911yescharacteristic
348C2×C4×D3—91no—
349C2×C4×D3—91no—
350C2×C4×D3C2×D911yescharacteristic
351C2×C4×D3C2×D911yescharacteristic, complemented
352C2×Dic6—31no—
353C3×C4⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—91no—
357C3×C22⋊C4—91no—
358C3×C22⋊C4—91no—
359C3×C22⋊C4—91no—
360C3×C42—21no—
361C3×C42C2×D911yescharacteristic, complemented
362C3×C42D3211yescharacteristic
363#217—91no—
364#217—91no—
365#217—91no—
366#217—91no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376(C2×D3)⋊C4—91no—
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—181no—
384(C2×D3)⋊C4—181no—
385(C2×D3)⋊C4—181no—
386(C2×D3)⋊C4C2×D911yescharacteristic
387(C2×D3)⋊C4C2×D911yescharacteristic, complemented
388C4⋊Dic3—91no—
389C4⋊Dic3—91no—
390C4⋊Dic3C2×D911yescharacteristic, complemented
391Dic3⋊C4—91no—
392Dic3⋊C4—91no—
393Dic3⋊C4—91no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—181no—
400Dic3⋊C4—181no—
401Dic3⋊C4—181no—
402C4×Dic3—91no—
403C4×Dic3—91no—
404C22×C32C23×D311yescharacteristic
405C2×C3⋊D3—61no—
406C2×C3⋊D3—61no—
407C2×C3⋊D3—61no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
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#23512yes—
420D32—124no—
421C32×C4—21no—
422C32×C4—21no—
423C32×C4—21no—
424C3⋊Dic3—61no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—61no—
430C3×Dic3—61no—
431C22×C9—21no—
432C22×C9—32no—
433C22×C9—61no—
434C22×C9—61no—
435C22×C9—61no—
436C22×C9—61no—
437C22×C9—61no—
438C22×C9C23×D311yescharacteristic
439C2×D9—21no—
440C2×D9—21no—
441C2×D9—21no—
442C2×D9—21no—
443C2×D9—21no—
444C2×D9—21no—
445C2×D9—61no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—121no—
449C2×D9—121no—
450C2×D9—121no—
451C2×D9—124no—
452C4×C9—21no—
453C4×C9—21no—
454C4×C9—21no—
455C4×C9—41no—
456C4×C9—41no—
457C4×C9—41no—
458C4×C9—61no—
459C4×C9—61no—
460Dic9—21no—
461Dic9—21no—
462Dic9—61no—
463Dic9—61no—
464Dic9—61no—
465Dic9—121no—
466Dic9—121no—
467Dic9—121no—
468#126—271no—
469#126—271no—
470#124—91no—
471#124—271no—
472#123—271no—
473#123—271no—
474C22⋊Q8—271no—
475#121—271no—
476#121—271no—
477#121—271no—
478#120—271no—
479#120—271no—
480C4×D4—31no—
481C4×D4—271no—
482C2×C22⋊C4—271no—
483C3×C9#53811yescharacteristic, complemented, Sylow
484C23×C3—31no—
485C23×C3—31no—
486C23×C3—91no—
487C23×C3—91no—
488C22×D3—31no—
489C22×D3—31no—
490C22×D3—91no—
491C22×D3—91no—
492C22×D3—181no—
493C22×D3—182no—
494C22×D3—182no—
495C22×D3—361no—
496C22×D3—361no—
497C22×D3—361no—
498C22×D3—361no—
499C22×D3C22×D911yescharacteristic
500C22×D3C22×D911yescharacteristic
501C3×Q8—361no—
502C3×D4—62no—
503C3×D4—361no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—121no—
512C2×C3×C4—121no—
513C2×C3×C4C22×D911yescharacteristic
514C2×C3×C4C22×D911yescharacteristic
515C2×C3×C4C22×D911yescharacteristic
516C2×C3×C4C2×D3211yescharacteristic
517C2×C3×C4C2×D3211yescharacteristic
518C2×C3×C4C2×D3211yescharacteristic
519#67—182no—
520#67—182no—
521#67—361no—
522#67—361no—
523#67—361no—
524#67—361no—
525#67—361no—
526#67—361no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—91no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—181no—
536C2×Dic3—181no—
537C2×Dic3—181no—
538C2×Dic3—361no—
539C2×Dic3—361no—
540C2×Dic3C22×D911yescharacteristic
541C2×Dic3C22×D911yescharacteristic
542D12—22no—
543D12—121no—
544D12—361no—
545D12—361no—
546C4×D3—41no—
547C4×D3—41no—
548C4×D3—361no—
549C4×D3—361no—
550Dic6—121no—
551C2×C32C2×#23511yescharacteristic
552C2×C32#100411yescharacteristic
553C2×C32#100911yescharacteristic
554C3⋊D3—121no—
555C3×D3—22no—
556C3×D3—41no—
557C3×D3—121no—
558C3×D3—121no—
559C2×C9—21no—
560C2×C9—21no—
561C2×C9—21no—
562C2×C9—62no—
563C2×C9—121no—
564C2×C9#100411yescharacteristic
565C2×C9D3×#4111yescharacteristic
566C2×C9#100911yescharacteristic
567D9—41no—
568D9—41no—
569D9—121no—
570D9—241no—
571C24—271no—
572C2×Q8—91no—
573C2×D4—31no—
574C2×D4—91no—
575C2×D4—271no—
576C2×D4—271no—
577C2×D4—271no—
578C2×D4—271no—
579C2×D4—271no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—271no—
583C22×C4—271no—
584C4⋊C4—31no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C4⋊C4—271no—
588C4⋊C4—271no—
589C4⋊C4—271no—
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—91no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C42—271no—
605C42D3×D911yescharacteristic, complemented
606C22×C3—21no—
607C22×C3—32no—
608C22×C3—61no—
609C22×C3—61no—
610C22×C3—61no—
611C22×C3—61no—
612C22×C3—61no—
613C22×C3—181no—
614C22×C3—181no—
615C22×C3—181no—
616C22×C3—181no—
617C22×C3—181no—
618C22×C3—181no—
619C22×C3C23×D911yescharacteristic
620C22×C3C22×D3211yescharacteristic
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—21no—
626C2×D3—61no—
627C2×D3—61no—
628C2×D3—61no—
629C2×D3—61no—
630C2×D3—61no—
631C2×D3—61no—
632C2×D3—181no—
633C2×D3—181no—
634C2×D3—181no—
635C2×D3—181no—
636C2×D3—181no—
637C2×D3—181no—
638C2×D3—361no—
639C2×D3—361no—
640C2×D3—361no—
641C2×D3—364no—
642C2×D3—364no—
643C2×D3#369712yes—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—181no—
656C3×C4—181no—
657Dic3—21no—
658Dic3—21no—
659Dic3—61no—
660Dic3—61no—
661Dic3—181no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—361no—
668Dic3—361no—
669Dic3—361no—
670C32#556011yescharacteristic
671C9—21no—
672C9#567811yescharacteristic, complemented
673C23—31no—
674C23—31no—
675C23—91no—
676C23—91no—
677C23—271no—
678C23—542no—
679C23—1081no—
680C23—1081no—
681Q8—361no—
682D4—62no—
683D4—361no—
684D4—542no—
685D4—1081no—
686D4—1081no—
687D4—1081no—
688D4—1081no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—271no—
696C2×C4—271no—
697C2×C4—271no—
698C2×C4—1081no—
699C2×C4—1081no—
700C2×C4C2×D3×D911yescharacteristic
701C2×C4C2×D3×D911yescharacteristic
702C2×C4C2×D3×D911yescharacteristic
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—62no—
707C2×C3—121no—
708C2×C3—361no—
709C2×C3—361no—
710C2×C3C2×#369711yescharacteristic
711C2×C3#6371011yescharacteristic
712C2×C3#6371511yescharacteristic
713C2×C3D3×#23511yescharacteristic
714C2×C3#6430711yescharacteristic
715C2×C3#6430711yescharacteristic
716D3—22no—
717D3—41no—
718D3—121no—
719D3—121no—
720D3—361no—
721D3—361no—
722D3—721no—
723C22—32no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—61no—
728C22—61no—
729C22—181no—
730C22—181no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22—181no—
735C22—541no—
736C22—541no—
737C22—541no—
738C22—1084no—
739C22C22×D3×D911yescharacteristic
740C4—21no—
741C4—21no—
742C4—21no—
743C4—61no—
744C4—61no—
745C4—181no—
746C4—181no—
747C4—541no—
748C4—541no—
749C4—541no—
750C3—21no—
751C3#1058966211yescharacteristic, complemented
752C3#1059401211yescharacteristic
753C2—62no—
754C2—121no—
755C2—361no—
756C2—361no—
757C2—1081no—
758C2D3×#369711yescharacteristic
759C2#1172247611yescharacteristic
760C2#1172247711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C42×C9C22
socleC22×C32C23×D3
hypercenterC42D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #11721713C2semidirect
2. C4×C9×D12C2semidirect
3. C3×#63437C2semidirect
4. #11721050C2semidirect
5. #11721049C2semidirect
6. D3×(C2×D9)⋊C4C2semidirect
7. #11721035C2semidirect
8. #11721034C2semidirect
9. #11721032C2semidirect
10. #11721018C2semidirect
11. #11721016C2semidirect
12. #11720988C2semidirect
13. #11720982C2semidirect
14. #11720976C2semidirect
15. #11720946C2semidirect
21. C2×C4×D3×C9C22semidirect
23. C2×C3×Dic18C22semidirect
27. C2×#6194C22semidirect
30. C2×Dic3×D9C22semidirect
31. C3×C42×C9C22semidirect
35. #88534C22semidirect
36. #88534C22semidirect
37. #88534C22semidirect
39. C9×(C2×D3)⋊C4C22semidirect
42. C3×(C2×D9)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C9×C4⋊Dic3C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
83. #63437D3semidirect
163. C2×Dic18C2×D3semidirect
168. C42×C9C2×D3semidirect
182. (C2×D9)⋊C4C2×D3semidirect
183. (C2×D9)⋊C4C2×D3semidirect
250. C4×D12D9semidirect
351. C2×C4×D3C2×D9semidirect
361. C3×C42C2×D9semidirect
387. (C2×D3)⋊C4C2×D9semidirect
390. C4⋊Dic3C2×D9semidirect
483. C3×C9#538semidirect
605. C42D3×D9semidirect
672. C9#5678semidirect
751. C3#10589662semidirect

Maximal subgroups

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

subgroupindex
#117217132
C4×C9×D122
C3×#634372
#117210502
#117210492
D3×(C2×D9)⋊C42
#117210352
#117210342
#117210322
#117210182
#117210162
#117209882
#117209822
#117209762
#117209462
#105940123
#105896623