Finite Group Databasebeta

← #13150575

Subgroups — #13150575

Order 1728.

828 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721818C211yesmaximal, characteristic, complemented
2C9×#930C211yesmaximal, characteristic, complemented
3C3×C4×#611C211yesmaximal, characteristic, complemented
4#11721292C211yesmaximal, characteristic, complemented
5#11721282C211yesmaximal, characteristic, complemented
6#11721270C211yesmaximal, characteristic, complemented
7#11721263C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721015C211yesmaximal, characteristic, complemented
11#11721012C211yesmaximal, characteristic, complemented
12#11720999C211yesmaximal, characteristic, complemented
13#11720963C211yesmaximal, characteristic, complemented
14#11720956C211yesmaximal, characteristic, complemented
15#11720920C211yesmaximal, characteristic, complemented
16#10595086—31nomaximal
17#10589715—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C22×C3×C4×C9C2211yescharacteristic, complemented
20C2×#6233C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C2×C9×D12C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×D3×Dic9C2211yescharacteristic, complemented
29C2×Dic3×D9C2211yescharacteristic
30C2×#6189C2211yescharacteristic, complemented
31#88551C2211yescharacteristic, complemented
32#88536C2211yescharacteristic
33#88536C2211yescharacteristic
34#88534C2211yescharacteristic, complemented
35#88534C2211yescharacteristic, complemented
36C3×#3676C2211yescharacteristic, complemented
37C9×(C2×D3)⋊C4C2211yescharacteristic
38C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C3×(C2×D9)⋊C4C2211yescharacteristic
40C9×C4⋊Dic3C2211yescharacteristic, complemented
41C3×Dic9⋊C4C2211yescharacteristic, complemented
42C3×C4×Dic9C2211yescharacteristic, complemented
43(C2×D3)⋊Dic9C2211yescharacteristic
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47#88445C2211yescharacteristic
48#88445C2211yescharacteristic
49(C2×D9)⋊Dic3C2211yescharacteristic
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64138—31no—
54C3×#930D311yescharacteristic
55C3×C4×#67—31no—
56#63983—31no—
57#63971—31no—
58#63970—31no—
59#63959—31no—
60#63922—31no—
61D3×(C2×D3)⋊C4—31no—
62#63899—31no—
63#63884—31no—
64#63879—31no—
65#63859—31no—
66#63852—31no—
67#63848—31no—
68C9×#121—31no—
69#63501—31no—
70#63500—31no—
71#63499—31no—
72#63499—31no—
73#63498—31no—
74#63497—31no—
75#63491—31no—
76#63491—61no—
77C4×#611D311yescharacteristic, complemented
78#63460—31no—
79#63458—31no—
80#63447—31no—
81#611⋊C4—31no—
82C22⋊C4×D9—31no—
83#63441—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×C3×D9C2311yescharacteristic
89C2×D3×D9—22no—
90C2×D3×D9—41no—
91C2×D3×D9—41no—
92C2×C3×C4×C9—41no—
93C2×C3×C4×C9C2311yescharacteristic
94C2×C3×C4×C9C2311yescharacteristic
95#6233—41no—
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C9×#67—41no—
100C9×#67—41no—
101C3×#611—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C9×D12—41no—
108C3×C4×D9—41no—
109#6195—41no—
110#6194—22no—
111D3×Dic9—41no—
112Dic3×D9—41no—
113#6189—41no—
114#5613—91no—
115#5560—91no—
116C22×D32—31no—
117C22×C32×C4C2×D311yescharacteristic
118C2×#638—31no—
119C2×C3×#67—31no—
120C2×C3×#67C2×D311yescharacteristic
121C2×C3×#67C2×D311yescharacteristic
122C2×C3×D12C2×D311yescharacteristic
123C2×C3×C4×D3—31no—
124C2×#627—31no—
125C2×#626—31no—
126C2×#625—31no—
127C2×D3×Dic3—31no—
128C2×D3×Dic3—31no—
129C23×D9—31no—
130#3757—31no—
131#3752—31no—
132#3752—31no—
133#3750—31no—
134#3750—31no—
135C3×#217—31no—
136C3×(C2×D3)⋊C4—31no—
137C3×(C2×D3)⋊C4C2×D311yescharacteristic
138C3×(C2×D3)⋊C4C2×D311yescharacteristic
139C3×C4⋊Dic3C2×D311yescharacteristic
140C3×Dic3⋊C4—31no—
141C3×C4×Dic3—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144#3722—31no—
145#3722—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×D4×C9—31no—
153C2×D4×C9—31no—
154C2×D4×C9—31no—
155C22×C4×C9—21no—
156C22×C4×C9C2×D311yescharacteristic, complemented
157C2×#611—31no—
158C2×#611—31no—
159C2×#611—31no—
160C2×#611—61no—
161C2×#611C2×D311yescharacteristic
162C22×Dic9—31no—
163C2×C4×D9—31no—
164C2×C4×D9C2×D311yescharacteristic
165C2×Dic18—31no—
166C9×C4⋊C4—31no—
167C9×C22⋊C4—31no—
168C9×C22⋊C4—31no—
169#3676—31no—
170#3676—31no—
171#3676—31no—
172#3676—31no—
173#3676—31no—
174#3676—61no—
175#3676C2×D311yescharacteristic, complemented
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—61no—
182(C2×D9)⋊C4—61no—
183(C2×D9)⋊C4C2×D311yescharacteristic
184C4⋊Dic9—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—61no—
189Dic9⋊C4—61no—
190Dic9⋊C4C2×D311yescharacteristic, complemented
191C4×Dic9—31no—
192C4×Dic9C2×D311yescharacteristic, complemented
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9C2411yescharacteristic
197C2×C3⋊D9—21no—
198C2×C3⋊D9—21no—
199C2×C3⋊D9—21no—
200C2×D3×C9—21no—
201C2×D3×C9—21no—
202C2×D3×C9—21no—
203C2×D3×C9—21no—
204C2×D3×C9—21no—
205C2×D3×C9—21no—
206C2×C3×D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9#4112yes—
209D3×D9—44no—
210C3×C4×C9—21no—
211C3×C4×C9—21no—
212C3⋊Dic9—21no—
213C3⋊Dic9—21no—
214C3⋊Dic9—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#121—31no—
221C3×C4×D4—91no—
222#939—91no—
223#939—91no—
224#938—91no—
225#937—91no—
226#937—91no—
227#937—91no—
228#936—91no—
229#935—91no—
230#930D911yescharacteristic, complemented
231#929—91no—
232#929—91no—
233#929—181no—
234C4×#67—31no—
235C4×#67—91no—
236C2×(C2×D3)⋊C4—91no—
237#898—91no—
238#898—91no—
239#896—91no—
240#894—91no—
241#885—91no—
242#885—91no—
243#884—91no—
244#882—91no—
245#67⋊C4—91no—
246D3×C22⋊C4—91no—
247#879—91no—
248#878—91no—
249#876—91no—
250#875—91no—
251C23×C32C22×D311yescharacteristic
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×C4—41no—
260C2×C32×C4C22×D311yescharacteristic
261C2×C32×C4C22×D311yescharacteristic
262#638—121no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C2×C3⋊Dic3—31no—
266C3×#67—41no—
267C3×#67—41no—
268C3×#67—62no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3C22×D311yescharacteristic
273C2×C3×Dic3C22×D311yescharacteristic
274C3×D12—41no—
275C3×C4×D3—121no—
276#627—121no—
277#626—121no—
278#625—62no—
279D3×Dic3—121no—
280D3×Dic3—121no—
281C23×C9—21no—
282C23×C9—31no—
283C23×C9—31no—
284C23×C9C22×D311yescharacteristic
285C22×D9—31no—
286C22×D9—61no—
287C22×D9—62no—
288C22×D9—121no—
289C22×D9—121no—
290C22×D9C22×D311yescharacteristic
291D4×C9—121no—
292D4×C9—121no—
293D4×C9—121no—
294C2×C4×C9—21no—
295C2×C4×C9—21no—
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—41no—
299C2×C4×C9—42no—
300C2×C4×C9C22×D311yescharacteristic
301C2×C4×C9C22×D311yescharacteristic
302#611—22no—
303#611—62no—
304#611—121no—
305#611—121no—
306#611—122no—
307C2×Dic9—31no—
308C2×Dic9—31no—
309C2×Dic9—31no—
310C2×Dic9—61no—
311C2×Dic9—61no—
312C2×Dic9—61no—
313C2×Dic9—121no—
314C2×Dic9C22×D311yescharacteristic
315C2×Dic9C22×D311yescharacteristic
316C2×Dic9C22×D311yescharacteristic
317C4×D9—41no—
318C4×D9—121no—
319Dic18—121no—
320#538—271noSylow
321C2×C3×C9—41no—
322C2×C3×C9C2×#4111yescharacteristic
323C2×C3×C9H(5,𝔽2)11yescharacteristic
324C2×C3×C9H(5,𝔽2)11yescharacteristic
325C3⋊D9—41no—
326D3×C9—41no—
327D3×C9—41no—
328C3×D9—22no—
329C23×D3—91no—
330C23×D3—91no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—91no—
335C22×C3×C4—21no—
336C22×C3×C4—91no—
337C22×C3×C4C2×D911yescharacteristic, complemented
338C22×C3×C4D3211yescharacteristic
339C2×#67—31no—
340C2×#67—91no—
341C2×#67—91no—
342C2×#67—91no—
343C2×#67—91no—
344C2×#67—91no—
345C2×#67—181no—
346C2×#67C2×D911yescharacteristic
347C2×#67C2×D911yescharacteristic, complemented
348C22×Dic3—91no—
349C22×Dic3—91no—
350C2×D12—91no—
351C2×D12C2×D911yescharacteristic
352C2×C4×D3—31no—
353C2×C4×D3—91no—
354C2×C4×D3—91no—
355C2×Dic6—91no—
356C2×Dic6—91no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—91no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—91no—
362C3×C22⋊C4—91no—
363C3×C42—91no—
364#217—31no—
365#217—91no—
366#217—91no—
367#217—91no—
368#217—91no—
369#217—91no—
370#217—91no—
371#217—91no—
372#217—181no—
373(C2×D3)⋊C4—31no—
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—91no—
384(C2×D3)⋊C4—91no—
385(C2×D3)⋊C4—91no—
386(C2×D3)⋊C4—91no—
387(C2×D3)⋊C4—181no—
388(C2×D3)⋊C4—181no—
389(C2×D3)⋊C4C2×D911yescharacteristic
390(C2×D3)⋊C4C2×D911yescharacteristic, complemented
391C4⋊Dic3—91no—
392C4⋊Dic3C2×D911yescharacteristic, complemented
393Dic3⋊C4—31no—
394Dic3⋊C4—91no—
395Dic3⋊C4—91no—
396Dic3⋊C4—91no—
397Dic3⋊C4—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—181no—
402Dic3⋊C4—181no—
403C4×Dic3—31no—
404C4×Dic3—91no—
405C4×Dic3—91no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C23×D311yescharacteristic
410C2×C3⋊D3—61no—
411C2×C3⋊D3—61no—
412C2×C3⋊D3—61no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—32no—
420C2×C3×D3—61no—
421C2×C3×D3—61no—
422D32—124no—
423C32×C4—21no—
424C32×C4—21no—
425C3⋊Dic3—61no—
426C3⋊Dic3—61no—
427C3⋊Dic3—61no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—61no—
431C3×Dic3—61no—
432C3×Dic3—61no—
433C22×C9—22no—
434C22×C9—21no—
435C22×C9—21no—
436C22×C9—21no—
437C22×C9—21no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9—61no—
441C22×C9—61no—
442C22×C9—61no—
443C22×C9—61no—
444C22×C9—61no—
445C22×C9—61no—
446C22×C9C23×D311yescharacteristic
447C2×D9—21no—
448C2×D9—21no—
449C2×D9—61no—
450C2×D9—61no—
451C2×D9—61no—
452C2×D9—121no—
453C2×D9—121no—
454C2×D9—121no—
455C2×D9—124no—
456C2×D9#23512yes—
457C4×C9—21no—
458C4×C9—21no—
459C4×C9—41no—
460C4×C9—41no—
461C4×C9—61no—
462C4×C9—61no—
463Dic9—21no—
464Dic9—21no—
465Dic9—21no—
466Dic9—61no—
467Dic9—61no—
468Dic9—61no—
469Dic9—121no—
470Dic9—121no—
471Dic9—121no—
472#126—271no—
473#126—271no—
474#124—271no—
475#124—271no—
476#123—271no—
477#123—271no—
478C22⋊Q8—271no—
479#121—31no—
480#121—271no—
481#121—271no—
482#120—271no—
483#120—271no—
484C4×D4—91no—
485C4×D4—271no—
486C2×C22⋊C4—271no—
487C3×C9#53811yescharacteristic, complemented, Sylow
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—31no—
491C23×C3—91no—
492C23×C3C22×D911yescharacteristic
493C23×C3C2×D3211yescharacteristic
494C22×D3—31no—
495C22×D3—91no—
496C22×D3—91no—
497C22×D3—181no—
498C22×D3—182no—
499C22×D3—182no—
500C22×D3—361no—
501C22×D3—361no—
502C22×D3—361no—
503C22×D3—361no—
504C22×D3C22×D911yescharacteristic
505C22×D3C22×D911yescharacteristic
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—121no—
509C3×D4—182no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—42no—
517C2×C3×C4—91no—
518C2×C3×C4—91no—
519C2×C3×C4—91no—
520C2×C3×C4—361no—
521C2×C3×C4C22×D911yescharacteristic
522C2×C3×C4C22×D911yescharacteristic
523C2×C3×C4C2×D3211yescharacteristic
524C2×C3×C4C2×D3211yescharacteristic
525#67—41no—
526#67—41no—
527#67—62no—
528#67—182no—
529#67—182no—
530#67—361no—
531#67—361no—
532#67—361no—
533#67—362no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—91no—
538C2×Dic3—91no—
539C2×Dic3—91no—
540C2×Dic3—91no—
541C2×Dic3—91no—
542C2×Dic3—91no—
543C2×Dic3—181no—
544C2×Dic3—181no—
545C2×Dic3—181no—
546C2×Dic3—361no—
547C2×Dic3—361no—
548C2×Dic3C22×D911yescharacteristic
549C2×Dic3C22×D911yescharacteristic
550D12—41no—
551D12—361no—
552C4×D3—121no—
553C4×D3—361no—
554C4×D3—361no—
555Dic6—361no—
556Dic6—361no—
557C2×C32—41no—
558C2×C32#100411yescharacteristic
559C2×C32#100411yescharacteristic
560C2×C32D3×#4111yescharacteristic
561C3⋊D3—121no—
562C3×D3—41no—
563C3×D3—41no—
564C3×D3—62no—
565C2×C9—21no—
566C2×C9—21no—
567C2×C9—21no—
568C2×C9—42no—
569C2×C9—41no—
570C2×C9—121no—
571C2×C9—121no—
572C2×C9C2×#23511yescharacteristic
573C2×C9#100411yescharacteristic
574C2×C9#100911yescharacteristic
575D9—22no—
576D9—121no—
577D9—241no—
578C24—271no—
579C2×Q8—271no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—91no—
584C2×D4—271no—
585C2×D4—271no—
586C2×D4—271no—
587C22×C4—91no—
588C22×C4—271no—
589C22×C4—271no—
590C22×C4D3×D911yescharacteristic, complemented
591C4⋊C4—31no—
592C4⋊C4—91no—
593C4⋊C4—271no—
594C4⋊C4—271no—
595C4⋊C4—271no—
596C4⋊C4—271no—
597C22⋊C4—31no—
598C22⋊C4—31no—
599C22⋊C4—91no—
600C22⋊C4—91no—
601C22⋊C4—271no—
602C22⋊C4—271no—
603C22⋊C4—271no—
604C22⋊C4—271no—
605C22⋊C4—271no—
606C22⋊C4—271no—
607C22⋊C4—271no—
608C22⋊C4—271no—
609C22⋊C4—271no—
610C22⋊C4—271no—
611C42—91no—
612C42—271no—
613C22×C3—22no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—92no—
630C22×C3—181no—
631C22×C3—181no—
632C22×C3C23×D911yescharacteristic
633C22×C3C22×D3211yescharacteristic
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—32no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—181no—
644C2×D3—181no—
645C2×D3—181no—
646C2×D3—181no—
647C2×D3—181no—
648C2×D3—181no—
649C2×D3—361no—
650C2×D3—361no—
651C2×D3—361no—
652C2×D3—364no—
653C2×D3—364no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—181no—
663C3×C4—181no—
664C3×C4—181no—
665Dic3—21no—
666Dic3—21no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—181no—
671Dic3—181no—
672Dic3—181no—
673Dic3—181no—
674Dic3—181no—
675Dic3—181no—
676Dic3—361no—
677Dic3—361no—
678Dic3—361no—
679C32#561311yescharacteristic
680C9—21no—
681C9#556011yescharacteristic, complemented
682C23—31no—
683C23—31no—
684C23—91no—
685C23—271no—
686C23—542no—
687C23—1081no—
688C23—1081no—
689C23C2×D3×D911yescharacteristic
690Q8—1081no—
691D4—121no—
692D4—121no—
693D4—121no—
694D4—182no—
695D4—542no—
696D4—1081no—
697D4—1081no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—41no—
701C2×C4—91no—
702C2×C4—91no—
703C2×C4—91no—
704C2×C4—271no—
705C2×C4—271no—
706C2×C4—271no—
707C2×C4—361no—
708C2×C4—1081no—
709C2×C4—1081no—
710C2×C4C2×D3×D911yescharacteristic
711C2×C4C2×D3×D911yescharacteristic
712C2×C3—21no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—42no—
716C2×C3—41no—
717C2×C3—41no—
718C2×C3—121no—
719C2×C3—121no—
720C2×C3—182no—
721C2×C3#6371011yescharacteristic
722C2×C3#6371011yescharacteristic
723C2×C3#41×D911yescharacteristic
724C2×C3D3×#23511yescharacteristic
725C2×C3#6430711yescharacteristic
726C2×C3#6433011yescharacteristic
727D3—41no—
728D3—41no—
729D3—62no—
730D3—361no—
731D3—361no—
732D3—721no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—61no—
742C22—92no—
743C22—181no—
744C22—181no—
745C22—541no—
746C22—541no—
747C22—541no—
748C22—1084no—
749C22C22×D3×D911yescharacteristic
750C4—21no—
751C4—21no—
752C4—61no—
753C4—61no—
754C4—181no—
755C4—181no—
756C4—181no—
757C4—541no—
758C4—541no—
759C4—541no—
760C3—21no—
761C3#1058971511yescharacteristic, complemented
762C3#1059508611yescharacteristic
763C2—41no—
764C2—121no—
765C2—121no—
766C2—182no—
767C2—1081no—
768C2D9×#23511yescharacteristic
769C2#1172247611yescharacteristic
770C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. #11721818C2semidirect
2. C9×#930C2semidirect
3. C3×C4×#611C2semidirect
4. #11721292C2semidirect
5. #11721282C2semidirect
6. #11721270C2semidirect
7. #11721263C2semidirect
8. #11721050C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721015C2semidirect
11. #11721012C2semidirect
12. #11720999C2semidirect
13. #11720963C2semidirect
14. #11720956C2semidirect
15. #11720920C2semidirect
19. C22×C3×C4×C9C22semidirect
22. C2×C9×#67C22semidirect
28. C2×D3×Dic9C22semidirect
30. C2×#6189C22semidirect
31. #88551C22semidirect
34. #88534C22semidirect
35. #88534C22semidirect
36. C3×#3676C22semidirect
38. C9×(C2×D3)⋊C4C22semidirect
40. C9×C4⋊Dic3C22semidirect
41. C3×Dic9⋊C4C22semidirect
42. C3×C4×Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic3×Dic9C22semidirect
77. C4×#611D3semidirect
156. C22×C4×C9C2×D3semidirect
175. #3676C2×D3semidirect
190. Dic9⋊C4C2×D3semidirect
192. C4×Dic9C2×D3semidirect
230. #930D9semidirect
337. C22×C3×C4C2×D9semidirect
347. C2×#67C2×D9semidirect
390. (C2×D3)⋊C4C2×D9semidirect
392. C4⋊Dic3C2×D9semidirect
487. C3×C9#538semidirect
590. C22×C4D3×D9semidirect
681. C9#5560semidirect
761. C3#10589715semidirect

Maximal subgroups

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

subgroupindex
#117218182
C9×#9302
C3×C4×#6112
#117212922
#117212822
#117212702
#117212632
#117210502
D9×(C2×D3)⋊C42
#117210152
#117210122
#117209992
#117209632
#117209562
#117209202
#105950863
#105897153