Finite Group Databasebeta

← #13151998

Subgroups — #13151998

Order 1728.

880 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721874C211yesmaximal, characteristic, complemented
2C3×#63515C211yesmaximal, characteristic, complemented
3C2×C9×#217C211yesmaximal, characteristic, complemented
4#11721277C211yesmaximal, characteristic, complemented
5#11721275C211yesmaximal, characteristic, complemented
6Dic3×#611C211yesmaximal, characteristic, complemented
7#11721271C211yesmaximal, characteristic, complemented
8#11721269C211yesmaximal, characteristic, complemented
9#11721257C211yesmaximal, characteristic, complemented
10#11721256C211yesmaximal, characteristic, complemented
11#11721249C211yesmaximal, characteristic, complemented
12#11721247C211yesmaximal, characteristic, complemented
13#11721246C211yesmaximal, characteristic, complemented
14#11721242C211yesmaximal, characteristic, complemented
15#11721240C211yesmaximal, characteristic, complemented
16#10595507—31nomaximal
17#10589596—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic
26C22×C9×Dic3C2211yescharacteristic
27C2×#6192C2211yescharacteristic, complemented
28C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
29C2×Dic3×D9C2211yescharacteristic, complemented
30C2×#6189C2211yescharacteristic, complemented
31#88551C2211yescharacteristic
32#88551C2211yescharacteristic
33#88551C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C9×#217C2211yescharacteristic
36C9×#217C2211yescharacteristic
37C9×#217C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39C3×#3676C2211yescharacteristic
40C3×#3676C2211yescharacteristic
41#88445C2211yescharacteristic, complemented
42#88445C2211yescharacteristic, complemented
43(C2×D9)⋊Dic3C2211yescharacteristic, complemented
44(C2×D9)⋊Dic3C2211yescharacteristic, complemented
45Dic3⋊Dic9C2211yescharacteristic, complemented
46Dic3⋊Dic9C2211yescharacteristic, complemented
47#88442C2211yescharacteristic, complemented
48#88442C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic9⋊Dic3C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64162—31no—
54C3×#953—31no—
55C2×C3×#217D311yescharacteristic
56#63978—31no—
57#63975—31no—
58Dic3×#67—31no—
59#63971—31no—
60#63969—31no—
61#63964—31no—
62#63959—31no—
63#63958—31no—
64#63956—31no—
65#63956—31no—
66#63953—31no—
67#63952—31no—
68C2×C9×C22⋊C4—31no—
69#63515—31no—
70#63515—61no—
71#63515D311yescharacteristic, complemented
72#63492—31no—
73C4×#611—31no—
74C4×#611—31no—
75#63486—31no—
76#63447—31no—
77#63447—31no—
78#63446—31no—
79#63446—31no—
80#63445—31no—
81#63445—31no—
82#63441—31no—
83#63441—31no—
84C23×C3×C9—22no—
85C23×C3×C9—41no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3⋊D9C2311yescharacteristic
91C22×C3×D9C2311yescharacteristic
92#6233—22no—
93#6233—41no—
94#6233—41no—
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C3×#611—22no—
99C3×#611—41no—
100C3×#611—41no—
101C2×C9×Dic3—41no—
102C2×C9×Dic3—41no—
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110#6192—41no—
111(C3⋊D9)⋊C4—41no—
112Dic3×D9—41no—
113#6189—41no—
114#5593—91no—
115#5494—91no—
116C24×C32C2×D311yescharacteristic
117C2×#638—31no—
118C2×#638—31no—
119C2×#638—31no—
120C2×C3×#67—31no—
121C2×C3×#67—31no—
122C2×C3×#67—31no—
123C22×C3×Dic3C2×D311yescharacteristic
124C22×C3×Dic3C2×D311yescharacteristic
125C2×#627—31no—
126C2×#626—31no—
127C2×#624—31no—
128C2×D3×Dic3—31no—
129C24×C9—21no—
130C24×C9C2×D311yescharacteristic
131#3757—31no—
132#3757—31no—
133#3757—31no—
134C3×#217—31no—
135C3×#217—31no—
136C3×#217—31no—
137C3×#217C2×D311yescharacteristic
138C3×#217C2×D311yescharacteristic
139C3×#217C2×D311yescharacteristic
140C3×#217C2×D311yescharacteristic
141#3724—31no—
142#3724—31no—
143Dic3⋊Dic3—31no—
144Dic3⋊Dic3—31no—
145Dic3⋊Dic3—31no—
146Dic3⋊Dic3—31no—
147#3722—31no—
148#3722—31no—
149(C2×D3)⋊Dic3—31no—
150(C2×D3)⋊Dic3—31no—
151Dic32—31no—
152Dic32—31no—
153C22×C4×C9—31no—
154C22×C4×C9—31no—
155C2×#611—31no—
156C2×#611—31no—
157C2×#611—31no—
158C2×#611—61no—
159C2×#611—61no—
160C2×#611—61no—
161C2×#611C2×D311yescharacteristic
162C2×#611C2×D311yescharacteristic
163C2×#611C2×D311yescharacteristic
164C2×D36—31no—
165C2×C4×D9—31no—
166C2×C4×D9—31no—
167C2×Dic18—31no—
168C9×C22⋊C4—31no—
169C9×C22⋊C4—31no—
170C9×C22⋊C4—31no—
171C9×C22⋊C4—31no—
172#3676—31no—
173#3676—31no—
174#3676—31no—
175#3676—61no—
176#3676—61no—
177#3676—61no—
178#3676C2×D311yescharacteristic
179#3676C2×D311yescharacteristic
180#3676C2×D311yescharacteristic
181(C2×D9)⋊C4—31no—
182(C2×D9)⋊C4—31no—
183(C2×D9)⋊C4—31no—
184(C2×D9)⋊C4—31no—
185C4⋊Dic9—31no—
186C4⋊Dic9—31no—
187Dic9⋊C4—31no—
188Dic9⋊C4—31no—
189Dic9⋊C4—31no—
190Dic9⋊C4—31no—
191C4×Dic9—31no—
192C4×Dic9—31no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—21no—
198C22×C3×C9—21no—
199C22×C3×C9—21no—
200C22×C3×C9—21no—
201C22×C3×C9—44no—
202C22×C3×C9#4112yes—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9—21no—
207C2×C3×D9—21no—
208C2×C3×D9—21no—
209C2×C3×D9—21no—
210C3⋊Dic9—21no—
211C3⋊Dic9—21no—
212C3⋊Dic9—21no—
213C9×Dic3—21no—
214C9×Dic3—21no—
215C9×Dic3—21no—
216C9×Dic3—21no—
217C3×Dic9—21no—
218C3×Dic9—21no—
219C3×Dic9—21no—
220C3×#120—91no—
221C2×C3×C22⋊C4—31no—
222#953—31no—
223#953—91no—
224#953—91no—
225#953—181no—
226C2×#217D911yescharacteristic, complemented
227#939—91no—
228#939—91no—
229#938—91no—
230#936—91no—
231#935—91no—
232D4×Dic3—91no—
233#930—91no—
234C4×#67—91no—
235C4×#67—91no—
236#924—91no—
237#885—91no—
238#885—91no—
239#885—91no—
240#884—91no—
241#884—91no—
242#883—91no—
243#883—91no—
244#883—91no—
245#67⋊C4—91no—
246#879—91no—
247#879—91no—
248#879—91no—
249#879—91no—
250#878—91no—
251C23×C32—22no—
252C23×C32—41no—
253C23×C32—41no—
254C23×C32C22×D311yescharacteristic
255C23×C32C22×D311yescharacteristic
256C23×C32C22×D311yescharacteristic
257C22×C3⋊D3—31no—
258C22×C3×D3—31no—
259#638—62no—
260#638—121no—
261#638—121no—
262C2×C3⋊Dic3—31no—
263C2×C3⋊Dic3—31no—
264C2×C3⋊Dic3—31no—
265C3×#67—62no—
266C3×#67—121no—
267C3×#67—121no—
268C2×C3×Dic3—31no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—41no—
272C2×C3×Dic3—41no—
273C2×C3×Dic3C22×D311yescharacteristic
274C2×C3×Dic3C22×D311yescharacteristic
275C2×C3×Dic3C22×D311yescharacteristic
276C2×C3×Dic3C22×D311yescharacteristic
277#627—121no—
278#626—121no—
279#624—121no—
280D3×Dic3—121no—
281C23×C9—22no—
282C23×C9—21no—
283C23×C9—21no—
284C23×C9—21no—
285C23×C9—42no—
286C23×C9—41no—
287C23×C9—41no—
288C23×C9—42no—
289C23×C9—42no—
290C23×C9C22×D311yescharacteristic
291C23×C9C22×D311yescharacteristic
292C23×C9C22×D311yescharacteristic
293C22×D9—31no—
294C22×D9—61no—
295C22×D9C22×D311yescharacteristic
296C2×C4×C9—31no—
297C2×C4×C9—31no—
298C2×C4×C9—31no—
299C2×C4×C9—31no—
300C2×C4×C9—121no—
301C2×C4×C9—121no—
302#611—22no—
303#611—41no—
304#611—41no—
305#611—62no—
306#611—122no—
307#611—121no—
308#611—121no—
309#611—122no—
310#611—122no—
311C2×Dic9—31no—
312C2×Dic9—31no—
313C2×Dic9—31no—
314C2×Dic9—61no—
315C2×Dic9—61no—
316C2×Dic9—61no—
317C2×Dic9C22×D311yescharacteristic
318C2×Dic9C22×D311yescharacteristic
319C2×Dic9C22×D311yescharacteristic
320D36—121no—
321C4×D9—121no—
322C4×D9—121no—
323Dic18—121no—
324#538—271noSylow
325C2×C3×C9—22no—
326C2×C3×C9—41no—
327C2×C3×C9—41no—
328C2×C3×C9C2×#4111yescharacteristic
329C2×C3×C9H(5,𝔽2)11yescharacteristic
330C2×C3×C9H(5,𝔽2)11yescharacteristic
331C3⋊D9—41no—
332C3×D9—41no—
333C24×C3—21no—
334C24×C3C2×D911yescharacteristic
335C24×C3D3211yescharacteristic
336C2×C3×D4—91no—
337C2×C3×D4—91no—
338C2×C3×D4—91no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C2×#67—31no—
342C2×#67—31no—
343C2×#67—31no—
344C2×#67—91no—
345C2×#67—91no—
346C2×#67—91no—
347C2×#67—91no—
348C2×#67—91no—
349C2×#67—91no—
350C2×#67—91no—
351C2×#67—181no—
352C2×#67—181no—
353C2×#67—181no—
354C22×Dic3—91no—
355C22×Dic3C2×D911yescharacteristic
356C22×Dic3C2×D911yescharacteristic
357C2×D12—91no—
358C2×C4×D3—91no—
359C2×C4×D3—91no—
360C2×C4×D3—91no—
361C2×Dic6—91no—
362C2×Dic6—91no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—91no—
368C3×C22⋊C4—91no—
369C3×C22⋊C4—91no—
370#217—31no—
371#217—31no—
372#217—31no—
373#217—91no—
374#217—91no—
375#217—91no—
376#217—91no—
377#217—91no—
378#217—91no—
379#217—91no—
380#217—91no—
381#217—181no—
382#217—181no—
383#217—181no—
384#217C2×D911yescharacteristic
385#217C2×D911yescharacteristic
386#217C2×D911yescharacteristic
387#217C2×D911yescharacteristic
388(C2×D3)⋊C4—91no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—91no—
391(C2×D3)⋊C4—91no—
392(C2×D3)⋊C4—91no—
393(C2×D3)⋊C4—91no—
394C4⋊Dic3—91no—
395C4⋊Dic3—91no—
396C4⋊Dic3—91no—
397C4⋊Dic3—91no—
398Dic3⋊C4—91no—
399Dic3⋊C4—91no—
400Dic3⋊C4—91no—
401Dic3⋊C4—91no—
402Dic3⋊C4—91no—
403Dic3⋊C4—91no—
404Dic3⋊C4—91no—
405Dic3⋊C4—91no—
406C4×Dic3—91no—
407C4×Dic3—91no—
408C4×Dic3—91no—
409C4×Dic3—91no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—44no—
419C22×C32#23512yes—
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—61no—
422C2×C3⋊D3—61no—
423C2×C3⋊D3—61no—
424C2×C3×D3—61no—
425C2×C3×D3—61no—
426C2×C3×D3—61no—
427C3⋊Dic3—61no—
428C3⋊Dic3—61no—
429C3⋊Dic3—61no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—61no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C22×C9—21no—
438C22×C9—21no—
439C22×C9—22no—
440C22×C9—22no—
441C22×C9—21no—
442C22×C9—21no—
443C22×C9—21no—
444C22×C9—21no—
445C22×C9—21no—
446C22×C9—21no—
447C22×C9—21no—
448C22×C9—22no—
449C22×C9—41no—
450C22×C9—41no—
451C22×C9—41no—
452C22×C9—41no—
453C22×C9—41no—
454C22×C9—41no—
455C22×C9—44no—
456C22×C9—48no—
457C22×C9#23712yes—
458C22×C9C23×D311yescharacteristic
459C2×D9—21no—
460C2×D9—21no—
461C2×D9—21no—
462C2×D9—61no—
463C2×D9—61no—
464C2×D9—61no—
465C2×D9—121no—
466C2×D9—121no—
467C2×D9—121no—
468C4×C9—61no—
469C4×C9—61no—
470C4×C9—61no—
471C4×C9—61no—
472Dic9—21no—
473Dic9—21no—
474Dic9—21no—
475Dic9—61no—
476Dic9—61no—
477Dic9—61no—
478Dic9—121no—
479Dic9—121no—
480Dic9—121no—
481#126—271no—
482#126—271no—
483#124—271no—
484#124—271no—
485#123—271no—
486#123—271no—
487C22⋊Q8—271no—
488#121—271no—
489#121—271no—
490#121—271no—
491#120—91no—
492#120—271no—
493C4×D4—271no—
494C4×D4—271no—
495C2×C22⋊C4—31no—
496C3×C9#53811yescharacteristic, complemented, Sylow
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3—42no—
503C23×C3—41no—
504C23×C3—41no—
505C23×C3—41no—
506C23×C3—41no—
507C23×C3—42no—
508C23×C3—42no—
509C23×C3—91no—
510C23×C3C22×D911yescharacteristic
511C23×C3C22×D911yescharacteristic
512C23×C3C22×D911yescharacteristic
513C23×C3C2×D3211yescharacteristic
514C23×C3C2×D3211yescharacteristic
515C23×C3C2×D3211yescharacteristic
516C22×D3—31no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—181no—
520C3×D4—182no—
521C3×D4—361no—
522C3×D4—361no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—31no—
527C2×C3×C4—91no—
528C2×C3×C4—91no—
529C2×C3×C4—91no—
530C2×C3×C4—121no—
531C2×C3×C4—121no—
532#67—62no—
533#67—121no—
534#67—121no—
535#67—182no—
536#67—182no—
537#67—362no—
538#67—361no—
539#67—361no—
540#67—361no—
541#67—361no—
542#67—361no—
543#67—362no—
544#67—362no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—41no—
549C2×Dic3—41no—
550C2×Dic3—91no—
551C2×Dic3—91no—
552C2×Dic3—91no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—181no—
557C2×Dic3—181no—
558C2×Dic3—181no—
559C2×Dic3—361no—
560C2×Dic3C22×D911yescharacteristic
561C2×Dic3C22×D911yescharacteristic
562C2×Dic3C22×D911yescharacteristic
563C2×Dic3C22×D911yescharacteristic
564D12—361no—
565C4×D3—361no—
566C4×D3—361no—
567C4×D3—361no—
568Dic6—361no—
569Dic6—361no—
570C2×C32—22no—
571C2×C32—41no—
572C2×C32—41no—
573C2×C32C2×#23511yescharacteristic
574C2×C32#100411yescharacteristic
575C2×C32#100411yescharacteristic
576C3⋊D3—121no—
577C3×D3—121no—
578C2×C9—22no—
579C2×C9—21no—
580C2×C9—21no—
581C2×C9—21no—
582C2×C9—42no—
583C2×C9—42no—
584C2×C9—42no—
585C2×C9—41no—
586C2×C9—41no—
587C2×C9C2×#23711yescharacteristic
588C2×C9#100411yescharacteristic
589C2×C9#100411yescharacteristic
590D9—41no—
591D9—121no—
592D9—241no—
593C24D3×D911yescharacteristic
594C2×Q8—271no—
595C2×D4—91no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—271no—
599C2×D4—271no—
600C2×D4—271no—
601C2×D4—271no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—271no—
605C22×C4—271no—
606C4⋊C4—271no—
607C4⋊C4—271no—
608C4⋊C4—271no—
609C4⋊C4—271no—
610C4⋊C4—271no—
611C4⋊C4—271no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—91no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—271no—
620C22⋊C4—271no—
621C22⋊C4—271no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C42—271no—
627C42—271no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—22no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—44no—
655C22×C3—44no—
656C22×C3—48no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3#369712yes—
661C22×C3C23×D911yescharacteristic
662C22×C3#380412yes—
663C22×C3C22×D3211yescharacteristic
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—181no—
670C2×D3—181no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—361no—
674C2×D3—361no—
675C2×D3—361no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—181no—
681C3×C4—181no—
682C3×C4—181no—
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—181no—
691Dic3—181no—
692Dic3—181no—
693Dic3—181no—
694Dic3—181no—
695Dic3—181no—
696Dic3—361no—
697Dic3—361no—
698Dic3—361no—
699C32#549411yescharacteristic
700C9—21no—
701C9#559311yescharacteristic, complemented
702C23—22no—
703C23—41no—
704C23—41no—
705C23—91no—
706C23—271no—
707C23C2×D3×D911yescharacteristic
708C23C2×D3×D911yescharacteristic
709C23C2×D3×D911yescharacteristic
710Q8—1081no—
711D4—182no—
712D4—361no—
713D4—361no—
714D4—542no—
715D4—1081no—
716D4—1081no—
717D4—1081no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—271no—
730C2×C4—1081no—
731C2×C4—1081no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—41no—
741C2×C3—41no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—361no—
745C2×C3C2×#369711yescharacteristic
746C2×C3#6371011yescharacteristic
747C2×C3#6371011yescharacteristic
748C2×C3C2×#380411yescharacteristic
749C2×C3#6433011yescharacteristic
750C2×C3#6433011yescharacteristic
751D3—121no—
752D3—361no—
753D3—361no—
754D3—721no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—44no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—541no—
768C22—541no—
769C22—541no—
770C22#8865812yes—
771C22C22×D3×D911yescharacteristic
772C4—61no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—181no—
777C4—181no—
778C4—181no—
779C4—541no—
780C4—541no—
781C4—541no—
782C3—21no—
783C3#1058959611yescharacteristic, complemented
784C3#1059550711yescharacteristic
785C2—22no—
786C2—41no—
787C2—41no—
788C2—361no—
789C2—1081no—
790C2C2×#8865811yescharacteristic
791C2#1172253511yescharacteristic
792C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
hypercenterC24D3×D9
hypocenterC3×C9#538
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #11721874C2semidirect
2. C3×#63515C2semidirect
3. C2×C9×#217C2semidirect
4. #11721277C2semidirect
5. #11721275C2semidirect
6. Dic3×#611C2semidirect
7. #11721271C2semidirect
8. #11721269C2semidirect
9. #11721257C2semidirect
10. #11721256C2semidirect
11. #11721249C2semidirect
12. #11721247C2semidirect
13. #11721246C2semidirect
14. #11721242C2semidirect
15. #11721240C2semidirect
27. C2×#6192C22semidirect
28. C2×(C3⋊D9)⋊C4C22semidirect
29. C2×Dic3×D9C22semidirect
30. C2×#6189C22semidirect
41. #88445C22semidirect
42. #88445C22semidirect
43. (C2×D9)⋊Dic3C22semidirect
44. (C2×D9)⋊Dic3C22semidirect
45. Dic3⋊Dic9C22semidirect
46. Dic3⋊Dic9C22semidirect
47. #88442C22semidirect
48. #88442C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic9⋊Dic3C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
71. #63515D3semidirect
226. C2×#217D9semidirect
496. C3×C9#538semidirect
701. C9#5593semidirect
783. C3#10589596semidirect

Maximal subgroups

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

subgroupindex
#117218742
C3×#635152
C2×C9×#2172
#117212772
#117212752
Dic3×#6112
#117212712
#117212692
#117212572
#117212562
#117212492
#117212472
#117212462
#117212422
#117212402
#105955073
#105895963