Finite Group Databasebeta

← #13151982

Subgroups — #13151982

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#611C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721874C211yesmaximal, characteristic, complemented
4C2×C9×#217C211yesmaximal, characteristic, complemented
5#11721277C211yesmaximal, characteristic, complemented
6#11721276C211yesmaximal, characteristic, complemented
7Dic3×#611C211yesmaximal, characteristic, complemented
8#11721271C211yesmaximal, characteristic, complemented
9#11721269C211yesmaximal, characteristic, complemented
10D9×#217C211yesmaximal, characteristic, complemented
11#11721259C211yesmaximal, characteristic, complemented
12#11721257C211yesmaximal, characteristic, complemented
13#11721256C211yesmaximal, characteristic, complemented
14#11721253C211yesmaximal, characteristic, complemented
15#11721241C211yesmaximal, characteristic, complemented
16#10595493—31nomaximal
17#10589592—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C3×#611—24no—
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C22×C9×Dic3C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic
31C2×#6192C2211yescharacteristic, complemented
32C2×#6192C2211yescharacteristic, complemented
33C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
34#88658—24no—
35C2×Dic3×D9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic
39#88551C2211yescharacteristic, complemented
40#88551C2211yescharacteristic, complemented
41C9×#217C2211yescharacteristic
42C9×#217C2211yescharacteristic
43C9×#217C2211yescharacteristic, complemented
44C9×#217C2211yescharacteristic, complemented
45#88445C2211yescharacteristic, complemented
46(C2×D9)⋊Dic3C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×C3×#67—31no—
56C2×#3804—31no—
57#64162—31no—
58C2×C3×#217D311yescharacteristic
59#63978—31no—
60#63977—31no—
61Dic3×#67—31no—
62#63971—31no—
63#63969—31no—
64D3×#217—31no—
65#63964—31no—
66#63961—31no—
67#63959—31no—
68#63958—31no—
69#63952—31no—
70C22×#611D311yescharacteristic, complemented
71C2×#3697—31no—
72C2×C9×C22⋊C4—31no—
73#63515—31no—
74#63515—61no—
75#63492—31no—
76#63491—31no—
77C4×#611—31no—
78#63447—31no—
79#63446—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9—22no—
87C23×C3×C9—22no—
88C23×C3×C9—41no—
89C23×C3×C9C2311yescharacteristic
90C23×C3×C9C2311yescharacteristic
91C23×C3×C9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—41no—
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98#6233—22no—
99#6233—22no—
100#6233—41no—
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C3×#611—22no—
105C3×#611—22no—
106C3×#611—22no—
107C3×#611D414yescomplemented
108C2×C9×Dic3—22no—
109C2×C9×Dic3—41no—
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C3×Dic9—22no—
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117#6192—22no—
118#6192—41no—
119(C3⋊D9)⋊C4—22no—
120Dic3×D9—22no—
121Dic3×D9—41no—
122#6189—22no—
123#5806—91no—
124#5490—91no—
125C24×C32C2×D311yescharacteristic
126C23×C3×D3—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—64no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3C2×D311yescharacteristic
137C22×C3×Dic3C2×D311yescharacteristic
138C2×#627—31no—
139C2×#626—31no—
140C2×#626—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—21no—
146C24×C9C2×D311yescharacteristic
147C23×D9C2×D311yescharacteristic
148#3757—31no—
149#3757—31no—
150#3757—31no—
151C3×#217C2×D311yescharacteristic
152C3×#217C2×D311yescharacteristic
153C3×#217C2×D311yescharacteristic
154C3×#217C2×D311yescharacteristic
155#3724—31no—
156#3724—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159#3722—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164Dic32—31no—
165C22×C4×C9—31no—
166C22×C4×C9—31no—
167C2×#611—24no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—61no—
172C2×#611—61no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C2×#611C2×D311yescharacteristic
176C2×#611C2×D311yescharacteristic
177C2×#611C2×D311yescharacteristic
178C22×Dic9C2×D311yescharacteristic
179#3697—64no—
180C2×D36—31no—
181C2×D36—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×Dic18—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—61no—
194#3676—61no—
195#3676—61no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201C4⋊Dic9—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205C4×Dic9—31no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—44no—
214C22×C3×C9C2×D412yes—
215C22×C3×C9#4112yescomplemented
216C22×C3×C9C2411yescharacteristic
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×C3⋊D9—21no—
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9C2×D412yes—
227C3⋊Dic9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C9×Dic3—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×C3×D4—91no—
237C22×#67—31no—
238C2×#237—91no—
239C2×#235—91no—
240C2×C3×C22⋊C4—31no—
241#953—91no—
242#953—91no—
243#953—91no—
244#953—181no—
245C2×#217—91no—
246C2×#217D911yescharacteristic, complemented
247#939—91no—
248#939—91no—
249#938—91no—
250#936—91no—
251#935—91no—
252#935—91no—
253D4×Dic3—91no—
254#930—91no—
255#929—91no—
256C4×#67—91no—
257C4×#67—91no—
258#924—91no—
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—22no—
268C23×C32—22no—
269C23×C32—41no—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279#638—62no—
280#638—62no—
281#638—121no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C3×#67—34no—
286C3×#67—62no—
287C3×#67—62no—
288C3×#67—62no—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—41no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298#627—62no—
299#626—62no—
300#626—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—22no—
305C23×C9—22no—
306C23×C9—21no—
307C23×C9—21no—
308C23×C9—21no—
309C23×C9—42no—
310C23×C9—42no—
311C23×C9—41no—
312C23×C9—42no—
313C23×C9C22×D311yescharacteristic
314C23×C9C22×D311yescharacteristic
315C23×C9C22×D311yescharacteristic
316C22×D9—22no—
317C22×D9—22no—
318C22×D9—31no—
319C22×D9—41no—
320C22×D9—61no—
321C22×D9C22×D311yescharacteristic
322C22×D9C22×D311yescharacteristic
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9—31no—
327C2×C4×C9—62no—
328C2×C4×C9—121no—
329#611—22no—
330#611—22no—
331#611—22no—
332#611—62no—
333#611—62no—
334#611—122no—
335#611—122no—
336#611—121no—
337#611—122no—
338#611#6714yescomplemented
339C2×Dic9—22no—
340C2×Dic9—31no—
341C2×Dic9—31no—
342C2×Dic9—31no—
343C2×Dic9—61no—
344C2×Dic9—61no—
345C2×Dic9—61no—
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348D36—62no—
349D36—121no—
350C4×D9—62no—
351C4×D9—62no—
352C4×D9—121no—
353Dic18—62no—
354#546—271noSylow
355C2×C3×C9—22no—
356C2×C3×C9—22no—
357C2×C3×C9—41no—
358C2×C3×C9C22×D411yescharacteristic
359C2×C3×C9C2×#4111yescharacteristic
360C2×C3×C9H(5,𝔽2)11yescharacteristic
361C3⋊D9—41no—
362C3×D9—22no—
363C3×D9—41no—
364C24×C3—21no—
365C24×C3—91no—
366C24×C3C2×D911yescharacteristic
367C24×C3D3211yescharacteristic
368C23×D3—31no—
369C2×C3×D4—91no—
370C2×C3×D4—91no—
371C2×C3×D4—91no—
372C2×C3×D4—91no—
373C2×C3×D4—184no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—91no—
377C2×#67—31no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—64no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—91no—
387C2×#67—91no—
388C2×#67—91no—
389C2×#67—91no—
390C2×#67—181no—
391C2×#67—181no—
392C2×#67—181no—
393C22×Dic3—31no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3C2×D911yescharacteristic, complemented
397C22×Dic3C2×D911yescharacteristic, complemented
398#237—184no—
399#235—184no—
400C2×D12—91no—
401C2×D12—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×Dic6—91no—
407C2×Dic6—91no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—31no—
412#217—91no—
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—181no—
423#217—181no—
424#217—181no—
425#217C2×D911yescharacteristic
426#217C2×D911yescharacteristic
427#217C2×D911yescharacteristic, complemented
428#217C2×D911yescharacteristic, complemented
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—44no—
453C22×C32#23512yes—
454C22×C32D3×D412yes—
455C22×C32C23×D311yescharacteristic
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—61no—
459C2×C3×D3—32no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—124no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—21no—
471C3×Dic3—21no—
472C3×Dic3—21no—
473C3×Dic3—32no—
474C3×Dic3—61no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—21no—
481C22×C9—21no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—22no—
485C22×C9—22no—
486C22×C9—41no—
487C22×C9—41no—
488C22×C9—41no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—44no—
493C22×C9—48no—
494C22×C9#23712yescomplemented
495C22×C9C2×#6712yes—
496C22×C9C23×D311yescharacteristic
497C2×D9—21no—
498C2×D9—21no—
499C2×D9—21no—
500C2×D9—21no—
501C2×D9—21no—
502C2×D9—44no—
503C2×D9—61no—
504C2×D9—61no—
505C2×D9—61no—
506C2×D9—121no—
507C2×D9—121no—
508C2×D9—121no—
509C2×D9C2×#6712yes—
510C4×C9—61no—
511C4×C9—61no—
512C4×C9—61no—
513C4×C9—61no—
514Dic9—21no—
515Dic9—61no—
516Dic9—61no—
517Dic9—61no—
518Dic9—121no—
519Dic9—121no—
520Dic9—121no—
521Dic9C2×#6712yes—
522C2×#41—271no—
523C22×D4—91no—
524#124—271no—
525#123—271no—
526#123—271no—
527C22⋊Q8—271no—
528#121—271no—
529#121—271no—
530#121—271no—
531#120—271no—
532#120—271no—
533C4×D4—271no—
534C4×D4—271no—
535C2×C22⋊C4—31no—
536C2×C22⋊C4—271no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—42no—
546C23×C3—42no—
547C23×C3—41no—
548C23×C3—41no—
549C23×C3—42no—
550C23×C3—91no—
551C23×C3—91no—
552C23×C3—182no—
553C23×C3—182no—
554C23×C3—361no—
555C23×C3C22×D911yescharacteristic
556C23×C3C22×D911yescharacteristic
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—91no—
566C22×D3—91no—
567C22×D3—121no—
568C22×D3—181no—
569C3×D4—94no—
570C3×D4—182no—
571C3×D4—182no—
572C3×D4—182no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—31no—
576C2×C3×C4—31no—
577C2×C3×C4—62no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—121no—
581C2×C3×C4—182no—
582#67—34no—
583#67—62no—
584#67—62no—
585#67—62no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—182no—
590#67—182no—
591#67—362no—
592#67—362no—
593#67—361no—
594#67—361no—
595#67—361no—
596#67—362no—
597C2×Dic3—22no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—41no—
601C2×Dic3—62no—
602C2×Dic3—91no—
603C2×Dic3—91no—
604C2×Dic3—91no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—91no—
608C2×Dic3—181no—
609C2×Dic3—181no—
610C2×Dic3—181no—
611C2×Dic3—182no—
612C2×Dic3—361no—
613C2×Dic3C22×D911yescharacteristic
614C2×Dic3C22×D911yescharacteristic
615C2×Dic3C22×D911yescharacteristic
616C2×Dic3C22×D911yescharacteristic
617D12—182no—
618D12—361no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—361no—
623Dic6—182no—
624Dic6—182no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—41no—
628C2×C32C2×#23511yescharacteristic
629C2×C32C2×D3×D411yescharacteristic
630C2×C32#100411yescharacteristic
631C3⋊D3—121no—
632C3×D3—62no—
633C3×D3—121no—
634C2×C9—22no—
635C2×C9—22no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—21no—
639C2×C9—42no—
640C2×C9—42no—
641C2×C9—42no—
642C2×C9—41no—
643C2×C9C2×#23711yescharacteristic
644C2×C9#100411yescharacteristic
645C2×C9C22×#6711yescharacteristic
646D9—22no—
647D9—41no—
648D9—121no—
649D9—241no—
650C24—91no—
651C24D3×D911yescharacteristic
652#41—544no—
653C2×Q8—271no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—184no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—271no—
664C22×C4—31no—
665C22×C4—31no—
666C22×C4—91no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C4⋊C4—271no—
671C4⋊C4—271no—
672C4⋊C4—271no—
673C4⋊C4—271no—
674C22⋊C4—31no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—31no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C22⋊C4—271no—
682C22⋊C4—271no—
683C22⋊C4—271no—
684C22⋊C4—271no—
685C22⋊C4—271no—
686C42—271no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—44no—
712C22×C3—44no—
713C22×C3—48no—
714C22×C3—92no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3—181no—
720C22×C3—364no—
721C22×C3#369712yescomplemented
722C22×C3D4×D912yes—
723C22×C3C23×D911yescharacteristic
724C22×C3#380412yes—
725C22×C3D3×#6712yes—
726C22×C3C22×D3211yescharacteristic
727C2×D3—32no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—61no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—124no—
734C2×D3—181no—
735C2×D3—181no—
736C2×D3—181no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3—361no—
741C2×D3—361no—
742C2×D3—361no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—61no—
746C3×C4—61no—
747C3×C4—92no—
748C3×C4—181no—
749Dic3—21no—
750Dic3—21no—
751Dic3—21no—
752Dic3—21no—
753Dic3—32no—
754Dic3—61no—
755Dic3—181no—
756Dic3—181no—
757Dic3—181no—
758Dic3—181no—
759Dic3—181no—
760Dic3—181no—
761Dic3—361no—
762Dic3—361no—
763Dic3—361no—
764C32#549011yescharacteristic
765C9—21no—
766C9#580611yescharacteristic, complemented
767C23—22no—
768C23—22no—
769C23—41no—
770C23—91no—
771C23—91no—
772C23—182no—
773C23—182no—
774C23—271no—
775C23—361no—
776C23C2×D3×D911yescharacteristic
777C23C2×D3×D911yescharacteristic
778C23C2×D3×D911yescharacteristic
779Q8—542no—
780D4—94no—
781D4—182no—
782D4—182no—
783D4—182no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—31no—
792C2×C4—31no—
793C2×C4—62no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—121no—
797C2×C4—182no—
798C2×C4—271no—
799C2×C4—271no—
800C2×C4—271no—
801C2×C4—542no—
802C2×C4—542no—
803C2×C4—1081no—
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—22no—
807C2×C3—22no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—41no—
815C2×C3—41no—
816C2×C3—182no—
817C2×C3—361no—
818C2×C3C2×#369711yescharacteristic
819C2×C3C2×D4×D911yescharacteristic
820C2×C3#6371011yescharacteristic
821C2×C3C2×#380411yescharacteristic
822C2×C3C2×D3×#6711yescharacteristic
823C2×C3#6433011yescharacteristic
824D3—62no—
825D3—121no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—44no—
837C22—92no—
838C22—181no—
839C22—181no—
840C22—181no—
841C22—181no—
842C22—181no—
843C22—364no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22#8865812yescomplemented
848C22D9×#6712yes—
849C22C22×D3×D911yescharacteristic
850C4—61no—
851C4—61no—
852C4—61no—
853C4—61no—
854C4—92no—
855C4—181no—
856C4—541no—
857C4—541no—
858C4—541no—
859C3—21no—
860C3#1058959211yescharacteristic, complemented
861C3#1059549311yescharacteristic
862C2—22no—
863C2—22no—
864C2—41no—
865C2—182no—
866C2—361no—
867C2—1081no—
868C2C2×#8865811yescharacteristic
869C2C2×D9×#6711yescharacteristic
870C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
hypercenterC24D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C22×C3×#611C2semidirect
2. C2×#88658C2semidirect
3. #11721874C2semidirect
4. C2×C9×#217C2semidirect
5. #11721277C2semidirect
6. #11721276C2semidirect
7. Dic3×#611C2semidirect
8. #11721271C2semidirect
9. #11721269C2semidirect
10. D9×#217C2semidirect
11. #11721259C2semidirect
12. #11721257C2semidirect
13. #11721256C2semidirect
14. #11721253C2semidirect
15. #11721241C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
28. C22×C9×Dic3C22semidirect
29. C22×C9×Dic3C22semidirect
31. C2×#6192C22semidirect
32. C2×#6192C22semidirect
33. C2×(C3⋊D9)⋊C4C22semidirect
35. C2×Dic3×D9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
39. #88551C22semidirect
40. #88551C22semidirect
43. C9×#217C22semidirect
44. C9×#217C22semidirect
45. #88445C22semidirect
46. (C2×D9)⋊Dic3C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
70. C22×#611D3semidirect
107. C3×#611D4semidirect
215. C22×C3×C9#41semidirect
246. C2×#217D9semidirect
338. #611#67semidirect
396. C22×Dic3C2×D9semidirect
397. C22×Dic3C2×D9semidirect
427. #217C2×D9semidirect
428. #217C2×D9semidirect
494. C22×C9#237semidirect
537. C3×C9#546semidirect
721. C22×C3#3697semidirect
766. C9#5806semidirect
847. C22#88658semidirect
860. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6112
C2×#886582
#117218742
C2×C9×#2172
#117212772
#117212762
Dic3×#6112
#117212712
#117212692
D9×#2172
#117212592
#117212572
#117212562
#117212532
#117212412
#105954933
#105895923