Finite Group Databasebeta

← #13152011

Subgroups — #13152011

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×C9×#67C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721874C211yesmaximal, characteristic, complemented
4C2×C3×#3676C211yesmaximal, characteristic, complemented
5#11721288C211yesmaximal, characteristic, complemented
6#11721287C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8#11721282C211yesmaximal, characteristic, complemented
9#11721280C211yesmaximal, characteristic, complemented
10D3×#3676C211yesmaximal, characteristic, complemented
11#11721265C211yesmaximal, characteristic, complemented
12#11721263C211yesmaximal, characteristic, complemented
13#11721262C211yesmaximal, characteristic, complemented
14#11721249C211yesmaximal, characteristic, complemented
15#11721240C211yesmaximal, characteristic, complemented
16#10595493—31nomaximal
17#10589908—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×C9×#67—24no—
24C2×C9×#67C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic
27C2×C9×#67C2211yescharacteristic
28C22×C9×Dic3C2211yescharacteristic
29C22×C3×Dic9C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic, complemented
31C2×#6195C2211yescharacteristic, complemented
32C2×#6195C2211yescharacteristic, complemented
33#88662—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic
39#88551C2211yescharacteristic, complemented
40#88551C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43C3×#3676C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52#88442C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×C3×#67D311yescharacteristic
56C2×#3804—31no—
57#64162—31no—
58C2×C3×#217—31no—
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×D4×C9—31no—
71C2×#3699—31no—
72#63515—31no—
73#63515—31no—
74#63515—61no—
75C2×#3676—31no—
76C2×#3676D311yescharacteristic, complemented
77#63501—31no—
78#63501—31no—
79#63500—31no—
80#63498—31no—
81#63497—31no—
82#63497—31no—
83D4×Dic9—31no—
84C4×#611—31no—
85#63486—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×D3×C9—22no—
94C22×D3×C9—22no—
95C22×D3×C9—41no—
96C22×D3×C9C2311yescharacteristic
97C22×D3×C9C2311yescharacteristic
98#6233—22no—
99#6233—22no—
100#6233—41no—
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C9×#67—22no—
105C9×#67—22no—
106C9×#67—22no—
107C9×#67D414yescomplemented
108C2×C9×Dic3—22no—
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9—22no—
112C2×C3×Dic9—41no—
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117#6195—22no—
118#6195—41no—
119D3×Dic9—22no—
120D3×Dic9—41no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5806—91no—
124#5490—91no—
125C24×C32C2×D311yescharacteristic
126C23×C3×D3C2×D311yescharacteristic
127C2×#638—31no—
128C2×#638—31no—
129C2×#638—31no—
130C2×C3×#67—24no—
131C2×C3×#67C2×D311yescharacteristic
132C2×C3×#67C2×D311yescharacteristic
133C2×C3×#67C2×D311yescharacteristic
134C2×C3×#67C2×D311yescharacteristic
135C22×C3×Dic3—31no—
136C22×C3×Dic3—31no—
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×C9—31no—
147C24×C9C2×D311yescharacteristic
148#3757—31no—
149#3757—31no—
150#3757—31no—
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—31no—
154C3×#217—31no—
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—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×D4×C9—31no—
168C2×D4×C9—31no—
169C2×D4×C9—64no—
170C22×C4×C9—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—61no—
177C2×#611—61no—
178C2×#611—61no—
179C22×Dic9—31no—
180C22×Dic9—31no—
181C22×Dic9C2×D311yescharacteristic, complemented
182C22×Dic9C2×D311yescharacteristic, complemented
183#3699—64no—
184C2×C4×D9—31no—
185C2×Dic18—31no—
186#3676—31no—
187#3676—31no—
188#3676—31no—
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—61no—
194#3676—61no—
195#3676—61no—
196#3676C2×D311yescharacteristic
197#3676C2×D311yescharacteristic
198#3676C2×D311yescharacteristic, complemented
199#3676C2×D311yescharacteristic, complemented
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×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9—21no—
225C2×D3×C9—44no—
226C2×D3×C9C2×D412yes—
227C3⋊Dic9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C9×Dic3—21no—
231C9×Dic3C2×D412yes—
232C3×Dic9—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×C3×D4—31no—
237C22×#67D911yescharacteristic, complemented
238C2×#237—91no—
239C2×#235—91no—
240C2×C3×C22⋊C4—91no—
241#953—91no—
242#953—91no—
243#953—91no—
244#953—181no—
245C2×#217—31no—
246C2×#217—91no—
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—22no—
275C22×C3×D3—22no—
276C22×C3×D3—41no—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
279#638—62no—
280#638—62no—
281#638—121no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C3×#67—22no—
286C3×#67—22no—
287C3×#67—22no—
288C3×#67#6714yes—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—121no—
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—31no—
310C23×C9—31no—
311C23×C9—42no—
312C23×C9—42no—
313C23×C9—41no—
314C23×C9—42no—
315C23×C9—62no—
316C23×C9—62no—
317C23×C9—121no—
318C23×C9C22×D311yescharacteristic
319C23×C9C22×D311yescharacteristic
320C23×C9C22×D311yescharacteristic
321C22×D9—31no—
322C22×D9—61no—
323D4×C9—34no—
324D4×C9—62no—
325D4×C9—62no—
326D4×C9—62no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—62no—
330#611—62no—
331#611—62no—
332#611—62no—
333#611—122no—
334#611—122no—
335#611—121no—
336#611—121no—
337#611—122no—
338C2×Dic9—22no—
339C2×Dic9—31no—
340C2×Dic9—31no—
341C2×Dic9—31no—
342C2×Dic9—41no—
343C2×Dic9—61no—
344C2×Dic9—61no—
345C2×Dic9—61no—
346C2×Dic9—62no—
347C2×Dic9—121no—
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350C2×Dic9C22×D311yescharacteristic
351C2×Dic9C22×D311yescharacteristic
352C4×D9—62no—
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—
362D3×C9—22no—
363D3×C9—41no—
364C24×C3—21no—
365C24×C3—31no—
366C24×C3C2×D911yescharacteristic
367C24×C3D3211yescharacteristic
368C23×D3C2×D911yescharacteristic
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—31no—
373C2×C3×D4—64no—
374C22×C3×C4—31no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C2×#67—24no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67—181no—
387C2×#67—181no—
388C2×#67—181no—
389C2×#67C2×D911yescharacteristic
390C2×#67C2×D911yescharacteristic
391C2×#67C2×D911yescharacteristic
392C2×#67C2×D911yescharacteristic
393C22×Dic3—31no—
394C22×Dic3—31no—
395C22×Dic3—91no—
396C22×Dic3—91no—
397C22×Dic3C2×D911yescharacteristic
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—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4—91no—
412#217—31no—
413#217—31no—
414#217—31no—
415#217—31no—
416#217—91no—
417#217—91no—
418#217—91no—
419#217—91no—
420#217—91no—
421#217—91no—
422#217—91no—
423#217—91no—
424#217—91no—
425#217—91no—
426#217—181no—
427#217—181no—
428#217—181no—
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#23712yes—
454C22×C32C2×#6712yes—
455C22×C32C23×D311yescharacteristic
456C2×C3⋊D3—61no—
457C2×C3⋊D3—61no—
458C2×C3⋊D3—61no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—21no—
463C2×C3×D3—21no—
464C2×C3×D3—44no—
465C2×C3×D3C2×#6712yes—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3C2×#6712yes—
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—32no—
487C22×C9—41no—
488C22×C9—41no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—41no—
493C22×C9—44no—
494C22×C9—48no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9—61no—
500C22×C9—124no—
501C22×C9#23512yescomplemented
502C22×C9D3×D412yes—
503C22×C9C23×D311yescharacteristic
504C2×D9—61no—
505C2×D9—61no—
506C2×D9—61no—
507C2×D9—121no—
508C2×D9—121no—
509C2×D9—121no—
510C4×C9—32no—
511C4×C9—61no—
512Dic9—21no—
513Dic9—21no—
514Dic9—21no—
515Dic9—21no—
516Dic9—61no—
517Dic9—61no—
518Dic9—61no—
519Dic9—121no—
520Dic9—121no—
521Dic9—121no—
522C2×#41—271no—
523C22×D4—31no—
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—91no—
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—31no—
546C23×C3—31no—
547C23×C3—42no—
548C23×C3—42no—
549C23×C3—41no—
550C23×C3—41no—
551C23×C3—42no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3—121no—
555C23×C3C22×D911yescharacteristic
556C23×C3C22×D911yescharacteristic
557C23×C3C22×D911yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C23×C3C2×D3211yescharacteristic
560C23×C3C2×D3211yescharacteristic
561C22×D3—22no—
562C22×D3—22no—
563C22×D3—41no—
564C22×D3—91no—
565C22×D3—91no—
566C22×D3—181no—
567C22×D3C22×D911yescharacteristic
568C22×D3C22×D911yescharacteristic
569C3×D4—34no—
570C3×D4—62no—
571C3×D4—62no—
572C3×D4—62no—
573C2×C3×C4—31no—
574C2×C3×C4—31no—
575C2×C3×C4—62no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578C2×C3×C4—91no—
579C2×C3×C4—91no—
580C2×C3×C4—182no—
581C2×C3×C4—361no—
582#67—22no—
583#67—22no—
584#67—22no—
585#67—182no—
586#67—182no—
587#67—182no—
588#67—182no—
589#67—182no—
590#67—362no—
591#67—362no—
592#67—361no—
593#67—361no—
594#67—361no—
595#67—362no—
596#67#61114yescomplemented
597C2×Dic3—22no—
598C2×Dic3—31no—
599C2×Dic3—31no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—62no—
603C2×Dic3—91no—
604C2×Dic3—91no—
605C2×Dic3—91no—
606C2×Dic3—91no—
607C2×Dic3—91no—
608C2×Dic3—91no—
609C2×Dic3—121no—
610C2×Dic3—181no—
611C2×Dic3—181no—
612C2×Dic3—181no—
613C2×Dic3—182no—
614C2×Dic3—361no—
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×#23711yescharacteristic
629C2×C32#100411yescharacteristic
630C2×C32C22×#6711yescharacteristic
631C3⋊D3—121no—
632C3×D3—22no—
633C3×D3—41no—
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×C9—62no—
644C2×C9—121no—
645C2×C9C2×#23511yescharacteristic
646C2×C9C2×D3×D411yescharacteristic
647C2×C9#100411yescharacteristic
648D9—121no—
649D9—241no—
650C24—31no—
651C24D3×D911yescharacteristic
652#41—544no—
653C2×Q8—271no—
654C2×D4—31no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—31no—
658C2×D4—64no—
659C2×D4—271no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—271no—
663C2×D4—271no—
664C22×C4—31no—
665C22×C4—91no—
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—91no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—91no—
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—32no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—44no—
713C22×C3—44no—
714C22×C3—48no—
715C22×C3—61no—
716C22×C3—61no—
717C22×C3—61no—
718C22×C3—61no—
719C22×C3—61no—
720C22×C3—124no—
721C22×C3#369912yescomplemented
722C22×C3C2×#61112yes—
723C22×C3C23×D911yescharacteristic
724C22×C3#380412yes—
725C22×C3D3×#6712yes—
726C22×C3C22×D3211yescharacteristic
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—44no—
733C2×D3—181no—
734C2×D3—181no—
735C2×D3—181no—
736C2×D3—181no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—361no—
740C2×D3—361no—
741C2×D3—361no—
742C2×D3C2×#61112yes—
743C3×C4—32no—
744C3×C4—61no—
745C3×C4—181no—
746C3×C4—181no—
747C3×C4—181no—
748C3×C4—181no—
749Dic3—21no—
750Dic3—61no—
751Dic3—61no—
752Dic3—61no—
753Dic3—61no—
754Dic3—181no—
755Dic3—181no—
756Dic3—181no—
757Dic3—181no—
758Dic3—181no—
759Dic3—181no—
760Dic3—361no—
761Dic3—361no—
762Dic3—361no—
763Dic3C2×#61112yes—
764C32#580611yescharacteristic
765C9—21no—
766C9#549011yescharacteristic, complemented
767C23—22no—
768C23—22no—
769C23—31no—
770C23—31no—
771C23—41no—
772C23—62no—
773C23—62no—
774C23—121no—
775C23—271no—
776C23C2×D3×D911yescharacteristic
777C23C2×D3×D911yescharacteristic
778C23C2×D3×D911yescharacteristic
779Q8—542no—
780D4—34no—
781D4—62no—
782D4—62no—
783D4—62no—
784D4—542no—
785D4—542no—
786D4—542no—
787D4—1081no—
788D4—1081no—
789C2×C4—31no—
790C2×C4—31no—
791C2×C4—62no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—182no—
797C2×C4—271no—
798C2×C4—271no—
799C2×C4—271no—
800C2×C4—361no—
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—62no—
817C2×C3—121no—
818C2×C3C2×#369911yescharacteristic
819C2×C3#6371011yescharacteristic
820C2×C3C22×#61111yescharacteristic
821C2×C3C2×#380411yescharacteristic
822C2×C3C2×D3×#6711yescharacteristic
823C2×C3#6433011yescharacteristic
824D3—22no—
825D3—41no—
826D3—361no—
827D3—361no—
828D3—721no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—32no—
837C22—44no—
838C22—61no—
839C22—61no—
840C22—61no—
841C22—61no—
842C22—61no—
843C22—124no—
844C22—541no—
845C22—541no—
846C22—541no—
847C22#8866212yescomplemented
848C22D3×#61112yes—
849C22C22×D3×D911yescharacteristic
850C4—32no—
851C4—61no—
852C4—181no—
853C4—181no—
854C4—181no—
855C4—181no—
856C4—541no—
857C4—541no—
858C4—541no—
859C3—21no—
860C3#1058990811yescharacteristic, complemented
861C3#1059549311yescharacteristic
862C2—22no—
863C2—22no—
864C2—41no—
865C2—62no—
866C2—121no—
867C2—1081no—
868C2C2×#8866211yescharacteristic
869C2C2×D3×#61111yescharacteristic
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×C9×#67C2semidirect
2. C2×#88662C2semidirect
3. #11721874C2semidirect
4. C2×C3×#3676C2semidirect
5. #11721288C2semidirect
6. #11721287C2semidirect
7. #67×Dic9C2semidirect
8. #11721282C2semidirect
9. #11721280C2semidirect
10. D3×#3676C2semidirect
11. #11721265C2semidirect
12. #11721263C2semidirect
13. #11721262C2semidirect
14. #11721249C2semidirect
15. #11721240C2semidirect
21. C2×#6233C22semidirect
22. C2×#6233C22semidirect
29. C22×C3×Dic9C22semidirect
30. C22×C3×Dic9C22semidirect
31. C2×#6195C22semidirect
32. C2×#6195C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×#6189C22semidirect
39. #88551C22semidirect
40. #88551C22semidirect
43. C3×#3676C22semidirect
44. C3×#3676C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. #88442C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
76. C2×#3676D3semidirect
107. C9×#67D4semidirect
181. C22×Dic9C2×D3semidirect
182. C22×Dic9C2×D3semidirect
198. #3676C2×D3semidirect
199. #3676C2×D3semidirect
215. C22×C3×C9#41semidirect
237. C22×#67D9semidirect
501. C22×C9#235semidirect
537. C3×C9#546semidirect
596. #67#611semidirect
721. C22×C3#3699semidirect
766. C9#5490semidirect
847. C22#88662semidirect
860. C3#10589908semidirect

Maximal subgroups

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

subgroupindex
C22×C9×#672
C2×#886622
#117218742
C2×C3×#36762
#117212882
#117212872
#67×Dic92
#117212822
#117212802
D3×#36762
#117212652
#117212632
#117212622
#117212492
#117212402
#105954933
#105899083