Finite Group Databasebeta

← #13152012

Subgroups — #13152012

Order 1728.

1134 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#67C211yesmaximal, characteristic, complemented
2C2×#88663C211yesmaximal, characteristic, complemented
3C2×#88551C211yesmaximal, characteristic, complemented
4C3×#63515C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#11721286C211yesmaximal, characteristic, complemented
7#67⋊Dic9C211yesmaximal, characteristic, complemented
8#11721281C211yesmaximal, characteristic, complemented
9#11721280C211yesmaximal, characteristic, complemented
10D3×#3676C211yesmaximal, characteristic, complemented
11Dic3×#611C211yesmaximal, characteristic, complemented
12#11721270C211yesmaximal, characteristic, complemented
13#11721266C211yesmaximal, characteristic, complemented
14#11721263C211yesmaximal, characteristic, complemented
15#11721249C211yesmaximal, characteristic, complemented
16#10595494—31nomaximal
17#10589908—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C23×D3×C9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic, complemented
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C9×#67—24no—
23C2×C9×#67C2211yescharacteristic
24C2×C9×#67C2211yescharacteristic
25C2×C9×#67C2211yescharacteristic
26C2×C9×#67C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C22×C9×Dic3C2211yescharacteristic
31C2×#6194C2211yescharacteristic, complemented
32C2×#6194C2211yescharacteristic, complemented
33#88663—24no—
34C2×D3×Dic9C2211yescharacteristic, complemented
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88551C2211yescharacteristic
39#88551C2211yescharacteristic
40#88551C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
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(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50Dic3⋊Dic9C2211yescharacteristic, complemented
51#88442C2211yescharacteristic, complemented
52Dic9⋊Dic3C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C22×C3×#67D311yescharacteristic
56C2×#3805—31no—
57C2×#3757—31no—
58C3×#953—31no—
59#63980—31no—
60#63976—31no—
61#67⋊Dic3—31no—
62Dic3×#67—31no—
63#63970—31no—
64#63970—31no—
65#63969—31no—
66D3×#217—31no—
67#63964—31no—
68#63962—31no—
69#63959—31no—
70C22×D4×C9—31no—
71C2×#3699—31no—
72#63515—31no—
73#63515D311yescharacteristic, complemented
74C2×#3676—31no—
75C2×#3676—31no—
76C2×#3676—61no—
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×D3×C9—22no—
93C22×D3×C9—22no—
94C22×D3×C9—41no—
95C22×D3×C9C2311yescharacteristic
96C22×D3×C9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C2×C3⋊Dic9—22no—
99C2×C3⋊Dic9—41no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C9×#67—22no—
105C9×#67—22no—
106C9×#67—22no—
107C9×#67D414yescomplemented
108C3×#611—22no—
109C3×#611—22no—
110C3×#611—41no—
111C2×C9×Dic3—22no—
112C2×C9×Dic3C2311yescharacteristic
113C2×C9×Dic3C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117#6194—22no—
118#6194—41no—
119D3×Dic9—22no—
120D3×Dic9—41no—
121Dic3×D9—22no—
122#6189—22no—
123#5806—91no—
124#5591—91no—
125C24×C32C2×D311yescharacteristic
126C23×C3×D3C2×D311yescharacteristic
127C22×C3⋊Dic3—31no—
128C22×C3⋊Dic3—31no—
129C2×C3×#67—24no—
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67C2×D311yescharacteristic
134C2×C3×#67C2×D311yescharacteristic
135C2×C3×#67C2×D311yescharacteristic
136C2×C3×#67C2×D311yescharacteristic
137C22×C3×Dic3C2×D311yescharacteristic
138C2×#627—31no—
139C2×#625—31no—
140C2×#625—31no—
141#3805—64no—
142C2×D3×Dic3—31no—
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—
151#3757—31no—
152C3×#217—31no—
153C3×#217—31no—
154C3×#217—31no—
155#3724—31no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—31no—
158Dic3⋊Dic3—31no—
159(C2×D3)⋊Dic3—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×#611C2×D311yescharacteristic
174C2×#611C2×D311yescharacteristic, complemented
175C2×#611C2×D311yescharacteristic, complemented
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—31no—
179C22×Dic9—31no—
180C22×Dic9—61no—
181C22×Dic9—61no—
182#3699—64no—
183C2×C4×D9—31no—
184C2×Dic18—31no—
185#3676—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#3676—61no—
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×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×D3×C9—44no—
223C2×D3×C9C2×D412yes—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C3⋊Dic9—21no—
228C3⋊Dic9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3C2×D412yes—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×C3×D4—31no—
237C22×#67D911yescharacteristic, complemented
238C2×#237—91no—
239C2×#237—91no—
240C3×#120—91no—
241#953—31no—
242#953—91no—
243C2×#217—91no—
244C2×#217—91no—
245C2×#217—91no—
246C2×#217—181no—
247#939—91no—
248#939—91no—
249#939—91no—
250#939—91no—
251#938—91no—
252#938—91no—
253#937—91no—
254#936—91no—
255#935—91no—
256#935—91no—
257D4×Dic3—91no—
258D4×Dic3—91no—
259C4×#67—91no—
260#924—91no—
261#886—91no—
262#885—91no—
263#883—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—22no—
274C22×C3×D3—22no—
275C22×C3×D3—31no—
276C22×C3×D3—41no—
277C22×C3×D3C22×D311yescharacteristic
278C22×C3×D3C22×D311yescharacteristic
279C2×C3⋊Dic3—31no—
280C2×C3⋊Dic3—31no—
281C2×C3⋊Dic3—31no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—62no—
284C2×C3⋊Dic3—121no—
285C3×#67—22no—
286C3×#67—22no—
287C3×#67—22no—
288C3×#67—62no—
289C3×#67—62no—
290C3×#67—121no—
291C3×#67#6714yes—
292C2×C3×Dic3—22no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298#627—62no—
299#625—62no—
300#625—121no—
301D3×Dic3—62no—
302D3×Dic3—62no—
303D3×Dic3—121no—
304C23×C9—24no—
305C23×C9—22no—
306C23×C9—22no—
307C23×C9—21no—
308C23×C9—21no—
309C23×C9—21no—
310C23×C9—31no—
311C23×C9—31no—
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×D9C22×D311yescharacteristic
322D4×C9—34no—
323D4×C9—62no—
324D4×C9—62no—
325D4×C9—62no—
326C2×C4×C9—31no—
327C2×C4×C9—31no—
328C2×C4×C9—62no—
329#611—22no—
330#611—22no—
331#611—41no—
332#611—62no—
333#611—121no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—31no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—62no—
343C2×Dic9—62no—
344C2×Dic9—122no—
345C2×Dic9—121no—
346C2×Dic9—121no—
347C2×Dic9—122no—
348C2×Dic9C22×D311yescharacteristic
349C2×Dic9C22×D311yescharacteristic
350C2×Dic9C22×D311yescharacteristic
351C4×D9—62no—
352Dic18—62no—
353#546—271noSylow
354C2×C3×C9—22no—
355C2×C3×C9—22no—
356C2×C3×C9—41no—
357C2×C3×C9C22×D411yescharacteristic
358C2×C3×C9C2×#4111yescharacteristic
359C2×C3×C9H(5,𝔽2)11yescharacteristic
360D3×C9—22no—
361D3×C9—41no—
362C3×D9—41no—
363C24×C3—21no—
364C24×C3—31no—
365C24×C3C2×D911yescharacteristic
366C24×C3D3211yescharacteristic
367C23×D3C2×D911yescharacteristic
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—64no—
373C2×C3×D4—91no—
374C2×C3×D4—91no—
375C2×C3×D4—91no—
376C22×C3×C4—31no—
377C2×#67—24no—
378C2×#67—31no—
379C2×#67—31no—
380C2×#67—31no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—91no—
384C2×#67—91no—
385C2×#67C2×D911yescharacteristic
386C2×#67C2×D911yescharacteristic
387C2×#67C2×D911yescharacteristic
388C2×#67C2×D911yescharacteristic
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—91no—
392C22×Dic3—91no—
393C22×Dic3—91no—
394C22×Dic3—91no—
395C22×Dic3—91no—
396C22×Dic3—181no—
397C22×Dic3—181no—
398C22×Dic3C2×D911yescharacteristic
399#237—184no—
400#237—184no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C22⋊C4—91no—
407C3×C22⋊C4—91no—
408C3×C22⋊C4—91no—
409#217—31no—
410#217—31no—
411#217—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—91no—
423#217—91no—
424#217—91no—
425#217—181no—
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—
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—91no—
439Dic3⋊C4—91no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—44no—
452C22×C32#23712yes—
453C22×C32C2×#6712yes—
454C22×C32C23×D311yescharacteristic
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—44no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3C2×#6712yes—
465C3⋊Dic3—61no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3⋊Dic3—61no—
469C3×Dic3—21no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3C2×#6712yes—
474C22×C9—22no—
475C22×C9—22no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—22no—
481C22×C9—21no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—21no—
485C22×C9—22no—
486C22×C9—22no—
487C22×C9—32no—
488C22×C9—41no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—44no—
493C22×C9—48no—
494C22×C9—61no—
495C22×C9—61no—
496C22×C9—61no—
497C22×C9—61no—
498C22×C9—61no—
499C22×C9—124no—
500C22×C9D3×D412yes—
501C22×C9#23712yescomplemented
502C22×C9C23×D311yescharacteristic
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C4×C9—32no—
507C4×C9—61no—
508Dic9—21no—
509Dic9—21no—
510Dic9—21no—
511Dic9—61no—
512Dic9—61no—
513Dic9—61no—
514Dic9—61no—
515Dic9—121no—
516Dic9—121no—
517Dic9—121no—
518Dic9—121no—
519C2×#41—271no—
520C22×D4—31no—
521#124—271no—
522#123—271no—
523#123—271no—
524C22⋊Q8—271no—
525#121—271no—
526#121—271no—
527#121—271no—
528#120—91no—
529#120—271no—
530C4×D4—271no—
531C4×D4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C3×C9#54611yescharacteristic, complemented, Sylow
535C23×C3—24no—
536C23×C3—22no—
537C23×C3—22no—
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—42no—
546C23×C3—41no—
547C23×C3—41no—
548C23×C3—42no—
549C23×C3—62no—
550C23×C3—62no—
551C23×C3—91no—
552C23×C3—121no—
553C23×C3C22×D911yescharacteristic
554C23×C3C22×D911yescharacteristic
555C23×C3C22×D911yescharacteristic
556C23×C3C2×D3211yescharacteristic
557C23×C3C2×D3211yescharacteristic
558C23×C3C2×D3211yescharacteristic
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—31no—
562C22×D3—41no—
563C22×D3C22×D911yescharacteristic
564C22×D3C22×D911yescharacteristic
565C3×D4—34no—
566C3×D4—62no—
567C3×D4—62no—
568C3×D4—62no—
569C3×D4—182no—
570C3×D4—182no—
571C3×D4—361no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—62no—
575C2×C3×C4—91no—
576C2×C3×C4—91no—
577C2×C3×C4—91no—
578#67—22no—
579#67—22no—
580#67—22no—
581#67—62no—
582#67—62no—
583#67—121no—
584#67—182no—
585#67—182no—
586#67—361no—
587#67—361no—
588#67#61114yescomplemented
589C2×Dic3—22no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—91no—
601C2×Dic3—181no—
602C2×Dic3—181no—
603C2×Dic3—181no—
604C2×Dic3—181no—
605C2×Dic3—182no—
606C2×Dic3—182no—
607C2×Dic3—182no—
608C2×Dic3—182no—
609C2×Dic3—362no—
610C2×Dic3—361no—
611C2×Dic3—361no—
612C2×Dic3—361no—
613C2×Dic3—362no—
614C2×Dic3C22×D911yescharacteristic
615C2×Dic3C22×D911yescharacteristic
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—361no—
619Dic6—182no—
620Dic6—182no—
621C2×C32—22no—
622C2×C32—22no—
623C2×C32—41no—
624C2×C32C2×#23711yescharacteristic
625C2×C32#100411yescharacteristic
626C2×C32C22×#6711yescharacteristic
627C3×D3—22no—
628C3×D3—41no—
629C3×D3—121no—
630C2×C9—24no—
631C2×C9—22no—
632C2×C9—22no—
633C2×C9—21no—
634C2×C9—21no—
635C2×C9—21no—
636C2×C9—42no—
637C2×C9—42no—
638C2×C9—41no—
639C2×C9—62no—
640C2×C9—121no—
641C2×C9C2×D3×D411yescharacteristic
642C2×C9C2×#23711yescharacteristic
643C2×C9#100411yescharacteristic
644D9—41no—
645C24—31no—
646C24D3×D911yescharacteristic
647#41—544no—
648C2×Q8—271no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—31no—
653C2×D4—64no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—271no—
658C2×D4—271no—
659C22×C4—31no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C4⋊C4—271no—
666C4⋊C4—271no—
667C4⋊C4—271no—
668C4⋊C4—271no—
669C22⋊C4—91no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4—271no—
680C22⋊C4—271no—
681C42—271no—
682C22×C3—22no—
683C22×C3—22no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—22no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—32no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—44no—
708C22×C3—44no—
709C22×C3—48no—
710C22×C3—61no—
711C22×C3—61no—
712C22×C3—61no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—124no—
716C22×C3—181no—
717C22×C3—181no—
718C22×C3—181no—
719C22×C3#369912yescomplemented
720C22×C3C2×#61112yes—
721C22×C3C23×D911yescharacteristic
722C22×C3#380512yes—
723C22×C3D3×#6712yes—
724C22×C3C22×D3211yescharacteristic
725C2×D3—21no—
726C2×D3—21no—
727C2×D3—21no—
728C2×D3—21no—
729C2×D3—21no—
730C2×D3—44no—
731C2×D3—61no—
732C2×D3—61no—
733C2×D3—61no—
734C2×D3C2×#61112yes—
735C3×C4—32no—
736C3×C4—61no—
737C3×C4—181no—
738C3×C4—181no—
739C3×C4—181no—
740Dic3—21no—
741Dic3—61no—
742Dic3—61no—
743Dic3—61no—
744Dic3—181no—
745Dic3—181no—
746Dic3—181no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—181no—
752Dic3—361no—
753Dic3—361no—
754Dic3—361no—
755Dic3—361no—
756Dic3C2×#61112yes—
757C32#580611yescharacteristic
758C9—21no—
759C9#559111yescharacteristic, complemented
760C23—22no—
761C23—22no—
762C23—31no—
763C23—31no—
764C23—41no—
765C23—62no—
766C23—62no—
767C23—91no—
768C23—121no—
769C23C2×D3×D911yescharacteristic
770C23C2×D3×D911yescharacteristic
771C23C2×D3×D911yescharacteristic
772Q8—542no—
773D4—34no—
774D4—62no—
775D4—62no—
776D4—62no—
777D4—182no—
778D4—182no—
779D4—361no—
780D4—542no—
781D4—1081no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—62no—
785C2×C4—91no—
786C2×C4—91no—
787C2×C4—91no—
788C2×C4—271no—
789C2×C4—271no—
790C2×C4—271no—
791C2×C4—271no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4—542no—
795C2×C4—1081no—
796C2×C4—1081no—
797C2×C3—24no—
798C2×C3—22no—
799C2×C3—22no—
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—41no—
808C2×C3—41no—
809C2×C3—62no—
810C2×C3—121no—
811C2×C3—361no—
812C2×C3C2×#369911yescharacteristic
813C2×C3#6371011yescharacteristic
814C2×C3C22×#61111yescharacteristic
815C2×C3C2×#380511yescharacteristic
816C2×C3C2×D3×#6711yescharacteristic
817C2×C3#6433011yescharacteristic
818D3—22no—
819D3—41no—
820D3—121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—32no—
829C22—44no—
830C22—61no—
831C22—61no—
832C22—61no—
833C22—61no—
834C22—61no—
835C22—124no—
836C22—181no—
837C22—181no—
838C22—181no—
839C22#8866312yescomplemented
840C22D3×#61112yes—
841C22C22×D3×D911yescharacteristic
842C4—32no—
843C4—61no—
844C4—181no—
845C4—181no—
846C4—181no—
847C4—541no—
848C4—541no—
849C4—541no—
850C4—541no—
851C3—21no—
852C3#1058990811yescharacteristic, complemented
853C3#1059549411yescharacteristic
854C2—22no—
855C2—22no—
856C2—41no—
857C2—62no—
858C2—121no—
859C2—361no—
860C2C2×#8866311yescharacteristic
861C2C2×D3×#61111yescharacteristic
862C2#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×#88663C2semidirect
3. C2×#88551C2semidirect
4. C3×#63515C2semidirect
5. #11721290C2semidirect
6. #11721286C2semidirect
7. #67⋊Dic9C2semidirect
8. #11721281C2semidirect
9. #11721280C2semidirect
10. D3×#3676C2semidirect
11. Dic3×#611C2semidirect
12. #11721270C2semidirect
13. #11721266C2semidirect
14. #11721263C2semidirect
15. #11721249C2semidirect
20. C22×C3⋊Dic9C22semidirect
21. C22×C3⋊Dic9C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C3×#611C22semidirect
31. C2×#6194C22semidirect
32. C2×#6194C22semidirect
34. C2×D3×Dic9C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
40. #88551C22semidirect
41. #88551C22semidirect
43. C3×#3676C22semidirect
44. C3×#3676C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. Dic3⋊Dic9C22semidirect
51. #88442C22semidirect
52. Dic9⋊Dic3C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
73. #63515D3semidirect
107. C9×#67D4semidirect
174. C2×#611C2×D3semidirect
175. C2×#611C2×D3semidirect
198. #3676C2×D3semidirect
199. #3676C2×D3semidirect
215. C22×C3×C9#41semidirect
237. C22×#67D9semidirect
501. C22×C9#237semidirect
534. C3×C9#546semidirect
588. #67#611semidirect
719. C22×C3#3699semidirect
759. C9#5591semidirect
839. C22#88663semidirect
852. 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×#886632
C2×#885512
C3×#635152
#117212902
#117212862
#67⋊Dic92
#117212812
#117212802
D3×#36762
Dic3×#6112
#117212702
#117212662
#117212632
#117212492
#105954943
#105899083