Finite Group Databasebeta

← #11903855

Subgroups — #11903855

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#556C211yesmaximal, characteristic, complemented
2#10589827C211yesmaximal, characteristic, complemented
3#10589823C211yesmaximal, characteristic, complemented
4#10589811C214yesmaximal, complemented
5#10589808C214yesmaximal, complemented
6#10589783C212yesmaximal, complemented
7#10589770C212yesmaximal, complemented
8#10589735C212yesmaximal, complemented
9#10589726C212yesmaximal, complemented
10#10589687C211yesmaximal, characteristic, complemented
11C4×#3701C212yesmaximal, complemented
12C4×Q8×D9C211yesmaximal, characteristic, complemented
13#10589670C212yesmaximal, complemented
14#10589655C211yesmaximal, characteristic, complemented
15C4×#3699C211yesmaximal, characteristic, complemented
16#10589632C212yesmaximal, complemented
17#10589624C212yesmaximal, complemented
18#86980—31nomaximal
19C2×#3701C2212yes—
20C2×Q8×D9C2211yescharacteristic
21C2×#3699C2211yescharacteristic
22C2×#3697C2212yes—
23C9×C4⋊Q8C2211yescharacteristic
24C9×#126C2214yes—
25C9×#124C2212yes—
26C9×C22⋊Q8C2212yes—
27C4×Q8×C9C2212yes—
28C4×Q8×C9C2211yescharacteristic
29C4×D4×C9C2211yescharacteristic
30C9×#117C2212yes—
31#63509C2212yes—
32#63509C2212yes—
33Q8×Dic9C2211yescharacteristic
34Q8×Dic9C2212yes—
35#63506C2212yes—
36#63502C2212yes—
37D4×Dic9C2211yescharacteristic
38#63492C2212yes—
39C4×#611C2212yes—
40C2×C4×Dic9C2212yes—
41#63460C2214yes—
42#63458C2214yes—
43#63457C2212yes—
44#63457C2212yes—
45#63456C2214yes—
46#63455C2212yes—
47#63455C2214yes—
48#63455C2212yes—
49#63455C2212yes—
50#63455C2212yes—
51#63454C2214yes—
52#63454C2211yescharacteristic
53C4⋊C4×D9C2212yes—
54C4⋊C4×D9C2211yescharacteristic
55#63452C2212yes—
56#63451C2214yes—
57#63449C2212yes—
58#63449C2212yes—
59#63449C2211yescharacteristic
60#63449C2211yescharacteristic
61#63448C2214yes—
62#63447C2214yes—
63#63446C2214yes—
64#63446C2214yes—
65#63446C2214yes—
66#63445C2214yes—
67#611⋊C4C2214yes—
68#611⋊C4C2214yes—
69#611⋊C4C2214yes—
70#611⋊C4C2212yes—
71#63439C2212yes—
72#63438C2214yes—
73#63437C2212yes—
74#63436C2211yescharacteristic
75C4×D36C2212yes—
76C4×D36C2214yes—
77#63434C2214yes—
78C42×D9C2212yes—
79C42×D9C2214yes—
80C42×D9C2211yescharacteristic
81C4×Dic18C2212yes—
82C4×Dic18C2211yescharacteristic
83C4×Dic18C2211yescharacteristic
84C3×#556D311yescharacteristic
85#5725—31no—
86#5721—31no—
87#5709—34no—
88#5706—34no—
89#5681—32no—
90#5668—32no—
91#5633—32no—
92#5624—32no—
93#5585—31no—
94C4×#239—32no—
95C4×D3×Q8—31no—
96#5568—32no—
97#5553—31no—
98C4×#237—31no—
99#5530—32no—
100#5522—32no—
101C2×Q8×C9C2312yes—
102C2×Q8×C9C2311yescharacteristic
103C2×D4×C9C2311yescharacteristic
104C22×C4×C9C2312yes—
105C2×#611C2312yes—
106C2×#611C2314yes—
107C2×#611C2314yes—
108C22×Dic9C2312yes—
109C22×Dic9C2312yes—
110#3701—28no—
111Q8×D9—24no—
112#3699—24no—
113#3697—28no—
114C2×D36C2312yes—
115C2×D36C2312yes—
116C2×D36C2314yes—
117C2×D36C2312yes—
118C2×C4×D9C2311yescharacteristic
119C2×C4×D9C2314yes—
120C2×C4×D9C2314yes—
121C2×C4×D9C2312yes—
122C2×C4×D9C2314yes—
123C2×C4×D9C2312yes—
124C2×C4×D9C2311yescharacteristic
125C2×C4×D9C2311yescharacteristic
126C2×Dic18C2311yescharacteristic
127C2×Dic18C2312yes—
128C2×Dic18C2311yescharacteristic
129C9×C4⋊C4C2311yescharacteristic
130C9×C4⋊C4C2312yes—
131C9×C4⋊C4C2311yescharacteristic
132C9×C4⋊C4C2314yes—
133C9×C4⋊C4C2312yes—
134C9×C4⋊C4C2312yes—
135C9×C22⋊C4C2314yes—
136C9×C22⋊C4C2312yes—
137C9×C22⋊C4C2314yes—
138C42×C9C2314yes—
139C42×C9C2311yescharacteristic
140C42×C9C2312yes—
141#3676C2312yes—
142(C2×D9)⋊C4C2312yes—
143(C2×D9)⋊C4C2314yes—
144(C2×D9)⋊C4C2314yes—
145(C2×D9)⋊C4C2314yes—
146(C2×D9)⋊C4C2314yes—
147(C2×D9)⋊C4C2314yes—
148(C2×D9)⋊C4C2314yes—
149C4⋊Dic9C2311yescharacteristic
150C4⋊Dic9C2311yescharacteristic
151C4⋊Dic9C2312yes—
152C4⋊Dic9C2314yes—
153Dic9⋊C4C2312yes—
154Dic9⋊C4C2314yes—
155Dic9⋊C4C2314yes—
156Dic9⋊C4C2312yes—
157Dic9⋊C4C2312yes—
158Dic9⋊C4C2312yes—
159Dic9⋊C4C2312yes—
160C4×Dic9C2312yes—
161C4×Dic9C2311yescharacteristic
162C4×Dic9C2312yes—
163C4×Dic9C2312yes—
164C4×Dic9C2314yes—
165C4×Dic9C2311yescharacteristic
166C4×Dic9C2312yes—
167C4×Dic9C2312yes—
168C4×Dic9C2311yescharacteristic
169C4×Dic9C2312yes—
170#3480—91noSylow
171C2×#239—32no—
172C2×D3×Q8—31no—
173C2×#237—31no—
174C2×#235—32no—
175C3×C4⋊Q8C2×D311yescharacteristic
176C3×#126C2×D314yes—
177C3×#124C2×D312yes—
178C3×C22⋊Q8C2×D312yes—
179C3×C4×Q8C2×D312yes—
180C3×C4×Q8C2×D311yescharacteristic
181C3×C4×D4C2×D311yescharacteristic
182C3×#117C2×D312yes—
183#947—32no—
184#947—32no—
185Q8×Dic3—32no—
186Q8×Dic3—31no—
187#944—32no—
188#940—32no—
189D4×Dic3—31no—
190#930—32no—
191C4×#67—32no—
192C2×C4×Dic3—32no—
193#898—34no—
194#896—34no—
195#895—32no—
196#895—32no—
197#894—34no—
198#893—34no—
199#893—32no—
200#893—32no—
201#893—32no—
202#893—32no—
203#892—34no—
204#892—31no—
205D3×C4⋊C4—32no—
206D3×C4⋊C4—31no—
207#890—32no—
208#889—34no—
209#887—32no—
210#887—32no—
211#887—31no—
212#887—31no—
213#886—34no—
214#885—34no—
215#884—34no—
216#884—34no—
217#884—34no—
218#883—34no—
219#67⋊C4—34no—
220#67⋊C4—34no—
221#67⋊C4—34no—
222#67⋊C4—32no—
223#877—32no—
224#876—34no—
225#875—32no—
226#874—31no—
227C4×D12—32no—
228C4×D12—34no—
229#872—34no—
230C42×D3—32no—
231C42×D3—34no—
232C42×D3—31no—
233C4×Dic6—32no—
234C4×Dic6—31no—
235C4×Dic6—31no—
236C23×C9C2412yes—
237C22×D9C2414yes—
238C22×D9C2411yescharacteristic
239Q8×C9—22no—
240Q8×C9—24no—
241D4×C9—22no—
242C2×C4×C9—24no—
243C2×C4×C9C2412yes—
244C2×C4×C9C2411yescharacteristic
245C2×C4×C9C2414yes—
246C2×C4×C9C2412yes—
247C2×C4×C9C2412yes—
248C2×C4×C9C2411yescharacteristic
249C2×C4×C9C2411yescharacteristic
250#611—24no—
251#611—28no—
252#611—44no—
253C2×Dic9—24no—
254C2×Dic9—42no—
255C2×Dic9C2411yescharacteristic
256C2×Dic9C2412yes—
257C2×Dic9C2412yes—
258C2×Dic9C2412yes—
259C2×Dic9C2411yescharacteristic
260C2×Dic9C2411yescharacteristic
261C2×Dic9C2412yes—
262D36—28no—
263D36—24no—
264D36—24no—
265D36—42no—
266C4×D9—22no—
267C4×D9—28no—
268C4×D9—24no—
269C4×D9—28no—
270C4×D9—44no—
271C4×D9—41no—
272C4×D9—42no—
273C4×D9#4114yescomplemented
274Dic18—22no—
275Dic18—24no—
276Dic18#4114yescomplemented
277#559—92no—
278#559—91no—
279#557—91no—
280#556—92no—
281#556D911yescharacteristic, complemented
282#553—94no—
283#553—92no—
284#550—91no—
285#548—92no—
286#532—91no—
287#532—92no—
288#529—94no—
289#529—92no—
290C4×#41—92no—
291C4×#41—91no—
292C4×#41—92no—
293C2×C4×Q8—91no—
294C2×C3×Q8C22×D312yes—
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4C22×D312yes—
298C2×#67—34no—
299C2×#67—32no—
300C2×#67—34no—
301C22×Dic3—32no—
302C22×Dic3—32no—
303#239—68no—
304D3×Q8—64no—
305#237—64no—
306#235—68no—
307C2×D12—32no—
308C2×D12—34no—
309C2×D12—32no—
310C2×D12—32no—
311C2×C4×D3—31no—
312C2×C4×D3—34no—
313C2×C4×D3—34no—
314C2×C4×D3—32no—
315C2×C4×D3—31no—
316C2×C4×D3—34no—
317C2×C4×D3—32no—
318C2×C4×D3—31no—
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—32no—
322C3×C4⋊C4C22×D312yes—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D312yes—
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D312yes—
327C3×C4⋊C4C22×D314yes—
328C3×C22⋊C4C22×D312yes—
329C3×C22⋊C4C22×D314yes—
330C3×C22⋊C4C22×D314yes—
331C3×C42C22×D311yescharacteristic
332C3×C42C22×D312yes—
333C3×C42C22×D314yes—
334#217—32no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4—34no—
337(C2×D3)⋊C4—32no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—34no—
342C4⋊Dic3—31no—
343C4⋊Dic3—32no—
344C4⋊Dic3—31no—
345C4⋊Dic3—34no—
346Dic3⋊C4—32no—
347Dic3⋊C4—32no—
348Dic3⋊C4—32no—
349Dic3⋊C4—32no—
350Dic3⋊C4—34no—
351Dic3⋊C4—32no—
352Dic3⋊C4—34no—
353C4×Dic3—31no—
354C4×Dic3—32no—
355C4×Dic3—32no—
356C4×Dic3—32no—
357C4×Dic3—32no—
358C4×Dic3—31no—
359C4×Dic3—32no—
360C4×Dic3—34no—
361C4×Dic3—31no—
362C4×Dic3—32no—
363C22×C9—22no—
364C22×C9—22no—
365C22×C9—22no—
366C22×C9C2511yescharacteristic
367C2×D9—21no—
368C2×D9—21no—
369C2×D9—24no—
370C2×D9—24no—
371C2×D9—24no—
372C2×D9C2×#4112yes—
373C4×C9—22no—
374C4×C9—22no—
375C4×C9—24no—
376C4×C9—22no—
377C4×C9—21no—
378C4×C9C2×#4112yes—
379C4×C9C2×#4112yes—
380Dic9—21no—
381Dic9—22no—
382Dic9—22no—
383Dic9—21no—
384Dic9—22no—
385Dic9C2×#4114yes—
386Dic9C2×#4112yes—
387C2×#41—92no—
388C2×#41—91no—
389C2×#41—92no—
390C22×Q8—91no—
391C4⋊Q8—92no—
392C4⋊Q8C2×D911yescharacteristic
393#127—92no—
394#127—91no—
395#126—94no—
396#126—94no—
397#126C2×D914yes—
398#125—94no—
399#125—92no—
400#124—92no—
401#124—92no—
402#124—94no—
403#124—92no—
404#124C2×D912yes—
405#123—94no—
406#123—94no—
407#123—94no—
408C22⋊Q8—94no—
409C22⋊Q8C2×D912yes—
410#121—92no—
411#121—92no—
412#121—92no—
413#121—94no—
414#121—94no—
415#121—94no—
416C4×Q8—91no—
417C4×Q8—92no—
418C4×Q8—91no—
419C4×Q8—92no—
420C4×Q8—92no—
421C4×Q8—91no—
422C4×Q8—91no—
423C4×Q8—92no—
424C4×Q8—91no—
425C4×Q8C2×D911yescharacteristic
426C4×Q8C2×D912yes—
427C4×D4—91no—
428C4×D4—92no—
429C4×D4—92no—
430C4×D4—94no—
431C4×D4—92no—
432C4×D4—92no—
433C4×D4—92no—
434C4×D4—94no—
435C4×D4—92no—
436C4×D4—94no—
437C4×D4—94no—
438C4×D4—94no—
439C4×D4—92no—
440C4×D4C2×D911yescharacteristic
441#117—91no—
442#117—94no—
443#117—92no—
444#117—94no—
445#117C2×D912yes—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—91no—
448C2×C42—92no—
449C2×C42—91no—
450C2×C42—92no—
451C2×C42—94no—
452C23×C3C23×D312yes—
453C22×D3—31no—
454C22×D3—34no—
455C3×Q8—22no—
456C3×Q8—24no—
457C3×D4—22no—
458C2×C3×C4—24no—
459C2×C3×C4C23×D312yes—
460C2×C3×C4C23×D311yescharacteristic
461C2×C3×C4C23×D314yes—
462C2×C3×C4C23×D312yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D311yescharacteristic
465C2×C3×C4C23×D311yescharacteristic
466#67—68no—
467#67—64no—
468#67—124no—
469C2×Dic3—31no—
470C2×Dic3—32no—
471C2×Dic3—31no—
472C2×Dic3—32no—
473C2×Dic3—32no—
474C2×Dic3—32no—
475C2×Dic3—31no—
476C2×Dic3—64no—
477C2×Dic3—122no—
478D12—68no—
479D12—64no—
480D12—64no—
481D12—122no—
482C4×D3—34no—
483C4×D3—68no—
484C4×D3—64no—
485C4×D3—68no—
486C4×D3—62no—
487C4×D3—124no—
488C4×D3—121no—
489C4×D3—122no—
490Dic6—34no—
491Dic6—64no—
492Dic6—62no—
493C2×C9—42no—
494C2×C9C22×#4111yescharacteristic
495C2×C9C22×#4111yescharacteristic
496C2×C9#58511yescharacteristic
497D9—22no—
498D9—44no—
499#41—188no—
500#41—184no—
501#41—188no—
502C2×Q8—91no—
503C2×Q8—92no—
504C2×Q8—91no—
505C2×Q8—184no—
506C2×Q8C22×D911yescharacteristic
507C2×Q8C22×D912yes—
508C2×D4—92no—
509C2×D4—94no—
510C2×D4—94no—
511C2×D4—94no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—92no—
515C2×D4C22×D911yescharacteristic
516C22×C4—91no—
517C22×C4—92no—
518C22×C4—92no—
519C22×C4—92no—
520C22×C4—91no—
521C22×C4—94no—
522C22×C4—94no—
523C22×C4—91no—
524C22×C4—92no—
525C22×C4—94no—
526C22×C4C22×D912yes—
527C4⋊C4—92no—
528C4⋊C4—92no—
529C4⋊C4—91no—
530C4⋊C4—92no—
531C4⋊C4—92no—
532C4⋊C4—91no—
533C4⋊C4—94no—
534C4⋊C4—92no—
535C4⋊C4—92no—
536C4⋊C4—94no—
537C4⋊C4—94no—
538C4⋊C4C22×D911yescharacteristic
539C4⋊C4C22×D912yes—
540C4⋊C4C22×D911yescharacteristic
541C4⋊C4C22×D914yes—
542C4⋊C4C22×D912yes—
543C4⋊C4C22×D912yes—
544C22⋊C4—92no—
545C22⋊C4—92no—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4—94no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—94no—
552C22⋊C4C22×D912yes—
553C22⋊C4C22×D914yes—
554C22⋊C4C22×D914yes—
555C42—92no—
556C42—92no—
557C42—91no—
558C42—91no—
559C42—92no—
560C42—92no—
561C42—94no—
562C42—92no—
563C42—91no—
564C42—92no—
565C42C22×D914yes—
566C42C22×D912yes—
567C42C22×D911yescharacteristic
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3C24×D311yescharacteristic
572C2×D3—32no—
573C2×D3—61no—
574C2×D3—61no—
575C2×D3—64no—
576C2×D3—64no—
577C2×D3—64no—
578C3×C4—22no—
579C3×C4—22no—
580C3×C4—24no—
581C3×C4—22no—
582C3×C4—21no—
583C3×C4D3×#4112yes—
584C3×C4D3×#4112yes—
585Dic3—34no—
586Dic3—32no—
587Dic3—61no—
588Dic3—62no—
589Dic3—62no—
590Dic3—61no—
591Dic3—62no—
592C9#348011yescharacteristic, complemented, Sylow
593C23—91no—
594C23—94no—
595C23C23×D912yes—
596Q8—22no—
597Q8—24no—
598Q8—94no—
599Q8—184no—
600Q8—182no—
601D4—22no—
602D4—188no—
603D4—188no—
604D4—184no—
605D4—184no—
606D4—184no—
607D4—362no—
608D4—364no—
609C2×C4—24no—
610C2×C4—91no—
611C2×C4—92no—
612C2×C4—94no—
613C2×C4—92no—
614C2×C4—91no—
615C2×C4—91no—
616C2×C4—92no—
617C2×C4—92no—
618C2×C4—184no—
619C2×C4—188no—
620C2×C4—188no—
621C2×C4—184no—
622C2×C4—182no—
623C2×C4—364no—
624C2×C4—362no—
625C2×C4—361no—
626C2×C4—362no—
627C2×C4C23×D912yes—
628C2×C4C23×D912yes—
629C2×C4C23×D912yes—
630C2×C4C23×D914yes—
631C2×C4C23×D911yescharacteristic
632C2×C4C23×D911yescharacteristic
633C2×C4C23×D911yescharacteristic
634C2×C3—42no—
635C2×C3C2×D3×#4111yescharacteristic
636C2×C3C2×D3×#4111yescharacteristic
637C2×C3#596811yescharacteristic
638D3—62no—
639D3—124no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—92no—
644C22—181no—
645C22—181no—
646C22—184no—
647C22—184no—
648C22—184no—
649C22C24×D911yescharacteristic
650C4—22no—
651C4—24no—
652C4—22no—
653C4—22no—
654C4—21no—
655C4—92no—
656C4—94no—
657C4—182no—
658C4—181no—
659C4—182no—
660C4—181no—
661C4—182no—
662C4#41×D912yes—
663C4#41×D912yes—
664C3#8698011yescharacteristic
665C2—42no—
666C2—182no—
667C2—364no—
668C2C2×#41×D911yescharacteristic
669C2C2×#41×D911yescharacteristic
670C2#1059314311yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#556C2
hypercenter#556D9
hypocenterC9#3480
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C9×#556C2semidirect
2. #10589827C2semidirect
3. #10589823C2semidirect
4. #10589811C2semidirect
5. #10589808C2semidirect
6. #10589783C2semidirect
7. #10589770C2semidirect
8. #10589735C2semidirect
9. #10589726C2semidirect
10. #10589687C2semidirect
11. C4×#3701C2semidirect
12. C4×Q8×D9C2semidirect
13. #10589670C2semidirect
14. #10589655C2semidirect
15. C4×#3699C2semidirect
16. #10589632C2semidirect
17. #10589624C2semidirect
273. C4×D9#41semidirect
276. Dic18#41semidirect
281. #556D9semidirect
592. C9#3480semidirect

Maximal subgroups

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

subgroupindex
C9×#5562
#105898272
#105898232
#105898112
#105898082
#105897832
#105897702
#105897352
#105897262
#105896872
C4×#37012
C4×Q8×D92
#105896702
#105896552
C4×#36992
#105896322
#105896242
#869803