Finite Group Databasebeta

← #11909744

Subgroups — #11909744

Order 1152.

1656 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×#554C211yesmaximal, characteristic, complemented
2#10589827C211yesmaximal, characteristic, complemented
3#10589824C211yesmaximal, characteristic, complemented
4#10589793C212yesmaximal, complemented
5#10589792C212yesmaximal, complemented
6#10589745C212yesmaximal, complemented
7#10589742C214yesmaximal, complemented
8#10589735C212yesmaximal, complemented
9#10589733C214yesmaximal, complemented
10#10589687C211yesmaximal, characteristic, complemented
11C4×Q8×D9C211yesmaximal, characteristic, complemented
12#10589661C212yesmaximal, complemented
13#10589659C211yesmaximal, characteristic, complemented
14#10589655C211yesmaximal, characteristic, complemented
15#10589650C212yesmaximal, complemented
16#10589609C212yesmaximal, complemented
17#10589606C212yesmaximal, complemented
18#86936—31nomaximal
19C2×#3701C2212yes—
20C2×Q8×D9C2211yescharacteristic
21C2×#3697C2212yes—
22C2×#3697C2214yes—
23C9×C4⋊Q8C2211yescharacteristic
24C9×#125C2212yes—
25C9×C22⋊Q8C2214yes—
26C9×C22⋊Q8C2212yes—
27C4×Q8×C9C2211yescharacteristic
28C4×D4×C9C2212yes—
29C4×D4×C9C2211yescharacteristic
30C2×C9×C4⋊C4C2212yes—
31#63509C2212yes—
32#63509C2212yes—
33Q8×Dic9C2211yescharacteristic
34#63506C2214yes—
35#63502C2212yes—
36#63500C2211yescharacteristic
37#63498C2211yescharacteristic
38#63492C2212yes—
39#63491C2214yes—
40C4×#611C2214yes—
41C4×#611C2212yes—
42C4×#611C2214yes—
43#63488C2212yes—
44#63460C2214yes—
45#63459C2214yes—
46#63459C2211yescharacteristic
47#63458C2214yes—
48#63458C2214yes—
49#63457C2212yes—
50#63457C2212yes—
51#63456C2214yes—
52#63456C2214yes—
53#63455C2214yes—
54#63455C2212yes—
55#63455C2212yes—
56#63455C2212yes—
57#63455C2212yes—
58#63454C2214yes—
59C4⋊C4×D9C2212yes—
60C4⋊C4×D9C2214yes—
61C4⋊C4×D9C2211yescharacteristic
62#63452C2211yescharacteristic
63#63450C2212yes—
64#63450C2212yes—
65#63449C2212yes—
66#63449C2212yes—
67#63449C2212yes—
68#63449C2211yescharacteristic
69#63447C2214yes—
70#63447C2214yes—
71#63446C2214yes—
72#63446C2214yes—
73#63445C2212yes—
74#63445C2214yes—
75#63441C2212yes—
76#63437C2212yes—
77#63436C2211yescharacteristic
78C4×D36C2212yes—
79C42×D9C2212yes—
80C42×D9C2211yescharacteristic
81C4×Dic18C2212yes—
82C4×Dic18C2211yescharacteristic
83C4×Dic18C2211yescharacteristic
84C3×#554D311yescharacteristic
85#5725—31no—
86#5722—31no—
87#5691—32no—
88#5690—32no—
89#5643—32no—
90#5640—34no—
91#5633—32no—
92#5631—34no—
93#5585—31no—
94C4×D3×Q8—31no—
95#5559—32no—
96#5557—31no—
97#5553—31no—
98#5548—32no—
99#5507—32no—
100#5504—32no—
101C2×Q8×C9C2311yescharacteristic
102C2×Q8×C9C2312yes—
103C2×D4×C9C2311yescharacteristic
104C22×C4×C9C2312yes—
105C22×C4×C9C2314yes—
106C2×#611C2314yes—
107C2×#611C2312yes—
108C2×#611C2314yes—
109#3701—44no—
110Q8×D9—24no—
111#3697—28no—
112#3697—48no—
113C2×D36C2312yes—
114C2×D36C2312yes—
115C2×D36C2314yes—
116C2×D36C2312yes—
117C2×C4×D9C2311yescharacteristic
118C2×C4×D9C2311yescharacteristic
119C2×C4×D9C2311yescharacteristic
120C2×C4×D9C2312yes—
121C2×C4×D9C2312yes—
122C2×C4×D9C2314yes—
123C2×C4×D9C2314yes—
124C2×C4×D9C2314yes—
125C2×Dic18C2311yescharacteristic
126C2×Dic18C2312yes—
127C2×Dic18C2314yes—
128C2×Dic18C2311yescharacteristic
129C9×C4⋊C4C2311yescharacteristic
130C9×C4⋊C4C2314yes—
131C9×C4⋊C4C2312yes—
132C9×C4⋊C4C2311yescharacteristic
133C9×C4⋊C4C2312yes—
134C9×C4⋊C4C2312yes—
135C9×C4⋊C4C2314yes—
136C9×C22⋊C4C2312yes—
137C9×C22⋊C4C2314yes—
138C42×C9C2312yes—
139C42×C9C2311yescharacteristic
140#3676C2312yes—
141#3676C2312yes—
142#3676C2312yes—
143(C2×D9)⋊C4C2314yes—
144(C2×D9)⋊C4C2314yes—
145(C2×D9)⋊C4C2312yes—
146(C2×D9)⋊C4C2314yes—
147(C2×D9)⋊C4C2314yes—
148(C2×D9)⋊C4C2314yes—
149(C2×D9)⋊C4C2314yes—
150C4⋊Dic9C2312yes—
151C4⋊Dic9C2312yes—
152C4⋊Dic9C2311yescharacteristic
153C4⋊Dic9C2311yescharacteristic
154C4⋊Dic9C2312yes—
155Dic9⋊C4C2312yes—
156Dic9⋊C4C2314yes—
157Dic9⋊C4C2312yes—
158Dic9⋊C4C2312yes—
159Dic9⋊C4C2314yes—
160Dic9⋊C4C2312yes—
161Dic9⋊C4C2312yes—
162C4×Dic9C2311yescharacteristic
163C4×Dic9C2312yes—
164C4×Dic9C2312yes—
165C4×Dic9C2314yes—
166C4×Dic9C2311yescharacteristic
167C4×Dic9C2312yes—
168C4×Dic9C2312yes—
169C4×Dic9C2311yescharacteristic
170#3522—91noSylow
171C2×#239—32no—
172C2×D3×Q8—31no—
173C2×#235—32no—
174C2×#235—34no—
175C3×C4⋊Q8C2×D311yescharacteristic
176C3×#125C2×D312yes—
177C3×C22⋊Q8C2×D312yes—
178C3×C22⋊Q8C2×D314yes—
179C3×C4×Q8C2×D311yescharacteristic
180C3×C4×D4C2×D312yes—
181C3×C4×D4C2×D311yescharacteristic
182C2×C3×C4⋊C4C2×D312yes—
183#947—32no—
184#947—32no—
185Q8×Dic3—31no—
186#944—34no—
187#940—32no—
188#938—31no—
189#936—31no—
190#930—32no—
191#929—34no—
192C4×#67—32no—
193C4×#67—34no—
194C4×#67—34no—
195#926—32no—
196#898—34no—
197#897—34no—
198#897—31no—
199#896—34no—
200#896—34no—
201#895—32no—
202#895—32no—
203#894—34no—
204#894—34no—
205#893—34no—
206#893—32no—
207#893—32no—
208#893—32no—
209#893—32no—
210#892—34no—
211D3×C4⋊C4—34no—
212D3×C4⋊C4—31no—
213D3×C4⋊C4—32no—
214#890—31no—
215#888—32no—
216#888—32no—
217#887—32no—
218#887—32no—
219#887—32no—
220#887—31no—
221#885—34no—
222#885—34no—
223#884—34no—
224#884—34no—
225#883—34no—
226#883—32no—
227#879—32no—
228#875—32no—
229#874—31no—
230C4×D12—32no—
231C42×D3—32no—
232C42×D3—31no—
233C4×Dic6—32no—
234C4×Dic6—31no—
235C4×Dic6—31no—
236C23×C9C2412yes—
237C22×D9C2414yes—
238C22×D9C2411yescharacteristic
239Q8×C9—22no—
240Q8×C9—42no—
241D4×C9—22no—
242C2×C4×C9—24no—
243C2×C4×C9—44no—
244C2×C4×C9C2411yescharacteristic
245C2×C4×C9C2412yes—
246C2×C4×C9C2414yes—
247C2×C4×C9C2412yes—
248C2×C4×C9C2412yes—
249C2×C4×C9C2411yescharacteristic
250C2×C4×C9C2411yescharacteristic
251#611—24no—
252#611—28no—
253#611—44no—
254C2×Dic9C2411yescharacteristic
255C2×Dic9C2412yes—
256C2×Dic9C2412yes—
257C2×Dic9C2411yescharacteristic
258C2×Dic9C2411yescharacteristic
259C2×Dic9C2412yes—
260C2×Dic9C2412yes—
261D36—28no—
262D36—24no—
263D36—24no—
264D36—42no—
265C4×D9—24no—
266C4×D9—22no—
267C4×D9—22no—
268C4×D9—22no—
269C4×D9—28no—
270C4×D9—24no—
271C4×D9—44no—
272C4×D9—44no—
273Dic18—22no—
274Dic18—24no—
275Dic18—44no—
276Dic18#4114yescomplemented
277#559—91no—
278#559—92no—
279Q82—91no—
280#554—92no—
281#554D911yescharacteristic, complemented
282#550—91no—
283#548—92no—
284#547—94no—
285#547—92no—
286#542—94no—
287#542—92no—
288#532—91no—
289#532—92no—
290#529—92no—
291#529—91no—
292#520—92no—
293C2×C4×Q8—91no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D312yes—
296C2×C3×D4C22×D311yescharacteristic
297C22×C3×C4C22×D312yes—
298C22×C3×C4C22×D314yes—
299C2×#67—32no—
300C2×#67—34no—
301C2×#67—34no—
302#239—124no—
303D3×Q8—64no—
304#235—68no—
305#235—128no—
306C2×D12—32no—
307C2×D12—32no—
308C2×D12—34no—
309C2×D12—32no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—32no—
313C2×C4×D3—32no—
314C2×C4×D3—31no—
315C2×C4×D3—34no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—32no—
321C2×Dic6—34no—
322C3×C4⋊C4C22×D312yes—
323C3×C4⋊C4C22×D312yes—
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D312yes—
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D314yes—
328C3×C4⋊C4C22×D314yes—
329C3×C22⋊C4C22×D312yes—
330C3×C22⋊C4C22×D314yes—
331C3×C42C22×D311yescharacteristic
332C3×C42C22×D312yes—
333#217—32no—
334#217—32no—
335#217—32no—
336(C2×D3)⋊C4—34no—
337(C2×D3)⋊C4—34no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—32no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—34no—
342(C2×D3)⋊C4—34no—
343C4⋊Dic3—31no—
344C4⋊Dic3—32no—
345C4⋊Dic3—31no—
346C4⋊Dic3—32no—
347C4⋊Dic3—32no—
348Dic3⋊C4—32no—
349Dic3⋊C4—32no—
350Dic3⋊C4—32no—
351Dic3⋊C4—32no—
352Dic3⋊C4—32no—
353Dic3⋊C4—34no—
354Dic3⋊C4—34no—
355C4×Dic3—32no—
356C4×Dic3—31no—
357C4×Dic3—32no—
358C4×Dic3—31no—
359C4×Dic3—32no—
360C4×Dic3—32no—
361C4×Dic3—31no—
362C4×Dic3—34no—
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×D9H(5,𝔽2)12yes—
373C4×C9—22no—
374C4×C9—22no—
375C4×C9—24no—
376C4×C9—22no—
377C4×C9—21no—
378C4×C9C2×#4112yes—
379C4×C92−1+412yes—
380Dic9—21no—
381Dic9—22no—
382Dic9—22no—
383Dic9—21no—
384Dic9—22no—
385Dic9—21no—
386Dic9C2×#4114yes—
387C2×#41—92no—
388C2×#41—92no—
389C2×#41—94no—
390C22×Q8—91no—
391C4⋊Q8—94no—
392C4⋊Q8—92no—
393C4⋊Q8—92no—
394C4⋊Q8C2×D911yescharacteristic
395#127—92no—
396#127—91no—
397#126—94no—
398#126—92no—
399#125—91no—
400#125C2×D912yes—
401#124—92no—
402#124—92no—
403#124—91no—
404#124—94no—
405#124—94no—
406#124—92no—
407#123—94no—
408#123—94no—
409#123—94no—
410#123—92no—
411#123—94no—
412C22⋊Q8—91no—
413C22⋊Q8—94no—
414C22⋊Q8—94no—
415C22⋊Q8—94no—
416C22⋊Q8C2×D914yes—
417C22⋊Q8C2×D912yes—
418#121—91no—
419#121—92no—
420#121—92no—
421#121—92no—
422#121—94no—
423#121—94no—
424C4×Q8—91no—
425C4×Q8—91no—
426C4×Q8—92no—
427C4×Q8—92no—
428C4×Q8—92no—
429C4×Q8—91no—
430C4×Q8—92no—
431C4×Q8—91no—
432C4×Q8C2×D911yescharacteristic
433C4×D4—94no—
434C4×D4—94no—
435C4×D4—92no—
436C4×D4—92no—
437C4×D4—92no—
438C4×D4—94no—
439C4×D4—92no—
440C4×D4—92no—
441C4×D4—92no—
442C4×D4C2×D911yescharacteristic
443C4×D4C2×D912yes—
444#117—92no—
445#117—94no—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—94no—
449C2×C4⋊C4C2×D912yes—
450C2×C42—91no—
451C2×C42—92no—
452C23×C3C23×D312yes—
453C22×D3—31no—
454C22×D3—34no—
455C3×Q8—22no—
456C3×Q8—42no—
457C3×D4—22no—
458C2×C3×C4—24no—
459C2×C3×C4—44no—
460C2×C3×C4C23×D311yescharacteristic
461C2×C3×C4C23×D312yes—
462C2×C3×C4C23×D314yes—
463C2×C3×C4C23×D312yes—
464C2×C3×C4C23×D312yes—
465C2×C3×C4C23×D311yescharacteristic
466C2×C3×C4C23×D311yescharacteristic
467#67—68no—
468#67—64no—
469#67—124no—
470C2×Dic3—32no—
471C2×Dic3—31no—
472C2×Dic3—32no—
473C2×Dic3—32no—
474C2×Dic3—31no—
475C2×Dic3—31no—
476C2×Dic3—32no—
477D12—68no—
478D12—64no—
479D12—64no—
480D12—122no—
481C4×D3—68no—
482C4×D3—64no—
483C4×D3—64no—
484C4×D3—62no—
485C4×D3—62no—
486C4×D3—62no—
487C4×D3—124no—
488C4×D3—124no—
489Dic6—34no—
490Dic6—64no—
491Dic6—62no—
492Dic6—124no—
493C2×C9—42no—
494C2×C9C22×#4111yescharacteristic
495C2×C9C2×H(5,𝔽2)11yescharacteristic
496C2×C9C2×2−1+411yescharacteristic
497D9—22no—
498D9—44no—
499#41—188no—
500#41—368no—
501#41—364no—
502C2×Q8—91no—
503C2×Q8—91no—
504C2×Q8—92no—
505C2×Q8—94no—
506C2×Q8—184no—
507C2×Q8C22×D911yescharacteristic
508C2×Q8C22×D912yes—
509C2×D4—94no—
510C2×D4—92no—
511C2×D4—94no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—94no—
515C2×D4—92no—
516C2×D4C22×D911yescharacteristic
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—92no—
520C22×C4—92no—
521C22×C4—91no—
522C22×C4—94no—
523C22×C4—94no—
524C22×C4—94no—
525C22×C4C22×D912yes—
526C22×C4C22×D914yes—
527C4⋊C4—92no—
528C4⋊C4—92no—
529C4⋊C4—94no—
530C4⋊C4—92no—
531C4⋊C4—91no—
532C4⋊C4—92no—
533C4⋊C4—92no—
534C4⋊C4—92no—
535C4⋊C4—91no—
536C4⋊C4—92no—
537C4⋊C4—94no—
538C4⋊C4—92no—
539C4⋊C4C22×D911yescharacteristic
540C4⋊C4C22×D914yes—
541C4⋊C4C22×D912yes—
542C4⋊C4C22×D912yes—
543C4⋊C4C22×D911yescharacteristic
544C4⋊C4C22×D912yes—
545C4⋊C4C22×D914yes—
546C22⋊C4—92no—
547C22⋊C4—92no—
548C22⋊C4—92no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—92no—
552C22⋊C4—94no—
553C22⋊C4—94no—
554C22⋊C4—94no—
555C22⋊C4—94no—
556C22⋊C4C22×D912yes—
557C22⋊C4C22×D914yes—
558C42—92no—
559C42—91no—
560C42—91no—
561C42—92no—
562C42—91no—
563C42—92no—
564C42—94no—
565C42—92no—
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×C4#100712yes—
584C3×C4D3×#4112yes—
585Dic3—34no—
586Dic3—62no—
587Dic3—61no—
588Dic3—61no—
589Dic3—62no—
590Dic3—62no—
591Dic3—61no—
592C9#352211yescharacteristic, complemented, Sylow
593C23—91no—
594C23—94no—
595C23C23×D912yes—
596Q8—22no—
597Q8—42no—
598Q8—94no—
599Q8—184no—
600Q8—182no—
601Q8—364no—
602D4—22no—
603D4—188no—
604D4—188no—
605D4—184no—
606D4—184no—
607D4—184no—
608D4—362no—
609D4—364no—
610C2×C4—24no—
611C2×C4—44no—
612C2×C4—92no—
613C2×C4—91no—
614C2×C4—92no—
615C2×C4—91no—
616C2×C4—91no—
617C2×C4—92no—
618C2×C4—92no—
619C2×C4—184no—
620C2×C4—188no—
621C2×C4—184no—
622C2×C4—182no—
623C2×C4—182no—
624C2×C4—182no—
625C2×C4—364no—
626C2×C4—364no—
627C2×C4C23×D912yes—
628C2×C4C23×D912yes—
629C2×C4C23×D911yescharacteristic
630C2×C4C23×D914yes—
631C2×C4C23×D912yes—
632C2×C4C23×D911yescharacteristic
633C2×C4C23×D911yescharacteristic
634C2×C3—42no—
635C2×C3C2×#100711yescharacteristic
636C2×C3C2×D3×#4111yescharacteristic
637C2×C3D3×H(5,𝔽2)11yescharacteristic
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—22no—
652C4—22no—
653C4—24no—
654C4—21no—
655C4—94no—
656C4—181no—
657C4—182no—
658C4—181no—
659C4—181no—
660C4—182no—
661C4—182no—
662C4#6371312yes—
663C4#41×D912yes—
664C3#8693611yescharacteristic
665C2—42no—
666C2—182no—
667C2—364no—
668C2C2×#6371311yescharacteristic
669C2C2×#41×D911yescharacteristic
670C2D9×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC22C24×D9
commutator, cosocleC22×C9C25
Frattini, socleC22×C3C24×D3
FittingC9×#554C2
hypercenter#554D9
hypocenterC9#3522
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C9×#554C2semidirect
2. #10589827C2semidirect
3. #10589824C2semidirect
4. #10589793C2semidirect
5. #10589792C2semidirect
6. #10589745C2semidirect
7. #10589742C2semidirect
8. #10589735C2semidirect
9. #10589733C2semidirect
10. #10589687C2semidirect
11. C4×Q8×D9C2semidirect
12. #10589661C2semidirect
13. #10589659C2semidirect
14. #10589655C2semidirect
15. #10589650C2semidirect
16. #10589609C2semidirect
17. #10589606C2semidirect
276. Dic18#41semidirect
281. #554D9semidirect
592. C9#3522semidirect

Maximal subgroups

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

subgroupindex
C9×#5542
#105898272
#105898242
#105897932
#105897922
#105897452
#105897422
#105897352
#105897332
#105896872
C4×Q8×D92
#105896612
#105896592
#105896552
#105896502
#105896092
#105896062
#869363