Finite Group Databasebeta

← #11889788

Subgroups — #11889788

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#552C211yesmaximal, characteristic, complemented
2#10589653C211yesmaximal, characteristic
3#10588747C211yesmaximal, characteristic, complemented
4#10588746C211yesmaximal, characteristic, complemented
5#10588730C211yesmaximal, characteristic, complemented
6#10588730C211yesmaximal, characteristic, complemented
7#10588728C211yesmaximal, characteristic, complemented
8#10588727C211yesmaximal, characteristic, complemented
9#10588709C211yesmaximal, characteristic, complemented
10#10588707C211yesmaximal, characteristic, complemented
11#10588688C211yesmaximal, characteristic, complemented
12#10588683C211yesmaximal, characteristic, complemented
13#10588680C211yesmaximal, characteristic, complemented
14#10588649C211yesmaximal, characteristic, complemented
15#10588646C211yesmaximal, characteristic, complemented
16#83600—31nomaximal
17C2×#3697C2211yescharacteristic
18C2×#3697C2211yescharacteristic
19C9×#126—21no—
20C9×#125—21no—
21C9×#125C2211yescharacteristic
22C9×#123—21no—
23C9×C22⋊Q8C2211yescharacteristic
24C9×C22⋊Q8C2211yescharacteristic
25C4×Q8×C9C2211yescharacteristic
26C4×D4×C9C2211yescharacteristic
27C9×#117—21no—
28C9×#117C2211yescharacteristic
29C2×C9×C4⋊C4C2211yescharacteristic
30C2×#3675C2211yescharacteristic
31C2×#3674C2211yescharacteristic
32C2×#3674C2211yescharacteristic
33#63500—21no—
34#63486C2211yescharacteristic
35#63486C2211yescharacteristic
36C2×#3667C2211yescharacteristic
37C22×C9⋊C8C2211yescharacteristic
38C4⋊C4×D9—21no—
39#63445—21no—
40#63445—21no—
41C4×D36C2211yescharacteristic
42#63431C2211yescharacteristic
43#63395C2211yescharacteristic
44#63389C2211yescharacteristic
45#63389C2211yescharacteristic
46#63369C2211yescharacteristic
47#63369C2211yescharacteristic
48#63369C2211yescharacteristic
49#63368C2211yescharacteristic
50#63368C2211yescharacteristic
51#63368C2211yescharacteristic
52#63368C2211yescharacteristic
53#63368C2211yescharacteristic
54#63368C2211yescharacteristic
55#63367C2211yescharacteristic
56#63366C2211yescharacteristic
57#63366C2211yescharacteristic
58C4⋊(C9⋊C8)C2211yescharacteristic
59#63362C2211yescharacteristic
60C3×#552D311yescharacteristic
61#5551—31no—
62#5069—31no—
63#5066—31no—
64#5052—31no—
65#5051—31no—
66#5047—31no—
67#5047—31no—
68#5031—31no—
69#5026—31no—
70#5011—31no—
71#5002—31no—
72#4996—31no—
73#4970—31no—
74#4966—31no—
75C2×Q8×C9C2311yescharacteristic
76C2×D4×C9D411yescharacteristic
77C22×C4×C9—21no—
78C22×C4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C2×#611—21no—
81C2×#611—21no—
82#3697—22no—
83#3697—22no—
84#3697—41no—
85#3697—41no—
86C2×D36C2311yescharacteristic
87C2×C4×D9—21no—
88C2×C4×D9—21no—
89C2×C4×D9—21no—
90C2×Dic18C2311yescharacteristic
91C2×Dic18C2311yescharacteristic
92C9×C4⋊C4—21no—
93C9×C4⋊C4—21no—
94C9×C4⋊C4—21no—
95C9×C4⋊C4—21no—
96C9×C4⋊C4—21no—
97C9×C4⋊C4—21no—
98C9×C4⋊C4D411yescharacteristic
99C9×C4⋊C4C2311yescharacteristic
100C9×C4⋊C4C2311yescharacteristic
101C9×C4⋊C4C2311yescharacteristic
102C9×C22⋊C4—21no—
103C9×C22⋊C4—21no—
104C9×C22⋊C4—21no—
105C9×C22⋊C4D411yescharacteristic
106C9×C22⋊C4D411yescharacteristic
107C42×C9—21no—
108C42×C9—21no—
109C42×C9C2311yescharacteristic
110#3676—21no—
111#3676—21no—
112#3675—22no—
113#3674—41no—
114#3674—41no—
115(C2×D9)⋊C4—21no—
116C4⋊Dic9—21no—
117C4⋊Dic9—21no—
118C4⋊Dic9C2311yescharacteristic
119Dic9⋊C4—21no—
120Dic9⋊C4—21no—
121#3667—41no—
122C2×C9⋊C8—41no—
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C2×C9⋊C8C2311yescharacteristic
126C2×C9⋊C8C2311yescharacteristic
127#3315—91noSylow
128C2×#235—31no—
129C2×#235—31no—
130C3×#126—21no—
131C3×#125—21no—
132C3×#125C2×D311yescharacteristic
133C3×#123—21no—
134C3×C22⋊Q8C2×D311yescharacteristic
135C3×C22⋊Q8C2×D311yescharacteristic
136C3×C4×Q8C2×D311yescharacteristic
137C3×C4×D4C2×D311yescharacteristic
138C3×#117—21no—
139C3×#117C2×D311yescharacteristic
140C2×C3×C4⋊C4C2×D311yescharacteristic
141C2×#216—31no—
142C2×#216—31no—
143C2×#215—31no—
144#938—61no—
145#924—31no—
146#924—31no—
147C2×#208—31no—
148C22×C3⋊C8—31no—
149D3×C4⋊C4—61no—
150#883—61no—
151#883—61no—
152C4×D12—31no—
153#869—31no—
154#835—31no—
155#830—31no—
156#830—31no—
157#810—31no—
158#810—31no—
159#810—31no—
160#810—31no—
161#810—31no—
162#810—31no—
163#809—31no—
164#809—31no—
165#809—31no—
166#808—31no—
167#807—31no—
168#807—31no—
169C4⋊(C3⋊C8)—31no—
170#803—31no—
171C23×C9C2×D411yescharacteristic
172C23×C9C2×D411yescharacteristic
173C22×D9—21no—
174Q8×C9—21no—
175Q8×C9—21no—
176D4×C9—41no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—42no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2×D411yescharacteristic
188C2×C4×C9C2×D411yescharacteristic
189C2×C4×C9C2×D411yescharacteristic
190C2×C4×C9C2411yescharacteristic
191#611—42no—
192#611—42no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196D36—21no—
197D36#4112yes—
198C4×D9—42no—
199C4×D9—42no—
200C4×D9—42no—
201Dic18—21no—
202Dic18—21no—
203Dic18—21no—
204Dic18—21no—
205C9⋊C8—21no—
206C9⋊C8—21no—
207C9⋊C8—21no—
208C9⋊C8—21no—
209#552D911yescharacteristic, complemented
210#547—91no—
211#491—91no—
212#485—91no—
213#484—91no—
214#478—91no—
215#470—91no—
216#467—91no—
217#462—91no—
218#452—91no—
219#452—91no—
220#440—91no—
221#435—91no—
222#417—91no—
223#416—91no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×D4#6711yescharacteristic
226C22×C3×C4—21no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—61no—
230C2×#67—61no—
231#235—62no—
232#235—62no—
233#235—121no—
234#235—121no—
235C2×D12—31no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×Dic6—31no—
240C2×Dic6—31no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4#6711yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C4⋊C4C22×D311yescharacteristic
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—21no—
254C3×C22⋊C4#6711yescharacteristic
255C3×C22⋊C4#6711yescharacteristic
256C3×C42—21no—
257C3×C42—21no—
258C3×C42C22×D311yescharacteristic
259#217—61no—
260#217—61no—
261#216—121no—
262#216—121no—
263#215—62no—
264(C2×D3)⋊C4—61no—
265C4⋊Dic3—31no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270#208—121no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—121no—
276C22×C9—21no—
277C22×C9—21no—
278C22×C9—21no—
279C22×C9—21no—
280C22×C9—21no—
281C22×C9—21no—
282C22×C9C22×D411yescharacteristic
283C2×D9—22no—
284C2×D9—41no—
285C2×D9—41no—
286C4×C9—21no—
287C4×C9—21no—
288C4×C9—21no—
289C4×C9—21no—
290C4×C9—41no—
291C4×C9—41no—
292C4×C9—41no—
293C4×C9—41no—
294C4×C9C2×#4111yescharacteristic
295C4×C9H(5,𝔽2)11yescharacteristic
296Dic9—41no—
297Dic9—41no—
298Dic9—41no—
299C2×#41—91no—
300C2×#41—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8—91no—
307#126—21no—
308#125—21no—
309#125C2×D911yescharacteristic
310#123—21no—
311#123—181no—
312#123—181no—
313C22⋊Q8—91no—
314C22⋊Q8—91no—
315C22⋊Q8C2×D911yescharacteristic
316C22⋊Q8C2×D911yescharacteristic
317#121—181no—
318C4×Q8C2×D911yescharacteristic
319C4×D4—91no—
320C4×D4C2×D911yescharacteristic
321#117—21no—
322#117C2×D911yescharacteristic
323C2×C4⋊C4—181no—
324C2×C4⋊C4C2×D911yescharacteristic
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341#97—91no—
342C23×C3C2×#6711yescharacteristic
343C23×C3C2×#6711yescharacteristic
344C22×D3—61no—
345C3×Q8—21no—
346C3×Q8—21no—
347C3×D4—41no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—42no—
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C2×#6711yescharacteristic
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362#67—122no—
363#67—122no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367D12—32no—
368D12—61no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—122no—
372Dic6—61no—
373Dic6—61no—
374Dic6—61no—
375Dic6—61no—
376C3⋊C8—61no—
377C3⋊C8—61no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C2×C9—41no—
381C2×C9—41no—
382C2×C9#54611yescharacteristic
383C2×C9#57511yescharacteristic
384C2×C9#57811yescharacteristic
385D9—42no—
386#41—182no—
387#41—182no—
388#41—361no—
389#41—361no—
390C2×Q8—91no—
391C2×Q8—91no—
392C2×Q8C22×D911yescharacteristic
393C2×D4—91no—
394C2×D4—181no—
395C2×D4—181no—
396C2×D4#61111yescharacteristic
397C22×C4—21no—
398C22×C4—181no—
399C22×C4—181no—
400C22×C4—181no—
401C22×C4C22×D911yescharacteristic
402C22×C4C22×D911yescharacteristic
403Q16—361no—
404Q16—361no—
405SD16—182no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—361no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—91no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4#61111yescharacteristic
424C4⋊C4C22×D911yescharacteristic
425C4⋊C4C22×D911yescharacteristic
426C4⋊C4C22×D911yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4#61111yescharacteristic
434C22⋊C4#61111yescharacteristic
435C42—21no—
436C42—21no—
437C42C22×D911yescharacteristic
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—21no—
444C22×C3C22×#6711yescharacteristic
445C2×D3—62no—
446C2×D3—121no—
447C2×D3—121no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4D3×#4111yescharacteristic
457C3×C4#100911yescharacteristic
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461C9#331511yescharacteristic, complemented, Sylow
462C23—181no—
463C23C2×#61111yescharacteristic
464C23C2×#61111yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—181no—
468Q8—181no—
469Q8—181no—
470Q8—181no—
471D4—41no—
472D4—92no—
473D4—181no—
474D4—362no—
475D4—362no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—42no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4C2×#61111yescharacteristic
492C2×C4C2×#61111yescharacteristic
493C2×C4C2×#61111yescharacteristic
494C2×C4C2×#61111yescharacteristic
495C2×C4C23×D911yescharacteristic
496C8—181no—
497C8—181no—
498C8—181no—
499C8—181no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3#582211yescharacteristic
503C2×C3#582911yescharacteristic
504C2×C3#583811yescharacteristic
505D3—122no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—182no—
513C22—361no—
514C22—361no—
515C22C22×#61111yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—361no—
525C4—361no—
526C4—361no—
527C4#41×D911yescharacteristic
528C4#6371511yescharacteristic
529C3#8360011yescharacteristic
530C2—41no—
531C2—41no—
532C2—362no—
533C2#1058992511yescharacteristic
534C2#1058993111yescharacteristic
535C2#1058994011yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#552C2
socleC22×C3C22×#67
prime radical#10589653C2
hypercenter#552D9
hypocenterC9#3315
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C9×#552C2semidirect
3. #10588747C2semidirect
4. #10588746C2semidirect
5. #10588730C2semidirect
6. #10588730C2semidirect
7. #10588728C2semidirect
8. #10588727C2semidirect
9. #10588709C2semidirect
10. #10588707C2semidirect
11. #10588688C2semidirect
12. #10588683C2semidirect
13. #10588680C2semidirect
14. #10588649C2semidirect
15. #10588646C2semidirect
209. #552D9semidirect
461. C9#3315semidirect

Maximal subgroups

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

subgroupindex
C9×#5522
#105896532
#105887472
#105887462
#105887302
#105887282
#105887272
#105887092
#105887072
#105886882
#105886832
#105886802
#105886492
#105886462
#836003