Finite Group Databasebeta

← #11887595

Subgroups — #11887595

Order 1152.

582 conjugacy classes of subgroups.

The subgroup lattice has 531 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#611C211yesmaximal, characteristic
2#10589613C211yesmaximal, characteristic
3C2×C9×#103C211yesmaximal, characteristic, complemented
4#10588907C211yesmaximal, characteristic, complemented
5C8×#611C211yesmaximal, characteristic
6#10588788C211yesmaximal, characteristic, complemented
7#10588646C211yesmaximal, characteristic, complemented
8#10588493C211yesmaximal, characteristic, complemented
9#10588491C211yesmaximal, characteristic, complemented
10#10588489C211yesmaximal, characteristic, complemented
11D9×#103C211yesmaximal, characteristic, complemented
12#10588475C211yesmaximal, characteristic, complemented
13#10588473C211yesmaximal, characteristic, complemented
14#10588472C211yesmaximal, characteristic, complemented
15#10588470C211yesmaximal, characteristic, complemented
16#78806—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C2×Q8×D9C2211yescharacteristic
19C22×C8×C9C2211yescharacteristic
20C2×C9×C4⋊C4C2211yescharacteristic
21#63508—21no—
22#63508C2211yescharacteristic
23Q8×Dic9C2211yescharacteristic
24#63506—21no—
25#63506C2211yescharacteristic
26C2×#3674C2211yescharacteristic
27C2×#3674C2211yescharacteristic
28C4×#611—21no—
29C4×#611—21no—
30C4×#611C2211yescharacteristic
31#63486—21no—
32#63486—21no—
33#63486C2211yescharacteristic
34#63486C2211yescharacteristic
35C2×C8×D9C2211yescharacteristic
36C2×Dic36C2211yescharacteristic
37#63459C2211yescharacteristic
38#63458—21no—
39C4⋊C4×D9C2211yescharacteristic
40#63451—21no—
41#63450C2211yescharacteristic
42#63449C2211yescharacteristic
43C9×#103C2211yescharacteristic
44C9×#103C2211yescharacteristic
45C9×#103C2211yescharacteristic
46C9×#103C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63389C2211yescharacteristic
50(C2×D9)⋊C8C2211yescharacteristic
51#63378C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54Dic9⋊C8C2211yescharacteristic
55C8×Dic9C2211yescharacteristic
56#63368C2211yescharacteristic
57#63368C2211yescharacteristic
58#63366C2211yescharacteristic
59#63366C2211yescharacteristic
60Q8×#67—31no—
61#5511—31no—
62C2×C3×#103D311yescharacteristic
63#5228—31no—
64#5116—31no—
65C8×#67—31no—
66#4970—31no—
67#4813—31no—
68#4811—31no—
69#4809—31no—
70D3×#103—31no—
71#4795—31no—
72#4793—31no—
73#4792—31no—
74#4790—31no—
75C2×Q8×C9—21no—
76C2×Q8×C9—22no—
77C2×Q8×C9—41no—
78C2×Q8×C9C2311yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C22×C4×C9—21no—
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×#611D411yescharacteristic
84Q8×D9—22no—
85Q8×D9—41no—
86C2×C4×D9—21no—
87C2×C4×D9—21no—
88C2×C4×D9C2311yescharacteristic
89C2×Dic18—21no—
90C2×Dic18—21no—
91C2×Dic18C2311yescharacteristic
92C2×Dic18C2311yescharacteristic
93C2×C8×C9—41no—
94C2×C8×C9C2311yescharacteristic
95C2×C8×C9C2311yescharacteristic
96C9×C4⋊C4—21no—
97C9×C4⋊C4C2311yescharacteristic
98C9×C4⋊C4C2311yescharacteristic
99#3676—21no—
100#3676—21no—
101#3676D411yescharacteristic
102#3674—22no—
103#3674—41no—
104(C2×D9)⋊C4—21no—
105(C2×D9)⋊C4—21no—
106(C2×D9)⋊C4D411yescharacteristic
107C4⋊Dic9—21no—
108C4⋊Dic9—21no—
109C4⋊Dic9C2311yescharacteristic
110C4⋊Dic9C2311yescharacteristic
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4—21no—
115Dic9⋊C4—21no—
116Dic9⋊C4—21no—
117Dic9⋊C4—21no—
118Dic9⋊C4—21no—
119Dic9⋊C4D411yescharacteristic
120C4×Dic9—21no—
121C4×Dic9—21no—
122C4×Dic9C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124C2×C9⋊C8C2311yescharacteristic
125C8×D9—41no—
126Dic36—41no—
127#3299—91noSylow
128C22×C3×Q8C2×D311yescharacteristic
129C2×D3×Q8—31no—
130C22×C3×C8C2×D311yescharacteristic
131C2×C3×C4⋊C4C2×D311yescharacteristic
132#946—31no—
133#946—61no—
134Q8×Dic3—31no—
135#944—31no—
136#944—61no—
137C2×#216—31no—
138C2×#216—31no—
139C4×#67—31no—
140C4×#67—61no—
141C4×#67—61no—
142#924—31no—
143#924—31no—
144#924—61no—
145#924—61no—
146C2×Dic12—31no—
147C2×D3×C8—31no—
148#897—31no—
149#896—61no—
150D3×C4⋊C4—31no—
151#889—61no—
152#888—31no—
153#887—31no—
154C3×#103C2×D311yescharacteristic
155C3×#103C2×D311yescharacteristic
156C3×#103C2×D311yescharacteristic
157C3×#103C2×D311yescharacteristic
158#835—31no—
159#835—31no—
160#830—31no—
161(C2×D3)⋊C8—31no—
162#818—31no—
163#816—31no—
164#816—31no—
165Dic3⋊C8—31no—
166C8×Dic3—31no—
167#810—31no—
168#810—31no—
169#807—31no—
170#807—31no—
171C23×C9C2×D411yescharacteristic
172C22×D9C2×D411yescharacteristic
173Q8×C9—21no—
174Q8×C9—21no—
175Q8×C9—21no—
176Q8×C9—42no—
177Q8×C9#4112yes—
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—42no—
185C2×C4×C9—81no—
186C2×C4×C9C2×D411yescharacteristic
187C2×C4×C9C2411yescharacteristic
188#611Q1614yescomplemented
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
193C2×Dic9C2×D411yescharacteristic
194C2×Dic9C2×D411yescharacteristic
195C2×Dic9C2×D411yescharacteristic
196C4×D9—21no—
197C4×D9—21no—
198C4×D9—42no—
199C4×D9—81no—
200Dic18—21no—
201Dic18—21no—
202Dic18—21no—
203Dic18—21no—
204Dic18—42no—
205Dic18—81no—
206C8×C9—21no—
207C8×C9—21no—
208C9⋊C8—21no—
209C9⋊C8—21no—
210#554—91no—
211D4×Q8—91no—
212#487—91no—
213#484—91no—
214#484—91no—
215#477—91no—
216#467—91no—
217#467—91no—
218#462—91no—
219#451—91no—
220#451—91no—
221C4×Q16—91no—
222C8×D4—91no—
223C2×#103—91no—
224C2×#103D911yescharacteristic, complemented
225C2×C3×Q8—21no—
226C2×C3×Q8—22no—
227C2×C3×Q8—41no—
228C2×C3×Q8C22×D311yescharacteristic
229C2×C3×Q8C22×D311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4C22×D311yescharacteristic
233C2×#67—31no—
234D3×Q8—62no—
235D3×Q8—121no—
236C2×C4×D3—31no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×Dic6—31no—
240C2×Dic6—31no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×C3×C8—41no—
244C2×C3×C8C22×D311yescharacteristic
245C2×C3×C8C22×D311yescharacteristic
246C3×C4⋊C4—21no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249#217—31no—
250#217—61no—
251#217—61no—
252#216—62no—
253#216—121no—
254(C2×D3)⋊C4—31no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—61no—
260C4⋊Dic3—61no—
261Dic3⋊C4—31no—
262Dic3⋊C4—61no—
263Dic3⋊C4—61no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—61no—
267Dic3⋊C4—61no—
268Dic3⋊C4—61no—
269Dic3⋊C4—61no—
270C4×Dic3—31no—
271C4×Dic3—61no—
272C4×Dic3—61no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275Dic12—121no—
276D3×C8—121no—
277C22×C9—21no—
278C22×C9—21no—
279C22×C9C2×Q1612yes—
280C22×C9C22×D411yescharacteristic
281C2×D9—21no—
282C2×D9—21no—
283C2×D9C2×Q1612yes—
284C4×C9—22no—
285C4×C9—21no—
286C4×C9—41no—
287C4×C9—41no—
288C4×C9—41no—
289C4×C9C2×#4111yescharacteristic
290C4×C9H(5,𝔽2)11yescharacteristic
291Dic9—21no—
292Dic9—21no—
293Dic9—41no—
294Dic9—41no—
295Dic9—41no—
296Dic9—41no—
297Dic9C2×Q1612yes—
298C22×Q8—91no—
299C22×Q8C2×D911yescharacteristic
300C2×Q16—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C22×C8—91no—
304C22×C8C2×D911yescharacteristic
305C4⋊Q8—91no—
306C4⋊Q8—91no—
307C4⋊Q8—181no—
308#125—181no—
309C22⋊Q8—91no—
310C22⋊Q8—91no—
311C22⋊Q8—91no—
312C22⋊Q8—91no—
313C22⋊Q8—181no—
314C22⋊Q8—181no—
315C22⋊Q8—181no—
316C22⋊Q8—181no—
317C4×Q8—91no—
318C4×Q8—91no—
319C4×D4—91no—
320C4×D4—181no—
321C4×D4—181no—
322C2×C4⋊C4—91no—
323C2×C4⋊C4C2×D911yescharacteristic
324#107—91no—
325#107—91no—
326#107—91no—
327C4⋊C8—91no—
328#103—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103C2×D911yescharacteristic
335#103C2×D911yescharacteristic
336#103C2×D911yescharacteristic
337#103C2×D911yescharacteristic
338C22⋊C8—91no—
339C22⋊C8—91no—
340C4×C8—91no—
341C23×C3D3×D411yescharacteristic
342C22×D3—31no—
343C3×Q8—21no—
344C3×Q8—21no—
345C3×Q8—21no—
346C3×Q8—42no—
347C3×Q8#23512yes—
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—42no—
355C2×C3×C4—81no—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—34no—
359C2×Dic3—31no—
360C2×Dic3—31no—
361C2×Dic3—31no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C4×D3—61no—
367C4×D3—61no—
368C4×D3—122no—
369C4×D3—241no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—61no—
374Dic6—122no—
375Dic6—241no—
376C3×C8—21no—
377C3×C8—21no—
378C3⋊C8—61no—
379C3⋊C8—61no—
380C2×C9—22no—
381C2×C9#54611yescharacteristic
382C2×C9C22×Q1611yescharacteristic
383C2×C9#57711yescharacteristic
384D9—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—41no—
388C2×Q8—91no—
389C2×Q8—91no—
390C2×Q8—181no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—361no—
394C2×Q8C22×D911yescharacteristic
395C2×Q8C22×D911yescharacteristic
396C2×D4—91no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—91no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C22×D911yescharacteristic
403Q16—182no—
404Q16—361no—
405Q16—361no—
406C2×C8—41no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—361no—
410C2×C8C22×D911yescharacteristic
411C2×C8C22×D911yescharacteristic
412C4⋊C4—21no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4C22×D911yescharacteristic
427C4⋊C4C22×D911yescharacteristic
428C22⋊C4—91no—
429C22⋊C4—91no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C22⋊C4—181no—
434C42—91no—
435C42—181no—
436C42—181no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3D3×Q1612yes—
440C22×C3C2×D3×D411yescharacteristic
441C2×D3—32no—
442C2×D3—61no—
443C2×D3—61no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—41no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4C2×#23511yescharacteristic
450C3×C4#100411yescharacteristic
451Dic3—32no—
452Dic3—61no—
453Dic3—61no—
454Dic3—121no—
455Dic3—121no—
456Dic3—121no—
457Dic3—121no—
458C9#329911yescharacteristic, complemented, Sylow
459C23—91no—
460C23D4×D911yescharacteristic
461Q8—21no—
462Q8—21no—
463Q8—21no—
464Q8—42no—
465Q8—181no—
466Q8—181no—
467Q8—181no—
468Q8—181no—
469Q8—362no—
470Q8—721no—
471Q8#369712yes—
472D4—94no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—91no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—362no—
491C2×C4—721no—
492C2×C4D4×D911yescharacteristic
493C2×C4C23×D911yescharacteristic
494C8—21no—
495C8—21no—
496C8—181no—
497C8—181no—
498C2×C3—22no—
499C2×C3#549011yescharacteristic
500C2×C3#576211yescharacteristic
501C2×C3C2×D3×Q1611yescharacteristic
502D3—62no—
503C22—21no—
504C22—21no—
505C22—92no—
506C22—181no—
507C22—181no—
508C22Q16×D912yes—
509C22C2×D4×D911yescharacteristic
510C4—21no—
511C4—22no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—92no—
516C4—181no—
517C4—181no—
518C4—361no—
519C4—361no—
520C4—361no—
521C4—361no—
522C4C2×#369711yescharacteristic
523C4#6371011yescharacteristic
524C3#7880611yescharacteristic
525C2—22no—
526C2—182no—
527C2#1058959211yescharacteristic
528C2#1058986411yescharacteristic
529C2C2×Q16×D911yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC2×C9×#103C2
socleC22×C3C2×D3×D4
prime radicalC2×#611D4
hypercenterC2×#103D9
hypocenterC9#3299
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. C2×C9×#103C2semidirect
4. #10588907C2semidirect
6. #10588788C2semidirect
7. #10588646C2semidirect
8. #10588493C2semidirect
9. #10588491C2semidirect
10. #10588489C2semidirect
11. D9×#103C2semidirect
12. #10588475C2semidirect
13. #10588473C2semidirect
14. #10588472C2semidirect
15. #10588470C2semidirect
188. #611Q16semidirect
224. C2×#103D9semidirect
458. C9#3299semidirect

Maximal subgroups

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

subgroupindex
Q8×#6112
#105896132
C2×C9×#1032
#105889072
C8×#6112
#105887882
#105886462
#105884932
#105884912
#105884892
D9×#1032
#105884752
#105884732
#105884722
#105884702
#788063