Finite Group Databasebeta

← #11887172

Subgroups — #11887172

Order 1152.

790 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 790 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595274C211yesmaximal, characteristic, complemented
2D4×#625C211yesmaximal, characteristic
3D4×#622C211yesmaximal, characteristic, complemented
4#10593526C212yesmaximal, complemented
5#10593523C212yesmaximal, complemented
6#10593497C212yesmaximal, complemented
7C2×#63739C212yesmaximal, complemented
8#10593439C211yesmaximal, characteristic, complemented
9C4×#3775C211yesmaximal, characteristic, complemented
10#10593366C211yesmaximal, characteristic, complemented
11#10593359C211yesmaximal, characteristic, complemented
12C2×C3×D3×D4—21no—
13C22×#625C2212yes—
14C22×#622C2212yescomplemented
15C2×#3775C2211yescharacteristic
16C2×#3775C2212yescomplemented
17D4×C3⋊Dic3C2211yescharacteristic
18C3×D4×Dic3—21no—
19#63982C2212yescomplemented
20#63980C2212yes—
21#63976—22no—
22C2×#3724C2212yescomplemented
23#63964—22no—
24#63919C2211yescharacteristic, complemented
25C4×#627C2211yescharacteristic, complemented
26#63914C2211yescharacteristic
27#63908—21no—
28C4×#625C2211yescharacteristic
29#63869—21no—
30C22⋊#622C2212yescomplemented
31C4⋊#622C2211yescharacteristic, complemented
32C4×#622C2211yescharacteristic, complemented
33#63742C2212yescomplemented
34#63742C2211yescharacteristic, complemented
35#63740C2211yescharacteristic, complemented
36#63739C2212yes—
37#63739C2211yescharacteristic
38#63739C2212yescomplemented
39#63739C2212yescomplemented
40#63739C2212yescomplemented
41D4×#67—61no—
42#5539—61no—
43C23×C3×D3—22no—
44C2×C32×D4D411yescharacteristic
45C22×C3⋊Dic3C2312yes—
46C2×C3×#67—22no—
47C22×C3×Dic3—22no—
48C3×D3×D4—44no—
49C2×C3×D12—21no—
50C2×C3×C4×D3—21no—
51C2×#627—21no—
52C2×#627C2311yescharacteristic
53C2×#625—24no—
54C2×#625—22no—
55C2×#625—21no—
56C2×#625—42no—
57C2×#625C2312yes—
58C2×#625C2311yescharacteristic
59C2×#622—42no—
60C2×#622C2311yescharacteristic
61C2×#622C2311yescharacteristic
62C2×#622C2312yes—
63#3775—22no—
64#3775—42no—
65#3757D412yes—
66C4⋊(C3⋊Dic3)D411yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68C3×#217—22no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71#3724—22no—
72#3724C2311yescharacteristic
73#3724C2311yescharacteristic
74#3724C2312yes—
75Dic3⋊Dic3—22no—
76Dic3⋊Dic3—21no—
77(C2×D3)⋊Dic3—21no—
78(C2×D3)⋊Dic3—22no—
79#3295—91nomaximal, Sylow
80C22×C3×D4—61no—
81C22×#67—62no—
82C2×D3×D4—21no—
83C3×C4×D4—61no—
84#953—62no—
85#940—61no—
86#939—62no—
87#938—61no—
88#937—62no—
89D4×Dic3—21no—
90D4×Dic3—61no—
91D4×Dic3—61no—
92#930—61no—
93C4×#67—61no—
94#924—62no—
95C2×Dic3⋊C4—62no—
96#890—61no—
97#888—61no—
98#878—62no—
99#878—62no—
100#870—61no—
101C4×Dic6—61no—
102C23×C32C2×D412yes—
103C22×C3×D3—21no—
104C22×C3×D3—22no—
105C22×C3×D3—44no—
106C22×C3×D3—44no—
107C22×C3×D3—82no—
108C32×D4SD1614yescomplemented
109C2×C32×C4C2×D411yescharacteristic
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2×D411yescharacteristic
114C2×C3⋊Dic3C2411yescharacteristic
115C3×#67—44no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—22no—
120C2×C3×Dic3—82no—
121C3×D12—42no—
122C3×C4×D3—42no—
123#627—21no—
124#627—21no—
125#627—81no—
126#625—21no—
127#625—22no—
128#625—22no—
129#625—44no—
130#625—81no—
131#625#4112yes—
132#622—21no—
133#622—22no—
134#622—21no—
135#554—91no—
136D42—91no—
137#486—91no—
138#481—92no—
139#476—91no—
140#465—92no—
141#460—91no—
142#450—92no—
143C4×SD16—91no—
144C8×D4—91no—
145C2×#102—92no—
146C24×C3—62no—
147C23×D3—22no—
148C2×C3×D4—21no—
149C2×C3×D4—21no—
150C2×C3×D4—61no—
151C2×C3×D4—62no—
152C2×C3×D4—124no—
153C22×C3×C4—61no—
154C22×C3×C4—62no—
155C2×#67—22no—
156C2×#67—61no—
157C2×#67—62no—
158C2×#67—62no—
159C2×#67—62no—
160C2×#67—62no—
161C2×#67—124no—
162C2×#67—124no—
163C22×Dic3—22no—
164C22×Dic3—62no—
165C22×Dic3—62no—
166D3×D4—44no—
167C2×D12—21no—
168C2×C4×D3—21no—
169C2×Dic6—61no—
170C2×Dic6—62no—
171C3×C4⋊C4—61no—
172C3×C22⋊C4—62no—
173C3×C42—61no—
174#217—22no—
175#217—62no—
176#217—62no—
177#217—61no—
178#217—62no—
179(C2×D3)⋊C4—61no—
180(C2×D3)⋊C4—62no—
181C4⋊Dic3—21no—
182C4⋊Dic3—61no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185C4⋊Dic3—62no—
186Dic3⋊C4—61no—
187Dic3⋊C4—62no—
188Dic3⋊C4—61no—
189Dic3⋊C4—61no—
190Dic3⋊C4—62no—
191Dic3⋊C4—62no—
192Dic3⋊C4—62no—
193C4×Dic3—21no—
194C4×Dic3—61no—
195C4×Dic3—61no—
196C22×C32—22no—
197C22×C32—22no—
198C22×C32C2×SD1614yes—
199C22×C32C22×D411yescharacteristic
200C2×C3×D3—22no—
201C2×C3×D3—41no—
202C2×C3×D3—41no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C2×C3×D3—42no—
206C2×C3×D3—88no—
207C32×C4C2×SD1612yes—
208C3⋊Dic3—22no—
209C3⋊Dic3—21no—
210C3⋊Dic3C2×#4111yescharacteristic
211C3⋊Dic3H(5,𝔽2)11yescharacteristic
212C3×Dic3—41no—
213C3×Dic3—41no—
214C3×Dic3—42no—
215C3×Dic3—41no—
216C22×D4—61no—
217C22×D4—92no—
218C2×SD16—91no—
219C2×SD16—92no—
220C22×C8—92no—
221C4⋊Q8—91no—
222#127—91no—
223#125—181no—
224C22⋊Q8—92no—
225C22⋊Q8—182no—
226#121—92no—
227#121—181no—
228#120—182no—
229C4×Q8—91no—
230C4×D4—61no—
231C4×D4—91no—
232C4×D4—91no—
233C2×C4⋊C4—92no—
234#106—91no—
235#106—92no—
236C4⋊C8—91no—
237#103—91no—
238#102—91no—
239#102—92no—
240#102—92no—
241#102—92no—
242#102—92no—
243C22⋊C8—92no—
244C4×C8—91no—
245C23×C3—22no—
246C23×C3—22no—
247C23×C3—61no—
248C23×C3—62no—
249C23×C3—124no—
250C23×C3—124no—
251C23×C3—242no—
252C22×D3—21no—
253C22×D3—22no—
254C22×D3—44no—
255C22×D3—44no—
256C22×D3—82no—
257C3×D4—24no—
258C3×D4—24no—
259C3×D4—122no—
260C3×D4—124no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—62no—
266C2×C3×C4—61no—
267C2×C3×C4—122no—
268C2×C3×C4—242no—
269#67—44no—
270#67—62no—
271#67—62no—
272#67—122no—
273#67—122no—
274#67—124no—
275#67—124no—
276#67—242no—
277C2×Dic3—21no—
278C2×Dic3—21no—
279C2×Dic3—22no—
280C2×Dic3—21no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—82no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3—122no—
291C2×Dic3—122no—
292D12—42no—
293C4×D3—42no—
294Dic6—121no—
295Dic6—121no—
296Dic6—242no—
297C2×C32—24no—
298C2×C32#54611yescharacteristic
299C2×C32C22×SD1611yescharacteristic
300C2×C32#57611yescharacteristic
301C3×D3—42no—
302C3×D3—82no—
303C24—62no—
304C2×Q8—91no—
305C2×Q8—181no—
306C2×D4—62no—
307C2×D4—61no—
308C2×D4—91no—
309C2×D4—92no—
310C2×D4—124no—
311C2×D4—182no—
312C2×D4—181no—
313C2×D4—184no—
314C2×D4—362no—
315C2×D4GO+(4,𝔽2)11yescharacteristic
316C22×C4—62no—
317C22×C4—61no—
318C22×C4—92no—
319SD16—182no—
320SD16—362no—
321C2×C8—91no—
322C2×C8—91no—
323C2×C8—92no—
324C2×C8—362no—
325C4⋊C4—61no—
326C4⋊C4—91no—
327C4⋊C4—92no—
328C4⋊C4—91no—
329C4⋊C4—91no—
330C4⋊C4—182no—
331C4⋊C4—181no—
332C4⋊C4—182no—
333C22⋊C4—62no—
334C22⋊C4—92no—
335C22⋊C4—181no—
336C22⋊C4—182no—
337C42—61no—
338C42—91no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—24no—
342C22×C3—24no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—62no—
348C22×C3—121no—
349C22×C3—121no—
350C22×C3—122no—
351C22×C3—122no—
352C22×C3—122no—
353C22×C3—248no—
354C2×D3—22no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—42no—
358C2×D3—42no—
359C2×D3—42no—
360C2×D3—88no—
361C3×C4—22no—
362C3×C4—22no—
363C3×C4—121no—
364C3×C4—122no—
365C3×C4—121no—
366C3×C4—121no—
367Dic3—41no—
368Dic3—42no—
369Dic3—41no—
370Dic3—41no—
371Dic3—61no—
372Dic3—61no—
373Dic3—61no—
374Dic3—61no—
375Dic3—121no—
376Dic3—122no—
377Dic3—122no—
378Dic3—121no—
379C32#329511yescharacteristic, complemented, Sylow
380C23—61no—
381C23—62no—
382C23—124no—
383C23—124no—
384C23—242no—
385C23C2×GO+(4,𝔽2)12yes—
386Q8—181no—
387Q8—181no—
388Q8—721no—
389D4—92no—
390D4—124no—
391D4—122no—
392D4—181no—
393D4—182no—
394D4—182no—
395D4—364no—
396D4—721no—
397D4#377514yescomplemented
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—62no—
401C2×C4—61no—
402C2×C4—91no—
403C2×C4—91no—
404C2×C4—92no—
405C2×C4—122no—
406C2×C4—182no—
407C2×C4—182no—
408C2×C4—242no—
409C2×C4C2×GO+(4,𝔽2)11yescharacteristic
410C8—181no—
411C8—182no—
412C8—181no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—44no—
420C2×C3—44no—
421C2×C3—122no—
422C2×C3—242no—
423D3—42no—
424D3—82no—
425C22—22no—
426C22—22no—
427C22—62no—
428C22—121no—
429C22—121no—
430C22—122no—
431C22—122no—
432C22—122no—
433C22—248no—
434C22C2×#377514yes—
435C22C22×GO+(4,𝔽2)11yescharacteristic
436C4—91no—
437C4—91no—
438C4—121no—
439C4—122no—
440C4—121no—
441C4—121no—
442C4—181no—
443C4—182no—
444C4C2×#377512yes—
445C3—21no—
446C3—21no—
447C2—24no—
448C2—122no—
449C2—242no—
450C2#1059651411yescharacteristic
451C2#1059651811yescharacteristic
452C2C22×#377511yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C24
FittingC2×C32×D4D4
socleC22×C32C22×D4
prime radicalD4×#625C2
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#3295
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #10595274C2semidirect
3. D4×#622C2semidirect
4. #10593526C2semidirect
5. #10593523C2semidirect
6. #10593497C2semidirect
7. C2×#63739C2semidirect
8. #10593439C2semidirect
9. C4×#3775C2semidirect
10. #10593366C2semidirect
11. #10593359C2semidirect
14. C22×#622C22semidirect
16. C2×#3775C22semidirect
19. #63982C22semidirect
22. C2×#3724C22semidirect
24. #63919C22semidirect
25. C4×#627C22semidirect
30. C22⋊#622C22semidirect
31. C4⋊#622C22semidirect
32. C4×#622C22semidirect
33. #63742C22semidirect
34. #63742C22semidirect
35. #63740C22semidirect
38. #63739C22semidirect
39. #63739C22semidirect
40. #63739C22semidirect
108. C32×D4SD16semidirect
379. C32#3295semidirect
397. D4#3775semidirect

Maximal subgroups

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

subgroupindex
#105952742
D4×#6252
D4×#6222
#105935262
#105935232
#105934972
C2×#637392
#105934392
C4×#37752
#105933662
#105933592
#32959