Finite Group Databasebeta

← #11860787

Subgroups — #11860787

Order 1152.

794 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#64227C211yesmaximal, characteristic
2#10594606C211yesmaximal, characteristic
3#10594347C211yesmaximal, characteristic, complemented
4#10593748C211yesmaximal, characteristic, complemented
5#10593433C212yesmaximal, complemented
6#10593432C212yesmaximal, complemented
7#10593431C212yesmaximal, complemented
8C4×#3775C212yesmaximal, complemented
9#10593389C211yesmaximal, characteristic, complemented
10#10593374C211yesmaximal, characteristic, complemented
11#10593363C211yesmaximal, characteristic
12C2×#3802C2211yescharacteristic
13C2×#3797C2211yescharacteristic
14C2×#3788C2211yescharacteristic
15C2×#3787C2211yescharacteristic
16C2×#3775C2212yes—
17C2×#3775C2212yes—
18#64227C418yescomplemented
19#64101C2211yescharacteristic
20C3×#893—21no—
21C3×#887—21no—
22D3×(C2×D3)⋊C4—22no—
23C4×#627C2212yescomplemented
24#63902C2212yes—
25C4×#625C2212yes—
26Dic3×D12—21no—
27#63874C2211yescharacteristic
28#63874C2211yescharacteristic
29Dic3×Dic6—21no—
30#63838C2212yescomplemented
31#63836—22no—
32#63777C2212yescomplemented
33C4×#622C2212yescomplemented
34#63743C2211yescharacteristic, complemented
35#63743C2211yescharacteristic, complemented
36#63742C2211yescharacteristic, complemented
37#63742C2211yescharacteristic, complemented
38#63740C2212yescomplemented
39#63740C2212yescomplemented
40#63739C2212yes—
41#63739C2212yes—
42#5572—61no—
43#5545—61no—
44C22×D32—21no—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C3×D12—21no—
47C2×C3×C4×D3—22no—
48C2×C3×Dic6—21no—
49C2×#627C2312yes—
50C2×#625C2312yes—
51C2×#624—21no—
52C2×D3×Dic3—22no—
53#3802—22no—
54#3802C2×C414yes—
55#3797—22no—
56#3797C2×C414yescomplemented
57C2×#622C2312yes—
58C2×#622C2311yescharacteristic
59C2×#622C2311yescharacteristic
60#3788—22no—
61#3787C2×C414yescomplemented
62#3775C2×C418yescomplemented
63#3775C2×C418yescomplemented
64C32×C4⋊C4D411yescharacteristic
65#3752D412yes—
66C4⋊(C3⋊Dic3)D411yescharacteristic
67C4×C3⋊Dic3C2312yes—
68C3×(C2×D3)⋊C4—22no—
69C3×Dic3⋊C4—22no—
70C3×C4×Dic3—22no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73#3724C2311yescharacteristic
74#3724C2311yescharacteristic
75#3724C2311yescharacteristic
76#3724C2311yescharacteristic
77Dic3⋊Dic3—22no—
78#3722—21no—
79#3722—21no—
80(C2×D3)⋊Dic3—22no—
81Dic32—22no—
82#2949—91nomaximal, Sylow
83C2×D3×Q8—61no—
84C2×D3×D4—61no—
85C3×C4×Q8—61no—
86C3×C4×D4—61no—
87Q8×Dic3—61no—
88D4×Dic3—61no—
89C4×#67—62no—
90C2×(C2×D3)⋊C4—62no—
91#893—21no—
92#892—61no—
93#892—61no—
94#892—62no—
95#887—21no—
96#887—62no—
97#67⋊C4—62no—
98D3×C22⋊C4—62no—
99C4×D12—61no—
100#872—61no—
101#872—61no—
102#872—62no—
103C4×Dic6—62no—
104C4×Dic6—61no—
105C22×C3⋊D3C2×D411yescharacteristic
106C22×C3×D3—22no—
107C2×D32—24no—
108C2×D32—81no—
109C2×D32—81no—
110C2×C32×C4C2×D412yes—
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3C2×D412yes—
113C2×C3⋊Dic3C2411yescharacteristic
114C4×C3⋊D3C22×C412yes—
115C4×C3⋊D3#4112yes—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—21no—
118C2×C3×Dic3—21no—
119C2×C3×Dic3—21no—
120C2×C3×Dic3—21no—
121C3×D12—24no—
122C3×C4×D3—82no—
123C3×Dic6—24no—
124#627—22no—
125#627C22×C414yes—
126#625—22no—
127#625C22×C414yes—
128#624—24no—
129D3×Dic3—82no—
130#622—22no—
131#622C22×C412yes—
132#622C22×C412yes—
133C22×SD16—91no—
134#519—91no—
135#518—91no—
136#440—92no—
137#440—92no—
138C4×SD16—92no—
139C4×SD16—92no—
140#427—91no—
141#419—91no—
142#418—91no—
143#405—91no—
144C23×D3—62no—
145C2×C3×Q8—61no—
146C2×C3×D4—61no—
147C22×C3×C4—62no—
148C2×#67—62no—
149C22×Dic3—62no—
150D3×Q8—64no—
151D3×Q8—64no—
152D3×D4—64no—
153D3×D4—64no—
154C2×D12—21no—
155C2×C4×D3—22no—
156C2×C4×D3—61no—
157C2×C4×D3—61no—
158C2×C4×D3—62no—
159C2×C4×D3—62no—
160C2×Dic6—21no—
161C2×Dic6—62no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—62no—
165C3×C22⋊C4—62no—
166C3×C42—61no—
167C3×C42—62no—
168C3×C42—61no—
169#217—62no—
170(C2×D3)⋊C4—22no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—62no—
173(C2×D3)⋊C4—61no—
174(C2×D3)⋊C4—61no—
175(C2×D3)⋊C4—61no—
176(C2×D3)⋊C4—61no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—61no—
179C4⋊Dic3—61no—
180C4⋊Dic3—62no—
181Dic3⋊C4—22no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—62no—
187C4×Dic3—22no—
188C4×Dic3—21no—
189C4×Dic3—21no—
190C4×Dic3—62no—
191C4×Dic3—62no—
192C4×Dic3—62no—
193C4×Dic3—62no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3C4×D412yes—
198C2×C3×D3—24no—
199C2×C3×D3—42no—
200C2×C3×D3—42no—
201D32—84no—
202C32×C4—22no—
203C32×C4C4×D412yes—
204C3⋊Dic3—22no—
205C3⋊Dic3C23×C411yescharacteristic
206C3⋊Dic3C2×#4111yescharacteristic
207C3×Dic3—24no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C3×Dic3—41no—
211C3×Dic3—41no—
212C22×Q8—91no—
213C22×D4—91no—
214C2×SD16—92no—
215C2×SD16—92no—
216C2×SD16—98no—
217C2×M16—91no—
218C22×C8—91no—
219C4×Q8—61no—
220C4×Q8—92no—
221C4×Q8—92no—
222C4×Q8—181no—
223C4×D4—61no—
224C4×D4—92no—
225C4×D4—92no—
226C4×D4—181no—
227#117—91no—
228#117—91no—
229#117—91no—
230#117—182no—
231C2×C22⋊C4—182no—
232#107—91no—
233#107—91no—
234#106—91no—
235#106—91no—
236#103—92no—
237#103—92no—
238#102—92no—
239#102—92no—
240#97—92no—
241C4×C8—92no—
242C23×C3—62no—
243C22×D3—22no—
244C22×D3—61no—
245C22×D3—61no—
246C22×D3—68no—
247C22×D3—242no—
248C22×D3—242no—
249C3×Q8—64no—
250C3×D4—64no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—62no—
256C2×C3×C4—61no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—242no—
261#67—64no—
262#67—64no—
263C2×Dic3—22no—
264C2×Dic3—21no—
265C2×Dic3—21no—
266C2×Dic3—21no—
267C2×Dic3—21no—
268C2×Dic3—61no—
269C2×Dic3—61no—
270C2×Dic3—62no—
271C2×Dic3—62no—
272C2×Dic3—242no—
273D12—24no—
274C4×D3—62no—
275C4×D3—62no—
276C4×D3—62no—
277C4×D3—62no—
278C4×D3—68no—
279C4×D3—82no—
280C4×D3—242no—
281Dic6—24no—
282Dic6—64no—
283Dic6—64no—
284C2×C32C2×C4×D411yescharacteristic
285C2×C32#57711yescharacteristic
286C2×C32#57711yescharacteristic
287C3⋊D3—22no—
288C3×D3—44no—
289C24—181no—
290C2×Q8—61no—
291C2×Q8—92no—
292C2×Q8—94no—
293C2×Q8—182no—
294C2×D4—61no—
295C2×D4—94no—
296C2×D4—92no—
297C2×D4—182no—
298C22×C4—62no—
299C22×C4—91no—
300C22×C4—181no—
301C22×C4—182no—
302SD16—98no—
303SD16—98no—
304M16—182no—
305C2×C8—91no—
306C2×C8—91no—
307C2×C8—94no—
308C2×C8—92no—
309C4⋊C4—62no—
310C4⋊C4—91no—
311C4⋊C4—91no—
312C4⋊C4—91no—
313C4⋊C4—91no—
314C4⋊C4—91no—
315C4⋊C4—182no—
316C4⋊C4GO+(4,𝔽2)11yescharacteristic
317C22⋊C4—62no—
318C22⋊C4—92no—
319C22⋊C4—181no—
320C22⋊C4—181no—
321C22⋊C4—182no—
322C42—61no—
323C42—61no—
324C42—62no—
325C42—92no—
326C42—182no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—64no—
330C22×C3—122no—
331C22×C3—122no—
332C2×D3—24no—
333C2×D3—42no—
334C2×D3—42no—
335C2×D3—62no—
336C2×D3—62no—
337C2×D3—121no—
338C2×D3—121no—
339C2×D3—121no—
340C2×D3—121no—
341C2×D3—248no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—42no—
345C3×C4—42no—
346C3×C4—64no—
347C3×C4—121no—
348C3×C4—121no—
349C3×C4—121no—
350C3×C4—121no—
351Dic3—24no—
352Dic3—41no—
353Dic3—41no—
354Dic3—41no—
355Dic3—41no—
356Dic3—61no—
357Dic3—61no—
358Dic3—61no—
359Dic3—61no—
360Dic3—122no—
361Dic3—122no—
362C32#294911yescharacteristic, complemented, Sylow
363C23—62no—
364C23—91no—
365C23—184no—
366C23—721no—
367C23—721no—
368Q8—64no—
369Q8—94no—
370Q8—182no—
371D4—64no—
372D4—94no—
373D4—182no—
374C2×C4—62no—
375C2×C4—61no—
376C2×C4—61no—
377C2×C4—61no—
378C2×C4—61no—
379C2×C4—91no—
380C2×C4—92no—
381C2×C4—92no—
382C2×C4—92no—
383C2×C4—184no—
384C2×C4—242no—
385C2×C4—722no—
386C2×C4C2×GO+(4,𝔽2)12yes—
387C2×C4C2×GO+(4,𝔽2)11yescharacteristic
388C8—92no—
389C8—92no—
390C8—182no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—21no—
394C2×C3—21no—
395C2×C3—21no—
396C2×C3—21no—
397C2×C3—124no—
398D3—44no—
399D3—122no—
400D3—122no—
401C22—64no—
402C22—92no—
403C22—122no—
404C22—122no—
405C22—181no—
406C22—181no—
407C22—724no—
408C22C22×GO+(4,𝔽2)11yescharacteristic
409C4—22no—
410C4—64no—
411C4—91no—
412C4—91no—
413C4—121no—
414C4—121no—
415C4—121no—
416C4—121no—
417C4—182no—
418C4C4×GO+(4,𝔽2)12yes—
419C3—21no—
420C3—21no—
421C2—124no—
422C2—182no—
423C2C2×C4×GO+(4,𝔽2)11yescharacteristic
424C2#1059651511yescharacteristic
425C2#1059652111yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#3802C22
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2949
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #10594347C2semidirect
4. #10593748C2semidirect
5. #10593433C2semidirect
6. #10593432C2semidirect
7. #10593431C2semidirect
8. C4×#3775C2semidirect
9. #10593389C2semidirect
10. #10593374C2semidirect
18. #64227C4semidirect
23. C4×#627C22semidirect
30. #63838C22semidirect
32. #63777C22semidirect
33. C4×#622C22semidirect
34. #63743C22semidirect
35. #63743C22semidirect
36. #63742C22semidirect
37. #63742C22semidirect
38. #63740C22semidirect
39. #63740C22semidirect
56. #3797C2×C4semidirect
61. #3787C2×C4semidirect
62. #3775C2×C4semidirect
63. #3775C2×C4semidirect
362. C32#2949semidirect

Maximal subgroups

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

subgroupindex
C2×#642272
#105946062
#105943472
#105937482
#105934332
#105934322
#105934312
C4×#37752
#105933892
#105933742
#105933632
#29499