Finite Group Databasebeta

← #11860977

Subgroups — #11860977

Order 1152.

1101 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1101 conjugacy classes of subgroups — too many to draw. Only its 232 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×#64121C211yesmaximal, characteristic
2#10595219C212yesmaximal, complemented
3C3×#5152C212yesmaximal, complemented
4#10591418C212yesmaximal, complemented
5#10591401C214yesmaximal, complemented
6#10590810C212yesmaximal, complemented
7#10590703C211yesmaximal, characteristic, complemented
8#10590685C211yesmaximal, characteristic, complemented
9#79868—32nomaximal
10C2×#3830C2212yes—
11C2×C32×D8C2211yescharacteristic
12C2×#3754C2212yes—
13#64121C418yescomplemented
14C2×#3746C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C3×D4×Dic3C2214yes—
17C2×#3724—22no—
18#63957—22no—
19#63952—24no—
20#63900C2212yes—
21#63874C2211yescharacteristic
22#63844C2214yes—
23C2×#3712C2211yescharacteristic
24C3×#832C2214yes—
25C3×#817C2212yes—
26C3×#815C2212yes—
27#63574C2212yes—
28#63567C2214yes—
29Dic3×C3⋊C8C2212yes—
30C2×#912—32no—
31C2×#912—61no—
32#5546—34no—
33C3×#442—32no—
34#5152D312yescomplemented
35C4×#214—34no—
36D3×#106—32no—
37#4853—32no—
38#4771—34no—
39#4758—34no—
40#4716—32no—
41#4708—32no—
42C2×C32×D4C2312yes—
43C2×#638—22no—
44C22×C3⋊Dic3—22no—
45#3830—24no—
46#3830C2×C418yescomplemented
47C2×C4×C3⋊D3C2311yescharacteristic
48C2×#634C2312yes—
49C22×C3×Dic3—24no—
50C2×#624—22no—
51C32×D8C2×C414yescomplemented
52C2×C32×C8C2311yescharacteristic
53#3754C2×C418yescomplemented
54C2×C3⋊(C3⋊C8)C2311yescharacteristic
55#3746C2×C414yescomplemented
56C8×C3⋊D3C2×C414yescomplemented
57C3×#217—24no—
58C3×C4⋊Dic3C2314yes—
59C3×C4×Dic3C2312yes—
60C2×C3×C3⋊C8C2312yes—
61#3724—22no—
62#3724—24no—
63#3724D412yes—
64#3722D412yes—
65Dic32—24no—
66#3712—22no—
67#2952—91noSylow
68C2×#237—34no—
69C2×#237—62no—
70C2×C3×D8—21no—
71C2×C3×D8C2×D312yes—
72C3×C4×D4—34no—
73D4×Dic3C2×D314yes—
74C2×#214—34no—
75C2×#214—62no—
76C4×#67—64no—
77C2×Dic3⋊C4—64no—
78#912—316no—
79#912—68no—
80C2×Dic12—32no—
81C2×Dic12—61no—
82C2×ΓL(1,𝔽25)—32no—
83C2×D3×C8—32no—
84C2×D3×C8—61no—
85D3×C4⋊C4—34no—
86#887—34no—
87#67⋊C4—64no—
88#877—64no—
89#872—32no—
90C4×Dic6—34no—
91C3×#106—32no—
92C3×#102—34no—
93C3×#97—32no—
94#832C2×D314yes—
95#817C2×D312yes—
96#816—34no—
97#815C2×D312yes—
98C8×Dic3—32no—
99#810—34no—
100#808—34no—
101C4×C3⋊C8—32no—
102C23×C32—22no—
103C22×C3⋊D3C2×D411yescharacteristic
104C32×D4—22no—
105C32×D4C22×C414yes—
106C2×C32×C4C2411yescharacteristic
107#638—28no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—28no—
110C2×C3⋊Dic3C2×D411yescharacteristic
111C4×C3⋊D3C22×C412yes—
112C4×C3⋊D3#4112yes—
113#634—22no—
114#634C22×C414yes—
115C2×C3×Dic3—24no—
116C2×C3×Dic3—84no—
117C2×C3×Dic3C2×D414yes—
118#624—82no—
119C32×C8C22×C412yes—
120C3⋊(C3⋊C8)C22×C412yes—
121C3×C3⋊C8—22no—
122C2×#135—91no—
123#520—92no—
124#442—32no—
125#441—92no—
126C4×SD16—94no—
127C2×#106—91no—
128#417—92no—
129#405—91no—
130C2×C3×D4—22no—
131C2×C3×D4C22×D314yes—
132C22×C3×C4—64no—
133C2×#67—64no—
134C2×#67—122no—
135C22×Dic3—24no—
136C22×Dic3—64no—
137C22×Dic3—122no—
138#237—316no—
139#237—68no—
140#237—68no—
141#237—124no—
142C2×C4×D3—32no—
143C2×C4×D3—61no—
144C2×C4×D3—64no—
145C2×Dic6—34no—
146C2×Dic6—62no—
147C3×D8—24no—
148C3×D8C4×D318yescomplemented
149C2×C3×C8—21no—
150C2×C3×C8—32no—
151C2×C3×C8C22×D312yes—
152C3×C4⋊C4—34no—
153C3×C22⋊C4—64no—
154C3×C42—32no—
155#217—24no—
156#214—316no—
157#214—68no—
158(C2×D3)⋊C4—34no—
159C4⋊Dic3C22×D314yes—
160Dic3⋊C4—34no—
161Dic3⋊C4—64no—
162Dic3⋊C4—64no—
163Dic3⋊C4—64no—
164C4×Dic3—64no—
165C4×Dic3—64no—
166C4×Dic3C22×D312yes—
167C2×C3⋊C8—32no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8C22×D312yes—
170Dic12—38no—
171Dic12—64no—
172ΓL(1,𝔽25)—64no—
173D3×C8—38no—
174D3×C8—64no—
175C22×C32—24no—
176C22×C32—42no—
177C22×C32—42no—
178C22×C32C22×D411yescharacteristic
179C2×C3⋊D3—22no—
180C2×C3⋊D3C4×D412yes—
181C32×C4C23×C411yescharacteristic
182C32×C4C2×#4111yescharacteristic
183C3⋊Dic3—24no—
184C3⋊Dic3C4×D412yes—
185C3×Dic3—24no—
186C3×Dic3—44no—
187C2×#41—92no—
188#135—98no—
189C2×Q16—91no—
190C2×SD16—92no—
191C2×D8D3211yescharacteristic
192C2×M16—91no—
193C22×C8—91no—
194C4×Q8—94no—
195C4×D4—34no—
196C4×D4—184no—
197#117—91no—
198#117—182no—
199C2×C4⋊C4—92no—
200C2×C4⋊C4—182no—
201#106—32no—
202#106—92no—
203#103—94no—
204#102—34no—
205#97—32no—
206C4×C8—92no—
207C23×C3—24no—
208C23×C3—42no—
209C22×D3—32no—
210C22×D3—61no—
211C3×D4—24no—
212C3×D4—24no—
213C3×D4—42no—
214C3×D4C2×C4×D318yes—
215C2×C3×C4—21no—
216C2×C3×C4—34no—
217C2×C3×C4—64no—
218C2×C3×C4—244no—
219C2×C3×C4C23×D312yes—
220#67—616no—
221#67—128no—
222C2×Dic3—24no—
223C2×Dic3—32no—
224C2×Dic3—61no—
225C2×Dic3—616no—
226C2×Dic3—64no—
227C2×Dic3—84no—
228C2×Dic3—128no—
229C2×Dic3—122no—
230C2×Dic3D3×D414yes—
231C4×D3—34no—
232C4×D3—34no—
233C4×D3—62no—
234C4×D3—62no—
235C4×D3—244no—
236Dic6—38no—
237Dic6—64no—
238Dic6—64no—
239Dic6—122no—
240C3×C8—22no—
241C3×C8—62no—
242C3×C8C2×C4×D314yes—
243C3⋊C8—22no—
244C3⋊C8—34no—
245C3⋊C8—62no—
246C2×C32—44no—
247C2×C32C2×C4×D411yescharacteristic
248C2×C32#57712yes—
249C3⋊D3—22no—
250#41—98no—
251#41—184no—
252C2×Q8—92no—
253C2×D4—182no—
254C2×D4C2×D3212yes—
255C22×C4—64no—
256C22×C4—91no—
257C22×C4—182no—
258C22×C4—182no—
259Q16—94no—
260SD16—98no—
261D8#62414yescomplemented
262M16—182no—
263C2×C8—32no—
264C2×C8—91no—
265C2×C8—94no—
266C2×C8C2×D3211yescharacteristic
267C4⋊C4—34no—
268C4⋊C4—92no—
269C4⋊C4—184no—
270C4⋊C4—182no—
271C22⋊C4—64no—
272C22⋊C4—92no—
273C42—32no—
274C42—184no—
275C22×C3—28no—
276C22×C3—21no—
277C22×C3—44no—
278C22×C3—44no—
279C22×C3—44no—
280C22×C3—82no—
281C22×C3—82no—
282C22×C3C2×D3×D412yes—
283C2×D3—34no—
284C2×D3—62no—
285C2×D3—64no—
286C2×D3—122no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—64no—
290C3×C4—124no—
291C3×C4C22×C4×D312yes—
292C3×C4D3×#4112yes—
293Dic3—24no—
294Dic3—34no—
295Dic3—44no—
296Dic3—62no—
297Dic3—68no—
298Dic3—124no—
299C32#295211yescharacteristic, complemented, Sylow
300C23—22no—
301C23—91no—
302Q8—94no—
303Q8—182no—
304D4—22no—
305D4—188no—
306D4C2×#62414yes—
307C2×C4—34no—
308C2×C4—64no—
309C2×C4—91no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—188no—
313C2×C4—182no—
314C2×C4—244no—
315C2×C4—722no—
316C2×C4C22×D3211yescharacteristic
317C8—62no—
318C8—92no—
319C8C2×#62412yes—
320C2×C3—21no—
321C2×C3—22no—
322C2×C3—48no—
323C2×C3—84no—
324C2×C3C4×D3×D412yes—
325C2×C3#577514yes—
326D3—64no—
327D3—122no—
328C22—24no—
329C22—42no—
330C22—42no—
331C22—92no—
332C22—182no—
333C22D32×D411yescharacteristic
334C4—64no—
335C4—92no—
336C4—124no—
337C4—184no—
338C4#6431211yescharacteristic
339C4C22×#62411yescharacteristic
340C3—21no—
341C3#7986812yescomplemented
342C2—44no—
343C2—182no—
344C2#1059473312yes—
345C2D4×#62411yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC2×#64121C2
cosocleC2×C32×C4C24
hypercenterC2×D8D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #10595219C2semidirect
3. C3×#5152C2semidirect
4. #10591418C2semidirect
5. #10591401C2semidirect
6. #10590810C2semidirect
7. #10590703C2semidirect
8. #10590685C2semidirect
13. #64121C4semidirect
34. #5152D3semidirect
46. #3830C2×C4semidirect
51. C32×D8C2×C4semidirect
53. #3754C2×C4semidirect
55. #3746C2×C4semidirect
56. C8×C3⋊D3C2×C4semidirect
148. C3×D8C4×D3semidirect
261. D8#624semidirect
299. C32#2952semidirect
341. C3#79868semidirect

Maximal subgroups

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

subgroupindex
C2×#641212
#105952192
C3×#51522
#105914182
#105914012
#105908102
#105907032
#105906852
#798683