Finite Group Databasebeta

← #11780011

Subgroups — #11780011

Order 1152.

432 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5722C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic
3#10590384C211yesmaximal, characteristic
4#10590285C211yesmaximal, characteristic
5#10589412C211yesmaximal, characteristic
6#10589084C211yesmaximal, characteristic
7#10589084C211yesmaximal, characteristic
8#71941—31nomaximal
9#71239—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×#944—22no—
12C3×#888—21no—
13C3×#888—21no—
14C3×#887—21no—
15C3×#887—21no—
16C3×#869C2211yescharacteristic
17C3×C4×Dic6C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3718—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#835—22no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63574—21no—
25#63565—21no—
26#63565—21no—
27C3×Q82—31no—
28#5722D311yescharacteristic
29C3×#487—31no—
30#5094—31no—
31#5090—31no—
32#5079D311yescharacteristic
33#5031—31no—
34#5020—31no—
35#4546—31no—
36#4546—31no—
37#4546—61no—
38#4535—31no—
39#4535—31no—
40#4456—31no—
41#4456—31no—
42C2×C32×Q8D412yes—
43C2×C3×Dic6—21no—
44C2×C3×Dic6—22no—
45C2×C3×Dic6D411yescharacteristic
46C2×C3×Dic6D411yescharacteristic
47C32×C4⋊C4—21no—
48C32×C4⋊C4—21no—
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×Dic3⋊C4—22no—
57C3×Dic3⋊C4—22no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#3718—42no—
65#1645—91noSylow
66C3×C4⋊Q8—21no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—61no—
69C3×C4⋊Q8—61no—
70C3×C4⋊Q8—62no—
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×C4⋊Q8C2×D311yescharacteristic
73C3×C4×Q8—31no—
74C3×C4×Q8—31no—
75C3×C4×Q8—61no—
76C3×C4×Q8—61no—
77#944—22no—
78C2×#216—61no—
79C2×#216—61no—
80#888—21no—
81#888—21no—
82#887—21no—
83#887—21no—
84#869C2×D311yescharacteristic
85C4×Dic6C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#103—62no—
88C3×C4×C8—31no—
89#835—22no—
90#835—61no—
91#835—61no—
92#810—61no—
93#810—61no—
94#808—61no—
95#808—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C32×Q8—42no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3×Dic3—21no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×Dic6—21no—
114C3×Dic6—21no—
115C3×Dic6—41no—
116C3×Dic6—41no—
117C3×Dic6—82no—
118C3×Dic6SD1612yes—
119C3×Dic6Q1612yescomplemented
120C3⋊(C3⋊C8)—41no—
121C3⋊(C3⋊C8)—41no—
122C3×C3⋊C8—41no—
123Q82—31no—
124#487—31no—
125#475—91no—
126#462—91no—
127#333—91no—
128Q8⋊C8—91no—
129Q8⋊C8—91no—
130C2×C3×Q8—22no—
131C2×C3×Q8—31no—
132C2×C3×Q8—31no—
133C2×C3×Q8—62no—
134C2×C3×Q8—61no—
135C2×C3×Q8#6712yes—
136C2×C3×Q8#6712yes—
137C2×Dic6—21no—
138C2×Dic6—22no—
139C2×Dic6#6711yescharacteristic
140C2×Dic6#6711yescharacteristic
141C2×C3×C8—61no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—41no—
149C3×C4⋊C4—41no—
150C3×C4⋊C4—62no—
151C3×C4⋊C4—62no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C42—21no—
157C3×C42—62no—
158C3×C42—61no—
159C3×C42—61no—
160C3×C42C22×D311yescharacteristic
161C3×C42C22×D311yescharacteristic
162#216—122no—
163#216—122no—
164C4⋊Dic3—21no—
165C4⋊Dic3—21no—
166C4⋊Dic3#6711yescharacteristic
167C4⋊Dic3#6711yescharacteristic
168Dic3⋊C4—22no—
169Dic3⋊C4—22no—
170Dic3⋊C4—21no—
171Dic3⋊C4—21no—
172C4×Dic3—22no—
173C4×Dic3—21no—
174C4×Dic3—21no—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—121no—
181C2×C3⋊C8—121no—
182C22×C32#12011yescharacteristic
183C32×C4—21no—
184C32×C4—42no—
185C32×C4C2×SD1611yescharacteristic
186C32×C4C2×Q1611yescharacteristic
187C32×C4#13711yescharacteristic
188C32×C4#13711yescharacteristic
189C3×Dic3—22no—
190C3×Dic3—22no—
191C3×Dic3—41no—
192C3×Dic3—41no—
193C3×Dic3—81no—
194C2×Q16—181no—
195C4⋊Q8—31no—
196C4⋊Q8—61no—
197C4⋊Q8—61no—
198C4⋊Q8—62no—
199C4⋊Q8D3211yescharacteristic
200C4×Q8—31no—
201C4×Q8—31no—
202C4×Q8—61no—
203C4×Q8—61no—
204#106—181no—
205C4⋊C8—91no—
206C4⋊C8—91no—
207#103—62no—
208#103—181no—
209#103—181no—
210C4×C8—31no—
211C3×Q8—32no—
212C3×Q8—32no—
213C3×Q8—42no—
214C3×Q8—42no—
215C3×Q8—61no—
216C3×Q8—61no—
217C3×Q8—82no—
218C3×Q8—121no—
219C3×Q8—121no—
220C3×Q8—242no—
221C2×C3×C4—22no—
222C2×C3×C4—22no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—42no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—61no—
230C2×C3×C4—61no—
231C2×C3×C4—121no—
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—41no—
243Dic6—21no—
244Dic6—21no—
245Dic6—41no—
246Dic6—41no—
247Dic6—82no—
248Dic6#21512yes—
249Dic6#21612yescomplemented
250C3×C8—121no—
251C3⋊C8—41no—
252C3⋊C8—121no—
253C3⋊C8—121no—
254C3⋊C8—121no—
255C3⋊C8—121no—
256C3⋊C8—241no—
257C3⋊C8—241no—
258C2×C32#44811yescharacteristic
259C2×C32#45111yescharacteristic
260C2×C32#45511yescharacteristic
261C2×Q8—31no—
262C2×Q8—31no—
263C2×Q8—62no—
264C2×Q8—61no—
265C2×Q8#62512yes—
266Q16—362no—
267C2×C8—61no—
268C2×C8—181no—
269C2×C8—181no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C42—62no—
281C42—61no—
282C42—61no—
283C42C2×D3211yescharacteristic
284C22×C3—21no—
285C22×C3#93711yescharacteristic
286C22×C3#95311yescharacteristic
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4—42no—
296C3×C4—62no—
297C3×C4—62no—
298C3×C4—82no—
299C3×C4—121no—
300C3×C4—121no—
301C3×C4—241no—
302C3×C4D3×SD1611yescharacteristic
303C3×C4#91511yescharacteristic
304C3×C4D3×Q1611yescharacteristic
305C3×C4#91811yescharacteristic
306C3×C4C2×#21511yescharacteristic
307C3×C4#94211yescharacteristic
308C3×C4#94211yescharacteristic
309C3×C4C2×#21611yescharacteristic
310Dic3—22no—
311Dic3—22no—
312Dic3—41no—
313Dic3—41no—
314Dic3—81no—
315C32#164511yescharacteristic, complemented, Sylow
316Q8—32no—
317Q8—32no—
318Q8—42no—
319Q8—61no—
320Q8—61no—
321Q8—121no—
322Q8—121no—
323Q8—242no—
324C2×C4—22no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—121no—
330C2×C4C2×#62511yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C2×C4D3×#6711yescharacteristic
333C8—121no—
334C8—361no—
335C8—361no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3#506111yescharacteristic
340C2×C3#517011yescharacteristic
341C2×C3#518611yescharacteristic
342C2×C3#522711yescharacteristic
343C2×C3#522811yescharacteristic
344C2×C3#524211yescharacteristic
345C22#6397611yescharacteristic
346C4—21no—
347C4—42no—
348C4—62no—
349C4—62no—
350C4—121no—
351C4—121no—
352C4—241no—
353C4D3×#21511yescharacteristic
354C4D3×#21611yescharacteristic
355C4#6394611yescharacteristic
356C4#6394811yescharacteristic
357C3—21no—
358C3#7123911yescharacteristic, complemented
359C3#7194111yescharacteristic, complemented
360C2#1059151211yescharacteristic
361C2#1059158311yescharacteristic
362C2#1059159411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1645
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
119. C3×Dic6Q16semidirect
249. Dic6#216semidirect
315. C32#1645semidirect
358. C3#71239semidirect
359. C3#71941semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
C3×#50792
#105903842
#105902852
#105894122
#105890842
#719413
#712393