Finite Group Databasebeta

← #11781496

Subgroups — #11781496

Order 1152.

396 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592547C211yesmaximal, characteristic
2#10590388C211yesmaximal, characteristic, complemented
3#10590281C211yesmaximal, characteristic
4#10590254C211yesmaximal, characteristic, complemented
5C3×#4482C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic
8#68590—31nomaximal
9#68470—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3719—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63648—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63572—21no—
21#63566—21no—
22#63564—21no—
23#63564—21no—
24#63553—21no—
25#5090—31no—
26#5088—31no—
27#4849—31no—
28#4848—31no—
29#4848—31no—
30#4848—61no—
31#4830—31no—
32#4694—31no—
33C8×Dic6—31no—
34C3×#335—31no—
35C3×#332—31no—
36#4485—31no—
37#4485—31no—
38#4482D311yescharacteristic, complemented
39#4479D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634D411yescharacteristic
44C2×C3×Dic6—21no—
45C2×C32×C8—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)D411yescharacteristic
48#3750—21no—
49C4×C3⋊Dic3—21no—
50#3744—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3719—42no—
58#1682—91noSylow
59C3×C4⋊Q8—31no—
60C2×#216—61no—
61C2×Dic12—61no—
62C2×#204—61no—
63C2×#204—61no—
64C2×#204—62no—
65#874—31no—
66#874—31no—
67#874—61no—
68#869C2×D311yescharacteristic
69C4×Dic6—31no—
70C4×Dic6—31no—
71C4×Dic6—61no—
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4×C8—31no—
78#835—61no—
79#821—61no—
80#821—61no—
81#821—61no—
82#821—61no—
83#821—62no—
84#816—61no—
85Dic3⋊C8—61no—
86Dic3⋊C8—61no—
87C8×Dic3—61no—
88C8×Dic3—61no—
89#809—61no—
90#809—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—41no—
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4#4111yescharacteristic
98C2×C3⋊Dic3—21no—
99C2×C3⋊Dic3—21no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—81no—
105#634—21no—
106#634D812yes—
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C32×C8—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—91no—
116#462—91no—
117#460—91no—
118C8×Q8—91no—
119#335—31no—
120#332—31no—
121#331—91no—
122C2×C3×Q8—61no—
123C2×D12—62no—
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—121no—
131C2×D12—121no—
132C2×Dic6—21no—
133C2×Dic6—31no—
134C2×Dic6—31no—
135C2×Dic6—61no—
136C2×C3×C8—22no—
137C2×C3×C8—21no—
138C2×C3×C8—21no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C3×C4⋊C4—61no—
144C3×C4⋊C4—61no—
145C3×C42—21no—
146C3×C42C22×D311yescharacteristic
147C3×C42C22×D311yescharacteristic
148#216—122no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—31no—
152C4⋊Dic3—31no—
153C4⋊Dic3—61no—
154Dic3⋊C4—61no—
155Dic3⋊C4—61no—
156Dic3⋊C4—121no—
157C4×Dic3—61no—
158C4×Dic3—61no—
159C4×Dic3—121no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8D1211yescharacteristic
163C2×C3⋊C8D1211yescharacteristic
164Dic12—122no—
165#204—122no—
166#204—122no—
167#204—124no—
168C22×C32#12111yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3⋊D3—81no—
172C32×C4—21no—
173C32×C4C2×D811yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4#13511yescharacteristic
176C32×C4#13711yescharacteristic
177C3⋊Dic3—22no—
178C3⋊Dic3—41no—
179C3×Dic3—81no—
180C2×Q16—181no—
181C2×SD16—181no—
182C4⋊Q8—31no—
183#127—91no—
184C4×Q8—91no—
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—181no—
188C4⋊C8D3211yescharacteristic
189#103—181no—
190#102—181no—
191#102—181no—
192#102—181no—
193C4×C8—31no—
194C4×C8—181no—
195C22×D3—122no—
196C22×D3—121no—
197C22×D3—121no—
198C3×Q8—121no—
199C3×Q8—121no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—121no—
204C2×C3×C4C2×D1211yescharacteristic
205C2×C3×C4#23511yescharacteristic
206C2×C3×C4D3×D411yescharacteristic
207C2×C3×C4D3×D411yescharacteristic
208C2×C3×C4D3×D411yescharacteristic
209C2×C3×C4#23911yescharacteristic
210C2×Dic3—41no—
211C2×Dic3—61no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—61no—
215C2×Dic3—121no—
216C2×Dic3—121no—
217D12—122no—
218D12—122no—
219D12—121no—
220D12—121no—
221D12—121no—
222D12—121no—
223D12—121no—
224D12—121no—
225D12—121no—
226D12—121no—
227D12—241no—
228D12—241no—
229D12—241no—
230D12—241no—
231D12—242no—
232Dic6—32no—
233Dic6—32no—
234Dic6—41no—
235Dic6—41no—
236Dic6—62no—
237Dic6—61no—
238Dic6—61no—
239Dic6—121no—
240C3×C8—42no—
241C3×C8—41no—
242C3×C8—41no—
243C3×C8—61no—
244C3×C8—61no—
245C3×C8—121no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—21no—
249C3⋊C8—41no—
250C3⋊C8—41no—
251C2×C32#46411yescharacteristic
252C2×C32#46611yescharacteristic
253C2×C32#47111yescharacteristic
254C3⋊D3—161no—
255C2×Q8—61no—
256C2×Q8—91no—
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260Q16—362no—
261SD16—362no—
262C2×C8—21no—
263C2×C8—31no—
264C2×C8—31no—
265C2×C8—61no—
266C2×C8—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—91no—
270C4⋊C4—181no—
271C42—181no—
272C42C2×D3211yescharacteristic
273C22×C3—21no—
274C22×C3#88411yescharacteristic
275C22×C3#89511yescharacteristic
276C2×D3—242no—
277C2×D3—242no—
278C2×D3—242no—
279C2×D3—241no—
280C2×D3—241no—
281C2×D3—241no—
282C2×D3—241no—
283C2×D3—241no—
284C2×D3—241no—
285C3×C4—21no—
286C3×C4—21no—
287C3×C4—21no—
288C3×C4—21no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—41no—
292C3×C4—241no—
293C3×C4#90411yescharacteristic
294C3×C4#90911yescharacteristic
295C3×C4D3×D811yescharacteristic
296C3×C4D3×D811yescharacteristic
297C3×C4#91611yescharacteristic
298C3×C4#91611yescharacteristic
299C3×C4#91811yescharacteristic
300C3×C4#91911yescharacteristic
301Dic3—62no—
302Dic3—62no—
303Dic3—81no—
304Dic3—122no—
305Dic3—121no—
306Dic3—121no—
307Dic3—241no—
308C32#168211yescharacteristic, complemented, Sylow
309C23—361no—
310Q8—92no—
311Q8—121no—
312Q8—121no—
313Q8—181no—
314D4—361no—
315D4—361no—
316D4—361no—
317D4—361no—
318D4—721no—
319C2×C4—121no—
320C2×C4—181no—
321C2×C4—181no—
322C2×C4#379911yescharacteristic
323C2×C4D3×D1211yescharacteristic
324C2×C4#381111yescharacteristic
325C8—41no—
326C8—61no—
327C8—61no—
328C8—121no—
329C8—121no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3#475411yescharacteristic
334C2×C3#477511yescharacteristic
335C2×C3#479811yescharacteristic
336C2×C3#484511yescharacteristic
337C2×C3#488311yescharacteristic
338C2×C3#489811yescharacteristic
339D3—482no—
340D3—481no—
341D3—481no—
342C22—721no—
343C22—721no—
344C22—721no—
345C22#6391011yescharacteristic
346C4—21no—
347C4—182no—
348C4—241no—
349C4—361no—
350C4#6380111yescharacteristic
351C4#6380611yescharacteristic
352C4#6392611yescharacteristic
353C4#6395011yescharacteristic
354C3—21no—
355C3#6847011yescharacteristic, complemented
356C3#6859011yescharacteristic, complemented
357C2—1441no—
358C2#1059050911yescharacteristic
359C2#1059081311yescharacteristic
360C2#1059099011yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#64083C22
hypercenterC4⋊C8D32
hypocenterC32#1682
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590388C2semidirect
4. #10590254C2semidirect
5. C3×#4482C2semidirect
6. C3×#4479C2semidirect
38. #4482D3semidirect
39. #4479D3semidirect
308. C32#1682semidirect
355. C3#68470semidirect
356. C3#68590semidirect

Maximal subgroups

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

subgroupindex
#105925472
#105903882
#105902812
#105902542
C3×#44822
C3×#44792
#105890912
#685903
#684703