Finite Group Databasebeta

← #11781542

Subgroups — #11781542

Order 1152.

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

normal subgroups only

This group has 374 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#10592545C211yesmaximal, characteristic
2#10590327C211yesmaximal, characteristic
3#10590300C211yesmaximal, characteristic
4#10590288C211yesmaximal, characteristic, complemented
5C3×#4481C211yesmaximal, characteristic, complemented
6C3×#4479C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#68581—31nomaximal
9#68499—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C2×#3710—21no—
14C32×C4⋊C8C2211yescharacteristic
15#63648—21no—
16#63645—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63567—21no—
22#63567—21no—
23#63564—21no—
24#63557—21no—
25#5093—31no—
26#5084—31no—
27#4846—31no—
28#4846—31no—
29#4846—61no—
30#4842—31no—
31#4834—31no—
32C8×D12—31no—
33#4681—31no—
34C3×#335—31no—
35C3×#333—31no—
36#4486—31no—
37#4482—31no—
38#4481D311yescharacteristic, complemented
39#4479D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)D411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8—21no—
45C32×C42C2311yescharacteristic
46#3752—21no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3710—42no—
57#1683—91noSylow
58C3×C4⋊Q8—31no—
59C2×D3×C8—61no—
60C2×D3×C8—61no—
61C4×D12—31no—
62C4×D12—31no—
63C4×D12—61no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68C3×C4⋊C8—21no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8C2×D311yescharacteristic
72C3×C4⋊C8C2×D311yescharacteristic
73C3×C4×C8—31no—
74#821—61no—
75#821—61no—
76#821—61no—
77#821—62no—
78(C2×D3)⋊C8—61no—
79(C2×D3)⋊C8—61no—
80#818—61no—
81#818—61no—
82#818—62no—
83#817—61no—
84#816—61no—
85#816—61no—
86#810—61no—
87#810—61no—
88#809—61no—
89#808—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8C2×D311yescharacteristic
93C22×C3⋊D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—41no—
99C4⋊(C3⋊D3)—21no—
100C4⋊(C3⋊D3)Q1612yes—
101C4×C3⋊D3—41no—
102C4×C3⋊D3—41no—
103#634—41no—
104#634—41no—
105C2×C3×Dic3—41no—
106C3×Dic6—81no—
107C32×C8—41no—
108C3×C3⋊C8—21no—
109C3×C3⋊C8—21no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—91no—
115C8×D4—91no—
116#335—31no—
117#333—31no—
118#332—91no—
119C2×C3×Q8—61no—
120C2×D12—31no—
121C2×D12—31no—
122C2×D12—61no—
123C2×C4×D3—61no—
124C2×C4×D3—61no—
125C2×C4×D3—121no—
126C2×Dic6—21no—
127C2×Dic6—61no—
128C2×Dic6—61no—
129C2×Dic6—121no—
130C2×C3×C8—22no—
131C2×C3×C8—21no—
132C2×C3×C8—21no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—61no—
136C2×C3×C8—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C42—21no—
140C3×C42C22×D311yescharacteristic
141C3×C42C22×D311yescharacteristic
142(C2×D3)⋊C4—61no—
143(C2×D3)⋊C4—61no—
144(C2×D3)⋊C4—121no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—31no—
148C4⋊Dic3—31no—
149C4⋊Dic3—61no—
150C4⋊Dic3—62no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—61no—
155C4⋊Dic3—121no—
156C2×C3⋊C8—21no—
157C2×C3⋊C8—21no—
158C2×C3⋊C8D1211yescharacteristic
159C2×C3⋊C8D1211yescharacteristic
160D3×C8—122no—
161D3×C8—122no—
162C22×C32#12111yescharacteristic
163C2×C3⋊D3—22no—
164C2×C3⋊D3—41no—
165C2×C3⋊D3—41no—
166C32×C4—21no—
167C32×C4C2×Q1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C3⋊Dic3—41no—
172C3⋊Dic3—81no—
173C3×Dic3—81no—
174C22×C8—181no—
175C4⋊Q8—31no—
176C4⋊Q8—91no—
177C4×D4—91no—
178#107—181no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8D3211yescharacteristic
183#103—181no—
184#103—181no—
185#102—181no—
186#102—181no—
187C22⋊C8—181no—
188C4×C8—31no—
189C22×D3—61no—
190C22×D3—61no—
191C22×D3—121no—
192C3×Q8—241no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—121no—
197C2×C3×C4C2×D1211yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4D3×D411yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4D3×D411yescharacteristic
202C2×C3×C4#23911yescharacteristic
203C2×Dic3—41no—
204C2×Dic3—61no—
205C2×Dic3—61no—
206C2×Dic3—121no—
207C2×Dic3—122no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210D12—32no—
211D12—32no—
212D12—62no—
213D12—61no—
214D12—61no—
215D12—121no—
216C4×D3—121no—
217C4×D3—121no—
218C4×D3—121no—
219C4×D3—121no—
220C4×D3—241no—
221C4×D3—241no—
222Dic6—81no—
223Dic6—121no—
224Dic6—121no—
225Dic6—121no—
226Dic6—121no—
227Dic6—241no—
228Dic6—241no—
229C3×C8—42no—
230C3×C8—41no—
231C3×C8—41no—
232C3×C8—61no—
233C3×C8—61no—
234C3×C8—121no—
235C3×C8—121no—
236C3⋊C8—21no—
237C3⋊C8—21no—
238C3⋊C8—41no—
239C3⋊C8—41no—
240C2×C32#46311yescharacteristic
241C2×C32#46711yescharacteristic
242C2×C32#47111yescharacteristic
243C3⋊D3—42no—
244C2×Q8—61no—
245C2×Q8—181no—
246C2×D4—91no—
247C22×C4—181no—
248C2×C8—21no—
249C2×C8—31no—
250C2×C8—31no—
251C2×C8—61no—
252C2×C8—61no—
253C2×C8—362no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—91no—
257C4⋊C4—181no—
258C4⋊C4—181no—
259C22⋊C4—181no—
260C42C2×D3211yescharacteristic
261C22×C3—21no—
262C22×C3#88411yescharacteristic
263C22×C3#89511yescharacteristic
264C2×D3—62no—
265C2×D3—62no—
266C2×D3—122no—
267C2×D3—121no—
268C2×D3—121no—
269C2×D3—121no—
270C2×D3—121no—
271C2×D3—241no—
272C2×D3—241no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—41no—
280C3×C4—241no—
281C3×C4#90411yescharacteristic
282C3×C4#90811yescharacteristic
283C3×C4#91211yescharacteristic
284C3×C4#91411yescharacteristic
285C3×C4#91611yescharacteristic
286C3×C4D3×Q1611yescharacteristic
287C3×C4D3×Q1611yescharacteristic
288C3×C4#91911yescharacteristic
289Dic3—81no—
290Dic3—121no—
291Dic3—121no—
292Dic3—241no—
293Dic3—242no—
294Dic3—241no—
295Dic3—241no—
296C32#168311yescharacteristic, complemented, Sylow
297C23—181no—
298Q8—241no—
299Q8—361no—
300Q8—361no—
301D4—92no—
302D4—181no—
303C2×C4—121no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4#379911yescharacteristic
309C2×C4D3×D1211yescharacteristic
310C2×C4#381111yescharacteristic
311C8—41no—
312C8—61no—
313C8—61no—
314C8—121no—
315C8—121no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—21no—
319C2×C3#474811yescharacteristic
320C2×C3#481311yescharacteristic
321C2×C3#481911yescharacteristic
322C2×C3#484411yescharacteristic
323C2×C3#488711yescharacteristic
324C2×C3#489811yescharacteristic
325D3—122no—
326D3—122no—
327D3—242no—
328C22—182no—
329C22—361no—
330C22—361no—
331C22#6391011yescharacteristic
332C4—21no—
333C4—241no—
334C4—361no—
335C4—721no—
336C4#6379411yescharacteristic
337C4#6380811yescharacteristic
338C4#6393611yescharacteristic
339C4#6394411yescharacteristic
340C3—21no—
341C3#6849911yescharacteristic, complemented
342C3#6858111yescharacteristic, complemented
343C2—362no—
344C2#1059052511yescharacteristic
345C2#1059077011yescharacteristic
346C2#1059098911yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4⋊C8D32
hypocenterC32#1683
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
4. #10590288C2semidirect
5. C3×#4481C2semidirect
6. C3×#4479C2semidirect
7. #10589094C2semidirect
38. #4481D3semidirect
39. #4479D3semidirect
296. C32#1683semidirect
341. C3#68499semidirect
342. C3#68581semidirect

Maximal subgroups

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

subgroupindex
#105925452
#105903272
#105903002
#105902882
C3×#44812
C3×#44792
#105890942
#685813
#684993