Finite Group Databasebeta

← #11781489

Subgroups — #11781489

Order 1152.

396 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592726C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic
5#10589099C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic
8#71055—31nomaximal
9#70941—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C2×#3755—21no—
12#64083C2211yescharacteristic
13C2×C3×#216—21no—
14C3×#869C2211yescharacteristic
15#63636—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#810—21no—
18C3×C4⋊(C3⋊C8)—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8—21no—
22C3×C4×C3⋊C8C2211yescharacteristic
23#63564—21no—
24#63564—21no—
25C3×#462—31no—
26C3×C8×Q8—31no—
27#5088—31no—
28#5031D311yescharacteristic, complemented
29#5027—31no—
30#5027—31no—
31#5027—61no—
32Q8×C3⋊C8D311yescharacteristic, complemented
33#4694—31no—
34#4547—31no—
35#4486—31no—
36#4485—31no—
37#4485—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×Q8D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C3×Dic6—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C42—21no—
48C32×C42C2311yescharacteristic
49#3755—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×#216—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1682—91noSylow
59C2×C3×Q16—61no—
60C3×C4⋊Q8—31no—
61C3×C4×Q8—21no—
62C3×C4×Q8C2×D311yescharacteristic
63C3×C4×Q8C2×D311yescharacteristic
64C2×#216—21no—
65C2×#215—62no—
66C2×#215—61no—
67C2×#215—61no—
68#874—31no—
69#874—31no—
70#874—61no—
71#869C2×D311yescharacteristic
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—61no—
75C3×#103—61no—
76C3×C4×C8—31no—
77C3×C4×C8—61no—
78#821—61no—
79#821—61no—
80#810—21no—
81#809—62no—
82#809—61no—
83#809—61no—
84#809—61no—
85#809—61no—
86C4⋊(C3⋊C8)—21no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—21no—
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—41no—
95C32×Q8—21no—
96C32×Q8D812yes—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—81no—
107C2×C3×Dic3—41no—
108C3×Dic6—41no—
109C3×Dic6—41no—
110C3⋊(C3⋊C8)—41no—
111C3×C3⋊C8—21no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—41no—
114C3×C3⋊C8—41no—
115#486—91no—
116#462—31no—
117#460—91no—
118C8×Q8—31no—
119#335—91no—
120#332—91no—
121#331—91no—
122C2×C3×Q8—21no—
123C2×C3×Q8—61no—
124C2×C3×Q8D1211yescharacteristic
125C2×C3×Q8#6711yescharacteristic
126C2×D12—62no—
127C2×D12—61no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—121no—
134C2×D12—121no—
135C2×Dic6—21no—
136C3×Q16—122no—
137C2×C3×C8—31no—
138C2×C3×C8—31no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—41no—
145C3×C4⋊C4—61no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4D1211yescharacteristic
148C3×C4⋊C4#6711yescharacteristic
149C3×C42—21no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—41no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#216—42no—
156#215—124no—
157#215—122no—
158#215—122no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—62no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8#6711yescharacteristic
167C2×C3⋊C8#6711yescharacteristic
168C22×C32#12111yescharacteristic
169C2×C3⋊D3—81no—
170C2×C3⋊D3—81no—
171C2×C3⋊D3—81no—
172C32×C4—22no—
173C32×C4—21no—
174C32×C4—41no—
175C32×C4C2×D811yescharacteristic
176C32×C4#13511yescharacteristic
177C32×C4#13511yescharacteristic
178C32×C4#13711yescharacteristic
179C3×Dic3—81no—
180C2×Q16—61no—
181C2×SD16—181no—
182C4⋊Q8—31no—
183#127—91no—
184C4×Q8D3211yescharacteristic
185C4⋊C8—31no—
186C4⋊C8—31no—
187C4⋊C8—61no—
188C4⋊C8—91no—
189#103—61no—
190#102—181no—
191#102—181no—
192#102—181no—
193C4×C8—31no—
194C4×C8—61no—
195C22×D3—122no—
196C22×D3—121no—
197C22×D3—121no—
198C3×Q8—21no—
199C3×Q8—21no—
200C3×Q8—22no—
201C3×Q8—41no—
202C3×Q8—121no—
203C3×Q8—121no—
204C3×Q8D2412yes—
205C3×Q8#21312yes—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—41no—
214C2×C3×C4—41no—
215C2×C3×C4—121no—
216C2×C3×C4C2×D1211yescharacteristic
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4#23711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—41no—
223D12—122no—
224D12—122no—
225D12—121no—
226D12—121no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—241no—
234D12—241no—
235D12—241no—
236D12—241no—
237D12—242no—
238Dic6—41no—
239Dic6—41no—
240C3×C8—61no—
241C3×C8—61no—
242C3×C8—121no—
243C3×C8—121no—
244C3⋊C8—21no—
245C3⋊C8—21no—
246C3⋊C8—41no—
247C3⋊C8—41no—
248C3⋊C8—122no—
249C3⋊C8—121no—
250C3⋊C8—121no—
251C2×C32#46411yescharacteristic
252C2×C32#46611yescharacteristic
253C2×C32#47111yescharacteristic
254C3⋊D3—161no—
255C2×Q8—61no—
256C2×Q8#62611yescharacteristic
257C2×D4—181no—
258C2×D4—181no—
259C2×D4—181no—
260Q16—122no—
261SD16—362no—
262C2×C8—31no—
263C2×C8—31no—
264C2×C8—61no—
265C2×C8—61no—
266C2×C8—181no—
267C4⋊C4—21no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4#62611yescharacteristic
271C42—21no—
272C42C2×D3211yescharacteristic
273C22×C3—21no—
274C22×C3#93011yescharacteristic
275C22×C3#93911yescharacteristic
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—22no—
288C3×C4—22no—
289C3×C4—21no—
290C3×C4—21no—
291C3×C4—21no—
292C3×C4—21no—
293C3×C4—41no—
294C3×C4—42no—
295C3×C4—41no—
296C3×C4—41no—
297C3×C4—81no—
298C3×C4—241no—
299C3×C4C2×D2411yescharacteristic
300C3×C4#90411yescharacteristic
301C3×C4#91811yescharacteristic
302C3×C4#91911yescharacteristic
303C3×C4C2×#21311yescharacteristic
304C3×C4#94211yescharacteristic
305C3×C4#95011yescharacteristic
306C3×C4#95011yescharacteristic
307Dic3—81no—
308C32#168211yescharacteristic, complemented, Sylow
309C23—361no—
310Q8—21no—
311Q8—121no—
312Q8—121no—
313Q8#371412yes—
314D4—361no—
315D4—361no—
316D4—361no—
317D4—361no—
318D4—721no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—121no—
322C2×C4#380411yescharacteristic
323C2×C4C2×#62611yescharacteristic
324C2×C4D3×#6711yescharacteristic
325C8—61no—
326C8—61no—
327C8—121no—
328C8—121no—
329C8—361no—
330C2×C3—21no—
331C2×C3—21no—
332C2×C3—21no—
333C2×C3#502811yescharacteristic
334C2×C3#503811yescharacteristic
335C2×C3#511511yescharacteristic
336C2×C3#514111yescharacteristic
337C2×C3#518511yescharacteristic
338C2×C3#520311yescharacteristic
339D3—482no—
340D3—481no—
341D3—481no—
342C22—721no—
343C22—721no—
344C22—721no—
345C22#6397811yescharacteristic
346C4—22no—
347C4—21no—
348C4—41no—
349C4—241no—
350C4C2×#371411yescharacteristic
351C4#6382911yescharacteristic
352C4#6394811yescharacteristic
353C4#6394911yescharacteristic
354C3—21no—
355C3#7094111yescharacteristic, complemented
356C3#7105511yescharacteristic, complemented
357C2—1441no—
358C2#1059116411yescharacteristic
359C2#1059160711yescharacteristic
360C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#121
prime radical#64083C22
hypercenterC4×Q8D32
hypocenterC32#1682
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
2. C3×#5031C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
5. #10589099C2semidirect
6. #10589092C2semidirect
28. #5031D3semidirect
32. Q8×C3⋊C8D3semidirect
308. C32#1682semidirect
355. C3#70941semidirect
356. C3#71055semidirect

Maximal subgroups

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

subgroupindex
#105927262
C3×#50312
C3×Q8×C3⋊C82
#105902812
#105890992
#105890922
#105890912
#710553
#709413