Finite Group Databasebeta

← #11781445

Subgroups — #11781445

Order 1152.

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

normal subgroups only

This group has 424 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#10592718C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71007—31nomaximal
9#70849—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3754—21no—
12#64078C2211yescharacteristic
13C2×C3×#213—21no—
14C22×C3×C3⋊C8—21no—
15C3×#874C2211yescharacteristic
16#63637—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#830—21no—
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63563—21no—
25C3×#459—31no—
26C3×C8×D4—31no—
27#5070—31no—
28#5019—31no—
29#5019—31no—
30#5019—61no—
31#5015D311yescharacteristic
32D4×C3⋊C8D311yescharacteristic, complemented
33#4694—31no—
34#4544—31no—
35#4486—31no—
36#4485—31no—
37#4482—31no—
38#4479—31no—
39#4458—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3754—42no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×#213—42no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—42no—
57C2×C3×C3⋊C8D411yescharacteristic
58C2×C3×C3⋊C8D411yescharacteristic
59#1681—91noSylow
60C2×C3×D8—61no—
61C22×C3×C8—61no—
62C3×#127—31no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C2×D311yescharacteristic
66C2×#214—62no—
67C2×#214—61no—
68C2×#214—61no—
69C2×#213—21no—
70C22×C3⋊C8—21no—
71#874C2×D311yescharacteristic
72#869—31no—
73#869—31no—
74#869—61no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#102—61no—
78C3×C22⋊C8—61no—
79C3×C4×C8—31no—
80#832—61no—
81#832—61no—
82#830—21no—
83#821—61no—
84#821—61no—
85#810—62no—
86#810—61no—
87#810—61no—
88#809—21no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C23×C32—21no—
96C22×C3×D3—41no—
97C32×D4—21no—
98C32×D4D812yes—
99C2×C32×C4—21no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—41no—
106#634—41no—
107#634—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—81no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—91no—
119#461—91no—
120#459—31no—
121C8×D4—31no—
122#335—91no—
123#332—91no—
124#331—91no—
125C2×C3×D4—21no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4D1211yescharacteristic
130C2×C3×D4#6711yescharacteristic
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—41no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—21no—
137C2×Dic6—62no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C3×D8—122no—
141C2×C3×C8—31no—
142C2×C3×C8—31no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C2×C3×C8—122no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4D1211yescharacteristic
148C3×C4⋊C4#6711yescharacteristic
149C3×C22⋊C4—21no—
150C3×C22⋊C4—21no—
151C3×C22⋊C4—41no—
152C3×C42—21no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#214—124no—
156#214—122no—
157#214—122no—
158#213—42no—
159C4⋊Dic3—61no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—121no—
164C4⋊Dic3—121no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8—42no—
168C2×C3⋊C8—62no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8#6711yescharacteristic
172C2×C3⋊C8#6711yescharacteristic
173C22×C32—22no—
174C22×C32—41no—
175C22×C32—41no—
176C22×C32#12111yescharacteristic
177C2×C3×D3—81no—
178C2×C3×D3—81no—
179C2×C3×D3—81no—
180C32×C4—21no—
181C32×C4—41no—
182C32×C4C2×D811yescharacteristic
183C32×C4#13511yescharacteristic
184C32×C4#13511yescharacteristic
185C32×C4AGL(1,ℤ/8)11yescharacteristic
186C3⋊Dic3—81no—
187C2×SD16—181no—
188C2×D8—61no—
189C22×C8—61no—
190C4⋊Q8—91no—
191#127—31no—
192C4×D4D3211yescharacteristic
193C4⋊C8—31no—
194C4⋊C8—31no—
195C4⋊C8—91no—
196#103—181no—
197#102—61no—
198#102—181no—
199#102—181no—
200C22⋊C8—61no—
201C4×C8—31no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—41no—
205C23×C3—121no—
206C22×D3—41no—
207C3×D4—21no—
208C3×D4—21no—
209C3×D4—22no—
210C3×D4—41no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—241no—
216C3×D4D2412yes—
217C3×D4#21312yes—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—81no—
229C2×C3×C4—81no—
230C2×C3×C4C2×D1211yescharacteristic
231C2×C3×C4#23511yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4#23711yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×Dic3—122no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239D12—41no—
240D12—41no—
241D12—41no—
242D12—41no—
243D12—81no—
244Dic6—122no—
245Dic6—122no—
246Dic6—121no—
247Dic6—121no—
248Dic6—121no—
249Dic6—121no—
250C3×C8—61no—
251C3×C8—61no—
252C3×C8—121no—
253C3×C8—121no—
254C3⋊C8—21no—
255C3⋊C8—21no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C3⋊C8—122no—
259C3⋊C8—121no—
260C3⋊C8—121no—
261C2×C32—42no—
262C2×C32#46311yescharacteristic
263C2×C32#46611yescharacteristic
264C2×C32#47111yescharacteristic
265C3×D3—161no—
266C2×Q8—181no—
267C2×D4—61no—
268C2×D4—61no—
269C2×D4—61no—
270C2×D4#62611yescharacteristic
271C22×C4—21no—
272SD16—362no—
273D8—122no—
274C2×C8—31no—
275C2×C8—31no—
276C2×C8—61no—
277C2×C8—61no—
278C2×C8—122no—
279C2×C8—181no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C4⋊C4#62611yescharacteristic
283C22⋊C4—21no—
284C42C2×D3211yescharacteristic
285C22×C3—22no—
286C22×C3—22no—
287C22×C3—21no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—81no—
294C22×C3—81no—
295C22×C3—241no—
296C22×C3—241no—
297C22×C3—241no—
298C22×C3#93011yescharacteristic
299C22×C3#93911yescharacteristic
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—81no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—41no—
312C3×C4—81no—
313C3×C4C2×D2411yescharacteristic
314C3×C4#90411yescharacteristic
315C3×C4#91111yescharacteristic
316C3×C4#91211yescharacteristic
317C3×C4C2×#21311yescharacteristic
318C3×C4#93211yescharacteristic
319C3×C4#95011yescharacteristic
320C3×C4#95011yescharacteristic
321Dic3—242no—
322Dic3—241no—
323Dic3—241no—
324C32#168111yescharacteristic, complemented, Sylow
325C23—21no—
326C23—121no—
327Q8—361no—
328Q8—361no—
329D4—21no—
330D4—121no—
331D4—121no—
332D4—121no—
333D4—121no—
334D4—241no—
335D4#371412yes—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—361no—
340C2×C4#380411yescharacteristic
341C2×C4C2×#62611yescharacteristic
342C2×C4D3×#6711yescharacteristic
343C8—61no—
344C8—61no—
345C8—121no—
346C8—121no—
347C8—361no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—21no—
351C2×C3—42no—
352C2×C3—42no—
353C2×C3—82no—
354C2×C3—481no—
355C2×C3#501611yescharacteristic
356C2×C3#503811yescharacteristic
357C2×C3#511511yescharacteristic
358C2×C3#514111yescharacteristic
359C2×C3#515311yescharacteristic
360C2×C3#520011yescharacteristic
361D3—161no—
362C22—22no—
363C22—41no—
364C22—41no—
365C22—241no—
366C22—241no—
367C22—241no—
368C22#6397811yescharacteristic
369C4—21no—
370C4—41no—
371C4—721no—
372C4C2×#371411yescharacteristic
373C4#6382911yescharacteristic
374C4#6393211yescharacteristic
375C4#6393311yescharacteristic
376C3—21no—
377C3#7084911yescharacteristic, complemented
378C3#7100711yescharacteristic, complemented
379C2—42no—
380C2—481no—
381C2#1059116411yescharacteristic
382C2#1059146811yescharacteristic
383C2#1059167911yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1681
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10592718C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10590273C2semidirect
5. #10589099C2semidirect
6. #10589094C2semidirect
7. #10589090C2semidirect
32. D4×C3⋊C8D3semidirect
324. C32#1681semidirect
377. C3#70849semidirect
378. C3#71007semidirect

Maximal subgroups

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

subgroupindex
#105927182
C3×#50152
C3×D4×C3⋊C82
#105902732
#105890992
#105890942
#105890902
#710073
#708493