Finite Group Databasebeta

← #11781443

Subgroups — #11781443

Order 1152.

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

normal subgroups only

This group has 434 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#10592714C211yesmaximal, characteristic
2C3×#5019C211yesmaximal, characteristic, complemented
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5#10589099C211yesmaximal, characteristic, complemented
6#10589092C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71039—31nomaximal
9#70849—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3753—21no—
12#64083C2211yescharacteristic
13C2×C3×#214—21no—
14C22×C3×C3⋊C8—21no—
15C3×#869C2211yescharacteristic
16#63636—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#830—21no—
19C3×#810—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63564—21no—
24#63564—21no—
25C3×#461—31no—
26C3×C8×D4—31no—
27#5088—31no—
28#5019D311yescharacteristic, complemented
29#5015—31no—
30#5015—31no—
31#5015—61no—
32D4×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×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C3×Dic6—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3753—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×#214—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
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×SD16—61no—
61C22×C3×C8—61no—
62C3×C4⋊Q8—31no—
63C3×C4×D4—21no—
64C3×C4×D4C2×D311yescharacteristic
65C3×C4×D4C2×D311yescharacteristic
66C2×#214—21no—
67C2×#213—62no—
68C2×#213—61no—
69C2×#213—61no—
70C22×C3⋊C8—21no—
71#874—31no—
72#874—31no—
73#874—61no—
74#869C2×D311yescharacteristic
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#103—61no—
78C3×C22⋊C8—61no—
79C3×C4×C8—31no—
80#830—21no—
81#821—61no—
82#821—61no—
83#810—21no—
84#809—62no—
85#809—61no—
86#809—61no—
87#809—61no—
88#809—61no—
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
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—41no—
109C4⋊(C3⋊D3)—81no—
110C2×C3×Dic3—41no—
111C3×Dic6—41no—
112C3×Dic6—41no—
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—31no—
120#459—91no—
121C8×D4—31no—
122#335—91no—
123#332—91no—
124#331—91no—
125C2×C3×Q8—61no—
126C2×C3×D4—21no—
127C2×C3×D4D1211yescharacteristic
128C2×C3×D4#6711yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—41no—
132C2×D12—62no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—121no—
140C2×D12—121no—
141C2×Dic6—21no—
142C3×SD16—122no—
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C2×C3×C8—122no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—61no—
150C3×C4⋊C4—61no—
151C3×C4⋊C4D1211yescharacteristic
152C3×C4⋊C4#6711yescharacteristic
153C3×C22⋊C4—21no—
154C3×C22⋊C4—21no—
155C3×C22⋊C4—41no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#214—42no—
160#213—124no—
161#213—122no—
162#213—122no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
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—61no—
188C2×D8—181no—
189C22×C8—61no—
190C4⋊Q8—31no—
191#127—91no—
192C4×D4D3211yescharacteristic
193C4⋊C8—31no—
194C4⋊C8—31no—
195C4⋊C8—91no—
196#103—61no—
197#102—181no—
198#102—181no—
199#102—181no—
200C22⋊C8—61no—
201C4×C8—31no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—41no—
205C22×D3—122no—
206C22×D3—121no—
207C22×D3—121no—
208C3×Q8—121no—
209C3×Q8—121no—
210C3×D4—21no—
211C3×D4—21no—
212C3×D4—22no—
213C3×D4—41no—
214C3×D4D2412yes—
215C3×D4#21312yes—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—41no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—81no—
227C2×C3×C4—81no—
228C2×C3×C4—121no—
229C2×C3×C4C2×D1211yescharacteristic
230C2×C3×C4#23511yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4#23711yescharacteristic
233C2×C3×C4C2×#6711yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×Dic3—41no—
236D12—122no—
237D12—122no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—121no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—241no—
247D12—241no—
248D12—241no—
249D12—241no—
250D12—242no—
251Dic6—41no—
252Dic6—41no—
253C3×C8—61no—
254C3×C8—61no—
255C3×C8—121no—
256C3×C8—121no—
257C3⋊C8—21no—
258C3⋊C8—21no—
259C3⋊C8—41no—
260C3⋊C8—41no—
261C3⋊C8—122no—
262C3⋊C8—121no—
263C3⋊C8—121no—
264C2×C32—42no—
265C2×C32#46311yescharacteristic
266C2×C32#46611yescharacteristic
267C2×C32#47111yescharacteristic
268C3⋊D3—161no—
269C2×Q8—61no—
270C2×D4—181no—
271C2×D4—181no—
272C2×D4—181no—
273C2×D4#62611yescharacteristic
274C22×C4—21no—
275SD16—122no—
276D8—362no—
277C2×C8—31no—
278C2×C8—31no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8—122no—
282C2×C8—181no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4#62611yescharacteristic
286C22⋊C4—21no—
287C42C2×D3211yescharacteristic
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3#93011yescharacteristic
299C22×C3#93911yescharacteristic
300C2×D3—242no—
301C2×D3—242no—
302C2×D3—242no—
303C2×D3—241no—
304C2×D3—241no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4—81no—
319C3×C4—241no—
320C3×C4C2×D2411yescharacteristic
321C3×C4#90411yescharacteristic
322C3×C4#91411yescharacteristic
323C3×C4#91611yescharacteristic
324C3×C4C2×#21311yescharacteristic
325C3×C4#93211yescharacteristic
326C3×C4#95011yescharacteristic
327C3×C4#95011yescharacteristic
328Dic3—81no—
329C32#168111yescharacteristic, complemented, Sylow
330C23—21no—
331C23—361no—
332Q8—121no—
333Q8—121no—
334D4—21no—
335D4—361no—
336D4—361no—
337D4—361no—
338D4—361no—
339D4—721no—
340D4#371412yes—
341C2×C4—21no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—121no—
345C2×C4#380411yescharacteristic
346C2×C4C2×#62611yescharacteristic
347C2×C4D3×#6711yescharacteristic
348C8—61no—
349C8—61no—
350C8—121no—
351C8—121no—
352C8—361no—
353C2×C3—21no—
354C2×C3—21no—
355C2×C3—21no—
356C2×C3—42no—
357C2×C3—42no—
358C2×C3—82no—
359C2×C3#501611yescharacteristic
360C2×C3#503811yescharacteristic
361C2×C3#511511yescharacteristic
362C2×C3#514111yescharacteristic
363C2×C3#516511yescharacteristic
364C2×C3#520311yescharacteristic
365D3—482no—
366D3—481no—
367D3—481no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—721no—
372C22—721no—
373C22—721no—
374C22#6397811yescharacteristic
375C4—21no—
376C4—41no—
377C4—241no—
378C4C2×#371411yescharacteristic
379C4#6382911yescharacteristic
380C4#6393411yescharacteristic
381C4#6393511yescharacteristic
382C3—21no—
383C3#7084911yescharacteristic, complemented
384C3#7103911yescharacteristic, complemented
385C2—42no—
386C2—1441no—
387C2#1059116411yescharacteristic
388C2#1059147111yescharacteristic
389C2#1059168011yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radical#10592714C2
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
2. C3×#5019C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10590281C2semidirect
5. #10589099C2semidirect
6. #10589092C2semidirect
7. #10589091C2semidirect
28. #5019D3semidirect
32. D4×C3⋊C8D3semidirect
329. C32#1681semidirect
383. C3#70849semidirect
384. C3#71039semidirect

Maximal subgroups

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

subgroupindex
#105927142
C3×#50192
C3×D4×C3⋊C82
#105902812
#105890992
#105890922
#105890912
#710393
#708493