Finite Group Databasebeta

← #11781536

Subgroups — #11781536

Order 1152.

387 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 94 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
1D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic
2C3×#5008C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic, complemented
5#10589100C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71135—31nomaximal
9#71103—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63657—21no—
15C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#832—21no—
18C3×#832—21no—
19C3×#808—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63565—21no—
24#63565—21no—
25C3×#476—31no—
26C3×#474—31no—
27#5093—31no—
28#5079—31no—
29D4×C3⋊C8—31no—
30D4×C3⋊C8—31no—
31D4×C3⋊C8—61no—
32#5008D311yescharacteristic
33#5007D311yescharacteristic
34#4547—31no—
35#4546—31no—
36#4486—31no—
37#4481—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4D411yescharacteristic
45C32×C22⋊C4—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)—42no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#1683—91noSylow
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8—31no—
60C3×C4×D4—21no—
61C3×C4×D4C2×D311yescharacteristic
62C3×C4×D4C2×D311yescharacteristic
63C22×C3⋊C8—61no—
64C22×C3⋊C8—61no—
65C22×C3⋊C8—62no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×#107—61no—
69C3×#106—61no—
70C3×C4⋊C8—31no—
71C3×C4⋊C8—31no—
72C3×#102—61no—
73C3×#102—61no—
74#835—61no—
75#835—61no—
76#832—21no—
77#832—21no—
78#830—61no—
79#830—61no—
80#830—62no—
81#810—61no—
82#810—61no—
83#808—21no—
84#807—21no—
85C4⋊(C3⋊C8)—31no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—61no—
88C4⋊(C3⋊C8)C2×D311yescharacteristic
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4×C3⋊C8—31no—
91C4×C3⋊C8—31no—
92C4×C3⋊C8—61no—
93C23×C32—21no—
94C32×D4—21no—
95C32×D4Q1612yes—
96C2×C32×C4—21no—
97C2×C32×C4—41no—
98C2×C32×C4—41no—
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4#4111yescharacteristic
102C2×C3×Dic3—41no—
103C2×C3×Dic3—41no—
104C3×Dic6—41no—
105C3×Dic6—41no—
106C3×Dic6—81no—
107C3⋊(C3⋊C8)—21no—
108C3⋊(C3⋊C8)—21no—
109C3⋊(C3⋊C8)—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—31no—
114#474—31no—
115C8×D4—91no—
116#335—91no—
117#333—91no—
118#332—91no—
119C2×C3×Q8—61no—
120C2×C3×Q8—61no—
121C2×C3×D4—21no—
122C2×C3×D4#6711yescharacteristic
123C2×C3×D4#6711yescharacteristic
124C22×C3×C4—22no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C2×Dic6—21no—
128C2×Dic6—21no—
129C2×C3×C8—61no—
130C2×C3×C8—61no—
131C3×C4⋊C4—21no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4#6711yescharacteristic
137C3×C4⋊C4#6711yescharacteristic
138C3×C22⋊C4—22no—
139C3×C22⋊C4—21no—
140C3×C22⋊C4—21no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144C4⋊Dic3—21no—
145C4⋊Dic3—21no—
146C4⋊Dic3—21no—
147C4⋊Dic3—21no—
148C2×C3⋊C8—21no—
149C2×C3⋊C8—21no—
150C2×C3⋊C8—31no—
151C2×C3⋊C8—31no—
152C2×C3⋊C8—31no—
153C2×C3⋊C8—31no—
154C2×C3⋊C8—61no—
155C2×C3⋊C8—61no—
156C2×C3⋊C8—62no—
157C2×C3⋊C8—61no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—124no—
160C2×C3⋊C8—122no—
161C2×C3⋊C8—122no—
162C22×C32—22no—
163C22×C32—41no—
164C22×C32—41no—
165C22×C32#12111yescharacteristic
166C32×C4—21no—
167C32×C4—41no—
168C32×C4C2×Q1611yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4#13511yescharacteristic
171C32×C4AGL(1,ℤ/8)11yescharacteristic
172C3×Dic3—81no—
173C3×Dic3—81no—
174C22×C8—181no—
175C4⋊Q8—31no—
176C4⋊Q8—31no—
177C4×D4D3211yescharacteristic
178#107—61no—
179#106—61no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—91no—
183#103—181no—
184#103—181no—
185#102—61no—
186#102—61no—
187C22⋊C8—181no—
188C4×C8—91no—
189C23×C3—22no—
190C23×C3—21no—
191C23×C3—21no—
192C3×Q8—121no—
193C3×Q8—121no—
194C3×Q8—241no—
195C3×D4—22no—
196C3×D4—21no—
197C3×D4—21no—
198C3×D4—22no—
199C3×D4#21612yes—
200C3×D4#21612yes—
201C2×C3×C4—22no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—42no—
208C2×C3×C4—42no—
209C2×C3×C4—41no—
210C2×C3×C4—41no—
211C2×C3×C4—41no—
212C2×C3×C4—41no—
213C2×C3×C4—121no—
214C2×C3×C4—121no—
215C2×C3×C4D3×D411yescharacteristic
216C2×C3×C4D3×D411yescharacteristic
217C2×C3×C4#23711yescharacteristic
218C2×C3×C4#23711yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×Dic3—41no—
222C2×Dic3—41no—
223Dic6—41no—
224Dic6—41no—
225Dic6—81no—
226C3×C8—121no—
227C3×C8—121no—
228C3⋊C8—41no—
229C3⋊C8—41no—
230C3⋊C8—62no—
231C3⋊C8—61no—
232C3⋊C8—61no—
233C3⋊C8—61no—
234C3⋊C8—61no—
235C3⋊C8—121no—
236C3⋊C8—122no—
237C3⋊C8—121no—
238C3⋊C8—121no—
239C2×C32—42no—
240C2×C32#46311yescharacteristic
241C2×C32#46711yescharacteristic
242C2×C32#47111yescharacteristic
243C2×Q8—61no—
244C2×Q8—61no—
245C2×D4#62511yescharacteristic
246C22×C4—21no—
247C2×C8—61no—
248C2×C8—61no—
249C2×C8—91no—
250C2×C8—91no—
251C2×C8—181no—
252C2×C8—362no—
253C4⋊C4—61no—
254C4⋊C4—61no—
255C4⋊C4—61no—
256C4⋊C4—61no—
257C4⋊C4#62511yescharacteristic
258C22⋊C4—21no—
259C42C2×D3211yescharacteristic
260C22×C3—24no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—21no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3#93911yescharacteristic
271C22×C3#93911yescharacteristic
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—42no—
280C3×C4—41no—
281C3×C4—41no—
282C3×C4—241no—
283C3×C4—241no—
284C3×C4#91111yescharacteristic
285C3×C4#91211yescharacteristic
286C3×C4#91411yescharacteristic
287C3×C4#91611yescharacteristic
288C3×C4C2×#21611yescharacteristic
289C3×C4C2×#21611yescharacteristic
290C3×C4#95011yescharacteristic
291C3×C4#95011yescharacteristic
292Dic3—81no—
293Dic3—81no—
294C32#168311yescharacteristic, complemented, Sylow
295C23—21no—
296Q8—121no—
297Q8—121no—
298Q8—241no—
299D4—21no—
300D4#371812yes—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—121no—
305C2×C4—121no—
306C2×C4#380511yescharacteristic
307C2×C4C2×#62511yescharacteristic
308C2×C4#381111yescharacteristic
309C8—121no—
310C8—121no—
311C8—181no—
312C8—181no—
313C8—361no—
314C2×C3—21no—
315C2×C3—21no—
316C2×C3—21no—
317C2×C3—44no—
318C2×C3—42no—
319C2×C3—42no—
320C2×C3#505111yescharacteristic
321C2×C3#505111yescharacteristic
322C2×C3#515311yescharacteristic
323C2×C3#516511yescharacteristic
324C2×C3#520011yescharacteristic
325C2×C3#520311yescharacteristic
326C22—22no—
327C22—41no—
328C22—41no—
329C22#6398011yescharacteristic
330C4—21no—
331C4—41no—
332C4—241no—
333C4—241no—
334C4#6382211yescharacteristic
335C4C2×#371811yescharacteristic
336C4#6393611yescharacteristic
337C4#6393711yescharacteristic
338C3—21no—
339C3#7110311yescharacteristic, complemented
340C3#7113511yescharacteristic, complemented
341C2—42no—
342C2#1059118811yescharacteristic
343C2#1059147611yescharacteristic
344C2#1059168111yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1683
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
4. #10590290C2semidirect
5. #10589100C2semidirect
6. #10589095C2semidirect
7. #10589092C2semidirect
294. C32#1683semidirect
339. C3#71103semidirect
340. C3#71135semidirect

Maximal subgroups

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

subgroupindex
D4×C3⋊(C3⋊C8)2
C3×#50082
C3×#50072
#105902902
#105891002
#105890952
#105890922
#711353
#711033