Finite Group Databasebeta

← #11781350

Subgroups — #11781350

Order 1152.

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

normal subgroups only

This group has 399 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×#5019C211yesmaximal, characteristic
3C3×#5007C211yesmaximal, characteristic
4#10590290C211yesmaximal, characteristic, complemented
5#10589098C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589092C211yesmaximal, characteristic, complemented
8#71102—31nomaximal
9#71038—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C22×C3⋊(C3⋊C8)—21no—
12C2×C3×#214—21no—
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63657—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#832—21no—
19C3×#810—21no—
20C3×#807—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63565—21no—
24#63565—21no—
25C3×#474—31no—
26C3×#461—31no—
27#5093—31no—
28#5079—31no—
29#5019D311yescharacteristic
30D4×C3⋊C8—31no—
31D4×C3⋊C8—31no—
32D4×C3⋊C8—61no—
33#5007D311yescharacteristic
34#4547—31no—
35#4547—31no—
36#4486—31no—
37#4482—31no—
38#4480—31no—
39#4480—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×#214—42no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3—21no—
56C2×C3×C3⋊C8—21no—
57C2×C3×C3⋊C8—21no—
58#1679—91noSylow
59C2×C3×SD16—61no—
60C3×C4⋊Q8—31no—
61C3×C4⋊Q8—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#214—21no—
66C22×C3⋊C8—61no—
67C22×C3⋊C8—61no—
68C22×C3⋊C8—62no—
69#869C2×D311yescharacteristic
70#869C2×D311yescharacteristic
71C3×#107—61no—
72C3×C4⋊C8—31no—
73C3×C4⋊C8—31no—
74C3×#103—61no—
75C3×#102—61no—
76#835—61no—
77#835—61no—
78#832—21no—
79#830—61no—
80#830—61no—
81#830—62no—
82#810—21no—
83#810—61no—
84#810—61no—
85#807—21no—
86C4⋊(C3⋊C8)—31no—
87C4⋊(C3⋊C8)—31no—
88C4⋊(C3⋊C8)—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4×C3⋊C8—31no—
92C4×C3⋊C8—31no—
93C4×C3⋊C8—61no—
94C23×C32—21no—
95C32×D4—21no—
96C32×D4SD1612yes—
97C2×C32×C4—21no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4#4111yescharacteristic
103C2×C3×Dic3—41no—
104C2×C3×Dic3—41no—
105C3×Dic6—41no—
106C3×Dic6—41no—
107C3×Dic6—41no—
108C3×Dic6—41no—
109C3⋊(C3⋊C8)—21no—
110C3⋊(C3⋊C8)—21no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—41no—
113C3×C3⋊C8—41no—
114#487—91no—
115#474—31no—
116#461—31no—
117C8×D4—91no—
118#334—91no—
119#332—91no—
120#332—91no—
121C2×C3×Q8—61no—
122C2×C3×Q8—61no—
123C2×C3×D4—21no—
124C2×C3×D4#6711yescharacteristic
125C2×C3×D4#6711yescharacteristic
126C22×C3×C4—22no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C3×SD16—122no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—61no—
136C3×C4⋊C4—61no—
137C3×C4⋊C4—61no—
138C3×C4⋊C4—61no—
139C3×C4⋊C4#6711yescharacteristic
140C3×C4⋊C4#6711yescharacteristic
141C3×C22⋊C4—22no—
142C3×C22⋊C4—21no—
143C3×C22⋊C4—21no—
144C3×C42—21no—
145C3×C42C22×D311yescharacteristic
146C3×C42C22×D311yescharacteristic
147#214—42no—
148C4⋊Dic3—21no—
149C4⋊Dic3—21no—
150C4⋊Dic3—21no—
151C4⋊Dic3—21no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—21no—
154C2×C3⋊C8—31no—
155C2×C3⋊C8—31no—
156C2×C3⋊C8—31no—
157C2×C3⋊C8—31no—
158C2×C3⋊C8—61no—
159C2×C3⋊C8—61no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—124no—
164C2×C3⋊C8—122no—
165C2×C3⋊C8—122no—
166C22×C32—22no—
167C22×C32—41no—
168C22×C32—41no—
169C22×C32#12111yescharacteristic
170C32×C4—21no—
171C32×C4—41no—
172C32×C4C2×SD1611yescharacteristic
173C32×C4#13511yescharacteristic
174C32×C4#13511yescharacteristic
175C32×C4AGL(1,ℤ/8)11yescharacteristic
176C3×Dic3—81no—
177C3×Dic3—81no—
178C2×SD16—61no—
179C22×C8—181no—
180C4⋊Q8—31no—
181C4⋊Q8—31no—
182C4×D4D3211yescharacteristic
183#107—61no—
184C4⋊C8—31no—
185C4⋊C8—31no—
186C4⋊C8—91no—
187#103—61no—
188#103—181no—
189#103—181no—
190#102—61no—
191C22⋊C8—181no—
192C4×C8—91no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C3×Q8—121no—
197C3×Q8—121no—
198C3×Q8—121no—
199C3×Q8—121no—
200C3×D4—22no—
201C3×D4—21no—
202C3×D4—21no—
203C3×D4—22no—
204C3×D4#21412yes—
205C3×D4#21512yes—
206C2×C3×C4—22no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—42no—
213C2×C3×C4—42no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—121no—
219C2×C3×C4—121no—
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4#23711yescharacteristic
223C2×C3×C4#23711yescharacteristic
224C2×C3×C4C2×#6711yescharacteristic
225C2×C3×C4C2×#6711yescharacteristic
226C2×Dic3—41no—
227C2×Dic3—41no—
228Dic6—41no—
229Dic6—41no—
230Dic6—41no—
231Dic6—41no—
232C3×C8—121no—
233C3×C8—121no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—62no—
237C3⋊C8—61no—
238C3⋊C8—61no—
239C3⋊C8—61no—
240C3⋊C8—61no—
241C3⋊C8—121no—
242C3⋊C8—122no—
243C3⋊C8—121no—
244C3⋊C8—121no—
245C2×C32—42no—
246C2×C32#46311yescharacteristic
247C2×C32#46511yescharacteristic
248C2×C32#47311yescharacteristic
249C2×Q8—61no—
250C2×Q8—61no—
251C2×D4#62511yescharacteristic
252C22×C4—21no—
253SD16—122no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8—91no—
257C2×C8—91no—
258C2×C8—181no—
259C2×C8—362no—
260C4⋊C4—61no—
261C4⋊C4—61no—
262C4⋊C4—61no—
263C4⋊C4—61no—
264C4⋊C4#62511yescharacteristic
265C22⋊C4—21no—
266C42C2×D3211yescharacteristic
267C22×C3—24no—
268C22×C3—22no—
269C22×C3—22no—
270C22×C3—21no—
271C22×C3—42no—
272C22×C3—42no—
273C22×C3—41no—
274C22×C3—41no—
275C22×C3—41no—
276C22×C3—41no—
277C22×C3#93911yescharacteristic
278C22×C3#93911yescharacteristic
279C3×C4—21no—
280C3×C4—21no—
281C3×C4—21no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—41no—
286C3×C4—42no—
287C3×C4—41no—
288C3×C4—41no—
289C3×C4—241no—
290C3×C4—241no—
291C3×C4#91111yescharacteristic
292C3×C4#91211yescharacteristic
293C3×C4#91411yescharacteristic
294C3×C4#91611yescharacteristic
295C3×C4C2×#21411yescharacteristic
296C3×C4C2×#21511yescharacteristic
297C3×C4#95011yescharacteristic
298C3×C4#95011yescharacteristic
299Dic3—81no—
300Dic3—81no—
301C32#167911yescharacteristic, complemented, Sylow
302C23—21no—
303Q8—121no—
304Q8—121no—
305Q8—121no—
306Q8—121no—
307D4—21no—
308D4#371512yes—
309C2×C4—21no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—121no—
313C2×C4—121no—
314C2×C4#380511yescharacteristic
315C2×C4C2×#62511yescharacteristic
316C2×C4#381111yescharacteristic
317C8—121no—
318C8—121no—
319C8—181no—
320C8—181no—
321C8—361no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—21no—
325C2×C3—44no—
326C2×C3—42no—
327C2×C3—42no—
328C2×C3#504111yescharacteristic
329C2×C3#504811yescharacteristic
330C2×C3#515311yescharacteristic
331C2×C3#516511yescharacteristic
332C2×C3#520411yescharacteristic
333C2×C3#520411yescharacteristic
334C22—22no—
335C22—41no—
336C22—41no—
337C22#6398011yescharacteristic
338C4—21no—
339C4—41no—
340C4—241no—
341C4—241no—
342C4#6382211yescharacteristic
343C4C2×#371511yescharacteristic
344C4#6393611yescharacteristic
345C4#6393711yescharacteristic
346C3—21no—
347C3#7103811yescharacteristic, complemented
348C3#7110211yescharacteristic, complemented
349C2—42no—
350C2#1059117911yescharacteristic
351C2#1059147611yescharacteristic
352C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#1679
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. #10589098C2semidirect
6. #10589093C2semidirect
7. #10589092C2semidirect
301. C32#1679semidirect
347. C3#71038semidirect
348. C3#71102semidirect

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×#50192
C3×#50072
#105902902
#105890982
#105890932
#105890922
#711023
#710383