Finite Group Databasebeta

← #11785316

Subgroups — #11785316

Order 1152.

622 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C4×#3832C211yesmaximal, characteristic
2C2×#63785C212yesmaximal
3C4×C4⋊#157C211yesmaximal, characteristic, complemented
4#10593729C211yesmaximal, characteristic, complemented
5#10590164C212yesmaximal, complemented
6C2×#3832C2211yescharacteristic
7C2×C4⋊#157—21no—
8C2×C4×#157C2212yes—
9C2×#3788C2212yes—
10C32×C4×Q8C411yescharacteristic, complemented
11Q8×C3⋊Dic3C411yescharacteristic, complemented
12#64102—21no—
13#64102C411yescharacteristic, complemented
14#64101—21no—
15#64101C2211yescharacteristic
16C4×C4⋊(C3⋊D3)—21no—
17C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
18C42×C3⋊D3—21no—
19C42×C3⋊D3C2211yescharacteristic
20#63785—24no—
21#63781—21no—
22#63779—21no—
23#63779—21no—
24C4×#239—62no—
25C22×#157—22no—
26C2×C32×Q8C2×C411yescharacteristic
27#3832—21no—
28#3832—21no—
29#3832D412yes—
30#3832Q812yes—
31C2×C4⋊(C3⋊D3)—21no—
32C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3D411yescharacteristic
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×#622—22no—
40C4⋊#157—24no—
41C4×#157—22no—
42C4×#157—22no—
43#3788—22no—
44#3788—22no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4C2×C411yescharacteristic
47C32×C42—21no—
48C32×C42C2×C411yescharacteristic
49#3752—21no—
50#3752—21no—
51#3752—21no—
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59#1806—91nomaximal, Sylow
60C2×#239—62no—
61C3×C4×Q8—22no—
62Q8×Dic3—62no—
63#893—62no—
64#893—64no—
65#892—62no—
66#892—64no—
67C4×D12—62no—
68C4×D12—64no—
69C42×D3—62no—
70C42×D3—64no—
71C22×C3⋊D3—21no—
72C22×C3⋊D3C2×D411yescharacteristic
73C2×#157—24no—
74C2×#157—42no—
75C2×#157—42no—
76C32×Q8—21no—
77C32×Q8C4⋊C412yescomplemented
78C2×C32×C4—21no—
79C2×C32×C4—21no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C32×C4C22×C411yescharacteristic
83C2×C3⋊Dic3—21no—
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C2×C3⋊Dic3C22⋊C411yescharacteristic
86C2×C3⋊Dic3C2×D411yescharacteristic
87C4⋊(C3⋊D3)—22no—
88C4⋊(C3⋊D3)—22no—
89C4⋊(C3⋊D3)—21no—
90C4⋊(C3⋊D3)C4⋊C412yescomplemented
91C4×C3⋊D3—22no—
92C4×C3⋊D3—22no—
93C4×C3⋊D3—22no—
94C4×C3⋊D3—41no—
95C4×C3⋊D3—42no—
96C4×C3⋊D3—42no—
97C4×C3⋊D3C2×D411yescharacteristic
98C4×C3⋊D3C2×Q811yescharacteristic
99C4×C3⋊D3#4111yescharacteristic
100C4×C3⋊D3#4111yescharacteristic
101#622—42no—
102C4×#41—91no—
103#423—91no—
104C2×#104—92no—
105C4×C4⋊C4—91no—
106#339—92no—
107C2×C3×Q8—22no—
108#239—64no—
109#239—64no—
110#239—64no—
111#239—64no—
112C2×D12—62no—
113C2×D12—64no—
114C2×C4×D3—62no—
115C2×C4×D3—62no—
116C2×C4×D3—62no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C2×C4×D3—64no—
120C3×C4⋊C4—24no—
121C3×C4⋊C4—22no—
122C3×C42—24no—
123C3×C42—22no—
124(C2×D3)⋊C4—64no—
125(C2×D3)⋊C4—64no—
126(C2×D3)⋊C4—64no—
127C4⋊Dic3—62no—
128C4⋊Dic3—64no—
129C4×Dic3—62no—
130C4×Dic3—62no—
131C4×Dic3—62no—
132C4×Dic3—64no—
133C4×Dic3—64no—
134C22×C32C2×C22⋊C411yescharacteristic
135C2×C3⋊D3—22no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3—21no—
138C2×C3⋊D3—41no—
139C2×C3⋊D3—41no—
140C2×C3⋊D3#12111yescharacteristic
141C2×C3⋊D3C22⋊Q811yescharacteristic
142#157—44no—
143C32×C4—22no—
144C32×C4—21no—
145C32×C4—21no—
146C32×C4—41no—
147C32×C4C2×C4⋊C411yescharacteristic
148C32×C4#11711yescharacteristic
149C3⋊Dic3—21no—
150C3⋊Dic3—41no—
151C3⋊Dic3#10412yescomplemented
152C3⋊Dic3#12111yescharacteristic
153C3⋊Dic3C22⋊Q811yescharacteristic
154C2×#41—91no—
155C2×M16—92no—
156C4×Q8—91no—
157C4×Q8#15711yescharacteristic, complemented
158C4×D4—91no—
159C4×D4—91no—
160C4×D4—181no—
161C4×D4—181no—
162#117—91no—
163#117—181no—
164C2×C4⋊C4—181no—
165C2×C42—91no—
166C2×C42—92no—
167C2×C42—181no—
168C4⋊C8—181no—
169C4⋊C8—181no—
170#104—184no—
171#95—181no—
172C22×D3—62no—
173C22×D3—64no—
174C3×Q8—24no—
175C3×Q8—24no—
176C2×C3×C4—24no—
177C2×C3×C4—24no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×Dic3—62no—
182C2×Dic3—62no—
183C2×Dic3—62no—
184C2×Dic3—64no—
185D12—64no—
186D12—68no—
187D12—68no—
188D12—64no—
189C4×D3—62no—
190C4×D3—62no—
191C4×D3—62no—
192C4×D3—62no—
193C4×D3—68no—
194C4×D3—68no—
195C4×D3—124no—
196C4×D3—128no—
197C4×D3—124no—
198C4×D3—128no—
199C2×C32#38011yescharacteristic
200C2×C32C2×#10411yescharacteristic
201C2×C32#42111yescharacteristic
202C3⋊D3—21no—
203C3⋊D3—21no—
204C3⋊D3—42no—
205#41—92no—
206#41—92no—
207#41—181no—
208#41—181no—
209C2×Q8C2×#15711yescharacteristic
210C2×D4—91no—
211C2×D4—181no—
212C22×C4—91no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—181no—
216C22×C4—181no—
217C22×C4—182no—
218C22×C4—181no—
219M16—182no—
220M16—182no—
221C2×C8—182no—
222C4⋊C4—21no—
223C4⋊C4—91no—
224C4⋊C4—181no—
225C4⋊C4—184no—
226C4⋊C4C2×#15711yescharacteristic
227C22⋊C4—181no—
228C22⋊C4—181no—
229C22⋊C4—181no—
230C42—21no—
231C42—91no—
232C42—91no—
233C42—91no—
234C42—181no—
235C42—181no—
236C42—182no—
237C42—182no—
238C42C2×#15711yescharacteristic
239C22×C3—22no—
240C2×D3—62no—
241C2×D3—62no—
242C2×D3—68no—
243C2×D3—122no—
244C2×D3—122no—
245C2×D3—124no—
246C2×D3—124no—
247C3×C4—28no—
248C3×C4—24no—
249C3×C4—22no—
250C3×C4—22no—
251C3×C4—42no—
252C3×C4—44no—
253Dic3—62no—
254Dic3—62no—
255Dic3—64no—
256Dic3—122no—
257Dic3—124no—
258C32#180611yescharacteristic, complemented, Sylow
259C23—91no—
260C23—181no—
261Q8—21no—
262Q8C4⋊#15712yescomplemented
263D4—92no—
264D4—182no—
265D4—182no—
266D4—181no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—91no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—91no—
275C2×C4—91no—
276C2×C4—182no—
277C2×C4—182no—
278C2×C4—182no—
279C2×C4—184no—
280C2×C4—181no—
281C2×C4—361no—
282C2×C4—362no—
283C2×C4—362no—
284C2×C4—362no—
285C2×C4—362no—
286C2×C4C22⋊#15711yescharacteristic
287C2×C4C22⋊#15711yescharacteristic
288C2×C4C22×#15711yescharacteristic
289C8—362no—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—22no—
293D3—122no—
294D3—122no—
295D3—128no—
296C22—91no—
297C22—91no—
298C22—181no—
299C22—181no—
300C22—182no—
301C22—361no—
302C22—361no—
303C22C2×C22⋊#15711yescharacteristic
304C4—22no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—91no—
309C4—91no—
310C4—92no—
311C4—181no—
312C4—364no—
313C4—361no—
314C4C2×C4⋊#15711yescharacteristic
315C4#6428611yescharacteristic
316C3—22no—
317C2—181no—
318C2—181no—
319C2—362no—
320C2#1059381211yescharacteristic
321C2#1059383111yescharacteristic
322C2#1059383911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1806
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊#157C2semidirect
4. #10593729C2semidirect
5. #10590164C2semidirect
10. C32×C4×Q8C4semidirect
11. Q8×C3⋊Dic3C4semidirect
13. #64102C4semidirect
17. C4×C4⋊(C3⋊D3)C4semidirect
77. C32×Q8C4⋊C4semidirect
90. C4⋊(C3⋊D3)C4⋊C4semidirect
151. C3⋊Dic3#104semidirect
157. C4×Q8#157semidirect
258. C32#1806semidirect
262. Q8C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C2×#637852
C4×C4⋊#1572
#105937292
#105901642
#18069