Finite Group Databasebeta

← C4×#63782 #11783939

Subgroups — C4×#63782 #11783939

Order 1152.

822 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 110 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×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#63782C212yesmaximal
3C4×C4⋊#157C211yesmaximal, characteristic, complemented
4C4×#3787C211yesmaximal, characteristic, complemented
5#10590163C212yesmaximal, complemented
6C2×D4×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3—21no—
8C2×C4⋊#157C2212yes—
9C2×C4×#157—21no—
10C2×#3787C2212yes—
11C32×C4×D4C411yescharacteristic, complemented
12D4×C3⋊Dic3C411yescharacteristic, complemented
13C4×#638—21no—
14#64102C411yescharacteristic, complemented
15C4⋊C4×C3⋊D3C2211yescharacteristic
16#64090—21no—
17C22⋊C4×C3⋊D3—21no—
18C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
19C42×C3⋊D3C2211yescharacteristic
20#63782C418yesdirect product factor
21#63781—21no—
22C4×#622—21no—
23C4×#622—21no—
24C4×D3×D4—62no—
25C23×C3⋊D3—21no—
26C22×#157—22no—
27C2×C32×D4C2×C411yescharacteristic
28C22×C32×C4—21no—
29C2×#638—21no—
30C22×C3⋊Dic3—21no—
31D4×C3⋊D3—22no—
32D4×C3⋊D3C2×C414yes—
33C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C4×C3⋊D3—21no—
36C2×C4×C3⋊D3—21no—
37C2×C4×C3⋊D3—42no—
38C2×C4×C3⋊D3—42no—
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3C2311yescharacteristic
42C2×#622—22no—
43C4⋊#157—22no—
44C4⋊#157C2×C414yescomplemented
45C4×#157—42no—
46#3787—22no—
47#3787C2×C414yescomplemented
48C32×C4⋊C4C2×C411yescharacteristic
49C32×C22⋊C4—21no—
50C32×C42C2×C411yescharacteristic
51#3757—21no—
52#3752—21no—
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3D411yescharacteristic
58C4×C3⋊Dic3D411yescharacteristic
59C4×#102—91nomaximal, Sylow
60C2×D3×D4—62no—
61C22×C4×D3—64no—
62C3×C4×D4—22no—
63D4×Dic3—62no—
64C4×#67—64no—
65#893—62no—
66D3×C4⋊C4—62no—
67#67⋊C4—64no—
68D3×C22⋊C4—64no—
69C4×D12—62no—
70C42×D3—62no—
71C23×C32—21no—
72C22×C3⋊D3—21no—
73C22×C3⋊D3—24no—
74C22×C3⋊D3—41no—
75C22×C3⋊D3—41no—
76C22×C3⋊D3—42no—
77C22×C3⋊D3C2×D411yescharacteristic
78C2×#157—24no—
79C2×#157—42no—
80C2×#157—42no—
81C32×D4—21no—
82C32×D4C4212yescomplemented
83C2×C32×C4—21no—
84C2×C32×C4—42no—
85C2×C32×C4C22⋊C411yescharacteristic
86C2×C32×C4C22⋊C411yescharacteristic
87C2×C32×C4C22×C411yescharacteristic
88#638—24no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3C22⋊C411yescharacteristic
92C2×C3⋊Dic3C22⋊C411yescharacteristic
93C2×C3⋊Dic3C2×D411yescharacteristic
94C4⋊(C3⋊D3)—21no—
95C4⋊(C3⋊D3)C4212yescomplemented
96C4×C3⋊D3—22no—
97C4×C3⋊D3—41no—
98C4×C3⋊D3—41no—
99C4×C3⋊D3—42no—
100C4×C3⋊D3—42no—
101C4×C3⋊D3D812yes—
102C4×C3⋊D3SD1612yes—
103C4×C3⋊D3C22×C412yes—
104C4×C3⋊D3#4112yes—
105#622—24no—
106C2×C4×D4—91no—
107C2×#102—92no—
108C2×C4×C8—91no—
109C4×C4⋊C4—91no—
110#340—92no—
111C23×D3—64no—
112C2×C3×D4—22no—
113C22×C3×C4—24no—
114C2×#67—64no—
115C22×Dic3—64no—
116D3×D4—68no—
117D3×D4—68no—
118C2×D12—62no—
119C2×C4×D3—62no—
120C2×C4×D3—62no—
121C2×C4×D3—62no—
122C2×C4×D3—64no—
123C2×C4×D3—64no—
124C2×C4×D3—64no—
125C2×C4×D3—128no—
126C2×C4×D3—128no—
127C3×C4⋊C4—22no—
128C3×C22⋊C4—24no—
129C3×C42—22no—
130#217—64no—
131(C2×D3)⋊C4—64no—
132(C2×D3)⋊C4—64no—
133C4⋊Dic3—62no—
134Dic3⋊C4—64no—
135C4×Dic3—62no—
136C4×Dic3—62no—
137C4×Dic3—62no—
138C22×C32—22no—
139C22×C32—41no—
140C22×C32—41no—
141C22×C32C2×C22⋊C411yescharacteristic
142C2×C3⋊D3—22no—
143C2×C3⋊D3—41no—
144C2×C3⋊D3—41no—
145C2×C3⋊D3—44no—
146C2×C3⋊D3—44no—
147C2×C3⋊D3C4×D412yes—
148C2×C3⋊D3C2×D811yescharacteristic
149C2×C3⋊D3C2×SD1611yescharacteristic
150C2×C3⋊D3#13512yes—
151#157—44no—
152C32×C4—21no—
153C32×C4—41no—
154C32×C4#10212yescomplemented
155C32×C4C2×C4211yescharacteristic
156C32×C4#11711yescharacteristic
157C3⋊Dic3—21no—
158C3⋊Dic3—41no—
159C3⋊Dic3#10212yescomplemented
160C3⋊Dic3C4×D412yes—
161C22×D4—91no—
162C23×C4—181no—
163C22×C8—92no—
164C4×D4—91no—
165C4×D4—91no—
166C4×D4—91no—
167C4×D4—181no—
168C4×D4—181no—
169C4×D4#15711yescharacteristic, complemented
170C2×C4⋊C4—92no—
171C2×C4⋊C4—91no—
172C2×C22⋊C4—181no—
173C2×C42—91no—
174C2×C42—181no—
175#102—98no—
176C4×C8—181no—
177C4×C8—181no—
178#95—181no—
179C23×C3—24no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—616no—
183C22×D3—124no—
184C22×D3—124no—
185C22×D3—128no—
186C3×D4—24no—
187C3×D4—24no—
188C2×C3×C4—24no—
189C2×C3×C4—22no—
190C2×C3×C4—22no—
191C2×C3×C4—22no—
192C2×C3×C4—48no—
193#67—616no—
194C2×Dic3—62no—
195C2×Dic3—62no—
196C2×Dic3—62no—
197C2×Dic3—64no—
198C2×Dic3—128no—
199D12—64no—
200D12—64no—
201C4×D3—64no—
202C4×D3—64no—
203C4×D3—64no—
204C4×D3—64no—
205C4×D3—124no—
206C4×D3—128no—
207C4×D3—128no—
208C4×D3—124no—
209C4×D3—124no—
210C2×C32—42no—
211C2×C32C4×C22⋊C411yescharacteristic
212C2×C32C2×#10211yescharacteristic
213C2×C32#41611yescharacteristic
214C3⋊D3—42no—
215C3⋊D3C4×D812yes—
216C3⋊D3C4×SD1612yes—
217C24—181no—
218C2×D4—94no—
219C2×D4—91no—
220C2×D4—182no—
221C2×D4—181no—
222C2×D4C2×#15711yescharacteristic
223C22×C4—21no—
224C22×C4—91no—
225C22×C4—91no—
226C22×C4—91no—
227C22×C4—181no—
228C22×C4—181no—
229C22×C4—181no—
230C22×C4—182no—
231C22×C4—181no—
232C22×C4—362no—
233C22×C4—362no—
234C2×C8—94no—
235C2×C8—182no—
236C2×C8—182no—
237C4⋊C4—94no—
238C4⋊C4—91no—
239C4⋊C4—181no—
240C4⋊C4—182no—
241C4⋊C4C2×#15711yescharacteristic
242C22⋊C4—21no—
243C22⋊C4—181no—
244C22⋊C4—181no—
245C22⋊C4—181no—
246C42—91no—
247C42—91no—
248C42—91no—
249C42—362no—
250C42C2×#15711yescharacteristic
251C22×C3—28no—
252C22×C3—22no—
253C22×C3—44no—
254C22×C3—44no—
255C2×D3—62no—
256C2×D3—62no—
257C2×D3—64no—
258C2×D3—64no—
259C2×D3—68no—
260C2×D3—1216no—
261C2×D3—1216no—
262C2×D3—124no—
263C2×D3—124no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—24no—
267C3×C4—42no—
268C3×C4—44no—
269Dic3—64no—
270Dic3—64no—
271Dic3—122no—
272Dic3—124no—
273C32C4×#10211yescharacteristic, complemented, Sylow
274C23—21no—
275C23—91no—
276C23—184no—
277C23—181no—
278C23—361no—
279C23—361no—
280C23—362no—
281D4—21no—
282D4—92no—
283D4—184no—
284D4—181no—
285D4C4×#15712yescomplemented
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—91no—
289C2×C4—91no—
290C2×C4—92no—
291C2×C4—92no—
292C2×C4—92no—
293C2×C4—92no—
294C2×C4—91no—
295C2×C4—182no—
296C2×C4—184no—
297C2×C4—181no—
298C2×C4—362no—
299C2×C4—361no—
300C2×C4—361no—
301C2×C4—362no—
302C2×C4—362no—
303C2×C4—362no—
304C2×C4—362no—
305C2×C4C22⋊#15711yescharacteristic
306C2×C4C22⋊#15711yescharacteristic
307C2×C4C22×#15711yescharacteristic
308C8—184no—
309C2×C3—22no—
310C2×C3—22no—
311C2×C3—22no—
312C2×C3—48no—
313D3—64no—
314D3—64no—
315D3—128no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—92no—
320C22—91no—
321C22—91no—
322C22—92no—
323C22—182no—
324C22—364no—
325C22—364no—
326C22—361no—
327C22—361no—
328C22C2×C22⋊#15711yescharacteristic
329C4—21no—
330C4—41no—
331C4—92no—
332C4—92no—
333C4—181no—
334C4—364no—
335C4—361no—
336C4#6378212yesdirect product factor
337C4C2×C4×#15711yescharacteristic
338C4#6428611yescharacteristic
339C3—22no—
340C2—42no—
341C2—92no—
342C2—92no—
343C2—362no—
344C2C4×C22⋊#15711yescharacteristic
345C2C2×#6378211yescharacteristic
346C2#1059384111yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenterC4×D4#157
hypocenterC32C4×#102
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. C4×C4⋊#157C2semidirect
4. C4×#3787C2semidirect
5. #10590163C2semidirect
11. C32×C4×D4C4semidirect
12. D4×C3⋊Dic3C4semidirect
14. #64102C4semidirect
18. C4×C4⋊(C3⋊D3)C4semidirect
20. #63782C4direct (N × H)
44. C4⋊#157C2×C4semidirect
47. #3787C2×C4semidirect
82. C32×D4C42semidirect
95. C4⋊(C3⋊D3)C42semidirect
154. C32×C4#102semidirect
159. C3⋊Dic3#102semidirect
169. C4×D4#157semidirect
273. C32C4×#102semidirect
285. D4C4×#157semidirect
336. C4#63782direct (N × H)

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C2×#637822
C4×C4⋊#1572
C4×#37872
#105901632
C4×#1029