Finite Group Databasebeta

← C4×#63727 #11783793

Subgroups — C4×#63727 #11783793

Order 1152.

644 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 91 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×#3802C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic, complemented
3C2×#63727C212yesmaximal
4C4×#3712C211yesmaximal, characteristic, complemented
5#10590052C212yesmaximal, complemented
6C2×#3802C2211yescharacteristic
7C2×C4×D32C412yes—
8C2×#3788C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×C4×D12—21no—
11#63921C412yes—
12#63902—21no—
13C4×#625—21no—
14#63900C2211yescharacteristic
15#63898—21no—
16C2×#3712C2212yes—
17#63777—21no—
18C4×#622—21no—
19#63727C418yesdirect product factor
20C3×C4×C3⋊C8—21no—
21#63555—21no—
22C4×D3×D4—61no—
23C4×ΓL(1,𝔽25)—61no—
24C22×D32C2×C412yes—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×D12—21no—
29C2×C3×C4×D3—22no—
30C2×#625—21no—
31C2×#624C2×C412yes—
32C2×D3×Dic3—22no—
33#3802—22no—
34#3802C2×C414yes—
35C4×D32—44no—
36C2×#622—22no—
37#3788—22no—
38#3788C2×C414yescomplemented
39C32×C42D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3D411yescharacteristic
42C4×C3⋊Dic3D411yescharacteristic
43C3×(C2×D3)⋊C4—22no—
44C3×C4⋊Dic3—21no—
45C2×C3×C3⋊C8—22no—
46#3724—21no—
47(C2×D3)⋊Dic3—22no—
48#3712—22no—
49#3712C2×C414yescomplemented
50C4×#100—91nomaximal, Sylow
51C2×D3×D4—61no—
52C22×C4×D3—62no—
53C3×C4×D4—61no—
54D4×Dic3—61no—
55C4×#67—62no—
56C2×ΓL(1,𝔽25)—62no—
57#893—61no—
58D3×C4⋊C4—61no—
59#67⋊C4—62no—
60D3×C22⋊C4—62no—
61C4×D12—21no—
62C42×D3—61no—
63C42×D3—61no—
64C3×C4×C8—61no—
65#815—62no—
66C4×C3⋊C8—21no—
67C22×C3⋊D3C22×C411yescharacteristic
68C22×C3×D3—22no—
69C2×D32—22no—
70C2×D32—42no—
71C2×D32—42no—
72C2×D32C4214yes—
73C2×C32×C4C22⋊C411yescharacteristic
74C2×C32×C4C22⋊C411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—41no—
81C4×C3⋊D3C22×C412yes—
82C4×C3⋊D3#4112yes—
83C2×C3×Dic3—22no—
84C3×D12—24no—
85C3×C4×D3—44no—
86#625—24no—
87#624—42no—
88D3×Dic3—44no—
89#622—24no—
90C3×C3⋊C8—24no—
91C2×C4×D4—91no—
92C2×#100—92no—
93C4×M16—91no—
94C4×M16—91no—
95#343—92no—
96C23×D3—62no—
97C2×C3×D4—61no—
98C22×C3×C4—62no—
99C2×#67—62no—
100C22×Dic3—62no—
101D3×D4—64no—
102D3×D4—64no—
103C2×D12—21no—
104C2×C4×D3—22no—
105C2×C4×D3—61no—
106C2×C4×D3—61no—
107C2×C4×D3—61no—
108C2×C4×D3—62no—
109C2×C4×D3—61no—
110C2×C4×D3—61no—
111C2×C4×D3—61no—
112C2×C4×D3—62no—
113C2×C4×D3—128no—
114C2×C3×C8—62no—
115C3×C4⋊C4—61no—
116C3×C22⋊C4—62no—
117C3×C42—21no—
118C3×C42—21no—
119#217—62no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—62no—
122C4⋊Dic3—21no—
123Dic3⋊C4—62no—
124C4×Dic3—61no—
125C4×Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C4×Dic3—61no—
129C4×Dic3—61no—
130C2×C3⋊C8—22no—
131ΓL(1,𝔽25)—64no—
132ΓL(1,𝔽25)—64no—
133C22×C32C2×C22⋊C411yescharacteristic
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3C2×C4211yescharacteristic
137C2×C3⋊D3#11711yescharacteristic
138C2×C3×D3—24no—
139C2×C3×D3—42no—
140C2×C3×D3—42no—
141D32—44no—
142D32—44no—
143C32×C4—21no—
144C32×C4#10012yescomplemented
145C32×C4C4×D412yes—
146C3⋊Dic3—21no—
147C3⋊Dic3—21no—
148C3⋊Dic3C4×D412yes—
149C3×Dic3—42no—
150C22×D4—91no—
151C23×C4—92no—
152C2×M16—92no—
153C2×M16—92no—
154C4×D4—61no—
155C4×D4—181no—
156C4×D4—181no—
157C4×D4—181no—
158C2×C4⋊C4—91no—
159C2×C22⋊C4—92no—
160C2×C42—91no—
161#100—98no—
162#97—181no—
163#97—181no—
164C4×C8—61no—
165C4×C8—181no—
166C23×C3—62no—
167C22×D3—22no—
168C22×D3—64no—
169C22×D3—61no—
170C22×D3—61no—
171C22×D3—64no—
172C22×D3—124no—
173C22×D3—124no—
174C3×D4—64no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—62no—
182C2×C3×C4—124no—
183#67—68no—
184C2×Dic3—22no—
185C2×Dic3—61no—
186C2×Dic3—61no—
187C2×Dic3—61no—
188C2×Dic3—61no—
189C2×Dic3—61no—
190C2×Dic3—61no—
191C2×Dic3—124no—
192D12—24no—
193C4×D3—44no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C4×D3—62no—
198C4×D3—64no—
199C4×D3—122no—
200C4×D3—124no—
201C4×D3—124no—
202C4×D3—122no—
203C4×D3—122no—
204C3×C8—64no—
205C3⋊C8—24no—
206C2×C32C4×C22⋊C411yescharacteristic
207C2×C32C2×#10011yescharacteristic
208C2×C32#41311yescharacteristic
209C3⋊D3—21no—
210C3⋊D3—21no—
211C3×D3—44no—
212C24—92no—
213C2×D4—61no—
214C2×D4—94no—
215C2×D4—182no—
216C2×D4—181no—
217C22×C4—62no—
218C22×C4—92no—
219C22×C4—91no—
220C22×C4—91no—
221C22×C4—91no—
222C22×C4—182no—
223C22×C4—364no—
224M16—94no—
225M16—94no—
226M16—182no—
227M16—182no—
228C2×C8—62no—
229C2×C8—182no—
230C4⋊C4—61no—
231C4⋊C4—181no—
232C22⋊C4—62no—
233C22⋊C4—182no—
234C42—91no—
235C42—91no—
236C42—91no—
237C42GO+(4,𝔽2)11yescharacteristic
238C22×C3—21no—
239C22×C3—21no—
240C22×C3—64no—
241C22×C3—122no—
242C22×C3—122no—
243C2×D3—24no—
244C2×D3—42no—
245C2×D3—42no—
246C2×D3—61no—
247C2×D3—61no—
248C2×D3—61no—
249C2×D3—61no—
250C2×D3—62no—
251C2×D3—62no—
252C2×D3—121no—
253C2×D3—121no—
254C2×D3—128no—
255C2×D3—128no—
256C3×C4—22no—
257C3×C4—22no—
258C3×C4—22no—
259C3×C4—22no—
260C3×C4—22no—
261C3×C4—41no—
262C3×C4—122no—
263Dic3—42no—
264Dic3—62no—
265Dic3—62no—
266Dic3—62no—
267Dic3—121no—
268Dic3—121no—
269Dic3—121no—
270C32C4×#10011yescharacteristic, complemented, Sylow
271C23—62no—
272C23—94no—
273C23—91no—
274C23—182no—
275C23—362no—
276C23—362no—
277D4—64no—
278D4—184no—
279C2×C4—62no—
280C2×C4—91no—
281C2×C4—92no—
282C2×C4—92no—
283C2×C4—91no—
284C2×C4—91no—
285C2×C4—124no—
286C2×C4—182no—
287C2×C4—361no—
288C2×C4—364no—
289C2×C4—362no—
290C2×C4D32⋊C411yescharacteristic
291C2×C4D32⋊C411yescharacteristic
292C2×C4C2×GO+(4,𝔽2)11yescharacteristic
293C8—64no—
294C8—184no—
295C2×C3—21no—
296C2×C3—21no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—124no—
302D3—44no—
303D3—62no—
304D3—62no—
305D3—121no—
306D3—121no—
307C22—64no—
308C22—91no—
309C22—91no—
310C22—122no—
311C22—122no—
312C22—181no—
313C22—181no—
314C22—364no—
315C22—364no—
316C22C2×D32⋊C411yescharacteristic
317C4—21no—
318C4—92no—
319C4—122no—
320C4—181no—
321C4—181no—
322C4#6372712yesdirect product factor
323C4C4×GO+(4,𝔽2)12yes—
324C3—21no—
325C3—21no—
326C2—124no—
327C2—181no—
328C2—181no—
329C2C2×#6372711yescharacteristic
330C2#1059331111yescharacteristic
331C2C4×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C2×C42
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C22
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32C4×#100
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3788C2semidirect
4. C4×#3712C2semidirect
5. #10590052C2semidirect
19. #63727C4direct (N × H)
38. #3788C2×C4semidirect
49. #3712C2×C4semidirect
144. C32×C4#100semidirect
270. C32C4×#100semidirect
322. C4#63727direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#38022
C4×#37882
C2×#637272
C4×#37122
#105900522
C4×#1009