Finite Group Databasebeta

← C2×#10590164 #11783176

Subgroups — C2×#10590164 #11783176

Order 1152.

818 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×C4×#157C211yesmaximal, characteristic
2C22×#3788C211yesmaximal, characteristic
3C2×#64101C211yesmaximal, characteristic
4#10590164C214yesmaximal, direct product factor
5C23×#157—21no—
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×#622—21no—
8C2×C4×#157—22no—
9C2×C4×#157—21no—
10C2×C4×#157C414yescomplemented
11C2×C4×#157C2212yes—
12C2×#3788—21no—
13C2×#3788—22no—
14C2×#3788C414yescomplemented
15C2×#3788C2212yes—
16C2×C32×C4⋊C4C411yescharacteristic, complemented
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
19C2×C4×C3⋊Dic3—21no—
20#64101—21no—
21#64101—21no—
22#64101C412yescomplemented
23#64101C2212yes—
24C2×#892—62no—
25C23×C3⋊D3D411yescharacteristic
26C22×#157—24no—
27C22×#157—24no—
28C22×#157—24no—
29C22×#157—22no—
30C22×C32×C4—21no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3C2×C412yes—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3Q812yes—
41C2×C4×C3⋊D3C2311yescharacteristic
42C2×#622—24no—
43C2×#622—22no—
44C4×#157—24no—
45C4×#157—22no—
46C4×#157C2×C414yescomplemented
47#3788—24no—
48#3788—22no—
49#3788C2×C414yescomplemented
50C32×C4⋊C4—21no—
51C32×C4⋊C4C2×C412yescomplemented
52#3752—22no—
53#3752—22no—
54C4⋊(C3⋊Dic3)—21no—
55C4⋊(C3⋊Dic3)C2×C412yescomplemented
56C4×C3⋊Dic3—22no—
57C4×C3⋊Dic3—22no—
58C2×#339—91nomaximal, Sylow
59C22×C4×D3—62no—
60C2×C3×C4⋊C4—22no—
61C2×(C2×D3)⋊C4—64no—
62C2×C4⋊Dic3—62no—
63C2×C4×Dic3—64no—
64#892—64no—
65#892—64no—
66#892—64no—
67#892—64no—
68C23×C32C22⋊C411yescharacteristic
69C22×C3⋊D3—22no—
70C22×C3⋊D3—22no—
71C22×C3⋊D3C22⋊C411yescharacteristic
72C22×C3⋊D3C22⋊C412yes—
73C22×C3⋊D3C4⋊C412yes—
74C22×C3⋊D3C2×D411yescharacteristic
75C2×#157—216no—
76C2×#157—24no—
77C2×#157—24no—
78C2×#157—24no—
79C2×C32×C4—22no—
80C2×C32×C4—42no—
81C2×C32×C4C4212yes—
82C2×C32×C4C22⋊C411yescharacteristic
83C2×C32×C4C4⋊C412yes—
84C2×C32×C4C22×C411yescharacteristic
85C2×C3⋊Dic3—22no—
86C2×C3⋊Dic3—42no—
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C22⋊C412yes—
89C2×C3⋊Dic3C4⋊C412yes—
90C2×C3⋊Dic3C2×D411yescharacteristic
91C4×C3⋊D3C4212yes—
92C4×C3⋊D3C22⋊C412yes—
93C4×C3⋊D3C22⋊C412yes—
94C4×C3⋊D3C4⋊C412yes—
95C4×C3⋊D3C4⋊C412yes—
96C4×C3⋊D3C4⋊C412yes—
97C4×C3⋊D3C22×C411yescharacteristic
98C4×C3⋊D3C22×C411yescharacteristic
99C4×C3⋊D3C2×D411yescharacteristic
100C4×C3⋊D3C2×Q811yescharacteristic
101#622—24no—
102C22×M16—91no—
103C2×#117—91no—
104C22×C42—91no—
105#339—94no—
106C23×D3—62no—
107C22×C3×C4—24no—
108C22×C3×C4—22no—
109C22×Dic3—62no—
110C22×Dic3—64no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—62no—
115C2×C4×D3—64no—
116C2×C4×D3—64no—
117C2×C4×D3—64no—
118C2×C4×D3—64no—
119C3×C4⋊C4—24no—
120C3×C4⋊C4—24no—
121(C2×D3)⋊C4—68no—
122(C2×D3)⋊C4—68no—
123C4⋊Dic3—64no—
124C4⋊Dic3—64no—
125C4×Dic3—68no—
126C4×Dic3—68no—
127C22×C32#9512yes—
128C22×C32#10412yes—
129C22×C32#10412yes—
130C22×C32C2×C22⋊C411yescharacteristic
131C2×C3⋊D3—24no—
132C2×C3⋊D3—24no—
133C2×C3⋊D3—21no—
134C2×C3⋊D3—21no—
135C2×C3⋊D3—21no—
136C2×C3⋊D3—21no—
137C2×C3⋊D3#9512yes—
138C2×C3⋊D3C2×C22⋊C411yescharacteristic
139C2×C3⋊D3C2×C4⋊C411yescharacteristic
140#157—28no—
141C32×C4—42no—
142C32×C4#9512yes—
143C32×C4C2×C4211yescharacteristic
144C32×C4C2×C4⋊C411yescharacteristic
145C3⋊Dic3—42no—
146C3⋊Dic3#9512yes—
147C3⋊Dic3C2×C22⋊C411yescharacteristic
148C3⋊Dic3C2×C4⋊C411yescharacteristic
149C23×C4—91no—
150C23×C4—181no—
151C2×M16—94no—
152C2×M16—92no—
153C2×M16—182no—
154C2×M16—181no—
155C22×C8—181no—
156#117—92no—
157#117—92no—
158#117—181no—
159#117—181no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4#15711yescharacteristic, complemented
162C2×C22⋊C4—181no—
163C2×C42—94no—
164C2×C42—92no—
165C2×C42—181no—
166C2×C42—182no—
167C2×C42—181no—
168C23×C3—22no—
169C22×D3—62no—
170C22×D3—64no—
171C22×D3—64no—
172C22×D3—62no—
173C22×D3—124no—
174C22×D3—124no—
175C2×C3×C4—28no—
176C2×C3×C4—22no—
177C2×C3×C4—24no—
178C2×C3×C4—24no—
179C2×C3×C4—22no—
180C2×C3×C4—48no—
181C2×Dic3—62no—
182C2×Dic3—64no—
183C2×Dic3—64no—
184C2×Dic3—62no—
185C2×Dic3—68no—
186C2×Dic3—128no—
187C4×D3—64no—
188C4×D3—64no—
189C4×D3—64no—
190C4×D3—64no—
191C4×D3—64no—
192C4×D3—64no—
193C4×D3—62no—
194C4×D3—62no—
195C4×D3—62no—
196C4×D3—62no—
197C2×C32#33914yescomplemented
198C2×C32C2×#9511yescharacteristic
199C2×C32C2×#10411yescharacteristic
200C2×C32C2×#10411yescharacteristic
201C3⋊D3—21no—
202C3⋊D3—22no—
203C3⋊D3—21no—
204C24—91no—
205C22×C4—21no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—92no—
210C22×C4—92no—
211C22×C4—92no—
212C22×C4—92no—
213C22×C4—91no—
214C22×C4—91no—
215C22×C4—184no—
216C22×C4—182no—
217C22×C4—184no—
218C22×C4—184no—
219C22×C4—181no—
220C22×C4C2×#15711yescharacteristic
221M16—94no—
222M16—182no—
223M16—184no—
224C2×C8—184no—
225C2×C8—182no—
226C4⋊C4—21no—
227C4⋊C4—92no—
228C4⋊C4—181no—
229C4⋊C4C2×#15712yescomplemented
230C22⋊C4—182no—
231C22⋊C4—182no—
232C42—94no—
233C42—182no—
234C42—182no—
235C42—182no—
236C42—184no—
237C22×C3—24no—
238C22×C3—22no—
239C22×C3—24no—
240C22×C3—24no—
241C2×D3—64no—
242C2×D3—62no—
243C2×D3—62no—
244C2×D3—122no—
245C2×D3—122no—
246C2×D3—122no—
247C2×D3—122no—
248C2×D3—128no—
249C2×D3—128no—
250C3×C4—22no—
251C3×C4—22no—
252C3×C4—24no—
253C3×C4—48no—
254Dic3—64no—
255Dic3—62no—
256Dic3—62no—
257Dic3—128no—
258C32C2×#33911yescharacteristic, complemented, Sylow
259C23—92no—
260C23—92no—
261C23—91no—
262C23—91no—
263C23—182no—
264C23—182no—
265C23C22⋊#15711yescharacteristic
266C2×C4—22no—
267C2×C4—42no—
268C2×C4—92no—
269C2×C4—92no—
270C2×C4—91no—
271C2×C4—91no—
272C2×C4—91no—
273C2×C4—91no—
274C2×C4—92no—
275C2×C4—91no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—92no—
280C2×C4—92no—
281C2×C4—92no—
282C2×C4—184no—
283C2×C4—184no—
284C2×C4—184no—
285C2×C4—1816no—
286C2×C4—182no—
287C2×C4—362no—
288C2×C4C4×#15712yes—
289C2×C4C4⋊#15712yes—
290C2×C4C22⋊#15711yescharacteristic
291C2×C4C22×#15711yescharacteristic
292C8—184no—
293C2×C3—22no—
294C2×C3—22no—
295C2×C3—22no—
296C2×C3—28no—
297D3—122no—
298D3—124no—
299D3—122no—
300C22—91no—
301C22—91no—
302C22—92no—
303C22—181no—
304C22—181no—
305C22—181no—
306C22—181no—
307C22—184no—
308C22—184no—
309C22#6378112yes—
310C22#6378312yes—
311C22#6378512yes—
312C22C2×C22⋊#15711yescharacteristic
313C4—42no—
314C4—91no—
315C4—92no—
316C4—91no—
317C4—188no—
318C4—362no—
319C4#6378112yes—
320C4C2×C4×#15711yescharacteristic
321C4C2×C4⋊#15711yescharacteristic
322C3—22no—
323C2—181no—
324C2—181no—
325C2—182no—
326C2#1059016414yesdirect product factor
327C2C2×#6378111yescharacteristic
328C2C2×#6378311yescharacteristic
329C2C2×#6378511yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC23×C32C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32C2×#339
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590164C2direct (N × H)
10. C2×C4×#157C4semidirect
14. C2×#3788C4semidirect
16. C2×C32×C4⋊C4C4semidirect
18. C2×C4⋊(C3⋊Dic3)C4semidirect
22. #64101C4semidirect
46. C4×#157C2×C4semidirect
49. #3788C2×C4semidirect
51. C32×C4⋊C4C2×C4semidirect
55. C4⋊(C3⋊Dic3)C2×C4semidirect
161. C2×C4⋊C4#157semidirect
197. C2×C32#339semidirect
229. C4⋊C4C2×#157semidirect
258. C32C2×#339semidirect
326. C2#10590164direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#1572
C22×#37882
C2×#641012
#105901642
C2×#3399