Finite Group Databasebeta

← C2×#10593825 #11857590

Subgroups — C2×#10593825 #11857590

Order 1152.

2354 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 2354 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×C3⋊D3C211yesmaximal, characteristic
2C2×#64283C212yesmaximal, complemented
3C2×#63788C214yesmaximal, complemented
4#10593825C218yesmaximal, direct product factor
5C24×C3⋊D3C412yes—
6C22×C32×D4C411yescharacteristic
7C22×#638C2212yes—
8C2×D4×C3⋊D3—22no—
9C2×D4×C3⋊D3—22no—
10C2×D4×C3⋊D3—24no—
11C2×D4×C3⋊D3C414yes—
12C2×D4×C3⋊D3C2214yes—
13C22×C4⋊(C3⋊D3)C411yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×#3792C2214yescomplemented
16#64283—24no—
17#64283C2218yescomplemented
18C2×#3788—22no—
19C2×#3787—22no—
20#63788C22116yescomplemented
21C22×D3×D4—62no—
22C24×C32C2×C412yes—
23C23×C3⋊D3—24no—
24C23×C3⋊D3—22no—
25C23×C3⋊D3—22no—
26C23×C3⋊D3—48no—
27C23×C3⋊D3C2×C411yescharacteristic
28C23×C3⋊D3C2×C412yes—
29C23×C3⋊D3C2×C418yes—
30C2×C32×D4—22no—
31C2×C32×D4—22no—
32C2×C32×D4C2×C414yes—
33C22×C32×C4C2×C411yescharacteristic
34C2×#638—24no—
35C2×#638—24no—
36C2×#638C2×C414yes—
37C2×#638C2314yes—
38C22×C3⋊Dic3C2311yescharacteristic
39D4×C3⋊D3—28no—
40D4×C3⋊D3—28no—
41D4×C3⋊D3—28no—
42D4×C3⋊D3—28no—
43C2×C4⋊(C3⋊D3)—22no—
44C2×C4⋊(C3⋊D3)—22no—
45C2×C4⋊(C3⋊D3)C2×C414yes—
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3D412yes—
48C2×C4×C3⋊D3D412yes—
49C2×C4×C3⋊D3D414yes—
50C2×C4×C3⋊D3C2312yes—
51#3792—24no—
52#3792C2318yescomplemented
53C2×#622—24no—
54#3788—28no—
55#3787—28no—
56C22×#100—91nomaximal, Sylow
57C24×D3—64no—
58C22×C3×D4—22no—
59C22×#67—64no—
60C2×D3×D4—68no—
61C2×D3×D4—68no—
62C2×D3×D4—68no—
63C2×D3×D4—68no—
64C2×D3×D4—616no—
65C22×D12—62no—
66C22×C4×D3—62no—
67C23×C32—22no—
68C23×C32—22no—
69C23×C32—44no—
70C23×C32C22×C411yescharacteristic
71C23×C32C22×C414yes—
72C22×C3⋊D3—24no—
73C22×C3⋊D3—22no—
74C22×C3⋊D3—22no—
75C22×C3⋊D3—28no—
76C22×C3⋊D3—28no—
77C22×C3⋊D3—48no—
78C22×C3⋊D3—416no—
79C22×C3⋊D3—416no—
80C22×C3⋊D3—48no—
81C22×C3⋊D3—44no—
82C22×C3⋊D3C22⋊C411yescharacteristic
83C22×C3⋊D3C22⋊C412yes—
84C22×C3⋊D3C22⋊C411yescharacteristic
85C22×C3⋊D3C22×C412yes—
86C22×C3⋊D3C22×C414yes—
87C32×D4—28no—
88C2×C32×C4C22⋊C412yes—
89C2×C32×C4C22⋊C412yes—
90C2×C32×C4C22×C412yes—
91#638—28no—
92#638—28no—
93C2×C3⋊Dic3C22×C411yescharacteristic
94C2×C3⋊Dic3C2×D412yes—
95C2×C3⋊Dic3C2×D412yes—
96C2×C3⋊Dic3C2411yescharacteristic
97C4⋊(C3⋊D3)—28no—
98C4×C3⋊D3C22⋊C414yes—
99C4×C3⋊D3C22⋊C414yes—
100C4×C3⋊D3C2×D414yes—
101C4×C3⋊D3C2×D414yes—
102#622—28no—
103C23×D4—91no—
104C22×M16—92no—
105C2×#100—98no—
106C2×#100—94no—
107C24×C3—24no—
108C23×D3—62no—
109C23×D3—64no—
110C23×D3—616no—
111C23×D3—616no—
112C23×D3—68no—
113C23×D3—68no—
114C23×D3—1232no—
115C2×C3×D4—28no—
116C2×C3×D4—28no—
117C2×C3×D4—28no—
118C22×C3×C4—22no—
119C2×#67—68no—
120C2×#67—68no—
121C2×#67—616no—
122C2×#67—616no—
123C22×Dic3—62no—
124D3×D4—632no—
125D3×D4—632no—
126D3×D4—632no—
127D3×D4—632no—
128C2×D12—68no—
129C2×D12—68no—
130C2×D12—68no—
131C2×C4×D3—64no—
132C2×C4×D3—64no—
133C2×C4×D3—64no—
134C2×C4×D3—68no—
135C2×C4×D3—64no—
136C22×C32—22no—
137C22×C32—24no—
138C22×C32—44no—
139C22×C32—44no—
140C22×C32—44no—
141C22×C32C2×C22⋊C411yescharacteristic
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32C23×C411yescharacteristic
144C2×C3⋊D3—22no—
145C2×C3⋊D3—24no—
146C2×C3⋊D3—24no—
147C2×C3⋊D3—24no—
148C2×C3⋊D3—416no—
149C2×C3⋊D3—44no—
150C2×C3⋊D3—44no—
151C2×C3⋊D3—416no—
152C2×C3⋊D3—44no—
153C2×C3⋊D3#10014yescomplemented
154C2×C3⋊D3C2×C22⋊C412yes—
155C2×C3⋊D3C2×C22⋊C412yes—
156C32×C4C2×C22⋊C414yes—
157C3⋊Dic3C2×C22⋊C412yes—
158C3⋊Dic3C22×D412yes—
159C25—92no—
160C22×D4—92no—
161C22×D4—94no—
162C22×D4—94no—
163C22×D4—91no—
164C22×D4—182no—
165C22×D4—184no—
166C22×D4—182no—
167C22×D4#15711yescharacteristic
168C23×C4—91no—
169C2×M16—98no—
170C2×M16—94no—
171C2×M16—182no—
172C2×M16—184no—
173C22×C8—182no—
174#100—916no—
175C23×C3—28no—
176C23×C3—28no—
177C23×C3—22no—
178C23×C3—28no—
179C23×C3—416no—
180C22×D3—62no—
181C22×D3—64no—
182C22×D3—62no—
183C22×D3—64no—
184C22×D3—68no—
185C22×D3—616no—
186C22×D3—68no—
187C22×D3—68no—
188C22×D3—632no—
189C22×D3—632no—
190C22×D3—1232no—
191C22×D3—1264no—
192C22×D3—1264no—
193C22×D3—1232no—
194C22×D3—1216no—
195C3×D4—232no—
196C2×C3×C4—24no—
197C2×C3×C4—24no—
198C2×C3×C4—24no—
199#67—632no—
200#67—632no—
201C2×Dic3—62no—
202C2×Dic3—64no—
203C2×Dic3—64no—
204C2×Dic3—62no—
205D12—632no—
206C4×D3—68no—
207C4×D3—68no—
208C4×D3—68no—
209C4×D3—68no—
210C2×C32—21no—
211C2×C32—21no—
212C2×C32—44no—
213C2×C32C2×#10012yescomplemented
214C2×C32C22×C22⋊C411yescharacteristic
215C3⋊D3—22no—
216C3⋊D3—44no—
217C3⋊D3C2×#10014yescomplemented
218C24—91no—
219C24—98no—
220C24—92no—
221C24—184no—
222C24—182no—
223C24—182no—
224C24—368no—
225C24C2×#15712yes—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—94no—
229C2×D4—94no—
230C2×D4—94no—
231C2×D4—188no—
232C2×D4—188no—
233C2×D4—188no—
234C2×D4—188no—
235C2×D4—184no—
236C2×D4—184no—
237C2×D4—182no—
238C2×D4—182no—
239C2×D4C2×#15714yes—
240C22×C4—91no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—92no—
244C22×C4—94no—
245C22×C4—92no—
246C22×C4C2×#15711yescharacteristic
247M16—98no—
248M16—188no—
249M16—184no—
250C2×C8—188no—
251C2×C8—184no—
252C22×C3—28no—
253C22×C3—216no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—22no—
257C22×C3—416no—
258C22×C3—416no—
259C22×C3—416no—
260C2×D3—64no—
261C2×D3—64no—
262C2×D3—68no—
263C2×D3—616no—
264C2×D3—616no—
265C2×D3—68no—
266C2×D3—616no—
267C2×D3—1264no—
268C2×D3—1264no—
269C2×D3—1216no—
270C2×D3—1216no—
271C2×D3—1216no—
272C3×C4—28no—
273Dic3—64no—
274Dic3—64no—
275C32C22×#10011yescharacteristic, complemented, Sylow
276C23—22no—
277C23—22no—
278C23—44no—
279C23—91no—
280C23—92no—
281C23—91no—
282C23—92no—
283C23—94no—
284C23—184no—
285C23—188no—
286C23—188no—
287C23—182no—
288C23—182no—
289C23—364no—
290C23—368no—
291C23—3616no—
292C23—3616no—
293C23—368no—
294C23C22×#15711yescharacteristic
295C23C22×#15714yes—
296D4—28no—
297D4—188no—
298D4—188no—
299D4—188no—
300C2×C4—92no—
301C2×C4—92no—
302C2×C4—91no—
303C2×C4—91no—
304C2×C4—94no—
305C2×C4—94no—
306C2×C4—94no—
307C2×C4—94no—
308C2×C4C22⋊#15712yes—
309C2×C4C22⋊#15712yes—
310C2×C4C22×#15712yes—
311C8—188no—
312C2×C3—24no—
313C2×C3—24no—
314C2×C3—24no—
315C2×C3—22no—
316C2×C3—416no—
317D3—68no—
318D3—68no—
319D3—1216no—
320C22—22no—
321C22—24no—
322C22—44no—
323C22—44no—
324C22—44no—
325C22—94no—
326C22—92no—
327C22—92no—
328C22—184no—
329C22—184no—
330C22—182no—
331C22—184no—
332C22—364no—
333C22—364no—
334C22—3616no—
335C22—3616no—
336C22—364no—
337C22C2×C22⋊#15711yescharacteristic
338C22C2×C22⋊#15711yescharacteristic
339C22C23×#15711yescharacteristic
340C4—92no—
341C4—92no—
342C4C2×C22⋊#15714yes—
343C3—22no—
344C2—21no—
345C2—21no—
346C2—44no—
347C2—94no—
348C2—182no—
349C2—364no—
350C2#1059382512yesdirect product factor
351C2C22×C22⋊#15711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC22×C32C23×C4
FrattiniC22C23×#157
FittingC22×C32×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×D4×C3⋊D3C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×D4#157
hypocenterC32C22×#100
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#64283C2semidirect
3. C2×#63788C2semidirect
4. #10593825C2direct (N × H)
15. C2×#3792C22semidirect
17. #64283C22semidirect
20. #63788C22semidirect
52. #3792C23semidirect
153. C2×C3⋊D3#100semidirect
213. C2×C32C2×#100semidirect
217. C3⋊D3C2×#100semidirect
275. C32C22×#100semidirect
350. C2#10593825direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×#642832
C2×#637882
#105938252
C22×#1009