Finite Group Databasebeta

← C22⋊C8×#3633 #17981595

Subgroups — C22⋊C8×#3633 #17981595

Order 4352.

726 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#3633C211yesmaximal, characteristic
2C4×C22⋊#3633C211yesmaximal, characteristic
3C2×C8×#3633C212yesmaximal, complemented
4(C2×#3633)⋊C8C212yesmaximal, complemented
5C22⋊C8×#595C211yesmaximal, characteristic
6C23×#3633C412yes—
7C2×C22⋊#3633C412yes—
8C2×C4×#3633—24no—
9C2×C4×#3633C412yes—
10C2×C4×#3633C2211yescharacteristic
11C2×C4×#3633C2212yes—
12C2×C4×#3633C2211yescharacteristic
13(C2×#3633)⋊C4C412yes—
14C8×#3633—24no—
15C22×C4×#595C2211yescharacteristic
16#11763777C411yescharacteristic
17C2×C8×#595C2212yes—
18#11763674C412yes—
19C22⋊C8×D17C411yescharacteristic
20C23×#595C2×C411yescharacteristic
21C23×#595C2×C411yescharacteristic
22C22×#3633—24no—
23C22×#3633—24no—
24C22×#3633C818yescomplemented
25C22×#3633C2×C412yes—
26C22×#3633C2×C414yes—
27C22×#3633C2×C412yes—
28C22×C4×D17C2×C411yescharacteristic
29C2×C4×#595—22no—
30C2×C4×#595—22no—
31C2×C4×#595C2×C411yescharacteristic
32C2×C4×#595C2×C411yescharacteristic
33C2×C4×#595C2×C411yescharacteristic
34C2×C4×#595C2311yescharacteristic
35C2×#63242C2×C412yes—
36C22⋊#3633C818yescomplemented
37C4×#3633—24no—
38C4×#3633—22no—
39C4×#3633—22no—
40C4×#3633—22no—
41C4×#3633D414yes—
42C2×C8×D17C2×C412yes—
43C22⋊#3624C812yescomplemented
44#10587543C812yescomplemented
45C8×#595—22no—
46C8×#595—22no—
47C17×C22⋊C8C811yescharacteristic, complemented
48C22⋊#3622C811yescharacteristic, complemented
49#10587491C812yescomplemented
50C23×D17C4211yescharacteristic
51C22×#595—21no—
52C22×#595—21no—
53C22×#595—22no—
54C22×#595—22no—
55C22×#595—22no—
56C22×#595C4211yescharacteristic
57C22×#595C4211yescharacteristic
58C22×#595C2×C814yes—
59C22×#595C2×C814yes—
60C22×#595C22×C411yescharacteristic
61C22×#595C22×C411yescharacteristic
62C2×#3633—22no—
63C2×#3633—24no—
64C2×#3633—22no—
65C2×#3633—24no—
66C2×#3633—216no—
67C2×#3633C22⋊C414yes—
68C2×#3633C2×C814yes—
69C2×#3633C2×C814yes—
70C2×#3633C2×C818yescomplemented
71C2×#3633M1614yes—
72C22×C4×C17C2×C811yescharacteristic
73C22×Dic17C2×C811yescharacteristic
74C2×C4×D17—22no—
75C2×C4×D17—22no—
76C2×C4×D17C4211yescharacteristic
77C2×C4×D17C2×C811yescharacteristic
78C2×C4×D17C2×C811yescharacteristic
79C2×C4×D17C22×C411yescharacteristic
80C2×#3624C2×C814yescomplemented
81C4×#595—21no—
82C4×#595—21no—
83C4×#595—22no—
84C4×#595—22no—
85C4×#595C2×D412yes—
86C4×#595#4112yes—
87#63242—22no—
88#63242—22no—
89C2×C8×C17C2×C812yescomplemented
90C2×#3622C2×C812yescomplemented
91C8×D17—22no—
92C8×D17—22no—
93C8×C22⋊C8—171nomaximal, Sylow
94C23×C17C4×C811yescharacteristic
95C22×D17—21no—
96C22×D17—21no—
97C22×D17—21no—
98C22×D17—21no—
99C22×D17C4×C811yescharacteristic
100C22×D17C4×C812yes—
101C22×D17C4×C812yes—
102C22×D17C2×C4211yescharacteristic
103C2×#595—21no—
104C2×#595—21no—
105C2×#595—21no—
106C2×#595—21no—
107C2×#595—24no—
108C2×#595—24no—
109C2×#595—28no—
110C2×#595C4×C812yes—
111C2×#595C4×C812yes—
112C2×#595C2×C22⋊C411yescharacteristic
113C2×#595#11711yescharacteristic
114C2×#595C4×D412yes—
115C2×#595C22×C812yes—
116C2×#595C22×C812yes—
117C2×#595C2×M1612yes—
118C2×#595#13112yes—
119#3633—24no—
120#3633—28no—
121#3633C22⋊C818yesdirect product factor
122C2×C4×C17—22no—
123C2×C4×C17C4×C811yescharacteristic
124C2×C4×C17C22×C811yescharacteristic
125C2×Dic17—22no—
126C2×Dic17C4×C811yescharacteristic
127C2×Dic17C22×C811yescharacteristic
128C4×D17—21no—
129C4×D17—21no—
130C4×D17—22no—
131C4×D17—22no—
132C4×D17C4×D412yes—
133C4×D17#13112yes—
134#3624—24no—
135C8×C17—22no—
136#3622—22no—
137C22×C4×C8—171no—
138C4×C22⋊C8—171no—
139C4×C22⋊C8—171no—
140C2×C82—172no—
141#1273—172no—
142C22×C17—21no—
143C22×C17—21no—
144C22×C17C8212yescomplemented
145C22×C17C2×C4×C811yescharacteristic
146C2×D17—21no—
147C2×D17—21no—
148C2×D17—22no—
149C2×D17—22no—
150C2×D17—22no—
151C2×D17—22no—
152C2×D17C8212yescomplemented
153C2×D17C4×C22⋊C411yescharacteristic
154C2×D17C2×C4×C811yescharacteristic
155C2×D17C2×C4×C811yescharacteristic
156C2×D17C4×M1611yescharacteristic
157C2×D17#40511yescharacteristic
158C2×D17#40511yescharacteristic
159#595—22no—
160#595—22no—
161#595C2×C22⋊C812yes—
162#595#43112yes—
163#595C8×D414yes—
164C4×C17—21no—
165C4×C17C8×D412yes—
166Dic17—21no—
167Dic17C8×D412yes—
168C23×C8—172no—
169C22×C42—171no—
170C2×C22⋊C8—171no—
171C2×C22⋊C8—172no—
172C2×C22⋊C8—171no—
173C2×C4×C8—171no—
174C2×C4×C8—172no—
175C2×C4×C8—172no—
176C2×C4×C8—171no—
177C2×C4×C8—172no—
178C2×C4×C8—344no—
179#336—172no—
180#336—172no—
181C82—344no—
182C2×C17—22no—
183C2×C17C2×C8211yescharacteristic
184C2×C17C8×M1611yescharacteristic
185C2×C17C8×C22⋊C411yescharacteristic
186D17—22no—
187D17C8×M1611yescharacteristic
188D17#145011yescharacteristic
189D17C4×C22⋊C811yescharacteristic
190D17C8×C22⋊C411yescharacteristic
191C23×C4—171no—
192C23×C4—171no—
193C23×C4—171no—
194C22×C8—172no—
195C22×C8—172no—
196C22×C8—178no—
197C22×C8—172no—
198C22×C8—174no—
199C22×C8—172no—
200C22×C8—344no—
201C22×C8—344no—
202C2×C42—171no—
203C2×C42—171no—
204C2×C42—171no—
205C2×C42—171no—
206C2×C42—342no—
207C2×C42—342no—
208C22⋊C8—178no—
209C22⋊C8—172no—
210C22⋊C8—172no—
211C22⋊C8—171no—
212C22⋊C8—172no—
213C22⋊C8#363311yescharacteristic, direct product factor
214C4×C8—174no—
215C4×C8—342no—
216C4×C8—342no—
217C4×C8—342no—
218C4×C8—342no—
219C4×C8—342no—
220C4×C8—344no—
221C17C8×C22⋊C811yescharacteristic, complemented, Sylow
222C24—171no—
223C22×C4—171no—
224C22×C4—171no—
225C22×C4—171no—
226C22×C4—171no—
227C22×C4—171no—
228C22×C4—174no—
229C22×C4—174no—
230C22×C4—171no—
231C22×C4—171no—
232C22×C4—171no—
233C22×C4—171no—
234C22×C4—342no—
235C22×C4—342no—
236C22×C4—341no—
237C22×C4—342no—
238C22×C4—341no—
239C22×C4—342no—
240C22×C4—342no—
241C22×C4C2×#363311yescharacteristic
242C2×C8—174no—
243C2×C8—174no—
244C2×C8—174no—
245C2×C8—174no—
246C2×C8—174no—
247C2×C8—178no—
248C2×C8—172no—
249C2×C8—342no—
250C2×C8—342no—
251C2×C8—3416no—
252C2×C8—342no—
253C2×C8—342no—
254C2×C8—342no—
255C2×C8—344no—
256C2×C8—344no—
257C2×C8—342no—
258C2×C8C2×#363312yescomplemented
259C42—172no—
260C42—172no—
261C42—341no—
262C42—342no—
263C42—341no—
264C42—342no—
265C23—171no—
266C23—172no—
267C23—172no—
268C23—171no—
269C23—341no—
270C23—341no—
271C23—341no—
272C23—341no—
273C23C4×#363311yescharacteristic
274C2×C4—22no—
275C2×C4—171no—
276C2×C4—172no—
277C2×C4—171no—
278C2×C4—172no—
279C2×C4—172no—
280C2×C4—172no—
281C2×C4—172no—
282C2×C4—171no—
283C2×C4—172no—
284C2×C4—172no—
285C2×C4—172no—
286C2×C4—172no—
287C2×C4—171no—
288C2×C4—342no—
289C2×C4—341no—
290C2×C4—341no—
291C2×C4—342no—
292C2×C4—344no—
293C2×C4—348no—
294C2×C4—344no—
295C2×C4—341no—
296C2×C4—341no—
297C2×C4—341no—
298C2×C4—341no—
299C2×C4—342no—
300C2×C4C4×#363311yescharacteristic
301C2×C4C22×#363311yescharacteristic
302C8—22no—
303C8—178no—
304C8—344no—
305C8—344no—
306C8—348no—
307C8—342no—
308C22—21no—
309C22—21no—
310C22—171no—
311C22—171no—
312C22—171no—
313C22—171no—
314C22—171no—
315C22—171no—
316C22—172no—
317C22—342no—
318C22—342no—
319C22—342no—
320C22—342no—
321C22—341no—
322C22—341no—
323C22C8×#363312yescomplemented
324C22C2×C4×#363311yescharacteristic
325C4—21no—
326C4—172no—
327C4—174no—
328C4—172no—
329C4—172no—
330C4—342no—
331C4—342no—
332C4—341no—
333C4D4×#363312yes—
334C2—22no—
335C2—171no—
336C2—171no—
337C2—171no—
338C2—171no—
339C2—342no—
340C2C2×C8×#363311yescharacteristic
341C2M16×#363311yescharacteristic
342C2C22⋊C4×#363311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#3633
commutatorC2×C17C2×C82
FittingC17×C22⋊C8C8
socleC22×C17C2×C4×C8
prime radicalC23×D17C42
cosocleC2×C4×#595C23
hypercenterC22⋊C8#3633
hypocenterC17C8×C22⋊C8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×C8×#3633C2semidirect
4. (C2×#3633)⋊C8C2semidirect
24. C22×#3633C8semidirect
36. C22⋊#3633C8semidirect
43. C22⋊#3624C8semidirect
44. #10587543C8semidirect
47. C17×C22⋊C8C8semidirect
48. C22⋊#3622C8semidirect
49. #10587491C8semidirect
70. C2×#3633C2×C8semidirect
80. C2×#3624C2×C8semidirect
89. C2×C8×C17C2×C8semidirect
90. C2×#3622C2×C8semidirect
121. #3633C22⋊C8direct (N × H)
144. C22×C17C82semidirect
152. C2×D17C82semidirect
213. C22⋊C8#3633direct (N × H)
221. C17C8×C22⋊C8semidirect
258. C2×C8C2×#3633semidirect
323. C22C8×#3633semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#36332
C4×C22⋊#36332
C2×C8×#36332
(C2×#3633)⋊C82
C22⋊C8×#5952
C8×C22⋊C817