Finite Group Databasebeta

← C2×#14543824 #17960457

Subgroups — C2×#14543824 #17960457

Order 4352.

630 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10587530C211yesmaximal, characteristic
2C22×#10587532C211yesmaximal, characteristic
3#14543824C214yesmaximal, direct product factor
4C22×#10587469C211yesmaximal, characteristic
5C22×#63242C411yescharacteristic
6C22×C4×#595C411yescharacteristic
7C2×#10587530—22no—
8C2×#10587530—22no—
9C2×#10587530C412yescomplemented
10C2×#10587530C2212yes—
11C22×#63216C412yescomplemented
12C2×#10587532—22no—
13C2×#10587532—22no—
14C2×#10587532C412yes—
15C2×#10587532C2212yes—
16C22×C8×D17C2211yescharacteristic
17C2×#10587469—22no—
18C2×#10587469—22no—
19C2×#10587469C412yescomplemented
20C2×#10587469C2212yes—
21C22×#63214C411yescharacteristic, complemented
22C22×C16×C17C411yescharacteristic, complemented
23C23×#595—21no—
24C22×C4×D17C2×C411yescharacteristic
25C22×#3624—21no—
26C2×C4×#595—22no—
27C2×C4×#595—21no—
28C2×C4×#595C814yes—
29C2×C4×#595C2×C412yes—
30C2×#63242—22no—
31C2×#63242—21no—
32C2×#63242C814yes—
33C2×#63242C2×C412yes—
34C22×C8×C17C2×C411yescharacteristic
35C22×#3622C2×C411yescharacteristic
36C2×C8×D17C2×C411yescharacteristic
37C2×C8×D17C2×C411yescharacteristic
38C2×C8×D17C2×C411yescharacteristic
39C2×C8×D17D412yes—
40C2×C8×D17D412yes—
41C2×C8×D17D412yes—
42C2×C8×D17Q812yes—
43C2×C8×D17C2311yescharacteristic
44C2×#63216—24no—
45C2×#63216C2×C414yescomplemented
46#10587532—24no—
47#10587532—22no—
48#10587532—22no—
49#10587530—24no—
50#10587530—22no—
51#10587530—22no—
52C2×C16×C17—22no—
53C2×C16×C17C2×C412yescomplemented
54C2×#63214—22no—
55C2×#63214C2×C412yescomplemented
56#10587469—24no—
57#10587469—22no—
58#10587469—22no—
59C23×D17M1611yescharacteristic
60C22×#595—24no—
61C22×#595—22no—
62C22×#595—42no—
63C22×#595—42no—
64C22×C4×C17C4211yescharacteristic
65C22×Dic17M1611yescharacteristic
66C2×C4×D17C4211yescharacteristic
67C2×C4×D17C22⋊C412yes—
68C2×C4×D17C4⋊C412yes—
69C2×C4×D17C2×C812yes—
70C2×C4×D17C2×C812yes—
71C2×C4×D17M1611yescharacteristic
72C2×C4×D17M1611yescharacteristic
73C2×C4×D17C22×C411yescharacteristic
74C2×#3624—24no—
75C2×#3624—22no—
76C4×#595—24no—
77C4×#595—22no—
78C4×#595C2×C814yes—
79#63242—24no—
80#63242—22no—
81#63242C2×C814yes—
82C2×C8×C17C4211yescharacteristic
83C2×C8×C17C22⋊C412yes—
84C2×C8×C17C4⋊C412yes—
85C2×C8×C17C22×C411yescharacteristic
86C2×#3622C4211yescharacteristic
87C2×#3622C22⋊C412yes—
88C2×#3622C4⋊C412yes—
89C2×#3622C22×C411yescharacteristic
90C8×D17C22⋊C412yes—
91C8×D17C22⋊C412yes—
92C8×D17C22⋊C412yes—
93C8×D17C4⋊C412yes—
94C8×D17C4⋊C412yes—
95C8×D17C4⋊C412yes—
96C8×D17C2×D411yescharacteristic
97C8×D17C2×D411yescharacteristic
98C8×D17C2×D411yescharacteristic
99C8×D17C2×Q811yescharacteristic
100#63216—24no—
101C16×C17—22no—
102#63214—22no—
103C2×#1375—171nomaximal, Sylow
104C23×C17#9711yescharacteristic
105C22×D17—22no—
106C22×D17—22no—
107C22×D17#9711yescharacteristic
108C22×D17C22⋊C812yes—
109C22×D17C4⋊C812yes—
110C22×D17C2×M1611yescharacteristic
111C2×#595—24no—
112C2×#595—42no—
113C2×#595—42no—
114C2×#595—48no—
115C2×C4×C17#9512yes—
116C2×C4×C17C4×C812yes—
117C2×C4×C17#9711yescharacteristic
118C2×C4×C17C2×C4211yescharacteristic
119C2×Dic17#9711yescharacteristic
120C2×Dic17C22⋊C812yes—
121C2×Dic17C4⋊C812yes—
122C2×Dic17C2×M1611yescharacteristic
123C4×D17#9512yes—
124C4×D17C4×C812yes—
125C4×D17C22⋊C812yes—
126C4×D17C22⋊C812yes—
127C4×D17C4⋊C812yes—
128C4×D17C4⋊C812yes—
129C4×D17C2×C22⋊C411yescharacteristic
130C4×D17C2×C4⋊C411yescharacteristic
131C4×D17C22×C811yescharacteristic
132C4×D17C22×C811yescharacteristic
133#3624—24no—
134C8×C17#9512yes—
135C8×C17C2×C22⋊C411yescharacteristic
136C8×C17C2×C4⋊C411yescharacteristic
137#3622#9512yes—
138#3622C2×C22⋊C411yescharacteristic
139#3622C2×C4⋊C411yescharacteristic
140C22×M32—171no—
141C22×M32—171no—
142C22×#97—171no—
143#1375—174no—
144C22×C17#33612yes—
145C22×C17#34712yes—
146C22×C17#34712yes—
147C22×C17C2×#9711yescharacteristic
148C2×D17—21no—
149C2×D17—21no—
150C2×D17—21no—
151C2×D17—21no—
152C2×D17—24no—
153C2×D17—24no—
154C2×D17#33612yes—
155C2×D17C2×C22⋊C811yescharacteristic
156C2×D17C2×C4⋊C811yescharacteristic
157#595—44no—
158C4×C17#33612yes—
159C4×C17C2×#9511yescharacteristic
160C4×C17C2×C4×C811yescharacteristic
161Dic17#33612yes—
162Dic17C2×C22⋊C811yescharacteristic
163Dic17C2×C4⋊C811yescharacteristic
164C23×C8—171no—
165C23×C8—171no—
166C22×C42—171no—
167C2×M32—172no—
168C2×M32—172no—
169C2×M32—172no—
170C2×M32—172no—
171C2×M32—342no—
172C2×M32—342no—
173C2×M32—342no—
174C2×M32—342no—
175C22×C16—172no—
176C22×C16—171no—
177C22×C16#59511yescharacteristic, complemented
178C2×#97—172no—
179C2×#97—172no—
180C2×#97—342no—
181C2×#97—342no—
182C2×C17#137514yescomplemented
183C2×C17C2×#33611yescharacteristic
184C2×C17C2×#34711yescharacteristic
185C2×C17C2×#34711yescharacteristic
186D17—21no—
187D17—22no—
188D17—21no—
189C23×C4—171no—
190C23×C4—341no—
191C22×C8—171no—
192C22×C8—171no—
193C22×C8—171no—
194C22×C8—172no—
195C22×C8—172no—
196C22×C8—172no—
197C22×C8—172no—
198C22×C8—171no—
199C22×C8—171no—
200C22×C8—174no—
201C22×C8—172no—
202C22×C8—341no—
203C22×C8—342no—
204C22×C8—341no—
205C22×C8C2×#59511yescharacteristic
206C2×C42—174no—
207C2×C42—172no—
208C2×C42—342no—
209C2×C42—341no—
210M32—342no—
211M32—342no—
212M32—344no—
213M32—342no—
214M32—342no—
215M32—344no—
216C2×C16—22no—
217C2×C16—174no—
218C2×C16—172no—
219C2×C16—344no—
220C2×C16—342no—
221C2×C16C2×#59512yescomplemented
222#97—342no—
223#97—342no—
224#97—344no—
225C17C2×#137511yescharacteristic, complemented, Sylow
226C24—171no—
227C22×C4—171no—
228C22×C4—171no—
229C22×C4—171no—
230C22×C4—172no—
231C22×C4—172no—
232C22×C4—171no—
233C22×C4—171no—
234C22×C4—172no—
235C22×C4—172no—
236C22×C4—342no—
237C22×C4—344no—
238C22×C4—682no—
239C22×C4—682no—
240C22×C4C4×#59511yescharacteristic
241C2×C8—171no—
242C2×C8—171no—
243C2×C8—172no—
244C2×C8—172no—
245C2×C8—171no—
246C2×C8—172no—
247C2×C8—171no—
248C2×C8—171no—
249C2×C8—171no—
250C2×C8—172no—
251C2×C8—172no—
252C2×C8—172no—
253C2×C8—172no—
254C2×C8—172no—
255C2×C8—174no—
256C2×C8—342no—
257C2×C8—344no—
258C2×C8—342no—
259C2×C8—344no—
260C2×C8C4×#59511yescharacteristic
261C2×C8C4⋊#59512yes—
262C2×C8C22⋊#59512yes—
263C2×C8C22×#59511yescharacteristic
264C42—174no—
265C42—342no—
266C42—344no—
267C16—22no—
268C16—344no—
269C16—342no—
270C23—171no—
271C23—171no—
272C23—172no—
273C23—172no—
274C23—342no—
275C23—342no—
276C23#1058753211yescharacteristic
277C2×C4—171no—
278C2×C4—171no—
279C2×C4—172no—
280C2×C4—172no—
281C2×C4—171no—
282C2×C4—172no—
283C2×C4—171no—
284C2×C4—171no—
285C2×C4—171no—
286C2×C4—172no—
287C2×C4—172no—
288C2×C4—172no—
289C2×C4—172no—
290C2×C4—172no—
291C2×C4—344no—
292C2×C4—682no—
293C2×C4—682no—
294C2×C4—688no—
295C2×C4C8×#59512yes—
296C2×C4#1058753211yescharacteristic
297C2×C4(C2×#595)⋊C412yes—
298C2×C4C2×C4×#59511yescharacteristic
299C8—171no—
300C8—172no—
301C8—171no—
302C8—344no—
303C8(C2×#595)⋊C412yes—
304C8C2×C4⋊#59511yescharacteristic
305C8C2×C22⋊#59511yescharacteristic
306C22—171no—
307C22—172no—
308C22—171no—
309C22—341no—
310C22—341no—
311C22—341no—
312C22—341no—
313C22—344no—
314C22—344no—
315C22#1176367412yes—
316C22#1176369912yes—
317C22#1176370012yes—
318C22C2×#1058753211yescharacteristic
319C4—171no—
320C4—172no—
321C4—171no—
322C4—684no—
323C4#1176367412yes—
324C4C2×(C2×#595)⋊C411yescharacteristic
325C4C2×C8×#59511yescharacteristic
326C2—341no—
327C2—342no—
328C2—341no—
329C2#1454382414yesdirect product factor
330C2C2×#1176367411yescharacteristic
331C2C2×#1176369911yescharacteristic
332C2C2×#1176370011yescharacteristic
subgroupG/H
centerC22×C4C4×#595
commutatorC4×C17C2×C4×C8
FrattiniC2×C8C22×#595
FittingC22×C16×C17C4
socleC23×C17#97
prime radicalC23×D17M16
cosocleC2×C8×D17C23
hypercenterC22×C16#595
hypocenterC17C2×#1375
LCSG ▷ C4×C17 ▷ C17
UCSC1 ◁ C22×C4 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
3. #14543824C2direct (N × H)
9. C2×#10587530C4semidirect
11. C22×#63216C4semidirect
19. C2×#10587469C4semidirect
21. C22×#63214C4semidirect
22. C22×C16×C17C4semidirect
45. C2×#63216C2×C4semidirect
53. C2×C16×C17C2×C4semidirect
55. C2×#63214C2×C4semidirect
177. C22×C16#595semidirect
182. C2×C17#1375semidirect
221. C2×C16C2×#595semidirect
225. C17C2×#1375semidirect
329. C2#14543824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#105875302
C22×#105875322
#145438242
C22×#105874692
C2×#137517