Finite Group Databasebeta

← C2×#14544336 #17966317

Subgroups — C2×#14544336 #17966317

Order 4352.

834 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763828C211yesmaximal, characteristic
2C2×#11763810C211yesmaximal, characteristic
3#14544336C218yesmaximal, direct product factor
4C2×#11763673C211yesmaximal, characteristic, complemented
5C2×#11763672C211yesmaximal, characteristic, complemented
6C2×#11763671C211yesmaximal, characteristic, complemented
7C2×#11763670C211yesmaximal, characteristic, complemented
8C2×#11762761C211yesmaximal, characteristic
9C22×#63242—21no—
10#11763828—22no—
11#11763828C2214yes—
12C2×#10587544—21no—
13#11763810—22no—
14#11763810C2214yes—
15C2×C4⋊#3624C2211yescharacteristic
16C2×C4⋊#3624C2211yescharacteristic
17C2×C4⋊#3624C2211yescharacteristic
18C2×C4⋊#3624C2211yescharacteristic
19C2×#10587543—21no—
20C2×C4×#3624—21no—
21#11763673C2214yescomplemented
22#11763672C2214yescomplemented
23#11763671C2214yescomplemented
24#11763670C2214yescomplemented
25C22×#63218C411yescharacteristic
26C22×#63218C411yescharacteristic
27C2×C42×D17C2211yescharacteristic
28#11762761C414yes—
29#11762761C2214yes—
30C2×#10587474C411yescharacteristic
31C2×C8×Dic17C2211yescharacteristic
32C2×C8×Dic17C2211yescharacteristic
33C2×C17×#97C411yescharacteristic
34C22×C4×D17C2×C411yescharacteristic
35C22×C4×D17D411yescharacteristic
36C22×C4×D17Q811yescharacteristic
37C22×#3624—21no—
38C22×#3624—21no—
39C22×#3624—21no—
40C22×#3624—21no—
41C2×#63242—24no—
42C2×#63242—44no—
43C22×C8×C17C2×C411yescharacteristic
44C22×C8×C17C2×C411yescharacteristic
45C2×C42×C17C2×C411yescharacteristic
46C2×C4×Dic17D411yescharacteristic
47C2×C4×Dic17Q811yescharacteristic
48C2×C4×Dic17C2311yescharacteristic
49C22×#3622C2×C411yescharacteristic
50C22×#3622C2×C411yescharacteristic
51C2×#63218—24no—
52C2×#63218C818yescomplemented
53C2×#63218C2×C414yes—
54C2×#63218C2×C414yes—
55C42×D17C2×C412yes—
56C42×D17D412yes—
57C42×D17Q812yes—
58C42×D17C2312yes—
59#10587544—24no—
60#10587543—24no—
61C4⋊#3624—21no—
62C4⋊#3624—21no—
63C4⋊#3624—21no—
64C4⋊#3624—21no—
65C4⋊#3624C2312yes—
66C4⋊#3624C2312yes—
67C4⋊#3624C2312yes—
68C4⋊#3624C2312yes—
69C4×#3624—24no—
70C17×#97C2×C414yes—
71C8×Dic17C2×C412yes—
72C8×Dic17C2×C412yes—
73C8×Dic17C2312yes—
74C8×Dic17C2312yes—
75#10587474C2×C414yes—
76C23×D17C4⋊C411yescharacteristic
77C22×C4×C17C4⋊C411yescharacteristic
78C22×C4×C17C4⋊C411yescharacteristic
79C22×C4×C17C22×C411yescharacteristic
80C22×Dic17C4⋊C411yescharacteristic
81C22×Dic17C2×D411yescharacteristic
82C22×Dic17C2×Q811yescharacteristic
83C2×C4×D17—22no—
84C2×C4×D17—22no—
85C2×C4×D17—42no—
86C2×C4×D17C4⋊C412yes—
87C2×C4×D17C4⋊C412yes—
88C2×C4×D17C4⋊C412yes—
89C2×C4×D17C2×C814yes—
90C2×C4×D17M1614yes—
91C2×C4×D17C22×C412yes—
92C2×C4×D17C2×D412yes—
93C2×C4×D17C2×Q812yes—
94C2×#3624—22no—
95C2×#3624—22no—
96C2×#3624—22no—
97C2×#3624—22no—
98C2×#3624—42no—
99C2×#3624—42no—
100C2×#3624—42no—
101C2×#3624—42no—
102#63242—48no—
103C2×C8×C17—22no—
104C2×C8×C17C2×C814yescomplemented
105C2×C8×C17C22×C412yes—
106C2×C8×C17C22×C412yes—
107C42×C17C4⋊C412yes—
108C42×C17C22×C412yes—
109C4×Dic17C4⋊C412yes—
110C4×Dic17C4⋊C412yes—
111C4×Dic17C22×C411yescharacteristic
112C4×Dic17C2×D412yes—
113C4×Dic17C2×D411yescharacteristic
114C4×Dic17C2×Q811yescharacteristic
115C4×Dic17C2×Q812yes—
116C4×Dic17C2411yescharacteristic
117C2×#3622—22no—
118C2×#3622C2×C814yescomplemented
119C2×#3622C22×C412yes—
120C2×#3622C22×C412yes—
121#63218—28no—
122#63218C2×C8116yescomplemented
123C2×#1565—171nomaximal, Sylow
124C23×C17C2×C4⋊C411yescharacteristic
125C22×D17—22no—
126C22×D17—22no—
127C22×D17C4⋊C814yes—
128C22×D17C2×C4⋊C412yes—
129C2×C4×C17—22no—
130C2×C4×C17—22no—
131C2×C4×C17C2×C4⋊C412yes—
132C2×C4×C17C2×C4⋊C412yes—
133C2×C4×C17C2×C4⋊C411yescharacteristic
134C2×C4×C17C22×C812yes—
135C2×C4×C17C2×M1612yes—
136C2×C4×C17C23×C411yescharacteristic
137C2×Dic17—22no—
138C2×Dic17C4⋊C814yes—
139C2×Dic17C2×C4⋊C411yescharacteristic
140C2×Dic17C2×C4⋊C412yes—
141C2×Dic17C2×C4⋊C411yescharacteristic
142C2×Dic17AGL(1,ℤ/8)12yes—
143C2×Dic17#13712yes—
144C2×Dic17C22×D411yescharacteristic
145C2×Dic17C22×Q811yescharacteristic
146C4×D17—22no—
147C4×D17—22no—
148C4×D17—24no—
149C4×D17—42no—
150C4×D17—42no—
151C4×D17C4⋊C818yes—
152C4×D17C22×C814yes—
153C4×D17C2×M1614yes—
154#3624—42no—
155#3624—42no—
156#3624—42no—
157#3624—42no—
158C8×C17—22no—
159C8×C17C22×C814yescomplemented
160#3622—22no—
161#3622C22×C814yescomplemented
162C2×#431—171no—
163C22×C4⋊C8—171no—
164C2×C4×M16—171no—
165#1565—178no—
166C2×#335—171no—
167C2×#335—171no—
168C2×#334—171no—
169C2×#334—171no—
170C22×C17C2×C4⋊C812yes—
171C22×C17#42812yes—
172C22×C17#43012yes—
173C22×C17C22×C4⋊C411yescharacteristic
174C2×D17—28no—
175C2×D17—22no—
176C2×D17—22no—
177C2×D17C2×C4⋊C814yes—
178C4×C17—22no—
179C4×C17—22no—
180C4×C17C2×C4⋊C812yes—
181C4×C17C23×C811yescharacteristic
182C4×C17C22×M1611yescharacteristic
183Dic17—21no—
184Dic17—21no—
185Dic17C2×C4⋊C814yes—
186Dic17#42812yes—
187Dic17C2×AGL(1,ℤ/8)11yescharacteristic
188Dic17C2×#13711yescharacteristic
189C22×M16—171no—
190C22×M16—171no—
191C23×C8—341no—
192C22×C42—171no—
193#431—174no—
194#431—342no—
195C2×C4⋊C8—171no—
196C2×C4⋊C8—171no—
197C2×C4⋊C8—171no—
198C2×C4⋊C8—171no—
199C2×C4⋊C8—174no—
200C2×C4⋊C8—342no—
201C2×C4⋊C8—341no—
202C2×C22⋊C8—341no—
203C4×M16—174no—
204C4×M16—174no—
205C2×#97—171no—
206C2×#97#59511yescharacteristic
207C2×C4×C8—171no—
208C2×C4×C8—171no—
209C2×C4×C8—341no—
210#335—174no—
211#335—174no—
212#334—174no—
213#334—174no—
214C2×C17#156514yescomplemented
215C2×C17C22×C4⋊C811yescharacteristic
216C2×C17C2×#42811yescharacteristic
217C2×C17C2×#43011yescharacteristic
218D17—24no—
219C23×C4—171no—
220C23×C4—171no—
221C23×C4—171no—
222C2×M16—178no—
223C2×M16—174no—
224C2×M16—174no—
225C2×M16—344no—
226C22×C8—171no—
227C22×C8—171no—
228C22×C8—344no—
229C22×C8—341no—
230C22×C8—341no—
231C22×C8—341no—
232C22×C8—341no—
233C22×C8—684no—
234C22×C8C2×#59511yescharacteristic
235C22×C8C2×#59511yescharacteristic
236C2×C42—171no—
237C2×C42—171no—
238C2×C42—171no—
239C2×C42—172no—
240C2×C42—172no—
241C2×C42—172no—
242C2×C42—172no—
243C2×C42C2×#59511yescharacteristic
244C4⋊C8—172no—
245C4⋊C8—172no—
246C4⋊C8—172no—
247C4⋊C8—172no—
248C4⋊C8—341no—
249C4⋊C8—341no—
250C4⋊C8—341no—
251C4⋊C8—341no—
252C4⋊C8—344no—
253C22⋊C8—344no—
254#97—174no—
255#97C2×#59514yes—
256C4×C8—172no—
257C4×C8—172no—
258C4×C8—172no—
259C4×C8—172no—
260C4×C8—344no—
261C17C2×#156511yescharacteristic, complemented, Sylow
262C24—171no—
263C22×C4—171no—
264C22×C4—171no—
265C22×C4—174no—
266C22×C4—174no—
267C22×C4—172no—
268C22×C4—172no—
269C22×C4—171no—
270C22×C4—172no—
271C22×C4—172no—
272C22×C4—172no—
273C22×C4—172no—
274C22×C4—342no—
275C22×C4—342no—
276C22×C4—682no—
277C22×C4C4⋊#59511yescharacteristic
278C22×C4C4⋊#59511yescharacteristic
279C22×C4C22×#59511yescharacteristic
280M16—1716no—
281M16—348no—
282C2×C8—22no—
283C2×C8—174no—
284C2×C8—172no—
285C2×C8—172no—
286C2×C8—342no—
287C2×C8—342no—
288C2×C8—342no—
289C2×C8—342no—
290C2×C8—342no—
291C2×C8—682no—
292C2×C8—682no—
293C2×C8—682no—
294C2×C8—682no—
295C2×C8—688no—
296C2×C8#6324214yescomplemented
297C2×C8C22×#59512yes—
298C2×C8C22×#59512yes—
299C42—172no—
300C42—171no—
301C42—172no—
302C42—172no—
303C42—172no—
304C42—171no—
305C42—171no—
306C42—171no—
307C42C4⋊#59512yes—
308C42C22×#59512yes—
309C23—174no—
310C23—172no—
311C23—342no—
312C23—342no—
313C23C2×C4⋊#59511yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—174no—
317C2×C4—172no—
318C2×C4—172no—
319C2×C4—171no—
320C2×C4—172no—
321C2×C4—171no—
322C2×C4—178no—
323C2×C4—174no—
324C2×C4—174no—
325C2×C4—171no—
326C2×C4—171no—
327C2×C4—342no—
328C2×C4—342no—
329C2×C4—344no—
330C2×C4—342no—
331C2×C4—682no—
332C2×C4—682no—
333C2×C4C2×#6324212yes—
334C2×C4D17⋊M1612yes—
335C2×C4C2×C4⋊#59512yes—
336C2×C4C2×C4⋊#59512yes—
337C2×C4C2×C4⋊#59511yescharacteristic
338C2×C4C23×#59511yescharacteristic
339C8—22no—
340C8—174no—
341C8—342no—
342C8—682no—
343C8—682no—
344C8—682no—
345C8—682no—
346C8C2×#6324214yescomplemented
347C22—174no—
348C22—342no—
349C22—342no—
350C22—348no—
351C22#1176381012yes—
352C22#1176382012yes—
353C22#1176382412yes—
354C22C22×C4⋊#59511yescharacteristic
355C4—22no—
356C4—22no—
357C4—174no—
358C4—171no—
359C4—171no—
360C4—172no—
361C4—341no—
362C4—341no—
363C4#1176381012yes—
364C4C22×#6324211yescharacteristic
365C4C2×D17⋊M1611yescharacteristic
366C2—344no—
367C2#1454433614yesdirect product factor
368C2C2×#1176381011yescharacteristic
369C2C2×#1176382011yescharacteristic
370C2C2×#1176382411yescharacteristic
subgroupG/H
centerC23C2×C4⋊#595
commutatorC4×C17C23×C8
FrattiniC2×C4C23×#595
FittingC2×C17×#97C4
socleC23×C17C2×C4⋊C4
prime radicalC23×D17C4⋊C4
cosocleC4×Dic17C24
hypercenterC2×#97#595
hypocenterC17C2×#1565
LCSG ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
3. #14544336C2direct (N × H)
4. C2×#11763673C2semidirect
5. C2×#11763672C2semidirect
6. C2×#11763671C2semidirect
7. C2×#11763670C2semidirect
21. #11763673C22semidirect
22. #11763672C22semidirect
23. #11763671C22semidirect
24. #11763670C22semidirect
52. C2×#63218C8semidirect
104. C2×C8×C17C2×C8semidirect
118. C2×#3622C2×C8semidirect
122. #63218C2×C8semidirect
159. C8×C17C22×C8semidirect
161. #3622C22×C8semidirect
214. C2×C17#1565semidirect
261. C17C2×#1565semidirect
296. C2×C8#63242semidirect
346. C8C2×#63242semidirect
367. C2#14544336direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117638282
C2×#117638102
#145443362
C2×#117636732
C2×#117636722
C2×#117636712
C2×#117636702
C2×#117627612
C2×#156517