Finite Group Databasebeta

← C2×#22597191 #32861579

Subgroups — C2×#22597191 #32861579

Order 18176.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D568C211yesmaximal, characteristic
2C2×#17986473C212yesmaximal, complemented
3#22597191C2116yesmaximal, direct product factor
4C2×#17986110C214yesmaximal, complemented
5C2×#17986081C214yesmaximal, complemented
6C2×#17986003C212yesmaximal, complemented
7C2×#17985954C211yesmaximal, characteristic, complemented
8C2×#427×C71C211yesmaximal, characteristic, complemented
9C23×D284C2212yes—
10C22×D568C4116yescomplemented
11C22×D568C2212yes—
12C22×D568C2218yes—
13C22×D568C2212yes—
14C22×#11765849C2211yescharacteristic
15#17986473—28no—
16#17986473C22116yescomplemented
17C2×C4×D284—24no—
18C2×#14556090C2218yescomplemented
19C2×#14556087C2211yescharacteristic
20C2×C22⋊C4×D71—24no—
21#17986110C22132yescomplemented
22#17986081C22132yescomplemented
23#17986003C22116yescomplemented
24C2×#14556048C2218yescomplemented
25#17985954C2218yescomplemented
26C2×#14556038C2212yescomplemented
27C2×C8×Dic71C2212yescomplemented
28C23×C8×C71C2211yescharacteristic
29C2×#117×C71C2212yes—
30#427×C71C2218yescomplemented
31C2×#107×C71C2212yescomplemented
32C2×#106×C71C2212yescomplemented
33C24×D71—22no—
34C22×D284—22no—
35C22×D284—24no—
36C22×D284—28no—
37C22×D284C2×C4116yescomplemented
38C22×D284C2314yes—
39C22×D284C2318yes—
40C22×C4×D71—28no—
41C2×D568C2×C4116yescomplemented
42C2×D568C2×C4116yescomplemented
43C2×D568C2×C4164yescomplemented
44C2×D568C2318yes—
45C2×D568C2318yes—
46C2×#11765849—24no—
47C2×#11765849C2314yes—
48C22×C71⋊C8C2312yes—
49C4×D284—232no—
50#14556090—216no—
51#14556090C23132yescomplemented
52#14556087D414yes—
53#14556087C2314yes—
54C2×C4⋊Dic71D412yes—
55C2×C22⋊Dic71D412yes—
56C2×(C2×D71)⋊C4—28no—
57C22⋊C4×D71—232no—
58C2×C4×Dic71C2312yes—
59#14556048C23132yescomplemented
60#14556038C2318yescomplemented
61C8×Dic71C2318yescomplemented
62C23×C4×C71C2311yescharacteristic
63C22×C8×C71C2×C418yescomplemented
64C22×C8×C71C2311yescharacteristic
65C22×C8×C71C2311yescharacteristic
66C22×C8×C71C2314yes—
67#117×C71—24no—
68#117×C71C2318yes—
69C2×C4⋊C4×C71C2314yes—
70C2×C22⋊C4×C71—22no—
71C2×C42×C71—22no—
72#107×C71C2318yescomplemented
73#106×C71C2318yescomplemented
74C23×D71—24no—
75C23×D71—216no—
76C23×D71—28no—
77C23×D71—88no—
78C2×D284—232no—
79C2×D284—216no—
80C2×D284—24no—
81C2×D284—28no—
82C2×D284—28no—
83C2×D284—216no—
84C2×D284C22×C4116yes—
85C2×D284C22×C4132yescomplemented
86C2×D284C2418yes—
87C22×Dic71C2×D414yes—
88C2×C4×D71—232no—
89C2×C4×D71—816no—
90D568C22×C4132yescomplemented
91D568C22×C4132yescomplemented
92#11765849—28no—
93C2×C71⋊C8—24no—
94C2×C71⋊C8C2414yes—
95C4⋊Dic71C2×D418yes—
96C22⋊Dic71C2×D418yes—
97(C2×D71)⋊C4—232no—
98C4×Dic71C2×D414yes—
99C4×Dic71C2414yes—
100C24×C71C2×D411yescharacteristic
101C22×C4×C71—24no—
102C22×C4×C71C22×C414yes—
103C22×C4×C71C2×D411yescharacteristic
104C22×C4×C71C2×D412yes—
105C22×C4×C71#4114yes—
106C22×C4×C71C2411yescharacteristic
107C22×C4×C71C2412yes—
108C2×C8×C71C22×C414yes—
109C2×C8×C71C22×C414yes—
110C2×C8×C71C22×C4116yescomplemented
111C2×C8×C71C2412yes—
112C2×C8×C71C2412yes—
113C4⋊C4×C71—24no—
114C4⋊C4×C71C2418yes—
115C22⋊C4×C71—28no—
116C42×C71—28no—
117C23×C71—24no—
118C23×C71C4×D414yes—
119C23×C71C22×D412yes—
120C23×C71C22×D411yescharacteristic
121C22×D71—216no—
122C22×D71—28no—
123C22×D71—232no—
124C22×D71—416no—
125C22×D71—832no—
126C22×D71—816no—
127C2×C4×C71—28no—
128C2×C4×C71—48no—
129C2×C4×C71C4×D418yes—
130C2×C4×C71C4×D414yes—
131C2×C4×C71C23×C412yes—
132C2×C4×C71C23×C414yes—
133C2×C4×C71C22×D412yes—
134C2×C4×C71C22×D411yescharacteristic
135C2×C4×C71C2×#4112yes—
136C2×C4×C71C2×#4114yes—
137C2×C4×C71C2511yescharacteristic
138C2×Dic71—28no—
139C2×Dic71C22×D418yes—
140D284—216no—
141D284—232no—
142D284—28no—
143D284C23×C4116yes—
144C4×D71—832no—
145C8×C71C23×C414yes—
146C8×C71C23×C414yes—
147C71⋊C8—24no—
148C22×C71—28no—
149C22×C71—24no—
150C22×C71C2×C4×D414yes—
151C22×C71C2×C4×D412yes—
152C22×C71#57614yes—
153C22×C71C23×D411yescharacteristic
154C2×D71—216no—
155C2×D71—432no—
156C2×D71—416no—
157C2×D71—832no—
158C4×C71—48no—
159C4×C71C2×C4×D412yes—
160C4×C71C2×C4×D414yes—
161C4×C71C24×C411yescharacteristic
162C4×C71C22×#4111yescharacteristic
163Dic71—28no—
164C2×#2948—711nomaximal, Sylow
165C2×C71—24no—
166C2×C71#294814yescomplemented
167C2×C71C22×C4×D411yescharacteristic
168C2×C71C2×#57612yes—
169D71—416no—
170C23×D8—711no—
171C2×#518—712no—
172#2948—7116no—
173C2×#442—714no—
174C2×C4×D8—714no—
175C2×#427D7111yescharacteristic, complemented
176C2×#418—712no—
177C2×#405—711no—
178C71C2×#294811yescharacteristic, complemented, Sylow
179C23×D4—712no—
180C22×D8—7116no—
181C22×D8—712no—
182C22×D8—712no—
183C22×D8—718no—
184C22×M16—711no—
185C23×C8C2×D7111yescharacteristic
186#518—7116no—
187#518—1428no—
188C2×C4×D4—718no—
189C2×C4×D4—1424no—
190C2×#117—711no—
191C2×#117C2×D7112yes—
192C22×C22⋊C4—1424no—
193#442—7132no—
194C4×D8—7132no—
195#427C2×D7118yescomplemented
196C2×#107C2×D7112yescomplemented
197C2×#106C2×D7112yescomplemented
198#418—7116no—
199C2×#102—718no—
200#405—718no—
201C2×#97—712no—
202C2×C4×C8—712no—
203C25—1422no—
204C22×D4—7116no—
205C22×D4—714no—
206C22×D4—718no—
207C22×D4—1422no—
208C22×D4—1424no—
209C22×D4—1428no—
210C23×C4—1428no—
211C23×C4C22×D7111yescharacteristic
212C2×D8—7116no—
213C2×D8—7116no—
214C2×D8—7164no—
215C2×D8—718no—
216C2×D8—718no—
217C2×M16—714no—
218C2×M16—1424no—
219C22×C8—712no—
220C22×C8C4×D7118yescomplemented
221C22×C8C22×D7111yescharacteristic
222C22×C8C22×D7111yescharacteristic
223C22×C8C22×D7114yes—
224C4×D4—7132no—
225C4×D4—14232no—
226C4×D4—14216no—
227#117—24no—
228#117—714no—
229#117—714no—
230#117C22×D7118yes—
231C2×C4⋊C4—712no—
232C2×C4⋊C4C22×D7114yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—712no—
235C2×C22⋊C4—14232no—
236C2×C22⋊C4—1428no—
237C2×C42—22no—
238C2×C42—712no—
239#107C22×D7118yescomplemented
240#106C22×D7118yescomplemented
241#102—7132no—
242#97—718no—
243C4×C8—718no—
244C24—5688no—
245C24—1424no—
246C24—1428no—
247C24—14216no—
248C24D4×D7111yescharacteristic
249C2×D4—7116no—
250C2×D4—7132no—
251C2×D4—718no—
252C2×D4—1428no—
253C2×D4—1424no—
254C2×D4—1428no—
255C2×D4—14216no—
256C2×D4—14216no—
257C2×D4—14232no—
258C22×C4—24no—
259C22×C4—56816no—
260C22×C4—714no—
261C22×C4—14232no—
262C22×C4C2×C4×D7114yes—
263C22×C4D4×D7112yes—
264C22×C4D4×D7111yescharacteristic
265C22×C4#1176586614yes—
266C22×C4C23×D7112yes—
267C22×C4C23×D7111yescharacteristic
268D8—7132no—
269D8—7132no—
270M16—1428no—
271C2×C8—714no—
272C2×C8—1424no—
273C2×C8C2×C4×D7114yes—
274C2×C8C2×C4×D7114yes—
275C2×C8C2×C4×D71116yescomplemented
276C2×C8C23×D7112yes—
277C2×C8C23×D7112yes—
278C4⋊C4—24no—
279C4⋊C4—718no—
280C4⋊C4C23×D7118yes—
281C22⋊C4—28no—
282C22⋊C4—718no—
283C22⋊C4—14232no—
284C42—28no—
285C42—714no—
286C42—714no—
287C23—24no—
288C23—28416no—
289C23—56832no—
290C23—56816no—
291C23—1428no—
292C23—14216no—
293C23—14232no—
294C23#1455609014yes—
295C23C2×D4×D7112yes—
296C23C2×D4×D7111yescharacteristic
297D4—7116no—
298D4—1428no—
299D4—14216no—
300D4—14232no—
301C2×C4—28no—
302C2×C4—48no—
303C2×C4—56832no—
304C2×C4—718no—
305C2×C4—1428no—
306C2×C4#1455609018yes—
307C2×C4#1455609014yes—
308C2×C4C22×C4×D7112yes—
309C2×C4C22×C4×D7114yes—
310C2×C4C2×D4×D7112yes—
311C2×C4C2×D4×D7111yescharacteristic
312C2×C4C2×#1176586612yes—
313C2×C4C2×#1176586614yes—
314C2×C4C24×D7111yescharacteristic
315C8—1424no—
316C8C22×C4×D7114yes—
317C8C22×C4×D7114yes—
318C22—28no—
319C22—24no—
320C22—28432no—
321C22—28416no—
322C22—56832no—
323C22—14216no—
324C22C2×#1455609014yes—
325C22C2×#1455609012yes—
326C22#1798680114yes—
327C22C22×D4×D7111yescharacteristic
328C4—48no—
329C4—1428no—
330C4C2×#1455609012yes—
331C4C2×#1455609014yes—
332C4C23×C4×D7111yescharacteristic
333C4C22×#1176586611yescharacteristic
334C2—24no—
335C2—28416no—
336C2#2259719114yesdirect product factor
337C2C22×#1455609011yescharacteristic
338C2C2×#1798680112yes—
subgroupG/H
centerC23C2×D4×D71
commutatorC4×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#427×C71C2
socleC23×C71C22×D4
prime radicalC23×D568C2
cosocleC2×C4×C71C25
hypercenterC2×#427D71
hypocenterC71C2×#2948
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#17986473C2semidirect
3. #22597191C2direct (N × H)
4. C2×#17986110C2semidirect
5. C2×#17986081C2semidirect
6. C2×#17986003C2semidirect
7. C2×#17985954C2semidirect
8. C2×#427×C71C2semidirect
10. C22×D568C4semidirect
16. #17986473C22semidirect
18. C2×#14556090C22semidirect
21. #17986110C22semidirect
22. #17986081C22semidirect
23. #17986003C22semidirect
24. C2×#14556048C22semidirect
25. #17985954C22semidirect
26. C2×#14556038C22semidirect
27. C2×C8×Dic71C22semidirect
30. #427×C71C22semidirect
31. C2×#107×C71C22semidirect
32. C2×#106×C71C22semidirect
37. C22×D284C2×C4semidirect
41. C2×D568C2×C4semidirect
42. C2×D568C2×C4semidirect
43. C2×D568C2×C4semidirect
51. #14556090C23semidirect
59. #14556048C23semidirect
60. #14556038C23semidirect
61. C8×Dic71C23semidirect
63. C22×C8×C71C2×C4semidirect
72. #107×C71C23semidirect
73. #106×C71C23semidirect
85. C2×D284C22×C4semidirect
90. D568C22×C4semidirect
91. D568C22×C4semidirect
110. C2×C8×C71C22×C4semidirect
166. C2×C71#2948semidirect
175. C2×#427D71semidirect
178. C71C2×#2948semidirect
195. #427C2×D71semidirect
196. C2×#107C2×D71semidirect
197. C2×#106C2×D71semidirect
220. C22×C8C4×D71semidirect
239. #107C22×D71semidirect
240. #106C22×D71semidirect
275. C2×C8C2×C4×D71semidirect
336. C2#22597191direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5682
C2×#179864732
#225971912
C2×#179861102
C2×#179860812
C2×#179860032
C2×#179859542
C2×#427×C712
C2×#294871