Finite Group Databasebeta

← #28399790

Subgroups — #28399790

Order 14464.

764 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14268647C211yesmaximal, characteristic, complemented
2C2×#16813642C212yesmaximal, complemented
3#20298758C212yesmaximal, complemented
4#20298753C211yesmaximal, characteristic, complemented
5#20298748C211yesmaximal, characteristic, complemented
6#20298741C212yesmaximal, complemented
7#20298736C211yesmaximal, characteristic, complemented
8#20298731C211yesmaximal, characteristic, complemented
9#20298592C212yesmaximal, complemented
10C2×C22⋊#11744751C211yesmaximal, characteristic, complemented
11#525×C113C211yesmaximal, characteristic, complemented
12C2×#14268647—28no—
13C2×#14268647—21no—
14C2×#14268647—21no—
15C2×#14268647C2212yes—
16C2×#14268647C2212yes—
17C22×Dic226C2211yescharacteristic
18C22×D452C2211yescharacteristic
19C22×C22⋊D113—21no—
20C22×C4×D113—21no—
21#16813642—28no—
22C2×#14268637C2212yescomplemented
23C2×#14268635C2212yescomplemented
24C2×#14268634C2212yescomplemented
25C2×#14268632C2212yescomplemented
26C22×#11744751C2212yescomplemented
27#16813545C2212yescomplemented
28#16813545C2212yescomplemented
29#16813542C2212yescomplemented
30#16813542C2212yescomplemented
31C22⋊#11744751C2211yescharacteristic
32C22⋊#11744751C2211yescharacteristic
33C22⋊#11744751C2212yescomplemented
34C2×#41×C113C2211yescharacteristic, complemented
35C23×C4×C113C2211yescharacteristic
36#123×C113—21no—
37C22⋊Q8×C113C2211yescharacteristic
38C22⋊Q8×C113C2211yescharacteristic, complemented
39#121×C113C2211yescharacteristic
40#121×C113C2211yescharacteristic, complemented
41#120×C113—21no—
42C4×D4×C113—21no—
43C4×D4×C113—21no—
44#117×C113C2211yescharacteristic, complemented
45C23×D113—21no—
46#14268647—28no—
47#14268647—28no—
48#14268647—24no—
49#14268647—24no—
50#14268647—24no—
51#14268647D418yescomplemented
52C2×Dic226—21no—
53C2×Dic226—24no—
54C2×Dic226C2312yes—
55C2×D452—21no—
56C2×D452—24no—
57C2×D452C2312yes—
58C2×C22⋊D113—28no—
59C2×C22⋊D113—22no—
60C2×C22⋊D113—22no—
61C22×Dic113—21no—
62C2×C4×D113—28no—
63C2×C4×D113—22no—
64C2×C4×D113—22no—
65#14268637—24no—
66#14268635—24no—
67#14268634—24no—
68#14268632—24no—
69C2×#11744751—24no—
70C2×#11744751C2312yes—
71C2×#11744751C2312yes—
72C24×C113D411yescharacteristic
73#41×C113—24no—
74C2×Q8×C113C2311yescharacteristic
75C2×D4×C113—21no—
76C2×D4×C113—21no—
77C2×D4×C113—21no—
78C2×D4×C113C2311yescharacteristic
79C22×C4×C113—24no—
80C22×C4×C113—21no—
81C22×C4×C113D411yescharacteristic
82C22×C4×C113D411yescharacteristic
83C22×C4×C113D411yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C4⋊C4×C113—21no—
88C4⋊C4×C113—21no—
89C4⋊C4×C113C2311yescharacteristic
90C4⋊C4×C113C2311yescharacteristic
91C22⋊C4×C113—21no—
92C22⋊C4×C113—21no—
93C22⋊C4×C113—21no—
94C22⋊C4×C113—21no—
95C22⋊C4×C113—21no—
96C42×C113—21no—
97C23×C113—22no—
98C23×C113—22no—
99C23×C113—21no—
100C23×C113—41no—
101C23×C113C2×D411yescharacteristic
102C23×C113C2×D411yescharacteristic
103C23×C113C2×D411yescharacteristic
104C22×D113—24no—
105C22×D113—22no—
106C22×D113—42no—
107C22×D113—42no—
108Q8×C113—22no—
109D4×C113—22no—
110D4×C113—42no—
111D4×C113—42no—
112D4×C113—42no—
113C2×C4×C113—22no—
114C2×C4×C113—22no—
115C2×C4×C113—22no—
116C2×C4×C113—22no—
117C2×C4×C113—22no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—42no—
122C2×C4×C113C2×D414yes—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2×D411yescharacteristic
126C2×C4×C113C2411yescharacteristic
127C22⋊D113—28no—
128C22⋊D113—28no—
129C2×Dic113—24no—
130C2×Dic113—22no—
131D452—24no—
132D452—22no—
133D452C2×D414yes—
134C4×D113—28no—
135C4×D113—28no—
136Dic226—24no—
137Dic226—22no—
138Dic226C2×D414yes—
139#11744751—22no—
140#11744751—22no—
141C22×C113—21no—
142C22×C113—21no—
143C22×C113—21no—
144C22×C113—21no—
145C22×C113—21no—
146C22×C113—21no—
147C22×C113—21no—
148C22×C113—44no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113#12012yes—
153C22×C113#13512yescomplemented
154C22×C113C22×D411yescharacteristic
155C2×D113—24no—
156C2×D113—48no—
157C2×D113—42no—
158C2×D113—42no—
159C4×C113—21no—
160C4×C113—21no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113#12012yes—
165C4×C113C22×D412yes—
166Dic113—24no—
167C2×C113—22no—
168C2×C113—22no—
169C2×C113—41no—
170C2×C113—81no—
171C2×C113C2×#12011yescharacteristic
172C2×C113C2×#13511yescharacteristic
173C2×C113#57511yescharacteristic
174D113—44no—
175#3002—1131nomaximal, Sylow
176C113#300211yescharacteristic, complemented, Sylow
177C22×#41—1131no—
178C2×#135—1132no—
179#525D11311yescharacteristic, complemented
180#452—1132no—
181#451—1131no—
182#450—1131no—
183#449—1132no—
184#448—1131no—
185#447—1131no—
186#416—1132no—
187C2×C22⋊C8—1131no—
188C2×#41—1132no—
189C2×#41—1132no—
190C2×#41—2268no—
191C2×#41—2261no—
192C2×#41—2261no—
193C2×#41C2×D11311yescharacteristic, complemented
194C22×Q8—1131no—
195C22×D4—1131no—
196C22×D4—2261no—
197C23×C4—2261no—
198C23×C4C2×D11311yescharacteristic
199#135—2268no—
200C2×Q16—1132no—
201C2×SD16—1132no—
202C2×SD16—1132no—
203C2×D8—1132no—
204C22×C8—1132no—
205#123—21no—
206C22⋊Q8C2×D11311yescharacteristic
207C22⋊Q8C2×D11311yescharacteristic, complemented
208#121C2×D11311yescharacteristic
209#121C2×D11311yescharacteristic, complemented
210#120—21no—
211C4×D4—21no—
212C4×D4—21no—
213#117C2×D11311yescharacteristic, complemented
214#103—1132no—
215#103—1132no—
216#102—1132no—
217#102—1132no—
218C22⋊C8—1131no—
219C22⋊C8—1131no—
220C22⋊C8—1132no—
221C24—2261no—
222C24C22⋊D11311yescharacteristic
223#41—24no—
224#41—1138no—
225#41—2264no—
226#41—2264no—
227#41—2268no—
228#41—2268no—
229#41—2264no—
230C2×Q8—1132no—
231C2×Q8—2264no—
232C2×Q8—2261no—
233C2×Q8C22×D11311yescharacteristic
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—1132no—
238C2×D4—2264no—
239C2×D4—2268no—
240C2×D4—2262no—
241C2×D4—2262no—
242C2×D4—2261no—
243C2×D4C22×D11311yescharacteristic
244C22×C4—24no—
245C22×C4—21no—
246C22×C4—2268no—
247C22×C4—2261no—
248C22×C4—2262no—
249C22×C4—2262no—
250C22×C4C22⋊D11311yescharacteristic
251C22×C4C22⋊D11311yescharacteristic
252C22×C4C22⋊D11311yescharacteristic
253C22×C4C22×D11311yescharacteristic
254C22×C4C22×D11311yescharacteristic
255C22×C4C22×D11311yescharacteristic
256Q16—2264no—
257SD16—2264no—
258SD16—2264no—
259D8—2264no—
260C2×C8—1132no—
261C2×C8—1132no—
262C2×C8—2264no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4C22×D11311yescharacteristic
266C4⋊C4C22×D11311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C42—21no—
273C23—22no—
274C23—22no—
275C23—21no—
276C23—41no—
277C23—4522no—
278C23—4522no—
279C23—2264no—
280C23—2262no—
281C23C2×C22⋊D11311yescharacteristic
282C23C2×C22⋊D11311yescharacteristic
283C23C2×C22⋊D11311yescharacteristic
284Q8—22no—
285Q8—1134no—
286Q8—2264no—
287Q8—2262no—
288D4—22no—
289D4—42no—
290D4—42no—
291D4—42no—
292D4—1134no—
293D4—2264no—
294D4—2268no—
295D4—2268no—
296D4—2262no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—2268no—
307C2×C4—2264no—
308C2×C4—2262no—
309C2×C4—2268no—
310C2×C4D4×D11314yes—
311C2×C4C2×C22⋊D11311yescharacteristic
312C2×C4C2×C22⋊D11311yescharacteristic
313C2×C4C2×C22⋊D11311yescharacteristic
314C2×C4C23×D11311yescharacteristic
315C8—2262no—
316C8—2262no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—44no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—4528no—
329C22—4522no—
330C22—4522no—
331C22—2264no—
332C22#1681359012yes—
333C22#1681364212yescomplemented
334C22C22×C22⋊D11311yescharacteristic
335C4—21no—
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—2264no—
341C4#1681359012yes—
342C4C2×D4×D11312yes—
343C2—22no—
344C2—22no—
345C2—41no—
346C2—81no—
347C2—4524no—
348C2C2×#1681359011yescharacteristic
349C2C2×#1681364211yescharacteristic
350C2#2029939611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#525×C113C2
socleC22×C113C22×D4
hypercenter#525D113
hypocenterC113#3002
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C22×#14268647C2semidirect
2. C2×#16813642C2semidirect
3. #20298758C2semidirect
4. #20298753C2semidirect
5. #20298748C2semidirect
6. #20298741C2semidirect
7. #20298736C2semidirect
8. #20298731C2semidirect
9. #20298592C2semidirect
10. C2×C22⋊#11744751C2semidirect
11. #525×C113C2semidirect
22. C2×#14268637C22semidirect
23. C2×#14268635C22semidirect
24. C2×#14268634C22semidirect
25. C2×#14268632C22semidirect
26. C22×#11744751C22semidirect
27. #16813545C22semidirect
28. #16813545C22semidirect
29. #16813542C22semidirect
30. #16813542C22semidirect
33. C22⋊#11744751C22semidirect
34. C2×#41×C113C22semidirect
38. C22⋊Q8×C113C22semidirect
40. #121×C113C22semidirect
44. #117×C113C22semidirect
51. #14268647D4semidirect
153. C22×C113#135semidirect
176. C113#3002semidirect
179. #525D113semidirect
193. C2×#41C2×D113semidirect
207. C22⋊Q8C2×D113semidirect
209. #121C2×D113semidirect
213. #117C2×D113semidirect
333. C22#16813642semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136422
#202987582
#202987532
#202987482
#202987412
#202987362
#202987312
#202985922
C2×C22⋊#117447512
#525×C1132
#3002113