Finite Group Databasebeta

← #28393108

Subgroups — #28393108

Order 14464.

656 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813600C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3C2×C42×D113C211yesmaximal, characteristic
4#20298502C211yesmaximal, characteristic, complemented
5#20298495C211yesmaximal, characteristic, complemented
6#20298482C211yesmaximal, characteristic, complemented
7#20298472C211yesmaximal, characteristic
8#20298469C211yesmaximal, characteristic
9#20298457C211yesmaximal, characteristic
10C4⋊C4×Dic113C211yesmaximal, characteristic, complemented
11#20298449C211yesmaximal, characteristic, complemented
12#20298449C211yesmaximal, characteristic, complemented
13#20298445C211yesmaximal, characteristic
14#20298445C211yesmaximal, characteristic
15#387×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20#16813600C418yescomplemented
21#16813587—24no—
22C2×C4⋊Dic113C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×#14268624C2211yescharacteristic
32C2×#14268624C2211yescharacteristic
33C2×C4×Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35C2×C4×Dic113C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39C2×C4×Dic113C2211yescharacteristic
40C42×D113—24no—
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C4⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53#95×C113C2211yescharacteristic
54C23×D113C2311yescharacteristic
55C2×Dic226—22no—
56C2×Dic226—22no—
57C2×Dic226C2×C414yescomplemented
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C2×C4×D113—22no—
66C2×C4×D113—22no—
67C2×C4×D113—22no—
68C2×C4×D113—22no—
69C2×C4×D113—22no—
70C2×C4×D113—22no—
71C2×C4×D113—22no—
72C2×C4×D113C2×C414yes—
73C2×C4×D113Q814yescomplemented
74C4⋊Dic113—22no—
75#14268626—22no—
76#14268626—22no—
77#14268626—22no—
78#14268626—22no—
79#14268626C2×C414yescomplemented
80#14268626C2×C414yescomplemented
81#14268624—22no—
82#14268624—22no—
83#14268624C2×C414yes—
84#14268624C2×C414yes—
85C4×Dic113—22no—
86C4×Dic113—22no—
87C4×Dic113—22no—
88C4×Dic113—22no—
89C4×Dic113—22no—
90C4×Dic113—22no—
91C4×Dic113D414yes—
92C22×C4×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C22×C4×C113C2311yescharacteristic
96C22×C4×C113C2311yescharacteristic
97C22×C4×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C4⋊C4×C113—22no—
100C4⋊C4×C113C2×C414yescomplemented
101C42×C113—22no—
102C23×C113C2411yescharacteristic
103C22×D113—21no—
104C22×D113—21no—
105C22×D113—21no—
106C22×D113—21no—
107C22×D113C22×C412yes—
108C22×D113C2×Q812yes—
109C22×D113#4112yes—
110C2×C4×C113—21no—
111C2×C4×C113—21no—
112C2×C4×C113—21no—
113C2×C4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—21no—
123C2×C4×C113—21no—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113C22×C412yes—
127C2×C4×C113C22×C412yes—
128C2×C4×C113C22×C412yes—
129C2×C4×C113C2×D412yes—
130C2×C4×C113C2×Q812yes—
131C2×Dic113—21no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113—21no—
140C2×Dic113—21no—
141C2×Dic113—21no—
142C2×Dic113—21no—
143C2×Dic113C22×C412yes—
144C2×Dic113C22×C412yes—
145C2×Dic113C22×C412yes—
146C2×Dic113C2×D412yes—
147C2×Dic113C2×D412yes—
148C2×Dic113C2×Q812yes—
149C2×Dic113#4112yes—
150C2×Dic113#4112yes—
151C2×Dic113#4112yes—
152C4×D113—28no—
153C4×D113—28no—
154C4×D113—28no—
155Dic226—28no—
156C22×C113C23×C411yescharacteristic
157C22×C113C22×D411yescharacteristic
158C22×C113C22×Q811yescharacteristic
159C22×C113C2×#4111yescharacteristic
160C22×C113C2×#4111yescharacteristic
161C22×C113C2×#4111yescharacteristic
162C22×C113C2×#4111yescharacteristic
163C2×D113—22no—
164C2×D113—22no—
165C2×D113—22no—
166C2×D113—22no—
167C2×D113—22no—
168C2×D113—22no—
169C2×D113C4×Q814yescomplemented
170C4×C113—22no—
171C4×C113—22no—
172C4×C113—22no—
173C4×C113—22no—
174C4×C113—22no—
175C4×C113—41no—
176C4×C113—41no—
177Dic113—22no—
178Dic113—22no—
179Dic113—22no—
180Dic113—41no—
181Dic113—41no—
182Dic113C4×D414yes—
183Dic113C22⋊Q814yescomplemented
184C2×C113C2×C4×D411yescharacteristic
185C2×C113C2×C4×Q811yescharacteristic
186C2×C113C4×#4111yescharacteristic
187C2×C113C2×C22⋊Q811yescharacteristic
188C2×C113#52511yescharacteristic
189C2×C113#52911yescharacteristic
190C2×C113#53311yescharacteristic
191D113—24no—
192C4×C22⋊Q8—1131nomaximal, Sylow
193C113C4×C22⋊Q811yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—1131no—
195C2×C4×Q8—1131no—
196C22×C42—1131no—
197#391—1131no—
198#389—1131no—
199#387—1131no—
200#387D11311yescharacteristic, complemented
201#385—1131no—
202#385—1131no—
203#380—1131no—
204C4×C4⋊C4—1131no—
205C4×C4⋊C4—1131no—
206C4×C4⋊C4—1131no—
207C4×C22⋊C4—1131no—
208C4×C22⋊C4—1131no—
209C22×Q8—1131no—
210C23×C4—1131no—
211C23×C4—1131no—
212C23×C4—1131no—
213C22⋊Q8—1138no—
214C4×Q8—2264no—
215C2×C4⋊C4—1131no—
216C2×C4⋊C4—1131no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4—1131no—
219C2×C4⋊C4—1131no—
220C2×C4⋊C4—1131no—
221C2×C4⋊C4—1131no—
222C2×C4⋊C4C2×D11311yescharacteristic
223C2×C4⋊C4C2×D11311yescharacteristic
224C2×C22⋊C4—1131no—
225C2×C22⋊C4—1131no—
226C2×C22⋊C4—1131no—
227C2×C22⋊C4—1131no—
228C2×C42—1131no—
229C2×C42—1131no—
230C2×C42—1131no—
231C2×C42—1131no—
232C2×C42—1131no—
233C2×C42—1131no—
234C2×C42—1131no—
235C2×C42—2264no—
236C2×C42C2×D11311yescharacteristic
237#95—1131no—
238#95—1131no—
239#95—1131no—
240#95—1131no—
241#95—1131no—
242#95—1131no—
243#95C2×D11311yescharacteristic
244#95C2×D11311yescharacteristic
245#95C2×D11311yescharacteristic
246#95C2×D11311yescharacteristic
247C24—1131no—
248C2×Q8—1134no—
249C2×Q8—2262no—
250C2×Q8—2262no—
251C22×C4—1131no—
252C22×C4—1131no—
253C22×C4—1131no—
254C22×C4—1131no—
255C22×C4—1131no—
256C22×C4—1134no—
257C22×C4—1134no—
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—2262no—
261C22×C4—2262no—
262C22×C4—2262no—
263C22×C4—2262no—
264C22×C4—2262no—
265C22×C4—2262no—
266C22×C4—2262no—
267C22×C4C22×D11311yescharacteristic
268C22×C4C22×D11311yescharacteristic
269C22×C4C22×D11311yescharacteristic
270C22×C4C22×D11311yescharacteristic
271C22×C4C22×D11311yescharacteristic
272C22×C4C22×D11311yescharacteristic
273C22×C4C22×D11311yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—1134no—
276C4⋊C4—1134no—
277C4⋊C4—2262no—
278C4⋊C4—2262no—
279C4⋊C4—2262no—
280C4⋊C4—2262no—
281C4⋊C4—2262no—
282C4⋊C4C4×D11314yescomplemented
283C22⋊C4—1134no—
284C22⋊C4—1134no—
285C22⋊C4—2262no—
286C22⋊C4—2262no—
287C42—22no—
288C42—1134no—
289C42—2262no—
290C42—2262no—
291C42—2262no—
292C42—2262no—
293C42—2262no—
294C42—2262no—
295C23—1132no—
296C23—1132no—
297C23—1132no—
298C23—2261no—
299C23—2261no—
300C23—2261no—
301C23—2261no—
302C23C23×D11311yescharacteristic
303Q8—2268no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—1132no—
321C2×C4—1132no—
322C2×C4—1132no—
323C2×C4—1132no—
324C2×C4—1132no—
325C2×C4—1132no—
326C2×C4—1132no—
327C2×C4—1132no—
328C2×C4—1132no—
329C2×C4—2268no—
330C2×C4—2268no—
331C2×C4—2268no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4—2261no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4—2261no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4C2×C4×D11312yes—
345C2×C4C2×C4×D11312yes—
346C2×C4C2×C4×D11312yes—
347C2×C4D4×D11312yes—
348C2×C4Q8×D11312yes—
349C22—1134no—
350C22—2262no—
351C22—2262no—
352C22—2262no—
353C22—2262no—
354C22—2262no—
355C22—2262no—
356C22C22×C4×D11311yescharacteristic
357C22C2×D4×D11311yescharacteristic
358C22C2×Q8×D11311yescharacteristic
359C22#41×D11311yescharacteristic
360C22#41×D11311yescharacteristic
361C22#41×D11311yescharacteristic
362C22#41×D11311yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—1134no—
371C4—1134no—
372C4—4521no—
373C4—4521no—
374C4—2262no—
375C4—2262no—
376C4—2262no—
377C2—2264no—
378C2C4×D4×D11311yescharacteristic
379C2C4×Q8×D11311yescharacteristic
380C2#2029906611yescharacteristic
381C2C22⋊Q8×D11311yescharacteristic
382C2#2029910611yescharacteristic
383C2#2029913111yescharacteristic
384C2#2029915411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#387×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenter#387D113
hypocenterC113C4×C22⋊Q8
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×#16813587C2semidirect
4. #20298502C2semidirect
5. #20298495C2semidirect
6. #20298482C2semidirect
10. C4⋊C4×Dic113C2semidirect
11. #20298449C2semidirect
12. #20298449C2semidirect
15. #387×C113C2semidirect
20. #16813600C4semidirect
57. C2×Dic226C2×C4semidirect
73. C2×C4×D113Q8semidirect
79. #14268626C2×C4semidirect
80. #14268626C2×C4semidirect
100. C4⋊C4×C113C2×C4semidirect
169. C2×D113C4×Q8semidirect
183. Dic113C22⋊Q8semidirect
193. C113C4×C22⋊Q8semidirect
200. #387D113semidirect
282. C4⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136002
C2×#168135872
C2×C42×D1132
#202985022
#202984952
#202984822
#202984722
#202984692
#202984572
C4⋊C4×Dic1132
#202984492
#202984452
#387×C1132
C4×C22⋊Q8113