Finite Group Databasebeta

← #28393249

Subgroups — #28393249

Order 14464.

556 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813599C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3C2×#16813578C211yesmaximal, characteristic
4#20298502C211yesmaximal, characteristic, complemented
5#20298496C211yesmaximal, characteristic, complemented
6#20298495C211yesmaximal, characteristic, complemented
7#20298493C211yesmaximal, characteristic, complemented
8#20298492C211yesmaximal, characteristic
9#20298492C211yesmaximal, characteristic
10#20298491C211yesmaximal, characteristic
11#20298481C211yesmaximal, characteristic, complemented
12#20298480C211yesmaximal, characteristic, complemented
13#20298456C211yesmaximal, characteristic
14C4×#14268626C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic
16C22×Dic226C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18#16813599C418yescomplemented
19#16813587—24no—
20#16813578—24no—
21C2×C4⋊Dic113C2211yescharacteristic
22C2×C4⋊Dic113C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×#14268626C2211yescharacteristic
27C2×#14268626C2211yescharacteristic
28C2×#14268626C2211yescharacteristic
29C2×#14268626C2211yescharacteristic
30C2×#14268626C2211yescharacteristic
31C2×C22⋊Dic113C2211yescharacteristic
32C2×C22⋊Dic113C2211yescharacteristic
33C2×C22⋊Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35C2×C4×Dic113C2211yescharacteristic
36C2×C4×Dic113C2211yescharacteristic
37C2×C4×Dic113C2211yescharacteristic
38C2×C4×Dic113C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45#16813529C2211yescharacteristic
46#16813529C2211yescharacteristic
47C2×C4⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C22⋊C4×C113C2211yescharacteristic
50C2×C22⋊C4×C113C2211yescharacteristic
51C2×C42×C113C2211yescharacteristic
52#95×C113C2211yescharacteristic
53#95×C113C2211yescharacteristic
54C2×Dic226—22no—
55C2×Dic226—22no—
56C2×Dic226C2×C414yes—
57C22×Dic113—22no—
58C22×Dic113—22no—
59C22×Dic113C2×C414yes—
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C4⋊Dic113—41no—
69C4⋊Dic113C2×C414yes—
70#14268626—22no—
71#14268626—22no—
72#14268626—22no—
73#14268626—22no—
74#14268626—22no—
75#14268626—41no—
76#14268626C2×C414yes—
77#14268626C2×C414yes—
78C22⋊Dic113—22no—
79C22⋊Dic113—41no—
80C22⋊Dic113C2×C414yes—
81C4×Dic113—22no—
82C4×Dic113—22no—
83C4×Dic113—22no—
84C4×Dic113—41no—
85C4×Dic113D414yes—
86C24×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—22no—
94C22⋊C4×C113—22no—
95C22⋊C4×C113—41no—
96C22⋊C4×C113C2×C414yes—
97C42×C113—41no—
98C23×C113—21no—
99C23×C113—21no—
100C23×C113—21no—
101C23×C113—21no—
102C23×C113—21no—
103C23×C113—21no—
104C23×C113C22×C412yes—
105C23×C113C2411yescharacteristic
106C2×C4×C113—21no—
107C2×C4×C113—21no—
108C2×C4×C113—21no—
109C2×C4×C113—21no—
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×C113C22×C412yes—
122C2×C4×C113C22×C412yes—
123C2×C4×C113C2×D412yes—
124C2×Dic113—21no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—21no—
130C2×Dic113—21no—
131C2×Dic113—21no—
132C2×Dic113—28no—
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×Dic113C22×C412yes—
143C2×Dic113C22×C412yes—
144C2×Dic113C22×C412yes—
145C2×Dic113C22×C412yes—
146C2×Dic113C2×D412yes—
147C2×Dic113C2×D412yes—
148C2×Dic113#4112yes—
149Dic226—28no—
150C22×C113—22no—
151C22×C113—22no—
152C22×C113—22no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113C23×C411yescharacteristic
158C22×C113C22×D411yescharacteristic
159C22×C113C2×#4111yescharacteristic
160C22×C113H(5,𝔽2)11yescharacteristic
161C22×C1132−1+411yescharacteristic
162C22×C1132−1+411yescharacteristic
163C22×C1132−1+411yescharacteristic
164C4×C113—22no—
165C4×C113—22no—
166C4×C113—22no—
167C4×C113—41no—
168C4×C113—41no—
169C4×C113—41no—
170Dic113—22no—
171Dic113—22no—
172Dic113—22no—
173Dic113—22no—
174Dic113—41no—
175Dic113—41no—
176Dic113—41no—
177Dic113C4×D414yes—
178C2×C113—42no—
179C2×C113C2×C4×D411yescharacteristic
180C2×C113#51911yescharacteristic
181C2×C113#52011yescharacteristic
182C2×C113#53611yescharacteristic
183C2×C113#53711yescharacteristic
184C2×C113#54111yescharacteristic
185C2×C113#54211yescharacteristic
186#2323—1131nomaximal, Sylow
187C113#232311yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—1131no—
189C2×C4×Q8—1131no—
190C2×#117—1131no—
191#391—1131no—
192#389—1131no—
193#389—1131no—
194#389—1131no—
195#388—1131no—
196#388—1131no—
197#388—1131no—
198#388D11311yescharacteristic
199#387—1131no—
200#387—1131no—
201#380—1131no—
202C4×C4⋊C4—1131no—
203C22×Q8—1131no—
204C23×C4—1131no—
205C22⋊Q8—1138no—
206C4×Q8—2264no—
207#117—2264no—
208C2×C4⋊C4—1131no—
209C2×C4⋊C4—1131no—
210C2×C4⋊C4—1131no—
211C2×C4⋊C4—1131no—
212C2×C4⋊C4—1131no—
213C2×C4⋊C4—1131no—
214C2×C4⋊C4—1131no—
215C2×C4⋊C4—1131no—
216C2×C4⋊C4—1131no—
217C2×C4⋊C4—1131no—
218C2×C4⋊C4C2×D11311yescharacteristic
219C2×C22⋊C4—1131no—
220C2×C22⋊C4—1131no—
221C2×C22⋊C4—1131no—
222C2×C22⋊C4C2×D11311yescharacteristic
223C2×C22⋊C4C2×D11311yescharacteristic
224C2×C22⋊C4C2×D11311yescharacteristic
225C2×C42—1131no—
226C2×C42—1131no—
227C2×C42—1131no—
228C2×C42—1131no—
229C2×C42—1131no—
230C2×C42C2×D11311yescharacteristic
231#95—1131no—
232#95—1131no—
233#95—1131no—
234#95—1131no—
235#95—1131no—
236#95—1131no—
237#95—1131no—
238#95—1131no—
239#95C2×D11311yescharacteristic
240#95C2×D11311yescharacteristic
241C24C22×D11311yescharacteristic
242C2×Q8—1134no—
243C2×Q8—2262no—
244C2×Q8—2262no—
245C22×C4—1131no—
246C22×C4—1134no—
247C22×C4—1131no—
248C22×C4—1131no—
249C22×C4—1131no—
250C22×C4—1131no—
251C22×C4—1131no—
252C22×C4—1131no—
253C22×C4—1131no—
254C22×C4—2262no—
255C22×C4—2262no—
256C22×C4C22×D11311yescharacteristic
257C22×C4C22×D11311yescharacteristic
258C22×C4C22×D11311yescharacteristic
259C22×C4C22×D11311yescharacteristic
260C22×C4C22×D11311yescharacteristic
261C22×C4C22×D11311yescharacteristic
262C4⋊C4—22no—
263C4⋊C4—1134no—
264C4⋊C4—1134no—
265C4⋊C4—1134no—
266C4⋊C4—4521no—
267C4⋊C4—4521no—
268C4⋊C4—2262no—
269C4⋊C4—2262no—
270C4⋊C4—2262no—
271C4⋊C4—2262no—
272C4⋊C4—2262no—
273C22⋊C4—22no—
274C22⋊C4—41no—
275C22⋊C4—1134no—
276C22⋊C4—4521no—
277C22⋊C4—2262no—
278C22⋊C4C4×D11314yes—
279C42—41no—
280C42—1134no—
281C42—4521no—
282C42—2262no—
283C42—2262no—
284C42—2262no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23C2×C4×D11312yes—
292C23C23×D11311yescharacteristic
293Q8—2268no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—1132no—
310C2×C4—1132no—
311C2×C4—1132no—
312C2×C4—1132no—
313C2×C4—1132no—
314C2×C4—1132no—
315C2×C4—1132no—
316C2×C4—2268no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4—2261no—
325C2×C4—2261no—
326C2×C4—2261no—
327C2×C4—2261no—
328C2×C4—2261no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4—2261no—
333C2×C4—2261no—
334C2×C4C2×C4×D11312yes—
335C2×C4C2×C4×D11312yes—
336C2×C4D4×D11312yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C22×C4×D11311yescharacteristic
345C22C2×D4×D11311yescharacteristic
346C22#41×D11311yescharacteristic
347C22#1681366711yescharacteristic
348C22#1681366911yescharacteristic
349C22#1681366911yescharacteristic
350C22#1681366911yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—1134no—
358C4—4521no—
359C4—4521no—
360C4—4521no—
361C4—2262no—
362C4—2262no—
363C4—2262no—
364C4—2262no—
365C2—42no—
366C2C4×D4×D11311yescharacteristic
367C2#2029907511yescharacteristic
368C2#2029907711yescharacteristic
369C2#2029916811yescharacteristic
370C2#2029917511yescharacteristic
371C2#2029920511yescharacteristic
372C2#2029921611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC24×C113C23
hypercenter#388D113
hypocenterC113#2323
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#16813587C2semidirect
4. #20298502C2semidirect
5. #20298496C2semidirect
6. #20298495C2semidirect
7. #20298493C2semidirect
11. #20298481C2semidirect
12. #20298480C2semidirect
14. C4×#14268626C2semidirect
18. #16813599C4semidirect
187. C113#2323semidirect

Maximal subgroups

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

subgroupindex
C2×#168135992
C2×#168135872
C2×#168135782
#202985022
#202984962
#202984952
#202984932
#202984922
#202984912
#202984812
#202984802
#202984562
C4×#142686262
#388×C1132
#2323113