Finite Group Databasebeta

← #28393513

Subgroups — #28393513

Order 14464.

588 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813584C211yesmaximal, characteristic
2#20298490C211yesmaximal, characteristic, complemented
3#20298488C211yesmaximal, characteristic, complemented
4#20298484C211yesmaximal, characteristic, complemented
5#20298476C211yesmaximal, characteristic
6#20298476C211yesmaximal, characteristic
7#20298465C211yesmaximal, characteristic, complemented
8#20298460C211yesmaximal, characteristic, complemented
9#20298455C211yesmaximal, characteristic, complemented
10C4×#14268624C211yesmaximal, characteristic, complemented
11C4×#14268624C211yesmaximal, characteristic, complemented
12#20298445C211yesmaximal, characteristic, complemented
13#20298443C211yesmaximal, characteristic, complemented
14#95×D113C211yesmaximal, characteristic, complemented
15#387×C113C211yesmaximal, characteristic, complemented
16C22×D452C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813584C418yescomplemented
22C2×C4⋊Dic113C2211yescharacteristic
23C2×#14268624C2211yescharacteristic
24C2×#14268624C2211yescharacteristic
25C2×#14268624C2211yescharacteristic
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×C4×Dic113C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33C2×C4×Dic113C2211yescharacteristic
34C2×C4×Dic113C2211yescharacteristic
35#16813529C2211yescharacteristic
36#16813529C2211yescharacteristic
37#16813529C2211yescharacteristic
38#16813529C2211yescharacteristic
39#16813529C2211yescharacteristic
40#16813529C2211yescharacteristic
41#16813529C2211yescharacteristic
42#16813529C2211yescharacteristic
43#16813529C2211yescharacteristic
44#16813529C2211yescharacteristic
45C2×C4⋊C4×C113C2211yescharacteristic
46C2×C4⋊C4×C113C2211yescharacteristic
47C2×C42×C113C2211yescharacteristic
48#95×C113C2211yescharacteristic
49#95×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C23×D113C2311yescharacteristic
53C23×D113C2311yescharacteristic
54C2×D452—22no—
55C2×D452—22no—
56C2×D452C2×C414yes—
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C2×C4×D113—22no—
64C2×C4×D113—22no—
65C2×C4×D113—22no—
66C2×C4×D113—22no—
67C2×C4×D113—41no—
68C2×C4×D113—41no—
69C2×C4×D113—41no—
70C2×C4×D113—41no—
71C2×C4×D113—41no—
72C2×C4×D113—41no—
73C2×C4×D113C2×C414yes—
74C2×C4×D113C2×C414yescomplemented
75C4⋊Dic113—41no—
76#14268624—22no—
77#14268624—22no—
78#14268624—22no—
79#14268624—22no—
80#14268624—41no—
81#14268624—41no—
82#14268624C2×C414yes—
83#14268624C2×C414yescomplemented
84C4×Dic113—22no—
85C4×Dic113—22no—
86C4×Dic113—41no—
87C4×Dic113C2×C414yescomplemented
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C22×C4×C113C2311yescharacteristic
94C22×C4×C113C2311yescharacteristic
95C4⋊C4×C113—41no—
96C4⋊C4×C113C2×C414yescomplemented
97C42×C113—41no—
98C23×C113C2411yescharacteristic
99C22×D113—21no—
100C22×D113—21no—
101C22×D113—21no—
102C22×D113—21no—
103C22×D113—21no—
104C22×D113—21no—
105C22×D113—21no—
106C22×D113—21no—
107C22×D113—21no—
108C22×D113—21no—
109C22×D113C22×C412yes—
110C22×D113C22×C412yes—
111C22×D113#4112yes—
112C22×D113#4112yes—
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×C113—21no—
127C2×C4×C113—21no—
128C2×C4×C113—21no—
129C2×C4×C113—21no—
130C2×C4×C113C22×C412yes—
131C2×C4×C113C22×C412yes—
132C2×C4×C113C22×C412yes—
133C2×C4×C113#4112yes—
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×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—21no—
149C2×Dic113C22×C412yes—
150C2×Dic113C22×C412yes—
151C2×Dic113#4112yes—
152D452—28no—
153C4×D113—44no—
154C4×D113—44no—
155C4×D113—44no—
156C4×D113—44no—
157C22×C113C23×C411yescharacteristic
158C22×C113C2×#4111yescharacteristic
159C22×C113C2×#4111yescharacteristic
160C22×C113C2×#4111yescharacteristic
161C22×C113C2×#4111yescharacteristic
162C22×C113H(5,𝔽2)11yescharacteristic
163C22×C113H(5,𝔽2)11yescharacteristic
164C2×D113—22no—
165C2×D113—22no—
166C2×D113—22no—
167C2×D113—22no—
168C2×D113—22no—
169C2×D113—22no—
170C2×D113—22no—
171C2×D113—22no—
172C2×D113—22no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C2×D113#11714yes—
178C4×C113—22no—
179C4×C113—22no—
180C4×C113—22no—
181C4×C113—22no—
182C4×C113—41no—
183C4×C113—41no—
184C4×C113—41no—
185Dic113—22no—
186Dic113—22no—
187Dic113—22no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113C2×#11711yescharacteristic
192C2×C113C4×#4111yescharacteristic
193C2×C113#51811yescharacteristic
194C2×C113#55111yescharacteristic
195C2×C113#55111yescharacteristic
196C2×C113#55311yescharacteristic
197C2×C113#55311yescharacteristic
198D113—24no—
199D113—42no—
200#2353—1131nomaximal, Sylow
201C113#235311yescharacteristic, complemented, Sylow
202C2×C4×D4—1131no—
203#388—1131no—
204#388—1131no—
205#387—1131no—
206#387D11311yescharacteristic, complemented
207#386—1131no—
208#386—1131no—
209#383—1131no—
210#381—1131no—
211#380—1131no—
212C4×C22⋊C4—1131no—
213C4×C22⋊C4—1131no—
214C4×C22⋊C4—1131no—
215#376—1131no—
216C2×#95—1131no—
217C22×D4—1131no—
218C23×C4—1131no—
219C23×C4—1131no—
220C23×C4—1131no—
221C23×C4—1131no—
222C4×D4—1138no—
223C2×C4⋊C4—1131no—
224C2×C4⋊C4C2×D11311yescharacteristic
225C2×C4⋊C4C2×D11311yescharacteristic
226C2×C22⋊C4—1131no—
227C2×C22⋊C4—1131no—
228C2×C22⋊C4—1131no—
229C2×C22⋊C4—1131no—
230C2×C22⋊C4—1131no—
231C2×C22⋊C4—1131no—
232C2×C22⋊C4—1131no—
233C2×C22⋊C4—1131no—
234C2×C42—1131no—
235C2×C42—1131no—
236C2×C42—1131no—
237C2×C42—1131no—
238C2×C42C2×D11311yescharacteristic
239#95—1131no—
240#95—1131no—
241#95—1131no—
242#95—1131no—
243#95—1131no—
244#95—1131no—
245#95—1131no—
246#95—1131no—
247#95—1131no—
248#95—1131no—
249#95C2×D11311yescharacteristic
250#95C2×D11311yescharacteristic
251#95C2×D11311yescharacteristic
252#95C2×D11311yescharacteristic
253C24—1131no—
254C24—1131no—
255C2×D4—1134no—
256C2×D4—2262no—
257C2×D4—2262no—
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—1131no—
261C22×C4—1134no—
262C22×C4—1134no—
263C22×C4—1131no—
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—4521no—
267C22×C4—4521no—
268C22×C4—4521no—
269C22×C4—4521no—
270C22×C4—4521no—
271C22×C4—4521no—
272C22×C4—2262no—
273C22×C4—2262no—
274C22×C4—2262no—
275C22×C4—2262no—
276C22×C4C22×D11311yescharacteristic
277C22×C4C22×D11311yescharacteristic
278C22×C4C22×D11311yescharacteristic
279C22×C4C22×D11311yescharacteristic
280C22×C4C22×D11311yescharacteristic
281C22×C4C22×D11311yescharacteristic
282C22×C4C22×D11311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—4521no—
285C4⋊C4C4×D11314yescomplemented
286C22⋊C4—1134no—
287C22⋊C4—1134no—
288C22⋊C4—4521no—
289C22⋊C4—4521no—
290C22⋊C4—2262no—
291C22⋊C4—2262no—
292C22⋊C4—2262no—
293C22⋊C4—2262no—
294C42—41no—
295C42—1134no—
296C42—4521no—
297C42—2262no—
298C42—2262no—
299C23—1132no—
300C23—1132no—
301C23—1132no—
302C23—1132no—
303C23—2261no—
304C23—2261no—
305C23—2261no—
306C23—2261no—
307C23—2261no—
308C23—2261no—
309C23—2261no—
310C23—2261no—
311C23—2261no—
312C23—2261no—
313C23C23×D11311yescharacteristic
314D4—2268no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1132no—
333C2×C4—1132no—
334C2×C4—1132no—
335C2×C4—4524no—
336C2×C4—4524no—
337C2×C4—4524no—
338C2×C4—4524no—
339C2×C4—2261no—
340C2×C4—2261no—
341C2×C4—2261no—
342C2×C4—2261no—
343C2×C4—2261no—
344C2×C4—2261no—
345C2×C4—2261no—
346C2×C4—2261no—
347C2×C4—2261no—
348C2×C4—2261no—
349C2×C4—2261no—
350C2×C4—2261no—
351C2×C4—2261no—
352C2×C4—2261no—
353C2×C4—2261no—
354C2×C4C2×C4×D11312yes—
355C2×C4C2×C4×D11312yes—
356C2×C4C2×C4×D11312yes—
357C2×C4#1426864812yes—
358C22—1134no—
359C22—4521no—
360C22—4521no—
361C22—4521no—
362C22—4521no—
363C22—2262no—
364C22—2262no—
365C22—2262no—
366C22—2262no—
367C22—2262no—
368C22—2262no—
369C22—2262no—
370C22—2262no—
371C22—2262no—
372C22C22×C4×D11311yescharacteristic
373C22#41×D11311yescharacteristic
374C22#41×D11311yescharacteristic
375C22#41×D11311yescharacteristic
376C22C2×#1426864811yescharacteristic
377C22#1681366711yescharacteristic
378C22#1681366811yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—22no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—4521no—
387C4—4521no—
388C4—4521no—
389C4—2262no—
390C4—2262no—
391C4—2262no—
392C2—4522no—
393C2—2264no—
394C2#117×D11311yescharacteristic
395C2C4×#1426864811yescharacteristic
396C2#2029907011yescharacteristic
397C2#2029927311yescharacteristic
398C2#2029927511yescharacteristic
399C2#2029929311yescharacteristic
400C2#2029930111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#387×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D452C22
hypercenter#387D113
hypocenterC113#2353
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20298490C2semidirect
3. #20298488C2semidirect
4. #20298484C2semidirect
7. #20298465C2semidirect
8. #20298460C2semidirect
9. #20298455C2semidirect
10. C4×#14268624C2semidirect
11. C4×#14268624C2semidirect
12. #20298445C2semidirect
13. #20298443C2semidirect
14. #95×D113C2semidirect
15. #387×C113C2semidirect
21. #16813584C4semidirect
74. C2×C4×D113C2×C4semidirect
83. #14268624C2×C4semidirect
87. C4×Dic113C2×C4semidirect
96. C4⋊C4×C113C2×C4semidirect
201. C113#2353semidirect
206. #387D113semidirect
285. C4⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135842
#202984902
#202984882
#202984842
#202984762
#202984652
#202984602
#202984552
C4×#142686242
#202984452
#202984432
#95×D1132
#387×C1132
#2353113