Finite Group Databasebeta

← #28393385

Subgroups — #28393385

Order 14464.

540 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16813608C211yesmaximal, characteristic
2#20298503C211yesmaximal, characteristic, complemented
3#20298502C211yesmaximal, characteristic, complemented
4#20298489C211yesmaximal, characteristic, complemented
5#20298487C211yesmaximal, characteristic, complemented
6#20298486C211yesmaximal, characteristic, complemented
7#20298475C211yesmaximal, characteristic
8#20298474C211yesmaximal, characteristic
9#20298470C211yesmaximal, characteristic, complemented
10#20298469C211yesmaximal, characteristic, complemented
11#20298465C211yesmaximal, characteristic, complemented
12C4×#14268626C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic113C211yesmaximal, characteristic, complemented
14#20298445C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic, complemented
16C22×Dic226C2211yescharacteristic
17C22×C22⋊D113C2211yescharacteristic
18C23×Dic113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20#16813608C418yescomplemented
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×C22⋊Dic113C2211yescharacteristic
25C2×C22⋊Dic113C2211yescharacteristic
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×C22⋊C4×C113C2211yescharacteristic
47C2×C22⋊C4×C113C2211yescharacteristic
48C2×C22⋊C4×C113C2211yescharacteristic
49C2×C42×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C23×D113C2311yescharacteristic
53C2×Dic226—41no—
54C2×Dic226—41no—
55C2×Dic226C2×C414yescomplemented
56C2×C22⋊D113—41no—
57C2×C22⋊D113—41no—
58C2×C22⋊D113C2×C414yes—
59C22×Dic113—22no—
60C22×Dic113—41no—
61C22×Dic113—41no—
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C22×Dic113C2311yescharacteristic
67C22×Dic113C2311yescharacteristic
68C22×Dic113C2311yescharacteristic
69C2×C4×D113—22no—
70C2×C4×D113—41no—
71C2×C4×D113—41no—
72#14268626—22no—
73#14268626—22no—
74#14268626—41no—
75C22⋊Dic113—22no—
76C22⋊Dic113C2×C414yescomplemented
77#14268624—22no—
78#14268624—41no—
79#14268624—41no—
80#14268624C2×C414yescomplemented
81#14268624C2×C414yescomplemented
82C4×Dic113—41no—
83C4×Dic113—41no—
84C4×Dic113—41no—
85C4×Dic113C2×C414yescomplemented
86C24×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C22×C4×C113C2311yescharacteristic
90C22×C4×C113C2311yescharacteristic
91C22×C4×C113C2311yescharacteristic
92C22×C4×C113C2311yescharacteristic
93C4⋊C4×C113—41no—
94C22⋊C4×C113—41no—
95C22⋊C4×C113—41no—
96C22⋊C4×C113C2×C414yescomplemented
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
106C22×D113—21no—
107C22×D113—21no—
108C22×D113—21no—
109C22×D113—21no—
110C22×D113—21no—
111C22×D113—21no—
112C22×D113C22×C412yes—
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×C113C22×C412yes—
130C2×C4×C113C22×C412yes—
131C22⋊D113—44no—
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×Dic113—21no—
144C2×Dic113—21no—
145C2×Dic113—21no—
146C2×Dic113—21no—
147C2×Dic113—21no—
148C2×Dic113—44no—
149C2×Dic113C22×C412yes—
150C2×Dic113C22×C412yes—
151C2×Dic113C22×C412yes—
152C2×Dic113#4112yes—
153C2×Dic113#4112yes—
154C4×D113—44no—
155Dic226—44no—
156C22×C113—22no—
157C22×C113—22no—
158C22×C113—22no—
159C22×C113—41no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113C23×C411yescharacteristic
164C22×C113C2×#4111yescharacteristic
165C22×C113C2×#4111yescharacteristic
166C22×C113H(5,𝔽2)11yescharacteristic
167C22×C113H(5,𝔽2)11yescharacteristic
168C22×C113H(5,𝔽2)11yescharacteristic
169C22×C1132−1+411yescharacteristic
170C2×D113—22no—
171C2×D113—22no—
172C2×D113—22no—
173C2×D113—41no—
174C2×D113—41no—
175C2×D113—41no—
176C2×D113—41no—
177C4×C113—22no—
178C4×C113—22no—
179C4×C113—41no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113—41no—
183Dic113—22no—
184Dic113—22no—
185Dic113—22no—
186Dic113—22no—
187Dic113—22no—
188Dic113—41no—
189Dic113—41no—
190C2×C113—42no—
191C2×C113C4×#4111yescharacteristic
192C2×C113#51811yescharacteristic
193C2×C113#52011yescharacteristic
194C2×C113#53811yescharacteristic
195C2×C113#53811yescharacteristic
196C2×C113#54211yescharacteristic
197C2×C113#54211yescharacteristic
198D113—42no—
199#2337—1131nomaximal, Sylow
200C113#233711yescharacteristic, complemented, Sylow
201C2×#124—1131no—
202#391—1131no—
203#391—1131no—
204#388—1131no—
205#388—1131no—
206#388—1131no—
207#388D11311yescharacteristic, complemented
208#386—1131no—
209#386—1131no—
210#385—1131no—
211#385—1131no—
212#383—1131no—
213C4×C4⋊C4—1131no—
214C4×C22⋊C4—1131no—
215C4×C22⋊C4—1131no—
216C22×Q8—1131no—
217C22×D4—1131no—
218C23×C4—1131no—
219C23×C4—1131no—
220#124—1138no—
221C2×C4⋊C4—1131no—
222C2×C4⋊C4—1131no—
223C2×C4⋊C4—1131no—
224C2×C4⋊C4C2×D11311yescharacteristic
225C2×C22⋊C4—1131no—
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⋊C4C2×D11311yescharacteristic
233C2×C22⋊C4C2×D11311yescharacteristic
234C2×C22⋊C4C2×D11311yescharacteristic
235C2×C42—1131no—
236C2×C42—1131no—
237C2×C42—1131no—
238C2×C42—1131no—
239C2×C42C2×D11311yescharacteristic
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#95—1131no—
250#95C2×D11311yescharacteristic
251#95C2×D11311yescharacteristic
252C24—1131no—
253C24C22×D11311yescharacteristic
254C2×Q8—1134no—
255C2×Q8—4521no—
256C2×Q8—4521no—
257C2×D4—1134no—
258C2×D4—4521no—
259C2×D4—4521no—
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—1131no—
264C22×C4—1131no—
265C22×C4—1131no—
266C22×C4—1131no—
267C22×C4—4521no—
268C22×C4—4521no—
269C22×C4—4521no—
270C22×C4—4521no—
271C22×C4—2262no—
272C22×C4—2262no—
273C22×C4C22×D11311yescharacteristic
274C22×C4C22×D11311yescharacteristic
275C22×C4C22×D11311yescharacteristic
276C22×C4C22×D11311yescharacteristic
277C22×C4C22×D11311yescharacteristic
278C22×C4C22×D11311yescharacteristic
279C4⋊C4—41no—
280C4⋊C4—4521no—
281C4⋊C4—2262no—
282C4⋊C4—2262no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—1134no—
286C22⋊C4—1134no—
287C22⋊C4—1134no—
288C22⋊C4—4521no—
289C22⋊C4—4521no—
290C22⋊C4—2262no—
291C22⋊C4—2262no—
292C22⋊C4C4×D11314yescomplemented
293C42—41no—
294C42—1134no—
295C42—4521no—
296C42—4521no—
297C42—4521no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1132no—
305C23—2261no—
306C23—2261no—
307C23—2261no—
308C23—2261no—
309C23—2261no—
310C23—2261no—
311C23C2×C4×D11312yes—
312C23C23×D11311yescharacteristic
313Q8—4524no—
314D4—4524no—
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—1132no—
332C2×C4—1132no—
333C2×C4—1132no—
334C2×C4—1132no—
335C2×C4—1132no—
336C2×C4—4524no—
337C2×C4—4524no—
338C2×C4—2261no—
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—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—4521no—
364C22—4521no—
365C22—4521no—
366C22—4521no—
367C22—2262no—
368C22—2262no—
369C22—2262no—
370C22C22×C4×D11311yescharacteristic
371C22#41×D11311yescharacteristic
372C22#41×D11311yescharacteristic
373C22#1681366711yescharacteristic
374C22#1681366711yescharacteristic
375C22#1681366811yescharacteristic
376C22#1681366911yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—4521no—
384C4—4521no—
385C4—2262no—
386C4—2262no—
387C4—2262no—
388C4—2262no—
389C4—2262no—
390C2—42no—
391C2—4522no—
392C2#2029906611yescharacteristic
393C2#2029907011yescharacteristic
394C2#2029907711yescharacteristic
395C2#2029918011yescharacteristic
396C2#2029918411yescharacteristic
397C2#2029921211yescharacteristic
398C2#2029921411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC22×C22⋊D113C22
hypercenter#388D113
hypocenterC113#2337
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20298503C2semidirect
3. #20298502C2semidirect
4. #20298489C2semidirect
5. #20298487C2semidirect
6. #20298486C2semidirect
9. #20298470C2semidirect
10. #20298469C2semidirect
11. #20298465C2semidirect
12. C4×#14268626C2semidirect
13. C22⋊C4×Dic113C2semidirect
14. #20298445C2semidirect
15. #388×C113C2semidirect
20. #16813608C4semidirect
55. C2×Dic226C2×C4semidirect
76. C22⋊Dic113C2×C4semidirect
80. #14268624C2×C4semidirect
81. #14268624C2×C4semidirect
85. C4×Dic113C2×C4semidirect
96. C22⋊C4×C113C2×C4semidirect
200. C113#2337semidirect
207. #388D113semidirect
292. C22⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136082
#202985032
#202985022
#202984892
#202984872
#202984862
#202984752
#202984742
#202984702
#202984692
#202984652
C4×#142686262
C22⋊C4×Dic1132
#202984452
#388×C1132
#2337113