Finite Group Databasebeta

← #28393204

Subgroups — #28393204

Order 14464.

568 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×#16813582C211yesmaximal, characteristic
2#20298491C211yesmaximal, characteristic, complemented
3#20298482C211yesmaximal, characteristic, complemented
4#20298480C211yesmaximal, characteristic, complemented
5#20298474C211yesmaximal, characteristic
6#20298474C211yesmaximal, characteristic
7#20298472C211yesmaximal, characteristic, complemented
8#20298469C211yesmaximal, characteristic, complemented
9#20298465C211yesmaximal, characteristic, complemented
10#20298463C211yesmaximal, characteristic, complemented
11#20298459C211yesmaximal, characteristic, complemented
12#20298456C211yesmaximal, characteristic, complemented
13C4×#14268624C211yesmaximal, characteristic, complemented
14#95×D113C211yesmaximal, characteristic, complemented
15#388×C113C211yesmaximal, characteristic, complemented
16C22×C22⋊D113C2211yescharacteristic
17C23×Dic113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C22×C4×D113C2211yescharacteristic
20C22×C4×D113C2211yescharacteristic
21#16813582C418yescomplemented
22C2×C4⋊Dic113C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C2×#14268626C2211yescharacteristic
26C2×C22⋊Dic113C2211yescharacteristic
27C2×C22⋊Dic113C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×#14268624C2211yescharacteristic
31C2×C4×Dic113C2211yescharacteristic
32C2×C4×Dic113C2211yescharacteristic
33#16813529C2211yescharacteristic
34#16813529C2211yescharacteristic
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×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55C2×C22⋊D113C2×C414yes—
56C22×Dic113—41no—
57C22×Dic113—41no—
58C22×Dic113C2×C414yescomplemented
59C22×Dic113C2311yescharacteristic
60C22×Dic113C2311yescharacteristic
61C22×Dic113C2311yescharacteristic
62C22×Dic113C2311yescharacteristic
63C22×Dic113C2311yescharacteristic
64C22×Dic113C2311yescharacteristic
65C22×Dic113C2311yescharacteristic
66C2×C4×D113—22no—
67C2×C4×D113—22no—
68C2×C4×D113—41no—
69C2×C4×D113—41no—
70C2×C4×D113—41no—
71C2×C4×D113—41no—
72C2×C4×D113—41no—
73C2×C4×D113—41no—
74C2×C4×D113C2×C414yes—
75C4⋊Dic113—41no—
76#14268626—41no—
77#14268626—41no—
78#14268626C2×C414yescomplemented
79C22⋊Dic113—41no—
80C22⋊Dic113—41no—
81#14268624—22no—
82#14268624—22no—
83#14268624C2×C414yes—
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×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×C113C22×C412yes—
130C2×C4×C113C22×C412yes—
131C22⋊D113—28no—
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—21no—
149C2×Dic113—21no—
150C2×Dic113—44no—
151C2×Dic113C22×C412yes—
152C2×Dic113C22×C412yes—
153C2×Dic113C22×C412yes—
154C4×D113—44no—
155C4×D113—44no—
156C4×D113—44no—
157C22×C113—22no—
158C22×C113—22no—
159C22×C113—22no—
160C22×C113—41no—
161C22×C113—41no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113C23×C411yescharacteristic
165C22×C113C2×#4111yescharacteristic
166C22×C113C2×#4111yescharacteristic
167C22×C113H(5,𝔽2)11yescharacteristic
168C22×C113H(5,𝔽2)11yescharacteristic
169C22×C113H(5,𝔽2)11yescharacteristic
170C22×C1132−1+411yescharacteristic
171C2×D113—22no—
172C2×D113—22no—
173C2×D113—22no—
174C2×D113—22no—
175C2×D113—22no—
176C2×D113—22no—
177C2×D113#11714yes—
178C4×C113—22no—
179C4×C113—22no—
180C4×C113—41no—
181C4×C113—41no—
182C4×C113—41no—
183C4×C113—41no—
184Dic113—22no—
185Dic113—22no—
186Dic113—22no—
187Dic113—41no—
188Dic113—41no—
189Dic113—41no—
190Dic113—41no—
191C2×C113—42no—
192C2×C113C2×#11711yescharacteristic
193C2×C113#51811yescharacteristic
194C2×C113#52011yescharacteristic
195C2×C113#53811yescharacteristic
196C2×C113#53811yescharacteristic
197C2×C113#53911yescharacteristic
198C2×C113#53911yescharacteristic
199D113—24no—
200#2318—1131nomaximal, Sylow
201C113#231811yescharacteristic, complemented, Sylow
202C2×C4×D4—1131no—
203#388—1131no—
204#388D11311yescharacteristic, complemented
205#387—1131no—
206#387—1131no—
207#386—1131no—
208#386—1131no—
209#385—1131no—
210#385—1131no—
211#383—1131no—
212#382—1131no—
213#381—1131no—
214#380—1131no—
215C4×C22⋊C4—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⋊C4—1131no—
225C2×C4⋊C4—1131no—
226C2×C4⋊C4—1131no—
227C2×C4⋊C4C2×D11311yescharacteristic
228C2×C22⋊C4—1131no—
229C2×C22⋊C4—1131no—
230C2×C22⋊C4—1131no—
231C2×C22⋊C4—1131no—
232C2×C22⋊C4—1131no—
233C2×C22⋊C4C2×D11311yescharacteristic
234C2×C22⋊C4C2×D11311yescharacteristic
235C2×C22⋊C4C2×D11311yescharacteristic
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#95—1131no—
250#95—1131no—
251#95C2×D11311yescharacteristic
252#95C2×D11311yescharacteristic
253C24—1131no—
254C24C22×D11311yescharacteristic
255C2×D4—1134no—
256C2×D4—2262no—
257C2×D4—2262no—
258C22×C4—1134no—
259C22×C4—1131no—
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1134no—
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—4521no—
272C22×C4—4521no—
273C22×C4—4521no—
274C22×C4—4521no—
275C22×C4—2262no—
276C22×C4—2262no—
277C22×C4C22×D11311yescharacteristic
278C22×C4C22×D11311yescharacteristic
279C22×C4C22×D11311yescharacteristic
280C22×C4C22×D11311yescharacteristic
281C22×C4C22×D11311yescharacteristic
282C22×C4C22×D11311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—1134no—
285C4⋊C4—4521no—
286C4⋊C4—4521no—
287C4⋊C4—4521no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—1134no—
291C22⋊C4—4521no—
292C22⋊C4—4521no—
293C22⋊C4—2262no—
294C22⋊C4—2262no—
295C22⋊C4C4×D11314yescomplemented
296C42—41no—
297C42—1134no—
298C42—4521no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—1132no—
306C23—1132no—
307C23—1132no—
308C23—2261no—
309C23—2261no—
310C23—2261no—
311C23—2261no—
312C23C2×C4×D11312yes—
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—1132no—
332C2×C4—1132no—
333C2×C4—1132no—
334C2×C4—4524no—
335C2×C4—4524no—
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×C4—2261no—
355C2×C4—2261no—
356C2×C4C2×C4×D11312yes—
357C2×C4C2×C4×D11312yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1134no—
366C22—2262no—
367C22—2262no—
368C22—2262no—
369C22—2262no—
370C22—2262no—
371C22—2262no—
372C22C22×C4×D11311yescharacteristic
373C22#41×D11311yescharacteristic
374C22#41×D11311yescharacteristic
375C22#1681366711yescharacteristic
376C22#1681366711yescharacteristic
377C22#1681366811yescharacteristic
378C22#1681366911yescharacteristic
379C4—22no—
380C4—22no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—4521no—
386C4—4521no—
387C4—4521no—
388C4—4521no—
389C4—2262no—
390C4—2262no—
391C4—2262no—
392C2—42no—
393C2—2264no—
394C2#117×D11311yescharacteristic
395C2#2029907011yescharacteristic
396C2#2029907711yescharacteristic
397C2#2029918011yescharacteristic
398C2#2029918211yescharacteristic
399C2#2029918911yescharacteristic
400C2#2029919111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#388×C113C2
socle, cosocleC23×C113C24
prime radicalC22×C22⋊D113C22
hypercenter#388D113
hypocenterC113#2318
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20298491C2semidirect
3. #20298482C2semidirect
4. #20298480C2semidirect
7. #20298472C2semidirect
8. #20298469C2semidirect
9. #20298465C2semidirect
10. #20298463C2semidirect
11. #20298459C2semidirect
12. #20298456C2semidirect
13. C4×#14268624C2semidirect
14. #95×D113C2semidirect
15. #388×C113C2semidirect
21. #16813582C4semidirect
58. C22×Dic113C2×C4semidirect
78. #14268626C2×C4semidirect
85. C4×Dic113C2×C4semidirect
96. C22⋊C4×C113C2×C4semidirect
201. C113#2318semidirect
204. #388D113semidirect
295. C22⋊C4C4×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135822
#202984912
#202984822
#202984802
#202984742
#202984722
#202984692
#202984652
#202984632
#202984592
#202984562
C4×#142686242
#95×D1132
#388×C1132
#2318113