Finite Group Databasebeta

← #28393173

Subgroups — #28393173

Order 14464.

512 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D113C211yesmaximal, characteristic
2#20298485C211yesmaximal, characteristic, complemented
3#20298484C211yesmaximal, characteristic, complemented
4#20298483C211yesmaximal, characteristic, complemented
5#20298482C211yesmaximal, characteristic, complemented
6#20298481C211yesmaximal, characteristic, complemented
7#20298480C211yesmaximal, characteristic, complemented
8#20298479C211yesmaximal, characteristic, complemented
9#20298460C211yesmaximal, characteristic
10#20298460C211yesmaximal, characteristic
11#20298457C211yesmaximal, characteristic
12#20298455C211yesmaximal, characteristic
13C4×#14268624C211yesmaximal, characteristic
14#20298445C211yesmaximal, characteristic
15#387×C113C211yesmaximal, characteristic, complemented
16C22×C4×D113C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C22×C4×D113C2211yescharacteristic
19C2×C4⋊Dic113C2211yescharacteristic
20C2×C4⋊Dic113C2211yescharacteristic
21C2×#14268626C2211yescharacteristic
22C2×#14268626C2211yescharacteristic
23C2×#14268626C2211yescharacteristic
24C2×#14268626C2211yescharacteristic
25C4⋊C4×D113C418yescomplemented
26C2×#14268624C2211yescharacteristic
27C2×#14268624C2211yescharacteristic
28C2×#14268624C2211yescharacteristic
29C2×#14268624C2211yescharacteristic
30C2×C4×Dic113C2211yescharacteristic
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×C4⋊C4×C113C2211yescharacteristic
47C2×C42×C113C2211yescharacteristic
48#95×C113C2211yescharacteristic
49#95×C113C2211yescharacteristic
50#95×C113C2211yescharacteristic
51#95×C113C2211yescharacteristic
52C23×D113C2311yescharacteristic
53C22×Dic113C2311yescharacteristic
54C22×Dic113C2311yescharacteristic
55C22×Dic113C2311yescharacteristic
56C22×Dic113C2311yescharacteristic
57C22×Dic113C2311yescharacteristic
58C22×Dic113C2311yescharacteristic
59C22×Dic113C2311yescharacteristic
60C2×C4×D113—22no—
61C2×C4×D113—22no—
62C2×C4×D113—41no—
63C2×C4×D113—41no—
64C2×C4×D113—41no—
65C2×C4×D113—41no—
66C2×C4×D113C2×C414yes—
67C2×C4×D113C2×C414yes—
68C2×C4×D113C2×C414yes—
69C4⋊Dic113—41no—
70C4⋊Dic113C2×C414yes—
71#14268626—41no—
72#14268626—41no—
73#14268626C2×C414yes—
74#14268626C2×C414yes—
75#14268624—22no—
76#14268624—22no—
77#14268624—22no—
78#14268624—22no—
79C4×Dic113—41no—
80C4×Dic113—41no—
81C4×Dic113—41no—
82C22×C4×C113C2311yescharacteristic
83C22×C4×C113C2311yescharacteristic
84C22×C4×C113C2311yescharacteristic
85C22×C4×C113C2311yescharacteristic
86C22×C4×C113C2311yescharacteristic
87C22×C4×C113C2311yescharacteristic
88C22×C4×C113C2311yescharacteristic
89C4⋊C4×C113—41no—
90C4⋊C4×C113C2×C414yes—
91C42×C113—41no—
92C23×C113C2411yescharacteristic
93C22×D113—21no—
94C22×D113—21no—
95C22×D113—21no—
96C22×D113—21no—
97C22×D113C22×C412yes—
98C22×D113#4112yes—
99C22×D113#4112yes—
100C2×C4×C113—21no—
101C2×C4×C113—21no—
102C2×C4×C113—21no—
103C2×C4×C113—21no—
104C2×C4×C113—21no—
105C2×C4×C113—21no—
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×C113C22×C412yes—
119C2×C4×C113C22×C412yes—
120C2×C4×C113C22×C412yes—
121C2×Dic113—21no—
122C2×Dic113—21no—
123C2×Dic113—21no—
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—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—21no—
136C2×Dic113—21no—
137C2×Dic113—21no—
138C2×Dic113—21no—
139C2×Dic113C22×C412yes—
140C2×Dic113C22×C412yes—
141C2×Dic113C22×C412yes—
142C4×D113—28no—
143C4×D113—44no—
144C4×D113—44no—
145C22×C113C23×C411yescharacteristic
146C22×C113C2×#4111yescharacteristic
147C22×C113C2×#4111yescharacteristic
148C22×C113H(5,𝔽2)11yescharacteristic
149C22×C113H(5,𝔽2)11yescharacteristic
150C22×C1132−1+411yescharacteristic
151C22×C1132−1+411yescharacteristic
152C2×D113—22no—
153C2×D113—22no—
154C2×D113—22no—
155C2×D113—22no—
156C2×D113—22no—
157C2×D113—22no—
158C2×D113#11714yes—
159C4×C113—22no—
160C4×C113—22no—
161C4×C113—22no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113—41no—
165C4×C113—41no—
166Dic113—22no—
167Dic113—22no—
168Dic113—22no—
169Dic113—41no—
170Dic113—41no—
171Dic113—41no—
172Dic113—41no—
173C2×C113C2×#11711yescharacteristic
174C2×C113#51811yescharacteristic
175C2×C113#51911yescharacteristic
176C2×C113#53911yescharacteristic
177C2×C113#53911yescharacteristic
178C2×C113#53911yescharacteristic
179C2×C113#53911yescharacteristic
180D113—24no—
181#2313—1131nomaximal, Sylow
182C113#231311yescharacteristic, complemented, Sylow
183C22×C4⋊C4—1131no—
184#387—1131no—
185#387—1131no—
186#387—1131no—
187#387—1131no—
188#387—1131no—
189#387—1131no—
190#387—1131no—
191#387D11311yescharacteristic, complemented
192#381—1131no—
193#381—1131no—
194#380—1131no—
195#380—1131no—
196C4×C22⋊C4—1131no—
197C4×C22⋊C4—1131no—
198C23×C4—1131no—
199C23×C4—1131no—
200C23×C4—1131no—
201C2×C4⋊C4—1131no—
202C2×C4⋊C4—1131no—
203C2×C4⋊C4—1131no—
204C2×C4⋊C4—1138no—
205C2×C4⋊C4—1131no—
206C2×C4⋊C4—1131no—
207C2×C4⋊C4—1131no—
208C2×C4⋊C4C2×D11311yescharacteristic
209C2×C4⋊C4C2×D11311yescharacteristic
210C2×C22⋊C4—1131no—
211C2×C22⋊C4—1131no—
212C2×C22⋊C4—1131no—
213C2×C22⋊C4—1131no—
214C2×C42—1131no—
215C2×C42—1131no—
216C2×C42—1131no—
217C2×C42C2×D11311yescharacteristic
218#95—1131no—
219#95—1131no—
220#95—1131no—
221#95—1131no—
222#95—1131no—
223#95—1131no—
224#95—1131no—
225#95—1131no—
226#95—1131no—
227#95—1131no—
228#95—1131no—
229#95—1131no—
230#95C2×D11311yescharacteristic
231#95C2×D11311yescharacteristic
232#95C2×D11311yescharacteristic
233#95C2×D11311yescharacteristic
234C24—1131no—
235C22×C4—1131no—
236C22×C4—1131no—
237C22×C4—1131no—
238C22×C4—1134no—
239C22×C4—1134no—
240C22×C4—1134no—
241C22×C4—1131no—
242C22×C4—1131no—
243C22×C4—1131no—
244C22×C4—1131no—
245C22×C4—4521no—
246C22×C4—4521no—
247C22×C4—4521no—
248C22×C4—4521no—
249C22×C4—2262no—
250C22×C4—2262no—
251C22×C4C22×D11311yescharacteristic
252C22×C4C22×D11311yescharacteristic
253C22×C4C22×D11311yescharacteristic
254C22×C4C22×D11311yescharacteristic
255C22×C4C22×D11311yescharacteristic
256C22×C4C22×D11311yescharacteristic
257C22×C4C22×D11311yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—1134no—
260C4⋊C4—1134no—
261C4⋊C4—1134no—
262C4⋊C4—4521no—
263C4⋊C4—4521no—
264C4⋊C4—4521no—
265C4⋊C4C4×D11314yes—
266C22⋊C4—2262no—
267C22⋊C4—2262no—
268C22⋊C4—2262no—
269C22⋊C4—2262no—
270C42—41no—
271C42—4521no—
272C42—4521no—
273C42—4521no—
274C23—1132no—
275C23—1132no—
276C23—1132no—
277C23—2261no—
278C23—2261no—
279C23—2261no—
280C23—2261no—
281C23C23×D11311yescharacteristic
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—1132no—
301C2×C4—1132no—
302C2×C4—1132no—
303C2×C4—4524no—
304C2×C4—4524no—
305C2×C4—2268no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4—2261no—
310C2×C4—2261no—
311C2×C4—2261no—
312C2×C4—2261no—
313C2×C4—2261no—
314C2×C4—2261no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4—2261no—
324C2×C4C2×C4×D11312yes—
325C2×C4C2×C4×D11312yes—
326C2×C4C2×C4×D11312yes—
327C22—1134no—
328C22—2262no—
329C22—2262no—
330C22—2262no—
331C22—2262no—
332C22—2262no—
333C22—2262no—
334C22C22×C4×D11311yescharacteristic
335C22#41×D11311yescharacteristic
336C22#41×D11311yescharacteristic
337C22#1681366711yescharacteristic
338C22#1681366811yescharacteristic
339C22#1681366911yescharacteristic
340C22#1681367011yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—4521no—
349C4—4521no—
350C4—4521no—
351C4—4521no—
352C4—2262no—
353C4—2262no—
354C4—2262no—
355C2—2264no—
356C2#117×D11311yescharacteristic
357C2#2029907011yescharacteristic
358C2#2029907411yescharacteristic
359C2#2029918911yescharacteristic
360C2#2029919111yescharacteristic
361C2#2029919411yescharacteristic
362C2#2029919611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
Fitting#387×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenter#387D113
hypocenterC113#2313
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20298485C2semidirect
3. #20298484C2semidirect
4. #20298483C2semidirect
5. #20298482C2semidirect
6. #20298481C2semidirect
7. #20298480C2semidirect
8. #20298479C2semidirect
15. #387×C113C2semidirect
25. C4⋊C4×D113C4semidirect
182. C113#2313semidirect
191. #387D113semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1132
#202984852
#202984842
#202984832
#202984822
#202984812
#202984802
#202984792
#202984602
#202984572
#202984552
C4×#142686242
#202984452
#387×C1132
#2313113