Finite Group Databasebeta

← #27173990

Subgroups — #27173990

Order 12928.

532 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×#15692211C211yesmaximal, characteristic
2#20265064C211yesmaximal, characteristic, complemented
3#20265064C211yesmaximal, characteristic, complemented
4#20265058C211yesmaximal, characteristic, complemented
5#20265058C211yesmaximal, characteristic, complemented
6#20265052C211yesmaximal, characteristic
7#20265044C211yesmaximal, characteristic, complemented
8#20265042C211yesmaximal, characteristic, complemented
9#20265038C211yesmaximal, characteristic
10C4⋊C4×Dic101C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic101C211yesmaximal, characteristic
12C4×C22⋊Dic101C211yesmaximal, characteristic
13#20265022C211yesmaximal, characteristic, complemented
14C2×#15692162C211yesmaximal, characteristic
15#385×C101C211yesmaximal, characteristic
16C23×Dic101C2211yescharacteristic
17C23×Dic101C2211yescharacteristic
18#15692211C418yescomplemented
19C2×C4⋊Dic101C2211yescharacteristic
20C2×C4⋊Dic101C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×#13108053C2211yescharacteristic
23C2×C22⋊Dic101C2211yescharacteristic
24C2×C22⋊Dic101C2211yescharacteristic
25C2×C4×Dic101C2211yescharacteristic
26C2×C4×Dic101C2211yescharacteristic
27C2×C4×Dic101C2211yescharacteristic
28C2×C4×Dic101C2211yescharacteristic
29C2×C4×Dic101C2211yescharacteristic
30C2×C4×Dic101C2211yescharacteristic
31#15692162C2211yescharacteristic
32#15692162C2211yescharacteristic
33#15692162C2211yescharacteristic
34#15692162C2211yescharacteristic
35#15692162C2211yescharacteristic
36#15692162C2211yescharacteristic
37#15692162C2211yescharacteristic
38#15692162C2211yescharacteristic
39#15692162C2211yescharacteristic
40#15692162C2211yescharacteristic
41#15692162C2211yescharacteristic
42#15692162C2211yescharacteristic
43#15692162C2211yescharacteristic
44#15692162C2211yescharacteristic
45C23×C4×C101C2211yescharacteristic
46C2×C4⋊C4×C101C2211yescharacteristic
47C2×C4⋊C4×C101C2211yescharacteristic
48C2×C22⋊C4×C101C2211yescharacteristic
49C2×C22⋊C4×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51#95×C101C2211yescharacteristic
52C22×Dic101—22no—
53C22×Dic101—22no—
54C22×Dic101—22no—
55C22×Dic101—22no—
56C22×Dic101—41no—
57C22×Dic101C2×C414yes—
58C22×Dic101C2311yescharacteristic
59C22×Dic101C2311yescharacteristic
60C22×Dic101C2311yescharacteristic
61C22×Dic101C2311yescharacteristic
62C22×Dic101C2311yescharacteristic
63C22×Dic101C2311yescharacteristic
64C22×Dic101C2311yescharacteristic
65C22×Dic101C2311yescharacteristic
66C4⋊Dic101—22no—
67C4⋊Dic101—41no—
68#13108053C2×C414yescomplemented
69#13108053C2×C414yescomplemented
70C22⋊Dic101—22no—
71C22⋊Dic101C2×C414yes—
72C4×Dic101—22no—
73C4×Dic101—22no—
74C4×Dic101—41no—
75C4×Dic101—41no—
76C4×Dic101C2×C414yescomplemented
77C4×Dic101C2×C414yescomplemented
78C24×C101C2311yescharacteristic
79C22×C4×C101—22no—
80C22×C4×C101—22no—
81C22×C4×C101—41no—
82C22×C4×C101C2311yescharacteristic
83C22×C4×C101C2311yescharacteristic
84C22×C4×C101C2311yescharacteristic
85C22×C4×C101C2311yescharacteristic
86C22×C4×C101C2311yescharacteristic
87C22×C4×C101C2311yescharacteristic
88C4⋊C4×C101—22no—
89C4⋊C4×C101—41no—
90C22⋊C4×C101—22no—
91C22⋊C4×C101C2×C414yes—
92C23×C101—21no—
93C23×C101—21no—
94C23×C101—21no—
95C23×C101—21no—
96C23×C101C22×C412yes—
97C23×C101#4112yes—
98C23×C101#4112yes—
99C23×C101C2411yescharacteristic
100C2×C4×C101—21no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—21no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—44no—
116C2×C4×C101C22×C412yes—
117C2×C4×C101C22×C412yes—
118C2×C4×C101#4112yes—
119C2×Dic101—28no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—21no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—21no—
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131C2×Dic101—21no—
132C2×Dic101—21no—
133C2×Dic101—21no—
134C2×Dic101—21no—
135C2×Dic101—21no—
136C2×Dic101—21no—
137C2×Dic101—21no—
138C2×Dic101—21no—
139C2×Dic101—44no—
140C2×Dic101C22×C412yes—
141C2×Dic101C22×C412yes—
142C2×Dic101C22×C412yes—
143C2×Dic101C22×C412yes—
144C2×Dic101#4112yes—
145C22×C101—22no—
146C22×C101—22no—
147C22×C101—22no—
148C22×C101—22no—
149C22×C101—22no—
150C22×C101—22no—
151C22×C101#11714yes—
152C22×C101C23×C411yescharacteristic
153C22×C101C2×#4111yescharacteristic
154C22×C101C2×#4111yescharacteristic
155C22×C101C2×#4111yescharacteristic
156C22×C101C2×#4111yescharacteristic
157C22×C101H(5,𝔽2)11yescharacteristic
158C22×C1012−1+411yescharacteristic
159C4×C101—22no—
160C4×C101—22no—
161C4×C101—22no—
162C4×C101—41no—
163C4×C101—41no—
164C4×C101—41no—
165Dic101—22no—
166Dic101—22no—
167Dic101—22no—
168Dic101—22no—
169Dic101—22no—
170Dic101—41no—
171Dic101—41no—
172Dic101—41no—
173C2×C101—24no—
174C2×C101C2×#11711yescharacteristic
175C2×C101C4×#4111yescharacteristic
176C2×C101#52011yescharacteristic
177C2×C101#55111yescharacteristic
178C2×C101#55111yescharacteristic
179C2×C101#55211yescharacteristic
180C2×C101#55211yescharacteristic
181#2343—1011nomaximal, Sylow
182C101#234311yescharacteristic, complemented, Sylow
183C2×#117—1011no—
184#387—1011no—
185#387—1011no—
186#387—1011no—
187#387—1011no—
188#385—1011no—
189#385D10111yescharacteristic
190#383—1011no—
191#382—1011no—
192#381—1011no—
193C4×C4⋊C4—1011no—
194C4×C22⋊C4—1011no—
195C4×C22⋊C4—1011no—
196#376—1011no—
197C2×#95—1011no—
198C23×C4—1011no—
199C23×C4—1011no—
200C23×C4C2×D10111yescharacteristic
201#117—1018no—
202C2×C4⋊C4—1011no—
203C2×C4⋊C4—1011no—
204C2×C4⋊C4—1011no—
205C2×C4⋊C4—1011no—
206C2×C4⋊C4C2×D10111yescharacteristic
207C2×C4⋊C4C2×D10111yescharacteristic
208C2×C22⋊C4—1011no—
209C2×C22⋊C4—1011no—
210C2×C22⋊C4C2×D10111yescharacteristic
211C2×C22⋊C4C2×D10111yescharacteristic
212C2×C42—1011no—
213C2×C42—1011no—
214C2×C42—1011no—
215C2×C42—1011no—
216C2×C42—1011no—
217C2×C42—1011no—
218#95—1011no—
219#95—1011no—
220#95—1011no—
221#95—1011no—
222#95—1011no—
223#95—1011no—
224#95—1011no—
225#95—1011no—
226#95—1011no—
227#95—1011no—
228#95—1011no—
229#95—1011no—
230#95—1011no—
231#95—1011no—
232#95C2×D10111yescharacteristic
233#95C2×D10111yescharacteristic
234C24C22×D10111yescharacteristic
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—41no—
238C22×C4—1014no—
239C22×C4—1011no—
240C22×C4—1011no—
241C22×C4—1011no—
242C22×C4—1011no—
243C22×C4—1011no—
244C22×C4—1011no—
245C22×C4—1011no—
246C22×C4—1011no—
247C22×C4—4041no—
248C22×C4—2022no—
249C22×C4—2022no—
250C22×C4—2022no—
251C22×C4—2022no—
252C22×C4C22×D10111yescharacteristic
253C22×C4C22×D10111yescharacteristic
254C22×C4C22×D10111yescharacteristic
255C22×C4C22×D10111yescharacteristic
256C22×C4C22×D10111yescharacteristic
257C22×C4C22×D10111yescharacteristic
258C4⋊C4—22no—
259C4⋊C4—41no—
260C4⋊C4—1014no—
261C4⋊C4—1014no—
262C4⋊C4—4041no—
263C4⋊C4—2022no—
264C22⋊C4—22no—
265C22⋊C4—1014no—
266C22⋊C4—2022no—
267C22⋊C4C4×D10114yes—
268C42—1014no—
269C42—1014no—
270C42—4041no—
271C42—4041no—
272C42—2022no—
273C42—2022no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D10112yes—
279C23#1310807312yes—
280C23#1310807512yes—
281C23C23×D10111yescharacteristic
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—44no—
298C2×C4—1012no—
299C2×C4—1012no—
300C2×C4—1012no—
301C2×C4—1012no—
302C2×C4—1012no—
303C2×C4—4044no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4—2021no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2021no—
319C2×C4—2021no—
320C2×C4—2021no—
321C2×C4—2021no—
322C2×C4—2021no—
323C2×C4—2028no—
324C2×C4C2×C4×D10112yes—
325C2×C4C2×C4×D10112yes—
326C2×C4#1310807312yes—
327C22—22no—
328C22—22no—
329C22—22no—
330C22—22no—
331C22—22no—
332C22—22no—
333C22#1569221314yes—
334C22C22×C4×D10111yescharacteristic
335C22#41×D10111yescharacteristic
336C22C2×#1310807311yescharacteristic
337C22C2×#1310807311yescharacteristic
338C22C2×#1310807511yescharacteristic
339C22#1569230011yescharacteristic
340C22#1569230211yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—4041no—
348C4—4041no—
349C4—4041no—
350C4—2022no—
351C4—2022no—
352C4—2022no—
353C4—2022no—
354C4—2022no—
355C2—24no—
356C2C2×#1569221311yescharacteristic
357C2C4×#1310807311yescharacteristic
358C2#2026565611yescharacteristic
359C2#2026585411yescharacteristic
360C2#2026585811yescharacteristic
361C2#2026586411yescharacteristic
362C2#2026586911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D101
commutatorC22×C101C23×C4
Fitting#385×C101C2
socle, cosocleC23×C101C24
prime radicalC24×C101C23
hypercenter#385D101
hypocenterC101#2343
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #20265064C2semidirect
3. #20265064C2semidirect
4. #20265058C2semidirect
5. #20265058C2semidirect
7. #20265044C2semidirect
8. #20265042C2semidirect
10. C4⋊C4×Dic101C2semidirect
13. #20265022C2semidirect
18. #15692211C4semidirect
68. #13108053C2×C4semidirect
69. #13108053C2×C4semidirect
76. C4×Dic101C2×C4semidirect
77. C4×Dic101C2×C4semidirect
182. C101#2343semidirect

Maximal subgroups

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

subgroupindex
C2×#156922112
#202650642
#202650582
#202650522
#202650442
#202650422
#202650382
C4⋊C4×Dic1012
C22⋊C4×Dic1012
C4×C22⋊Dic1012
#202650222
C2×#156921622
#385×C1012
#2343101