Finite Group Databasebeta

← #27169353

Subgroups — #27169353

Order 12928.

1088 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×D101C211yesmaximal, characteristic
2C22×#13108051C212yesmaximal
3C2×#15692162C211yesmaximal, characteristic, complemented
4C2×#15692162C212yesmaximal, complemented
5C2×#95×C101C211yesmaximal, characteristic, complemented
6C24×D101C2211yescharacteristic
7C23×Dic101C2212yes—
8C23×Dic101C2211yescharacteristic
9C22×C4×D101—24no—
10C22×C4×D101—24no—
11C22×C4×D101—22no—
12C22×C4×D101—22no—
13C22×C4×D101C414yescomplemented
14C2×#13108051—24no—
15C2×#13108051—24no—
16C2×#13108051C418yescomplemented
17#15692162—24no—
18#15692162—22no—
19C23×C4×C101C2212yes—
20C23×C4×C101C2211yescharacteristic
21#95×C101—22no—
22C23×D101—22no—
23C23×D101—21no—
24C23×D101—21no—
25C23×D101—21no—
26C23×D101—22no—
27C23×D101—21no—
28C23×D101C2×C412yes—
29C23×D101C2×C414yes—
30C23×D101D414yes—
31C23×D101D412yes—
32C23×D101Q812yes—
33C22×Dic101—22no—
34C22×Dic101—21no—
35C22×Dic101—21no—
36C22×Dic101—22no—
37C22×Dic101—22no—
38C22×Dic101—22no—
39C22×Dic101—22no—
40C22×Dic101—22no—
41C22×Dic101—22no—
42C22×Dic101C2×C412yes—
43C22×Dic101C2×C414yescomplemented
44C22×Dic101D414yes—
45C2×C4×D101—216no—
46C2×C4×D101—216no—
47C2×C4×D101—28no—
48C2×C4×D101—28no—
49C2×C4×D101—28no—
50#13108051—216no—
51C24×C101C2311yescharacteristic
52C22×C4×C101—22no—
53C22×C4×C101—22no—
54C22×C4×C101—22no—
55C22×C4×C101—22no—
56C22×C4×C101—22no—
57C22×C4×C101—22no—
58C22×C4×C101—22no—
59C22×C4×C101—22no—
60C22×C4×C101C2×C412yes—
61C22×C4×C101C2×C414yescomplemented
62C22×C4×C101D412yes—
63C22×C4×C101D412yes—
64C23×C101C22×C411yescharacteristic
65C23×C101C22×C412yes—
66C23×C101C2×D412yes—
67C23×C101C2×D411yescharacteristic
68C23×C101C2×D412yes—
69C23×C101C2×D411yescharacteristic
70C23×C101C2×D411yescharacteristic
71C23×C101C2×Q811yescharacteristic
72C23×C101#4111yescharacteristic
73C23×C101#4112yes—
74C23×C101#4111yescharacteristic
75C22×D101—22no—
76C22×D101—22no—
77C22×D101—22no—
78C22×D101—22no—
79C22×D101—24no—
80C22×D101—24no—
81C22×D101—24no—
82C22×D101—24no—
83C22×D101—24no—
84C22×D101—24no—
85C22×D101—22no—
86C22×D101—24no—
87C22×D101—22no—
88C22×D101—22no—
89C22×D101—24no—
90C22×D101—22no—
91C22×D101—24no—
92C22×D101—24no—
93C22×D101C4214yes—
94C22×D101C22⋊C418yes—
95C22×D101C22⋊C414yes—
96C22×D101C4⋊C414yes—
97C22×D101C4⋊C418yes—
98C2×C4×C101—22no—
99C2×C4×C101—22no—
100C2×C4×C101—24no—
101C2×C4×C101—24no—
102C2×C4×C101—24no—
103C2×C4×C101—24no—
104C2×C4×C101—24no—
105C2×C4×C101—42no—
106C2×C4×C101—42no—
107C2×C4×C101—42no—
108C2×C4×C101—42no—
109C2×C4×C101C22⋊C414yescomplemented
110C2×Dic101—22no—
111C2×Dic101—22no—
112C2×Dic101—24no—
113C2×Dic101—24no—
114C2×Dic101—24no—
115C2×Dic101—24no—
116C2×Dic101—24no—
117C2×Dic101—42no—
118C2×Dic101—42no—
119C2×Dic101—42no—
120C2×Dic101—42no—
121C2×Dic101C22⋊C414yescomplemented
122C4×D101—232no—
123C22×C101C2×C4211yescharacteristic
124C22×C101C2×C22⋊C411yescharacteristic
125C22×C101C2×C22⋊C412yes—
126C22×C101C2×C22⋊C411yescharacteristic
127C22×C101C2×C22⋊C411yescharacteristic
128C22×C101C2×C4⋊C411yescharacteristic
129C22×C101C2×C4⋊C412yes—
130C22×C101#11711yescharacteristic
131C22×C101#11711yescharacteristic
132C22×C101C4×D412yes—
133C22×C101C4×D412yes—
134C22×C101C4×D412yes—
135C22×C101C4×D412yes—
136C22×C101#12012yes—
137C22×C101#12012yes—
138C22×C101#12111yescharacteristic
139C22×C101#12112yes—
140C22×C101#12111yescharacteristic
141C22×C101C22⋊Q811yescharacteristic
142C22×C101C22⋊Q812yes—
143C22×C101C22⋊Q811yescharacteristic
144C22×C101#12312yes—
145C22×C101#12312yes—
146C2×D101—24no—
147C2×D101—24no—
148C2×D101—24no—
149C2×D101—24no—
150C2×D101—24no—
151C2×D101—24no—
152C2×D101—28no—
153C2×D101—28no—
154C2×D101—28no—
155C2×D101—28no—
156C2×D101#9518yescomplemented
157C4×C101—24no—
158C4×C101—44no—
159Dic101—24no—
160Dic101—44no—
161C2×C101C2×#9511yescharacteristic
162C2×C101C4×C22⋊C411yescharacteristic
163C2×C101C4×C22⋊C411yescharacteristic
164C2×C101#37911yescharacteristic
165C2×C101#38011yescharacteristic
166C2×C101#38011yescharacteristic
167C2×C101#38111yescharacteristic
168C2×C101#38512yes—
169C2×C101#38512yes—
170C2×C101#38612yes—
171C2×C101#38612yes—
172D101—28no—
173C22⋊#95—1011nomaximal, Sylow
174C101C22⋊#9511yescharacteristic, complemented, Sylow
175C24×C4—1011no—
176C22×C22⋊C4—1012no—
177C2×#95—1012no—
178C2×#95—1011no—
179C2×#95D10111yescharacteristic, complemented
180C25—1011no—
181C23×C4—1011no—
182C23×C4—1012no—
183C23×C4—1014no—
184C23×C4—2024no—
185C23×C4—2024no—
186C23×C4—2022no—
187C23×C4—2022no—
188C23×C4C2×D10112yes—
189C23×C4C2×D10111yescharacteristic
190C2×C22⋊C4—1018no—
191C2×C22⋊C4—2024no—
192C2×C22⋊C4—2024no—
193#95—22no—
194#95—2024no—
195#95—2022no—
196C24—1014no—
197C24—1012no—
198C24—1012no—
199C24—1014no—
200C24—1012no—
201C24—2022no—
202C24—2021no—
203C24—2021no—
204C24—2021no—
205C24—2022no—
206C24—2021no—
207C24C22×D10111yescharacteristic
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—1012no—
217C22×C4—1014no—
218C22×C4—1014no—
219C22×C4—2028no—
220C22×C4—2028no—
221C22×C4—20216no—
222C22×C4—20216no—
223C22×C4—2022no—
224C22×C4—2022no—
225C22×C4—2022no—
226C22×C4—2022no—
227C22×C4—2022no—
228C22×C4—2022no—
229C22×C4—2022no—
230C22×C4—2021no—
231C22×C4—2021no—
232C22×C4—2028no—
233C22×C4C4×D10112yes—
234C22×C4C4×D10114yescomplemented
235C22×C4D40412yes—
236C22×C4C22⋊D10112yes—
237C22⋊C4—20216no—
238C23—1014no—
239C23—1018no—
240C23—1014no—
241C23—1014no—
242C23—1018no—
243C23—2022no—
244C23—2022no—
245C23—2022no—
246C23—2022no—
247C23—2024no—
248C23—2024no—
249C23—2024no—
250C23—2024no—
251C23—2024no—
252C23—2024no—
253C23—2022no—
254C23—2024no—
255C23—2022no—
256C23—2022no—
257C23—2024no—
258C23—2022no—
259C23—2024no—
260C23—2024no—
261C23C2×C4×D10111yescharacteristic
262C23C2×C4×D10112yes—
263C23D4×D10112yes—
264C23D4×D10111yescharacteristic
265C23D4×D10112yes—
266C23C2×C22⋊D10111yescharacteristic
267C23C2×D40411yescharacteristic
268C23Q8×D10111yescharacteristic
269C23#1310807311yescharacteristic
270C23#1310807412yes—
271C23#1310807511yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—24no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—1014no—
284C2×C4—4042no—
285C2×C4—4042no—
286C2×C4—4042no—
287C2×C4—4042no—
288C2×C4—20232no—
289C2×C4—2024no—
290C2×C4—2024no—
291C2×C4—2024no—
292C2×C4—2022no—
293C2×C4—2022no—
294C2×C4—2024no—
295C2×C4—2024no—
296C2×C4#1310805114yescomplemented
297C22—1018no—
298C22—2024no—
299C22—2024no—
300C22—2024no—
301C22—2024no—
302C22—2024no—
303C22—2024no—
304C22—2028no—
305C22—2028no—
306C22—2028no—
307C22—2028no—
308C22C42×D10111yescharacteristic
309C22C22⋊C4×D10111yescharacteristic
310C22C22⋊C4×D10112yes—
311C22C22⋊C4×D10111yescharacteristic
312C22C2×#1310805111yescharacteristic
313C22C4⋊C4×D10111yescharacteristic
314C22C4⋊C4×D10112yes—
315C22#1569221211yescharacteristic
316C22#1569221311yescharacteristic
317C22#1569221512yes—
318C22C4×C22⋊D10112yes—
319C22#1569221712yes—
320C22C4×D40412yes—
321C22#1569222312yes—
322C22#1569222512yes—
323C22#1569222611yescharacteristic
324C22#1569222812yes—
325C22#1569223011yescharacteristic
326C22#1569223111yescharacteristic
327C22#1569223312yes—
328C22#1569223511yescharacteristic
329C22#1569223712yes—
330C22#1569224012yes—
331C4—24no—
332C4—44no—
333C4—4044no—
334C4—2024no—
335C2—2028no—
336C2#95×D10111yescharacteristic
337C2#2026502411yescharacteristic
338C2C4×#1310805111yescharacteristic
339C2#2026503211yescharacteristic
340C2#2026503411yescharacteristic
341C2#2026503611yescharacteristic
342C2#2026503911yescharacteristic
343C2#2026504812yes—
344C2#2026505112yes—
345C2#2026505312yes—
346C2#2026505512yes—
subgroupG/H
center, FrattiniC24C22×D101
commutatorC22×C101C2×C42
FittingC2×#95×C101C2
socle, cosocleC24×C101C23
prime radicalC24×D101C22
hypercenterC2×#95D101
hypocenterC101C22⋊#95
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C24 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. C2×#15692162C2semidirect
4. C2×#15692162C2semidirect
5. C2×#95×C101C2semidirect
13. C22×C4×D101C4semidirect
16. C2×#13108051C4semidirect
43. C22×Dic101C2×C4semidirect
61. C22×C4×C101C2×C4semidirect
109. C2×C4×C101C22⋊C4semidirect
121. C2×Dic101C22⋊C4semidirect
156. C2×D101#95semidirect
174. C101C22⋊#95semidirect
179. C2×#95D101semidirect
234. C22×C4C4×D101semidirect
296. C2×C4#13108051semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1012
C22×#131080512
C2×#156921622
C2×#95×C1012
C22⋊#95101