Finite Group Databasebeta

← #27174432

Subgroups — #27174432

Order 12928.

432 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101⋊#401C211yesmaximal, characteristic, complemented
2#20265119C211yesmaximal, characteristic, complemented
3#20265118C211yesmaximal, characteristic, complemented
4#20265117C211yesmaximal, characteristic, complemented
5#20265105C211yesmaximal, characteristic
6#20265105C211yesmaximal, characteristic
7#20265102C211yesmaximal, characteristic
8#20265100C211yesmaximal, characteristic
9C4×#13108053C211yesmaximal, characteristic, complemented
10C4×#13108053C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic101C211yesmaximal, characteristic, complemented
12C4×C22⋊Dic101C211yesmaximal, characteristic
13C4×C22⋊Dic101C211yesmaximal, characteristic
14#20265023C211yesmaximal, characteristic, complemented
15C4×C22⋊C4×C101C211yesmaximal, characteristic
16C2×C4⋊Dic101C2211yescharacteristic
17C2×C4⋊Dic101C2211yescharacteristic
18C2×#13108053C2211yescharacteristic
19C2×#13108053C2211yescharacteristic
20C2×#13108053C2211yescharacteristic
21C2×#13108053C2211yescharacteristic
22C2×C22⋊Dic101C2211yescharacteristic
23C2×C22⋊Dic101C2211yescharacteristic
24C2×C22⋊Dic101C2211yescharacteristic
25C2×C22⋊Dic101C2211yescharacteristic
26C2×C4×Dic101C2211yescharacteristic
27C2×C4×Dic101C2211yescharacteristic
28C2×C4×Dic101C2211yescharacteristic
29C2×C4×Dic101C2211yescharacteristic
30#15692162C2211yescharacteristic
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
44C23×C4×C101C2211yescharacteristic
45C2×C22⋊C4×C101C2211yescharacteristic
46C2×C22⋊C4×C101C2211yescharacteristic
47C2×C42×C101C2211yescharacteristic
48C2×C42×C101C2211yescharacteristic
49#95×C101C2211yescharacteristic
50#95×C101C2211yescharacteristic
51C22×Dic101C2311yescharacteristic
52C22×Dic101C2311yescharacteristic
53C22×Dic101C2311yescharacteristic
54C22×Dic101C2311yescharacteristic
55C22×Dic101C2311yescharacteristic
56C22×Dic101C2311yescharacteristic
57C22×Dic101C2311yescharacteristic
58C22×Dic101C2311yescharacteristic
59C4⋊Dic101—22no—
60C4⋊Dic101—22no—
61#13108053—22no—
62#13108053—22no—
63#13108053—22no—
64#13108053—22no—
65C22⋊Dic101—22no—
66C22⋊Dic101—22no—
67C22⋊Dic101—22no—
68C22⋊Dic101—22no—
69C4×Dic101—22no—
70C4×Dic101—22no—
71C4×Dic101—22no—
72C4×Dic101—22no—
73C24×C101C2311yescharacteristic
74C22×C4×C101—22no—
75C22×C4×C101—22no—
76C22×C4×C101—22no—
77C22×C4×C101C2311yescharacteristic
78C22×C4×C101C2311yescharacteristic
79C22×C4×C101C2311yescharacteristic
80C22×C4×C101C2311yescharacteristic
81C22×C4×C101C2311yescharacteristic
82C22×C4×C101C2311yescharacteristic
83C22⋊C4×C101—22no—
84C22⋊C4×C101—22no—
85C42×C101—22no—
86C42×C101—22no—
87C23×C101—21no—
88C23×C101—21no—
89C23×C101—21no—
90C23×C101—21no—
91C23×C101—21no—
92C23×C101—21no—
93C23×C101#4112yes—
94C23×C101C2411yescharacteristic
95C2×C4×C101—21no—
96C2×C4×C101—21no—
97C2×C4×C101—21no—
98C2×C4×C101—21no—
99C2×C4×C101—21no—
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—44no—
110C2×C4×C101#4112yes—
111C2×C4×C101#4112yes—
112C2×C4×C101#4112yes—
113C2×C4×C101#4112yes—
114C2×Dic101—21no—
115C2×Dic101—21no—
116C2×Dic101—21no—
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
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#4112yes—
137C2×Dic101#4112yes—
138C22×C101—22no—
139C22×C101—22no—
140C22×C101—22no—
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—41no—
144C22×C101—41no—
145C22×C101C2×#4111yescharacteristic
146C22×C101C2×#4111yescharacteristic
147C22×C101C2×#4111yescharacteristic
148C22×C101C2×#4111yescharacteristic
149C22×C101C2×#4111yescharacteristic
150C22×C101C2×#4111yescharacteristic
151C22×C101C2×#4111yescharacteristic
152C4×C101—22no—
153C4×C101—41no—
154C4×C101—41no—
155C4×C101—41no—
156C4×C101—41no—
157C4×C101#12614yes—
158Dic101—22no—
159Dic101—22no—
160Dic101—41no—
161Dic101—41no—
162Dic101—41no—
163Dic101—41no—
164Dic101—41no—
165Dic101—41no—
166C2×C101—42no—
167C2×C101C2×#12611yescharacteristic
168C2×C101#52911yescharacteristic
169C2×C101#52911yescharacteristic
170C2×C101#52911yescharacteristic
171C2×C101#52911yescharacteristic
172C2×C101#52911yescharacteristic
173C2×C101#52911yescharacteristic
174#2401—1011nomaximal, Sylow
175C101#240111yescharacteristic, complemented, Sylow
176#401—1011no—
177#400—1011no—
178#400—1011no—
179#400—1011no—
180#397—1011no—
181#397—1011no—
182#397—1011no—
183#396—1011no—
184C4×C4⋊C4—1011no—
185C4×C4⋊C4—1011no—
186C4×C4⋊C4—1011no—
187C4×C22⋊C4—1011no—
188C4×C22⋊C4—1011no—
189C4×C22⋊C4D10111yescharacteristic
190#376—1011no—
191C23×C4C2×D10111yescharacteristic
192C2×C4⋊C4—1011no—
193C2×C4⋊C4—1011no—
194C2×C4⋊C4—1011no—
195C2×C4⋊C4—1011no—
196C2×C4⋊C4—1011no—
197C2×C4⋊C4—1011no—
198C2×C22⋊C4—1011no—
199C2×C22⋊C4—1011no—
200C2×C22⋊C4—1011no—
201C2×C22⋊C4—1011no—
202C2×C22⋊C4C2×D10111yescharacteristic
203C2×C22⋊C4C2×D10111yescharacteristic
204C2×C42—1011no—
205C2×C42—1011no—
206C2×C42—1011no—
207C2×C42—1011no—
208C2×C42C2×D10111yescharacteristic
209C2×C42C2×D10111yescharacteristic
210#95—1011no—
211#95—1011no—
212#95—1011no—
213#95—1011no—
214#95—1011no—
215#95—1011no—
216#95—1011no—
217#95—1011no—
218#95—1011no—
219#95—1011no—
220#95—1011no—
221#95—1011no—
222#95—1011no—
223#95—1011no—
224#95C2×D10111yescharacteristic
225#95C2×D10111yescharacteristic
226C24C22×D10111yescharacteristic
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—1011no—
231C22×C4—1011no—
232C22×C4—1011no—
233C22×C4—1011no—
234C22×C4—1011no—
235C22×C4—1011no—
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4C22×D10111yescharacteristic
239C22×C4C22×D10111yescharacteristic
240C22×C4C22×D10111yescharacteristic
241C22×C4C22×D10111yescharacteristic
242C22×C4C22×D10111yescharacteristic
243C22×C4C22×D10111yescharacteristic
244C4⋊C4—2022no—
245C4⋊C4—2022no—
246C4⋊C4—2022no—
247C4⋊C4—2022no—
248C4⋊C4—2022no—
249C4⋊C4—2022no—
250C22⋊C4—22no—
251C22⋊C4—22no—
252C22⋊C4—2022no—
253C22⋊C4—2022no—
254C22⋊C4—2022no—
255C22⋊C4—2022no—
256C42—22no—
257C42—22no—
258C42—2022no—
259C42—2022no—
260C42—2022no—
261C42—2022no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23#1310807412yes—
269C23C23×D10111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—44no—
285C2×C4—1012no—
286C2×C4—1012no—
287C2×C4—2021no—
288C2×C4—2021no—
289C2×C4—2021no—
290C2×C4—2021no—
291C2×C4—2021no—
292C2×C4—2021no—
293C2×C4—2021no—
294C2×C4—2021no—
295C2×C4—2021no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4—2021no—
302C2×C4—2021no—
303C2×C4—2021no—
304C2×C4—2021no—
305C2×C4—2021no—
306C2×C4—2021no—
307C2×C4—2021no—
308C2×C4—2021no—
309C2×C4#1310807312yes—
310C2×C4#1310807312yes—
311C2×C4#1310807412yes—
312C2×C4#1310807412yes—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#41×D10111yescharacteristic
321C22#41×D10111yescharacteristic
322C22C2×#1310807311yescharacteristic
323C22C2×#1310807311yescharacteristic
324C22C2×#1310807411yescharacteristic
325C22C2×#1310807411yescharacteristic
326C22C2×#1310807411yescharacteristic
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—4041no—
333C4—4041no—
334C4—4041no—
335C4—4041no—
336C4—4041no—
337C4—4041no—
338C4—2022no—
339C4—2022no—
340C4#1569224814yes—
341C2—42no—
342C2C2×#1569224811yescharacteristic
343C2#2026570511yescharacteristic
344C2#2026570711yescharacteristic
345C2#2026570711yescharacteristic
346C2#2026570711yescharacteristic
347C2#2026570911yescharacteristic
348C2#2026571111yescharacteristic
subgroupG/H
centerC22×C4C22×D101
commutator, socle, cosocleC23×C101C24
FrattiniC23C23×D101
FittingC4×C22⋊C4×C101C2
prime radicalC24×C101C23
hypercenterC4×C22⋊C4D101
hypocenterC101#2401
LCSG ▷ C23×C101 ▷ C101
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C101⋊#401C2semidirect
2. #20265119C2semidirect
3. #20265118C2semidirect
4. #20265117C2semidirect
9. C4×#13108053C2semidirect
10. C4×#13108053C2semidirect
11. C4×C4⋊Dic101C2semidirect
14. #20265023C2semidirect
175. C101#2401semidirect

Maximal subgroups

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

subgroupindex
C101⋊#4012
#202651192
#202651182
#202651172
#202651052
#202651022
#202651002
C4×#131080532
C4×C4⋊Dic1012
C4×C22⋊Dic1012
#202650232
C4×C22⋊C4×C1012
#2401101