Finite Group Databasebeta

← #27179795

Subgroups — #27179795

Order 12928.

392 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265645C211yesmaximal, characteristic
2#20265238C211yesmaximal, characteristic, complemented
3#20265237C211yesmaximal, characteristic, complemented
4#20265237C211yesmaximal, characteristic, complemented
5#20265232C211yesmaximal, characteristic, complemented
6#20265231C211yesmaximal, characteristic, complemented
7#20265228C211yesmaximal, characteristic, complemented
8#20265227C211yesmaximal, characteristic, complemented
9#20265199C211yesmaximal, characteristic, complemented
10C4⋊C8×D101C211yesmaximal, characteristic, complemented
11#20265142C211yesmaximal, characteristic
12#20265142C211yesmaximal, characteristic
13#20265134C211yesmaximal, characteristic, complemented
14#20265131C211yesmaximal, characteristic, complemented
15#433×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×#13108057C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20C2×C8×D101C2211yescharacteristic
21#15692220C411yescharacteristic
22#15692220C411yescharacteristic
23#15692217C411yescharacteristic
24#15692217C411yescharacteristic
25#15692215C411yescharacteristic
26#15692215C411yescharacteristic
27#15692215C411yescharacteristic
28#15692215C411yescharacteristic
29#15692212C2211yescharacteristic
30#15692212C2211yescharacteristic
31C2×C4×Dic101C2211yescharacteristic
32C42×D101C2211yescharacteristic
33C42×D101C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic
35C4⋊#11717579C2211yescharacteristic
36#15692184C2211yescharacteristic
37#15692184C2211yescharacteristic
38#15692184C2211yescharacteristic
39#15692184C2211yescharacteristic
40C22⋊#11717579C2211yescharacteristic
41C22⋊#11717579C2211yescharacteristic
42#15692167C2211yescharacteristic
43#15692167C2211yescharacteristic
44#15692167C2211yescharacteristic
45#15692167C2211yescharacteristic
46#15692166C2211yescharacteristic
47#15692165C2211yescharacteristic
48#15692165C2211yescharacteristic
49C4×#11717579C2211yescharacteristic
50C8×Dic101C2211yescharacteristic
51C8×Dic101C2211yescharacteristic
52#117×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic
54C4⋊C8×C101C2211yescharacteristic
55C22⋊C8×C101C2211yescharacteristic
56C22⋊C8×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202C2×C411yescharacteristic
62C2×D404C2×C411yescharacteristic
63C2×C22⋊D101C2×C411yescharacteristic
64C2×C22⋊D101C2×C411yescharacteristic
65C22×Dic101C2×C411yescharacteristic
66C22×Dic101C2×C411yescharacteristic
67C2×C4×D101C2×C411yescharacteristic
68C2×C4×D101C2×C411yescharacteristic
69C2×C4×D101C2×C411yescharacteristic
70C2×C4×D101C2×C411yescharacteristic
71C2×C4×D101C2311yescharacteristic
72C2×C4×D101C2311yescharacteristic
73#13108057—22no—
74#13108057—22no—
75C2×#11717579C2311yescharacteristic
76C2×#11717579C2311yescharacteristic
77C2×#11717579C2311yescharacteristic
78C2×#11717579C2311yescharacteristic
79C8×D101—22no—
80C8×D101—22no—
81#13108053C2×C411yescharacteristic
82#13108053C2×C411yescharacteristic
83#13108053C2×C411yescharacteristic
84#13108053C2×C411yescharacteristic
85#13108051C2×C411yescharacteristic
86#13108051C2×C411yescharacteristic
87#13108051C2×C411yescharacteristic
88#13108051C2×C411yescharacteristic
89C4×Dic101C2×C411yescharacteristic
90C4×Dic101C2×C411yescharacteristic
91C4×Dic101C2×C411yescharacteristic
92C4×Dic101C2×C411yescharacteristic
93C4×Dic101C2×C411yescharacteristic
94C4×Dic101C2×C411yescharacteristic
95C4×Dic101C2311yescharacteristic
96C4×Dic101C2311yescharacteristic
97C22×C4×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C2×C8×C101C2311yescharacteristic
102C4⋊C4×C101C2×C411yescharacteristic
103C4⋊C4×C101C2×C411yescharacteristic
104C22⋊C4×C101C2×C411yescharacteristic
105C22⋊C4×C101C2×C411yescharacteristic
106C42×C101C2311yescharacteristic
107C42×C101C2311yescharacteristic
108C23×C101C22×C411yescharacteristic
109C22×D101C22×C411yescharacteristic
110C22×D101C22×C411yescharacteristic
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101C22×C411yescharacteristic
114C2×C4×C101C22×C411yescharacteristic
115C2×C4×C101C22×C411yescharacteristic
116C2×C4×C101C22×C411yescharacteristic
117C2×C4×C101C22×C411yescharacteristic
118C2×C4×C101C2411yescharacteristic
119C22⋊D101—22no—
120C22⋊D101—22no—
121C2×Dic101—22no—
122C2×Dic101—41no—
123C2×Dic101C22×C411yescharacteristic
124C2×Dic101C22×C411yescharacteristic
125C2×Dic101C22×C411yescharacteristic
126C2×Dic101C22×C411yescharacteristic
127C2×Dic101C22×C411yescharacteristic
128C2×Dic101C22×C411yescharacteristic
129D404—22no—
130C4×D101—21no—
131C4×D101—21no—
132C4×D101—22no—
133C4×D101—22no—
134C4×D101—41no—
135C4×D101—41no—
136C4×D101#4112yes—
137C4×D101#4112yes—
138Dic202—22no—
139C8×C101—21no—
140C8×C101—21no—
141C8×C101—21no—
142C8×C101—21no—
143#11717579—21no—
144#11717579—21no—
145#11717579—21no—
146#11717579—21no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101—21no—
150C22×C101C23×C411yescharacteristic
151C2×D101—21no—
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—21no—
155C2×D101—21no—
156C2×D101#11712yes—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101—21no—
161C4×C101—21no—
162C4×C101C2×#4111yescharacteristic
163C4×C101C2×#4111yescharacteristic
164Dic101—21no—
165Dic101—21no—
166Dic101—21no—
167Dic101—21no—
168Dic101#11712yes—
169Dic101#13112yes—
170C2×C101—41no—
171C2×C101C2×#11711yescharacteristic
172C2×C101C2×#13111yescharacteristic
173C2×C101#56811yescharacteristic
174D101—22no—
175D101—41no—
176#2925—1011nomaximal, Sylow
177C101#292511yescharacteristic, complemented, Sylow
178C4×#41—1011no—
179#433—1011no—
180#433—1011no—
181#433—1011no—
182#433D10111yescharacteristic, complemented
183#432—1011no—
184#432—1011no—
185#431—1011no—
186#431—1011no—
187#423—1011no—
188C2×C4⋊C8—1011no—
189#408—1011no—
190#408—1011no—
191#405—1011no—
192#405—1011no—
193C2×#41—1011no—
194C2×M16—1011no—
195C2×M16—1011no—
196C22×C8—1011no—
197C22×C8—1011no—
198C4×Q8—1011no—
199C4×Q8—1011no—
200C4×D4—1011no—
201C4×D4—1011no—
202C4×D4—1011no—
203C4×D4—1011no—
204C4×D4—1011no—
205C4×D4—1011no—
206#117—1011no—
207#117—1011no—
208#117C2×D10111yescharacteristic
209C2×C42—1011no—
210C2×C42—1011no—
211C2×C42—1011no—
212C4⋊C8—1011no—
213C4⋊C8—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216C4⋊C8—1011no—
217C4⋊C8—1011no—
218C4⋊C8C2×D10111yescharacteristic
219C4⋊C8C2×D10111yescharacteristic
220C22⋊C8—1011no—
221C22⋊C8—1011no—
222C22⋊C8—1011no—
223C22⋊C8—1011no—
224C22⋊C8—1011no—
225C22⋊C8—1011no—
226C22⋊C8C2×D10111yescharacteristic
227C22⋊C8C2×D10111yescharacteristic
228#97—1011no—
229#97—1011no—
230#97—1011no—
231#97C2×D10111yescharacteristic
232C4×C8—1011no—
233C4×C8—1011no—
234C4×C8—1011no—
235C4×C8C2×D10111yescharacteristic
236#41—2022no—
237#41—2022no—
238C2×Q8—1011no—
239C2×D4—1011no—
240C2×D4—1011no—
241C2×D4—1011no—
242C22×C4—1011no—
243C22×C4—1011no—
244C22×C4—1011no—
245C22×C4—1011no—
246C22×C4—1011no—
247C22×C4—1011no—
248C22×C4—1011no—
249C22×C4—1011no—
250C22×C4C22×D10111yescharacteristic
251M16—2022no—
252M16—2022no—
253C2×C8—1011no—
254C2×C8—1011no—
255C2×C8—1011no—
256C2×C8—1011no—
257C2×C8—2022no—
258C2×C8—2022no—
259C2×C8C22×D10111yescharacteristic
260C2×C8C22×D10111yescharacteristic
261C2×C8C22×D10111yescharacteristic
262C2×C8C22×D10111yescharacteristic
263C4⋊C4—1011no—
264C4⋊C4—1011no—
265C4⋊C4—1011no—
266C4⋊C4—1011no—
267C4⋊C4C4×D10111yescharacteristic
268C4⋊C4C4×D10111yescharacteristic
269C22⋊C4—1011no—
270C22⋊C4—1011no—
271C22⋊C4—1011no—
272C22⋊C4—1011no—
273C22⋊C4C4×D10111yescharacteristic
274C22⋊C4C4×D10111yescharacteristic
275C42—1011no—
276C42—1011no—
277C42—1011no—
278C42—1011no—
279C42—1011no—
280C42—1011no—
281C42—1011no—
282C42—1011no—
283C42C22×D10111yescharacteristic
284C42C22×D10111yescharacteristic
285C23—1011no—
286C23—1011no—
287C23C2×C4×D10111yescharacteristic
288Q8—2022no—
289D4—2022no—
290D4—2022no—
291D4—2022no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—1011no—
295C2×C4—1011no—
296C2×C4—1012no—
297C2×C4—1012no—
298C2×C4—1011no—
299C2×C4—1011no—
300C2×C4—1011no—
301C2×C4—1011no—
302C2×C4—4041no—
303C2×C4—4041no—
304C2×C4—4041no—
305C2×C4—2022no—
306C2×C4—2022no—
307C2×C4—2022no—
308C2×C4—2021no—
309C2×C4—2021no—
310C2×C4C2×C4×D10111yescharacteristic
311C2×C4C2×C4×D10111yescharacteristic
312C2×C4C2×C4×D10111yescharacteristic
313C2×C4C2×C4×D10111yescharacteristic
314C2×C4C2×C4×D10111yescharacteristic
315C2×C4C23×D10111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C8—2021no—
321C8—2021no—
322C8—2021no—
323C8—2021no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—1012no—
328C22—2021no—
329C22—2021no—
330C22—2021no—
331C22—2021no—
332C22—2021no—
333C22C22×C4×D10111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—1012no—
340C4—1012no—
341C4—2021no—
342C4—2021no—
343C4—2021no—
344C4—2021no—
345C4#41×D10111yescharacteristic
346C4#41×D10111yescharacteristic
347C2—41no—
348C2—4041no—
349C2—2022no—
350C2#117×D10111yescharacteristic
351C2#131×D10111yescharacteristic
352C2#2026594211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D101
commutator, socleC22×C101C23×C4
Fitting#433×C101C2
prime radicalC2×#13108074C22
cosocleC2×C4×C101C24
hypercenter#433D101
hypocenterC101#2925
LCSG ▷ C22×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ #433

Complements

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

NH ≅ G/Ntype
2. #20265238C2semidirect
3. #20265237C2semidirect
4. #20265237C2semidirect
5. #20265232C2semidirect
6. #20265231C2semidirect
7. #20265228C2semidirect
8. #20265227C2semidirect
9. #20265199C2semidirect
10. C4⋊C8×D101C2semidirect
13. #20265134C2semidirect
14. #20265131C2semidirect
15. #433×C101C2semidirect
177. C101#2925semidirect
182. #433D101semidirect

Maximal subgroups

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

subgroupindex
#202656452
#202652382
#202652372
#202652322
#202652312
#202652282
#202652272
#202651992
C4⋊C8×D1012
#202651422
#202651342
#202651312
#433×C1012
#2925101