Finite Group Databasebeta

← #27181096

Subgroups — #27181096

Order 12928.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265750C211yesmaximal, characteristic
2#20265657C211yesmaximal, characteristic
3#20265520C211yesmaximal, characteristic, complemented
4#20265518C211yesmaximal, characteristic, complemented
5#20265517C211yesmaximal, characteristic, complemented
6#20265513C211yesmaximal, characteristic, complemented
7#20265511C211yesmaximal, characteristic, complemented
8#20265509C211yesmaximal, characteristic, complemented
9#20265505C211yesmaximal, characteristic, complemented
10#20265216C211yesmaximal, characteristic, complemented
11#20265214C211yesmaximal, characteristic, complemented
12#20265184C211yesmaximal, characteristic, complemented
13#103×D101C211yesmaximal, characteristic, complemented
14#20265142C211yesmaximal, characteristic
15#485×C101C211yesmaximal, characteristic, complemented
16C2×#13108074C2211yescharacteristic
17C2×Q8×D101C2211yescharacteristic
18C2×#13108057C2211yescharacteristic
19C2×C8×D101C2211yescharacteristic
20#15692254—21no—
21#15692241—21no—
22#15692240—21no—
23#15692237—21no—
24#15692235C2211yescharacteristic
25#15692234C2211yescharacteristic
26#15692231C2211yescharacteristic
27C4×Dic202—21no—
28C4×D404—21no—
29#15692215—21no—
30#15692215—21no—
31#15692213C2211yescharacteristic
32#15692213C2211yescharacteristic
33#15692213C2211yescharacteristic
34C2×C4⋊Dic101C2211yescharacteristic
35C4⋊C4×D101C2211yescharacteristic
36C4⋊C4×D101C2211yescharacteristic
37#15692189C2211yescharacteristic
38#15692189C2211yescharacteristic
39#15692188C2211yescharacteristic
40#15692186C2211yescharacteristic
41#15692186C2211yescharacteristic
42#15692186C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692179C2211yescharacteristic
46#15692179C2211yescharacteristic
47#15692178C2211yescharacteristic
48#15692178C2211yescharacteristic
49C22⋊#11717579C2211yescharacteristic
50#15692167C2211yescharacteristic
51#15692167C2211yescharacteristic
52C22⋊Q8×C101C2211yescharacteristic
53#117×C101C2211yescharacteristic
54#107×C101C2211yescharacteristic
55#106×C101C2211yescharacteristic
56#103×C101C2211yescharacteristic
57#103×C101C2211yescharacteristic
58C22⋊C8×C101C2211yescharacteristic
59#13108074—22no—
60#13108074—22no—
61C2×Dic202—21no—
62C2×Dic202D411yescharacteristic
63C2×Dic202C2311yescharacteristic
64Q8×D101—22no—
65Q8×D101—22no—
66C2×D404D411yescharacteristic
67C2×C22⋊D101D411yescharacteristic
68C2×C22⋊D101D411yescharacteristic
69C22×Dic101—21no—
70C2×C4×D101—21no—
71C2×C4×D101—21no—
72C2×C4×D101—21no—
73C2×C4×D101C2311yescharacteristic
74C2×C4×D101C2311yescharacteristic
75#13108057—22no—
76C2×#11717579C2311yescharacteristic
77C2×#11717579C2311yescharacteristic
78C8×D101—22no—
79C4⋊Dic101—21no—
80C4⋊Dic101—21no—
81C4⋊Dic101C2311yescharacteristic
82C4⋊Dic101C2311yescharacteristic
83C4⋊Dic101C2311yescharacteristic
84#13108053—21no—
85#13108053—21no—
86#13108053—21no—
87#13108053—21no—
88C22⋊Dic101—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93#13108051—21no—
94C4×Dic101—21no—
95C4×Dic101—21no—
96C4×Dic101—21no—
97C2×Q8×C101C2311yescharacteristic
98C22×C4×C101C2311yescharacteristic
99C2×C8×C101C2311yescharacteristic
100C2×C8×C101C2311yescharacteristic
101C4⋊C4×C101—21no—
102C4⋊C4×C101C2311yescharacteristic
103C4⋊C4×C101C2311yescharacteristic
104C4⋊C4×C101C2311yescharacteristic
105C22⋊C4×C101—21no—
106C22⋊C4×C101—21no—
107C42×C101—21no—
108C23×C101C2×D411yescharacteristic
109C22×D101C2×D411yescharacteristic
110C22×D101C2×D411yescharacteristic
111Q8×C101—21no—
112Q8×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101C2×D411yescharacteristic
120C2×C4×C101C2411yescharacteristic
121C22⋊D101—22no—
122C22⋊D101—22no—
123C2×Dic101—21no—
124C2×Dic101—21no—
125C2×Dic101—21no—
126C2×Dic101—21no—
127C2×Dic101—81no—
128C2×Dic101C2×D411yescharacteristic
129C2×Dic101C2×D411yescharacteristic
130D404—22no—
131C4×D101—21no—
132C4×D101—21no—
133C4×D101—42no—
134C4×D101—81no—
135C4×D101—81no—
136C4×D101#4112yes—
137C4×D101#4112yes—
138Dic202—22no—
139Dic202—21no—
140Dic202—21no—
141Dic202—42no—
142C8×C101—21no—
143C8×C101—21no—
144#11717579—21no—
145#11717579—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101C22×D411yescharacteristic
150C2×D101—21no—
151C2×D101—21no—
152C2×D101—21no—
153C2×D101—21no—
154C2×D101—21no—
155C2×D101#12312yes—
156C4×C101—21no—
157C4×C101—41no—
158C4×C101—41no—
159C4×C101—41no—
160C4×C101—41no—
161C4×C101C2×#4111yescharacteristic
162C4×C101C2×#4111yescharacteristic
163Dic101—21no—
164Dic101—41no—
165Dic101—41no—
166Dic101—41no—
167Dic101—41no—
168Dic101#12312yes—
169C2×C101—41no—
170C2×C101C2×#12311yescharacteristic
171C2×C101#57711yescharacteristic
172C2×C101#57811yescharacteristic
173D101—22no—
174D101—41no—
175#3097—1011nomaximal, Sylow
176C101#309711yescharacteristic, complemented, Sylow
177#536—1011no—
178#520—1011no—
179#485—1011no—
180#485—1011no—
181#485—1011no—
182#485D10111yescharacteristic, complemented
183#484—1011no—
184#484—1011no—
185#483—1011no—
186#483—1011no—
187#428—1011no—
188#427—1011no—
189#419—1011no—
190C2×#103—1011no—
191#408—1011no—
192C2×#41—1011no—
193C22×Q8—1011no—
194C2×M16—1011no—
195C22×C8—1011no—
196C4⋊Q8—2021no—
197#124—2021no—
198#123—2021no—
199#123—2021no—
200C22⋊Q8—1011no—
201C22⋊Q8—1011no—
202C22⋊Q8—1011no—
203C22⋊Q8C2×D10111yescharacteristic
204C4×Q8—2021no—
205C4×D4—2021no—
206C4×D4—2021no—
207C4×D4—2021no—
208#117—1011no—
209#117—1011no—
210#117—1011no—
211#117C2×D10111yescharacteristic
212C2×C4⋊C4—1011no—
213C2×C4⋊C4—1011no—
214C2×C4⋊C4—1011no—
215#107—1011no—
216#107—1011no—
217#107—1011no—
218#107C2×D10111yescharacteristic
219#106—1011no—
220#106—1011no—
221#106—1011no—
222#106C2×D10111yescharacteristic
223#103—1011no—
224#103—1011no—
225#103—1011no—
226#103—1011no—
227#103—1011no—
228#103—1011no—
229#103C2×D10111yescharacteristic
230#103C2×D10111yescharacteristic
231C22⋊C8—1011no—
232C22⋊C8—1011no—
233C22⋊C8—1011no—
234C22⋊C8C2×D10111yescharacteristic
235#41—2022no—
236#41—2022no—
237C2×Q8—1011no—
238C2×Q8—1011no—
239C2×Q8—2021no—
240C2×Q8—2022no—
241C2×Q8—2022no—
242C2×Q8C22×D10111yescharacteristic
243C2×D4—1011no—
244C2×D4—1011no—
245C2×D4—1011no—
246C22×C4—1011no—
247C22×C4—1011no—
248C22×C4—2021no—
249C22×C4—2021no—
250C22×C4—2021no—
251C22×C4—2021no—
252C22×C4C22×D10111yescharacteristic
253M16—2022no—
254C2×C8—1011no—
255C2×C8—1011no—
256C2×C8—2022no—
257C2×C8C22×D10111yescharacteristic
258C2×C8C22×D10111yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—1011no—
261C4⋊C4—1011no—
262C4⋊C4—1011no—
263C4⋊C4—2021no—
264C4⋊C4—2021no—
265C4⋊C4—2021no—
266C4⋊C4—2021no—
267C4⋊C4—2021no—
268C4⋊C4—2021no—
269C4⋊C4C22×D10111yescharacteristic
270C4⋊C4C22×D10111yescharacteristic
271C4⋊C4C22×D10111yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—2021no—
275C22⋊C4—2021no—
276C22⋊C4—2021no—
277C22⋊C4—2021no—
278C22⋊C4—2021no—
279C22⋊C4—2021no—
280C42—21no—
281C42—2021no—
282C42—2021no—
283C42—2021no—
284C23—1011no—
285C23—1011no—
286C23D4×D10111yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—4042no—
290Q8—2022no—
291Q8—2021no—
292Q8—2021no—
293D4—2022no—
294D4—2022no—
295D4—2022no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—8081no—
303C2×C4—8081no—
304C2×C4—8081no—
305C2×C4—1011no—
306C2×C4—1012no—
307C2×C4—1012no—
308C2×C4—1011no—
309C2×C4—4042no—
310C2×C4—2021no—
311C2×C4—2021no—
312C2×C4—2021no—
313C2×C4—2021no—
314C2×C4—2021no—
315C2×C4—2021no—
316C2×C4D4×D10111yescharacteristic
317C2×C4C23×D10111yescharacteristic
318C8—21no—
319C8—21no—
320C8—2021no—
321C8—2021no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—1012no—
326C22—2021no—
327C22—2021no—
328C22—2021no—
329C22—2021no—
330C22—2021no—
331C22C2×D4×D10111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1012no—
338C4—4041no—
339C4—4041no—
340C4—4041no—
341C4—4041no—
342C4—2021no—
343C4#41×D10111yescharacteristic
344C4#41×D10111yescharacteristic
345C2—41no—
346C2—4041no—
347C2—2022no—
348C2#123×D10111yescharacteristic
349C2#2026598611yescharacteristic
350C2#2026599111yescharacteristic
subgroupG/H
centerC22C2×D4×D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#485×C101C2
socleC22×C101C22×D4
prime radicalC2×#13108074C22
hypercenter#485D101
hypocenterC101#3097
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20265520C2semidirect
4. #20265518C2semidirect
5. #20265517C2semidirect
6. #20265513C2semidirect
7. #20265511C2semidirect
8. #20265509C2semidirect
9. #20265505C2semidirect
10. #20265216C2semidirect
11. #20265214C2semidirect
12. #20265184C2semidirect
13. #103×D101C2semidirect
15. #485×C101C2semidirect
176. C101#3097semidirect
182. #485D101semidirect

Maximal subgroups

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

subgroupindex
#202657502
#202656572
#202655202
#202655182
#202655172
#202655132
#202655112
#202655092
#202655052
#202652162
#202652142
#202651842
#103×D1012
#202651422
#485×C1012
#3097101