Finite Group Databasebeta

← #27183887

Subgroups — #27183887

Order 12928.

358 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20265912C211yesmaximal, characteristic, complemented
2#20265887C211yesmaximal, characteristic, complemented
3#20265542C211yesmaximal, characteristic, complemented
4#20265537C211yesmaximal, characteristic, complemented
5#20265532C211yesmaximal, characteristic, complemented
6#20265485C211yesmaximal, characteristic, complemented
7#20265478C211yesmaximal, characteristic, complemented
8#20265458C211yesmaximal, characteristic, complemented
9#20265393C211yesmaximal, characteristic, complemented
10#20265393C211yesmaximal, characteristic, complemented
11#20265373C211yesmaximal, characteristic
12#20265290C211yesmaximal, characteristic, complemented
13#20265279C211yesmaximal, characteristic, complemented
14C4×D808C211yesmaximal, characteristic, complemented
15#446×C101C211yesmaximal, characteristic, complemented
16C2×#13108063C2211yescharacteristic
17C2×D808C2211yescharacteristic
18C2×D808C2211yescharacteristic
19#15692255C2211yescharacteristic
20#15692252C2211yescharacteristic
21#15692247C2211yescharacteristic
22#15692247C2211yescharacteristic
23#15692244—21no—
24#15692243C2211yescharacteristic
25#15692243C2211yescharacteristic
26#15692240—21no—
27#15692240—21no—
28#15692233—21no—
29#15692233—21no—
30#15692231—21no—
31C4×Dic202C2211yescharacteristic
32C4×D404C2211yescharacteristic
33C4×D404C2211yescharacteristic
34C4×D404C2211yescharacteristic
35C4×D404C2211yescharacteristic
36C4×D404C2211yescharacteristic
37#15692217—21no—
38C4⋊C4×D101—21no—
39#15692189C2211yescharacteristic
40#15692189C2211yescharacteristic
41#15692187C2211yescharacteristic
42#15692180C2211yescharacteristic
43#15692180C2211yescharacteristic
44#15692180C2211yescharacteristic
45#15692177C2211yescharacteristic
46#15692177C2211yescharacteristic
47#15692177C2211yescharacteristic
48#15692177C2211yescharacteristic
49#15692177C2211yescharacteristic
50#15692177C2211yescharacteristic
51#15692177C2211yescharacteristic
52C4×Q8×C101C2211yescharacteristic
53C4⋊C8×C101C2211yescharacteristic
54C4⋊C8×C101C2211yescharacteristic
55C4⋊C8×C101C2211yescharacteristic
56#97×C101C2211yescharacteristic
57#97×C101C2211yescharacteristic
58C4×C8×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×Dic202C2311yescharacteristic
61C2×D404—21no—
62C2×D404—21no—
63C2×D404C2311yescharacteristic
64C2×D404C2311yescharacteristic
65C2×D404C2311yescharacteristic
66C2×C4×D101—21no—
67C2×C4×D101—21no—
68C2×C4×D101—21no—
69C2×C4×D101—21no—
70C2×C4×D101—21no—
71#13108063—22no—
72D808—22no—
73D808—22no—
74C4⋊Dic101—21no—
75C4⋊Dic101C2311yescharacteristic
76C4⋊Dic101C2311yescharacteristic
77C4⋊Dic101C2311yescharacteristic
78C4⋊Dic101C2311yescharacteristic
79#13108053—21no—
80#13108053—21no—
81#13108053—21no—
82#13108053—21no—
83#13108053—21no—
84#13108051—21no—
85#13108051—21no—
86#13108051—21no—
87#13108051—21no—
88#13108051—21no—
89#13108051—21no—
90#13108051—21no—
91#13108051—21no—
92#13108051—21no—
93C4×Dic101—21no—
94C2×Q8×C101D411yescharacteristic
95C2×C8×C101C2311yescharacteristic
96C2×C8×C101C2311yescharacteristic
97C2×C8×C101C2311yescharacteristic
98C2×C8×C101C2311yescharacteristic
99C4⋊C4×C101D411yescharacteristic
100C4⋊C4×C101D411yescharacteristic
101C4⋊C4×C101D411yescharacteristic
102C42×C101C2311yescharacteristic
103C42×C101C2311yescharacteristic
104C42×C101C2311yescharacteristic
105C22×D101—21no—
106C22×D101—21no—
107C22×D101—21no—
108Q8×C101—41no—
109C2×C4×C101C2×D411yescharacteristic
110C2×C4×C101C2×D411yescharacteristic
111C2×C4×C101C2×D411yescharacteristic
112C2×C4×C101C2×D411yescharacteristic
113C2×C4×C101C2×D411yescharacteristic
114C2×C4×C101C2×D411yescharacteristic
115C2×C4×C101C2411yescharacteristic
116C2×Dic101—21no—
117C2×Dic101—21no—
118C2×Dic101—21no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121D404—21no—
122D404—21no—
123D404—21no—
124D404—21no—
125D404—21no—
126D404—42no—
127D404—81no—
128D404#4112yes—
129C4×D101—42no—
130C4×D101—81no—
131C4×D101—81no—
132C4×D101—81no—
133C4×D101—81no—
134Dic202—21no—
135Dic202—21no—
136Dic202—81no—
137C8×C101—21no—
138C8×C101—21no—
139C8×C101—21no—
140C8×C101—21no—
141C22×C101C22×D411yescharacteristic
142C2×D101—22no—
143C2×D101—41no—
144C2×D101—41no—
145C2×D101—41no—
146C2×D101—41no—
147C2×D101—41no—
148C2×D101—41no—
149C2×D101—41no—
150C2×D101—41no—
151C4×C101—21no—
152C4×C101—21no—
153C4×C101—21no—
154C4×C101—21no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101C2×#4111yescharacteristic
158C4×C1012−1+411yescharacteristic
159Dic101—41no—
160Dic101—41no—
161Dic101—41no—
162Dic101—41no—
163Dic101—41no—
164C2×C101#54811yescharacteristic
165C2×C101#57511yescharacteristic
166C2×C101#57611yescharacteristic
167D101—42no—
168D101—81no—
169D101—81no—
170#3370—1011nomaximal, Sylow
171C101#337011yescharacteristic, complemented, Sylow
172#559—1011no—
173#554—1011no—
174#490—1011no—
175#489—1011no—
176#488—1011no—
177#479—1011no—
178#478—1011no—
179#474—1011no—
180#463—1011no—
181#463—1011no—
182#459—1011no—
183#446D10111yescharacteristic, complemented
184#442—1011no—
185#440—1011no—
186C4×D8—1011no—
187C2×SD16—1011no—
188C2×D8—1011no—
189C2×D8—1011no—
190C4⋊Q8—1011no—
191#127—1011no—
192#125—1011no—
193#125—1011no—
194#124—1011no—
195#124—1011no—
196#124—2021no—
197#123—2021no—
198#123—2021no—
199C22⋊Q8—2021no—
200C22⋊Q8—2021no—
201C22⋊Q8—2021no—
202C4×Q8—1011no—
203C4×Q8C2×D10111yescharacteristic
204C4×D4—1011no—
205C4×D4—1011no—
206C4×D4—1011no—
207C4×D4—1011no—
208C4×D4—1011no—
209C4×D4—2021no—
210C2×C4⋊C4—2021no—
211#107—1011no—
212#107—1011no—
213#106—1011no—
214C4⋊C8C2×D10111yescharacteristic
215C4⋊C8C2×D10111yescharacteristic
216C4⋊C8C2×D10111yescharacteristic
217#103—1011no—
218#103—1011no—
219#103—1011no—
220#102—1011no—
221#102—1011no—
222#102—1011no—
223#102—1011no—
224#102—1011no—
225#102—1011no—
226#102—1011no—
227#97C2×D10111yescharacteristic
228#97C2×D10111yescharacteristic
229C4×C8C2×D10111yescharacteristic
230C2×Q8—1011no—
231C2×Q8—2021no—
232C2×Q8D40411yescharacteristic
233C2×D4—1011no—
234C2×D4—1011no—
235C2×D4—1011no—
236C2×D4—2021no—
237C2×D4—2021no—
238C22×C4—2021no—
239C22×C4—2021no—
240C22×C4—2021no—
241C22×C4—2021no—
242C22×C4—2021no—
243SD16—2022no—
244D8—2022no—
245D8—2022no—
246C2×C8C22×D10111yescharacteristic
247C2×C8C22×D10111yescharacteristic
248C2×C8C22×D10111yescharacteristic
249C2×C8C22×D10111yescharacteristic
250C4⋊C4—1011no—
251C4⋊C4—1011no—
252C4⋊C4—1011no—
253C4⋊C4—1011no—
254C4⋊C4—2021no—
255C4⋊C4—2021no—
256C4⋊C4—2021no—
257C4⋊C4—2021no—
258C4⋊C4—2021no—
259C4⋊C4—2021no—
260C4⋊C4D40411yescharacteristic
261C4⋊C4D40411yescharacteristic
262C4⋊C4D40411yescharacteristic
263C22⋊C4—2021no—
264C22⋊C4—2021no—
265C22⋊C4—2021no—
266C22⋊C4—2021no—
267C22⋊C4—2021no—
268C22⋊C4—2021no—
269C22⋊C4—2021no—
270C22⋊C4—2021no—
271C22⋊C4—2021no—
272C42—2021no—
273C42C22×D10111yescharacteristic
274C42C22×D10111yescharacteristic
275C42C22×D10111yescharacteristic
276C23—2021no—
277C23—2021no—
278C23—2021no—
279Q8—41no—
280Q8—8081no—
281Q8—2021no—
282Q8—2021no—
283D4—8081no—
284D4—1012no—
285D4—4042no—
286D4—2021no—
287D4—2021no—
288D4—2021no—
289D4—2021no—
290D4—2021no—
291C2×C4—8081no—
292C2×C4—8081no—
293C2×C4—8081no—
294C2×C4—8081no—
295C2×C4—4042no—
296C2×C4—2021no—
297C2×C4—2021no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4C2×D40411yescharacteristic
302C2×C4C2×D40411yescharacteristic
303C2×C4C2×D40411yescharacteristic
304C2×C4C2×D40411yescharacteristic
305C2×C4C2×D40411yescharacteristic
306C2×C4C2×D40411yescharacteristic
307C2×C4C23×D10111yescharacteristic
308C8—21no—
309C8—21no—
310C8—21no—
311C8—21no—
312C22—4041no—
313C22—4041no—
314C22—4041no—
315C22—4041no—
316C22—4041no—
317C22—4041no—
318C22—4041no—
319C22—4041no—
320C22—2022no—
321C22C22×D40411yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—4041no—
329C4—4041no—
330C4—4041no—
331C4—4041no—
332C4—4041no—
333C4#41×D10111yescharacteristic
334C4#1569230311yescharacteristic
335C2—8081no—
336C2—8081no—
337C2—4042no—
338C2#2026583911yescharacteristic
339C2#2026597711yescharacteristic
340C2#2026598211yescharacteristic
subgroupG/H
centerC22C22×D404
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#446×C101C2
socleC22×C101C22×D4
prime radical#20265373C2
hypercenter#446D101
hypocenterC101#3370
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #20265912C2semidirect
2. #20265887C2semidirect
3. #20265542C2semidirect
4. #20265537C2semidirect
5. #20265532C2semidirect
6. #20265485C2semidirect
7. #20265478C2semidirect
8. #20265458C2semidirect
9. #20265393C2semidirect
10. #20265393C2semidirect
12. #20265290C2semidirect
13. #20265279C2semidirect
14. C4×D808C2semidirect
15. #446×C101C2semidirect
171. C101#3370semidirect
183. #446D101semidirect

Maximal subgroups

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

subgroupindex
#202659122
#202658872
#202655422
#202655372
#202655322
#202654852
#202654782
#202654582
#202653932
#202653732
#202652902
#202652792
C4×D8082
#446×C1012
#3370101