Finite Group Databasebeta

← #27183879

Subgroups — #27183879

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#20265887C211yesmaximal, characteristic, complemented
2#20265541C211yesmaximal, characteristic, complemented
3#20265536C211yesmaximal, characteristic, complemented
4#20265531C211yesmaximal, characteristic, complemented
5#20265484C211yesmaximal, characteristic, complemented
6#20265477C211yesmaximal, characteristic, complemented
7#20265457C211yesmaximal, characteristic, complemented
8#20265389C211yesmaximal, characteristic, complemented
9#20265389C211yesmaximal, characteristic, complemented
10#20265369C211yesmaximal, characteristic
11#20265308C211yesmaximal, characteristic, complemented
12#20265287C211yesmaximal, characteristic, complemented
13#20265275C211yesmaximal, characteristic, complemented
14C4×#13108059C211yesmaximal, characteristic, complemented
15#559×C101C211yesmaximal, characteristic, complemented
16C2×#13108061C2211yescharacteristic
17C2×#13108059C2211yescharacteristic
18C2×#13108059C2211yescharacteristic
19#15692255C2211yescharacteristic
20#15692247C2211yescharacteristic
21#15692247C2211yescharacteristic
22#15692233—21no—
23#15692233—21no—
24#15692231—21no—
25C4×D404C2211yescharacteristic
26C4×D404C2211yescharacteristic
27C4×D404C2211yescharacteristic
28C4⋊C4×D101—21no—
29#15692188C2211yescharacteristic
30#15692188C2211yescharacteristic
31#15692186C2211yescharacteristic
32C4⋊#11717579C2211yescharacteristic
33C4⋊#11717579C2211yescharacteristic
34C4⋊#11717579C2211yescharacteristic
35#15692179C2211yescharacteristic
36#15692179C2211yescharacteristic
37#15692179C2211yescharacteristic
38#15692176C2211yescharacteristic
39#15692176C2211yescharacteristic
40#15692176C2211yescharacteristic
41#15692176C2211yescharacteristic
42#15692176C2211yescharacteristic
43#15692176C2211yescharacteristic
44#15692175C2211yescharacteristic
45#15692166C2211yescharacteristic
46#15692166C2211yescharacteristic
47C4×#11717579C2211yescharacteristic
48#127×C101C2211yescharacteristic
49#124×C101—21no—
50#124×C101C2211yescharacteristic
51#124×C101C2211yescharacteristic
52#123×C101—21no—
53#123×C101—21no—
54C4×Q8×C101C2211yescharacteristic
55C4×Q8×C101C2211yescharacteristic
56C4×D4×C101—21no—
57C4×D4×C101C2211yescharacteristic
58C4×D4×C101C2211yescharacteristic
59C2×Dic202—21no—
60C2×D404C2311yescharacteristic
61C2×C4×D101—21no—
62C2×C4×D101—21no—
63C2×C4×D101—21no—
64#13108061—22no—
65#13108059—22no—
66#13108059—22no—
67C2×#11717579C2311yescharacteristic
68C2×#11717579C2311yescharacteristic
69C2×#11717579C2311yescharacteristic
70C2×#11717579C2311yescharacteristic
71C4⋊Dic101—21no—
72C4⋊Dic101C2311yescharacteristic
73C4⋊Dic101C2311yescharacteristic
74C4⋊Dic101C2311yescharacteristic
75#13108053—21no—
76#13108053—21no—
77#13108053—21no—
78#13108053—21no—
79#13108051—21no—
80#13108051—21no—
81#13108051—21no—
82C2×Q8×C101D411yescharacteristic
83C2×Q8×C101C2311yescharacteristic
84C2×D4×C101—21no—
85C2×D4×C101—21no—
86C2×D4×C101C2311yescharacteristic
87C2×D4×C101C2311yescharacteristic
88C22×C4×C101—21no—
89C22×C4×C101—21no—
90C4⋊C4×C101—21no—
91C4⋊C4×C101D411yescharacteristic
92C4⋊C4×C101D411yescharacteristic
93C4⋊C4×C101D411yescharacteristic
94C4⋊C4×C101C2311yescharacteristic
95C22⋊C4×C101—21no—
96C22⋊C4×C101—21no—
97C22⋊C4×C101—21no—
98C22⋊C4×C101—21no—
99C22⋊C4×C101—21no—
100C22⋊C4×C101—21no—
101C42×C101—21no—
102C42×C101C2311yescharacteristic
103C42×C101C2311yescharacteristic
104C42×C101C2311yescharacteristic
105C23×C101—21no—
106C23×C101—21no—
107C22×D101—21no—
108Q8×C101—21no—
109Q8×C101—21no—
110Q8×C101—41no—
111D4×C101—21no—
112D4×C101—21no—
113D4×C101—21no—
114D4×C101—21no—
115D4×C101—42no—
116D4×C101—81no—
117C2×C4×C101—21no—
118C2×C4×C101—21no—
119C2×C4×C101—81no—
120C2×C4×C101—81no—
121C2×C4×C101C2×D411yescharacteristic
122C2×C4×C101C2×D411yescharacteristic
123C2×C4×C101C2×D411yescharacteristic
124C2×C4×C101C2×D411yescharacteristic
125C2×C4×C101C2×D411yescharacteristic
126C2×C4×C101C2×D411yescharacteristic
127C2×C4×C101C2411yescharacteristic
128C2×Dic101—21no—
129C2×Dic101—21no—
130C2×Dic101—21no—
131D404—21no—
132D404#4112yes—
133C4×D101—42no—
134C4×D101—81no—
135C4×D101—81no—
136Dic202—81no—
137#11717579—21no—
138#11717579—21no—
139#11717579—21no—
140#11717579—21no—
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—41no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101C22×D411yescharacteristic
148C2×D101—22no—
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×C101—41no—
158C4×C101—41no—
159C4×C101C2×#4111yescharacteristic
160C4×C1012−1+411yescharacteristic
161Dic101—41no—
162Dic101—41no—
163Dic101—41no—
164C2×C101—81no—
165C2×C101—81no—
166C2×C101#54811yescharacteristic
167C2×C101#57511yescharacteristic
168C2×C101#57611yescharacteristic
169D101—42no—
170#3370—1011nomaximal, Sylow
171C101#337011yescharacteristic, complemented, Sylow
172#559D10111yescharacteristic, complemented
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#446—1011no—
184#442—1011no—
185#440—1011no—
186C4×D8—1011no—
187C2×SD16—1011no—
188C2×D8—1011no—
189C2×D8—1011no—
190C4⋊Q8—1011no—
191#127C2×D10111yescharacteristic
192#125—1011no—
193#125—1011no—
194#124—21no—
195#124C2×D10111yescharacteristic
196#124C2×D10111yescharacteristic
197#123—21no—
198#123—21no—
199C22⋊Q8—2021no—
200C22⋊Q8—2021no—
201C22⋊Q8—2021no—
202C4×Q8C2×D10111yescharacteristic
203C4×Q8C2×D10111yescharacteristic
204C4×D4—21no—
205C4×D4—1011no—
206C4×D4—1011no—
207C4×D4—1011no—
208C4×D4C2×D10111yescharacteristic
209C4×D4C2×D10111yescharacteristic
210C2×C4⋊C4—2021no—
211#107—1011no—
212#107—1011no—
213#106—1011no—
214C4⋊C8—1011no—
215C4⋊C8—1011no—
216C4⋊C8—1011no—
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#97—1011no—
228#97—1011no—
229C4×C8—1011no—
230C2×Q8—2021no—
231C2×Q8C22⋊D10111yescharacteristic
232C2×Q8C22×D10111yescharacteristic
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—1011no—
236C2×D4C22×D10111yescharacteristic
237C2×D4C22×D10111yescharacteristic
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—2021no—
241C22×C4—2021no—
242C22×C4—2021no—
243SD16—2022no—
244D8—2022no—
245D8—2022no—
246C2×C8—1011no—
247C2×C8—1011no—
248C2×C8—1011no—
249C2×C8—1011no—
250C4⋊C4—21no—
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⋊C4C22⋊D10111yescharacteristic
260C4⋊C4C22⋊D10111yescharacteristic
261C4⋊C4C22⋊D10111yescharacteristic
262C4⋊C4C22×D10111yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—2021no—
270C22⋊C4—2021no—
271C22⋊C4—2021no—
272C42—21no—
273C42C22×D10111yescharacteristic
274C42C22×D10111yescharacteristic
275C42C22×D10111yescharacteristic
276C23—21no—
277C23—21no—
278C23—2021no—
279Q8—21no—
280Q8—21no—
281Q8—41no—
282Q8—8081no—
283D4—21no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—42no—
288D4—81no—
289D4—1012no—
290D4—2021no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—8081no—
296C2×C4—8081no—
297C2×C4—4042no—
298C2×C4—2021no—
299C2×C4—2021no—
300C2×C4—2021no—
301C2×C4C2×C22⋊D10111yescharacteristic
302C2×C4C2×C22⋊D10111yescharacteristic
303C2×C4C2×C22⋊D10111yescharacteristic
304C2×C4C2×C22⋊D10111yescharacteristic
305C2×C4C2×C22⋊D10111yescharacteristic
306C2×C4C2×C22⋊D10111yescharacteristic
307C2×C4C23×D10111yescharacteristic
308C8—2021no—
309C8—2021no—
310C8—2021no—
311C8—2021no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—4041no—
319C22—4041no—
320C22—2022no—
321C22C22×C22⋊D10111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—4041no—
331C4—4041no—
332C4—4041no—
333C4#41×D10111yescharacteristic
334C4#1569230211yescharacteristic
335C2—81no—
336C2—81no—
337C2—4042no—
338C2#2026583411yescharacteristic
339C2#2026597511yescharacteristic
340C2#2026598011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D101
commutator, cosocleC2×C4×C101C24
FrattiniC2×C4C23×D101
Fitting#559×C101C2
socleC22×C101C22×D4
prime radical#20265369C2
hypercenter#559D101
hypocenterC101#3370
LCSG ▷ C2×C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #20265887C2semidirect
2. #20265541C2semidirect
3. #20265536C2semidirect
4. #20265531C2semidirect
5. #20265484C2semidirect
6. #20265477C2semidirect
7. #20265457C2semidirect
8. #20265389C2semidirect
9. #20265389C2semidirect
11. #20265308C2semidirect
12. #20265287C2semidirect
13. #20265275C2semidirect
14. C4×#13108059C2semidirect
15. #559×C101C2semidirect
171. C101#3370semidirect
172. #559D101semidirect

Maximal subgroups

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

subgroupindex
#202658872
#202655412
#202655362
#202655312
#202654842
#202654772
#202654572
#202653892
#202653692
#202653082
#202652872
#202652752
C4×#131080592
#559×C1012
#3370101