Finite Group Databasebeta

← #29578552

Subgroups — #29578552

Order 15616.

398 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446537C211yesmaximal, characteristic
2C4×#14519710C211yesmaximal, characteristic
3C2×#16839514C211yesmaximal, characteristic
4C2×C8×#92418C211yesmaximal, characteristic
5#21443660C211yesmaximal, characteristic
6#21443658C211yesmaximal, characteristic
7C61×#1939C211yesmaximal, characteristic
8C2×#14519710C411yescharacteristic
9C2×#14519710C411yescharacteristic
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519706—21no—
12C2×C4×#92418C2211yescharacteristic
13C2×C4×#92418C2211yescharacteristic
14C4×C4⋊Dic61C2211yescharacteristic
15#16839524C411yescharacteristic
16#16839524C411yescharacteristic
17#16839516—21no—
18#16839514—22no—
19C8×#92418—22no—
20C2×C4⋊C8×C61—21no—
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4×C8×C61C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#336—21no—
25C22×#92418—21no—
26C22×#92418—21no—
27C22×#92418C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×C4×Dic61—21no—
32#14519710—22no—
33#14519710C814yescomplemented
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36#14519706—42no—
37C4×#92418—21no—
38C4×#92418D412yes—
39C4×#92418Q812yes—
40C4×#92418Q812yes—
41#14519684—21no—
42C22×C8×C61—21no—
43C22×C8×C61D411yescharacteristic
44C22×C8×C61D411yescharacteristic
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61C2×C411yescharacteristic
47C2×C42×C61—21no—
48C2×C42×C61C2311yescharacteristic
49C4⋊C8×C61—21no—
50C4⋊C8×C61—21no—
51C4⋊C8×C61—42no—
52C4×C8×C61—21no—
53C4×C8×C61—21no—
54#95×C61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22×C411yescharacteristic
58C22×C4×C61C2×D411yescharacteristic
59C22×C4×C61#4111yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C2×C8×C61—21no—
63C2×C8×C61—21no—
64C2×C8×C61—21no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61—41no—
69C2×C8×C61D812yes—
70C2×C8×C61Q1612yes—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61C2×C812yes—
75C42×C61—41no—
76C42×C61—41no—
77C42×C61C2×D411yescharacteristic
78C42×C61C2×Q811yescharacteristic
79C42×C61C2×Q811yescharacteristic
80C42×C61#4111yescharacteristic
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—21no—
84C4⋊Dic61C2×C812yes—
85C4×Dic61—41no—
86C4×Dic61—41no—
87C2×#92418—22no—
88C2×#92418—22no—
89C2×#92418—22no—
90C2×#92418—21no—
91C2×#92418—21no—
92C2×#92418—41no—
93C2×#92418—41no—
94C2×#92418—41no—
95C2×#92418C4⋊C412yes—
96C2×#92418C4⋊C412yes—
97C2×#92418C2×C812yes—
98C2×#92418M1612yes—
99C23×C61C4×D411yescharacteristic
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61C2×C4⋊C411yescharacteristic
109C2×C4×C61C4×Q811yescharacteristic
110C2×C4×C61#12111yescharacteristic
111C2×C4×C61C22⋊Q811yescharacteristic
112C2×C4×C61#12511yescharacteristic
113C2×C4×C61C4⋊Q811yescharacteristic
114C2×C4×C61C22×C811yescharacteristic
115C2×C4×C61C2×M1611yescharacteristic
116C2×C4×C61#13111yescharacteristic
117C2×C4×C61#13111yescharacteristic
118C2×C4×C61C2×D811yescharacteristic
119C2×C4×C61C2×Q1611yescharacteristic
120C2×C4×C61#13511yescharacteristic
121C2×C4×C61#13511yescharacteristic
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C8×C61—22no—
129C8×C61—22no—
130C8×C61—81no—
131#92418—24no—
132#92418—22no—
133#92418—81no—
134#92418C4⋊C814yescomplemented
135#9594—611nomaximal, Sylow
136C22×C61#38911yescharacteristic
137C22×C61C8×D411yescharacteristic
138C22×C61#43611yescharacteristic
139C22×C61C4×D811yescharacteristic
140C22×C61C4×Q1611yescharacteristic
141C22×C61#44311yescharacteristic
142C22×C61#44311yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—42no—
146C4×C61—81no—
147C4×C61C2×C4⋊C811yescharacteristic
148C4×C61#42411yescharacteristic
149C4×C61C8×Q811yescharacteristic
150C4×C61#44611yescharacteristic
151C4×C61#46611yescharacteristic
152C4×C61#46711yescharacteristic
153C4×C61#49911yescharacteristic
154C4×C61#50011yescharacteristic
155Dic61—42no—
156Dic61—81no—
157#1939—611no—
158#1939D6111yescharacteristic
159C4×#107—611no—
160C2×#335—611no—
161C2×C82—611no—
162#1279—611no—
163#1279—611no—
164C2×C61C8×D811yescharacteristic
165C2×C61C8×Q1611yescharacteristic
166C2×C61#158911yescharacteristic
167C2×C61#159111yescharacteristic
168C2×C61#193911yescharacteristic
169C2×C61#194211yescharacteristic
170C2×C61#194511yescharacteristic
171C2×#107—611no—
172C2×#107—611no—
173C2×C4⋊C8—21no—
174C2×C4⋊C8—611no—
175C2×C4⋊C8—1221no—
176C2×C4⋊C8C2×D6111yescharacteristic
177C2×C4×C8—611no—
178C2×C4×C8—611no—
179C2×C4×C8C2×D6111yescharacteristic
180C4×C4⋊C4—611no—
181C4×C4⋊C4C2×D6111yescharacteristic
182#340—611no—
183#340—611no—
184#336—21no—
185#336—1221no—
186#335—1222no—
187C82—1222no—
188C61#959411yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—611no—
191C22×C8—611no—
192C22×C8—1221no—
193C22×C8—1221no—
194C22×C8C22⋊D6111yescharacteristic
195C22×C8C22⋊D6111yescharacteristic
196C2×C4⋊C4—611no—
197C2×C4⋊C4—611no—
198C2×C4⋊C4C4×D6111yescharacteristic
199C2×C4⋊C4C4×D6111yescharacteristic
200C2×C42—21no—
201C2×C42—1221no—
202C2×C42C22×D6111yescharacteristic
203#107—614no—
204#107—1222no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—1221no—
209C4⋊C8—1221no—
210C4⋊C8—2442no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—612no—
214C4×C8—612no—
215C4×C8—612no—
216C4×C8—1221no—
217#95—21no—
218#95—1221no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1221no—
222C22×C4—1221no—
223C22×C4C2×C4×D6111yescharacteristic
224C22×C4#1175822211yescharacteristic
225C22×C4C2×C22⋊D6111yescharacteristic
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—612no—
234C2×C8—612no—
235C2×C8—612no—
236C2×C8—612no—
237C2×C8—1222no—
238C2×C8—1222no—
239C2×C8—1222no—
240C2×C8—1221no—
241C2×C8—1221no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C2×C8#1175819912yes—
246C2×C8#1175820212yes—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—612no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4C8×D6112yes—
255C42—41no—
256C42—41no—
257C42—2441no—
258C42—2441no—
259C42D4×D6111yescharacteristic
260C42#1175822411yescharacteristic
261C42Q8×D6111yescharacteristic
262C42Q8×D6111yescharacteristic
263C23C4×C22⋊D6111yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—1222no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4C4⋊C4×D6111yescharacteristic
279C2×C4#1451974211yescharacteristic
280C2×C4#1451974911yescharacteristic
281C2×C4#1451975511yescharacteristic
282C2×C4#1451976711yescharacteristic
283C2×C4#1451977511yescharacteristic
284C2×C4C2×C8×D6111yescharacteristic
285C2×C4M16×D6111yescharacteristic
286C2×C4#1451978311yescharacteristic
287C2×C4#1451978511yescharacteristic
288C2×C4C2×#1175819911yescharacteristic
289C2×C4C2×#1175820211yescharacteristic
290C2×C4#1451979711yescharacteristic
291C2×C4#1451979711yescharacteristic
292C8—22no—
293C8—22no—
294C8—81no—
295C8—614no—
296C8—1224no—
297C8—1222no—
298C8—4881no—
299C22#1683965711yescharacteristic
300C22C8×C22⋊D6111yescharacteristic
301C22#1683983811yescharacteristic
302C22C4×#1175819911yescharacteristic
303C22C4×#1175820211yescharacteristic
304C22#1683987711yescharacteristic
305C22#1683987711yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—4881no—
311C4—2442no—
312C4C4⋊C8×D6111yescharacteristic
313C4#1683978711yescharacteristic
314C4#1683988611yescharacteristic
315C4#1683989111yescharacteristic
316C4#1683999611yescharacteristic
317C4#1684000111yescharacteristic
318C4#1684016111yescharacteristic
319C4#1684016511yescharacteristic
320C2C8×#1175819911yescharacteristic
321C2C8×#1175820211yescharacteristic
322C2#2144470211yescharacteristic
323C2#2144471411yescharacteristic
324C2#2144653411yescharacteristic
325C2#2144654911yescharacteristic
326C2#2144656411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1939C2
socle, prime radicalC23×C61C4×D4
cosocleC2×C42×C61C23
hypercenter#1939D61
hypocenterC61#9594
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
33. #14519710C8semidirect
134. #92418C4⋊C8semidirect
188. C61#9594semidirect

Maximal subgroups

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

subgroupindex
#214465372
C4×#145197102
C2×#168395142
C2×C8×#924182
#214436602
#214436582
C61×#19392
#959461