Finite Group Databasebeta

← #30604839

Subgroups — #30604839

Order 15616.

452 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461522C211yesmaximal, characteristic
2D61⋊#324C211yesmaximal, characteristic
3#21460819C212yesmaximal, complemented
4#21460818C212yesmaximal, complemented
5#21451633C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7D61⋊(C22⋊C8)—21no—
8#16840642—21no—
9#16840642C2212yes—
10#16840608C2212yes—
11#16840607—21no—
12C2×#14519757C411yescharacteristic
13C2×C4⋊C4×D61C2211yescharacteristic
14#16839700C2211yescharacteristic
15#16839696—21no—
16#16839694—21no—
17#16839683C2211yescharacteristic
18#16839682C411yescharacteristic
19#16839636—21no—
20#16839624—21no—
21#16839621C411yescharacteristic
22C61×#400C411yescharacteristic
23C2×#11758213—41no—
24D61⋊M16—24no—
25D61⋊M16—42no—
26C2×#11758217—22no—
27C2×D61⋊C8—41no—
28C2×D61⋊C8—41no—
29#14519834—41no—
30C22⋊#92420—22no—
31C22×Dic122C2×C411yescharacteristic
32C22×C4×D61C2×C411yescharacteristic
33C22×C4×D61D411yescharacteristic
34C22×C4×D61D411yescharacteristic
35#14519757—41no—
36#14519757—41no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196D411yescharacteristic
43C2×#11758196C2311yescharacteristic
44C4⋊C4×D61—41no—
45C4⋊C4×D61—41no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C4⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61—21no—
57#95×C61C2×C411yescharacteristic
58C23×D61C22⋊C411yescharacteristic
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C2×D411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—22no—
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—81no—
77C2×C4×D61—81no—
78C2×C4×D61SD1612yes—
79C2×C4×D61Q1612yes—
80C2×Dic122—41no—
81C2×Dic122—81no—
82#11758217—24no—
83#11758217—42no—
84C2×#92420—42no—
85C2×#92420—42no—
86#11758213—44no—
87D61⋊C8—44no—
88D61⋊C8—82no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91#11758198—41no—
92#11758198—41no—
93#11758198—42no—
94C4⋊Dic61—41no—
95C4⋊Dic61—42no—
96C4⋊Dic61—81no—
97#11758196—41no—
98#11758196—41no—
99#11758196—81no—
100#11758196—81no—
101C23×C61C2×C22⋊C411yescharacteristic
102C22×D61—41no—
103C22×D61—41no—
104C22×D61#9911yescharacteristic
105C22×D61#9911yescharacteristic
106C22×D61#10312yes—
107C22×D61#10412yes—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—42no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61#10312yes—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61C2×SD1611yescharacteristic
133C2×Dic61C2×Q1611yescharacteristic
134C4×D61—22no—
135C4×D61—22no—
136C4×D61—22no—
137C4×D61—22no—
138C4×D61—42no—
139C4×D61—81no—
140C4×D61—81no—
141C4×D61—81no—
142Dic122—82no—
143#92420—44no—
144#92420—82no—
145#11722—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61C2×#9911yescharacteristic
149C22×C61C2×#10311yescharacteristic
150C22×C61C2×#10411yescharacteristic
151C2×D61—21no—
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—42no—
156C2×D61—42no—
157C2×D61#32812yes—
158C2×D61#32812yes—
159C4×C61—22no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—81no—
163C4×C61—81no—
164Dic61—21no—
165Dic61—21no—
166Dic61—41no—
167Dic61—41no—
168Dic61—81no—
169Dic61—81no—
170#2627—611no—
171C2×#343—611no—
172C2×#324—611no—
173#1354—612no—
174#1353—612no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61C2×#32811yescharacteristic
178C2×C61#212111yescharacteristic
179C2×C61#213311yescharacteristic
180D61—22no—
181D61—22no—
182C22×M16—1221no—
183C2×C22⋊Q8—611no—
184C22×C4⋊C4—611no—
185C2×C22⋊C8—1221no—
186#400—611no—
187#400#692311yescharacteristic
188#398—1221no—
189#398—1221no—
190#395—611no—
191#395—611no—
192#385—1221no—
193#381—1221no—
194#380—611no—
195#343—612no—
196#343—1221no—
197#324—612no—
198#324—1221no—
199C61#1172211yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C23×C4—611no—
202C23×C4—611no—
203C23×C4—611no—
204C2×M16—1222no—
205C2×M16—1224no—
206C2×M16—2442no—
207C2×M16—2441no—
208C22×C8—2441no—
209C22×C8—2441no—
210C22⋊Q8—2441no—
211C22⋊Q8—2441no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—2441no—
220C2×C4⋊C4—2441no—
221C2×C4⋊C4C2×#692311yescharacteristic
222C2×C4⋊C4C2×#692311yescharacteristic
223C2×C22⋊C4—1221no—
224C2×C22⋊C4—1221no—
225C22⋊C8—1222no—
226C22⋊C8—2441no—
227#95—21no—
228#95—21no—
229#95—611no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234#95C2×#692311yescharacteristic
235C24—611no—
236C2×Q8—4881no—
237C2×Q8—2441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—612no—
242C22×C4—612no—
243C22×C4—611no—
244C22×C4—611no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1222no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4—1221no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—4881no—
255C22×C4—4881no—
256C22×C4C22⋊#692311yescharacteristic
257C22×C4C22⋊#692311yescharacteristic
258C22×C4C22×#692311yescharacteristic
259M16—1224no—
260M16—2442no—
261M16—2444no—
262C2×C8—4882no—
263C2×C8—2442no—
264C2×C8—2444no—
265C2×C8—2442no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—4881no—
269C4⋊C4—4881no—
270C4⋊C4—4881no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2442no—
275C22⋊C4—2442no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C23—611no—
279C23—611no—
280C23—612no—
281C23—612no—
282C23—2441no—
283C23—2441no—
284C23C2×C22⋊#692311yescharacteristic
285Q8—4882no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—1222no—
300C2×C4—1222no—
301C2×C4—1222no—
302C2×C4—1222no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—4881no—
308C2×C4—4881no—
309C2×C4—4881no—
310C2×C4—2442no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4#1451984012yes—
320C8—4882no—
321C8—2444no—
322C22—21no—
323C22—21no—
324C22—612no—
325C22—612no—
326C22—1221no—
327C22—1221no—
328C22—1221no—
329C22—1221no—
330C22—2442no—
331C22—2442no—
332C22D61⋊#9911yescharacteristic
333C22C2×#1451984011yescharacteristic
334C22D61⋊#10411yescharacteristic
335C4—22no—
336C4—41no—
337C4—41no—
338C4—81no—
339C4—81no—
340C4—1221no—
341C4—1221no—
342C4—4881no—
343C4—4881no—
344C4—2441no—
345C4—2441no—
346C2—21no—
347C2—21no—
348C2—1222no—
349C2—1222no—
350C2D61⋊#32811yescharacteristic
351C2#2146207711yescharacteristic
352C2#2146211511yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#400C4
socleC22×C61C2×#99
prime radicalC23×D61C22⋊C4
cosocleC2×#11758196C23
hypercenter#400#6923
hypocenterC61#11722
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #21460819C2semidirect
4. #21460818C2semidirect
199. C61#11722semidirect

Maximal subgroups

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

subgroupindex
#214615222
D61⋊#3242
#214608192
#214608182
#214516332
#1172261