Finite Group Databasebeta

← #30605239

Subgroups — #30605239

Order 15616.

382 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 64 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#21461686C211yesmaximal, characteristic, complemented
2#21461083C211yesmaximal, characteristic, complemented
3#21460820C212yesmaximal, complemented
4#21460802C212yesmaximal
5#21451685C211yesmaximal, characteristic
6#16840782—21no—
7#16840765—21no—
8C2×#14519838—21no—
9#16840642C2212yes—
10#16840608—21no—
11#16840608C2212yes—
12C2×#14519766C411yescharacteristic
13C2×#14519742C2211yescharacteristic
14#16839697—21no—
15#16839681C2211yescharacteristic
16#16839680C2211yescharacteristic
17#16839679C411yescharacteristic
18#16839675—21no—
19#16839652—21no—
20#16839651—21no—
21#16839629C411yescharacteristic
22C61×#395C411yescharacteristic
23C2×#11758217—22no—
24#14519844—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27#14519838—42no—
28C22⋊#92420—22no—
29#14519832—41no—
30C22×Dic122D411yescharacteristic
31C22×D244C2×C411yescharacteristic
32#14519766—41no—
33#14519766—41no—
34#14519742—41no—
35#14519742—41no—
36C2×#11758196—21no—
37C2×#11758196D411yescharacteristic
38C2×#11758196C2311yescharacteristic
39C2×#11758198—21no—
40C2×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×C4×Dic61C2×C411yescharacteristic
46C2×C4×Dic61D411yescharacteristic
47C2×C4×Dic61D411yescharacteristic
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684C2×C411yescharacteristic
52C22×Q8×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61C2×C411yescharacteristic
55#95×C61—21no—
56#95×C61C2×C411yescharacteristic
57C23×D61—21no—
58C2×Q8×C61—41no—
59C2×Q8×C61—81no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61C22⋊C411yescharacteristic
67C22×Dic61C22⋊C411yescharacteristic
68C22×Dic61C2×D411yescharacteristic
69C22×Dic61C2×D411yescharacteristic
70C2×D244—41no—
71C2×D244—81no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—41no—
75C2×Dic122—41no—
76#11758217—42no—
77#11758217—42no—
78C2×#92420—42no—
79C2×#92420—42no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—81no—
82#11758198—42no—
83#11758198—42no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87#11758198—41no—
88#11758198—81no—
89#11758198—81no—
90#11758196—41no—
91#11758196—41no—
92#11758196—81no—
93C4×Dic61—21no—
94C4×Dic61—21no—
95C4×Dic61—21no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—21no—
99C23×C61C2×C22⋊C411yescharacteristic
100C22×D61—41no—
101C22×D61—41no—
102C22×D61—41no—
103C22×D61—41no—
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107Q8×C61—82no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61#9911yescharacteristic
133C2×Dic61#9911yescharacteristic
134C2×Dic61AGL(1,ℤ/8)11yescharacteristic
135C2×Dic61#13711yescharacteristic
136D244—82no—
137Dic122—42no—
138Dic122—42no—
139#92420—82no—
140#92420—82no—
141#11833—611nomaximal, Sylow
142C22×C61—21no—
143C22×C61—21no—
144C22×C61C2×#9911yescharacteristic
145C22×C61#41711yescharacteristic
146C22×C61#42111yescharacteristic
147C2×D61—81no—
148C2×D61—81no—
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—81no—
158C4×C61—81no—
159Dic61—21no—
160Dic61—21no—
161Dic61—21no—
162Dic61—21no—
163Dic61—41no—
164Dic61—41no—
165Dic61—81no—
166#2632—611no—
167#1801—611no—
168#1467—611no—
169#1354—612no—
170#1345—612no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61#151311yescharacteristic
174C2×C61#212211yescharacteristic
175C2×C61#213311yescharacteristic
176D61—161no—
177C2×#124—611no—
178C2×C4×Q8—611no—
179#432—1221no—
180#423—1221no—
181C2×#101—1221no—
182#399—1221no—
183#395—611no—
184#395#692311yescharacteristic
185#394—611no—
186#394—611no—
187#393—1221no—
188#388—1221no—
189#388—1221no—
190#383—611no—
191#343—612no—
192#324—612no—
193#324—1221no—
194C61#1183311yescharacteristic, complemented, Sylow
195C22×Q8—611no—
196C22×Q8C2×#692311yescharacteristic
197C22×D4—611no—
198C2×M16—1222no—
199#124—2441no—
200#124—2441no—
201C4×Q8—2441no—
202C4×Q8—2441no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4C2×#692311yescharacteristic
208C2×C22⋊C4—1221no—
209C2×C22⋊C4—1221no—
210C2×C22⋊C4—1221no—
211C2×C22⋊C4—1221no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C4⋊C8—2441no—
218C4⋊C8—2441no—
219C4⋊C8—2441no—
220#101—2442no—
221C22⋊C8—1222no—
222#97—2441no—
223#95—21no—
224#95—611no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95C2×#692311yescharacteristic
229C24—1221no—
230C2×Q8—41no—
231C2×Q8—81no—
232C2×Q8—1221no—
233C2×Q8—1221no—
234C2×Q8—2441no—
235C2×Q8—2441no—
236C2×D4—4881no—
237C2×D4—2441no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—611no—
243C22×C4—611no—
244C22×C4—1221no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22⋊#692311yescharacteristic
247C22×C4C22×#692311yescharacteristic
248M16—2442no—
249M16—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C4⋊C4—41no—
253C4⋊C4—81no—
254C4⋊C4—4881no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C22⋊C4—4881no—
258C22⋊C4—4881no—
259C22⋊C4—2442no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C22⋊C4—2442no—
265C42—1221no—
266C42—1221no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C23—2441no—
272C23—2441no—
273C23—2441no—
274C23—2441no—
275C23—2441no—
276C23—2441no—
277C23—2441no—
278C23C2×C22⋊#692311yescharacteristic
279Q8—82no—
280Q8—2442no—
281Q8—2442no—
282D4—4882no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—611no—
297C2×C4—611no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—1221no—
301C2×C4—1221no—
302C2×C4—1221no—
303C2×C4—1221no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C8—4882no—
312C8—4882no—
313C22—21no—
314C22—21no—
315C22—4881no—
316C22—4881no—
317C22—4881no—
318C22—4881no—
319C22—4881no—
320C22—4881no—
321C22—4881no—
322C22D61⋊#9911yescharacteristic
323C22#1684075311yescharacteristic
324C22#1684076111yescharacteristic
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—1221no—
331C4—1221no—
332C4—1221no—
333C4—1221no—
334C4—4881no—
335C4—2441no—
336C4—2441no—
337C2—21no—
338C2—21no—
339C2—9761no—
340C2#2146123711yescharacteristic
341C2#2146207911yescharacteristic
342C2#2146211711yescharacteristic
subgroupG/H
centerC22D61⋊#99
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#395C4
socleC22×C61C2×#99
prime radicalC22×D244C2×C4
cosocleC2×#11758196C23
hypercenter#395#6923
hypocenterC61#11833
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
1. #21461686C2semidirect
2. #21461083C2semidirect
3. #21460820C2semidirect
194. C61#11833semidirect

Maximal subgroups

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

subgroupindex
#214616862
#214610832
#214608202
#214608022
#214516852
#1183361