Finite Group Databasebeta

← #29593180

Subgroups — #29593180

Order 15616.

364 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 59 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#21446980C211yesmaximal, characteristic
2#21444826C211yesmaximal, characteristic
3#21444792C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443825C211yesmaximal, characteristic
6#21443753C211yesmaximal, characteristic
7C61×#2586C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16840092—21no—
10#16839918—21no—
11#16839771—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#398C2211yescharacteristic
19C61×#395—21no—
20C61×#395C2211yescharacteristic
21C61×#391—21no—
22C61×#391C2211yescharacteristic
23C61×#389—21no—
24C61×#387—21no—
25C61×#387—21no—
26C4×C4⋊C4×C61—21no—
27C2×#11758202—41no—
28C2×#11758194—21no—
29#14519776—41no—
30#14519768—41no—
31#14519756—21no—
32#14519756—21no—
33#14519736—21no—
34#14519708—41no—
35#14519701—41no—
36#14519701—41no—
37#14519701—41no—
38#14519700—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×Q8×C61D411yescharacteristic
42C22×Q8×C61D411yescharacteristic
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61—21no—
47C2×C4⋊C4×C61—21no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C42×C61—21no—
51C2×C42×C61—21no—
52C2×C42×C61D411yescharacteristic
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58#95×C61—21no—
59#95×C61—21no—
60#95×C61D411yescharacteristic
61#95×C61D411yescharacteristic
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61—42no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C2×Dic122—21no—
78C2×Dic122—21no—
79C4⋊C4×C61—24no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—81no—
86C4⋊C4×C61—81no—
87C42×C61—42no—
88C42×C61—41no—
89C42×C61—81no—
90C22⋊Dic61—41no—
91#11758202—82no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—41no—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C23×C61#12011yescharacteristic
105Q8×C61—42no—
106Q8×C61—42no—
107Q8×C61—81no—
108Q8×C61—81no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—41no—
136C2×Dic61—41no—
137Dic122—81no—
138Dic122—81no—
139#92418—81no—
140#92418—81no—
141#92418—81no—
142#12273—611nomaximal, Sylow
143C22×C61—21no—
144C22×C61—21no—
145C22×C61#45211yescharacteristic
146C22×C61#45511yescharacteristic
147C22×C61B(4,𝔽2)11yescharacteristic
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—42no—
151C4×C61—42no—
152C4×C61—42no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—42no—
156C4×C61—81no—
157C4×C61—81no—
158Dic61—81no—
159Dic61—81no—
160#2586D6111yescharacteristic
161#2028—611no—
162#1611—611no—
163#1605—611no—
164#1354—611no—
165#1346—611no—
166#1319—611no—
167C2×C61—21no—
168C2×C61—21no—
169C2×C61#160611yescharacteristic
170C2×C61#219711yescharacteristic
171C2×C61#220511yescharacteristic
172#544—611no—
173#483—1221no—
174#451—1221no—
175#419—1221no—
176#398C2×D6111yescharacteristic
177#395—21no—
178#395C2×D6111yescharacteristic
179#391—21no—
180#391C2×D6111yescharacteristic
181#389—21no—
182#387—21no—
183#387—21no—
184C4×C4⋊C4—21no—
185#343—611no—
186#339—1221no—
187#328—1221no—
188#328—1221no—
189#324—611no—
190#324—611no—
191C61#1227311yescharacteristic, complemented, Sylow
192C22×Q8C22⋊D6111yescharacteristic
193C22×Q8C22⋊D6111yescharacteristic
194C2×Q16—2441no—
195C2×M16—1221no—
196C4⋊Q8—2441no—
197#125—2441no—
198C22⋊Q8—1221no—
199C22⋊Q8—1221no—
200#117—1221no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C22⋊D6111yescharacteristic
207C2×C4⋊C4C22×D6111yescharacteristic
208C2×C42—21no—
209C2×C42—21no—
210C2×C42C22⋊D6111yescharacteristic
211#106—2441no—
212#103—2441no—
213#103—2441no—
214#103—2441no—
215#103—2441no—
216C22⋊C8—1221no—
217C22⋊C8—1221no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C22⋊D6111yescharacteristic
226#95C22⋊D6111yescharacteristic
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—1221no—
234C2×Q8—1221no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C2×C22⋊D6111yescharacteristic
242C22×C4C2×C22⋊D6111yescharacteristic
243C22×C4C2×C22⋊D6111yescharacteristic
244Q16—4882no—
245M16—2441no—
246M16—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C4⋊C4—24no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C4⋊C4—1221no—
259C4⋊C4—1221no—
260C4⋊C4—1221no—
261C4⋊C4—1221no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C22⋊C4—2441no—
265C42—41no—
266C42—42no—
267C42—81no—
268C42—2441no—
269C23#1451974611yescharacteristic
270Q8—42no—
271Q8—42no—
272Q8—81no—
273Q8—81no—
274Q8—4881no—
275Q8—4881no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
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—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4#1451979711yescharacteristic
303C2×C4#1451980711yescharacteristic
304C8—4881no—
305C8—4881no—
306C8—4881no—
307C22—21no—
308C22—21no—
309C22#1683992411yescharacteristic
310C22#1683994011yescharacteristic
311C22#1683994911yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—42no—
316C4—42no—
317C4—41no—
318C4—41no—
319C4—42no—
320C4—81no—
321C4—81no—
322C4—4881no—
323C4—4881no—
324C2—21no—
325C2—21no—
326C2#2144479911yescharacteristic
327C2#2144780911yescharacteristic
328C2#2144784911yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2586C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2586D61
hypocenterC61#12273
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2586

Complements

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

NH ≅ G/Ntype
191. C61#12273semidirect

Maximal subgroups

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

subgroupindex
#214469802
#214448262
#214447922
#214438492
#214438252
#214437532
C61×#25862
#1227361