Finite Group Databasebeta

← #29593079

Subgroups — #29593079

Order 15616.

352 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 63 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#21447169C211yesmaximal, characteristic
2#21444860C211yesmaximal, characteristic
3#21444792C211yesmaximal, characteristic
4#21443849C211yesmaximal, characteristic
5#21443846C211yesmaximal, characteristic
6#21443763C211yesmaximal, characteristic
7C61×#2612C211yesmaximal, characteristic
8#16840393C2211yescharacteristic
9#16840097—21no—
10#16839918—21no—
11#16839802—21no—
12#16839531C2211yescharacteristic
13#16839522—21no—
14#16839498—21no—
15#16839498—21no—
16#16839488C2211yescharacteristic
17#16839488C2211yescharacteristic
18C61×#400C2211yescharacteristic
19C61×#398—21no—
20C61×#395C2211yescharacteristic
21C61×#391—21no—
22C61×#389—21no—
23C61×#387—21no—
24C61×#387—21no—
25C61×#382C2211yescharacteristic
26C61×#376—21no—
27C2×#11758202—41no—
28C2×#11758194—21no—
29#14519776—41no—
30#14519768—41no—
31#14519756—21no—
32#14519756—21no—
33#14519736—21no—
34#14519710—41no—
35#14519710—41no—
36#14519708—41no—
37#14519701—41no—
38#14519700—41no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22×Q8×C61D411yescharacteristic
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61—21no—
45C2×C4⋊C4×C61—21no—
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61C2311yescharacteristic
49C2×C42×C61—21no—
50C2×C42×C61—21no—
51C2×C42×C61D411yescharacteristic
52#95×C61—21no—
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—42no—
63C2×Q8×C61—41no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C2×Dic122—21no—
74C2×Dic122—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—42no—
77C4⋊C4×C61—42no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—81no—
82C42×C61—21no—
83C42×C61—42no—
84C42×C61—42no—
85C42×C61Q1612yescomplemented
86C22⋊Dic61—41no—
87#11758202—82no—
88C4⋊Dic61—21no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92#11758196—41no—
93#11758196—41no—
94C4×Dic61—41no—
95#11758194—22no—
96#11758194—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C23×C61#12011yescharacteristic
101Q8×C61—42no—
102Q8×C61—81no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—22no—
106C2×C4×C61—22no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
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×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×C61C2×Q1611yescharacteristic
128C2×C4×C61#13711yescharacteristic
129C2×Dic61—41no—
130C2×Dic61—41no—
131Dic122—81no—
132Dic122—81no—
133#92418—42no—
134#92418—81no—
135#92418—81no—
136#12258—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61#45111yescharacteristic
140C22×C61#45611yescharacteristic
141C22×C61B(4,𝔽2)11yescharacteristic
142C4×C61—21no—
143C4×C61—21no—
144C4×C61—42no—
145C4×C61—42no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—42no—
149C4×C61—81no—
150C4×C61—81no—
151C4×C61—81no—
152Dic61—81no—
153Dic61—81no—
154#2612D6111yescharacteristic
155#2061—611no—
156#1617—611no—
157#1605—611no—
158#1354—611no—
159#1353—611no—
160#1324—611no—
161C2×C61—21no—
162C2×C61—21no—
163C2×C61#160511yescharacteristic
164C2×C61#219711yescharacteristic
165C2×C61#220411yescharacteristic
166#544—611no—
167#484—1221no—
168#451—1221no—
169#428—1221no—
170#400C2×D6111yescharacteristic
171#398—21no—
172#395C2×D6111yescharacteristic
173#391—21no—
174#389—21no—
175#387—21no—
176#387—21no—
177#382C2×D6111yescharacteristic
178#376—21no—
179#343—611no—
180#339—1221no—
181#328—1221no—
182#328—1221no—
183#324—611no—
184#324—611no—
185C61#1225811yescharacteristic, complemented, Sylow
186C22×Q8C22⋊D6111yescharacteristic
187C2×Q16—2441no—
188C2×M16—1221no—
189C4⋊Q8—2441no—
190#125—2441no—
191C22⋊Q8—1221no—
192C22⋊Q8—1221no—
193#117—1221no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C22⋊D6111yescharacteristic
199C2×C4⋊C4C22⋊D6111yescharacteristic
200C2×C4⋊C4C22×D6111yescharacteristic
201C2×C42—21no—
202C2×C42—21no—
203C2×C42C22⋊D6111yescharacteristic
204#107—2441no—
205#107—2441no—
206#106—2441no—
207#103—2441no—
208#103—2441no—
209C22⋊C8—1221no—
210C22⋊C8—1221no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C22⋊D6111yescharacteristic
220#95C22⋊D6111yescharacteristic
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—1221no—
224C2×Q8—1221no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4C2×C22⋊D6111yescharacteristic
232C22×C4C2×C22⋊D6111yescharacteristic
233C22×C4C2×C22⋊D6111yescharacteristic
234Q16—4882no—
235M16—1222no—
236M16—2441no—
237C2×C8—2441no—
238C2×C8—2441no—
239C2×C8—2441no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—81no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—2441no—
252C4⋊C4—2441no—
253C22⋊C4—2441no—
254C42—21no—
255C42—42no—
256C42—42no—
257C42—2441no—
258C42#1175820212yescomplemented
259C23#1451974611yescharacteristic
260Q8—42no—
261Q8—81no—
262Q8—4881no—
263Q8—4881no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4C2×#1175820211yescharacteristic
291C2×C4#1451980811yescharacteristic
292C8—4881no—
293C8—4881no—
294C8—2442no—
295C22—21no—
296C22—21no—
297C22#1683991811yescharacteristic
298C22#1683994511yescharacteristic
299C22#1683994911yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—42no—
304C4—41no—
305C4—41no—
306C4—42no—
307C4—81no—
308C4—81no—
309C4—81no—
310C4—4881no—
311C4—4881no—
312C2—21no—
313C2—21no—
314C2#2144479311yescharacteristic
315C2#2144780911yescharacteristic
316C2#2144784511yescharacteristic
subgroupG/H
centerC22#16839949
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2612C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#2612D61
hypocenterC61#12258
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2612

Complements

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

NH ≅ G/Ntype
85. C42×C61Q16semidirect
185. C61#12258semidirect
258. C42#11758202semidirect

Maximal subgroups

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

subgroupindex
#214471692
#214448602
#214447922
#214438492
#214438462
#214437632
C61×#26122
#1225861