Finite Group Databasebeta

← #29581446

Subgroups — #29581446

Order 15616.

474 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 85 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#21457025C211yesmaximal, characteristic
2#21456361C211yesmaximal, characteristic
3#21444536C211yesmaximal, characteristic
4#21444421C211yesmaximal, characteristic
5#21444330C211yesmaximal, characteristic
6#21443712C211yesmaximal, characteristic
7C61×#2660C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840172—21no—
10#16840168—22no—
11#16840165—21no—
12#16840158—21no—
13#16840132—21no—
14#16840097—21no—
15#16840092—21no—
16#16840066—22no—
17#16839819C2211yescharacteristic
18#16839819C2211yescharacteristic
19#16839802—22no—
20C4×#11758194C2211yescharacteristic
21#16839508—22no—
22#16839504—22no—
23#16839498—22no—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×#125×C61C2211yescharacteristic
26C61×#398—22no—
27C61×#395—22no—
28C61×#384—21no—
29C61×#382—21no—
30C61×#376C2211yescharacteristic
31C2×#11758194—21no—
32#14519777D411yescharacteristic
33#14519777D411yescharacteristic
34#14519769—21no—
35#14519756—21no—
36#14519756—21no—
37C4×Dic122—21no—
38C4×Dic122—21no—
39#14519736—21no—
40#14519710—24no—
41#14519710—22no—
42#14519708—24no—
43#14519708—22no—
44C4⋊#92418—21no—
45C4⋊#92418D412yes—
46#14519700—22no—
47#14519700—22no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519688—21no—
51#14519688—21no—
52#14519688D412yes—
53C4×#92418—21no—
54C22×Q8×C61—21no—
55C4⋊Q8×C61—21no—
56C4⋊Q8×C61—21no—
57C4⋊Q8×C61—21no—
58C4⋊Q8×C61—21no—
59#125×C61—21no—
60#125×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61D412yes—
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C4⋊C4×C61D411yescharacteristic
70C2×C42×C61—21no—
71C2×C42×C61C2311yescharacteristic
72#95×C61—24no—
73#95×C61—21no—
74#95×C61D412yes—
75C2×Q8×C61—41no—
76C2×Q8×C61—41no—
77C2×Q8×C61—82no—
78C22×C4×C61—22no—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×D411yescharacteristic
84C22×C4×C61C2×D411yescharacteristic
85C2×Dic122—21no—
86C2×Dic122—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—22no—
93C4⋊C4×C61—41no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—84no—
100C42×C61—24no—
101C42×C61C2×D411yescharacteristic
102C42×C61C2×D411yescharacteristic
103C42×C61C2×D411yescharacteristic
104C42×C61#4111yescharacteristic
105C22⋊Dic61—41no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110#11758196—41no—
111#11758196—41no—
112C4×Dic61—41no—
113#11758194—24no—
114C2×#92418—22no—
115C2×#92418—22no—
116C2×#92418—41no—
117C23×C61#12011yescharacteristic
118Q8×C61—82no—
119Q8×C61—82no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—24no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—44no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61#12011yescharacteristic
133C2×C4×C61#12011yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12711yescharacteristic
138C2×Dic61—41no—
139C2×Dic61—41no—
140Dic122—42no—
141Dic122—81no—
142#92418—24no—
143#92418—42no—
144#92418—81no—
145#10101—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#39211yescharacteristic
149C22×C61#45612yes—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—44no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—82no—
159C4×C61#45612yes—
160Dic61—81no—
161Dic61—81no—
162#3236—611no—
163#3165—611no—
164#2660D6111yescharacteristic
165#1556—611no—
166#1528—611no—
167#1506—611no—
168#1300—611no—
169C2×C61—22no—
170C2×C61#200511yescharacteristic
171C2×C61#200511yescharacteristic
172C2×C61#200811yescharacteristic
173#533—611no—
174C2×C4⋊Q8C2×D6111yescharacteristic
175C2×#125C2×D6111yescharacteristic
176#501—1222no—
177#501—1221no—
178#500—1221no—
179#498—1221no—
180#491—1221no—
181#484—1221no—
182#483—1221no—
183#479—1222no—
184#432—611no—
185#432—611no—
186#428—1222no—
187C4×M16—611no—
188#398—22no—
189#395—22no—
190#384—21no—
191#382—21no—
192#376C2×D6111yescharacteristic
193#332—1222no—
194#330—1222no—
195#328—1222no—
196C61#1010111yescharacteristic, complemented, Sylow
197C22×Q8—21no—
198C2×M16—1221no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—611no—
204C4⋊Q8—611no—
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—1221no—
210C22⋊Q8—1221no—
211C22⋊Q8—1221no—
212C4×Q8—1221no—
213C4×Q8—1221no—
214#117—1221no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4C22⋊D6111yescharacteristic
220C2×C4⋊C4C22⋊D6111yescharacteristic
221C2×C4⋊C4C22⋊D6112yes—
222C2×C42—21no—
223C2×C42C22×D6111yescharacteristic
224#107—1224no—
225#107—1222no—
226#106—1224no—
227#106—1222no—
228C4⋊C8—612no—
229C4⋊C8—1221no—
230#103—1222no—
231#103—1222no—
232C22⋊C8—1221no—
233C22⋊C8—1221no—
234#97—612no—
235#97—1221no—
236#97—1221no—
237C4×C8—1221no—
238#95—24no—
239#95—21no—
240#95C22⋊D6112yes—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—82no—
244C2×Q8—1221no—
245C2×Q8—1221no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4C2×C22⋊D6111yescharacteristic
251C22×C4C2×C22⋊D6111yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—1224no—
254C2×C8—1222no—
255C2×C8—1222no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—84no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C22⋊C4—2441no—
277C42—24no—
278C42—2441no—
279C42D4×D6111yescharacteristic
280C42D4×D6111yescharacteristic
281C42D4×D6111yescharacteristic
282C42#1175822411yescharacteristic
283C23#1451974611yescharacteristic
284Q8—82no—
285Q8—82no—
286Q8—4881no—
287Q8—2442no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—24no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4#1451974511yescharacteristic
303C2×C4#1451974511yescharacteristic
304C2×C4#1451974811yescharacteristic
305C2×C4#1451974911yescharacteristic
306C2×C4#1451974911yescharacteristic
307C2×C4#1451977311yescharacteristic
308C8—1224no—
309C8—4881no—
310C8—2442no—
311C22—21no—
312C22—21no—
313C22#1683967011yescharacteristic
314C22#1683994512yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—44no—
321C4—81no—
322C4—81no—
323C4—82no—
324C4—4881no—
325C4—4881no—
326C4#1683994412yes—
327C2—22no—
328C2#2144685311yescharacteristic
329C2#2144685511yescharacteristic
330C2#2144687211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2660C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#2660D61
hypocenterC61#10101
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2660

Complements

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

NH ≅ G/Ntype
196. C61#10101semidirect

Maximal subgroups

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

subgroupindex
#214570252
#214563612
#214445362
#214444212
#214443302
#214437122
C61×#26602
#1010161