Finite Group Databasebeta

← #29581444

Subgroups — #29581444

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#21456366C211yesmaximal, characteristic
2#21451940C211yesmaximal, characteristic
3#21444535C211yesmaximal, characteristic
4#21444421C211yesmaximal, characteristic
5#21444331C211yesmaximal, characteristic
6#21443711C211yesmaximal, characteristic
7C61×#3236C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9#16840172—22no—
10#16840165—21no—
11#16840158—21no—
12#16839819C2211yescharacteristic
13#16839805—22no—
14C4×#11758194C2211yescharacteristic
15#16839692—22no—
16#16839682—22no—
17#16839631—21no—
18#16839627—21no—
19#16839608C2211yescharacteristic
20#16839507—22no—
21#16839504—22no—
22#16839499—22no—
23C61×#533C2211yescharacteristic
24C2×#125×C61C2211yescharacteristic
25C61×#501—21no—
26C61×#491—21no—
27C61×#484—21no—
28C61×#483—21no—
29C61×#479—22no—
30C61×#432C2211yescharacteristic
31C22×Dic122—21no—
32C2×#11758194—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61D412yes—
39C2×#11758196—24no—
40C2×C4×Dic61—21no—
41#14519710—24no—
42#14519708—24no—
43C4⋊#92418—21no—
44C22⋊#92418—21no—
45#14519688—21no—
46#14519688D412yes—
47C4×#92418—21no—
48#14519684—24no—
49#14519684—21no—
50#14519684D412yes—
51C4⋊Q8×C61D411yescharacteristic
52C4⋊Q8×C61D411yescharacteristic
53#125×C61—21no—
54#125×C61—21no—
55#125×C61—21no—
56#125×C61—21no—
57#125×C61—21no—
58C22⋊Q8×C61—21no—
59C22⋊Q8×C61—21no—
60C4×Q8×C61—21no—
61C4×Q8×C61—21no—
62#117×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C42×C61C2311yescharacteristic
68#107×C61—22no—
69#106×C61—22no—
70C4⋊C8×C61D412yes—
71#103×C61—22no—
72#103×C61—22no—
73C22⋊C8×C61—21no—
74#97×C61—21no—
75C2×Q8×C61—21no—
76C2×Q8×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—22no—
83C22×Dic61—22no—
84C2×Dic122—41no—
85C2×Dic122—41no—
86C2×Dic122—82no—
87C2×C8×C61—22no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C4⋊C4×C61—41no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61—41no—
102C22⋊C4×C61—41no—
103C42×C61—41no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61#4111yescharacteristic
108C4⋊Dic61—22no—
109C4⋊Dic61—22no—
110C4⋊Dic61—41no—
111C4⋊Dic61—41no—
112#11758196—84no—
113C4×Dic61—24no—
114#11758194—24no—
115C2×#92418—22no—
116C2×#92418—41no—
117C23×C61#12011yescharacteristic
118Q8×C61—42no—
119Q8×C61—81no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—41no—
123C2×C4×C61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12711yescharacteristic
135C2×Dic61—24no—
136C2×Dic61—42no—
137C2×Dic61—42no—
138C2×Dic61—44no—
139C2×Dic61—42no—
140Dic122—82no—
141Dic122—82no—
142C8×C61—42no—
143#92418—24no—
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—81no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61#45612yes—
160Dic61—44no—
161Dic61—82no—
162#3236D6111yescharacteristic
163#3165—611no—
164#2660—611no—
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#533C2×D6111yescharacteristic
174C2×C4⋊Q8—611no—
175C2×#125C2×D6111yescharacteristic
176#501—21no—
177#501—1222no—
178#500—1221no—
179#498—1221no—
180#491—21no—
181#484—21no—
182#483—21no—
183#479—22no—
184#432—611no—
185#432C2×D6111yescharacteristic
186#428—1222no—
187C4×M16—611no—
188#398—1222no—
189#395—1222no—
190#384—1221no—
191#382—1221no—
192#376—611no—
193#332—1222no—
194#330—1222no—
195#328—1222no—
196C61#1010111yescharacteristic, complemented, Sylow
197C22×Q8—1221no—
198C2×M16—1221no—
199C4⋊Q8—1221no—
200C4⋊Q8—1221no—
201C4⋊Q8—1221no—
202C4⋊Q8—1221no—
203C4⋊Q8C22⋊D6111yescharacteristic
204C4⋊Q8C22⋊D6111yescharacteristic
205#125—21no—
206#125—21no—
207#125—21no—
208#125—21no—
209#125—21no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214#117—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—612no—
218C2×C4⋊C4—1224no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C22⋊D6111yescharacteristic
221C2×C4⋊C4C22⋊D6111yescharacteristic
222C2×C42—1221no—
223C2×C42C22×D6111yescharacteristic
224#107—22no—
225#107—1224no—
226#106—22no—
227#106—1224no—
228C4⋊C8—1221no—
229C4⋊C8C22⋊D6112yes—
230#103—22no—
231#103—22no—
232C22⋊C8—21no—
233C22⋊C8—1221no—
234#97—21no—
235#97—612no—
236#97—1221no—
237C4×C8—1221no—
238#95—612no—
239#95—1224no—
240#95—1221no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—4882no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4D4×D6111yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—1224no—
254C2×C8—22no—
255C2×C8—1222no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—1222no—
272C4⋊C4—1222no—
273C4⋊C4—4884no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C22⋊C4—41no—
277C42—41no—
278C42—1224no—
279C42D4×D6111yescharacteristic
280C42#1175822411yescharacteristic
281C42C2×C22⋊D6111yescharacteristic
282C42C2×C22⋊D6111yescharacteristic
283C23#1451974511yescharacteristic
284Q8—42no—
285Q8—81no—
286Q8—4882no—
287Q8—4882no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—1224no—
298C2×C4—2444no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4#1451974511yescharacteristic
303C2×C4#1451974611yescharacteristic
304C2×C4#1451974811yescharacteristic
305C2×C4#1451974911yescharacteristic
306C2×C4#1451974911yescharacteristic
307C2×C4#1451977311yescharacteristic
308C8—42no—
309C8—1224no—
310C8—4881no—
311C22—21no—
312C22—21no—
313C22#1683967011yescharacteristic
314C22#1683994312yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—4882no—
325C4—2444no—
326C4#1683994512yes—
327C2—22no—
328C2#2144685211yescharacteristic
329C2#2144685311yescharacteristic
330C2#2144686911yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#3236C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#3236D61
hypocenterC61#10101
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

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
#214563662
#214519402
#214445352
#214444212
#214443312
#214437112
C61×#32362
#1010161