Finite Group Databasebeta

← #29581434

Subgroups — #29581434

Order 15616.

474 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 83 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#21456200C211yesmaximal, characteristic
3#21451940C211yesmaximal, characteristic
4#21444544C211yesmaximal, characteristic
5#21444332C211yesmaximal, characteristic
6#21443713C211yesmaximal, characteristic
7C61×#1528C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840172—21no—
11#16840132—21no—
12#16840131—22no—
13#16840113—21no—
14#16840113—21no—
15#16840097—21no—
16#16840092—21no—
17#16840066—22no—
18#16839819C2211yescharacteristic
19#16839772—22no—
20#16839692—22no—
21#16839682—22no—
22#16839631—21no—
23#16839627—21no—
24#16839608C2211yescharacteristic
25#16839510—22no—
26#16839500—22no—
27C2×#125×C61C2211yescharacteristic
28C61×#432C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C61×#330—22no—
31C22×Dic122D412yes—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777D411yescharacteristic
37#14519777D411yescharacteristic
38#14519769—21no—
39#14519756—21no—
40#14519756—21no—
41C4×Dic122—21no—
42C4×Dic122—21no—
43#14519736—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—24no—
47C2×C4×Dic61—21no—
48#14519710—22no—
49#14519708—22no—
50C4⋊#92418D412yes—
51#14519702—24no—
52#14519702—24no—
53#14519700—22no—
54#14519700—22no—
55C22⋊#92418—21no—
56#14519688—21no—
57#14519684—24no—
58#14519684—21no—
59#14519684D412yes—
60C2×M16×C61—21no—
61#125×C61—21no—
62#125×C61—21no—
63#125×C61—21no—
64#125×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C4⋊C4×C61D411yescharacteristic
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72#97×C61—21no—
73#97×C61D412yes—
74C4×C8×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—22no—
81C22×Dic61—22no—
82C2×Dic122—22no—
83C2×Dic122—21no—
84C2×Dic122—22no—
85C2×Dic122—21no—
86C2×Dic122—44no—
87M16×C61—42no—
88C2×C8×C61—22no—
89C2×C8×C61—41no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61—41no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C4⋊C4×C61—41no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61#4111yescharacteristic
102C22⋊Dic61—41no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106C4⋊Dic61—21no—
107C4⋊Dic61—41no—
108C4⋊Dic61—41no—
109C4⋊Dic61—41no—
110C4⋊Dic61—41no—
111#11758196—41no—
112#11758196—41no—
113#11758196—84no—
114C4×Dic61—24no—
115C4×Dic61—41no—
116C2×#92418—22no—
117C23×C61#12011yescharacteristic
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—41no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61#12011yescharacteristic
127C2×C4×C61#12111yescharacteristic
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61#12711yescharacteristic
131C2×Dic61—24no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—42no—
137C2×Dic61—44no—
138Dic122—44no—
139Dic122—42no—
140Dic122—81no—
141Dic122—82no—
142C8×C61—42no—
143C8×C61—81no—
144#92418—42no—
145#10099—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#39211yescharacteristic
149C22×C61#45512yes—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—81no—
156C4×C61—81no—
157C4×C61#45612yes—
158Dic61—44no—
159Dic61—82no—
160Dic61—81no—
161Dic61—81no—
162#3236—611no—
163#3139—611no—
164#2660—611no—
165#1558—611no—
166#1528D6111yescharacteristic
167#1506—611no—
168#1300—611no—
169C2×C61—22no—
170C2×C61#200411yescharacteristic
171C2×C61#200511yescharacteristic
172C2×C61#200911yescharacteristic
173#533—611no—
174C2×C4⋊Q8—611no—
175C2×#125C2×D6111yescharacteristic
176#501—1221no—
177#491—1221no—
178#491—1222no—
179#487—1221no—
180#487—1221no—
181#484—1221no—
182#483—1221no—
183#479—1222no—
184#432—611no—
185#432C2×D6111yescharacteristic
186#419—1222no—
187C4×M16C2×D6111yescharacteristic
188#398—1222no—
189#395—1222no—
190#384—1221no—
191#382—1221no—
192#376—611no—
193#333—1222no—
194#330—22no—
195#328—1222no—
196C61#1009911yescharacteristic, complemented, Sylow
197C22×Q8—612no—
198C2×M16—21no—
199C4⋊Q8—611no—
200C4⋊Q8—611no—
201C4⋊Q8—1221no—
202C4⋊Q8—1221no—
203C4⋊Q8—1221no—
204C4⋊Q8—1221no—
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—1224no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4D24411yescharacteristic
221C2×C4⋊C4D24411yescharacteristic
222C2×C42—1221no—
223C2×C42C22×D6111yescharacteristic
224#107—1222no—
225#106—1222no—
226C4⋊C8—21no—
227C4⋊C8—612no—
228#103—1222no—
229#103—1222no—
230#103—1224no—
231#103—1224no—
232C22⋊C8—21no—
233C22⋊C8—1221no—
234#97—21no—
235#97—1221no—
236#97C22⋊D6112yes—
237C4×C8—21no—
238#95—612no—
239#95—1224no—
240#95—1221no—
241C2×Q8—1222no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1222no—
245C2×Q8—2444no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1222no—
249C22×C4—1222no—
250C22×C4C2×D24411yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4D4×D6111yescharacteristic
253M16—42no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—1222no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1221no—
266C4⋊C4—1221no—
267C4⋊C4—1221no—
268C4⋊C4—1221no—
269C4⋊C4—4884no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C22⋊C4—2441no—
277C42—1224no—
278C42—2441no—
279C42#1175822211yescharacteristic
280C42D4×D6111yescharacteristic
281C42D4×D6111yescharacteristic
282C42C2×C22⋊D6111yescharacteristic
283C23#1451974711yescharacteristic
284Q8—4881no—
285Q8—4882no—
286Q8—2444no—
287Q8—2442no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—1224no—
296C2×C4—2444no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2442no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4#1451974511yescharacteristic
303C2×C4#1451974711yescharacteristic
304C2×C4#1451975011yescharacteristic
305C2×C4#1451975011yescharacteristic
306C2×C4#1451975111yescharacteristic
307C2×C4#1451977311yescharacteristic
308C8—42no—
309C8—81no—
310C8—2442no—
311C22—21no—
312C22—21no—
313C22#1683967111yescharacteristic
314C22#1683994112yes—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—81no—
321C4—81no—
322C4—4882no—
323C4—4881no—
324C4—4881no—
325C4—2444no—
326C4#1683994712yes—
327C2—22no—
328C2#2144684711yescharacteristic
329C2#2144685711yescharacteristic
330C2#2144688011yescharacteristic
subgroupG/H
centerC22#16839671
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1528C2
socleC22×C61#392
prime radicalC23×C61#120
hypercenter#1528D61
hypocenterC61#10099
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
196. C61#10099semidirect

Maximal subgroups

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

subgroupindex
#214570252
#214562002
#214519402
#214445442
#214443322
#214437132
C61×#15282
#1009961