Finite Group Databasebeta

← #29569080

Subgroups — #29569080

Order 15616.

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

normal subgroups only

This group has 374 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#21452770C211yesmaximal, characteristic
2#21447377C211yesmaximal, characteristic
3#21447292C211yesmaximal, characteristic
4#21447292C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443643C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519768—21no—
9C2×#14519711—21no—
10C2×#14519711—21no—
11#16839695—21no—
12#16839695—21no—
13#16839694—21no—
14#16839660C2211yescharacteristic
15#16839660C2211yescharacteristic
16#16839659—21no—
17#16839648—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839524—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×#92418—21no—
28#14519768—42no—
29#14519768—42no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519711—42no—
45#14519711—42no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C22×C8×C61—21no—
52C22×C8×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61C2311yescharacteristic
57#95×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—41no—
68C2×C8×C61—22no—
69C2×C8×C61—22no—
70C2×C8×C61—41no—
71C2×C8×C61—41no—
72C2×C8×C61—41no—
73C2×C8×C61—41no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61Q1612yes—
79C42×C61—41no—
80C4⋊Dic61—21no—
81C4⋊Dic61—21no—
82C4⋊Dic61—21no—
83C4⋊Dic61—42no—
84C4⋊Dic61—42no—
85C4⋊Dic61—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—42no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61D812yes—
93#11758196—42no—
94#11758196—41no—
95#11758196—41no—
96#11758196—41no—
97#11758196—41no—
98#11758196—81no—
99C4×Dic61—42no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61#12011yescharacteristic
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—22no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61C2×D811yescharacteristic
117C2×C4×C61C2×Q1611yescharacteristic
118C2×C4×C61#13511yescharacteristic
119C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C61#13711yescharacteristic
122C2×Dic61—22no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C8×C61—42no—
138C8×C61—42no—
139#92418—81no—
140#7792—611nomaximal, Sylow
141C22×C61#44711yescharacteristic
142C22×C61#44911yescharacteristic
143C22×C61#45111yescharacteristic
144C22×C61#45411yescharacteristic
145C22×C61#45611yescharacteristic
146C22×C61#45611yescharacteristic
147C22×C61#45811yescharacteristic
148C4×C61—21no—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—42no—
155C4×C61—81no—
156Dic61—42no—
157Dic61—81no—
158Dic61—81no—
159Dic61—81no—
160Dic61—161no—
161#2726—611no—
162#2099—611no—
163#2083—611no—
164#2083—611no—
165#1271—611no—
166#1271—611no—
167#1271D6111yescharacteristic
168C2×C61#160911yescharacteristic
169C2×C61#161011yescharacteristic
170C2×C61#161711yescharacteristic
171C2×C61#162511yescharacteristic
172C2×C61#164811yescharacteristic
173C2×C61#164911yescharacteristic
174C2×C61#166311yescharacteristic
175C2×#125—1221no—
176C2×#107—1221no—
177C2×#107—1221no—
178#398—1221no—
179#398—1221no—
180#398—1221no—
181#389—611no—
182#389—611no—
183#389—1221no—
184#389C2×D6111yescharacteristic
185#387—1221no—
186#384—611no—
187#340—1221no—
188#340—1221no—
189#340—1221no—
190#340—1221no—
191#336—611no—
192#336C2×D6111yescharacteristic
193#336C2×D6111yescharacteristic
194C61#779211yescharacteristic, complemented, Sylow
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1221no—
198#125—2442no—
199#125—2442no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—611no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4—1221no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4—1221no—
214C2×C4⋊C4D24411yescharacteristic
215C2×C4⋊C4D24411yescharacteristic
216C2×C42—1221no—
217C2×C42C22×D6111yescharacteristic
218#107—2442no—
219#107—2442no—
220#95—21no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—1221no—
229C22×C4—1221no—
230C22×C4—1221no—
231C22×C4—1221no—
232C22×C4—2441no—
233C22×C4C2×D24411yescharacteristic
234C22×C4D4×D6111yescharacteristic
235C22×C4D4×D6111yescharacteristic
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—2441no—
243C2×C8—2441no—
244C2×C8—2441no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—612no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—4881no—
254C4⋊C4—2442no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2442no—
258C4⋊C4—2442no—
259C4⋊C4—2442no—
260C4⋊C4—2441no—
261C4⋊C4—2441no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4Dic24412yes—
269C42—41no—
270C42—2442no—
271C23#1451974711yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—1222no—
285C2×C4—4881no—
286C2×C4—4881no—
287C2×C4—4881no—
288C2×C4—2441no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4—2441no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4D8×D6111yescharacteristic
300C2×C4C2×Dic24411yescharacteristic
301C2×C4#1451980011yescharacteristic
302C2×C4#1451980411yescharacteristic
303C2×C4#1451980411yescharacteristic
304C2×C4#1451981011yescharacteristic
305C8—42no—
306C8—42no—
307C8—4881no—
308C22#1683989711yescharacteristic
309C22#1683991011yescharacteristic
310C22#1683992011yescharacteristic
311C22#1683993711yescharacteristic
312C22#1683994611yescharacteristic
313C22#1683994611yescharacteristic
314C22#1683995311yescharacteristic
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—42no—
322C4—81no—
323C4—9761no—
324C4—4881no—
325C4—4881no—
326C4—4881no—
327C4—2442no—
328C2#2144481911yescharacteristic
329C2#2144482311yescharacteristic
330C2#2144486311yescharacteristic
331C2#2144490911yescharacteristic
332C2#2144506411yescharacteristic
333C2#2144507111yescharacteristic
334C2#2144514811yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61#120
hypercenter#1271D61
hypocenterC61#7792
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
194. C61#7792semidirect

Maximal subgroups

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

subgroupindex
#214527702
#214473772
#214472922
#214436432
C61×#12712
#779261