Finite Group Databasebeta

← #29569178

Subgroups — #29569178

Order 15616.

366 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 87 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#21447362C211yesmaximal, characteristic
2#21447295C211yesmaximal, characteristic
3#21447290C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic
5#21443642C211yesmaximal, characteristic
6#21443642C211yesmaximal, characteristic
7C61×#2805C211yesmaximal, characteristic
8C2×#14519710—21no—
9C2×#14519708—21no—
10C2×#14519708—21no—
11C2×#14519701—21no—
12#16839632C2211yescharacteristic
13#16839524—21no—
14#16839524—21no—
15#16839517C2211yescharacteristic
16#16839517C2211yescharacteristic
17#16839517C2211yescharacteristic
18C61×#400—21no—
19C61×#400—21no—
20C61×#395—21no—
21C61×#391C2211yescharacteristic
22C61×#389—21no—
23C61×#389C2211yescharacteristic
24C61×#389C2211yescharacteristic
25C61×#387—21no—
26C61×#387—21no—
27C22×#92418—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33#14519710—42no—
34#14519708—42no—
35#14519708—42no—
36#14519701—42no—
37C22×Q8×C61D411yescharacteristic
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61—21no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61D411yescharacteristic
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61D411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C42×C61—21no—
48C2×C42×C61C2311yescharacteristic
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57#95×C61—21no—
58C2×Q8×C61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61—41no—
61C2×Q8×C61—41no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×Dic61—41no—
72C4⋊C4×C61—21no—
73C4⋊C4×C61—21no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—41no—
77C4⋊C4×C61—41no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—81no—
83C4⋊C4×C61—81no—
84C4⋊C4×C61SD1612yes—
85C42×C61—41no—
86C42×C61—81no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93C2×#92418—22no—
94C2×#92418—22no—
95C2×#92418—22no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C23×C61#12011yescharacteristic
103Q8×C61—42no—
104Q8×C61—81no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
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×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61C2×SD1611yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61#13511yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138#92418—42no—
139#92418—42no—
140#92418—42no—
141#7807—611nomaximal, Sylow
142C22×C61#44811yescharacteristic
143C22×C61#44911yescharacteristic
144C22×C61#45211yescharacteristic
145C22×C61#45311yescharacteristic
146C22×C61#45611yescharacteristic
147C22×C61#45611yescharacteristic
148C22×C61#45811yescharacteristic
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—42no—
156C4×C61—81no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61—81no—
160C4×C61—81no—
161Dic61—161no—
162#2805D6111yescharacteristic
163#2096—611no—
164#2084—611no—
165#2083—611no—
166#1272—611no—
167#1271—611no—
168#1271—611no—
169C2×C61#160911yescharacteristic
170C2×C61#161111yescharacteristic
171C2×C61#161811yescharacteristic
172C2×C61#162211yescharacteristic
173C2×C61#165011yescharacteristic
174C2×C61#165311yescharacteristic
175C2×C61#166011yescharacteristic
176C2×#107—1221no—
177C2×#106—1221no—
178C2×#106—1221no—
179C2×#103—1221no—
180#400—21no—
181#400—21no—
182#395—21no—
183#391C2×D6111yescharacteristic
184#389—21no—
185#389C2×D6111yescharacteristic
186#389C2×D6111yescharacteristic
187#387—21no—
188#387—21no—
189#384—611no—
190#340—1221no—
191#340—1221no—
192#336—611no—
193#336—611no—
194#336—611no—
195C61#780711yescharacteristic, complemented, Sylow
196C22×Q8C22⋊D6111yescharacteristic
197C22×C8—1221no—
198C22×C8—1221no—
199C22×C8—1221no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4C22⋊D6111yescharacteristic
208C2×C4⋊C4C22⋊D6111yescharacteristic
209C2×C4⋊C4C22⋊D6111yescharacteristic
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C4⋊C4C22⋊D6111yescharacteristic
212C2×C42—21no—
213C2×C42C22×D6111yescharacteristic
214#107—2442no—
215#106—2442no—
216#106—2442no—
217#103—2442no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—2441no—
238C22×C4C2×C22⋊D6111yescharacteristic
239C22×C4C2×C22⋊D6111yescharacteristic
240C22×C4C2×C22⋊D6111yescharacteristic
241C2×C8—1222no—
242C2×C8—1222no—
243C2×C8—1222no—
244C2×C8—2441no—
245C2×C8—2441no—
246C2×C8—2441no—
247C2×C8—2441no—
248C2×C8—2441no—
249C2×C8—2441no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—2441no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4#1175820112yes—
269C42—41no—
270C42—81no—
271C23#1451974611yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—4881no—
301C2×C4C2×#1175820111yescharacteristic
302C2×C4#1451979711yescharacteristic
303C2×C4#1451979711yescharacteristic
304C2×C4#1451980211yescharacteristic
305C2×C4#1451980711yescharacteristic
306C2×C4#1451980811yescharacteristic
307C8—2442no—
308C8—2442no—
309C8—2442no—
310C22#1683990111yescharacteristic
311C22#1683990711yescharacteristic
312C22#1683992411yescharacteristic
313C22#1683993011yescharacteristic
314C22#1683994511yescharacteristic
315C22#1683994511yescharacteristic
316C22#1683995211yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—42no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—9761no—
330C2#2144481611yescharacteristic
331C2#2144482711yescharacteristic
332C2#2144486711yescharacteristic
333C2#2144489111yescharacteristic
334C2#2144507511yescharacteristic
335C2#2144509611yescharacteristic
336C2#2144513011yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2805C2
socle, prime radicalC23×C61#120
hypercenter#2805D61
hypocenterC61#7807
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2805

Complements

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

NH ≅ G/Ntype
195. C61#7807semidirect

Maximal subgroups

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

subgroupindex
#214473622
#214472952
#214472902
#214436452
#214436422
C61×#28052
#780761