Finite Group Databasebeta

← #29592348

Subgroups — #29592348

Order 15616.

354 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 55 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#21453643C211yesmaximal, characteristic, complemented
2#21447040C211yesmaximal, characteristic
3#21444856C211yesmaximal, characteristic
4#21443847C211yesmaximal, characteristic, complemented
5#21443825C211yesmaximal, characteristic, complemented
6#21443764C211yesmaximal, characteristic, complemented
7C61×#1610C211yesmaximal, characteristic
8#16840078—21no—
9C2×#14519704—21no—
10#16839763—21no—
11#16839703—21no—
12#16839703—21no—
13#16839701C2211yescharacteristic
14#16839649—21no—
15#16839648—21no—
16#16839643—21no—
17#16839643—21no—
18#16839631C2211yescharacteristic
19#16839531C2211yescharacteristic
20#16839496—21no—
21#16839488C2211yescharacteristic
22C61×#537C2211yescharacteristic
23C61×#480—21no—
24C61×#398C2211yescharacteristic
25C61×#327—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61D411yescharacteristic
29C2×C4⋊Dic61D411yescharacteristic
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61D411yescharacteristic
35#14519708—41no—
36#14519704—42no—
37#14519701—41no—
38#14519698—41no—
39#14519698—41no—
40C22⋊#92418—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684D411yescharacteristic
50C2×#41×C61—21no—
51C22⋊Q8×C61—41no—
52#121×C61—21no—
53#121×C61—21no—
54#121×C61—41no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61D411yescharacteristic
57C2×C4⋊C4×C61C2311yescharacteristic
58#107×C61—41no—
59#102×C61—41no—
60C22⋊C8×C61—21no—
61#95×C61—21no—
62#95×C61D411yescharacteristic
63#41×C61—41no—
64#41×C61—41no—
65#41×C61—41no—
66#41×C61—41no—
67C2×Q8×C61—21no—
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—21no—
71C2×D4×C61—41no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—41no—
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C2×C8×C61—41no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C4⋊Dic61—41no—
92C4⋊Dic61—41no—
93#11758196—42no—
94#11758196—42no—
95#11758196—42no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—81no—
99#11758194—41no—
100#11758194—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C23×C61—41no—
104C23×C61#12011yescharacteristic
105Q8×C61—41no—
106Q8×C61—41no—
107D4×C61—41no—
108D4×C61—41no—
109D4×C61—81no—
110D4×C61—81no—
111D4×C61—81no—
112D4×C61—81no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
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—81no—
127C2×C4×C61—81no—
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—42no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C8×C61—81no—
142#92418—81no—
143#92418—81no—
144#12142—611nomaximal, Sylow
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—81no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61#44911yescharacteristic
151C22×C61#45411yescharacteristic
152C22×C61B(4,𝔽2)11yescharacteristic
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61—81no—
160Dic61—42no—
161Dic61—81no—
162Dic61—81no—
163Dic61—81no—
164#2794—611no—
165#2039—611no—
166#1616—611no—
167#1610D6111yescharacteristic
168#1353—611no—
169#1346—611no—
170#1325—611no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61—161no—
174C2×C61#159711yescharacteristic
175C2×C61#219811yescharacteristic
176C2×C61#220311yescharacteristic
177#537C2×D6111yescharacteristic
178#481—1221no—
179#480—21no—
180C2×#104—1221no—
181#417—1221no—
182#400—611no—
183#400—1221no—
184#400—1221no—
185#398C2×D6111yescharacteristic
186#387—1221no—
187#387—1221no—
188#387—1221no—
189#387—1221no—
190#384—611no—
191#343—611no—
192#327—21no—
193#327—1221no—
194#324—611no—
195#324C2×D6111yescharacteristic
196C61#1214211yescharacteristic, complemented, Sylow
197C2×#41—21no—
198C2×M16—1221no—
199C22⋊Q8—41no—
200#121—21no—
201#121—21no—
202#121—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C22⋊D6111yescharacteristic
210C2×C4⋊C4C22×D6111yescharacteristic
211C2×C42—611no—
212C2×C42—1221no—
213#107—41no—
214#106—2441no—
215#104—2442no—
216#103—2441no—
217#102—41no—
218#102—2441no—
219#102—2441no—
220C22⋊C8—21no—
221C22⋊C8—1221no—
222#95—21no—
223#95—611no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95C22⋊D6111yescharacteristic
233#41—41no—
234#41—41no—
235#41—41no—
236#41—41no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4D4×D6111yescharacteristic
250C22×C4D4×D6111yescharacteristic
251C22×C4C2×C22⋊D6111yescharacteristic
252M16—2441no—
253M16—2441no—
254C2×C8—41no—
255C2×C8—2441no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2442no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—1221no—
271C42—1221no—
272C42—4881no—
273C23—41no—
274C23#1451974511yescharacteristic
275Q8—41no—
276Q8—41no—
277D4—41no—
278D4—41no—
279D4—81no—
280D4—81no—
281D4—81no—
282D4—81no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
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—81no—
297C2×C4—81no—
298C2×C4—1222no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2442no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451979611yescharacteristic
310C2×C4#1451980111yescharacteristic
311C8—81no—
312C8—4881no—
313C8—4881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1683990411yescharacteristic
320C22#1683993311yescharacteristic
321C22#1683994811yescharacteristic
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—81no—
327C4—81no—
328C4—81no—
329C4—4881no—
330C4—4881no—
331C4—4881no—
332C4—2442no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2144474511yescharacteristic
337C2#2144781311yescharacteristic
338C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1610C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#537C22
hypercenter#1610D61
hypocenterC61#12142
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1610

Complements

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

NH ≅ G/Ntype
1. #21453643C2semidirect
4. #21443847C2semidirect
5. #21443825C2semidirect
6. #21443764C2semidirect
196. C61#12142semidirect

Maximal subgroups

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

subgroupindex
#214536432
#214470402
#214448562
#214438472
#214438252
#214437642
C61×#16102
#1214261