Finite Group Databasebeta

← #29592349

Subgroups — #29592349

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#21453639C211yesmaximal, characteristic, complemented
2#21444856C211yesmaximal, characteristic
3#21444822C211yesmaximal, characteristic
4#21443845C211yesmaximal, characteristic, complemented
5#21443824C211yesmaximal, characteristic, complemented
6#21443765C211yesmaximal, characteristic, complemented
7C61×#2039C211yesmaximal, characteristic
8#16840078—21no—
9#16840073—21no—
10#16839701C2211yescharacteristic
11#16839700—21no—
12#16839700—21no—
13#16839692C2211yescharacteristic
14#16839648—21no—
15#16839648—21no—
16#16839646—21no—
17#16839643—21no—
18#16839496—21no—
19#16839496—21no—
20#16839488C2211yescharacteristic
21#16839488C2211yescharacteristic
22C61×#537C2211yescharacteristic
23C2×#104×C61—21no—
24C61×#417—21no—
25C61×#384C2211yescharacteristic
26C61×#343C2211yescharacteristic
27C2×C4⋊Dic61D411yescharacteristic
28C2×C4⋊Dic61D411yescharacteristic
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×C4×Dic61—21no—
32#14519710—41no—
33#14519708—41no—
34#14519698—41no—
35#14519698—41no—
36C22⋊#92418—21no—
37C22⋊#92418—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684D411yescharacteristic
48#14519684D411yescharacteristic
49C2×#41×C61—21no—
50C2×M16×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×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61C2311yescharacteristic
59C2×C42×C61D411yescharacteristic
60#104×C61—42no—
61#103×C61—41no—
62#102×C61—41no—
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—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—42no—
89C4⋊C4×C61—42no—
90C4⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C42×C61—21no—
94C42×C61—21no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97#11758196—42no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—81no—
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—22no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
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—41no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—42no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
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—42no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—81no—
159C4×C61—81no—
160Dic61—81no—
161Dic61—81no—
162Dic61—81no—
163Dic61—81no—
164#2794—611no—
165#2039D6111yescharacteristic
166#1616—611no—
167#1610—611no—
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—1221no—
180C2×#104—21no—
181#417—21no—
182#400—611no—
183#400—1221no—
184#400—1221no—
185#398—611no—
186#387—1221no—
187#387—1221no—
188#387—1221no—
189#387—1221no—
190#384C2×D6111yescharacteristic
191#343C2×D6111yescharacteristic
192#327—1221no—
193#327—1221no—
194#324—611no—
195#324—611no—
196C61#1214211yescharacteristic, complemented, Sylow
197C2×#41—21no—
198C2×M16—21no—
199C22⋊Q8—41no—
200#121—21no—
201#121—21no—
202#121—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C22⋊D6111yescharacteristic
210C2×C4⋊C4C22×D6111yescharacteristic
211C2×C42—1221no—
212C2×C42C22⋊D6111yescharacteristic
213#107—2441no—
214#106—2441no—
215#104—42no—
216#103—41no—
217#102—41no—
218#102—2441no—
219#102—2441no—
220C22⋊C8—1221no—
221C22⋊C8—1221no—
222#95—611no—
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#95—1221no—
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—41no—
253M16—41no—
254C2×C8—41no—
255C2×C8—2441no—
256C2×C8—2441no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—21no—
271C42—21no—
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—22no—
286C2×C4—21no—
287C2×C4—21no—
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—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2442no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451979711yescharacteristic
310C2×C4#1451980311yescharacteristic
311C8—81no—
312C8—4881no—
313C8—4881no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22#1683990511yescharacteristic
320C22#1683993411yescharacteristic
321C22#1683994811yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—81no—
329C4—4881no—
330C4—4881no—
331C4—4881no—
332C4—4881no—
333C2—21no—
334C2—21no—
335C2—161no—
336C2#2144474611yescharacteristic
337C2#2144781411yescharacteristic
338C2#2144783811yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2039C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#537C22
hypercenter#2039D61
hypocenterC61#12142
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2039

Complements

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

NH ≅ G/Ntype
1. #21453639C2semidirect
4. #21443845C2semidirect
5. #21443824C2semidirect
6. #21443765C2semidirect
196. C61#12142semidirect

Maximal subgroups

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

subgroupindex
#214536392
#214448562
#214448222
#214438452
#214438242
#214437652
C61×#20392
#1214261