Finite Group Databasebeta

← #29592385

Subgroups — #29592385

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#21453314C211yesmaximal, characteristic, complemented
2#21447045C211yesmaximal, characteristic
3#21444822C211yesmaximal, characteristic
4#21443846C211yesmaximal, characteristic, complemented
5#21443826C211yesmaximal, characteristic, complemented
6#21443762C211yesmaximal, characteristic, complemented
7C61×#1616C211yesmaximal, characteristic
8#16840073—21no—
9C2×#14519704—21no—
10#16839763—21no—
11#16839704—21no—
12#16839695—21no—
13#16839692C2211yescharacteristic
14#16839659—21no—
15#16839649—21no—
16#16839647—21no—
17#16839629—21no—
18#16839627C2211yescharacteristic
19#16839531C2211yescharacteristic
20#16839496—21no—
21#16839488C2211yescharacteristic
22C61×#537C2211yescharacteristic
23C61×#481—21no—
24C61×#400C2211yescharacteristic
25C61×#327—21no—
26C61×#324C2211yescharacteristic
27C2×#11758194—21no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61D411yescharacteristic
30C2×C4⋊Dic61D411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61D411yescharacteristic
36#14519710—41no—
37#14519704—42no—
38#14519701—41no—
39#14519698—41no—
40#14519698—41no—
41C22⋊#92418—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×C61D411yescharacteristic
56C2×C4⋊C4×C61C2311yescharacteristic
57#106×C61—41no—
58#102×C61—41no—
59C22⋊C8×C61—21no—
60#95×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—
87C22⋊C4×C61—41no—
88C22⋊C4×C61—41no—
89C4⋊Dic61—42no—
90C4⋊Dic61—41no—
91C4⋊Dic61—41no—
92#11758196—42no—
93#11758196—41no—
94#11758196—41no—
95#11758196—81no—
96C4×Dic61—21no—
97C4×Dic61—21no—
98C4×Dic61—42no—
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—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C8×C61—81no—
143#92418—81no—
144#92418—81no—
145#12147—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—81no—
149C22×C61—81no—
150C22×C61—81no—
151C22×C61#44911yescharacteristic
152C22×C61#45411yescharacteristic
153C22×C61B(4,𝔽2)11yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—81no—
159C4×C61—81no—
160C4×C61—81no—
161Dic61—42no—
162Dic61—81no—
163Dic61—81no—
164Dic61—81no—
165#2769—611no—
166#2040—611no—
167#1616D6111yescharacteristic
168#1610—611no—
169#1353—611no—
170#1346—611no—
171#1324—611no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61—161no—
175C2×C61#159711yescharacteristic
176C2×C61#220111yescharacteristic
177C2×C61#220411yescharacteristic
178#537C2×D6111yescharacteristic
179#481—21no—
180#480—1221no—
181C2×#104—1221no—
182#417—1221no—
183#400—1221no—
184#400C2×D6111yescharacteristic
185#398—611no—
186#398—1221no—
187#389—1221no—
188#387—1221no—
189#387—1221no—
190#383—1221no—
191#382—611no—
192#343—611no—
193#327—21no—
194#327—1221no—
195#324—611no—
196#324C2×D6111yescharacteristic
197C61#1214711yescharacteristic, complemented, Sylow
198C2×#41—21no—
199C2×M16—1221no—
200C22⋊Q8—41no—
201#121—21no—
202#121—21no—
203#121—41no—
204C2×C4⋊C4—611no—
205C2×C4⋊C4—611no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4—1221no—
210C2×C4⋊C4C22⋊D6111yescharacteristic
211C2×C4⋊C4C22×D6111yescharacteristic
212C2×C42—611no—
213C2×C42—1221no—
214#107—2441no—
215#106—41no—
216#104—2442no—
217#103—2441no—
218#102—41no—
219#102—2441no—
220#102—2441no—
221C22⋊C8—21no—
222C22⋊C8—1221no—
223#95—21no—
224#95—21no—
225#95—611no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229#95—1221no—
230#95—1221no—
231#95—1221no—
232#95—1221no—
233#95C22⋊D6111yescharacteristic
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—1221no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4D4×D6111yescharacteristic
251C22×C4D4×D6111yescharacteristic
252C22×C4C2×C22⋊D6111yescharacteristic
253M16—2441no—
254M16—2441no—
255C2×C8—41no—
256C2×C8—2441no—
257C2×C8—2441no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C4⋊C4—2441no—
264C4⋊C4—2441no—
265C4⋊C4—2442no—
266C4⋊C4—2442no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C42—1221no—
272C42—1221no—
273C42—2442no—
274C23—41no—
275C23#1451974511yescharacteristic
276Q8—41no—
277Q8—41no—
278D4—41no—
279D4—41no—
280D4—81no—
281D4—81no—
282D4—81no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
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—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—1222no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4#1451979811yescharacteristic
312C2×C4#1451980411yescharacteristic
313C8—81no—
314C8—4881no—
315C8—4881no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22#1683990611yescharacteristic
322C22#1683993311yescharacteristic
323C22#1683994811yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—4881no—
332C4—4881no—
333C4—4881no—
334C4—2442no—
335C2—21no—
336C2—21no—
337C2—161no—
338C2#2144474711yescharacteristic
339C2#2144783011yescharacteristic
340C2#2144784311yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C4⋊C4×C61C23
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1616C2
socleC22×C61B(4,𝔽2)
prime radicalC61×#537C22
hypercenter#1616D61
hypocenterC61#12147
LCSG ▷ C2×C4⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1616

Complements

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

NH ≅ G/Ntype
1. #21453314C2semidirect
4. #21443846C2semidirect
5. #21443826C2semidirect
6. #21443762C2semidirect
197. C61#12147semidirect

Maximal subgroups

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

subgroupindex
#214533142
#214470452
#214448222
#214438462
#214438262
#214437622
C61×#16162
#1214761