Finite Group Databasebeta

← #29593709

Subgroups — #29593709

Order 15616.

312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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#21458684C211yesmaximal, characteristic, complemented
2#21448042C211yesmaximal, characteristic, complemented
3#21445176C211yesmaximal, characteristic, complemented
4#21443876C211yesmaximal, characteristic, complemented
5#21443797C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic, complemented
7C61×#2206C211yesmaximal, characteristic
8#16840469—21no—
9#16840167C2211yescharacteristic
10#16840163—21no—
11#16840060—22no—
12#16840052—21no—
13#16839959—21no—
14C8×Dic122C2211yescharacteristic
15D8×Dic61—21no—
16#16839563—22no—
17C4×#11758185C2211yescharacteristic
18#16839515C2211yescharacteristic
19#16839506—21no—
20C2×D16×C61—21no—
21C61×#493C2211yescharacteristic
22C4×D8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C61×#357—21no—
25C2×#11758200—41no—
26#14519777—21no—
27#14519768—22no—
28#14519756—41no—
29#14519754—42no—
30C4×Dic122D411yescharacteristic
31D4×Dic61—22no—
32C2×C4⋊Dic61—41no—
33C2×#11758185—21no—
34#14519711—21no—
35#14519711D412yes—
36#14519708—22no—
37C4⋊#92418—21no—
38C4⋊#92418D411yescharacteristic
39#14519706—21no—
40#14519698—22no—
41#14519698—41no—
42C8×Dic61—21no—
43C2×D8×C61—21no—
44C2×D8×C61—21no—
45C2×D8×C61D411yescharacteristic
46#127×C61—21no—
47C4×D4×C61—21no—
48D16×C61—42no—
49C2×C16×C61—21no—
50#107×C61D411yescharacteristic
51#102×C61—21no—
52C4×C8×C61C2311yescharacteristic
53C2×D4×C61—21no—
54C2×D4×C61—41no—
55C2×D4×C61—41no—
56C2×D4×C61—41no—
57C22×C4×C61—41no—
58C22×Dic61—42no—
59C2×Dic122—41no—
60C2×Dic122D811yescharacteristic
61D8×C61—21no—
62D8×C61—42no—
63D8×C61—41no—
64D8×C61—41no—
65D8×C61SD1612yescomplemented
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C22⋊C4×C61—41no—
70C42×C61C2×D411yescharacteristic
71C22⋊Dic61—42no—
72#11758200—82no—
73C4⋊Dic61—22no—
74C4⋊Dic61—42no—
75C4⋊Dic61—41no—
76C4⋊Dic61D811yescharacteristic
77#11758196—21no—
78#11758196—42no—
79C4×Dic61—21no—
80C2×#92418—21no—
81C2×#92418—41no—
82C16×C61—41no—
83#11758185—41no—
84C23×C61—41no—
85C23×C61—81no—
86D4×C61—22no—
87D4×C61—41no—
88D4×C61—81no—
89D4×C61—81no—
90D4×C61—81no—
91D4×C61—81no—
92D4×C61—161no—
93C2×C4×C61—41no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×C4×C61#12011yescharacteristic
97C2×C4×C61C2×D811yescharacteristic
98C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—42no—
102C2×Dic61—162no—
103Dic122—21no—
104Dic122—21no—
105Dic122—161no—
106C8×C61—21no—
107C8×C61C2×SD1611yescharacteristic
108C8×C61#13711yescharacteristic
109#92418—41no—
110#92418—81no—
111#12355—611nomaximal, Sylow
112C22×C61—42no—
113C22×C61—81no—
114C22×C61—81no—
115C22×C61—161no—
116C22×C61—161no—
117C22×C61—161no—
118C22×C61#44711yescharacteristic
119C4×C61—21no—
120C4×C61—81no—
121C4×C61#44811yescharacteristic
122C4×C61#45411yescharacteristic
123C4×C61#50811yescharacteristic
124C4×C61#50911yescharacteristic
125Dic61—41no—
126Dic61—41no—
127Dic61—82no—
128#3380—611no—
129#2240—611no—
130#2206D6111yescharacteristic
131#1668—611no—
132#1365—611no—
133Q8⋊C16—611no—
134#1331—611no—
135C2×C61—82no—
136C2×C61—321no—
137C2×C61#162711yescharacteristic
138C2×C61#218611yescharacteristic
139C2×C61#219211yescharacteristic
140#554—1221no—
141C2×D16—21no—
142#500—611no—
143#499—1221no—
144#493C2×D6111yescharacteristic
145#478—1222no—
146#476—1221no—
147#460—1221no—
148C8×Q8—611no—
149C4×D8—1221no—
150C4×D8C2×D6111yescharacteristic
151C4⋊C16C2×D6111yescharacteristic
152#357—21no—
153#357—1222no—
154C4×C16—611no—
155#335—611no—
156#331—1221no—
157C61#1235511yescharacteristic, complemented, Sylow
158C2×SD16—2441no—
159C2×D8—21no—
160C2×D8—21no—
161C2×D8C22⋊D6111yescharacteristic
162C4⋊Q8—1221no—
163#127—21no—
164#125—1222no—
165C22⋊Q8—2442no—
166C22⋊Q8—2441no—
167C4×Q8—611no—
168C4×D4—21no—
169C4×D4—1222no—
170C2×C4⋊C4—2441no—
171D16—42no—
172C2×C16—21no—
173C2×C16—1221no—
174#107—612no—
175#107—1221no—
176#107C22⋊D6111yescharacteristic
177#106—1222no—
178C4⋊C8—611no—
179C4⋊C8—1221no—
180C4⋊C8—1221no—
181#102—21no—
182#102—1222no—
183#102—2441no—
184C4×C8—1221no—
185C4×C8C22×D6111yescharacteristic
186C2×Q8—611no—
187C2×Q8—2441no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C22×C4—41no—
193C22×C4—2442no—
194SD16—4882no—
195D8—21no—
196D8—42no—
197D8—41no—
198D8—41no—
199D8#1175820012yescomplemented
200C2×C8—1221no—
201C2×C8—2441no—
202C2×C8D4×D6111yescharacteristic
203C2×C8C2×C22⋊D6111yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1222no—
208C4⋊C4—2442no—
209C4⋊C4—2442no—
210C4⋊C4—2441no—
211C22⋊C4—41no—
212C22⋊C4—2442no—
213C42—1221no—
214C42D4×D6111yescharacteristic
215C16—41no—
216C16—2441no—
217C23—41no—
218C23—81no—
219Q8—1221no—
220Q8—1221no—
221Q8—9761no—
222D4—22no—
223D4—41no—
224D4—81no—
225D4—81no—
226D4—81no—
227D4—81no—
228D4—161no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—9762no—
235C2×C4—2442no—
236C2×C4#1451974511yescharacteristic
237C2×C4D8×D6111yescharacteristic
238C2×C4#1451980111yescharacteristic
239C8—21no—
240C8—4881no—
241C8—2441no—
242C8C2×#1175820011yescharacteristic
243C8#1451980711yescharacteristic
244C22—42no—
245C22—81no—
246C22—81no—
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1683989411yescharacteristic
251C4—21no—
252C4—81no—
253C4—4882no—
254C4—2441no—
255C4—2441no—
256C4#1683990011yescharacteristic
257C4#1683993311yescharacteristic
258C4#1684019111yescharacteristic
259C4#1684019611yescharacteristic
260C2—82no—
261C2—321no—
262C2#2144492111yescharacteristic
263C2#2144773911yescharacteristic
264C2#2144777311yescharacteristic
subgroupG/H
centerC22#16839894
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
Fitting, prime radicalC61×#2206C2
socleC22×C61#447
hypercenter#2206D61
hypocenterC61#12355
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #21458684C2semidirect
2. #21448042C2semidirect
3. #21445176C2semidirect
4. #21443876C2semidirect
5. #21443797C2semidirect
6. #21443780C2semidirect
65. D8×C61SD16semidirect
157. C61#12355semidirect
199. D8#11758200semidirect

Maximal subgroups

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

subgroupindex
#214586842
#214480422
#214451762
#214438762
#214437972
#214437802
C61×#22062
#1235561