Finite Group Databasebeta

← #29593893

Subgroups — #29593893

Order 15616.

288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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#21458825C211yesmaximal, characteristic
2#21448047C211yesmaximal, characteristic
3#21447962C211yesmaximal, characteristic
4#21445213C211yesmaximal, characteristic
5#21443869C211yesmaximal, characteristic
6#21443784C211yesmaximal, characteristic
7C61×Q8⋊C16C211yesmaximal, characteristic
8#16840491—21no—
9#16840167C2211yescharacteristic
10#16840142—21no—
11#16840142C2211yescharacteristic
12#16839973—22no—
13#16839973—21no—
14#16839972—21no—
15C4×Dic244—21no—
16C4×Dic244C2211yescharacteristic
17#16839590—21no—
18#16839567—21no—
19#16839567—22no—
20#16839515C2211yescharacteristic
21#16839507—21no—
22C8×Q8×C61C2211yescharacteristic
23C61×C4⋊C16C2211yescharacteristic
24C4×C16×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—22no—
27C2×Dic244D411yescharacteristic
28C2×Dic244D412yes—
29C2×#11758202—41no—
30#14519777—22no—
31#14519777—21no—
32#14519777—21no—
33#14519768—42no—
34#14519768—41no—
35Q8×Dic61—41no—
36C4×Dic122—22no—
37C4×Dic122—21no—
38#14519711—21no—
39#14519711—21no—
40#14519711D411yescharacteristic
41C4⋊#92418—21no—
42#14519702—22no—
43#14519702—21no—
44#14519700—41no—
45C4×Q8×C61D411yescharacteristic
46C2×C16×C61—21no—
47C2×C16×C61—21no—
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50C4×C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61D811yescharacteristic
53C2×Dic122—21no—
54C2×Dic122—22no—
55C2×Dic122—41no—
56C2×C8×C61—21no—
57C2×C8×C61C2×D411yescharacteristic
58C2×C8×C61C2×D411yescharacteristic
59C4⋊C4×C61—21no—
60C4⋊C4×C61D811yescharacteristic
61C42×C61—21no—
62C42×C61C2×D411yescharacteristic
63#11758202—82no—
64C4⋊Dic61—21no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4⋊Dic61—41no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4⋊Dic61—41no—
71#11758196—42no—
72#11758196—41no—
73C4×Dic61—42no—
74C4×Dic61—41no—
75C2×#92418—41no—
76Dic244—21no—
77Dic244—21no—
78Dic244—42no—
79Dic244—41no—
80Dic244—41no—
81Dic244—82no—
82C16×C61—41no—
83C16×C61—41no—
84Q8×C61—21no—
85Q8×C61SD3212yes—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61#12011yescharacteristic
89C2×C4×C61C2×D811yescharacteristic
90C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
91C2×Dic61—41no—
92C2×Dic61—42no—
93C2×Dic61—41no—
94C2×Dic61—81no—
95Dic122—41no—
96Dic122—42no—
97Dic122—42no—
98Dic122—41no—
99Dic122—81no—
100Dic122—81no—
101C8×C61—21no—
102C8×C61—41no—
103C8×C61#13511yescharacteristic
104C8×C61#13711yescharacteristic
105#92418—81no—
106#12382—611nomaximal, Sylow
107C22×C61#44711yescharacteristic
108C4×C61—22no—
109C4×C61—21no—
110C4×C61—41no—
111C4×C61#45211yescharacteristic
112C4×C61#45511yescharacteristic
113C4×C61C2×SD3211yescharacteristic
114C4×C61#51011yescharacteristic
115Dic61—81no—
116Dic61—82no—
117Dic61—81no—
118Dic61—161no—
119#3395—611no—
120#2241—611no—
121#2225—611no—
122#1674—611no—
123#1362—611no—
124Q8⋊C16D6111yescharacteristic
125#1332—611no—
126C2×C61#164111yescharacteristic
127C2×C61#218511yescharacteristic
128C2×C61#219511yescharacteristic
129#557—1221no—
130#500—611no—
131#494—611no—
132#494—1221no—
133#462—1222no—
134#462—1221no—
135#462—1221no—
136C8×Q8C2×D6111yescharacteristic
137C4×Q16—611no—
138C4×Q16—1221no—
139#367—1221no—
140C4⋊C16C2×D6111yescharacteristic
141#358—1221no—
142#358—1222no—
143C4×C16C2×D6111yescharacteristic
144#335—611no—
145#332—1221no—
146C61#1238211yescharacteristic, complemented, Sylow
147C2×Q16—611no—
148C2×Q16—612no—
149C2×Q16—1222no—
150C2×Q16—1221no—
151C2×Q16—2441no—
152C4⋊Q8—1222no—
153C4⋊Q8—1221no—
154C4⋊Q8—1221no—
155#125—2442no—
156#125—2441no—
157C4×Q8—1222no—
158C4×Q8—1221no—
159C4×Q8—2441no—
160C4×Q8D24411yescharacteristic
161C2×C16—21no—
162C2×C16—21no—
163#107—611no—
164#107—1221no—
165#107—1221no—
166C4⋊C8—21no—
167C4⋊C8—1221no—
168C4⋊C8D24411yescharacteristic
169#103—1222no—
170#103—1221no—
171#103—2441no—
172C4×C8—21no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—1221no—
175C2×Q8—1222no—
176C2×Q8—2441no—
177C2×Q8D48811yescharacteristic
178Q16—1221no—
179Q16—1221no—
180Q16—4882no—
181Q16—4882no—
182Q16—2442no—
183Q16—2441no—
184Q16—2441no—
185C2×C8—21no—
186C2×C8—2441no—
187C2×C8D4×D6111yescharacteristic
188C2×C8D4×D6111yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—1221no—
191C4⋊C4—2442no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2441no—
195C4⋊C4—2441no—
196C4⋊C4—2441no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4D48811yescharacteristic
200C42—21no—
201C42—2442no—
202C42—2441no—
203C42C2×D24411yescharacteristic
204C16—41no—
205C16—41no—
206Q8—21no—
207Q8—4881no—
208Q8—4881no—
209Q8—2441no—
210Q8—2442no—
211Q8—2441no—
212Q8—2442no—
213Q8#1451972212yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—4881no—
217C2×C4—2441no—
218C2×C4—2442no—
219C2×C4—2441no—
220C2×C4#1451974711yescharacteristic
221C2×C4C2×D48811yescharacteristic
222C2×C4#1451980511yescharacteristic
223C8—21no—
224C8—41no—
225C8—4881no—
226C8#1451979811yescharacteristic
227C8#1451980911yescharacteristic
228C22#1683989811yescharacteristic
229C4—22no—
230C4—21no—
231C4—41no—
232C4—9761no—
233C4—4881no—
234C4—4881no—
235C4—4882no—
236C4#1683992711yescharacteristic
237C4#1683994111yescharacteristic
238C4C2×#1451972211yescharacteristic
239C4#1684020511yescharacteristic
240C2#2144501411yescharacteristic
241C2#2144773811yescharacteristic
242C2#2144779911yescharacteristic
subgroupG/H
centerC22#16839898
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×Q8⋊C16C2
socle, prime radicalC22×C61#447
hypercenterQ8⋊C16D61
hypocenterC61#12382
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ Q8⋊C16

Complements

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

NH ≅ G/Ntype
146. C61#12382semidirect

Maximal subgroups

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

subgroupindex
#214588252
#214480472
#214479622
#214452132
#214438692
#214437842
C61×Q8⋊C162
#1238261