Finite Group Databasebeta

← #29593891

Subgroups — #29593891

Order 15616.

288 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 75 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#21448046C211yesmaximal, characteristic
2#21447961C211yesmaximal, characteristic
3#21445213C211yesmaximal, characteristic
4#21443868C211yesmaximal, characteristic
5Q8⋊#11758185C211yesmaximal, characteristic
6#21443783C211yesmaximal, characteristic
7C61×#3395C211yesmaximal, characteristic
8#16840167C2211yescharacteristic
9#16839972—21no—
10#16839589—21no—
11C4⋊#11758185C2211yescharacteristic
12#16839566—21no—
13#16839566—22no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839507—21no—
17C61×#557—21no—
18C61×#494—21no—
19C61×#494C2211yescharacteristic
20C61×#462—22no—
21C61×#462—21no—
22C8×Q8×C61C2211yescharacteristic
23C4×Q16×C61—21no—
24C4×Q16×C61C2211yescharacteristic
25C2×#11758202—41no—
26#14519777—21no—
27C2×#11758185—21no—
28C2×#11758185—21no—
29#14519711—21no—
30#14519711—21no—
31C4⋊#92418—21no—
32#14519700—41no—
33C2×Q16×C61—22no—
34C2×Q16×C61—21no—
35C2×Q16×C61D411yescharacteristic
36C2×Q16×C61D412yes—
37C4⋊Q8×C61—22no—
38C4⋊Q8×C61—21no—
39#125×C61—42no—
40#125×C61—41no—
41C4×Q8×C61—22no—
42C4×Q8×C61—21no—
43C4×Q8×C61—41no—
44C4×Q8×C61D411yescharacteristic
45#107×C61D411yescharacteristic
46C4⋊C8×C61—21no—
47C4⋊C8×C61D411yescharacteristic
48#103×C61—22no—
49#103×C61—21no—
50C4×C8×C61—21no—
51C4×C8×C61C2311yescharacteristic
52C2×Q8×C61—21no—
53C2×Q8×C61—22no—
54C2×Q8×C61D811yescharacteristic
55C2×Dic122—41no—
56Q16×C61—21no—
57Q16×C61—21no—
58Q16×C61—42no—
59Q16×C61—41no—
60Q16×C61—41no—
61Q16×C61—82no—
62C2×C8×C61—21no—
63C2×C8×C61C2×D411yescharacteristic
64C2×C8×C61C2×D411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61—21no—
67C4⋊C4×C61—42no—
68C4⋊C4×C61—42no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61D811yescharacteristic
74C42×C61—21no—
75C42×C61—42no—
76C42×C61—41no—
77C42×C61C2×D411yescharacteristic
78#11758202—82no—
79C4⋊Dic61—41no—
80C4⋊Dic61—41no—
81C2×#92418—41no—
82#11758185—41no—
83#11758185—41no—
84Q8×C61—21no—
85Q8×C61—41no—
86Q8×C61—42no—
87Q8×C61—42no—
88Q8×C61—41no—
89Q8×C61SD3212yes—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—41no—
93C2×C4×C61—42no—
94C2×C4×C61—41no—
95C2×C4×C61#12011yescharacteristic
96C2×C4×C61C2×D811yescharacteristic
97C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
98C2×Dic61—81no—
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—81no—
112C4×C61—82no—
113C4×C61—81no—
114C4×C61#45211yescharacteristic
115C4×C61#45511yescharacteristic
116C4×C61C2×SD3211yescharacteristic
117C4×C61#51011yescharacteristic
118Dic61—161no—
119#3395D6111yescharacteristic
120#2241—611no—
121#2225—611no—
122#1674—611no—
123#1362—611no—
124Q8⋊C16—611no—
125#1332—611no—
126C2×C61#164111yescharacteristic
127C2×C61#218511yescharacteristic
128C2×C61#219511yescharacteristic
129#557—21no—
130#500—611no—
131#494—21no—
132#494C2×D6111yescharacteristic
133#462—22no—
134#462—21no—
135#462—1221no—
136C8×Q8C2×D6111yescharacteristic
137C4×Q16—21no—
138C4×Q16C2×D6111yescharacteristic
139#367—1221no—
140C4⋊C16—611no—
141#358—1221no—
142#358—1222no—
143C4×C16—611no—
144#335—611no—
145#332—1221no—
146C61#1238211yescharacteristic, complemented, Sylow
147C2×Q16—22no—
148C2×Q16—21no—
149C2×Q16—2441no—
150C2×Q16C22⋊D6111yescharacteristic
151C2×Q16C22⋊D6112yes—
152C4⋊Q8—22no—
153C4⋊Q8—21no—
154C4⋊Q8—1221no—
155#125—42no—
156#125—41no—
157C4×Q8—22no—
158C4×Q8—21no—
159C4×Q8—41no—
160C4×Q8C22⋊D6111yescharacteristic
161C2×C16—1221no—
162C2×C16—1221no—
163#107—1221no—
164#107—1221no—
165#107C22⋊D6111yescharacteristic
166C4⋊C8—21no—
167C4⋊C8—1221no—
168C4⋊C8C22⋊D6111yescharacteristic
169#103—22no—
170#103—21no—
171#103—2441no—
172C4×C8—21no—
173C4×C8C22×D6111yescharacteristic
174C2×Q8—22no—
175C2×Q8—21no—
176C2×Q8—2441no—
177C2×Q8#1175819911yescharacteristic
178Q16—21no—
179Q16—21no—
180Q16—42no—
181Q16—41no—
182Q16—41no—
183Q16—82no—
184Q16—4882no—
185C2×C8—21no—
186C2×C8—2441no—
187C2×C8C2×C22⋊D6111yescharacteristic
188C2×C8C2×C22⋊D6111yescharacteristic
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—2441no—
198C4⋊C4—2441no—
199C4⋊C4#1175819911yescharacteristic
200C42—21no—
201C42—42no—
202C42—41no—
203C42C2×C22⋊D6111yescharacteristic
204C16—2441no—
205C16—2441no—
206Q8—21no—
207Q8—42no—
208Q8—41no—
209Q8—41no—
210Q8—42no—
211Q8—4881no—
212Q8—4881no—
213Q8#1451972012yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—41no—
219C2×C4—4881no—
220C2×C4#1451974611yescharacteristic
221C2×C4C2×#1175819911yescharacteristic
222C2×C4#1451980311yescharacteristic
223C8—21no—
224C8—41no—
225C8—4881no—
226C8#1451979711yescharacteristic
227C8#1451980711yescharacteristic
228C22#1683989611yescharacteristic
229C4—22no—
230C4—21no—
231C4—41no—
232C4—81no—
233C4—82no—
234C4—81no—
235C4—9761no—
236C4#1683992411yescharacteristic
237C4#1683994011yescharacteristic
238C4C2×#1451972011yescharacteristic
239C4#1684020311yescharacteristic
240C2#2144501211yescharacteristic
241C2#2144773611yescharacteristic
242C2#2144779711yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3395C2
socle, prime radicalC22×C61#447
hypercenter#3395D61
hypocenterC61#12382
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3395

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
#214480462
#214479612
#214452132
#214438682
Q8⋊#117581852
#214437832
C61×#33952
#1238261