Finite Group Databasebeta

← #29593570

Subgroups — #29593570

Order 15616.

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

normal subgroups only

This group has 312 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#21448071C211yesmaximal, characteristic, complemented
2#21447864C211yesmaximal, characteristic
3#21445189C211yesmaximal, characteristic, complemented
4#21443868C211yesmaximal, characteristic, complemented
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443780C211yesmaximal, characteristic
7C61×#3393C211yesmaximal, characteristic
8C2×#14519723—22no—
9C2×#14519721—21no—
10#16840142C2211yescharacteristic
11#16840047—21no—
12C4⋊#11758185C2211yescharacteristic
13#16839565—21no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17C61×#556—21no—
18C61×#495—21no—
19C61×#494C2211yescharacteristic
20C61×#464—22no—
21C61×#461—21no—
22C8×Q8×C61C2211yescharacteristic
23C4×Q16×C61—21no—
24C4×D8×C61C2211yescharacteristic
25C2×Dic244—21no—
26C2×Dic244—21no—
27#14519777—21no—
28#14519723—44no—
29#14519721—42no—
30C2×#11758185—21no—
31C2×#11758185—21no—
32#14519708—41no—
33C4⋊#92418—21no—
34#14519701—41no—
35C2×Q16×C61—21no—
36C2×Q16×C61D412yes—
37C2×SD16×C61—22no—
38C2×D8×C61D411yescharacteristic
39C4⋊Q8×C61—21no—
40#126×C61—42no—
41#124×C61—22no—
42C22⋊Q8×C61—41no—
43C4×Q8×C61—22no—
44C4×Q8×C61D411yescharacteristic
45C4×D4×C61—21no—
46#117×C61—41no—
47#107×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#103×C61—22no—
51#102×C61—21no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—22no—
55C2×Q8×C61D811yescharacteristic
56C2×D4×C61—21no—
57C22×C4×C61—41no—
58C2×Dic122—41no—
59Q16×C61—42no—
60Q16×C61—41no—
61Q16×C61—41no—
62SD16×C61—82no—
63D8×C61—21no—
64D8×C61—21no—
65C2×C8×C61—21no—
66C2×C8×C61C2×D411yescharacteristic
67C2×C8×C61C2×D411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61—21no—
70C4⋊C4×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61D811yescharacteristic
74C22⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C22⋊C4×C61—41no—
77C42×C61—21no—
78C42×C61—42no—
79C42×C61C2×D411yescharacteristic
80C4⋊Dic61—41no—
81C4⋊Dic61—41no—
82C2×#92418—41no—
83Dic244—42no—
84Dic244—41no—
85Dic244—41no—
86#11758185—22no—
87#11758185—41no—
88C23×C61—41no—
89Q8×C61—21no—
90Q8×C61—21no—
91Q8×C61—42no—
92Q8×C61—42no—
93D4×C61—41no—
94D4×C61—41no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61—81no—
100C2×C4×C61—81no—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61C2×D811yescharacteristic
103C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
104C2×Dic61—81no—
105Dic122—81no—
106Dic122—81no—
107C8×C61—21no—
108C8×C61—41no—
109C8×C61#13511yescharacteristic
110C8×C61AGL(1,ℤ/8)11yescharacteristic
111#92418—81no—
112#12335—611nomaximal, Sylow
113C22×C61—81no—
114C22×C61—81no—
115C22×C61—81no—
116C22×C61#44711yescharacteristic
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61—82no—
121C4×C61—81no—
122C4×C61#44911yescharacteristic
123C4×C61#45311yescharacteristic
124C4×C61#50811yescharacteristic
125C4×C61#51011yescharacteristic
126Dic61—161no—
127#3393D6111yescharacteristic
128#2247—611no—
129#2208—611no—
130#1670—611no—
131#1362—611no—
132Q8⋊C16—611no—
133#1331—611no—
134C2×C61—161no—
135C2×C61#162111yescharacteristic
136C2×C61#218911yescharacteristic
137C2×C61#219511yescharacteristic
138#556—21no—
139C2×Q32—1222no—
140C2×SD32—1221no—
141#495—21no—
142#494—611no—
143#494C2×D6111yescharacteristic
144#475—1221no—
145#464—22no—
146#461—21no—
147C8×Q8C2×D6111yescharacteristic
148C4×Q16—21no—
149C4×D8C2×D6111yescharacteristic
150C4⋊C16—611no—
151#358—1221no—
152C4×C16—611no—
153#335—611no—
154#332—1221no—
155C61#1233511yescharacteristic, complemented, Sylow
156C2×Q16—21no—
157C2×Q16—1221no—
158C2×Q16—1221no—
159C2×Q16C22⋊D6112yes—
160C2×SD16—22no—
161C2×D8C22⋊D6111yescharacteristic
162C4⋊Q8—21no—
163C4⋊Q8—1221no—
164#126—42no—
165#124—22no—
166C22⋊Q8—41no—
167C4×Q8—22no—
168C4×Q8C22⋊D6111yescharacteristic
169C4×D4—21no—
170#117—41no—
171Q32—2444no—
172SD32—2442no—
173C2×C16—1221no—
174C2×C16—1221no—
175#107C22⋊D6111yescharacteristic
176#106—2441no—
177C4⋊C8—21no—
178C4⋊C8—1221no—
179C4⋊C8C22⋊D6111yescharacteristic
180#103—22no—
181#103—2441no—
182#102—21no—
183C4×C8—21no—
184C4×C8C22×D6111yescharacteristic
185C2×Q8—22no—
186C2×Q8—2441no—
187C2×Q8#1175819911yescharacteristic
188C2×D4—21no—
189C22×C4—41no—
190Q16—42no—
191Q16—41no—
192Q16—41no—
193Q16—2442no—
194Q16—2441no—
195Q16—2441no—
196SD16—82no—
197D8—21no—
198D8—21no—
199C2×C8—21no—
200C2×C8—2441no—
201C2×C8C2×C22⋊D6111yescharacteristic
202C2×C8C2×C22⋊D6111yescharacteristic
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—42no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—2441no—
209C4⋊C4—2441no—
210C4⋊C4#1175819911yescharacteristic
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—41no—
214C42—21no—
215C42—42no—
216C42C2×C22⋊D6111yescharacteristic
217C16—1222no—
218C16—2441no—
219C23—41no—
220Q8—21no—
221Q8—21no—
222Q8—42no—
223Q8—42no—
224Q8—4881no—
225Q8—4881no—
226D4—41no—
227D4—41no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—4881no—
235C2×C4#1451974611yescharacteristic
236C2×C4C2×#1175819911yescharacteristic
237C2×C4#1451980311yescharacteristic
238C8—21no—
239C8—41no—
240C8—4881no—
241C8#1451979711yescharacteristic
242C8#1451980211yescharacteristic
243C22—81no—
244C22—81no—
245C22—81no—
246C22#1683989611yescharacteristic
247C4—21no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4—81no—
252C4—9761no—
253C4#1683990711yescharacteristic
254C4#1683993011yescharacteristic
255C4#1684019211yescharacteristic
256C4#1684020211yescharacteristic
257C2—161no—
258C2#2144488411yescharacteristic
259C2#2144775911yescharacteristic
260C2#2144779711yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3393C2
socleC22×C61#447
prime radicalC2×D8×C61D4
hypercenter#3393D61
hypocenterC61#12335
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3393

Complements

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

NH ≅ G/Ntype
1. #21448071C2semidirect
3. #21445189C2semidirect
4. #21443868C2semidirect
5. Q8⋊#11758185C2semidirect
155. C61#12335semidirect

Maximal subgroups

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

subgroupindex
#214480712
#214478642
#214451892
#214438682
Q8⋊#117581852
#214437802
C61×#33932
#1233561