Finite Group Databasebeta

← #29593556

Subgroups — #29593556

Order 15616.

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

normal subgroups only

This group has 324 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#21448074C211yesmaximal, characteristic
2#21447869C211yesmaximal, characteristic, complemented
3#21445189C211yesmaximal, characteristic, complemented
4#21443865C211yesmaximal, characteristic
5Q8⋊#11758185C211yesmaximal, characteristic, complemented
6#21443783C211yesmaximal, characteristic, complemented
7C61×#3396C211yesmaximal, characteristic
8C2×#14519723—21no—
9C2×#14519721—22no—
10#16840142C2211yescharacteristic
11#16840047—21no—
12C4⋊#11758185C2211yescharacteristic
13#16839565—21no—
14C4×#11758185C2211yescharacteristic
15#16839515C2211yescharacteristic
16#16839509—21no—
17C61×#559—21no—
18C61×#495—21no—
19C61×#493C2211yescharacteristic
20C61×#463—22no—
21C61×#460—21no—
22C8×Q8×C61C2211yescharacteristic
23C4×Q16×C61C2211yescharacteristic
24C4×D8×C61—21no—
25C2×Dic244—21no—
26C2×Dic244—21no—
27#14519777—21no—
28#14519723—42no—
29#14519721—44no—
30C2×#11758185—21no—
31C2×#11758185—21no—
32#14519708—41no—
33C4⋊#92418—21no—
34#14519701—41no—
35C2×Q16×C61D411yescharacteristic
36C2×SD16×C61—22no—
37C2×D8×C61—21no—
38C2×D8×C61D412yes—
39#127×C61—21no—
40#124×C61—22no—
41#124×C61—41no—
42#123×C61—42no—
43C4×Q8×C61—21no—
44C4×Q8×C61D411yescharacteristic
45C4×D4×C61—22no—
46C4×D4×C61—41no—
47#107×C61D411yescharacteristic
48C4⋊C8×C61—21no—
49C4⋊C8×C61D411yescharacteristic
50#103×C61—21no—
51#102×C61—22no—
52C4×C8×C61—21no—
53C4×C8×C61C2311yescharacteristic
54C2×Q8×C61—21no—
55C2×Q8×C61D811yescharacteristic
56C2×D4×C61—22no—
57C2×D4×C61—41no—
58C2×D4×C61—41no—
59C22×C4×C61—42no—
60C2×Dic122—41no—
61Q16×C61—21no—
62Q16×C61—21no—
63SD16×C61—82no—
64D8×C61—42no—
65D8×C61—41no—
66D8×C61—41no—
67C2×C8×C61—21no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61—21no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61D811yescharacteristic
74C22⋊C4×C61—42no—
75C22⋊C4×C61—42no—
76C22⋊C4×C61—42no—
77C42×C61—21no—
78C42×C61—41no—
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—42no—
89Q8×C61—21no—
90Q8×C61—21no—
91Q8×C61—41no—
92Q8×C61—41no—
93D4×C61—42no—
94D4×C61—42no—
95D4×C61—81no—
96D4×C61—81no—
97D4×C61—161no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—162no—
103C2×C4×C61#12011yescharacteristic
104C2×C4×C61C2×D811yescharacteristic
105C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
106C2×Dic61—81no—
107Dic122—81no—
108Dic122—81no—
109C8×C61—21no—
110C8×C61—41no—
111C8×C61#13511yescharacteristic
112C8×C61AGL(1,ℤ/8)11yescharacteristic
113#92418—81no—
114#12333—611nomaximal, Sylow
115C22×C61—82no—
116C22×C61—82no—
117C22×C61—82no—
118C22×C61#44711yescharacteristic
119C4×C61—21no—
120C4×C61—41no—
121C4×C61—41no—
122C4×C61—81no—
123C4×C61—81no—
124C4×C61#44911yescharacteristic
125C4×C61#45311yescharacteristic
126C4×C61#50811yescharacteristic
127C4×C61#51011yescharacteristic
128Dic61—161no—
129#3396D6111yescharacteristic
130#2248—611no—
131#2209—611no—
132#1670—611no—
133#1361—611no—
134Q8⋊C16—611no—
135#1332—611no—
136C2×C61—162no—
137C2×C61#162111yescharacteristic
138C2×C61#218911yescharacteristic
139C2×C61#219411yescharacteristic
140#559—21no—
141C2×Q32—1221no—
142C2×SD32—1222no—
143#495—21no—
144#494—611no—
145#493C2×D6111yescharacteristic
146#475—1221no—
147#463—22no—
148#460—21no—
149C8×Q8C2×D6111yescharacteristic
150C4×Q16C2×D6111yescharacteristic
151C4×D8—21no—
152C4⋊C16—611no—
153#358—1221no—
154C4×C16—611no—
155#335—611no—
156#332—1221no—
157C61#1233311yescharacteristic, complemented, Sylow
158C2×Q16—1221no—
159C2×Q16—1221no—
160C2×Q16C22⋊D6111yescharacteristic
161C2×SD16—22no—
162C2×D8—21no—
163C2×D8C22⋊D6112yes—
164C4⋊Q8—1221no—
165#127—21no—
166#124—22no—
167#124—41no—
168#123—42no—
169C4×Q8—21no—
170C4×Q8C22⋊D6111yescharacteristic
171C4×D4—22no—
172C4×D4—41no—
173Q32—2442no—
174SD32—2444no—
175C2×C16—1221no—
176C2×C16—1221no—
177#107C22⋊D6111yescharacteristic
178#106—2441no—
179C4⋊C8—21no—
180C4⋊C8—1221no—
181C4⋊C8C22⋊D6111yescharacteristic
182#103—21no—
183#103—2441no—
184#102—22no—
185C4×C8—21no—
186C4×C8C22×D6111yescharacteristic
187C2×Q8—21no—
188C2×Q8—2441no—
189C2×Q8#1175819911yescharacteristic
190C2×D4—22no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—42no—
194Q16—21no—
195Q16—21no—
196Q16—2442no—
197Q16—2441no—
198Q16—2441no—
199SD16—82no—
200D8—42no—
201D8—41no—
202D8—41no—
203C2×C8—21no—
204C2×C8—2441no—
205C2×C8C2×C22⋊D6111yescharacteristic
206C2×C8C2×C22⋊D6111yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—41no—
210C4⋊C4—2441no—
211C4⋊C4—2441no—
212C4⋊C4#1175819911yescharacteristic
213C22⋊C4—42no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C42—21no—
217C42—41no—
218C42C2×C22⋊D6111yescharacteristic
219C16—1222no—
220C16—2441no—
221C23—42no—
222Q8—21no—
223Q8—21no—
224Q8—41no—
225Q8—41no—
226Q8—4881no—
227Q8—4881no—
228D4—42no—
229D4—42no—
230D4—81no—
231D4—81no—
232D4—161no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—162no—
238C2×C4—4881no—
239C2×C4#1451974611yescharacteristic
240C2×C4C2×#1175819911yescharacteristic
241C2×C4#1451980311yescharacteristic
242C8—21no—
243C8—41no—
244C8—4881no—
245C8#1451979711yescharacteristic
246C8#1451980211yescharacteristic
247C22—82no—
248C22—82no—
249C22—82no—
250C22#1683989611yescharacteristic
251C4—21no—
252C4—41no—
253C4—41no—
254C4—81no—
255C4—81no—
256C4—9761no—
257C4#1683990711yescharacteristic
258C4#1683993011yescharacteristic
259C4#1684019211yescharacteristic
260C4#1684020211yescharacteristic
261C2—162no—
262C2#2144488411yescharacteristic
263C2#2144775911yescharacteristic
264C2#2144779011yescharacteristic
subgroupG/H
centerC22#16839896
commutator, cosocleC4×C8×C61C23
FrattiniC4×C8C22×D61
FittingC61×#3396C2
socleC22×C61#447
prime radicalC61×#493C22
hypercenter#3396D61
hypocenterC61#12333
LCSG ▷ C4×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
2. #21447869C2semidirect
3. #21445189C2semidirect
5. Q8⋊#11758185C2semidirect
6. #21443783C2semidirect
157. C61#12333semidirect

Maximal subgroups

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

subgroupindex
#214480742
#214478692
#214451892
#214438652
Q8⋊#117581852
#214437832
C61×#33962
#1233361