Finite Group Databasebeta

← #29592002

Subgroups — #29592002

Order 15616.

210 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C4×#14519723C211yesmaximal, characteristic
2#21444717C211yesmaximal, characteristic
3#21443890C211yesmaximal, characteristic
4#21443783C211yesmaximal, characteristic
5#21443782C211yesmaximal, characteristic
6C8×#11758185C211yesmaximal, characteristic
7C61×#1591C211yesmaximal, characteristic
8C2×#14519723C411yescharacteristic
9#16839892—21no—
10C4×Dic244C2211yescharacteristic
11#16839587C411yescharacteristic
12#16839566C411yescharacteristic
13#16839565C411yescharacteristic
14C4×#11758185C2211yescharacteristic
15C4×#11758185C2211yescharacteristic
16#16839515C2211yescharacteristic
17#16839494—21no—
18C61×#446—21no—
19C4×Q16×C61C2211yescharacteristic
20C61×#335C2211yescharacteristic
21C61×Q8⋊C8—21no—
22C82×C61C2211yescharacteristic
23C2×Dic244C2×C411yescharacteristic
24C4×Dic122—21no—
25#14519723—22no—
26C2×#11758185—21no—
27C2×#11758185C2×C411yescharacteristic
28C2×#11758185C2×C411yescharacteristic
29#14519711C2×C411yescharacteristic
30C4⋊#92418—21no—
31#14519706—41no—
32#14519702—21no—
33#14519687—41no—
34C2×Q16×C61C2×C411yescharacteristic
35C4×Q8×C61—21no—
36#107×C61C2×C411yescharacteristic
37C4⋊C8×C61—21no—
38C4⋊C8×C61—41no—
39#103×C61—21no—
40#97×C61—41no—
41C4×C8×C61D411yescharacteristic
42C4×C8×C61D411yescharacteristic
43C4×C8×C61C2311yescharacteristic
44C2×Q8×C61—21no—
45C2×Dic122—21no—
46Q16×C61—21no—
47Q16×C61—21no—
48C2×C8×C61—21no—
49C2×C8×C61—41no—
50C2×C8×C61D811yescharacteristic
51C2×C8×C61D811yescharacteristic
52C2×C8×C61C22×C411yescharacteristic
53C2×C8×C61#4111yescharacteristic
54C4⋊C4×C61—21no—
55C4⋊C4×C61—41no—
56C42×C61—41no—
57C42×C61C2×D411yescharacteristic
58C4⋊Dic61—21no—
59#11758196—41no—
60C4×Dic61—41no—
61C2×#92418—41no—
62Dic244—21no—
63Dic244—21no—
64#11758185—22no—
65#11758185—21no—
66#11758185M1612yes—
67Q8×C61—41no—
68Q8×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C4×D411yescharacteristic
72C2×C4×C61C2×D811yescharacteristic
73C2×C4×C61#13511yescharacteristic
74C2×Dic61—41no—
75C2×Dic61—41no—
76Dic122—41no—
77Dic122—41no—
78C8×C61—22no—
79C8×C61—21no—
80C8×C61—21no—
81C8×C61—81no—
82C8×C61Q3212yescomplemented
83C8×C61C2×M1611yescharacteristic
84C8×C61#13111yescharacteristic
85#92418—81no—
86#12083—611nomaximal, Sylow
87C22×C61C4×D811yescharacteristic
88C4×C61—21no—
89C4×C61—81no—
90C4×C61—81no—
91C4×C61#43611yescharacteristic
92C4×C61#44311yescharacteristic
93C4×C61C2×Q3211yescharacteristic
94C4×C61#50811yescharacteristic
95Dic61—81no—
96Dic61—81no—
97C4×Q32—611no—
98#1591—611no—
99#1591D6111yescharacteristic
100#1371—611no—
101#1332—611no—
102#1332—611no—
103C8×C16—611no—
104C2×C61#158911yescharacteristic
105C2×C61C4×Q3211yescharacteristic
106C2×C61#217811yescharacteristic
107C2×Q32—611no—
108#446—21no—
109#446—1221no—
110C4×Q16—611no—
111C4×Q16C2×D6111yescharacteristic
112#366—611no—
113#358—611no—
114#358—611no—
115C4×C16—611no—
116C4×C16—611no—
117#335—611no—
118#335C2×D6111yescharacteristic
119Q8⋊C8—21no—
120Q8⋊C8—1221no—
121C82C2×D6111yescharacteristic
122C61#1208311yescharacteristic, complemented, Sylow
123C2×Q16—611no—
124C2×Q16C4×D6111yescharacteristic
125C4×Q8—21no—
126C4×Q8—1221no—
127Q32—1222no—
128C2×C16—611no—
129C2×C16—611no—
130C2×C16—1221no—
131#107—611no—
132#107C4×D6111yescharacteristic
133C4⋊C8—21no—
134C4⋊C8—41no—
135C4⋊C8—1221no—
136C4⋊C8—2441no—
137#103—21no—
138#103—1221no—
139#97—41no—
140#97—2441no—
141C4×C8C22⋊D6111yescharacteristic
142C4×C8C22⋊D6111yescharacteristic
143C4×C8C22×D6111yescharacteristic
144C2×Q8—21no—
145C2×Q8—1221no—
146Q16—21no—
147Q16—21no—
148Q16—1221no—
149Q16—1221no—
150C2×C8—21no—
151C2×C8—41no—
152C2×C8—2441no—
153C2×C8#1175819911yescharacteristic
154C2×C8#1175819911yescharacteristic
155C2×C8C2×C4×D6111yescharacteristic
156C2×C8#1175822211yescharacteristic
157C4⋊C4—21no—
158C4⋊C4—41no—
159C4⋊C4—1221no—
160C4⋊C4—2441no—
161C42—41no—
162C42—2441no—
163C42C2×C22⋊D6111yescharacteristic
164C16—612no—
165C16—1222no—
166C16—1221no—
167Q8—41no—
168Q8—41no—
169Q8—2441no—
170Q8—2441no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—2441no—
174C2×C4—2441no—
175C2×C4C4×C22⋊D6111yescharacteristic
176C2×C4C2×#1175819911yescharacteristic
177C2×C4#1451979711yescharacteristic
178C8—22no—
179C8—21no—
180C8—21no—
181C8—81no—
182C8—4881no—
183C8#1451972312yescomplemented
184C8M16×D6111yescharacteristic
185C8#1451978511yescharacteristic
186C22C4×#1175819911yescharacteristic
187C4—21no—
188C4—81no—
189C4—81no—
190C4—4881no—
191C4—4881no—
192C4#1683983811yescharacteristic
193C4#1683987711yescharacteristic
194C4C2×#1451972311yescharacteristic
195C4#1684019211yescharacteristic
196C2#2144470211yescharacteristic
197C2C4×#1451972311yescharacteristic
198C2#2144769811yescharacteristic
subgroupG/H
centerC2×C4C2×#11758199
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1591C2
socle, prime radicalC22×C61C4×D8
cosocleC4×C8×C61C23
hypercenter#1591D61
hypocenterC61#12083
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C82 ◁ #1591

Complements

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

NH ≅ G/Ntype
82. C8×C61Q32semidirect
122. C61#12083semidirect
183. C8#14519723semidirect

Maximal subgroups

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

subgroupindex
C4×#145197232
#214447172
#214438902
#214437832
#214437822
C8×#117581852
C61×#15912
#1208361