Finite Group Databasebeta

← #34014361

Subgroups — #34014361

Order 18688.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#22626204C212yesmaximal
2#22625072C214yesmaximal, complemented
3#22620277C211yesmaximal, characteristic
4#17989566—22no—
5#17989494—22no—
6#17989492C2214yes—
7#17989144C411yescharacteristic, complemented
8#17989137C2211yescharacteristic
9#17988956C412yescomplemented
10#17988952C2212yes—
11#17988947—22no—
12#17988584—22no—
13C2×#97×C73C411yescharacteristic, complemented
14#14556670—42no—
15#14556650—24no—
16#14556649—42no—
17C2×#11924028D412yes—
18#14556591—21no—
19#14556591C2×C411yescharacteristic
20#14556588C2311yescharacteristic
21#14556583C2×C412yes—
22#14556579D412yes—
23#14556570—41no—
24#14556565—41no—
25C4×Dic146—41no—
26C4×D292—41no—
27#14556550—21no—
28#14556516—24no—
29#14556513—24no—
30C22×C8×C73—21no—
31C2×C42×C73C2×C411yescharacteristic
32#97×C73—21no—
33#97×C73C2×C412yes—
34C4⋊#64408—82no—
35C22⋊#64408—44no—
36C4×#64408—82no—
37#11924028—42no—
38#11924028—42no—
39C2×Dic146—41no—
40C2×Dic146C22⋊C412yes—
41C2×D292—41no—
42C2×D292C2×D412yes—
43C2×C22⋊D73—22no—
44C2×C4×D73—22no—
45C4⋊Dic73—22no—
46C4⋊Dic73—41no—
47C4⋊Dic73—41no—
48#11924007—42no—
49C22⋊Dic73—41no—
50#11924005—42no—
51C4×Dic73—41no—
52C22×C4×C73—21no—
53C22×C4×C73C22⋊C411yescharacteristic
54C2×C8×C73—22no—
55C2×C8×C73—41no—
56C2×C8×C73—41no—
57C42×C73—21no—
58C42×C73C22⋊C411yescharacteristic
59C42×C73C22×C411yescharacteristic
60C23×C73#9911yescharacteristic
61C22×D73—22no—
62C2×#64408—84no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—81no—
68C2×C4×C73#9911yescharacteristic
69C2×C4×C73C2×C22⋊C411yescharacteristic
70C22⋊D73—82no—
71C2×Dic73—22no—
72C2×Dic73—42no—
73D292—42no—
74D292—82no—
75C4×D73—42no—
76C4×D73—42no—
77Dic146—42no—
78Dic146—82no—
79C8×C73—42no—
80C22×C73—21no—
81C22×C73—41no—
82C22×C73C2×#9911yescharacteristic
83C2×D73—42no—
84C2×D73—82no—
85#64408—164no—
86C4×C73—21no—
87C4×C73—41no—
88C4×C73—41no—
89C4×C73#35411yescharacteristic
90C4×C73#35411yescharacteristic
91Dic73—42no—
92Dic73—82no—
93#13594—731nomaximal, Sylow
94C2×C73—21no—
95C2×C73—41no—
96C2×C73C2×#35411yescharacteristic
97D73—82no—
98#3135—731no—
99#2126—732no—
100#1412—734no—
101C73#1359411yescharacteristic, complemented, Sylow
102#533—731no—
103#532—731no—
104#491—732no—
105#490—732no—
106#489—1462no—
107#416—1462no—
108#410—1462no—
109C2×#97#6440811yescharacteristic, complemented
110#354—1462no—
111#353—734no—
112C2×#41—732no—
113C22×C8—21no—
114C4⋊Q8—731no—
115C4⋊Q8—1461no—
116#127—731no—
117#125—732no—
118#124—732no—
119C22⋊Q8—2921no—
120#121—2921no—
121C4×Q8—2921no—
122C4×D4—2921no—
123#117—2922no—
124#117—1461no—
125C2×C42C2×#6440811yescharacteristic
126#103—1464no—
127#102—1464no—
128#99—2922no—
129#99—1464no—
130#97—21no—
131#97C2×#6440812yes—
132#41—2922no—
133#41—2922no—
134C2×Q8—2921no—
135C2×Q8—732no—
136C2×D4—2921no—
137C2×D4—732no—
138C2×D4—1462no—
139C22×C4—21no—
140C22×C4—1462no—
141C22×C4C22⋊#6440811yescharacteristic
142C2×C8—22no—
143C2×C8—41no—
144C2×C8—41no—
145C4⋊C4—2922no—
146C4⋊C4—2921no—
147C4⋊C4—2921no—
148C4⋊C4—5842no—
149C4⋊C4—1462no—
150C22⋊C4—2922no—
151C22⋊C4—2921no—
152C22⋊C4—2924no—
153C42—21no—
154C42—2921no—
155C42—5842no—
156C42C22⋊#6440811yescharacteristic
157C42C22×#6440811yescharacteristic
158C23—1462no—
159C23#1455665011yescharacteristic
160Q8—2922no—
161Q8—5842no—
162D4—2922no—
163D4—5842no—
164D4—5842no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—81no—
170C2×C4—2922no—
171C2×C4—2922no—
172C2×C4—2922no—
173C2×C4—5844no—
174C2×C4—1462no—
175C2×C4#1455665011yescharacteristic
176C2×C4C2×C22⋊#6440811yescharacteristic
177C8—42no—
178C22—21no—
179C22—41no—
180C22—2922no—
181C22—5842no—
182C22C2×#1455665011yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—2922no—
187C4—5842no—
188C4—11684no—
189C4#1798949411yescharacteristic
190C4#1798949411yescharacteristic
191C2—21no—
192C2—41no—
193C2—5842no—
194C2C2×#1798949411yescharacteristic
subgroupG/H
centerC4#17989494
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
FittingC2×#97×C73C4
socleC2×C73C2×#354
prime radical#17989137C22
cosocle#14556588C23
hypercenterC2×#97#64408
hypocenterC73#13594
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. #22625072C2semidirect
7. #17989144C4semidirect
9. #17988956C4semidirect
13. C2×#97×C73C4semidirect
101. C73#13594semidirect
109. C2×#97#64408semidirect

Maximal subgroups

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

subgroupindex
#226262042
#226250722
#226202772
#1359473