Finite Group Databasebeta

← #34003834

Subgroups — #34003834

Order 18688.

368 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 100 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#22626721C211yesmaximal, characteristic
2#22625437C211yesmaximal, characteristic
3#22625139C212yesmaximal
4#22624816C212yesmaximal
5#22608524C211yesmaximal, characteristic
6#17989639—22no—
7#17989636—22no—
8#17989605C2212yes—
9#17989594C412yes—
10#17989592C2211yescharacteristic
11#17989552C412yes—
12C4×#11924036C2211yescharacteristic
13#17989446C414yes—
14#17989429—22no—
15#17989429—22no—
16#17989143C2211yescharacteristic
17#17988539C2212yes—
18#17988329C411yescharacteristic
19#17988328C412yes—
20#330×C73C411yescharacteristic
21C2×#11924038C2×C412yes—
22C2×#11924036C2×C411yescharacteristic
23C2×#11924036C2×C411yescharacteristic
24#14556658—22no—
25#14556658—22no—
26#14556658C2×C414yes—
27C4⋊#10596833—22no—
28#14556648—22no—
29#14556646—22no—
30C4×#10596833—22no—
31C4×#10596833—22no—
32C4×#10596833D412yes—
33C4×#10596833D412yes—
34C2×#11924011—22no—
35#14556590C2×C412yes—
36#14556583C2×C411yescharacteristic
37#14556569—22no—
38#14556556—22no—
39#14556549C2×C412yes—
40C42×D73C2311yescharacteristic
41#14556502C2×C412yes—
42C8×Dic73—22no—
43#125×C73C2×C411yescharacteristic
44#97×C73C2×C412yes—
45#11924038—42no—
46#11924036—22no—
47#11924036—41no—
48C2×#10596833—22no—
49C2×#10596833—24no—
50C2×#10596833C22⋊C411yescharacteristic
51C2×#10596833C22⋊C412yes—
52C2×#10596833C22⋊C411yescharacteristic
53C2×Dic146—22no—
54C2×C4×D73C22×C411yescharacteristic
55C2×C4×D73#4112yes—
56#11924011—44no—
57C2×#10596831—22no—
58C4⋊Dic73C4212yes—
59#11924007—22no—
60#11924007—22no—
61#11924005—22no—
62C4×Dic73—22no—
63C4×Dic73C22×C411yescharacteristic
64C4×Dic73C2×D412yes—
65C2×C8×C73—22no—
66C4⋊C4×C73—22no—
67C4⋊C4×C73C4212yes—
68C42×C73C22×C411yescharacteristic
69C22×D73#11711yescharacteristic
70C2×C4×C73—22no—
71C2×C4×C73C2×C4211yescharacteristic
72C2×C4×C73C4×D412yes—
73C2×Dic73—22no—
74C2×Dic73C2×C22⋊C411yescharacteristic
75C2×Dic73C4×D412yes—
76C4×D73—21no—
77C4×D73—21no—
78C4×D73—24no—
79Dic146—44no—
80#10596833—21no—
81#10596833—22no—
82#10596833—42no—
83#10596833—44no—
84#10596833#10112yes—
85C8×C73—42no—
86#10596831—42no—
87C22×C73C4×C22⋊C411yescharacteristic
88C2×D73—21no—
89C2×D73—22no—
90C4×C73—21no—
91C4×C73—22no—
92C4×C73—42no—
93Dic73—42no—
94Dic73C2×#10111yescharacteristic
95Dic73#41311yescharacteristic
96Dic73#44414yes—
97#8244—731nomaximal, Sylow
98C2×C73C4×#10111yescharacteristic
99C2×C73#176512yes—
100D73—41no—
101#2960—731no—
102#1544—731no—
103#1526—731no—
104#1451—732no—
105#1299—732no—
106C73#824411yescharacteristic, complemented, Sylow
107#533—731no—
108#446—1462no—
109C8×Q8—1462no—
110#431—732no—
111#424—732no—
112#423—731no—
113#405—732no—
114C4×M16—732no—
115C2×C4×C8—731no—
116#332—734no—
117#330—731no—
118#330—732no—
119#330#6440811yescharacteristic
120#322—1462no—
121#322—1462no—
122C2×M16—732no—
123C2×M16—1462no—
124C22×C8—731no—
125C22×C8—731no—
126C4⋊Q8—732no—
127#125—731no—
128#125C2×#6440811yescharacteristic
129C22⋊Q8—1462no—
130C4×Q8—1462no—
131#117—732no—
132C2×C42—731no—
133C4⋊C8—734no—
134C4⋊C8—1462no—
135C4⋊C8—1462no—
136C4⋊C8—1462no—
137C22⋊C8—1462no—
138#97—732no—
139#97—1462no—
140#97C2×#6440812yes—
141C4×C8—732no—
142C4×C8—732no—
143C4×C8—1462no—
144C4×C8—1462no—
145C4×C8—1462no—
146C2×Q8—1462no—
147C22×C4—731no—
148C22×C4—732no—
149M16—2924no—
150M16—2922no—
151C2×C8—22no—
152C2×C8—2921no—
153C2×C8—731no—
154C2×C8—731no—
155C2×C8—732no—
156C2×C8—1462no—
157C2×C8—1464no—
158C2×C8—1462no—
159C2×C8—1462no—
160C4⋊C4—22no—
161C4⋊C4—732no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C4⋊C4C4×#6440812yes—
165C22⋊C4—1462no—
166C42—731no—
167C42—732no—
168C42—1462no—
169C42C22×#6440811yescharacteristic
170C23—731no—
171Q8—2924no—
172C2×C4—22no—
173C2×C4—731no—
174C2×C4—732no—
175C2×C4—1461no—
176C2×C4—1461no—
177C2×C4—1464no—
178C2×C4—1462no—
179C2×C4C2×C4×#6440811yescharacteristic
180C2×C4D4×#6440812yes—
181C8—42no—
182C8—2922no—
183C8—2922no—
184C8—2924no—
185C8—732no—
186C8—1462no—
187C8—1461no—
188C22—1461no—
189C22—1462no—
190C22C22⋊C4×#6440811yescharacteristic
191C4—21no—
192C4—22no—
193C4—42no—
194C4—2922no—
195C4—731no—
196C4—731no—
197C4—734no—
198C2—2921no—
199C2#101×#6440811yescharacteristic
200C2#2262571112yes—
subgroupG/H
centerC22C22⋊C4×#64408
commutatorC2×C4×C73C2×C42
FrattiniC42C22×#64408
Fitting#330×C73C4
socleC22×C73C4×C22⋊C4
prime radicalC22×D73#117
cosocleC42×D73C23
hypercenter#330#64408
hypocenterC73#8244
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
106. C73#8244semidirect

Maximal subgroups

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

subgroupindex
#226267212
#226254372
#226251392
#226248162
#226085242
#824473