Finite Group Databasebeta

← #34034369

Subgroups — #34034369

Order 18688.

334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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#22627120C211yesmaximal, characteristic
2#22627087C211yesmaximal, characteristic
3#22627011C214yesmaximal
4#22626721C211yesmaximal, characteristic
5C2×#14556688C2212yes—
6C2×#14556686C2212yes—
7C4⋊#11924040—22no—
8#17989681—22no—
9#17989639—22no—
10#17989636—22no—
11#17989594C412yes—
12#17989592C411yescharacteristic
13#17989552C2212yes—
14C4×#11924036C2211yescharacteristic
15#17989143C411yescharacteristic
16#14556688—24no—
17#14556686—22no—
18#14556686Q814yescomplemented
19C2×#11924040—22no—
20C2×#11924040—22no—
21C2×#11924038C2×C412yes—
22C2×#11924036C2×C411yescharacteristic
23C2×#11924036C2311yescharacteristic
24#14556658—22no—
25#14556658—22no—
26C4⋊#10596833—22no—
27#14556646—22no—
28C4×#10596833—22no—
29C4×#10596833D412yes—
30C4×#10596833D412yes—
31#14556590C812yes—
32#14556583C811yescharacteristic
33#14556569—22no—
34#14556556—22no—
35#14556549C2×C412yes—
36C42×D73C2×C411yescharacteristic
37#125×C73C811yescharacteristic
38#11924040—24no—
39#11924040—42no—
40#11924038—24no—
41#11924036—22no—
42#11924036C2×Q812yes—
43#11924036#4112yes—
44C2×#10596833—22no—
45C2×#10596833C22⋊C412yes—
46C2×#10596833C2×D411yescharacteristic
47C2×#10596833C2×D411yescharacteristic
48C2×Dic146—22no—
49C2×C4×D73M1612yes—
50C2×C4×D73C22×C411yescharacteristic
51C4⋊Dic73C2×C812yes—
52#11924007—22no—
53#11924007—22no—
54#11924005—22no—
55C4×Dic73—22no—
56C4×Dic73C22⋊C412yes—
57C4×Dic73C2×C811yescharacteristic
58C4⋊C4×C73—22no—
59C4⋊C4×C73C2×C812yes—
60C42×C73C2×C811yescharacteristic
61C22×D73C2×M1611yescharacteristic
62C2×C4×C73—22no—
63C2×C4×C73C22⋊C812yes—
64C2×C4×C73C22×C811yescharacteristic
65C2×Dic73—22no—
66C2×Dic73C22⋊C812yes—
67C2×Dic73C2×C22⋊C411yescharacteristic
68C4×D73—42no—
69C4×D73C4×Q812yes—
70C4×D73#13112yes—
71Dic146—44no—
72#10596833—22no—
73#10596833—42no—
74#10596833C22⋊Q812yes—
75#10596833#12411yescharacteristic
76#10596833C4⋊Q811yescharacteristic
77C22×C73C2×C22⋊C811yescharacteristic
78C2×D73—22no—
79C2×D73#44612yes—
80C4×C73—22no—
81C4×C73—42no—
82C4×C73C8×Q812yes—
83Dic73—22no—
84Dic73—42no—
85Dic73#39111yescharacteristic
86Dic73#40811yescharacteristic
87#13267—731nomaximal, Sylow
88C2×C73#198411yescharacteristic
89C2×C73#211712yes—
90D73—22no—
91#2960—731no—
92#2150—731no—
93C2×#346—731no—
94#1379—734no—
95C73#1326711yescharacteristic, complemented, Sylow
96#533—731no—
97C2×M32—732no—
98C22×C16—732no—
99#446—1462no—
100C8×Q8—1462no—
101#424—732no—
102#423—731no—
103#405—732no—
104C2×C4×C8—731no—
105C4⋊C16—1462no—
106#346—1462no—
107C2×M16—732no—
108C22×C8—731no—
109C22×C8—731no—
110C4⋊Q8—732no—
111#125—731no—
112#125#1059684211yescharacteristic
113C22⋊Q8—1462no—
114C4×Q8—1462no—
115#117—732no—
116C2×C42—731no—
117M32—1464no—
118C2×C16—734no—
119C2×C16—1462no—
120C2×C16—1462no—
121C2×C16—1462no—
122C4⋊C8—1462no—
123C4⋊C8—1462no—
124C4⋊C8—1462no—
125#97—1462no—
126C4×C8—732no—
127C4×C8—732no—
128C4×C8—1462no—
129C2×Q8—1462no—
130C22×C4—732no—
131C22×C4—731no—
132M16—1464no—
133C2×C8—731no—
134C2×C8—731no—
135C2×C8—732no—
136C2×C8—732no—
137C2×C8—732no—
138C2×C8—1462no—
139C2×C8—1462no—
140C4⋊C4—22no—
141C4⋊C4—732no—
142C4⋊C4—1462no—
143C4⋊C4—1462no—
144C4⋊C4C2×#1059684212yes—
145C22⋊C4—1462no—
146C42—732no—
147C42—731no—
148C42—1462no—
149C42C2×#1059684211yescharacteristic
150C16—2922no—
151C16—1464no—
152C23—731no—
153Q8—2924no—
154C2×C4—22no—
155C2×C4—2922no—
156C2×C4—731no—
157C2×C4—732no—
158C2×C4—732no—
159C2×C4—732no—
160C2×C4—1462no—
161C2×C4C22⋊#1059684212yes—
162C2×C4C22×#1059684211yescharacteristic
163C8—2922no—
164C8—731no—
165C8—732no—
166C8—731no—
167C8—1462no—
168C22—732no—
169C22—1462no—
170C22C2×C22⋊#1059684211yescharacteristic
171C4—22no—
172C4—42no—
173C4—2922no—
174C4—731no—
175C4—731no—
176C4—1462no—
177C4Q8×#1059684212yes—
178C2—1462no—
179C2(C2×#10596842)⋊Q811yescharacteristic
180C2#2262711412yes—
subgroupG/H
centerC22C2×C22⋊#10596842
commutatorC2×C4×C73C22×C8
FrattiniC2×C4C22×#10596842
Fitting#125×C73C8
socleC22×C73C2×C22⋊C8
prime radicalC22×D73C2×M16
cosocleC2×#11924036C23
hypercenter#125#10596842
hypocenterC73#13267
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
18. #14556686Q8semidirect
95. C73#13267semidirect

Maximal subgroups

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

subgroupindex
#226271202
#226270872
#226270112
#226267212
#1326773