Finite Group Databasebeta

← #34011494

Subgroups — #34011494

Order 18688.

296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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#22626306C211yesmaximal, characteristic, complemented
2#22626153C211yesmaximal, characteristic, complemented
3#22624933C214yesmaximal, complemented
4#22620578C211yesmaximal, characteristic
5#17989643—21no—
6#17989509—21no—
7#17989484—21no—
8#17989480—21no—
9#17989479C2212yes—
10#17989479C2212yes—
11#17989191C412yes—
12#17988989C411yescharacteristic
13#17988951C2212yes—
14#17988837—21no—
15#17988820—21no—
16#17988699—21no—
17D8×Dic73—21no—
18#17988541C2211yescharacteristic
19#493×C73C411yescharacteristic
20#14556666—22no—
21#14556665—22no—
22#14556665—22no—
23#14556664—22no—
24C2×#11924011D411yescharacteristic
25C2×C8×D73D411yescharacteristic
26#14556583C2×C412yes—
27#14556572—42no—
28#14556563—42no—
29#14556562—22no—
30D4×Dic73—22no—
31#14556548C2×C411yescharacteristic
32#14556525—21no—
33#14556523—21no—
34#14556512—22no—
35#14556512—22no—
36#14556502C2311yescharacteristic
37#14556501D411yescharacteristic
38C8×Dic73D411yescharacteristic
39C2×D8×C73—21no—
40C2×D8×C73—21no—
41#127×C73C2×C412yes—
42C4×C8×C73C2×C411yescharacteristic
43#11924031—24no—
44#11924031—42no—
45C2×C22⋊D73—42no—
46C22×Dic73—42no—
47C2×C4×D73C22⋊C411yescharacteristic
48#11924011—41no—
49C2×#10596831C2×D411yescharacteristic
50C2×#10596831C2×D411yescharacteristic
51C8×D73—21no—
52C8×D73—21no—
53C4⋊Dic73—22no—
54#11924007—21no—
55#11924007—42no—
56C22⋊Dic73—42no—
57C22⋊Dic73—42no—
58#11924005—21no—
59C4×Dic73C22⋊C411yescharacteristic
60C2×D4×C73—22no—
61C2×D4×C73—42no—
62D8×C73—42no—
63D8×C73—41no—
64D8×C73—41no—
65C2×C8×C73C22⋊C411yescharacteristic
66C2×C8×C73C22⋊C411yescharacteristic
67C42×C73C22×C411yescharacteristic
68C23×C73—42no—
69C22×D73#10011yescharacteristic
70D4×C73—42no—
71D4×C73—42no—
72D4×C73—162no—
73C2×C4×C73—21no—
74C2×C4×C73C2×C22⋊C411yescharacteristic
75C22⋊D73—162no—
76C2×Dic73—21no—
77C2×Dic73—42no—
78C2×Dic73—162no—
79C2×Dic73#10011yescharacteristic
80C4×D73—21no—
81C4×D73—21no—
82C8×C73—21no—
83C8×C73#10411yescharacteristic
84C8×C73#10411yescharacteristic
85#10596831—21no—
86#10596831—21no—
87C22×C73—82no—
88C22×C73—82no—
89C22×C73—82no—
90C22×C73C2×#10011yescharacteristic
91C2×D73—21no—
92C2×D73—41no—
93C4×C73—41no—
94C4×C73C2×#10411yescharacteristic
95C4×C73#42111yescharacteristic
96Dic73—21no—
97Dic73—41no—
98Dic73—82no—
99#11913—731nomaximal, Sylow
100C2×C73—21no—
101C2×C73—162no—
102C2×C73#153011yescharacteristic
103D73—41no—
104#3176—731no—
105#2166—731no—
106#2110—731no—
107#1355—734no—
108C73#1191311yescharacteristic, complemented, Sylow
109#540—732no—
110C2×M32—1461no—
111#499—731no—
112#493#6440811yescharacteristic
113#490—732no—
114#469—1461no—
115#466—1461no—
116#442—1461no—
117C4×D8—1461no—
118#405—731no—
119#364—1461no—
120#349—1461no—
121#347—732no—
122#347—732no—
123#347—1461no—
124C2×D8—21no—
125C2×D8—21no—
126C2×M16—731no—
127C22×C8—731no—
128#127C2×#6440812yes—
129#125—732no—
130#123—2922no—
131#121—2922no—
132#121—1462no—
133C4×D4—1462no—
134#117—731no—
135M32—1462no—
136M32—1462no—
137M32—1462no—
138C2×C16—1462no—
139#107—1461no—
140#106—1461no—
141#102—1462no—
142#102—1462no—
143#97—731no—
144#97—731no—
145C4×C8—731no—
146C4×C8C2×#6440811yescharacteristic
147C2×D4—22no—
148C2×D4—42no—
149C2×D4—2922no—
150C22×C4—2922no—
151C22×C4—731no—
152D8—42no—
153D8—41no—
154D8—41no—
155M16—2921no—
156C2×C8—731no—
157C2×C8—731no—
158C2×C8—1461no—
159C2×C8—1461no—
160C2×C8C22⋊#6440811yescharacteristic
161C2×C8C22⋊#6440811yescharacteristic
162C4⋊C4—2922no—
163C4⋊C4—1461no—
164C4⋊C4—1462no—
165C22⋊C4—2922no—
166C22⋊C4—2922no—
167C22⋊C4—1461no—
168C42—731no—
169C42C22×#6440811yescharacteristic
170C16—2922no—
171C16—1464no—
172C23—42no—
173C23—731no—
174D4—42no—
175D4—42no—
176D4—162no—
177D4—11682no—
178C2×C4—21no—
179C2×C4—2922no—
180C2×C4—731no—
181C2×C4—11682no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4C2×C22⋊#6440811yescharacteristic
186C8—21no—
187C8—1461no—
188C8—1461no—
189C8#1455665511yescharacteristic
190C8#1455665511yescharacteristic
191C22—82no—
192C22—82no—
193C22—82no—
194C22—2921no—
195C22—1461no—
196C22D73⋊#10011yescharacteristic
197C4—41no—
198C4—2921no—
199C4—5842no—
200C4—1461no—
201C4C2×#1455665511yescharacteristic
202C4#1798958511yescharacteristic
203C2—21no—
204C2—162no—
205C2—2921no—
206C2#2262540111yescharacteristic
subgroupG/H
centerC2#22625401
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#493×C73C4
socleC2×C73#1530
prime radical#22620578C2
cosocle#14556502C23
hypercenter#493#64408
hypocenterC73#11913
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #22626306C2semidirect
2. #22626153C2semidirect
3. #22624933C2semidirect
108. C73#11913semidirect

Maximal subgroups

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

subgroupindex
#226263062
#226261532
#226249332
#226205782
#1191373