Finite Group Databasebeta

← #34011498

Subgroups — #34011498

Order 18688.

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

normal subgroups only

This group has 272 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
2#22626153C211yesmaximal, characteristic
3#22624936C214yesmaximal, complemented
4#22620587C211yesmaximal, characteristic
5#17989643—21no—
6#17989509—21no—
7#17989484—21no—
8#17989480—21no—
9#17989479C2212yes—
10#17989479C2212yes—
11#17989198C412yes—
12#17988989C411yescharacteristic
13#17988955C2212yes—
14#17988842—21no—
15#17988825—21no—
16#17988694—21no—
17Q16×Dic73—21no—
18#17988541C2211yescharacteristic
19#494×C73C411yescharacteristic
20#14556666—22no—
21#14556665—22no—
22#14556665—22no—
23#14556664—22no—
24C2×#11924011D411yescharacteristic
25C2×C8×D73D411yescharacteristic
26#14556586—42no—
27#14556583C2×C412yes—
28#14556581—42no—
29#14556567—22no—
30Q8×Dic73—22no—
31#14556548C2×C411yescharacteristic
32#14556525—21no—
33#14556523—21no—
34#14556515—22no—
35#14556515—22no—
36#14556502C2311yescharacteristic
37#14556501D411yescharacteristic
38C8×Dic73D411yescharacteristic
39C2×Q16×C73—21no—
40C2×Q16×C73—21no—
41C4⋊Q8×C73C2×C412yes—
42C4×C8×C73C2×C411yescharacteristic
43#11924031—24no—
44#11924031—42no—
45C2×C4×D73C22⋊C411yescharacteristic
46#11924011—41no—
47C2×#10596831C2×D411yescharacteristic
48C2×#10596831C2×D411yescharacteristic
49C8×D73—21no—
50C8×D73—21no—
51C4⋊Dic73—22no—
52C4⋊Dic73—42no—
53#11924007—21no—
54#11924007—42no—
55#11924007—42no—
56#11924005—21no—
57#11924005—42no—
58C4×Dic73—42no—
59C4×Dic73C22⋊C411yescharacteristic
60C2×Q8×C73—22no—
61Q16×C73—42no—
62Q16×C73—41no—
63Q16×C73—41no—
64C2×C8×C73C22⋊C411yescharacteristic
65C2×C8×C73C22⋊C411yescharacteristic
66C4⋊C4×C73—42no—
67C42×C73C22×C411yescharacteristic
68C22×D73#10011yescharacteristic
69Q8×C73—42no—
70Q8×C73—42no—
71C2×C4×C73—21no—
72C2×C4×C73—42no—
73C2×C4×C73C2×C22⋊C411yescharacteristic
74C2×Dic73—21no—
75C2×Dic73—42no—
76C2×Dic73#10011yescharacteristic
77C4×D73—21no—
78C4×D73—21no—
79C8×C73—21no—
80C8×C73#10411yescharacteristic
81C8×C73#10411yescharacteristic
82#10596831—21no—
83#10596831—21no—
84C22×C73C2×#10011yescharacteristic
85C2×D73—21no—
86C2×D73—41no—
87C4×C73—41no—
88C4×C73—82no—
89C4×C73C2×#10411yescharacteristic
90C4×C73#42111yescharacteristic
91Dic73—21no—
92Dic73—41no—
93Dic73—82no—
94#11914—731nomaximal, Sylow
95C2×C73—21no—
96C2×C73#153011yescharacteristic
97D73—41no—
98#3177—731no—
99#2166—731no—
100#2110—731no—
101#1356—734no—
102C73#1191411yescharacteristic, complemented, Sylow
103#541—732no—
104C2×M32—1461no—
105#499—731no—
106#494#6440811yescharacteristic
107#491—732no—
108#470—1461no—
109#467—1461no—
110#441—1461no—
111C4×Q16—1461no—
112#405—731no—
113#364—1461no—
114#349—1461no—
115#347—732no—
116#347—732no—
117#347—1461no—
118C2×Q16—21no—
119C2×Q16—21no—
120C2×M16—731no—
121C22×C8—731no—
122C4⋊Q8C2×#6440812yes—
123#126—2922no—
124#125—2922no—
125#125—732no—
126C22⋊Q8—1462no—
127C4×Q8—1462no—
128#117—731no—
129M32—1462no—
130M32—1462no—
131M32—1462no—
132C2×C16—1462no—
133#107—1461no—
134#106—1461no—
135#103—1462no—
136#103—1462no—
137#97—731no—
138#97—731no—
139C4×C8—731no—
140C4×C8C2×#6440811yescharacteristic
141C2×Q8—22no—
142C22×C4—731no—
143Q16—42no—
144Q16—41no—
145Q16—41no—
146M16—2921no—
147C2×C8—731no—
148C2×C8—731no—
149C2×C8—1461no—
150C2×C8—1461no—
151C2×C8C22⋊#6440811yescharacteristic
152C2×C8C22⋊#6440811yescharacteristic
153C4⋊C4—42no—
154C4⋊C4—2922no—
155C4⋊C4—2922no—
156C4⋊C4—2922no—
157C4⋊C4—1461no—
158C4⋊C4—1462no—
159C22⋊C4—2922no—
160C22⋊C4—1461no—
161C42—2922no—
162C42—731no—
163C42C22×#6440811yescharacteristic
164C16—2922no—
165C16—1464no—
166C23—731no—
167Q8—42no—
168Q8—42no—
169C2×C4—21no—
170C2×C4—42no—
171C2×C4—2922no—
172C2×C4—731no—
173C2×C4—1461no—
174C2×C4—1461no—
175C2×C4—1461no—
176C2×C4C2×C22⋊#6440811yescharacteristic
177C8—21no—
178C8—1461no—
179C8—1461no—
180C8#1455665511yescharacteristic
181C8#1455665511yescharacteristic
182C22—2921no—
183C22—1461no—
184C22D73⋊#10011yescharacteristic
185C4—41no—
186C4—82no—
187C4—2921no—
188C4—5842no—
189C4—1461no—
190C4C2×#1455665511yescharacteristic
191C4#1798958511yescharacteristic
192C2—21no—
193C2—2921no—
194C2#2262540111yescharacteristic
subgroupG/H
centerC2#22625401
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#494×C73C4
socleC2×C73#1530
prime radicalC22×D73#100
cosocle#14556502C23
hypercenter#494#64408
hypocenterC73#11914
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #22624936C2semidirect
102. C73#11914semidirect

Maximal subgroups

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

subgroupindex
#226263062
#226261532
#226249362
#226205872
#1191473