Finite Group Databasebeta

← #34011499

Subgroups — #34011499

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#22624938C212yesmaximal, complemented
4#22624937C212yesmaximal, complemented
5#22620591C211yesmaximal, characteristic
6#17989643—21no—
7#17989509—21no—
8#17989484—21no—
9#17989480—21no—
10#17989479C2212yes—
11#17989479C2211yescharacteristic
12#17989479C2211yescharacteristic
13#17989200C412yes—
14#17988967C411yescharacteristic
15#17988957C2212yes—
16#17988846—21no—
17#17988829—21no—
18#17988693—21no—
19#17988681—21no—
20#17988541C2211yescharacteristic
21#499×C73C411yescharacteristic
22#14556666—22no—
23#14556665—21no—
24#14556665—21no—
25#14556665—22no—
26#14556664—22no—
27C2×Dic292—21no—
28C2×Dic292—21no—
29C2×#11924011D411yescharacteristic
30C2×C8×D73D411yescharacteristic
31#14556591C2×C412yes—
32#14556586—42no—
33#14556582—42no—
34#14556571—22no—
35#14556556—22no—
36#14556548C2×C411yescharacteristic
37#14556514—22no—
38#14556514—22no—
39#14556502C2311yescharacteristic
40#14556501D411yescharacteristic
41C8×Dic73D411yescharacteristic
42#125×C73C2×C412yes—
43#107×C73—21no—
44#106×C73—21no—
45C4×C8×C73C2×C411yescharacteristic
46#11924031—22no—
47#11924031—22no—
48#11924031—42no—
49C2×Dic146—22no—
50C2×C4×D73C22⋊C411yescharacteristic
51Dic292—42no—
52Dic292—41no—
53Dic292—41no—
54#11924011—41no—
55C2×#10596831C2×D411yescharacteristic
56C2×#10596831C2×D411yescharacteristic
57C8×D73—21no—
58C8×D73—21no—
59C4⋊Dic73—42no—
60C4⋊Dic73—42no—
61#11924007—21no—
62#11924007—42no—
63#11924005—21no—
64#11924005—42no—
65C4×Dic73—42no—
66C4×Dic73C22⋊C411yescharacteristic
67C2×C8×C73C22⋊C411yescharacteristic
68C2×C8×C73C22⋊C411yescharacteristic
69C4⋊C4×C73—22no—
70C4⋊C4×C73—42no—
71C42×C73C22×C411yescharacteristic
72C22×D73#10011yescharacteristic
73C2×C4×C73—21no—
74C2×C4×C73—42no—
75C2×C4×C73C2×C22⋊C411yescharacteristic
76C2×Dic73—21no—
77C2×Dic73—42no—
78C2×Dic73#10011yescharacteristic
79C4×D73—21no—
80C4×D73—21no—
81Dic146—42no—
82Dic146—42no—
83C8×C73—21no—
84C8×C73#10411yescharacteristic
85C8×C73#10411yescharacteristic
86#10596831—21no—
87#10596831—21no—
88C22×C73C2×#10011yescharacteristic
89C2×D73—21no—
90C2×D73—41no—
91C4×C73—41no—
92C4×C73—82no—
93C4×C73C2×#10411yescharacteristic
94C4×C73#42111yescharacteristic
95Dic73—21no—
96Dic73—41no—
97Dic73—82no—
98#11914—731nomaximal, Sylow
99C2×C73—21no—
100C2×C73#153011yescharacteristic
101D73—41no—
102#3177—731no—
103#2166—731no—
104#2110—731no—
105#1356—732no—
106#1356—732no—
107C73#1191411yescharacteristic, complemented, Sylow
108#541—732no—
109C2×M32—1461no—
110#499#6440811yescharacteristic
111#494—731no—
112#491—732no—
113#470—1461no—
114#467—1461no—
115#441—1461no—
116C4×Q16—1461no—
117#405—731no—
118#364—1461no—
119#349—1461no—
120#347—731no—
121#347—731no—
122#347—732no—
123#347—1461no—
124C2×Q16—1461no—
125C2×Q16—1461no—
126C2×M16—731no—
127C22×C8—731no—
128C4⋊Q8—732no—
129#126—2922no—
130#125—2922no—
131#125C2×#6440812yes—
132C22⋊Q8—1462no—
133C4×Q8—1462no—
134#117—731no—
135M32—1462no—
136M32—1461no—
137M32—1461no—
138M32—1462no—
139C2×C16—1462no—
140#107—21no—
141#106—21no—
142#103—1462no—
143#103—1462no—
144#97—731no—
145#97—731no—
146C4×C8—731no—
147C4×C8C2×#6440811yescharacteristic
148C2×Q8—1462no—
149C22×C4—731no—
150Q16—2922no—
151Q16—2921no—
152Q16—2921no—
153M16—2921no—
154C2×C8—731no—
155C2×C8—731no—
156C2×C8—1461no—
157C2×C8—1461no—
158C2×C8C22⋊#6440811yescharacteristic
159C2×C8C22⋊#6440811yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—42no—
162C4⋊C4—2922no—
163C4⋊C4—2922no—
164C4⋊C4—2922no—
165C4⋊C4—1461no—
166C22⋊C4—2922no—
167C22⋊C4—1461no—
168C42—2922no—
169C42—731no—
170C42C22×#6440811yescharacteristic
171C16—2922no—
172C16—1462no—
173C16—1462no—
174C23—731no—
175Q8—2922no—
176Q8—2922no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—2922no—
180C2×C4—731no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4C2×C22⋊#6440811yescharacteristic
185C8—21no—
186C8—1461no—
187C8—1461no—
188C8#1455665611yescharacteristic
189C8#1455665611yescharacteristic
190C22—2921no—
191C22—1461no—
192C22D73⋊#10011yescharacteristic
193C4—41no—
194C4—82no—
195C4—2921no—
196C4—5842no—
197C4—1461no—
198C4C2×#1455665611yescharacteristic
199C4#1798958611yescharacteristic
200C2—21no—
201C2—2921no—
202C2#2262540211yescharacteristic
subgroupG/H
centerC2#22625402
commutatorC42×C73C22×C4
FrattiniC42C22×#64408
Fitting#499×C73C4
socleC2×C73#1530
prime radicalC22×D73#100
cosocle#14556502C23
hypercenter#499#64408
hypocenterC73#11914
LCSG ▷ C42×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
3. #22624938C2semidirect
4. #22624937C2semidirect
107. C73#11914semidirect

Maximal subgroups

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

subgroupindex
#226263062
#226261532
#226249382
#226249372
#226205912
#1191473