Finite Group Databasebeta

← #34011643

Subgroups — #34011643

Order 18688.

284 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 76 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#22626294C211yesmaximal, characteristic
2#22625494C211yesmaximal, characteristic
3#22624948C214yesmaximal, complemented
4#22620442C211yesmaximal, characteristic
5#17989609—21no—
6#17989508C2212yes—
7#17989482—21no—
8#17989475—21no—
9#17989451—21no—
10#17989449C2212yes—
11#17989142—21no—
12#17988992C411yescharacteristic
13#17988988—21no—
14#17988988C2212yes—
15#17988983—21no—
16#17988624—21no—
17#17988624C412yes—
18C4×C8×D73C2211yescharacteristic
19#500×C73C411yescharacteristic
20C2×#11924031—22no—
21C4⋊#10596833—22no—
22#14556648—41no—
23#14556646—41no—
24C2×C8×D73C2×C411yescharacteristic
25C2×C8×D73D411yescharacteristic
26#14556591—21no—
27#14556582—22no—
28#14556571—41no—
29#14556567—41no—
30Q8×Dic73—41no—
31#14556556—41no—
32#14556549—22no—
33C42×D73D411yescharacteristic
34#14556525—21no—
35#14556525C2×C412yes—
36#14556522—22no—
37#14556522—22no—
38C4×#10596831D411yescharacteristic
39C8×Dic73D411yescharacteristic
40C8×Dic73C2311yescharacteristic
41C4⋊Q8×C73—21no—
42#107×C73—21no—
43#107×C73C2×C412yes—
44C4×C8×C73C2×C411yescharacteristic
45C2×#10596833—42no—
46#11924031—42no—
47C2×Dic146—41no—
48C2×C4×D73C22⋊C411yescharacteristic
49C2×C4×D73D811yescharacteristic
50C2×C4×D73SD1611yescharacteristic
51C2×#10596831C22⋊C411yescharacteristic
52C2×#10596831C2×D411yescharacteristic
53C8×D73—22no—
54C8×D73—22no—
55C4⋊Dic73—22no—
56C4⋊Dic73—41no—
57C4⋊Dic73—42no—
58#11924007—42no—
59#11924005—42no—
60C4×Dic73—42no—
61C4×Dic73D811yescharacteristic
62C4×Dic73SD1611yescharacteristic
63C4×Dic73C2×D411yescharacteristic
64C2×Q8×C73—41no—
65C2×C8×C73C22⋊C411yescharacteristic
66C2×C8×C73C22×C411yescharacteristic
67C4⋊C4×C73—22no—
68C4⋊C4×C73—41no—
69C42×C73C22⋊C411yescharacteristic
70C22×D73#10211yescharacteristic
71Q8×C73—82no—
72C2×C4×C73—42no—
73C2×C4×C73#10211yescharacteristic
74C2×C4×C73#10211yescharacteristic
75C2×C4×C73C2×C22⋊C411yescharacteristic
76C2×Dic73—42no—
77C2×Dic73#10211yescharacteristic
78C2×Dic73C2×D811yescharacteristic
79C2×Dic73C2×SD1611yescharacteristic
80C4×D73—21no—
81C4×D73—21no—
82C4×D73—41no—
83C4×D73—41no—
84Dic146—82no—
85#10596833—82no—
86C8×C73—21no—
87C8×C73—21no—
88#10596831#10112yes—
89#10596831#13712yes—
90C22×C73C2×#10211yescharacteristic
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—21no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—82no—
97C4×C73C2×#10111yescharacteristic
98C4×C73#41911yescharacteristic
99Dic73—21no—
100Dic73—21no—
101Dic73—21no—
102Dic73—82no—
103#11970—731nomaximal, Sylow
104C2×C73#154611yescharacteristic
105C2×C73#214311yescharacteristic
106C2×C73#214511yescharacteristic
107D73—41no—
108#3160—731no—
109#2163—731no—
110#1568—731no—
111#1363—734no—
112C73#1197011yescharacteristic, complemented, Sylow
113#533—1461no—
114#500—731no—
115#500#6440811yescharacteristic
116#499—732no—
117#499—1461no—
118#498—1461no—
119#432—1461no—
120#427—732no—
121#427—1461no—
122C2×C4×C8—731no—
123C4⋊C16—732no—
124C22⋊C16—1461no—
125#346—1461no—
126#335—1461no—
127#334—732no—
128C22×C8—731no—
129C22×C8—731no—
130C4⋊Q8—21no—
131C4⋊Q8—1461no—
132#125—1462no—
133C22⋊Q8—2921no—
134C22⋊Q8—2921no—
135C4×Q8—2921no—
136C4×Q8—2921no—
137#117—1462no—
138C2×C42—731no—
139C2×C16—1462no—
140#107—21no—
141#107—732no—
142#107—1461no—
143#107C2×#6440812yes—
144#106—1462no—
145#106—1462no—
146C4⋊C8—1462no—
147C22⋊C8—2921no—
148#97—2921no—
149C4×C8—731no—
150C4×C8—731no—
151C4×C8—731no—
152C4×C8C2×#6440811yescharacteristic
153C2×Q8—41no—
154C2×Q8—2921no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—731no—
158C2×C8—2922no—
159C2×C8—731no—
160C2×C8—731no—
161C2×C8—1462no—
162C2×C8—1462no—
163C2×C8C22⋊#6440811yescharacteristic
164C2×C8C22×#6440811yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—41no—
167C4⋊C4—2922no—
168C4⋊C4—2922no—
169C4⋊C4—2921no—
170C4⋊C4—1462no—
171C22⋊C4—2922no—
172C42—2922no—
173C42—731no—
174C42—731no—
175C42—731no—
176C42C22⋊#6440811yescharacteristic
177C16—2922no—
178C23—731no—
179Q8—82no—
180Q8—5842no—
181C2×C4—42no—
182C2×C4—2921no—
183C2×C4—2921no—
184C2×C4—2922no—
185C2×C4—731no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4#1455665311yescharacteristic
191C2×C4#1455665311yescharacteristic
192C2×C4C2×C22⋊#6440811yescharacteristic
193C8—21no—
194C8—21no—
195C8—5842no—
196C8—732no—
197C8—732no—
198C22—1461no—
199C22—1461no—
200C22—1461no—
201C22C2×#1455665311yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—5842no—
206C4—1461no—
207C4—1461no—
208C4—1461no—
209C4D73⋊#10111yescharacteristic
210C4#1798958011yescharacteristic
211C2—2921no—
212C2#2262544111yescharacteristic
213C2#2262624711yescharacteristic
214C2#2262625211yescharacteristic
subgroupG/H
centerC22C2×#14556653
commutatorC2×C8×C73C22×C4
FrattiniC2×C8C22×#64408
Fitting#500×C73C4
socleC22×C73C2×#102
prime radicalC22×D73#102
cosocleC8×Dic73C23
hypercenter#500#64408
hypocenterC73#11970
LCSG ▷ C2×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
3. #22624948C2semidirect
112. C73#11970semidirect

Maximal subgroups

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

subgroupindex
#226262942
#226254942
#226249482
#226204422
#1197073