Finite Group Databasebeta

← #32989066

Subgroups — #32989066

Order 18688.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#22618206C211yesmaximal, characteristic
2#22610904C212yesmaximal
3#22610750C211yesmaximal, characteristic
4#22607813C212yesmaximal
5C73×#1295C211yesmaximal, characteristic
6C2×#14556591C2211yescharacteristic
7C2×#14556514—22no—
8C2×#14556502C2211yescharacteristic
9#17988521—22no—
10#17988520—22no—
11#17988519—22no—
12#17988453C2212yes—
13#17988350—22no—
14#17988350—22no—
15C2×#97×C73C2212yes—
16#382×C73C2211yescharacteristic
17C22×Dic146—21no—
18C22×#10596831—21no—
19#14556591—22no—
20#14556591—21no—
21#14556591Q812yes—
22C2×C4⋊Dic73—22no—
23C2×C4⋊Dic73—22no—
24C2×C4⋊Dic73D412yes—
25C2×C4⋊Dic73D412yes—
26C2×#11924007—22no—
27C2×#11924007—22no—
28#14556514—44no—
29#14556502—22no—
30#14556498—22no—
31#14556498—22no—
32#14556498—22no—
33C22×C8×C73—22no—
34C2×C4⋊C4×C73D412yes—
35C2×C42×C73C2311yescharacteristic
36#97×C73—22no—
37#97×C73—22no—
38#95×C73—22no—
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×Dic146—42no—
42C2×Dic146—41no—
43C22×Dic73—22no—
44C22×Dic73—22no—
45C22×Dic73—41no—
46C2×#10596831—22no—
47C2×#10596831—41no—
48C2×#10596831—41no—
49C4⋊Dic73—24no—
50C4⋊Dic73—42no—
51C4⋊Dic73—42no—
52C4⋊Dic73—42no—
53C4⋊Dic73—82no—
54#11924007—82no—
55#11924007—82no—
56C22×C4×C73—22no—
57C22×C4×C73C2×D412yes—
58C22×C4×C73C2×D411yescharacteristic
59C2×C8×C73—24no—
60C2×C8×C73—42no—
61C2×C8×C73—42no—
62C4⋊C4×C73—42no—
63C42×C73C2×Q811yescharacteristic
64C42×C73#4111yescharacteristic
65C42×C73#4112yes—
66C23×C73#12011yescharacteristic
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—42no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73C22⋊Q812yes—
75C2×C4×C73C22⋊Q811yescharacteristic
76C2×C4×C73#12412yes—
77C2×C4×C73#12411yescharacteristic
78C2×Dic73—42no—
79C2×Dic73—42no—
80C2×Dic73—42no—
81C2×Dic73—42no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73—81no—
86C2×Dic73—81no—
87Dic146—44no—
88Dic146—82no—
89C8×C73—44no—
90#10596831—42no—
91C22×C73#39311yescharacteristic
92C22×C73#45311yescharacteristic
93C22×C73#45411yescharacteristic
94C22×C73#45512yes—
95C22×C73#45612yes—
96C4×C73—21no—
97C4×C73—21no—
98C4×C73—22no—
99C4×C73—22no—
100C4×C73—82no—
101Dic73—82no—
102Dic73—82no—
103Dic73—82no—
104#10361—731nomaximal, Sylow
105C2×C73#166112yes—
106C2×C73#166211yescharacteristic
107C2×C73#166311yescharacteristic
108C2×C73#202711yescharacteristic
109C2×C73#202812yes—
110#2845—731no—
111#1993—732no—
112#1960—731no—
113#1295—732no—
114#1295D7311yescharacteristic
115C73#1036111yescharacteristic, complemented, Sylow
116C2×C4⋊Q8—731no—
117C2×#103—1462no—
118C2×#97—731no—
119C2×#97C2×D7312yes—
120#398—1462no—
121#398—1462no—
122#398—1462no—
123#382—732no—
124#382C2×D7311yescharacteristic
125#340—1462no—
126#340—1462no—
127C22×Q8—1461no—
128C22×C8—22no—
129C22×C8—1461no—
130C4⋊Q8—732no—
131C4⋊Q8—1461no—
132C4⋊Q8—1462no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—732no—
135C2×C4⋊C4—1462no—
136C2×C4⋊C4—1462no—
137C2×C4⋊C4—1462no—
138C2×C4⋊C4—1462no—
139C2×C4⋊C4D29212yes—
140C2×C42C22×D7311yescharacteristic
141#103—2924no—
142#97—22no—
143#97—22no—
144#97—1462no—
145#95—22no—
146#95—1462no—
147#95—1462no—
148#95—1462no—
149C2×Q8—2922no—
150C2×Q8—2922no—
151C2×Q8—2921no—
152C2×Q8—1462no—
153C22×C4—22no—
154C22×C4—2921no—
155C22×C4—1462no—
156C22×C4—1462no—
157C22×C4D4×D7312yes—
158C22×C4C2×D29211yescharacteristic
159C2×C8—24no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—2921no—
163C2×C8—2921no—
164C2×C8—1462no—
165C4⋊C4—42no—
166C4⋊C4—2922no—
167C4⋊C4—2922no—
168C4⋊C4—2922no—
169C4⋊C4—5842no—
170C4⋊C4—5842no—
171C4⋊C4—5842no—
172C4⋊C4—1464no—
173C42Q8×D7311yescharacteristic
174C42#1192402711yescharacteristic
175C42#1192402812yes—
176C23#1455656111yescharacteristic
177Q8—2924no—
178Q8—5842no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—5841no—
194C2×C4—5841no—
195C2×C4#1455656912yes—
196C2×C4#1455657111yescharacteristic
197C2×C4#1455657712yes—
198C2×C4#1455657911yescharacteristic
199C8—44no—
200C8—2922no—
201C22#1798850011yescharacteristic
202C22#1798875711yescharacteristic
203C22#1798876211yescharacteristic
204C22#1798876612yes—
205C22#1798877112yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—5842no—
212C4—5842no—
213C4—5842no—
214C2#2260924912yes—
215C2#2260925511yescharacteristic
216C2#2260926011yescharacteristic
217C2#2261108811yescharacteristic
218C2#2261109112yes—
subgroupG/H
centerC23#14556561
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1295C2
socle, prime radicalC23×C73#120
hypercenter#1295D73
hypocenterC73#10361
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
115. C73#10361semidirect

Maximal subgroups

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

subgroupindex
#226182062
#226109042
#226107502
#226078132
C73×#12952
#1036173