Finite Group Databasebeta

← #32975293

Subgroups — #32975293

Order 18688.

350 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 83 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#22617919C211yesmaximal, characteristic
2#22611493C212yesmaximal
3#22607757C211yesmaximal, characteristic
4#22607753C212yesmaximal
5C73×#2095C211yesmaximal, characteristic
6#17988526—21no—
7#17988519—22no—
8#17988494—21no—
9#17988485C2212yes—
10#17988474—22no—
11#17988349—22no—
12#17988349—22no—
13#17988342C2212yes—
14C2×#107×C73—21no—
15C2×#103×C73—21no—
16#391×C73C2211yescharacteristic
17#384×C73C2211yescharacteristic
18#336×C73C2211yescharacteristic
19C22×#10596831—22no—
20C2×C4⋊Dic73—21no—
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73D412yes—
23C2×C4⋊Dic73D412yes—
24C2×#11924007—22no—
25C2×C4×Dic73—21no—
26#14556498—21no—
27#14556498—22no—
28#14556498—22no—
29#14556498—22no—
30C22×Q8×C73D411yescharacteristic
31C22×C8×C73—21no—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73—22no—
34C2×C4⋊C4×C73D411yescharacteristic
35C2×C42×C73C2311yescharacteristic
36#107×C73—42no—
37#103×C73—42no—
38#95×C73—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41C2×#10596831—42no—
42C2×#10596831—42no—
43C2×#10596831—42no—
44C4⋊Dic73—22no—
45C4⋊Dic73—22no—
46C4⋊Dic73—42no—
47C4⋊Dic73—81no—
48C4⋊Dic73—81no—
49#11924007—42no—
50#11924007—42no—
51C4×Dic73—81no—
52C2×Q8×C73—21no—
53C2×Q8×C73—41no—
54C2×Q8×C73—41no—
55C2×Q8×C73Q1612yes—
56C22×C4×C73—21no—
57C22×C4×C73—21no—
58C22×C4×C73—41no—
59C22×C4×C73C2×D412yes—
60C22×C4×C73C2×D411yescharacteristic
61C2×C8×C73—22no—
62C2×C8×C73—41no—
63C2×C8×C73—41no—
64C4⋊C4×C73—41no—
65C4⋊C4×C73—41no—
66C4⋊C4×C73—41no—
67C4⋊C4×C73—44no—
68C42×C73—41no—
69C23×C73#12011yescharacteristic
70Q8×C73—42no—
71Q8×C73—81no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—21no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—41no—
78C2×C4×C73—41no—
79C2×C4×C73—41no—
80C2×C4×C73—42no—
81C2×C4×C73—81no—
82C2×C4×C73—82no—
83C2×C4×C73C2×Q1611yescharacteristic
84C2×C4×C73#13512yes—
85C2×C4×C73#13711yescharacteristic
86C2×C4×C73#13712yes—
87C2×Dic73—42no—
88C2×Dic73—42no—
89C2×Dic73—42no—
90C2×Dic73—42no—
91C2×Dic73—42no—
92C2×Dic73—42no—
93C8×C73—42no—
94#10596831—82no—
95C22×C73#45111yescharacteristic
96C22×C73#45212yes—
97C22×C73#45311yescharacteristic
98C22×C73#45412yes—
99C22×C73#45811yescharacteristic
100C4×C73—21no—
101C4×C73—21no—
102C4×C73—22no—
103C4×C73—22no—
104C4×C73—42no—
105C4×C73—81no—
106C4×C73—161no—
107Dic73—82no—
108Dic73—82no—
109#7831—731nomaximal, Sylow
110C2×C73#161411yescharacteristic
111C2×C73#161512yes—
112C2×C73#163411yescharacteristic
113C2×C73#163612yes—
114C2×C73#165711yescharacteristic
115#2809—731no—
116#2100—732no—
117#2095D7311yescharacteristic
118#1272—731no—
119#1271—732no—
120C73#783111yescharacteristic, complemented, Sylow
121C2×#107—21no—
122C2×#103—21no—
123#400—1461no—
124#398—1462no—
125#391—1461no—
126#391C2×D7311yescharacteristic
127#389—732no—
128#387—1462no—
129#384C2×D7311yescharacteristic
130#340—1462no—
131#340—1462no—
132#336—732no—
133#336C2×D7311yescharacteristic
134C22×Q8C22⋊D7311yescharacteristic
135C22×C8—21no—
136C22×C8—1462no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—732no—
140C2×C4⋊C4—732no—
141C2×C4⋊C4—1462no—
142C2×C4⋊C4—1461no—
143C2×C4⋊C4—1461no—
144C2×C4⋊C4C22⋊D7311yescharacteristic
145C2×C42—1461no—
146C2×C42C22×D7311yescharacteristic
147#107—42no—
148#103—42no—
149#95—22no—
150#95—1461no—
151#95—1462no—
152#95—1462no—
153#95—1462no—
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8#1192401812yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—41no—
161C22×C4—1462no—
162C22×C4—1462no—
163C22×C4D4×D7312yes—
164C22×C4C2×C22⋊D7311yescharacteristic
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—2922no—
169C2×C8—2922no—
170C2×C8—2922no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—44no—
175C4⋊C4—2922no—
176C4⋊C4—2922no—
177C4⋊C4—2922no—
178C4⋊C4—5841no—
179C4⋊C4—5841no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C42—41no—
183C42—5841no—
184C23#1455655911yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—2922no—
199C2×C4—2922no—
200C2×C4—2922no—
201C2×C4—2922no—
202C2×C4—2922no—
203C2×C4—2922no—
204C2×C4C2×#1192401811yescharacteristic
205C2×C4#1455661412yes—
206C2×C4#1455662111yescharacteristic
207C2×C4#1455662312yes—
208C8—42no—
209C8—5842no—
210C22#1798874211yescharacteristic
211C22#1798874812yes—
212C22#1798875411yescharacteristic
213C22#1798875812yes—
214C22#1798877611yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—81no—
221C4—161no—
222C4—5842no—
223C4—5842no—
224C2#2260895511yescharacteristic
225C2#2260896112yes—
226C2#2260907411yescharacteristic
227C2#2260908812yes—
228C2#2260922711yescharacteristic
subgroupG/H
centerC23#14556559
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2095C2
socle, prime radicalC23×C73#120
hypercenter#2095D73
hypocenterC73#7831
LCSG ▷ C2×C42×C73 ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2095

Complements

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

NH ≅ G/Ntype
120. C73#7831semidirect

Maximal subgroups

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

subgroupindex
#226179192
#226114932
#226077572
#226077532
C73×#20952
#783173