Finite Group Databasebeta

← #32989078

Subgroups — #32989078

Order 18688.

416 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 97 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#22618309C211yesmaximal, characteristic
2#22610908C211yesmaximal, characteristic
3#22608496C212yesmaximal
4#22607790C212yesmaximal
5C73×#1276C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7C2×#14556591—21no—
8#17988611C2211yescharacteristic
9#17988493—24no—
10#17988453—21no—
11#17988453C2212yes—
12#17988347—21no—
13#17988347—21no—
14#17988325—24no—
15#431×C73C2212yes—
16C43×C73C2211yescharacteristic
17C22×Dic146—22no—
18C2×#11924012—21no—
19#14556591—42no—
20#14556591—42no—
21#14556591Q812yescomplemented
22#14556583—21no—
23#14556570—22no—
24C4×Dic146—22no—
25#14556550—21no—
26C2×C4⋊Dic73—22no—
27C2×C4⋊Dic73—22no—
28C4⋊#10596831—22no—
29#14556498—24no—
30#14556498—22no—
31#14556498D414yes—
32C2×C42×C73—22no—
33C2×C42×C73D411yescharacteristic
34C2×C42×C73D411yescharacteristic
35C2×C42×C73C2311yescharacteristic
36C4⋊C8×C73—22no—
37C22⋊C8×C73—22no—
38C4×C8×C73—22no—
39C2×Dic146—22no—
40C2×Dic146—44no—
41C2×Dic146—48no—
42C22×Dic73—24no—
43#11924012—41no—
44#11924012—41no—
45C2×#10596831—41no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73—44no—
49C4⋊Dic73—42no—
50C4⋊Dic73—42no—
51#11924007—42no—
52C22⋊Dic73—41no—
53C4×Dic73—41no—
54C22×C4×C73—21no—
55C22×C4×C73—21no—
56C22×C4×C73C2×D412yes—
57C22×C4×C73C2×D411yescharacteristic
58C2×C8×C73—42no—
59C42×C73—21no—
60C42×C73—21no—
61C42×C73—44no—
62C42×C73SD1612yes—
63C42×C73Q1612yes—
64C42×C73C2×Q811yescharacteristic
65C42×C73#4111yescharacteristic
66C42×C73#4112yes—
67C23×C73#12011yescharacteristic
68C2×C4×C73—24no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73—42no—
72C2×C4×C73—42no—
73C2×C4×C73C22⋊Q812yes—
74C2×C4×C73C22⋊Q811yescharacteristic
75C2×C4×C73#12412yes—
76C2×C4×C73#12411yescharacteristic
77C2×C4×C73C2×SD1611yescharacteristic
78C2×C4×C73C2×Q1611yescharacteristic
79C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C73#13711yescharacteristic
81C2×Dic73—48no—
82C2×Dic73—42no—
83C2×Dic73—44no—
84Dic146—88no—
85Dic146—82no—
86C8×C73—82no—
87#10596831—81no—
88C22×C73—22no—
89C22×C73#39311yescharacteristic
90C22×C73#45011yescharacteristic
91C22×C73#45111yescharacteristic
92C4×C73—24no—
93C4×C73—22no—
94C4×C73—22no—
95C4×C73—42no—
96C4×C73#47511yescharacteristic
97C4×C73#47711yescharacteristic
98C4×C73#48711yescharacteristic
99C4×C73#48911yescharacteristic
100Dic73—84no—
101Dic73—82no—
102#10363—731nomaximal, Sylow
103C2×C73—21no—
104C2×C73—21no—
105C2×C73#202411yescharacteristic
106C2×C73#203112yes—
107#2862—731no—
108#1994—731no—
109#1518—732no—
110#1286—732no—
111#1276D7311yescharacteristic
112C73#1036311yescharacteristic, complemented, Sylow
113#533—731no—
114C2×C4⋊Q8—1461no—
115#431C2×D7312yes—
116#423—731no—
117#391—1464no—
118#382—732no—
119#382—1461no—
120C43C2×D7311yescharacteristic
121#339—1461no—
122#339—1461no—
123#328—1464no—
124C22×Q8—1462no—
125C2×M16—1461no—
126C4⋊Q8—2922no—
127C4⋊Q8—2922no—
128C4⋊Q8—732no—
129#125—1461no—
130C22⋊Q8—1462no—
131C4×Q8—1462no—
132#117—1461no—
133C2×C4⋊C4—1462no—
134C2×C4⋊C4—1462no—
135C2×C42—22no—
136C2×C42D29211yescharacteristic
137C2×C42D29211yescharacteristic
138C2×C42C22×D7311yescharacteristic
139C4⋊C8—22no—
140C4⋊C8—1462no—
141C22⋊C8—22no—
142C4×C8—22no—
143#95—734no—
144#95—1464no—
145#95—1462no—
146C2×Q8—2924no—
147C2×Q8—2928no—
148C2×Q8—1462no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—1464no—
152C22×C4D4×D7312yes—
153C22×C4C2×D29211yescharacteristic
154M16—2921no—
155M16—2921no—
156C2×C8—42no—
157C2×C8—2921no—
158C4⋊C4—2924no—
159C4⋊C4—2922no—
160C4⋊C4—2922no—
161C4⋊C4—2922no—
162C4⋊C4—1462no—
163C4⋊C4—1462no—
164C22⋊C4—2921no—
165C42—21no—
166C42—21no—
167C42—44no—
168C42—2921no—
169C42#1192401712yes—
170C42Dic29212yes—
171C42Q8×D7311yescharacteristic
172C42#1192402711yescharacteristic
173C42#1192402812yes—
174C23#1455656111yescharacteristic
175Q8—5842no—
176Q8—5848no—
177C2×C4—24no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—2928no—
183C2×C4—2924no—
184C2×C4—2922no—
185C2×C4#1455656912yes—
186C2×C4#1455657111yescharacteristic
187C2×C4#1455657712yes—
188C2×C4#1455657911yescharacteristic
189C2×C4C2×#1192401711yescharacteristic
190C2×C4C2×Dic29211yescharacteristic
191C2×C4#1455661911yescharacteristic
192C2×C4#1455662411yescharacteristic
193C8—82no—
194C8—5841no—
195C22—22no—
196C22#1798850011yescharacteristic
197C22#1798874011yescharacteristic
198C22#1798874511yescharacteristic
199C4—24no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—5844no—
204C4—5842no—
205C4#1798887311yescharacteristic
206C4#1798888311yescharacteristic
207C4#1798893811yescharacteristic
208C4#1798894711yescharacteristic
209C2—21no—
210C2—21no—
211C2#2261107311yescharacteristic
212C2#2261110412yes—
subgroupG/H
centerC22#17988500
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1276C2
socleC22×C73#393
prime radicalC23×C73#120
hypercenter#1276D73
hypocenterC73#10363
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
21. #14556591Q8semidirect
112. C73#10363semidirect

Maximal subgroups

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

subgroupindex
#226183092
#226109082
#226084962
#226077902
C73×#12762
#1036373