Finite Group Databasebeta

← #33000745

Subgroups — #33000745

Order 18688.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#22612186C211yesmaximal, characteristic, complemented
2#22612159C211yesmaximal, characteristic, complemented
3#22612154C211yesmaximal, characteristic, complemented
4#22609536C211yesmaximal, characteristic, complemented
5#22609520C211yesmaximal, characteristic, complemented
6#22607850C211yesmaximal, characteristic, complemented
7C73×#2246C211yesmaximal, characteristic
8C2×#14556535—22no—
9#17988992C2211yescharacteristic
10#17988967C2211yescharacteristic
11#17988959—21no—
12#17988933—21no—
13#17988933—21no—
14#17988933—21no—
15#17988392—22no—
16#17988388—22no—
17C4×#11924003C2211yescharacteristic
18C8×#10596831C2211yescharacteristic
19C2×D16×C73—22no—
20#493×C73C2211yescharacteristic
21#493×C73C2211yescharacteristic
22C4×C16×C73C2211yescharacteristic
23C2×Dic292—21no—
24C2×Dic292—21no—
25C2×#11924016—42no—
26#14556591—21no—
27#14556591—21no—
28#14556535—44no—
29C2×#11924003D412yes—
30#14556525—21no—
31#14556525—21no—
32#14556512—42no—
33#14556512—42no—
34#14556512—42no—
35C4×#10596831D411yescharacteristic
36C4×#10596831D411yescharacteristic
37C2×D8×C73—21no—
38C2×D8×C73—21no—
39C2×D8×C73—21no—
40C2×D8×C73—21no—
41#127×C73—21no—
42#127×C73—21no—
43D16×C73—44no—
44C2×C16×C73D412yes—
45C4×C8×C73C2311yescharacteristic
46C2×Dic146—41no—
47C2×Dic146—41no—
48Dic292—42no—
49Dic292—42no—
50#11924016—84no—
51C2×#10596831D812yes—
52C2×#10596831D812yes—
53C4⋊Dic73—41no—
54C4⋊Dic73—41no—
55C4⋊Dic73—41no—
56C4⋊Dic73—41no—
57#11924003—22no—
58C2×D4×C73—41no—
59C2×D4×C73—41no—
60C2×D4×C73—41no—
61C2×D4×C73—41no—
62C2×D4×C73—41no—
63C2×D4×C73—41no—
64D8×C73—42no—
65D8×C73—42no—
66D8×C73—42no—
67D8×C73—42no—
68C2×C8×C73C2×D411yescharacteristic
69C2×C8×C73C2×D411yescharacteristic
70C42×C73C2×D411yescharacteristic
71C16×C73—22no—
72C23×C73—81no—
73C23×C73—81no—
74D4×C73—81no—
75D4×C73—81no—
76D4×C73—81no—
77D4×C73—81no—
78D4×C73—82no—
79D4×C73—82no—
80D4×C73—82no—
81D4×C73—82no—
82C2×C4×C73#12711yescharacteristic
83C2×C4×C73C2×D811yescharacteristic
84C2×C4×C73C2×D811yescharacteristic
85C2×Dic73—81no—
86C2×Dic73—81no—
87Dic146—81no—
88Dic146—81no—
89Dic146—82no—
90C8×C73AGL(1,ℤ/8)12yes—
91C8×C73AGL(1,ℤ/8)12yes—
92#10596831—22no—
93#10596831—22no—
94C22×C73—161no—
95C22×C73—161no—
96C22×C73—161no—
97C22×C73—161no—
98C22×C73—161no—
99C22×C73—161no—
100C22×C73#49311yescharacteristic
101C4×C73#49611yescharacteristic
102C4×C73#49611yescharacteristic
103C4×C73#50812yes—
104C4×C73#50912yes—
105Dic73—161no—
106Dic73—161no—
107#12527—731nomaximal, Sylow
108C2×C73—321no—
109C2×C73—321no—
110C2×C73#172111yescharacteristic
111C2×C73#224911yescharacteristic
112C2×C73#225011yescharacteristic
113#2248—731no—
114#2246D7311yescharacteristic
115#2241—731no—
116#2240—731no—
117#1709—731no—
118#1706—731no—
119#1312—731no—
120C73#1252711yescharacteristic, complemented, Sylow
121C2×SD32—1462no—
122C2×D16—22no—
123#500—731no—
124#494—731no—
125#493C2×D7311yescharacteristic
126#493C2×D7311yescharacteristic
127#492—1461no—
128#486—1461no—
129#486—1461no—
130#486—1461no—
131#358—1462no—
132#357—1462no—
133C4×C16—731no—
134C4×C16C2×D7311yescharacteristic
135C82—731no—
136C2×Q16—1461no—
137C2×Q16—1461no—
138C2×SD16—2922no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8—21no—
142C2×D8—21no—
143C4⋊Q8—1461no—
144C4⋊Q8—1461no—
145#127—21no—
146#127—21no—
147SD32—2924no—
148D16—44no—
149C2×C16—732no—
150C2×C16C22⋊D7312yes—
151#107—1461no—
152#107—1461no—
153#102—2922no—
154#102—2922no—
155#102—2922no—
156C4×C8—731no—
157C4×C8—731no—
158C4×C8C22×D7311yescharacteristic
159C2×Q8—2921no—
160C2×Q8—2921no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167Q16—2922no—
168Q16—2922no—
169SD16—5844no—
170D8—42no—
171D8—42no—
172D8—42no—
173D8—42no—
174C2×C8—732no—
175C2×C8—732no—
176C2×C8D4×D7311yescharacteristic
177C2×C8C2×C22⋊D7311yescharacteristic
178C4⋊C4—2921no—
179C4⋊C4—2921no—
180C4⋊C4—2921no—
181C4⋊C4—2921no—
182C42D4×D7311yescharacteristic
183C16—22no—
184C16—1462no—
185C23—81no—
186C23—81no—
187Q8—5841no—
188Q8—5841no—
189Q8—5842no—
190D4—81no—
191D4—81no—
192D4—81no—
193D4—81no—
194D4—82no—
195D4—82no—
196D4—82no—
197D4—82no—
198C2×C4—5841no—
199C2×C4—5841no—
200C2×C4#1455658711yescharacteristic
201C2×C4D8×D7311yescharacteristic
202C2×C4D8×D7311yescharacteristic
203C8—1462no—
204C8—1462no—
205C8#1455661512yes—
206C8#1455661712yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—161no—
211C22—161no—
212C22—161no—
213C22#1798896211yescharacteristic
214C4—11681no—
215C4—11681no—
216C4#1798897411yescharacteristic
217C4#1798897511yescharacteristic
218C4#1798901612yes—
219C4#1798902112yes—
220C2—321no—
221C2—321no—
222C2#2260959611yescharacteristic
223C2#2261218911yescharacteristic
224C2#2261219411yescharacteristic
subgroupG/H
centerC22#17988962
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
Fitting, prime radicalC73×#2246C2
socleC22×C73#493
hypercenter#2246D73
hypocenterC73#12527
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #22612186C2semidirect
2. #22612159C2semidirect
3. #22612154C2semidirect
4. #22609536C2semidirect
5. #22609520C2semidirect
6. #22607850C2semidirect
120. C73#12527semidirect

Maximal subgroups

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

subgroupindex
#226121862
#226121592
#226121542
#226095362
#226095202
#226078502
C73×#22462
#1252773