Finite Group Databasebeta

← #37508047

Subgroups — #37508047

Order 22912.

240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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#26039029C211yesmaximal, characteristic
2#26038757C211yesmaximal, characteristic, complemented
3#26038374C211yesmaximal, characteristic, complemented
4#26038176C211yesmaximal, characteristic, complemented
5#26038174C211yesmaximal, characteristic, complemented
6#26038162C211yesmaximal, characteristic, complemented
7#484×C179C211yesmaximal, characteristic, complemented
8#19153108—21no—
9#19153102—21no—
10#19153098—21no—
11#19153088—21no—
12#19153087C2211yescharacteristic
13#19153083—21no—
14(C22⋊D179)⋊C4—21no—
15C2×Dic179⋊C4—21no—
16C2×(C2×D179)⋊C4—21no—
17C2×(C2×D179)⋊C4C2211yescharacteristic
18#19153044—21no—
19#19153033—21no—
20C22⋊(C179⋊C8)C2211yescharacteristic
21C179⋊#95C2211yescharacteristic
22C22⋊Q8×C179C2211yescharacteristic
23C2×C4⋊C4×C179C2211yescharacteristic
24#107×C179—21no—
25#103×C179—21no—
26C22⋊C8×C179C2211yescharacteristic
27C23×D179D411yescharacteristic
28C2×D716—21no—
29C2×D716—21no—
30C2×D716D411yescharacteristic
31C2×C22⋊D179—21no—
32C22×Dic179—21no—
33C22×Dic179D411yescharacteristic
34C2×C4×D179—21no—
35C2×C179⋊C8—21no—
36C4⋊Dic179D411yescharacteristic
37Dic179⋊C4—21no—
38Dic179⋊C4—42no—
39(C2×D179)⋊C4—21no—
40(C2×D179)⋊C4—21no—
41(C2×D179)⋊C4—21no—
42(C2×D179)⋊C4—21no—
43(C2×D179)⋊C4—21no—
44(C2×D179)⋊C4—21no—
45(C2×D179)⋊C4—42no—
46C4×Dic179—21no—
47C2×Q8×C179D411yescharacteristic
48C22×C4×C179—21no—
49C22×C4×C179C2311yescharacteristic
50C2×C8×C179—21no—
51C4⋊C4×C179—21no—
52C4⋊C4×C179—21no—
53C4⋊C4×C179—21no—
54C4⋊C4×C179D411yescharacteristic
55C22⋊C4×C179—21no—
56C22×D179—21no—
57C22×D179—21no—
58C22×D179—21no—
59C22×D179—21no—
60C22×D179—41no—
61C22×D179—41no—
62D716—41no—
63D716—81no—
64D716—81no—
65C22⋊D179—41no—
66C22⋊D179—41no—
67C2×Dic179—22no—
68C2×Dic179—21no—
69C2×Dic179—21no—
70C2×Dic179—41no—
71C2×Dic179—41no—
72C2×Dic179—41no—
73C4×D179—81no—
74C179⋊C8—41no—
75C23×C179C2×D411yescharacteristic
76Q8×C179—41no—
77C2×C4×C179—21no—
78C2×C4×C179—21no—
79C2×C4×C179—41no—
80C2×C4×C179—41no—
81C2×C4×C179—41no—
82C2×C4×C179—41no—
83C2×C4×C179C2×D411yescharacteristic
84C2×C4×C179C2×D411yescharacteristic
85C8×C179—41no—
86C22×C179—21no—
87C22×C179—21no—
88C22×C179#12011yescharacteristic
89C22×C179#13511yescharacteristic
90C22×C179#13711yescharacteristic
91C2×D179—42no—
92C2×D179—41no—
93C2×D179—41no—
94C2×D179—41no—
95C2×D179—41no—
96C2×D179—41no—
97C2×D179—41no—
98C2×D179—81no—
99C4×C179—21no—
100C4×C179—21no—
101C4×C179—41no—
102C4×C179—41no—
103C4×C179—81no—
104Dic179—42no—
105Dic179—41no—
106Dic179—41no—
107C2×C179—21no—
108C2×C179—21no—
109C2×C179#45211yescharacteristic
110C2×C179#45311yescharacteristic
111C2×C179#45811yescharacteristic
112D179—81no—
113D179—81no—
114C179#161811yescharacteristic, complemented, Sylow
115#1618—1791nomaximal, Sylow
116#538—1791no—
117#484D17911yescharacteristic, complemented
118#481—1791no—
119#399—1791no—
120#328—1791no—
121#327—1791no—
122#323—1791no—
123#126—3581no—
124#124—3581no—
125#123—3581no—
126C22⋊Q8C2×D17911yescharacteristic
127#121—3581no—
128#121—1791no—
129#120—3581no—
130C4×D4—3581no—
131C2×C4⋊C4—3581no—
132C2×C4⋊C4C2×D17911yescharacteristic
133C2×C22⋊C4—3581no—
134C2×C22⋊C4—1791no—
135#107—21no—
136#106—3581no—
137#103—21no—
138#102—3581no—
139C22⋊C8—1791no—
140C22⋊C8C2×D17911yescharacteristic
141#95—1791no—
142C24—1791no—
143C2×Q8C22⋊D17911yescharacteristic
144C2×D4—3581no—
145C2×D4—3581no—
146C2×D4—3581no—
147C2×D4—1791no—
148C22×C4—21no—
149C22×C4—3581no—
150C22×C4—3581no—
151C22×C4—1791no—
152C22×C4C22×D17911yescharacteristic
153C2×C8—21no—
154C2×C8—3581no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—3581no—
159C4⋊C4—1791no—
160C4⋊C4—7162no—
161C4⋊C4C22⋊D17911yescharacteristic
162C22⋊C4—21no—
163C22⋊C4—3581no—
164C22⋊C4—3581no—
165C22⋊C4—3581no—
166C22⋊C4—3581no—
167C22⋊C4—3581no—
168C22⋊C4—3581no—
169C22⋊C4—7162no—
170C42—3581no—
171C23—3581no—
172C23—3581no—
173C23—3581no—
174C23—3581no—
175C23—7161no—
176C23—7161no—
177C23D4×D17911yescharacteristic
178Q8—41no—
179D4—14321no—
180D4—14321no—
181D4—7161no—
182D4—7161no—
183D4—7161no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—3582no—
191C2×C4—3581no—
192C2×C4—3581no—
193C2×C4—14321no—
194C2×C4—7161no—
195C2×C4—7161no—
196C2×C4—7161no—
197C2×C4D4×D17911yescharacteristic
198C2×C4C2×C22⋊D17911yescharacteristic
199C8—41no—
200C8—7161no—
201C22—21no—
202C22—21no—
203C22—14321no—
204C22—7162no—
205C22—7161no—
206C22—7161no—
207C22—7161no—
208C22—7161no—
209C22—7161no—
210C22—7161no—
211C22#1915308111yescharacteristic
212C22#1915313611yescharacteristic
213C22#1915314511yescharacteristic
214C4—21no—
215C4—21no—
216C4—41no—
217C4—41no—
218C4—81no—
219C4—7162no—
220C4—7161no—
221C4—7161no—
222C2—21no—
223C2—21no—
224C2—14321no—
225C2—14321no—
226C2#2603860011yescharacteristic
227C2#2603860511yescharacteristic
228C2#2603862811yescharacteristic
subgroupG/H
centerC22#19153081
commutator, cosocleC22×C4×C179C23
FrattiniC22×C4C22×D179
Fitting#484×C179C2
socleC22×C179#120
prime radical#26039029C2
hypercenter#484D179
hypocenterC179#1618
LCSG ▷ C22×C4×C179 ▷ C22×C179 ▷ C179
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #26038757C2semidirect
3. #26038374C2semidirect
4. #26038176C2semidirect
5. #26038174C2semidirect
6. #26038162C2semidirect
7. #484×C179C2semidirect
114. C179#1618semidirect
117. #484D179semidirect

Maximal subgroups

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

subgroupindex
#260390292
#260387572
#260383742
#260381762
#260381742
#260381622
#484×C1792
#1618179