Finite Group Databasebeta

← #22625356

Subgroups — #22625356

Order 9344.

284 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989555C211yesmaximal, characteristic, complemented
2#17989530C211yesmaximal, characteristic, complemented
3#17989440C212yesmaximal, complemented
4#17989438C212yesmaximal, complemented
5#17989097C211yesmaximal, characteristic
6C2×#11924036—21no—
7C2×C22⋊#64408—21no—
8#14556648C2212yes—
9C22⋊#10596833—21no—
10(C2×#64408)⋊C4—21no—
11(C2×#64408)⋊C4C2212yes—
12C2×#11924027C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556573—21no—
15#14556571C2211yescharacteristic
16#14556570C411yescharacteristic, complemented
17#14556562C2211yescharacteristic
18#14556559—21no—
19D4×Dic73—21no—
20#14556551—21no—
21#14556549C411yescharacteristic, complemented
22#121×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924036—42no—
25C2×#10596833—22no—
26C22⋊#64408—42no—
27C23×D73D411yescharacteristic
28#11924027—42no—
29C2×Dic146C2×C411yescharacteristic
30C2×C22⋊D73—21no—
31C2×C22⋊D73—21no—
32C22×Dic73—21no—
33C22×Dic73D411yescharacteristic
34C2×C4×D73—42no—
35C2×C4×D73C2×C411yescharacteristic
36C2×C4×D73D411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73C2311yescharacteristic
39C4⋊Dic73—21no—
40C4⋊Dic73C2×C411yescharacteristic
41#11924007—21no—
42C22⋊Dic73—21no—
43C22⋊Dic73—21no—
44#11924005—21no—
45#11924005—21no—
46C4×Dic73—21no—
47C2×D4×C73—21no—
48C2×D4×C73C2×C411yescharacteristic
49C22×C4×C73C2×C411yescharacteristic
50C4⋊C4×C73C2×C411yescharacteristic
51C22⋊C4×C73—21no—
52C23×C73—21no—
53C23×C73C22⋊C411yescharacteristic
54C22×D73—22no—
55C22×D73—22no—
56C22×D73—41no—
57C22×D73C22⋊C411yescharacteristic
58C22×D73C2×D411yescharacteristic
59C2×#64408—42no—
60C2×#64408—42no—
61C2×#64408—42no—
62D4×C73—41no—
63D4×C73—42no—
64C2×C4×C73—21no—
65C2×C4×C73—41no—
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C22×C411yescharacteristic
68C22⋊D73—42no—
69C22⋊D73—42no—
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73—41no—
73C2×Dic73—42no—
74C2×Dic73C22⋊C411yescharacteristic
75C2×Dic73C2×D411yescharacteristic
76C4×D73—22no—
77C4×D73—22no—
78C4×D73—41no—
79C4×D73—41no—
80Dic146—41no—
81#10596833—42no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73—41no—
86C22×C73—41no—
87C22×C73—41no—
88C22×C73C2×C22⋊C411yescharacteristic
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—44no—
94C2×D73#9912yes—
95C2×D73#13512yes—
96#64408—82no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—41no—
100Dic73—21no—
101Dic73—21no—
102Dic73—41no—
103Dic73—41no—
104C2×C73—41no—
105C2×C73—81no—
106C2×C73C2×#9911yescharacteristic
107C2×C73#41611yescharacteristic
108C2×C73#42111yescharacteristic
109D73—22no—
110D73—22no—
111#1516—731nomaximal, Sylow
112C73#151611yescharacteristic, complemented, Sylow
113#525—731no—
114C2×C22⋊C8—731no—
115#381—731no—
116#328—732no—
117#327—732no—
118C2×#41—731no—
119C23×C4—731no—
120C22×C8—1461no—
121#123—1461no—
122C22⋊Q8—731no—
123C22⋊Q8—731no—
124#121—731no—
125#121#6440811yescharacteristic, complemented
126#120—1461no—
127C4×D4—1461no—
128C4×D4—1461no—
129#117—731no—
130C2×C22⋊C4—1461no—
131C22⋊C8—732no—
132C22⋊C8—1461no—
133#95—732no—
134#95—1461no—
135C24—731no—
136#41—2922no—
137C2×Q8—731no—
138C2×D4—21no—
139C2×D4—1461no—
140C2×D4—1461no—
141C2×D4C2×#6440811yescharacteristic
142C22×C4—2922no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—731no—
148C22×C4—1462no—
149C22×C4—1461no—
150C22×C4C2×#6440811yescharacteristic
151C2×C8—2922no—
152C2×C8—1462no—
153C4⋊C4—731no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C4⋊C4C2×#6440811yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—2922no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C42—1461no—
164C23—21no—
165C23—2921no—
166C23—731no—
167C23—731no—
168C23—1462no—
169C23—1462no—
170C23C22⋊#6440811yescharacteristic
171Q8—2921no—
172D4—41no—
173D4—42no—
174D4—2922no—
175D4—2922no—
176C2×C4—21no—
177C2×C4—41no—
178C2×C4—2921no—
179C2×C4—2921no—
180C2×C4—2922no—
181C2×C4—2922no—
182C2×C4—2922no—
183C2×C4—2922no—
184C2×C4—2921no—
185C2×C4—731no—
186C2×C4—731no—
187C2×C4—1462no—
188C2×C4—1462no—
189C2×C4—1461no—
190C2×C4—1461no—
191C2×C4C22⋊#6440811yescharacteristic
192C2×C4C22×#6440811yescharacteristic
193C8—2922no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—2924no—
201C22—732no—
202C22—732no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22—1461no—
207C22C2×C22⋊#6440811yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—2921no—
212C4—2921no—
213C4—5842no—
214C4—1461no—
215C4—1461no—
216C2—41no—
217C2—81no—
218C2—1462no—
219C2—1462no—
220C2D73⋊#9911yescharacteristic
221C2#1798957711yescharacteristic
222C2#1798958511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#121×C73C4
socleC22×C73C2×C22⋊C4
hypercenter#121#64408
hypocenterC73#1516
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #17989555C2semidirect
2. #17989530C2semidirect
3. #17989440C2semidirect
4. #17989438C2semidirect
12. C2×#11924027C4semidirect
16. #14556570C4semidirect
21. #14556549C4semidirect
22. #121×C73C4semidirect
112. C73#1516semidirect
125. #121#64408semidirect