Finite Group Databasebeta

← #22625309

Subgroups — #22625309

Order 9344.

304 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C2×#14556648C211yesmaximal, characteristic, complemented
2C4×C22⋊#64408C211yesmaximal, characteristic, complemented
3#17989441C212yesmaximal, complemented
4#17989439C212yesmaximal, complemented
5#17989100C211yesmaximal, characteristic
6C22×#10596833—21no—
7C2×C22⋊#64408—21no—
8C2×C4×#64408—21no—
9#14556648—21no—
10#14556648C2212yes—
11(C2×#64408)⋊C4C2212yes—
12C2×#11924029C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556576—21no—
15#14556567C2211yescharacteristic
16#14556566C2211yescharacteristic
17#14556565C411yescharacteristic, complemented
18#14556561—21no—
19#14556553—21no—
20#14556551—21no—
21#14556549C411yescharacteristic, complemented
22C22⋊Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24C2×#10596833—22no—
25C2×#10596833—42no—
26C22⋊#64408—24no—
27C4×#64408—42no—
28C23×D73D411yescharacteristic
29#11924029—42no—
30C2×D292—21no—
31C2×D292—21no—
32C2×D292C2×C411yescharacteristic
33C2×C22⋊D73—21no—
34C22×Dic73D411yescharacteristic
35C2×C4×D73—21no—
36C2×C4×D73—42no—
37C2×C4×D73C2×C411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73C2311yescharacteristic
41C4⋊Dic73C2×C411yescharacteristic
42#11924007—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—21no—
46#11924005—21no—
47C4×Dic73—21no—
48C2×Q8×C73C2×C411yescharacteristic
49C22×C4×C73C2×C411yescharacteristic
50C4⋊C4×C73—21no—
51C4⋊C4×C73C2×C411yescharacteristic
52C22⋊C4×C73—21no—
53C23×C73C22⋊C411yescharacteristic
54C22×D73—22no—
55C22×D73—22no—
56C22×D73—21no—
57C22×D73—41no—
58C22×D73C22⋊C411yescharacteristic
59C22×D73C2×D411yescharacteristic
60C2×#64408—24no—
61C2×#64408—42no—
62C2×#64408—42no—
63Q8×C73—41no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—41no—
67C2×C4×C73C22⋊C411yescharacteristic
68C2×C4×C73C22×C411yescharacteristic
69C22⋊D73—42no—
70C2×Dic73—22no—
71C2×Dic73—21no—
72C2×Dic73C22⋊C411yescharacteristic
73C2×Dic73C2×D411yescharacteristic
74D292—41no—
75D292—42no—
76D292—42no—
77C4×D73—22no—
78C4×D73—22no—
79C4×D73—41no—
80C4×D73—41no—
81C4×D73—42no—
82#10596833—42no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73#10412yes—
86C22×C73C2×C22⋊C411yescharacteristic
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—44no—
93C2×D73—41no—
94C2×D73—41no—
95C2×D73—41no—
96C2×D73#13512yes—
97#64408—44no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—41no—
101C4×C73—41no—
102Dic73—21no—
103Dic73—41no—
104Dic73#9912yes—
105C2×C73—22no—
106C2×C73C2×#9911yescharacteristic
107C2×C73#41611yescharacteristic
108C2×C73C2×#10411yescharacteristic
109D73—22no—
110D73—41no—
111D73—81no—
112#1501—731nomaximal, Sylow
113C73#150111yescharacteristic, complemented, Sylow
114#525—731no—
115C2×C22⋊C8—731no—
116C4×C22⋊C4—731no—
117#328—732no—
118#327—732no—
119C2×#41—731no—
120C23×C4—731no—
121C22×C8—1461no—
122#123—1461no—
123C22⋊Q8—731no—
124C22⋊Q8#6440811yescharacteristic, complemented
125#121—731no—
126#121—731no—
127#120—1461no—
128C4×D4—1461no—
129C4×D4—1461no—
130#117—731no—
131C2×C22⋊C4—1461no—
132C2×C42—1461no—
133C22⋊C8—732no—
134C22⋊C8—1461no—
135#95—732no—
136C24—731no—
137#41—2922no—
138C2×Q8C2×#6440811yescharacteristic
139C2×D4—731no—
140C2×D4—1461no—
141C2×D4—1461no—
142C2×D4—1461no—
143C22×C4—2922no—
144C22×C4—731no—
145C22×C4—731no—
146C22×C4—731no—
147C22×C4—731no—
148C22×C4—731no—
149C22×C4—1461no—
150C22×C4—1462no—
151C22×C4C2×#6440811yescharacteristic
152C2×C8—2922no—
153C2×C8—1462no—
154C4⋊C4—21no—
155C4⋊C4—731no—
156C4⋊C4—1461no—
157C4⋊C4C2×#6440811yescharacteristic
158C22⋊C4—21no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1464no—
163C22⋊C4—1461no—
164C42—2922no—
165C42—1461no—
166C23—2921no—
167C23—731no—
168C23—731no—
169C23—1462no—
170C23—1461no—
171C23—1462no—
172C23C22⋊#6440811yescharacteristic
173Q8—41no—
174D4—2921no—
175D4—2922no—
176D4—2922no—
177D4—2922no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—2922no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1464no—
191C2×C4—1461no—
192C2×C4—1462no—
193C2×C4C22⋊#6440811yescharacteristic
194C2×C4C22×#6440811yescharacteristic
195C8—2922no—
196C22—21no—
197C22—21no—
198C22—2924no—
199C22—2921no—
200C22—2921no—
201C22—2921no—
202C22—732no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22—1461no—
207C22—1461no—
208C22#1455665612yes—
209C22C2×C22⋊#6440811yescharacteristic
210C4—21no—
211C4—21no—
212C4—41no—
213C4—41no—
214C4—2924no—
215C4—2921no—
216C4—732no—
217C4—1461no—
218C2—22no—
219C2—2921no—
220C2—5841no—
221C2—1462no—
222C2D73⋊#9911yescharacteristic
223C2#1798957711yescharacteristic
224C2C2×#1455665611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1501
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14556648C2semidirect
2. C4×C22⋊#64408C2semidirect
3. #17989441C2semidirect
4. #17989439C2semidirect
12. C2×#11924029C4semidirect
17. #14556565C4semidirect
21. #14556549C4semidirect
22. C22⋊Q8×C73C4semidirect
113. C73#1501semidirect
124. C22⋊Q8#64408semidirect