Finite Group Databasebeta

← #22625802

Subgroups — #22625802

Order 9344.

292 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 84 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#17989588C211yesmaximal, characteristic
2C2×#14556654C212yesmaximal
3#17989531C211yesmaximal, characteristic
4#17989460C212yesmaximal
5C4×Q8×D73C211yesmaximal, characteristic
6C2×#11924036C2212yes—
7C2×C4⋊#64408C2212yes—
8#14556658—21no—
9C4⋊#10596833—21no—
10#14556654—24no—
11(C2×#64408)⋊C4—21no—
12(C2×#64408)⋊C4—21no—
13C2×Q8×D73C2211yescharacteristic
14Q8×Dic73C411yescharacteristic, complemented
15C4×Dic146—21no—
16C4×Dic146C411yescharacteristic, complemented
17#14556556—21no—
18#14556556C411yescharacteristic, complemented
19C4⋊C4×D73—21no—
20C4⋊C4×D73C2211yescharacteristic
21C42×D73—21no—
22C42×D73C2211yescharacteristic
23C4×Q8×C73C411yescharacteristic, complemented
24C22×#64408—22no—
25#11924036—22no—
26#11924036—22no—
27C2×#10596833—22no—
28C4⋊#64408—22no—
29C4⋊#64408—22no—
30C2×Dic146—21no—
31C2×Dic146C2×C411yescharacteristic
32Q8×D73—21no—
33Q8×D73—21no—
34Q8×D73D412yes—
35Q8×D73Q812yes—
36C2×C4×D73—21no—
37C2×C4×D73—21no—
38C2×C4×D73D411yescharacteristic
39C2×C4×D73D411yescharacteristic
40C2×C4×D73C2311yescharacteristic
41C4⋊Dic73—21no—
42C4⋊Dic73C2×C411yescharacteristic
43#11924007—21no—
44#11924007—21no—
45#11924007—21no—
46C4×Dic73—21no—
47C4×Dic73—21no—
48C4×Dic73—21no—
49C4×Dic73C2×C411yescharacteristic
50C4×Dic73D411yescharacteristic
51C4×Dic73D411yescharacteristic
52C2×Q8×C73C2×C411yescharacteristic
53C4⋊C4×C73—21no—
54C4⋊C4×C73C2×C411yescharacteristic
55C42×C73—21no—
56C42×C73C2×C411yescharacteristic
57C22×D73C2×D411yescharacteristic
58C2×#64408—42no—
59C2×#64408—42no—
60C2×#64408—42no—
61Q8×C73—21no—
62Q8×C73C4⋊C412yes—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73C22⋊C411yescharacteristic
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C22×C411yescharacteristic
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73C22⋊C411yescharacteristic
71C2×Dic73C22⋊C411yescharacteristic
72C2×Dic73C2×D411yescharacteristic
73C4×D73—22no—
74C4×D73—22no—
75C4×D73—22no—
76C4×D73—22no—
77C4×D73—42no—
78C4×D73C2×D411yescharacteristic
79C4×D73C2×Q811yescharacteristic
80C4×D73#4111yescharacteristic
81C4×D73#4111yescharacteristic
82Dic146—21no—
83Dic146—22no—
84Dic146—22no—
85Dic146C4⋊C412yes—
86#10596833—42no—
87C22×C73C2×C22⋊C411yescharacteristic
88C2×D73#12111yescharacteristic
89C2×D73C22⋊Q811yescharacteristic
90C2×D73#13512yes—
91C2×D73#13712yes—
92#64408—82no—
93C4×C73—22no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—41no—
97C4×C73C2×C4⋊C411yescharacteristic
98C4×C73#11711yescharacteristic
99Dic73—22no—
100Dic73—21no—
101Dic73—21no—
102Dic73—41no—
103Dic73#12111yescharacteristic
104Dic73C22⋊Q811yescharacteristic
105C2×C73#38011yescharacteristic
106C2×C73#41611yescharacteristic
107C2×C73#41911yescharacteristic
108D73#46412yes—
109D73#47912yes—
110#1805—731nomaximal, Sylow
111C73#180511yescharacteristic, complemented, Sylow
112C2×C4×Q8—731no—
113C2×C4⋊C8—731no—
114C2×#103—732no—
115#382—731no—
116#340—732no—
117C22×Q8—731no—
118C22×C8—732no—
119C4×Q8—731no—
120C4×Q8—731no—
121C4×Q8—731no—
122C4×Q8—1461no—
123C4×Q8—1461no—
124C4×Q8#6440811yescharacteristic, complemented
125C2×C4⋊C4—731no—
126C2×C4⋊C4—732no—
127C2×C4⋊C4—1461no—
128C2×C42—731no—
129C2×C42—1461no—
130C4⋊C8—1461no—
131C4⋊C8—1461no—
132#103—1464no—
133#95—1461no—
134#95—1461no—
135C2×Q8—732no—
136C2×Q8—732no—
137C2×Q8—731no—
138C2×Q8—1461no—
139C2×Q8—1461no—
140C2×Q8—1461no—
141C2×Q8C2×#6440811yescharacteristic
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—1461no—
146C22×C4—1461no—
147C22×C4—1462no—
148C2×C8—1462no—
149C2×C8—1462no—
150C2×C8—1462no—
151C4⋊C4—21no—
152C4⋊C4—731no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C4⋊C4—1462no—
157C4⋊C4—1462no—
158C4⋊C4—1461no—
159C4⋊C4C2×#6440811yescharacteristic
160C42—21no—
161C42—731no—
162C42—731no—
163C42—731no—
164C42—1461no—
165C42—1461no—
166C42—1461no—
167C42C2×#6440811yescharacteristic
168C23—731no—
169Q8—21no—
170Q8—732no—
171Q8—1462no—
172Q8—1462no—
173Q8—1461no—
174Q8C4⋊#6440812yes—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4—2922no—
181C2×C4—731no—
182C2×C4—731no—
183C2×C4—731no—
184C2×C4—731no—
185C2×C4—731no—
186C2×C4—731no—
187C2×C4—731no—
188C2×C4—1462no—
189C2×C4—1462no—
190C2×C4—1462no—
191C2×C4—1462no—
192C2×C4—1461no—
193C2×C4—1461no—
194C2×C4C22⋊#6440811yescharacteristic
195C2×C4C22⋊#6440811yescharacteristic
196C2×C4C22×#6440811yescharacteristic
197C8—2922no—
198C22—731no—
199C22—731no—
200C22—732no—
201C22—732no—
202C22C2×C22⋊#6440811yescharacteristic
203C4—22no—
204C4—21no—
205C4—21no—
206C4—41no—
207C4—2921no—
208C4—5842no—
209C4—731no—
210C4—731no—
211C4—1462no—
212C4—1461no—
213C4—1461no—
214C4C2×C4⋊#6440811yescharacteristic
215C4#1455667011yescharacteristic
216C2—732no—
217C2—732no—
218C2#1798952911yescharacteristic
219C2#1798957711yescharacteristic
220C2#1798958011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC4×Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC4×Q8#64408
hypocenterC73#1805
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
14. Q8×Dic73C4semidirect
16. C4×Dic146C4semidirect
18. #14556556C4semidirect
23. C4×Q8×C73C4semidirect
111. C73#1805semidirect
124. C4×Q8#64408semidirect