Finite Group Databasebeta

← #22611594

Subgroups — #22611594

Order 9344.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#17989133C211yesmaximal, characteristic
2#17988561C211yesmaximal, characteristic, complemented
3#17988381C212yesmaximal, complemented
4#17988379C212yesmaximal, complemented
5#410×C73C211yesmaximal, characteristic, complemented
6C2×#11924028C411yescharacteristic, complemented
7#14556589C411yescharacteristic, complemented
8#14556587C2211yescharacteristic
9#14556580C411yescharacteristic, complemented
10#14556578C2211yescharacteristic
11#14556563—21no—
12#14556563—21no—
13C4×C22⋊D73—21no—
14C4×C22⋊D73—21no—
15#14556550—21no—
16C2×C4×Dic73C411yescharacteristic, complemented
17#14556506—21no—
18#14556506C2212yes—
19C2×#41×C73C2211yescharacteristic
20#117×C73—21no—
21#99×C73—21no—
22#99×C73C2212yes—
23#11924028—41no—
24#11924028—41no—
25C2×Dic146C2×C411yescharacteristic
26C2×D292C2×C411yescharacteristic
27C2×C22⋊D73—21no—
28C2×C22⋊D73—21no—
29C2×C22⋊D73—21no—
30C22×Dic73—21no—
31C2×C4×D73—21no—
32C4⋊Dic73—41no—
33#11924007—21no—
34#11924007—21no—
35C22⋊Dic73—21no—
36C22⋊Dic73—21no—
37C22⋊Dic73—22no—
38#11924005—21no—
39#11924005—21no—
40C4×Dic73—21no—
41C4×Dic73—41no—
42C4×Dic73C2×C411yescharacteristic
43C4×Dic73C2×C411yescharacteristic
44#41×C73—41no—
45#41×C73—41no—
46C2×Q8×C73C2×C411yescharacteristic
47C2×D4×C73D411yescharacteristic
48C2×D4×C73D411yescharacteristic
49C2×D4×C73C2311yescharacteristic
50C22×C4×C73C2×C411yescharacteristic
51C22×C4×C73D411yescharacteristic
52C22×C4×C73D411yescharacteristic
53C4⋊C4×C73—41no—
54C22⋊C4×C73—22no—
55C42×C73—41no—
56C23×C73C22⋊C411yescharacteristic
57C23×C73C2×D411yescharacteristic
58C23×C73C2×D411yescharacteristic
59C22×D73—21no—
60Q8×C73—41no—
61D4×C73—41no—
62D4×C73—41no—
63D4×C73—41no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—42no—
71C2×C4×C73C22⋊C411yescharacteristic
72C2×C4×C73C22⋊C411yescharacteristic
73C2×C4×C73C22⋊C411yescharacteristic
74C2×C4×C73C22×C411yescharacteristic
75C22⋊D73—42no—
76C22⋊D73—42no—
77C22⋊D73—42no—
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—42no—
82C2×Dic73—42no—
83D292—41no—
84C4×D73—41no—
85C4×D73—41no—
86Dic146—41no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73—21no—
90C22×C73—41no—
91C22×C73—41no—
92C22×C73—41no—
93C22×C73C2×C22⋊C411yescharacteristic
94C2×D73—41no—
95C2×D73—41no—
96C2×D73—41no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—82no—
101C4×C73#9911yescharacteristic
102C4×C73#9911yescharacteristic
103Dic73—22no—
104Dic73—41no—
105Dic73—41no—
106Dic73—82no—
107C2×C73—21no—
108C2×C73—41no—
109C2×C73—41no—
110C2×C73—41no—
111C2×C73C2×#9911yescharacteristic
112D73—81no—
113#2126—731nomaximal, Sylow
114C73#212611yescharacteristic, complemented, Sylow
115#532—731no—
116#410—731no—
117#410D7311yescharacteristic, complemented
118#354—732no—
119#353—732no—
120C2×#41—731no—
121C2×#41C2×D7311yescharacteristic
122C4⋊Q8—731no—
123#127—731no—
124#124—731no—
125#124—731no—
126#121—1461no—
127#121—1461no—
128C4×D4—1461no—
129C4×D4—1461no—
130#117—21no—
131#117—1461no—
132C2×C42—731no—
133#99—21no—
134#99—732no—
135#99—1461no—
136#99C2×D7312yes—
137#41—41no—
138#41—41no—
139#41—2921no—
140#41—2921no—
141C2×Q8—731no—
142C2×Q8C4×D7311yescharacteristic
143C2×D4—731no—
144C2×D4—1461no—
145C2×D4—1461no—
146C2×D4—1461no—
147C2×D4D29211yescharacteristic
148C2×D4C22⋊D7311yescharacteristic
149C2×D4C22×D7311yescharacteristic
150C22×C4—1461no—
151C22×C4—1461no—
152C22×C4C4×D7311yescharacteristic
153C22×C4D29211yescharacteristic
154C22×C4C22⋊D7311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—2921no—
157C4⋊C4—1461no—
158C4⋊C4—1461no—
159C22⋊C4—22no—
160C22⋊C4—1462no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C22⋊C4—1461no—
165C42—41no—
166C42—2921no—
167C42—731no—
168C42—731no—
169C42—1461no—
170C23—1461no—
171C23#1192400511yescharacteristic
172C23C2×C22⋊D7311yescharacteristic
173C23C2×D29211yescharacteristic
174Q8—41no—
175Q8—2921no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—2921no—
180D4—2922no—
181D4—2922no—
182D4—2922no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—2922no—
191C2×C4—2921no—
192C2×C4—2921no—
193C2×C4—2922no—
194C2×C4—1461no—
195C2×C4—1461no—
196C2×C4—1461no—
197C2×C4#1192400511yescharacteristic
198C2×C4#1192400511yescharacteristic
199C2×C4#1192400511yescharacteristic
200C2×C4C2×C4×D7311yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—2921no—
208C22—2921no—
209C22—2921no—
210C22C2×#1192400511yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—2921no—
216C4—2921no—
217C4—5842no—
218C4—1462no—
219C4#1455650511yescharacteristic
220C4#1455650511yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—5841no—
226C2C2×#1455650511yescharacteristic
subgroupG/H
centerC4#14556505
commutatorC2×C4×C73C22×C4
FrattiniC2×D4C22×D73
Fitting#410×C73C2
socleC2×C73C2×#99
hypercenter#410D73
hypocenterC73#2126
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #17988561C2semidirect
3. #17988381C2semidirect
4. #17988379C2semidirect
5. #410×C73C2semidirect
6. C2×#11924028C4semidirect
7. #14556589C4semidirect
9. #14556580C4semidirect
16. C2×C4×Dic73C4semidirect
114. C73#2126semidirect
117. #410D73semidirect