Finite Group Databasebeta

← #22625329

Subgroups — #22625329

Order 9344.

294 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 60 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#17989559C211yesmaximal, characteristic
2C4×C22⋊#64408C211yesmaximal, characteristic
3#17989441C212yesmaximal, complemented
4#17989440C212yesmaximal, complemented
5C22⋊Q8×D73C211yesmaximal, characteristic
6C2×#11924037—21no—
7C2×C22⋊#64408—21no—
8C2×C4×#64408—21no—
9#14556648—21no—
10#14556648C2212yes—
11(C2×#64408)⋊C4C2212yes—
12C2×Q8×D73C411yescharacteristic, complemented
13C22×C4×D73C2211yescharacteristic
14#14556571C2211yescharacteristic
15#14556570C411yescharacteristic, complemented
16#14556569—21no—
17#14556568—21no—
18#14556567C2211yescharacteristic
19C4⋊C4×D73—21no—
20C4⋊C4×D73C411yescharacteristic, complemented
21C22⋊C4×D73—21no—
22C22⋊Q8×C73C411yescharacteristic, complemented
23C22×#64408—22no—
24#11924037—42no—
25C2×#10596833—22no—
26C22⋊#64408—24no—
27C4×#64408—42no—
28C23×D73D411yescharacteristic
29C2×Dic146—21no—
30C2×Dic146C2×C411yescharacteristic
31Q8×D73—42no—
32C22×Dic73D411yescharacteristic
33C2×C4×D73—21no—
34C2×C4×D73—21no—
35C2×C4×D73—42no—
36C2×C4×D73C2×C411yescharacteristic
37C2×C4×D73D411yescharacteristic
38C2×C4×D73D411yescharacteristic
39C2×C4×D73C2311yescharacteristic
40C4⋊Dic73—21no—
41C4⋊Dic73C2×C411yescharacteristic
42#11924007—21no—
43#11924007—21no—
44#11924007—21no—
45C22⋊Dic73—21no—
46#11924005—21no—
47#11924005—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—41no—
57C22×D73C22⋊C411yescharacteristic
58C22×D73C2×D411yescharacteristic
59C2×#64408—24no—
60C2×#64408—42no—
61C2×#64408—42no—
62Q8×C73—41no—
63C2×C4×C73—21no—
64C2×C4×C73—21no—
65C2×C4×C73—41no—
66C2×C4×C73C22⋊C411yescharacteristic
67C2×C4×C73C22×C411yescharacteristic
68C2×Dic73—22no—
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73C22⋊C411yescharacteristic
72C2×Dic73C2×D411yescharacteristic
73C4×D73—22no—
74C4×D73—22no—
75C4×D73—41no—
76C4×D73—41no—
77C4×D73—42no—
78C4×D73—42no—
79Dic146—42no—
80Dic146—41no—
81#10596833—42no—
82C22×C73—21no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73C2×C22⋊C411yescharacteristic
86C2×D73—21no—
87C2×D73—21no—
88C2×D73—21no—
89C2×D73—21no—
90C2×D73—44no—
91C2×D73#10412yes—
92C2×D73#13712yes—
93#64408—44no—
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—41no—
97C4×C73—41no—
98Dic73—21no—
99Dic73—41no—
100Dic73—41no—
101Dic73#9912yes—
102C2×C73—41no—
103C2×C73C2×#9911yescharacteristic
104C2×C73#41911yescharacteristic
105C2×C73C2×#10411yescharacteristic
106D73—22no—
107D73—22no—
108#1508—731nomaximal, Sylow
109C73#150811yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—731no—
111#407—731no—
112C4×C22⋊C4—731no—
113#328—732no—
114#328—732no—
115C22×Q8—731no—
116C23×C4—731no—
117C2×M16—1461no—
118C22⋊Q8—731no—
119C22⋊Q8—731no—
120C22⋊Q8—731no—
121C22⋊Q8—1461no—
122C22⋊Q8—1461no—
123C22⋊Q8#6440811yescharacteristic, complemented
124C2×C4⋊C4—731no—
125C2×C4⋊C4—1461no—
126C2×C22⋊C4—1461no—
127C2×C22⋊C4—1461no—
128C2×C42—1461no—
129C22⋊C8—732no—
130C22⋊C8—1461no—
131#95—732no—
132C24—731no—
133C2×Q8—2922no—
134C2×Q8—731no—
135C2×Q8—1461no—
136C2×Q8C2×#6440811yescharacteristic
137C22×C4—2922no—
138C22×C4—731no—
139C22×C4—731no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—1461no—
144C22×C4—1461no—
145C22×C4—1462no—
146C22×C4C2×#6440811yescharacteristic
147M16—2922no—
148C2×C8—1462no—
149C4⋊C4—21no—
150C4⋊C4—731no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C4⋊C4C2×#6440811yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—1461no—
158C22⋊C4—1461no—
159C22⋊C4—1464no—
160C22⋊C4—1461no—
161C42—2922no—
162C23—2921no—
163C23—731no—
164C23—731no—
165C23—1462no—
166C23—1462no—
167C23C22⋊#6440811yescharacteristic
168Q8—41no—
169Q8—2921no—
170Q8—2922no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—2921no—
175C2×C4—2921no—
176C2×C4—2922no—
177C2×C4—2922no—
178C2×C4—2922no—
179C2×C4—2922no—
180C2×C4—731no—
181C2×C4—731no—
182C2×C4—1462no—
183C2×C4—1462no—
184C2×C4—1464no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4—1462no—
188C2×C4C22⋊#6440811yescharacteristic
189C2×C4C22×#6440811yescharacteristic
190C8—2922no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—2924no—
195C22—732no—
196C22—732no—
197C22—1461no—
198C22—1461no—
199C22—1461no—
200C22—1461no—
201C22C2×C22⋊#6440811yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—2924no—
207C4—2921no—
208C4—2921no—
209C4—732no—
210C4—1461no—
211C2—41no—
212C2—1462no—
213C2—1462no—
214C2D73⋊#9911yescharacteristic
215C2#1798958011yescharacteristic
216C2D73⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
FittingC22⋊Q8×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC22⋊Q8#64408
hypocenterC73#1508
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
3. #17989441C2semidirect
4. #17989440C2semidirect
12. C2×Q8×D73C4semidirect
15. #14556570C4semidirect
20. C4⋊C4×D73C4semidirect
22. C22⋊Q8×C73C4semidirect
109. C73#1508semidirect
123. C22⋊Q8#64408semidirect