Finite Group Databasebeta

← #22625977

Subgroups — #22625977

Order 9344.

362 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 66 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#17989654C211yesmaximal, characteristic, complemented
2#17989585C212yesmaximal, complemented
3D73⋊#100C211yesmaximal, characteristic, complemented
4#17989454C212yesmaximal, complemented
5#17989150C211yesmaximal, characteristic
6D73⋊M16C2212yes—
7D4×#64408—24no—
8#14556670C2212yes—
9C2×C22⋊#64408—22no—
10#14556655—24no—
11#14556651—22no—
12C2×#11924027C2211yescharacteristic
13C2×D4×D73C2211yescharacteristic
14#14556587C411yescharacteristic, complemented
15#14556579C411yescharacteristic, complemented
16#14556578C411yescharacteristic, complemented
17#14556563—22no—
18#14556559—22no—
19#14556548C2211yescharacteristic
20#127×C73C411yescharacteristic, complemented
21C22×#64408—24no—
22#11924038—22no—
23#11924037—22no—
24#11924036—22no—
25C4⋊#64408—22no—
26C22⋊#64408—24no—
27C22⋊#64408—22no—
28C4×#64408D414yescomplemented
29C23×D73D412yes—
30#11924027—22no—
31#11924027—22no—
32C2×Dic146C2×C411yescharacteristic, complemented
33C2×D292C2×C411yescharacteristic
34C2×C22⋊D73—21no—
35C2×C22⋊D73—22no—
36C2×C22⋊D73D412yes—
37D4×D73—22no—
38D4×D73—22no—
39C22×Dic73—21no—
40C2×C4×D73C2311yescharacteristic
41#11924007—21no—
42C22⋊Dic73—22no—
43#11924005—22no—
44#11924005—21no—
45C4×Dic73C2×C411yescharacteristic, complemented
46C2×D4×C73—22no—
47C2×D4×C73C2×C411yescharacteristic
48C2×D4×C73C2×C411yescharacteristic, complemented
49C42×C73C2×C411yescharacteristic, complemented
50C23×C73—21no—
51C23×C73C22⋊C412yes—
52C22×D73—22no—
53C22×D73—22no—
54C22×D73—82no—
55C22×D73C22⋊C412yes—
56C22×D73C2×D411yescharacteristic
57C2×#64408—24no—
58C2×#64408—84no—
59D4×C73—22no—
60D4×C73—22no—
61D4×C73—82no—
62C2×C4×C73—21no—
63C2×C4×C73C22×C411yescharacteristic
64C22⋊D73—24no—
65C22⋊D73—41no—
66C22⋊D73—41no—
67C22⋊D73—82no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—42no—
71C2×Dic73C2×D411yescharacteristic
72D292—22no—
73C4×D73C2×D412yes—
74C4×D73#4112yes—
75Dic146—22no—
76#10596833—42no—
77C22×C73—22no—
78C22×C73—42no—
79C22×C73—42no—
80C22×C73—41no—
81C22×C73C2×C22⋊C411yescharacteristic
82C2×D73—22no—
83C2×D73—41no—
84C2×D73—44no—
85C2×D73—42no—
86C2×D73—82no—
87C2×D73#12011yescharacteristic
88C2×D73#12311yescharacteristic
89#64408—44no—
90C4×C73—41no—
91C4×C73C4×D412yes—
92Dic73—41no—
93Dic73—41no—
94Dic73#12112yes—
95C2×C73—21no—
96C2×C73—42no—
97C2×C73—81no—
98C2×C73#38611yescharacteristic
99D73—21no—
100D73—21no—
101D73—42no—
102#1911—731nomaximal, Sylow
103C73#191111yescharacteristic, complemented, Sylow
104#535—731no—
105#518—731no—
106#421—732no—
107C2×#100—731no—
108H(3,ℤ/4)—732no—
109C2×#41—731no—
110C22×D4—731no—
111C2×M16—732no—
112#127—731no—
113#127#6440811yescharacteristic, complemented
114#124—731no—
115#124—731no—
116#121—1462no—
117#120—1462no—
118C4×D4—1464no—
119#117—732no—
120#117—731no—
121C2×C22⋊C4—1462no—
122#104—1464no—
123#100—1462no—
124C24—732no—
125#41—1462no—
126#41—1462no—
127C2×Q8—731no—
128C2×D4—22no—
129C2×D4—732no—
130C2×D4—731no—
131C2×D4—1462no—
132C2×D4—1462no—
133C2×D4—1461no—
134C2×D4—1462no—
135C2×D4C2×#6440811yescharacteristic
136C2×D4C2×#6440811yescharacteristic, complemented
137C22×C4—731no—
138C22×C4—1461no—
139C22×C4—1464no—
140M16—1462no—
141M16—1462no—
142C2×C8—1462no—
143C4⋊C4—1461no—
144C4⋊C4—1462no—
145C22⋊C4—1461no—
146C22⋊C4—1462no—
147C22⋊C4—1462no—
148C22⋊C4—1464no—
149C22⋊C4—1462no—
150C42—734no—
151C42—731no—
152C42C2×#6440811yescharacteristic, complemented
153C23—21no—
154C23—5842no—
155C23—731no—
156C23—732no—
157C23—1462no—
158C23—1462no—
159C23C22⋊#6440812yes—
160Q8—1462no—
161D4—22no—
162D4—22no—
163D4—82no—
164D4—2921no—
165D4—2921no—
166D4—5842no—
167D4—1464no—
168D4—1462no—
169C2×C4—21no—
170C2×C4—2922no—
171C2×C4—5844no—
172C2×C4—731no—
173C2×C4—732no—
174C2×C4—732no—
175C2×C4—1464no—
176C2×C4—1461no—
177C2×C4—1461no—
178C2×C4C22×#6440811yescharacteristic
179C8—2922no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22—2922no—
185C22—2921no—
186C22—2924no—
187C22—5842no—
188C22—731no—
189C22—731no—
190C22—1462no—
191C22C2×C22⋊#6440811yescharacteristic
192C4—41no—
193C4—2921no—
194C4—2924no—
195C4—2921no—
196C4—732no—
197C4D4×#6440812yes—
198C2—21no—
199C2—42no—
200C2—81no—
201C2—2922no—
202C2—1461no—
203C2—1461no—
204C2#1798953511yescharacteristic
subgroupG/H
centerC2#17989535
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#127×C73C4
socleC2×C73#386
hypercenter#127#64408
hypocenterC73#1911
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #17989654C2semidirect
2. #17989585C2semidirect
3. D73⋊#100C2semidirect
4. #17989454C2semidirect
14. #14556587C4semidirect
15. #14556579C4semidirect
16. #14556578C4semidirect
20. #127×C73C4semidirect
28. C4×#64408D4semidirect
32. C2×Dic146C2×C4semidirect
45. C4×Dic73C2×C4semidirect
48. C2×D4×C73C2×C4semidirect
49. C42×C73C2×C4semidirect
103. C73#1911semidirect
113. #127#64408semidirect
136. C2×D4C2×#64408semidirect
152. C42C2×#64408semidirect