Finite Group Databasebeta

← D73⋊#353 #22626197

Subgroups — D73⋊#353 #22626197

Order 9344.

368 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D73⋊#99C212yesmaximal, complemented
2#17989492C212yesmaximal, complemented
3#17989491C212yesmaximal, complemented
4#127×D73C211yesmaximal, characteristic
5C2×C22⋊#64408—22no—
6#14556650C2214yescomplemented
7#14556649—22no—
8C2×D4×D73—22no—
9C2×D4×D73C411yescharacteristic, complemented
10C2×D4×D73C2211yescharacteristic
11#14556588C2211yescharacteristic
12#14556587—22no—
13#14556587C411yescharacteristic, complemented
14#14556587C2211yescharacteristic
15C42×D73C411yescharacteristic, complemented
16#127×C73C411yescharacteristic, complemented
17C22×#64408—42no—
18C22⋊#64408—24no—
19C22⋊#64408—42no—
20C23×D73—21no—
21C23×D73D412yes—
22C2×D292—22no—
23C2×D292C2×C411yescharacteristic, complemented
24C2×D292C2311yescharacteristic
25C2×C22⋊D73—22no—
26C2×C22⋊D73—22no—
27C2×C22⋊D73—21no—
28C2×C22⋊D73D412yes—
29D4×D73—41no—
30D4×D73—41no—
31D4×D73—41no—
32D4×D73—41no—
33D4×D73—48no—
34C2×C4×D73—21no—
35C2×C4×D73C2×C411yescharacteristic
36C4×Dic73—21no—
37C4×Dic73C2×C411yescharacteristic, complemented
38C2×D4×C73—22no—
39C2×D4×C73C2×C411yescharacteristic
40C2×D4×C73C2×C411yescharacteristic, complemented
41C42×C73C2×C411yescharacteristic, complemented
42C23×C73—21no—
43C23×C73C22⋊C412yes—
44C22×D73—22no—
45C22×D73—22no—
46C22×D73—21no—
47C22×D73—44no—
48C22×D73—44no—
49C22×D73—41no—
50C22×D73—41no—
51C22×D73C22⋊C411yescharacteristic
52C22×D73C2×D412yes—
53C2×#64408—44no—
54C2×#64408—84no—
55D4×C73—41no—
56D4×C73—41no—
57D4×C73—44no—
58C2×C4×C73—21no—
59C2×C4×C73C22×C411yescharacteristic
60C22⋊D73—42no—
61C22⋊D73—44no—
62C22⋊D73—44no—
63C22⋊D73—42no—
64C2×Dic73—21no—
65C2×Dic73C22⋊C411yescharacteristic
66D292—41no—
67D292—41no—
68D292—44no—
69C4×D73—24no—
70C4×D73—21no—
71C4×D73—21no—
72C22×C73—22no—
73C22×C73—42no—
74C22×C73—42no—
75C22×C73—41no—
76C22×C73C2×C22⋊C411yescharacteristic
77C2×D73—22no—
78C2×D73—22no—
79C2×D73—44no—
80C2×D73—42no—
81C2×D73—42no—
82C2×D73—41no—
83C2×D73—82no—
84C2×D73—82no—
85C2×D73—82no—
86C2×D73#9911yescharacteristic
87C2×D73#9911yescharacteristic
88#64408—84no—
89C4×C73—22no—
90C4×C73—21no—
91Dic73—22no—
92Dic73—21no—
93C2×C73—21no—
94C2×C73—42no—
95C2×C73—81no—
96C2×C73C2×#9911yescharacteristic
97D73—21no—
98D73—42no—
99D73—81no—
100D73#35312yescomplemented
101C2×#353—731nomaximal, Sylow
102C73C2×#35311yescharacteristic, complemented, Sylow
103C2×#127—731no—
104C2×#99—732no—
105#353—732no—
106#353—732no—
107C22×D4—731no—
108C22×D4—731no—
109C22×D4—1462no—
110#127—731no—
111#127—731no—
112#127—731no—
113#127—1462no—
114#127#6440811yescharacteristic, complemented
115C2×C22⋊C4—1462no—
116C2×C42—731no—
117#99—734no—
118#99—1462no—
119C24—732no—
120C24—1461no—
121C2×D4—22no—
122C2×D4—2921no—
123C2×D4—2921no—
124C2×D4—2928no—
125C2×D4—2921no—
126C2×D4—2921no—
127C2×D4—732no—
128C2×D4—731no—
129C2×D4—731no—
130C2×D4—1462no—
131C2×D4—1461no—
132C2×D4—1462no—
133C2×D4—1462no—
134C2×D4C2×#6440811yescharacteristic
135C2×D4C2×#6440811yescharacteristic, complemented
136C22×C4—2922no—
137C22×C4—731no—
138C22×C4—1461no—
139C22⋊C4—2922no—
140C22⋊C4—1464no—
141C42—731no—
142C42—1461no—
143C42C2×#6440811yescharacteristic, complemented
144C23—21no—
145C23—2924no—
146C23—2921no—
147C23—2921no—
148C23—2924no—
149C23—732no—
150C23—731no—
151C23—1462no—
152C23—1462no—
153C23—1461no—
154C23C22⋊#6440812yes—
155D4—41no—
156D4—41no—
157D4—44no—
158D4—2921no—
159D4—2924no—
160D4—2921no—
161D4—2922no—
162D4—2924no—
163D4—2924no—
164D4—2922no—
165C2×C4—21no—
166C2×C4—2924no—
167C2×C4—5844no—
168C2×C4—731no—
169C2×C4—1461no—
170C2×C4—1461no—
171C2×C4—1464no—
172C2×C4—1461no—
173C2×C4C22×#6440811yescharacteristic
174C22—22no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—2922no—
179C22—2922no—
180C22—2924no—
181C22—2921no—
182C22—5842no—
183C22—5842no—
184C22—5842no—
185C22—731no—
186C22—731no—
187C22—1462no—
188C22—1462no—
189C22C2×C22⋊#6440811yescharacteristic
190C4—22no—
191C4—21no—
192C4—5844no—
193C4—1462no—
194C4—1461no—
195C2—21no—
196C2—42no—
197C2—81no—
198C2—2922no—
199C2—5841no—
200C2—732no—
201C2—1461no—
202C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#127×C73C4
socleC2×C73C2×#99
hypercenter#127#64408
hypocenterC73C2×#353
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
1. D73⋊#99C2semidirect
2. #17989492C2semidirect
3. #17989491C2semidirect
6. #14556650C22semidirect
9. C2×D4×D73C4semidirect
13. #14556587C4semidirect
15. C42×D73C4semidirect
16. #127×C73C4semidirect
23. C2×D292C2×C4semidirect
37. C4×Dic73C2×C4semidirect
40. C2×D4×C73C2×C4semidirect
41. C42×C73C2×C4semidirect
100. D73#353semidirect
102. C73C2×#353semidirect
114. #127#64408semidirect
135. C2×D4C2×#64408semidirect
143. C42C2×#64408semidirect