Finite Group Databasebeta

← #22626194

Subgroups — #22626194

Order 9344.

234 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 52 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#17989574C211yesmaximal, characteristic
2#17989567C211yesmaximal, characteristic
3#17989490C212yesmaximal, complemented
4#17989489C212yesmaximal, complemented
5#17989159C211yesmaximal, characteristic
6C2×#11924037—21no—
7#14556670—21no—
8#14556652—21no—
9#14556651C2212yes—
10#14556649—21no—
11#14556649C2212yes—
12C2×#11924027C2211yescharacteristic
13C22×Dic146C411yescharacteristic, complemented
14#14556590—21no—
15#14556577—21no—
16#14556575C2211yescharacteristic
17#14556574C2211yescharacteristic
18#14556572C411yescharacteristic, complemented
19#14556569—21no—
20#14556568—21no—
21#14556547C411yescharacteristic, complemented
22#123×C73C411yescharacteristic, complemented
23#11924037—22no—
24#11924037—41no—
25C2×#10596833—41no—
26C4⋊#64408—41no—
27C22⋊#64408—22no—
28C4×#64408—41no—
29#11924027—41no—
30#11924027—41no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—41no—
34C2×Dic146—41no—
35C2×Dic146D411yescharacteristic
36C2×C22⋊D73D411yescharacteristic
37C2×C22⋊D73C2311yescharacteristic
38C22×Dic73C2×C411yescharacteristic
39C22×Dic73C2×C411yescharacteristic
40C22×Dic73D411yescharacteristic
41C2×C4×D73D411yescharacteristic
42C4⋊Dic73—21no—
43#11924007—21no—
44#11924007—21no—
45#11924007—21no—
46C22⋊Dic73—21no—
47C22⋊Dic73C2×C411yescharacteristic
48#11924005—21no—
49#11924005—21no—
50C4×Dic73—21no—
51C2×D4×C73C2×C411yescharacteristic
52C22×C4×C73C2×C411yescharacteristic
53C4⋊C4×C73—21no—
54C22⋊C4×C73—21no—
55C22⋊C4×C73C2×C411yescharacteristic
56C23×C73C22⋊C411yescharacteristic
57C23×C73C22×C411yescharacteristic
58C22×D73C2×D411yescharacteristic
59C2×#64408—42no—
60D4×C73—41no—
61C2×C4×C73—21no—
62C2×C4×C73—21no—
63C2×C4×C73—41no—
64C2×C4×C73C22⋊C411yescharacteristic
65C22⋊D73—41no—
66C22⋊D73—41no—
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—41no—
74C2×Dic73C22⋊C411yescharacteristic
75C2×Dic73C22⋊C411yescharacteristic
76C2×Dic73C2×D411yescharacteristic
77C4×D73—21no—
78C4×D73—21no—
79Dic146—41no—
80Dic146—42no—
81Dic146—41no—
82Dic146—41no—
83#10596833—42no—
84C22×C73—21no—
85C22×C73—21no—
86C22×C73—41no—
87C22×C73—41no—
88C22×C73C2×C22⋊C411yescharacteristic
89C2×D73—21no—
90C2×D73—41no—
91#64408—82no—
92C4×C73—21no—
93C4×C73—41no—
94C4×C73—41no—
95Dic73—21no—
96Dic73—21no—
97Dic73—41no—
98Dic73—41no—
99Dic73#9911yescharacteristic
100Dic73#9911yescharacteristic
101C2×C73—21no—
102C2×C73—41no—
103C2×C73—41no—
104C2×C73C2×#9911yescharacteristic
105D73—41no—
106#2123—731nomaximal, Sylow
107C73#212311yescharacteristic, complemented, Sylow
108#536—731no—
109#413—731no—
110#410—731no—
111#352—732no—
112#352—732no—
113C2×#41—731no—
114C22×Q8—731no—
115C2×M16—1461no—
116C4⋊Q8—1461no—
117#124—1461no—
118#123—731no—
119#123—731no—
120#123—731no—
121#123#6440811yescharacteristic, complemented
122C22⋊Q8—1461no—
123C22⋊Q8—1461no—
124#117—731no—
125#117—1461no—
126#101—1461no—
127#100—732no—
128#99—732no—
129#99—1461no—
130#41—2921no—
131#41—2921no—
132C2×Q8—2921no—
133C2×Q8—2921no—
134C2×Q8—731no—
135C2×Q8—1461no—
136C2×Q8—1461no—
137C2×D4—731no—
138C2×D4—731no—
139C2×D4C2×#6440811yescharacteristic
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4C2×#6440811yescharacteristic
145M16—2921no—
146M16—1462no—
147C2×C8—2921no—
148C4⋊C4—21no—
149C4⋊C4—2921no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C22⋊C4—21no—
155C22⋊C4—731no—
156C22⋊C4—1461no—
157C22⋊C4—1461no—
158C22⋊C4—1462no—
159C22⋊C4—1461no—
160C22⋊C4C2×#6440811yescharacteristic
161C42—2921no—
162C42—1461no—
163C23—731no—
164C23C22⋊#6440811yescharacteristic
165C23C22×#6440811yescharacteristic
166Q8—2921no—
167Q8—2921no—
168Q8—2921no—
169Q8—2922no—
170D4—41no—
171D4—2921no—
172D4—2921no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—2921no—
177C2×C4—2922no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—731no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4—1461no—
188C2×C4—1461no—
189C2×C4C22⋊#6440811yescharacteristic
190C8—2922no—
191C22—21no—
192C22—21no—
193C22—41no—
194C22—41no—
195C22—2921no—
196C22—1461no—
197C22C2×C22⋊#6440811yescharacteristic
198C4—21no—
199C4—41no—
200C4—41no—
201C4—2921no—
202C4—2921no—
203C4—5842no—
204C4—731no—
205C4—731no—
206C4—1461no—
207C4—1461no—
208C2—21no—
209C2—41no—
210C2—41no—
211C2—2921no—
212C2D73⋊#9911yescharacteristic
subgroupG/H
centerC2D73⋊#99
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
Fitting#123×C73C4
socleC2×C73C2×#99
hypercenter#123#64408
hypocenterC73#2123
LCSG ▷ C23×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #123

Complements

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

NH ≅ G/Ntype
3. #17989490C2semidirect
4. #17989489C2semidirect
13. C22×Dic146C4semidirect
18. #14556572C4semidirect
21. #14556547C4semidirect
22. #123×C73C4semidirect
107. C73#2123semidirect
121. #123#64408semidirect