Finite Group Databasebeta

← #22608559

Subgroups — #22608559

Order 9344.

200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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#17989116C211yesmaximal, characteristic
2#17988642C211yesmaximal, characteristic, complemented
3#17988642C211yesmaximal, characteristic, complemented
4#17988328C211yesmaximal, characteristic, complemented
5#17988328C211yesmaximal, characteristic, complemented
6#17988327C211yesmaximal, characteristic, complemented
7#329×C73C211yesmaximal, characteristic, complemented
8#14556584—21no—
9#14556583C2211yescharacteristic
10#14556573—21no—
11#14556567C411yescharacteristic
12#14556562C411yescharacteristic
13Q8×Dic73C411yescharacteristic
14D4×Dic73C411yescharacteristic
15#14556551—21no—
16#14556547—21no—
17C42×D73C2211yescharacteristic
18#14556520—21no—
19#14556520—21no—
20#14556503—21no—
21#14556503—21no—
22#14556502C2211yescharacteristic
23#14556502C2211yescharacteristic
24#124×C73C2211yescharacteristic
25#97×C73C2211yescharacteristic
26#97×C73C2211yescharacteristic
27C2×C22⋊D73—21no—
28C22×Dic73—21no—
29C2×C4×D73C2×C411yescharacteristic
30C2×C4×D73D411yescharacteristic
31C2×C4×D73D411yescharacteristic
32C2×#10596831—21no—
33C2×#10596831—21no—
34C4⋊Dic73—21no—
35C4⋊Dic73C2×C411yescharacteristic
36C4⋊Dic73C2×C411yescharacteristic
37#11924007—21no—
38#11924007—21no—
39#11924007—21no—
40C22⋊Dic73—21no—
41C22⋊Dic73—21no—
42#11924005—21no—
43C4×Dic73—21no—
44C4×Dic73C2×C411yescharacteristic
45C4×Dic73D411yescharacteristic
46C4×Dic73D411yescharacteristic
47C2×Q8×C73C2×C411yescharacteristic
48C2×D4×C73C2×C411yescharacteristic
49C2×C8×C73—21no—
50C2×C8×C73—21no—
51C22⋊C4×C73—21no—
52C22⋊C4×C73—21no—
53C42×C73C2311yescharacteristic
54C23×C73—21no—
55C22×D73C22⋊C411yescharacteristic
56Q8×C73—41no—
57D4×C73—41no—
58C2×C4×C73—21no—
59C2×C4×C73C22×C411yescharacteristic
60C2×C4×C73C2×D411yescharacteristic
61C2×C4×C73C2×D411yescharacteristic
62C22⋊D73—42no—
63C2×Dic73—21no—
64C2×Dic73—21no—
65C2×Dic73—42no—
66C2×Dic73C22⋊C411yescharacteristic
67C2×Dic73C22⋊C411yescharacteristic
68C2×Dic73C22⋊C411yescharacteristic
69C4×D73—41no—
70C4×D73—41no—
71C4×D73—41no—
72C8×C73—41no—
73C8×C73—41no—
74#10596831—41no—
75#10596831—41no—
76C22×C73—41no—
77C22×C73—41no—
78C22×C73—41no—
79C22×C73C2×C22⋊C411yescharacteristic
80C2×D73—21no—
81C2×D73—21no—
82C2×D73—21no—
83C4×C73—21no—
84C4×C73—21no—
85C4×C73—21no—
86C4×C73—41no—
87Dic73—21no—
88Dic73—21no—
89Dic73—21no—
90Dic73—41no—
91Dic73—41no—
92C2×C73—81no—
93C2×C73#41311yescharacteristic
94C2×C73#42111yescharacteristic
95C2×C73#42111yescharacteristic
96D73—41no—
97#1535—731nomaximal, Sylow
98C73#153511yescharacteristic, complemented, Sylow
99#529—731no—
100#432—731no—
101#432—731no—
102#330—731no—
103#330—731no—
104#329—731no—
105#329D7311yescharacteristic, complemented
106#126—1461no—
107#125—731no—
108#124C2×D7311yescharacteristic
109#123—1461no—
110C22⋊Q8—731no—
111#121—731no—
112C4×Q8—731no—
113C4×D4—731no—
114C4×D4—1461no—
115#117—1461no—
116C2×C42—731no—
117C4⋊C8—1461no—
118C4⋊C8—1461no—
119C22⋊C8—1461no—
120C22⋊C8—1461no—
121#97—731no—
122#97—731no—
123#97C2×D7311yescharacteristic
124#97C2×D7311yescharacteristic
125C2×Q8C4×D7311yescharacteristic
126C2×D4—1461no—
127C2×D4C4×D7311yescharacteristic
128C22×C4—731no—
129C22×C4—731no—
130C22×C4—731no—
131C22×C4—1461no—
132C2×C8—21no—
133C2×C8—21no—
134C2×C8—1461no—
135C2×C8—1461no—
136C4⋊C4—731no—
137C4⋊C4—731no—
138C4⋊C4—1461no—
139C4⋊C4—1461no—
140C4⋊C4—1461no—
141C4⋊C4—1461no—
142C22⋊C4—21no—
143C22⋊C4—21no—
144C22⋊C4—1461no—
145C22⋊C4—1461no—
146C22⋊C4—1461no—
147C42—731no—
148C42—731no—
149C42—731no—
150C42—1461no—
151C42C22×D7311yescharacteristic
152C23—21no—
153C23—731no—
154Q8—41no—
155D4—41no—
156D4—2922no—
157C2×C4—21no—
158C2×C4—2921no—
159C2×C4—2921no—
160C2×C4—2921no—
161C2×C4—2922no—
162C2×C4—731no—
163C2×C4—731no—
164C2×C4—731no—
165C2×C4—1461no—
166C2×C4—1461no—
167C2×C4C2×C4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4D4×D7311yescharacteristic
170C8—41no—
171C8—41no—
172C8—2921no—
173C8—2921no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—1461no—
178C22—1461no—
179C22—1461no—
180C22C22⋊C4×D7311yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—41no—
185C4—2921no—
186C4—2921no—
187C4—1461no—
188C4—1461no—
189C4—1461no—
190C2—81no—
191C2—2921no—
192C2#1798856811yescharacteristic
193C2#1798860211yescharacteristic
194C2#1798860211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D73
commutatorC2×C4×C73C22×C4
FrattiniC42C22×D73
Fitting#329×C73C2
socleC22×C73C2×C22⋊C4
hypercenter#329D73
hypocenterC73#1535
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #17988642C2semidirect
3. #17988642C2semidirect
4. #17988328C2semidirect
5. #17988328C2semidirect
6. #17988327C2semidirect
7. #329×C73C2semidirect
98. C73#1535semidirect
105. #329D73semidirect