Finite Group Databasebeta

← #22610137

Subgroups — #22610137

Order 9344.

278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×M16×D73C211yesmaximal, characteristic
2C2×#14556527C211yesmaximal, characteristic, complemented
3C2×#14556526C211yesmaximal, characteristic, complemented
4#17988550C211yesmaximal, characteristic
5C2×#14556503C211yesmaximal, characteristic
6#17988351C211yesmaximal, characteristic, complemented
7#341×C73C211yesmaximal, characteristic, complemented
8C22×C4×D73C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C2×#11924012C2211yescharacteristic
11C2×#11924011—21no—
12M16×D73—22no—
13M16×D73—22no—
14C22×#10596831C2211yescharacteristic
15C2×C8×D73—21no—
16#14556527—22no—
17#14556526—22no—
18#14556503—21no—
19#14556503—21no—
20#14556503C412yes—
21#14556503C412yes—
22C2×M16×C73C2211yescharacteristic
23C2×M16×C73C2211yescharacteristic
24C22×C8×C73C2211yescharacteristic
25C23×D73Q811yescharacteristic
26C22×Dic73Q811yescharacteristic
27C2×C4×D73—21no—
28C2×C4×D73—21no—
29C2×C4×D73—21no—
30C2×C4×D73—21no—
31C2×C4×D73C2×C411yescharacteristic
32C2×C4×D73C2×C411yescharacteristic
33C2×C4×D73D411yescharacteristic
34C2×C4×D73D411yescharacteristic
35#11924012—21no—
36#11924012—21no—
37#11924012—21no—
38#11924012D412yes—
39#11924011—24no—
40C2×#10596831—21no—
41C2×#10596831—21no—
42C2×#10596831—21no—
43C2×#10596831—21no—
44C2×#10596831C2×C412yes—
45C8×D73—24no—
46C22×C4×C73C2311yescharacteristic
47M16×C73—21no—
48M16×C73—21no—
49M16×C73—21no—
50M16×C73D412yes—
51C2×C8×C73—21no—
52C2×C8×C73—21no—
53C2×C8×C73—21no—
54C2×C8×C73—21no—
55C2×C8×C73C2×C412yes—
56C23×C73C2×Q811yescharacteristic
57C22×D73—21no—
58C22×D73—21no—
59C22×D73—22no—
60C22×D73—41no—
61C22×D73C4⋊C411yescharacteristic
62C22×D73C4⋊C411yescharacteristic
63C2×C4×C73C22×C411yescharacteristic
64C2×C4×C73C2×D411yescharacteristic
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73#4111yescharacteristic
68C2×C4×C73#4111yescharacteristic
69C2×Dic73—21no—
70C2×Dic73—21no—
71C2×Dic73C4⋊C411yescharacteristic
72C2×Dic73C4⋊C411yescharacteristic
73C4×D73—21no—
74C4×D73—21no—
75C4×D73—21no—
76C4×D73—21no—
77C4×D73—21no—
78C4×D73—21no—
79C4×D73—21no—
80C4×D73—21no—
81C8×C73—22no—
82C8×C73—22no—
83C8×C73—41no—
84#10596831—22no—
85#10596831—22no—
86#10596831—41no—
87C22×C73—21no—
88C22×C73—21no—
89C22×C73C2×C4⋊C411yescharacteristic
90C22×C73C22⋊Q811yescharacteristic
91C22×C73C22⋊Q811yescharacteristic
92C2×D73—21no—
93C2×D73—21no—
94C2×D73—21no—
95C2×D73—21no—
96C2×D73—21no—
97C2×D73—42no—
98C2×D73—42no—
99C2×D73#10812yescomplemented
100C4×C73C4×D411yescharacteristic
101C4×C73C4×D411yescharacteristic
102C4×C73#12011yescharacteristic
103C4×C73#12311yescharacteristic
104Dic73—21no—
105Dic73—21no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73#38511yescharacteristic
109C2×C73C2×#10811yescharacteristic
110C2×C73#43011yescharacteristic
111D73—22no—
112D73—41no—
113#1855—731nomaximal, Sylow
114C73#185511yescharacteristic, complemented, Sylow
115C22×M16—731no—
116C2×#108—731no—
117C2×#108—731no—
118#407—731no—
119C2×C22⋊C8—731no—
120#341—731no—
121#341D7311yescharacteristic, complemented
122C23×C4—731no—
123C2×M16—731no—
124C2×M16—731no—
125C2×M16—1461no—
126C2×M16—1462no—
127C2×M16—1462no—
128C2×M16C2×D7311yescharacteristic
129C2×M16C2×D7311yescharacteristic
130C22×C8—731no—
131C22×C8—1461no—
132C22×C8C2×D7311yescharacteristic
133#108—1462no—
134#108—1462no—
135C22⋊C8—732no—
136C22⋊C8—732no—
137C22⋊C8—1461no—
138C22⋊C8—1461no—
139C24—731no—
140C22×C4—731no—
141C22×C4—731no—
142C22×C4—731no—
143C22×C4—731no—
144C22×C4—731no—
145C22×C4—1461no—
146C22×C4—1461no—
147C22×C4—1461no—
148C22×C4—1461no—
149C22×C4C22×D7311yescharacteristic
150M16—21no—
151M16—21no—
152M16—21no—
153M16—732no—
154M16—1464no—
155M16—1461no—
156M16—1461no—
157M16—1461no—
158M16D29212yes—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—732no—
164C2×C8—1464no—
165C2×C8—1461no—
166C2×C8—1461no—
167C2×C8—1461no—
168C2×C8—1461no—
169C2×C8C4×D7312yes—
170C23—2921no—
171C23—731no—
172C23—731no—
173C23—1462no—
174C23—1461no—
175C23—1461no—
176C23Q8×D7311yescharacteristic
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—1461no—
180C2×C4—1461no—
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×C4C2×C4×D7311yescharacteristic
190C2×C4D4×D7311yescharacteristic
191C2×C4D4×D7311yescharacteristic
192C2×C4C2×D29211yescharacteristic
193C2×C4#1192402711yescharacteristic
194C2×C4#1192402811yescharacteristic
195C8—22no—
196C8—22no—
197C8—41no—
198C8—2921no—
199C8—1462no—
200C8—1462no—
201C22—21no—
202C22—21no—
203C22—2922no—
204C22—2922no—
205C22—732no—
206C22—1461no—
207C22—1461no—
208C22—1461no—
209C22—1461no—
210C22—1461no—
211C22C4⋊C4×D7311yescharacteristic
212C22#1455656911yescharacteristic
213C22#1455657111yescharacteristic
214C4—1461no—
215C4—1461no—
216C4#1455655111yescharacteristic
217C4C4×D29211yescharacteristic
218C4#1455656111yescharacteristic
219C4#1455657311yescharacteristic
220C2—21no—
221C2—21no—
222C2—2921no—
223C2—1462no—
224C2#1798846111yescharacteristic
225C2#108×D7311yescharacteristic
226C2#1798863411yescharacteristic
subgroupG/H
centerC2×C4D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#341×C73C2
socleC22×C73C2×C4⋊C4
hypercenter#341D73
hypocenterC73#1855
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
2. C2×#14556527C2semidirect
3. C2×#14556526C2semidirect
6. #17988351C2semidirect
7. #341×C73C2semidirect
99. C2×D73#108semidirect
114. C73#1855semidirect
121. #341D73semidirect