Finite Group Databasebeta

← #22610174

Subgroups — #22610174

Order 9344.

262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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#17989353C211yesmaximal, characteristic
2#17988636C211yesmaximal, characteristic, complemented
3#17988610C211yesmaximal, characteristic, complemented
4#17988605C211yesmaximal, characteristic
5C2×#14556517C211yesmaximal, characteristic
6#17988346C211yesmaximal, characteristic, complemented
7#344×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556599—22no—
10#14556597—22no—
11C2×#11924012C2211yescharacteristic
12C2×#11924012C2211yescharacteristic
13M16×D73—22no—
14C2×C4×Dic73C2211yescharacteristic
15#14556527—22no—
16#14556520—22no—
17#14556519—22no—
18#14556517C412yescomplemented
19#14556517C412yescomplemented
20C2×M16×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22#117×C73C2211yescharacteristic
23#11924028—21no—
24#11924028—21no—
25#11924028C2×C412yes—
26#11924028D412yes—
27C2×Dic146Q811yescharacteristic
28C2×D292Q811yescharacteristic
29C2×C22⋊D73—21no—
30C22×Dic73—21no—
31C2×C4×D73—21no—
32#11924012—21no—
33#11924012—21no—
34#11924012—21no—
35#11924012D412yes—
36#11924011—24no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C8×D73—24no—
40C4×Dic73—21no—
41C4×Dic73C2×C411yescharacteristic
42C4×Dic73C2×C411yescharacteristic
43C22×C4×C73C2311yescharacteristic
44M16×C73—21no—
45M16×C73—21no—
46M16×C73—21no—
47M16×C73C2×C412yes—
48C2×C8×C73—21no—
49C2×C8×C73D412yes—
50C4⋊C4×C73—21no—
51C22⋊C4×C73—21no—
52C42×C73—21no—
53C23×C73#4111yescharacteristic
54C22×D73—21no—
55C2×C4×C73—41no—
56C2×C4×C73C22×C411yescharacteristic
57C2×C4×C73C2×D411yescharacteristic
58C2×C4×C73C2×D411yescharacteristic
59C2×C4×C73C2×D411yescharacteristic
60C2×C4×C73C2×Q811yescharacteristic
61C2×C4×C73#4111yescharacteristic
62C22⋊D73—22no—
63C22⋊D73—22no—
64C2×Dic73—21no—
65C2×Dic73—21no—
66C2×Dic73—21no—
67C2×Dic73—42no—
68D292—21no—
69D292C4⋊C412yes—
70C4×D73—22no—
71C4×D73—22no—
72Dic146—21no—
73Dic146C4⋊C412yes—
74C8×C73—22no—
75C8×C73—22no—
76#10596831—22no—
77#10596831—41no—
78C22×C73—41no—
79C22×C73C4×D411yescharacteristic
80C22×C73C22⋊Q811yescharacteristic
81C22×C73#12311yescharacteristic
82C2×D73—22no—
83C2×D73—81no—
84C4×C73—81no—
85C4×C73C2×C4⋊C411yescharacteristic
86C4×C73C4×D411yescharacteristic
87C4×C73#12011yescharacteristic
88C4×C73C22⋊Q811yescharacteristic
89Dic73—22no—
90Dic73—22no—
91Dic73—41no—
92C2×C73—21no—
93C2×C73—21no—
94C2×C73—21no—
95C2×C73#38511yescharacteristic
96D73—42no—
97#1861—731nomaximal, Sylow
98C73#186111yescharacteristic, complemented, Sylow
99#568—731no—
100#430—731no—
101#423—731no—
102#421—731no—
103C2×#104—731no—
104#344D7311yescharacteristic, complemented
105#339—731no—
106C2×#41—731no—
107#131—1462no—
108#131—1462no—
109C2×M16—731no—
110C2×M16—731no—
111C2×M16—1462no—
112C2×M16C2×D7311yescharacteristic
113C2×M16C2×D7311yescharacteristic
114#117C2×D7311yescharacteristic
115C2×C42—731no—
116#108—1462no—
117C4⋊C8—1462no—
118#104—732no—
119#104—732no—
120#104—1462no—
121#41—732no—
122#41—732no—
123#41—1461no—
124#41—1461no—
125C2×Q8—731no—
126C2×D4—731no—
127C2×D4—1461no—
128C22×C4—1461no—
129C22×C4—1461no—
130C22×C4C22×D7311yescharacteristic
131M16—21no—
132M16—21no—
133M16—21no—
134M16—732no—
135M16—1464no—
136M16—1461no—
137M16—1461no—
138M16—1461no—
139M16C4×D7312yes—
140C2×C8—21no—
141C2×C8—1464no—
142C2×C8—1461no—
143C2×C8—1461no—
144C2×C8D29212yes—
145C4⋊C4—21no—
146C22⋊C4—21no—
147C42—21no—
148C42—731no—
149C42—731no—
150C42—1461no—
151C23—1461no—
152C23#1192402811yescharacteristic
153Q8—732no—
154Q8—1461no—
155D4—732no—
156D4—1462no—
157D4—1462no—
158D4—1461no—
159C2×C4—41no—
160C2×C4—2922no—
161C2×C4—1461no—
162C2×C4—1461no—
163C2×C4—1461no—
164C2×C4—1462no—
165C2×C4—1462no—
166C2×C4C2×C4×D7311yescharacteristic
167C2×C4D4×D7311yescharacteristic
168C2×C4D4×D7311yescharacteristic
169C2×C4C2×D29211yescharacteristic
170C2×C4Q8×D7311yescharacteristic
171C2×C4#1192402711yescharacteristic
172C8—22no—
173C8—22no—
174C8—2921no—
175C8—1462no—
176C22—41no—
177C22—5841no—
178C22—1462no—
179C22C4×D29211yescharacteristic
180C22#1455656911yescharacteristic
181C22#1455657311yescharacteristic
182C4—81no—
183C4—2921no—
184C4—1462no—
185C4—1462no—
186C4C4⋊C4×D7311yescharacteristic
187C4#1455655111yescharacteristic
188C4#1455656111yescharacteristic
189C4#1455657111yescharacteristic
190C2—21no—
191C2—21no—
192C2—21no—
193C2—2922no—
194C2#1798846111yescharacteristic
subgroupG/H
centerC4#14556561
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#344×C73C2
socleC2×C73#385
hypercenter#344D73
hypocenterC73#1861
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. #17988636C2semidirect
3. #17988610C2semidirect
6. #17988346C2semidirect
7. #344×C73C2semidirect
18. #14556517C4semidirect
19. #14556517C4semidirect
98. C73#1861semidirect
104. #344D73semidirect