Finite Group Databasebeta

← #22626016

Subgroups — #22626016

Order 9344.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#17989598C211yesmaximal, characteristic
2#17989580C211yesmaximal, characteristic
3C2×#14556654C211yesmaximal, characteristic
4#17989553C211yesmaximal, characteristic
5#17989466C211yesmaximal, characteristic
6#17989462C211yesmaximal, characteristic
7#101×D73C211yesmaximal, characteristic
8D73⋊M16C2211yescharacteristic
9C2×#11924036C2211yescharacteristic
10#14556670C2211yescharacteristic
11C2×C4⋊#64408C2211yescharacteristic
12#14556660—21no—
13#14556659—21no—
14#14556654—21no—
15#14556654—21no—
16#14556654—21no—
17#14556654—21no—
18#14556645—21no—
19C8×#64408—21no—
20C2×Q8×D73C2211yescharacteristic
21M16×D73C2211yescharacteristic
22M16×D73C2211yescharacteristic
23#14556510C411yescharacteristic, complemented
24#14556509C411yescharacteristic, complemented
25#14556509C411yescharacteristic, complemented
26#101×C73C411yescharacteristic, complemented
27C22×#64408—21no—
28#11924038—21no—
29#11924037—21no—
30#11924036—21no—
31#11924036—21no—
32#11924036D411yescharacteristic
33#11924036D411yescharacteristic
34C2×#10596833—21no—
35C4⋊#64408—21no—
36C4⋊#64408—21no—
37C4⋊#64408D411yescharacteristic
38C4⋊#64408D411yescharacteristic
39C22⋊#64408—21no—
40C4×#64408—21no—
41C2×Dic146—21no—
42C2×Dic146C2×C411yescharacteristic
43Q8×D73—21no—
44Q8×D73—21no—
45Q8×D73—21no—
46Q8×D73—21no—
47C2×C4×D73—21no—
48C2×C4×D73C2311yescharacteristic
49#11924012C2×C411yescharacteristic
50#11924012C2×C411yescharacteristic
51#11924011—21no—
52#11924011—21no—
53C8×D73—21no—
54C8×D73—21no—
55C2×Q8×C73C2×C411yescharacteristic
56M16×C73C2×C411yescharacteristic
57M16×C73C2×C411yescharacteristic
58C22×D73#4111yescharacteristic
59C2×#64408—21no—
60C2×#64408—21no—
61C2×#64408—41no—
62C2×#64408—81no—
63Q8×C73—21no—
64Q8×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73C22×C411yescharacteristic
67C2×Dic73—21no—
68C2×Dic73#4111yescharacteristic
69C4×D73—41no—
70C4×D73—41no—
71C4×D73C2×D411yescharacteristic
72C4×D73C2×D411yescharacteristic
73C4×D73#4111yescharacteristic
74C4×D73#4111yescharacteristic
75Dic146—21no—
76Dic146—21no—
77Dic146—41no—
78Dic146—41no—
79#10596833—21no—
80#10596833—21no—
81#10596833—41no—
82C8×C73—21no—
83C8×C73—21no—
84#10596831—21no—
85#10596831—21no—
86C22×C73#11711yescharacteristic
87C2×D73—21no—
88C2×D73—21no—
89C2×D73#12111yescharacteristic
90C2×D73#12611yescharacteristic
91#64408—41no—
92#64408—41no—
93#64408—81no—
94C4×C73—41no—
95C4×C73C4×D411yescharacteristic
96C4×C73C4×D411yescharacteristic
97Dic73—41no—
98Dic73#12311yescharacteristic
99Dic73#12411yescharacteristic
100C2×C73—21no—
101C2×C73#38811yescharacteristic
102D73—21no—
103D73#47111yescharacteristic
104D73#47311yescharacteristic
105#1930—731nomaximal, Sylow
106C73#193011yescharacteristic, complemented, Sylow
107#428—731no—
108#419—731no—
109C2×#103—731no—
110C2×#101—731no—
111#405—731no—
112#343—731no—
113#341—731no—
114C22×Q8—731no—
115C2×M16—731no—
116C2×M16—731no—
117C2×M16—731no—
118C22×C8—731no—
119#117—731no—
120C2×C4⋊C4—731no—
121#107—1461no—
122#106—1461no—
123#103—1461no—
124#103—1461no—
125#103—1461no—
126#103—1461no—
127#101—731no—
128#101—731no—
129#101—731no—
130#101#6440811yescharacteristic, complemented
131#97—1461no—
132C4×C8—1461no—
133C2×Q8—731no—
134C2×Q8—1461no—
135C2×Q8—1461no—
136C2×Q8—1461no—
137C2×Q8—1461no—
138C2×Q8—1461no—
139C2×Q8C2×#6440811yescharacteristic
140C22×C4—731no—
141C22×C4—1461no—
142C22×C4—1461no—
143M16—731no—
144M16—731no—
145M16—1461no—
146M16—1461no—
147M16—1461no—
148M16—1461no—
149M16C2×#6440811yescharacteristic
150M16C2×#6440811yescharacteristic
151C2×C8—731no—
152C2×C8—731no—
153C2×C8—1461no—
154C2×C8—1461no—
155C2×C8—1461no—
156C2×C8—1461no—
157C2×C8—1461no—
158C4⋊C4—731no—
159C4⋊C4—731no—
160C4⋊C4—1461no—
161C4⋊C4—1461no—
162C22⋊C4—1461no—
163C42—1461no—
164C23—731no—
165Q8—21no—
166Q8—21no—
167Q8—2921no—
168Q8—2921no—
169Q8—1461no—
170Q8—1461no—
171C2×C4—21no—
172C2×C4—2921no—
173C2×C4—2921no—
174C2×C4—2921no—
175C2×C4—5841no—
176C2×C4—731no—
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—731no—
180C2×C4—731no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4C22×#6440811yescharacteristic
185C8—21no—
186C8—21no—
187C8—2921no—
188C8—1461no—
189C8—1461no—
190C8—1461no—
191C8—1461no—
192C22—731no—
193C22—731no—
194C22—1461no—
195C22—1461no—
196C22#1455667011yescharacteristic
197C4—41no—
198C4—2921no—
199C4—2921no—
200C4—2921no—
201C4—5841no—
202C4—731no—
203C4—731no—
204C4D4×#6440811yescharacteristic
205C4D4×#6440811yescharacteristic
206C2—21no—
207C2—731no—
208C2—731no—
209C2—1461no—
210C2#1798953711yescharacteristic
subgroupG/H
centerC2#17989537
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#101×C73C4
socleC2×C73#388
hypercenter#101#64408
hypocenterC73#1930
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #14556510C4semidirect
24. #14556509C4semidirect
25. #14556509C4semidirect
26. #101×C73C4semidirect
106. C73#1930semidirect
130. #101#64408semidirect