Finite Group Databasebeta

← #22611086

Subgroups — #22611086

Order 9344.

282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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#17989215C211yesmaximal, characteristic, complemented
2#17988593C211yesmaximal, characteristic
3#17988591C211yesmaximal, characteristic
4#17988489C211yesmaximal, characteristic
5#17988355C211yesmaximal, characteristic, complemented
6#17988347C211yesmaximal, characteristic, complemented
7#339×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10#14556591—21no—
11#14556590—21no—
12#14556583—21no—
13#14556582—21no—
14#14556568—22no—
15#14556550C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17C2×#11924005—22no—
18#14556513—21no—
19#14556513—21no—
20#14556511—21no—
21#14556511—21no—
22C2×M16×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24C2×C42×C73C2211yescharacteristic
25C23×D73—21no—
26C2×Dic146—22no—
27C2×D292—21no—
28C2×D292—21no—
29C2×D292—21no—
30C2×D292—21no—
31C2×D292—21no—
32C2×D292Q812yescomplemented
33C22×Dic73D412yes—
34#11924012—21no—
35#11924012—21no—
36C2×#10596831—21no—
37C4⋊Dic73—22no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73D411yescharacteristic
41C4⋊Dic73D411yescharacteristic
42#11924007—22no—
43#11924007—22no—
44C22⋊Dic73—21no—
45#11924005—44no—
46C4×Dic73—21no—
47C22×C4×C73—21no—
48C22×C4×C73C2311yescharacteristic
49M16×C73—21no—
50M16×C73—21no—
51C2×C8×C73—21no—
52C4⋊C4×C73D411yescharacteristic
53C4⋊C4×C73D411yescharacteristic
54C22⋊C4×C73—21no—
55C42×C73—21no—
56C42×C73—21no—
57C42×C73—21no—
58C23×C73C2×D411yescharacteristic
59C22×D73—22no—
60C22×D73—42no—
61C22×D73—42no—
62C22×D73—41no—
63C22×D73—41no—
64C2×C4×C73—22no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×Q811yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×Dic73—21no—
76C2×Dic73—21no—
77C2×Dic73—22no—
78C2×Dic73—42no—
79D292—22no—
80D292—22no—
81D292—41no—
82D292—41no—
83Dic146—82no—
84C8×C73—41no—
85#10596831—41no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73#12011yescharacteristic
89C22×C73C22⋊Q811yescharacteristic
90C22×C73#12411yescharacteristic
91C2×D73—44no—
92C2×D73—42no—
93C2×D73—82no—
94C2×D73—81no—
95C2×D73—81no—
96C4×C73—42no—
97C4×C73—41no—
98C4×C73—41no—
99C4×C73C22⋊Q811yescharacteristic
100C4×C73C22⋊Q811yescharacteristic
101C4×C73#12411yescharacteristic
102C4×C73#12411yescharacteristic
103Dic73—41no—
104Dic73—42no—
105Dic73—41no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73#39311yescharacteristic
109C2×C73#45311yescharacteristic
110C2×C73#45411yescharacteristic
111D73—82no—
112#2027—731nomaximal, Sylow
113C73#202711yescharacteristic, complemented, Sylow
114#544—731no—
115#418—731no—
116#418—731no—
117#390—731no—
118#343—731no—
119#339—731no—
120#339D7311yescharacteristic, complemented
121C22×D4—731no—
122C2×M16—731no—
123C2×M16C2×D7311yescharacteristic
124C4⋊Q8—1461no—
125C4⋊Q8—1461no—
126#125—1461no—
127#125—1461no—
128C22⋊Q8—1462no—
129#117—731no—
130#117C2×D7311yescharacteristic
131C2×C4⋊C4—731no—
132C2×C22⋊C4—1462no—
133C2×C42C2×D7311yescharacteristic
134#102—1461no—
135#102—1461no—
136#102—1461no—
137#102—1461no—
138C24—1461no—
139C2×Q8—1462no—
140C2×D4—732no—
141C2×D4—1461no—
142C2×D4—1461no—
143C2×D4—1461no—
144C2×D4—1461no—
145C2×D4—1461no—
146C22×C4—21no—
147C22×C4—732no—
148C22×C4C22×D7311yescharacteristic
149M16—21no—
150M16—21no—
151M16—1461no—
152M16—1461no—
153C2×C8—21no—
154C2×C8—1461no—
155C4⋊C4—731no—
156C4⋊C4—731no—
157C4⋊C4—1462no—
158C4⋊C4—1462no—
159C4⋊C4—1462no—
160C4⋊C4—1461no—
161C4⋊C4—1461no—
162C4⋊C4D29211yescharacteristic
163C4⋊C4D29211yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2924no—
166C22⋊C4—1461no—
167C42—21no—
168C42—21no—
169C42—21no—
170C42—1461no—
171C23—2922no—
172C23—2922no—
173C23—2921no—
174C23—2921no—
175C23—1462no—
176C23D4×D7311yescharacteristic
177Q8—5842no—
178D4—2921no—
179D4—2921no—
180D4—1462no—
181D4—1462no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2922no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4D4×D7311yescharacteristic
192C2×C4C2×D29211yescharacteristic
193C2×C4Q8×D7311yescharacteristic
194C2×C4#1192402711yescharacteristic
195C2×C4#1192402811yescharacteristic
196C2×C4#1192402811yescharacteristic
197C8—41no—
198C8—2921no—
199C22—21no—
200C22—21no—
201C22—2924no—
202C22—2922no—
203C22—5842no—
204C22—5841no—
205C22—5841no—
206C22#1455656111yescharacteristic
207C22#1455656911yescharacteristic
208C22#1455657711yescharacteristic
209C4—42no—
210C4—41no—
211C4—41no—
212C4—2922no—
213C4—2921no—
214C4—2921no—
215C4#1455656911yescharacteristic
216C4#1455657111yescharacteristic
217C4#1455657711yescharacteristic
218C4#1455657911yescharacteristic
219C2—21no—
220C2—21no—
221C2—5842no—
222C2#1798850011yescharacteristic
223C2#1798875611yescharacteristic
224C2#1798876111yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#339×C73C2
socleC22×C73#120
hypercenter#339D73
hypocenterC73#2027
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
5. #17988355C2semidirect
6. #17988347C2semidirect
7. #339×C73C2semidirect
32. C2×D292Q8semidirect
113. C73#2027semidirect
120. #339D73semidirect