Finite Group Databasebeta

← #22611085

Subgroups — #22611085

Order 9344.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#17988592C211yesmaximal, characteristic
3#17988490C211yesmaximal, characteristic
4#17988355C211yesmaximal, characteristic, complemented
5#17988348C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#418×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9#14556591—21no—
10#14556590—21no—
11#14556583—21no—
12#14556582—21no—
13#14556568—22no—
14#14556550C2211yescharacteristic
15C2×C4⋊Dic73C2211yescharacteristic
16C2×C22⋊Dic73—22no—
17C2×C4×Dic73C2211yescharacteristic
18#14556512—21no—
19#14556512—21no—
20C22×D4×C73C2211yescharacteristic
21C2×M16×C73C2211yescharacteristic
22#117×C73C2211yescharacteristic
23#102×C73—21no—
24#102×C73—21no—
25C2×Dic146—22no—
26C22×Dic73—21no—
27C22×Dic73D412yes—
28#11924012—21no—
29#11924012—21no—
30C2×#10596831—21no—
31C4⋊Dic73—22no—
32C4⋊Dic73—21no—
33C4⋊Dic73—21no—
34C4⋊Dic73D411yescharacteristic
35C4⋊Dic73D411yescharacteristic
36#11924007—22no—
37#11924007—22no—
38C22⋊Dic73—21no—
39C22⋊Dic73—44no—
40C4×Dic73—21no—
41C4×Dic73—21no—
42C4×Dic73—21no—
43C24×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73—21no—
49C2×D4×C73Q812yescomplemented
50C22×C4×C73C2311yescharacteristic
51M16×C73—21no—
52M16×C73—21no—
53C2×C8×C73—21no—
54C4⋊C4×C73D411yescharacteristic
55C4⋊C4×C73D411yescharacteristic
56C22⋊C4×C73—21no—
57C42×C73—21no—
58C23×C73—22no—
59C23×C73—42no—
60C23×C73—42no—
61C23×C73—41no—
62C23×C73—41no—
63C23×C73C2×D411yescharacteristic
64D4×C73—22no—
65D4×C73—22no—
66D4×C73—41no—
67D4×C73—41no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×Q811yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×Dic73—22no—
77C2×Dic73—21no—
78C2×Dic73—21no—
79C2×Dic73—22no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—42no—
83Dic146—82no—
84C8×C73—41no—
85#10596831—41no—
86C22×C73—21no—
87C22×C73—21no—
88C22×C73—44no—
89C22×C73—42no—
90C22×C73—82no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73#12011yescharacteristic
94C22×C73C22⋊Q811yescharacteristic
95C22×C73#12411yescharacteristic
96C4×C73—41no—
97C4×C73—41no—
98C4×C73C22⋊Q811yescharacteristic
99C4×C73C22⋊Q811yescharacteristic
100C4×C73#12411yescharacteristic
101C4×C73#12411yescharacteristic
102Dic73—42no—
103Dic73—41no—
104Dic73—42no—
105Dic73—41no—
106C2×C73—21no—
107C2×C73—21no—
108C2×C73—82no—
109C2×C73#39311yescharacteristic
110C2×C73#45311yescharacteristic
111C2×C73#45411yescharacteristic
112#2027—731nomaximal, Sylow
113C73#202711yescharacteristic, complemented, Sylow
114#544—731no—
115#418—731no—
116#418D7311yescharacteristic
117#390—731no—
118#343—731no—
119#339—731no—
120#339—731no—
121C22×D4C2×D7311yescharacteristic
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×C42—731no—
134#102—21no—
135#102—21no—
136#102—1461no—
137#102—1461no—
138C24—21no—
139C2×Q8—1462no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4Dic14612yescomplemented
146C22×C4—732no—
147C22×C4—1461no—
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⋊C4C22⋊D7311yescharacteristic
163C4⋊C4C22⋊D7311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—2924no—
166C22⋊C4—1461no—
167C42—21no—
168C42—1461no—
169C42—1461no—
170C42—1461no—
171C23—22no—
172C23—42no—
173C23—42no—
174C23—41no—
175C23—41no—
176C23D4×D7311yescharacteristic
177Q8—5842no—
178D4—22no—
179D4—22no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—2921no—
185C2×C4—2921no—
186C2×C4—2922no—
187C2×C4—1462no—
188C2×C4—1461no—
189C2×C4—1461no—
190C2×C4—1462no—
191C2×C4D4×D7311yescharacteristic
192C2×C4C2×C22⋊D7311yescharacteristic
193C2×C4C2×Dic14611yescharacteristic
194C2×C4#1192402711yescharacteristic
195C2×C4#1192402711yescharacteristic
196C2×C4#1192402811yescharacteristic
197C8—41no—
198C8—2921no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22#1455655911yescharacteristic
207C22#1455656811yescharacteristic
208C22#1455657711yescharacteristic
209C4—41no—
210C4—41no—
211C4—2922no—
212C4—2922no—
213C4—2921no—
214C4—2921no—
215C4#1455656811yescharacteristic
216C4#1455657011yescharacteristic
217C4#1455657711yescharacteristic
218C4#1455657811yescharacteristic
219C2—21no—
220C2—21no—
221C2—82no—
222C2#1798849911yescharacteristic
223C2#1798875311yescharacteristic
224C2#1798875811yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#418×C73C2
socleC22×C73#120
hypercenter#418D73
hypocenterC73#2027
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
4. #17988355C2semidirect
5. #17988348C2semidirect
6. #17988346C2semidirect
49. C2×D4×C73Q8semidirect
113. C73#2027semidirect
145. C2×D4Dic146semidirect