Finite Group Databasebeta

← #22622712

Subgroups — #22622712

Order 9344.

340 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989316C211yesmaximal, characteristic, complemented
2#17988957C212yesmaximal, complemented
3#17988939C211yesmaximal, characteristic, complemented
4#17988891C212yesmaximal, complemented
5#17988879C211yesmaximal, characteristic, complemented
6#17988792C211yesmaximal, characteristic
7#17988792C212yesmaximal
8#17988718C211yesmaximal, characteristic, complemented
9#17988687C212yesmaximal
10C4×#11924016C211yesmaximal, characteristic
11#554×C73C211yesmaximal, characteristic
12C2×#11924016C2211yescharacteristic
13C2×#11924016C2212yes—
14#14556591C2211yescharacteristic
15#14556591C2212yes—
16#14556582—21no—
17#14556582—22no—
18Q8×Dic73—21no—
19C4×Dic146C2211yescharacteristic
20C4×Dic146C2212yes—
21#14556524C2212yes—
22#14556522C2211yescharacteristic
23C4⋊#10596831C2211yescharacteristic
24C4⋊#10596831C2212yes—
25#14556514C2212yes—
26#14556514C2212yes—
27#14556514C2212yes—
28#14556514C2211yescharacteristic
29#14556514C2212yes—
30#14556512C2211yescharacteristic
31#14556502C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34#125×C73C2212yes—
35C22⋊Q8×C73—21no—
36C22⋊Q8×C73—22no—
37C4×Q8×C73C2211yescharacteristic
38C4×D4×C73C2211yescharacteristic
39C4×D4×C73C2212yes—
40C2×C4⋊C4×C73—21no—
41C2×Dic146C2311yescharacteristic
42C2×Dic146C2312yes—
43#11924016—22no—
44#11924016—24no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2312yes—
48C4⋊Dic73—22no—
49C4⋊Dic73—21no—
50C4⋊Dic73—21no—
51C4⋊Dic73—22no—
52C4⋊Dic73C2311yescharacteristic
53#11924007—21no—
54#11924007—22no—
55C4×Dic73—22no—
56C4×Dic73—21no—
57C2×Q8×C73—21no—
58C2×Q8×C73D411yescharacteristic
59C2×D4×C73C2311yescharacteristic
60C22×C4×C73—21no—
61C22×C4×C73—22no—
62C4⋊C4×C73—22no—
63C4⋊C4×C73—21no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73D411yescharacteristic
66C4⋊C4×C73D412yes—
67C4⋊C4×C73C2311yescharacteristic
68C4⋊C4×C73C2312yes—
69C22⋊C4×C73—21no—
70C22⋊C4×C73—22no—
71C42×C73C2312yes—
72C42×C73C2311yescharacteristic
73C23×C73—21no—
74Q8×C73—22no—
75Q8×C73—81no—
76D4×C73—21no—
77D4×C73#4112yes—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—42no—
81C2×C4×C73—82no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—21no—
90Dic146—21no—
91Dic146—22no—
92Dic146—21no—
93Dic146—22no—
94#10596831—21no—
95#10596831—22no—
96#10596831—21no—
97C22×C73—22no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73C22×D411yescharacteristic
101C4×C73—22no—
102C4×C73—22no—
103C4×C73—21no—
104C4×C73—41no—
105C4×C73—42no—
106C4×C73#13712yes—
107C4×C73C2×#4111yescharacteristic
108C4×C732−1+411yescharacteristic
109Dic73—41no—
110Dic73—42no—
111Dic73—41no—
112C2×C73—42no—
113C2×C73#54811yescharacteristic
114C2×C73C2×#13711yescharacteristic
115C2×C73#57711yescharacteristic
116#3372—731nomaximal, Sylow
117C73#337211yescharacteristic, complemented, Sylow
118#557—731no—
119#554D7311yescharacteristic
120#491—732no—
121#487—731no—
122#479—732no—
123#477—731no—
124#461—732no—
125#461—731no—
126#446—731no—
127#440—732no—
128C4×SD16—731no—
129C2×SD16—731no—
130C2×SD16—732no—
131C4⋊Q8—731no—
132C4⋊Q8—732no—
133C4⋊Q8C2×D7311yescharacteristic
134#125—1461no—
135#125—1462no—
136#125C2×D7312yes—
137C22⋊Q8—21no—
138C22⋊Q8—22no—
139C4×Q8—731no—
140C4×Q8—732no—
141C4×Q8—1461no—
142C4×Q8C2×D7311yescharacteristic
143C4×D4C2×D7311yescharacteristic
144C4×D4C2×D7312yes—
145C2×C4⋊C4—21no—
146#107—732no—
147#106—731no—
148C4⋊C8—731no—
149C4⋊C8—732no—
150#103—731no—
151#103—732no—
152#103—732no—
153#103—732no—
154#103—732no—
155#102—731no—
156#97—732no—
157C4×C8—731no—
158C2×Q8—21no—
159C2×Q8—731no—
160C2×Q8—732no—
161C2×Q8C22⋊D7311yescharacteristic
162C2×D4C22×D7311yescharacteristic
163C22×C4—21no—
164C22×C4—22no—
165SD16—1462no—
166SD16—1464no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—732no—
170C4⋊C4—22no—
171C4⋊C4—21no—
172C4⋊C4—22no—
173C4⋊C4—731no—
174C4⋊C4—1461no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1461no—
178C4⋊C4—1461no—
179C4⋊C4—1462no—
180C4⋊C4C22⋊D7311yescharacteristic
181C4⋊C4C22⋊D7312yes—
182C4⋊C4C22×D7311yescharacteristic
183C4⋊C4C22×D7312yes—
184C22⋊C4—21no—
185C22⋊C4—22no—
186C42—1462no—
187C42—1461no—
188C42C22×D7311yescharacteristic
189C42C22×D7312yes—
190C23—21no—
191Q8—22no—
192Q8—81no—
193Q8—1461no—
194Q8—1462no—
195Q8—1461no—
196Q8—1462no—
197D4—21no—
198D4#1192402912yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—82no—
203C2×C4—1461no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4C2×C22⋊D7312yes—
207C2×C4C2×C22⋊D7311yescharacteristic
208C2×C4C2×C22⋊D7312yes—
209C2×C4C2×C22⋊D7311yescharacteristic
210C2×C4C23×D7311yescharacteristic
211C8—1461no—
212C8—1462no—
213C8—1461no—
214C22—22no—
215C22—41no—
216C22—41no—
217C22C22×C22⋊D7311yescharacteristic
218C4—22no—
219C4—22no—
220C4—21no—
221C4—41no—
222C4—42no—
223C4—2921no—
224C4—2922no—
225C4—2921no—
226C4#1455662112yes—
227C4C2×#1192402911yescharacteristic
228C4#1455663911yescharacteristic
229C2—42no—
230C2#1798924811yescharacteristic
231C2C2×#1455662111yescharacteristic
232C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#554×C73C2
socleC22×C73C22×D4
hypercenter#554D73
hypocenterC73#3372
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #554

Complements

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

NH ≅ G/Ntype
1. #17989316C2semidirect
2. #17988957C2semidirect
3. #17988939C2semidirect
4. #17988891C2semidirect
5. #17988879C2semidirect
8. #17988718C2semidirect
117. C73#3372semidirect