Finite Group Databasebeta

← #22622359

Subgroups — #22622359

Order 9344.

340 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989305C212yesmaximal
2#17988991C211yesmaximal, characteristic, complemented
3#17988931C212yesmaximal, complemented
4#17988928C212yesmaximal, complemented
5#17988871C212yesmaximal, complemented
6#17988829C211yesmaximal, characteristic, complemented
7#17988828C211yesmaximal, characteristic, complemented
8#17988681C211yesmaximal, characteristic, complemented
9C8×C22⋊D73C211yesmaximal, characteristic
10#17988624C211yesmaximal, characteristic, complemented
11#427×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×C8×D73C2211yescharacteristic
14#14556590C2212yes—
15#14556585—22no—
16#14556584—22no—
17#14556577—22no—
18#14556571C2212yes—
19#14556570C2212yes—
20C4×Dic146—22no—
21#14556556C2212yes—
22C4×C22⋊D73C2211yescharacteristic
23#14556549C2212yes—
24#14556525C2211yescharacteristic
25#14556524C2212yes—
26#14556522C2212yes—
27#14556520C2211yescharacteristic
28#14556516C2212yes—
29#14556514C2212yes—
30#14556514C2212yes—
31C22⋊#10596831C2211yescharacteristic
32#14556503C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C22×C8×C73C2211yescharacteristic
35#117×C73C2212yes—
36#107×C73C2211yescharacteristic
37#107×C73C2211yescharacteristic
38#106×C73C2212yes—
39C2×Dic146—22no—
40C2×Dic146C2312yes—
41C2×C22⋊D73D411yescharacteristic
42C2×C4×D73C2311yescharacteristic
43Dic292—22no—
44C2×#10596831C2311yescharacteristic
45C2×#10596831C2311yescharacteristic
46C8×D73—22no—
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50#11924007—22no—
51#11924007—22no—
52#11924007D411yescharacteristic
53C22⋊Dic73—22no—
54C22⋊Dic73D411yescharacteristic
55#11924005—22no—
56#11924005—22no—
57#11924005D411yescharacteristic
58C4×Dic73—22no—
59C4×Dic73—22no—
60C4×Dic73C2311yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C2×C8×C73—22no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73C2312yes—
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C42×C73—22no—
69C23×C73C2×D411yescharacteristic
70C22×D73C2×D411yescharacteristic
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—22no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2411yescharacteristic
77C22⋊D73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73C2×D411yescharacteristic
81C2×Dic73C2×D411yescharacteristic
82C2×Dic73C2×D411yescharacteristic
83C4×D73—21no—
84C4×D73—21no—
85Dic146—22no—
86Dic146—22no—
87Dic146—44no—
88C8×C73—21no—
89C8×C73#4112yes—
90#10596831—21no—
91#10596831—21no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73C22×D411yescharacteristic
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C4×C73—21no—
100C4×C73—42no—
101C4×C73—42no—
102C4×C73C2×#4111yescharacteristic
103C4×C732−1+411yescharacteristic
104Dic73—21no—
105Dic73—21no—
106Dic73—42no—
107Dic73—42no—
108Dic73#13512yes—
109C2×C73—41no—
110C2×C73#54711yescharacteristic
111C2×C73C2×#13511yescharacteristic
112C2×C73#57811yescharacteristic
113D73—41no—
114#3342—731nomaximal, Sylow
115C73#334211yescharacteristic, complemented, Sylow
116#556—732no—
117#500—731no—
118#485—732no—
119#485—732no—
120#475—732no—
121#467—731no—
122#467—731no—
123C4×Q16—731no—
124C8×D4—731no—
125#427—731no—
126#427D7311yescharacteristic, complemented
127C2×Q16—731no—
128C22×C8—731no—
129C22×C8C2×D7311yescharacteristic
130C4⋊Q8—732no—
131#126—1462no—
132#126—1462no—
133#124—1462no—
134C22⋊Q8—732no—
135C22⋊Q8—732no—
136C4×Q8—732no—
137C4×Q8—1462no—
138C4×D4—731no—
139#117—732no—
140#117C2×D7312yes—
141#107—731no—
142#107—732no—
143#107C2×D7311yescharacteristic
144#107C2×D7311yescharacteristic
145#106—732no—
146#106C2×D7312yes—
147C4⋊C8—731no—
148#103—732no—
149#103—732no—
150#103—732no—
151C22⋊C8—731no—
152C22⋊C8—731no—
153C4×C8—731no—
154C2×Q8—732no—
155C2×Q8—1462no—
156C2×D4—731no—
157C22×C4—731no—
158C22×C4C22×D7311yescharacteristic
159Q16—1462no—
160C2×C8—22no—
161C2×C8—731no—
162C2×C8—731no—
163C2×C8—1462no—
164C2×C8C22×D7311yescharacteristic
165C2×C8C22×D7311yescharacteristic
166C4⋊C4—731no—
167C4⋊C4—732no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4C22×D7312yes—
173C4⋊C4C22×D7312yes—
174C22⋊C4—22no—
175C22⋊C4—731no—
176C22⋊C4—731no—
177C22⋊C4—1462no—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C42—22no—
181C42—731no—
182C42—1462no—
183C42—1462no—
184C23—731no—
185C23D4×D7311yescharacteristic
186Q8—2924no—
187Q8—1462no—
188Q8—1462no—
189D4—1462no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—731no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4—1461no—
200C2×C4—1461no—
201C2×C4D4×D7311yescharacteristic
202C2×C4C23×D7311yescharacteristic
203C8—21no—
204C8—1461no—
205C8—1461no—
206C8#1192402812yes—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—1461no—
211C22—1461no—
212C22—1461no—
213C22C2×D4×D7311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2922no—
218C4—2922no—
219C4—732no—
220C4—1461no—
221C4—1461no—
222C4C2×#1192402811yescharacteristic
223C4#1455663911yescharacteristic
224C2—41no—
225C2—2921no—
226C2#1798923811yescharacteristic
227C2#135×D7311yescharacteristic
228C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#427×C73C2
socleC22×C73C22×D4
hypercenter#427D73
hypocenterC73#3342
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
2. #17988991C2semidirect
3. #17988931C2semidirect
4. #17988928C2semidirect
5. #17988871C2semidirect
6. #17988829C2semidirect
7. #17988828C2semidirect
8. #17988681C2semidirect
10. #17988624C2semidirect
11. #427×C73C2semidirect
115. C73#3342semidirect
126. #427D73semidirect