Finite Group Databasebeta

← #22620469

Subgroups — #22620469

Order 9344.

340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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#17989218C211yesmaximal, characteristic
2#17989215C211yesmaximal, characteristic
3#17988995C212yesmaximal, complemented
4#17988994C212yesmaximal, complemented
5#17988991C212yesmaximal, complemented
6#17988987C212yesmaximal, complemented
7#17988629C211yesmaximal, characteristic
8#17988623C211yesmaximal, characteristic
9C2×#14556524C211yesmaximal, characteristic
10#17988545C211yesmaximal, characteristic
11#428×C73C211yesmaximal, characteristic
12C22×#10596831C2211yescharacteristic
13#14556591—21no—
14#14556590—21no—
15#14556590C2212yes—
16#14556590C2212yes—
17#14556583—21no—
18#14556582—21no—
19#14556582C2212yes—
20#14556582C2212yes—
21#14556570—22no—
22#14556568—22no—
23#14556550C2211yescharacteristic
24#14556550C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26#14556525C2212yes—
27#14556524C2212yes—
28#14556524C2212yes—
29#14556524C2211yescharacteristic
30#14556524C2211yescharacteristic
31#14556523C2212yes—
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34#14556501C2212yes—
35C8×Dic73C2212yes—
36C2×M16×C73C2211yescharacteristic
37#117×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#107×C73C2212yes—
40#106×C73C2212yes—
41C2×Dic146—22no—
42C2×Dic146—22no—
43C22×Dic73—21no—
44C2×#10596831Q814yescomplemented
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C4⋊Dic73—21no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73D411yescharacteristic
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2312yes—
55#11924007—22no—
56#11924007—22no—
57#11924007—22no—
58#11924007—22no—
59C22⋊Dic73—21no—
60C22⋊Dic73D412yes—
61C4×Dic73—21no—
62C4×Dic73C2312yes—
63C22×C4×C73—21no—
64C22×C4×C73C2311yescharacteristic
65M16×C73Q814yescomplemented
66C2×C8×C73C2312yes—
67C4⋊C4×C73—21no—
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2312yes—
70C4⋊C4×C73C2311yescharacteristic
71C22⋊C4×C73—21no—
72C42×C73—21no—
73C23×C73C2×D411yescharacteristic
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—81no—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×Q812yes—
80C2×C4×C73C2×Q812yes—
81C2×C4×C73C2411yescharacteristic
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—22no—
85C2×Dic73—81no—
86C2×Dic73C2×D412yes—
87C2×Dic73C2×D412yes—
88Dic146—82no—
89Dic146—82no—
90C8×C73C2×Q814yes—
91#10596831C2×Q812yes—
92#10596831C2×Q812yes—
93C22×C73—21no—
94C22×C73—21no—
95C22×C73C4⋊Q812yes—
96C22×C73C22×D411yescharacteristic
97C4×C73—41no—
98C4×C73—42no—
99C4×C73—41no—
100C4×C73C4⋊Q812yes—
101C4×C73C22×Q811yescharacteristic
102C4×C73C22×Q811yescharacteristic
103Dic73—22no—
104Dic73—22no—
105Dic73—41no—
106Dic73—42no—
107Dic73—41no—
108C2×C73—22no—
109C2×C73C2×C4⋊Q811yescharacteristic
110C2×C73#57611yescharacteristic
111C2×C73#57811yescharacteristic
112#3164—731nomaximal, Sylow
113C73#316411yescharacteristic, complemented, Sylow
114#544—731no—
115#544—731no—
116#501—732no—
117#501—732no—
118#500—732no—
119#499—732no—
120#428—731no—
121#428D7311yescharacteristic
122#427—731no—
123C2×#107—731no—
124#405—731no—
125C2×M16C2×D7311yescharacteristic
126C22×C8—731no—
127C4⋊Q8—732no—
128C4⋊Q8—732no—
129C4⋊Q8—1461no—
130C4⋊Q8—1461no—
131#125—732no—
132#125—732no—
133#125—1461no—
134#125—1461no—
135C22⋊Q8—1462no—
136C22⋊Q8—1462no—
137#117—731no—
138#117—731no—
139#117C2×D7311yescharacteristic
140C2×C4⋊C4—731no—
141C2×C4⋊C4C2×D7311yescharacteristic
142#107—732no—
143#107—732no—
144#107—732no—
145#107—731no—
146#107—731no—
147#107C2×D7312yes—
148#106—732no—
149#106—731no—
150#106—731no—
151#106C2×D7312yes—
152#97—732no—
153C4×C8—732no—
154C2×Q8—1462no—
155C2×Q8—1462no—
156C22×C4—21no—
157C22×C4—1461no—
158C22×C4C22×D7311yescharacteristic
159M16Dic14614yescomplemented
160C2×C8—734no—
161C2×C8—731no—
162C2×C8—731no—
163C2×C8C22×D7312yes—
164C4⋊C4—21no—
165C4⋊C4—731no—
166C4⋊C4—731no—
167C4⋊C4—731no—
168C4⋊C4—732no—
169C4⋊C4—731no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1461no—
177C4⋊C4C22×D7311yescharacteristic
178C4⋊C4C22×D7311yescharacteristic
179C4⋊C4C22×D7312yes—
180C22⋊C4—21no—
181C22⋊C4—732no—
182C22⋊C4—1461no—
183C42—21no—
184C42—732no—
185C42—1461no—
186C23D4×D7311yescharacteristic
187Q8—5842no—
188Q8—5842no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—81no—
193C2×C4—5841no—
194C2×C4—732no—
195C2×C4—732no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1462no—
199C2×C4D4×D7311yescharacteristic
200C2×C4Q8×D7312yes—
201C2×C4C2×Dic14612yes—
202C2×C4C23×D7311yescharacteristic
203C8—732no—
204C8—732no—
205C8C2×Dic14614yes—
206C22—21no—
207C22—21no—
208C22#1455659012yes—
209C22C2×D4×D7311yescharacteristic
210C4—42no—
211C4—41no—
212C4—41no—
213C4—2922no—
214C4—2921no—
215C4—2921no—
216C4—1462no—
217C4—1462no—
218C4#1455659012yes—
219C4C2×Q8×D7311yescharacteristic
220C4C22×Dic14611yescharacteristic
221C2—22no—
222C2C2×#1455659011yescharacteristic
223C2#1798939111yescharacteristic
224C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3164
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #17988995C2semidirect
4. #17988994C2semidirect
5. #17988991C2semidirect
6. #17988987C2semidirect
44. C2×#10596831Q8semidirect
65. M16×C73Q8semidirect
113. C73#3164semidirect
159. M16Dic146semidirect