Finite Group Databasebeta

← #22610175

Subgroups — #22610175

Order 9344.

362 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#14556553C211yesmaximal, characteristic
2C2×#14556513C211yesmaximal, characteristic
3C2×#14556511C211yesmaximal, characteristic
4#17988483C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#107×C73C211yesmaximal, characteristic, complemented
8C22×D292C2211yescharacteristic
9C22×C4×D73—21no—
10C22×#10596831C2211yescharacteristic
11#14556553—22no—
12#14556553—22no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007—21no—
15C2×#11924005—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556513C414yescomplemented
18#14556511—22no—
19#14556498—21no—
20C22×C8×C73C2211yescharacteristic
21C2×C4⋊C4×C73C2211yescharacteristic
22C2×C4⋊C4×C73C2211yescharacteristic
23#107×C73—22no—
24C23×D73—21no—
25C2×D292—21no—
26C2×D292—21no—
27C2×D292—21no—
28C2×D292C2×C412yes—
29C2×D292D412yes—
30C2×D292Q812yes—
31C22×Dic73—21no—
32C22×Dic73D411yescharacteristic
33C22×Dic73D411yescharacteristic
34C2×C4×D73—24no—
35C2×C4×D73—42no—
36C2×C4×D73—42no—
37C2×#10596831—21no—
38C2×#10596831—21no—
39C2×#10596831—21no—
40C4⋊Dic73—21no—
41C4⋊Dic73C2×C412yescomplemented
42#11924007—42no—
43#11924005—24no—
44C4×Dic73—21no—
45C4×Dic73—21no—
46C22×C4×C73—21no—
47C22×C4×C73—21no—
48C22×C4×C73C2311yescharacteristic
49C2×C8×C73—21no—
50C2×C8×C73—21no—
51C2×C8×C73C2×C412yescomplemented
52C4⋊C4×C73—21no—
53C4⋊C4×C73—21no—
54C4⋊C4×C73—21no—
55C4⋊C4×C73D412yes—
56C23×C73C2×D411yescharacteristic
57C22×D73—22no—
58C22×D73—22no—
59C22×D73—22no—
60C22×D73—41no—
61C22×D73—41no—
62C22×D73—41no—
63C22×D73—41no—
64C2×C4×C73—22no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73—41no—
69C2×C4×C73—41no—
70C2×C4×C73C22×C411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×Q811yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—22no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73D812yes—
85D292—22no—
86D292—22no—
87D292—22no—
88D292C4⋊C414yescomplemented
89C4×D73—48no—
90C8×C73—22no—
91#10596831—41no—
92C22×C73C4×D411yescharacteristic
93C22×C73#12011yescharacteristic
94C22×C73C22⋊Q811yescharacteristic
95C22×C73C2×D811yescharacteristic
96C22×C73#13511yescharacteristic
97C22×C73AGL(1,ℤ/8)11yescharacteristic
98C22×C73#13711yescharacteristic
99C2×D73—24no—
100C2×D73—42no—
101C2×D73—42no—
102C2×D73—42no—
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C4×C73—42no—
107C4×C73—81no—
108C4×C73C2×C4⋊C411yescharacteristic
109C4×C73C4×D411yescharacteristic
110C4×C73C22⋊Q811yescharacteristic
111C4×C73#12311yescharacteristic
112Dic73—22no—
113Dic73—42no—
114Dic73—41no—
115C2×C73#38511yescharacteristic
116C2×C73C4×D811yescharacteristic
117C2×C73#44011yescharacteristic
118C2×C73#44711yescharacteristic
119C2×C73#45211yescharacteristic
120C2×C73#47411yescharacteristic
121C2×C73#47811yescharacteristic
122D73—44no—
123#1862—731nomaximal, Sylow
124C73#186211yescharacteristic, complemented, Sylow
125C2×C4×D4—731no—
126C2×#107D7311yescharacteristic, complemented
127C2×#102—731no—
128C2×#102—731no—
129#389—731no—
130#340—731no—
131#336—731no—
132C22×D4—731no—
133C23×C4—1461no—
134C22×C8—731no—
135C22×C8C2×D7311yescharacteristic
136C4×D4—1462no—
137C4×D4—1462no—
138C2×C4⋊C4—731no—
139C2×C4⋊C4—1461no—
140C2×C4⋊C4C2×D7311yescharacteristic
141C2×C4⋊C4C2×D7311yescharacteristic
142C2×C22⋊C4—1461no—
143C2×C42—731no—
144#107—22no—
145#102—734no—
146#102—1462no—
147#95—1461no—
148C24—1461no—
149C2×D4—732no—
150C2×D4—732no—
151C2×D4—732no—
152C2×D4—1461no—
153C2×D4—1461no—
154C2×D4—1461no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—2922no—
158C22×C4—2922no—
159C22×C4—731no—
160C22×C4—731no—
161C22×C4—1464no—
162C22×C4—1461no—
163C22×C4C22×D7311yescharacteristic
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—1461no—
167C2×C8—1461no—
168C2×C8—1461no—
169C2×C8C4×D7312yescomplemented
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2922no—
174C4⋊C4—732no—
175C4⋊C4—1461no—
176C4⋊C4C22⋊D7312yes—
177C22⋊C4—1464no—
178C42—1461no—
179C42—1461no—
180C23—2921no—
181C23—2921no—
182C23—2921no—
183C23—2921no—
184C23—1462no—
185C23—1462no—
186C23—1462no—
187C23D4×D7311yescharacteristic
188D4—734no—
189D4—1462no—
190D4—1462no—
191D4—1462no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—2928no—
199C2×C4—2921no—
200C2×C4—2921no—
201C2×C4—732no—
202C2×C4—1462no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1461no—
207C2×C4—1461no—
208C2×C4C2×C4×D7311yescharacteristic
209C2×C4D4×D7311yescharacteristic
210C2×C4C2×C22⋊D7311yescharacteristic
211C2×C4Q8×D7311yescharacteristic
212C2×C4#1192402811yescharacteristic
213C2×C4#1192402911yescharacteristic
214C8—22no—
215C8—2921no—
216C22—2922no—
217C22—2922no—
218C22—2922no—
219C22—2922no—
220C22—2922no—
221C22—2922no—
222C22—1464no—
223C22#1455655311yescharacteristic
224C22#1455655911yescharacteristic
225C22#1455656911yescharacteristic
226C22D8×D7311yescharacteristic
227C22#1455661411yescharacteristic
228C22#1455661511yescharacteristic
229C22#1455662311yescharacteristic
230C4—42no—
231C4—81no—
232C4—2922no—
233C4—2921no—
234C4—1462no—
235C4C4⋊C4×D7311yescharacteristic
236C4C4×C22⋊D7311yescharacteristic
237C4#1455656711yescharacteristic
238C4#1455657611yescharacteristic
239C2—2924no—
240C2#1798845811yescharacteristic
241C2#1798866911yescharacteristic
242C2#1798868611yescharacteristic
243C2#1798871911yescharacteristic
244C2#1798874811yescharacteristic
245C2#1798886611yescharacteristic
246C2#1798889011yescharacteristic
subgroupG/H
centerC23D4×D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#107×C73C2
socleC23×C73C2×D4
hypercenterC2×#107D73
hypocenterC73#1862
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
4. #17988483C2semidirect
5. #17988349C2semidirect
6. #17988341C2semidirect
7. C2×#107×C73C2semidirect
17. #14556513C4semidirect
41. C4⋊Dic73C2×C4semidirect
51. C2×C8×C73C2×C4semidirect
88. D292C4⋊C4semidirect
124. C73#1862semidirect
126. C2×#107D73semidirect
169. C2×C8C4×D73semidirect