Finite Group Databasebeta

← #22611135

Subgroups — #22611135

Order 9344.

316 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14556570C211yesmaximal, characteristic
2C2×#14556525C211yesmaximal, characteristic, complemented
3C2×#14556516C211yesmaximal, characteristic, complemented
4C2×#14556516C211yesmaximal, characteristic, complemented
5#17988447C211yesmaximal, characteristic
6#17988350C211yesmaximal, characteristic, complemented
7C2×C22⋊C8×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9#14556570—22no—
10#14556570—22no—
11C2×C4⋊Dic73C2211yescharacteristic
12C2×C4⋊Dic73C2211yescharacteristic
13C2×C4⋊Dic73C2211yescharacteristic
14C2×#11924007—21no—
15C2×C22⋊Dic73—21no—
16C2×C22⋊Dic73—21no—
17#14556525—22no—
18#14556516—22no—
19#14556516—22no—
20#14556498—21no—
21C23×C4×C73C2211yescharacteristic
22C22×C8×C73C2211yescharacteristic
23C22×C8×C73C2211yescharacteristic
24C22⋊C8×C73—22no—
25C2×Dic146—21no—
26C2×Dic146—21no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146D412yes—
31C22×Dic73—21no—
32C22×Dic73—21no—
33C22×Dic73—21no—
34C22×Dic73—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73D412yes—
41#11924007—24no—
42C22⋊Dic73—24no—
43C22⋊Dic73—42no—
44C24×C73D411yescharacteristic
45C22×C4×C73—21no—
46C22×C4×C73—21no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73D411yescharacteristic
52C22×C4×C73C2311yescharacteristic
53C2×C8×C73—21no—
54C2×C8×C73—21no—
55C2×C8×C73—21no—
56C2×C8×C73—21no—
57C2×C8×C73—21no—
58C2×C8×C73D412yes—
59C23×C73—21no—
60C23×C73—21no—
61C23×C73—21no—
62C23×C73—21no—
63C23×C73—21no—
64C23×C73—21no—
65C23×C73Q1612yes—
66C23×C73C2×D411yescharacteristic
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73—41no—
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73C2×D411yescharacteristic
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C2×C4×C73#4111yescharacteristic
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85C2×Dic73—41no—
86C2×Dic73—41no—
87C2×Dic73—41no—
88C2×Dic73—41no—
89C2×Dic73—41no—
90C2×Dic73—41no—
91C2×Dic73—41no—
92Dic146—22no—
93Dic146—22no—
94Dic146—41no—
95Dic146—41no—
96C8×C73—22no—
97C8×C73—41no—
98C22×C73—22no—
99C22×C73—22no—
100C22×C73—22no—
101C22×C73—41no—
102C22×C73—41no—
103C22×C73—41no—
104C22×C73—41no—
105C22×C73#12011yescharacteristic
106C22×C73#12111yescharacteristic
107C22×C73#12311yescharacteristic
108C22×C73C2×Q1611yescharacteristic
109C22×C73#13511yescharacteristic
110C22×C73AGL(1,ℤ/8)11yescharacteristic
111C22×C73#13711yescharacteristic
112C4×C73—41no—
113C4×C73#12111yescharacteristic
114C4×C73#12111yescharacteristic
115C4×C73#12311yescharacteristic
116C4×C73#12411yescharacteristic
117Dic73—42no—
118Dic73—42no—
119Dic73—81no—
120Dic73—81no—
121C2×C73—42no—
122C2×C73#39411yescharacteristic
123C2×C73#44911yescharacteristic
124C2×C73#45111yescharacteristic
125C2×C73#46711yescharacteristic
126C2×C73#46811yescharacteristic
127C2×C73#48411yescharacteristic
128C2×C73#48511yescharacteristic
129#2036—731nomaximal, Sylow
130C73#203611yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—731no—
132C2×#107—731no—
133C2×#103—731no—
134C2×#103—731no—
135C2×C22⋊C8D7311yescharacteristic
136#380—731no—
137#340—731no—
138C22×Q8—731no—
139C23×C4C2×D7311yescharacteristic
140C22×C8C2×D7311yescharacteristic
141C22×C8C2×D7311yescharacteristic
142C22⋊Q8—1462no—
143C22⋊Q8—1462no—
144C2×C4⋊C4—731no—
145C2×C4⋊C4—731no—
146C2×C4⋊C4—731no—
147C2×C4⋊C4—1461no—
148C2×C22⋊C4—1461no—
149C2×C22⋊C4—1461no—
150#107—1462no—
151#103—1462no—
152#103—1462no—
153C22⋊C8—22no—
154#95—1461no—
155C24D29211yescharacteristic
156C2×Q8—732no—
157C2×Q8—1461no—
158C2×Q8—1461no—
159C2×Q8—1461no—
160C2×Q8—1461no—
161C2×Q8—1461no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1461no—
169C22×C4—1461no—
170C22×C4—1461no—
171C22×C4—1461no—
172C22×C4D29211yescharacteristic
173C22×C4C22×D7311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8C22⋊D7312yes—
180C4⋊C4—732no—
181C4⋊C4—1464no—
182C4⋊C4—1461no—
183C4⋊C4—1461no—
184C4⋊C4—1461no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C22⋊C4—2922no—
188C22⋊C4—1464no—
189C23—21no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—21no—
194C23—21no—
195C23Dic29212yes—
196C23C2×D29211yescharacteristic
197Q8—2921no—
198Q8—2921no—
199Q8—1462no—
200Q8—1462no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—2921no—
209C2×C4—2921no—
210C2×C4—2921no—
211C2×C4—2921no—
212C2×C4—2921no—
213C2×C4—2921no—
214C2×C4—2921no—
215C2×C4—2921no—
216C2×C4—2921no—
217C2×C4—2921no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4D4×D7311yescharacteristic
221C2×C4D4×D7311yescharacteristic
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4#1192402711yescharacteristic
224C2×C4#1192402711yescharacteristic
225C2×C4#1192402811yescharacteristic
226C8—22no—
227C8—41no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—41no—
235C22#1455656111yescharacteristic
236C22#1455656511yescharacteristic
237C22#1455657511yescharacteristic
238C22C2×Dic29211yescharacteristic
239C22#1455661311yescharacteristic
240C22#1455661911yescharacteristic
241C22#1455662411yescharacteristic
242C4—41no—
243C4—2922no—
244C4—2922no—
245C4—5841no—
246C4—5841no—
247C4#1455656211yescharacteristic
248C4#1455656311yescharacteristic
249C4#1455657311yescharacteristic
250C4#1455657711yescharacteristic
251C2—42no—
252C2#1798850311yescharacteristic
253C2#1798873411yescharacteristic
254C2#1798874511yescharacteristic
255C2#1798882811yescharacteristic
256C2#1798883311yescharacteristic
257C2#1798892311yescharacteristic
258C2#1798892911yescharacteristic
subgroupG/H
centerC23C2×D292
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×C22⋊C8×C73C2
socleC23×C73C2×D4
hypercenterC2×C22⋊C8D73
hypocenterC73#2036
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14556525C2semidirect
3. C2×#14556516C2semidirect
4. C2×#14556516C2semidirect
6. #17988350C2semidirect
130. C73#2036semidirect