Finite Group Databasebeta

← #22610258

Subgroups — #22610258

Order 9344.

324 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14556611C211yesmaximal, characteristic
2C2×#14556518C211yesmaximal, characteristic, complemented
3C2×#14556517C211yesmaximal, characteristic, complemented
4#17988553C211yesmaximal, characteristic, complemented
5#17988351C211yesmaximal, characteristic, complemented
6#17988341C211yesmaximal, characteristic, complemented
7C2×#131×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9#14556611—22no—
10#14556611—22no—
11C2×#11924018C411yescharacteristic, complemented
12C2×#11924016C411yescharacteristic, complemented
13C2×#11924015C411yescharacteristic, complemented
14C2×#11924013C411yescharacteristic, complemented
15C2×#11924012C2211yescharacteristic
16C22×#10596831C2211yescharacteristic
17C2×C4×Dic73C2211yescharacteristic
18#14556518—22no—
19#14556517—22no—
20#14556503—21no—
21#14556503—21no—
22C2×#41×C73C2211yescharacteristic
23#131×C73—22no—
24#131×C73—22no—
25C2×M16×C73—21no—
26C2×M16×C73C2211yescharacteristic
27C22×C8×C73—21no—
28C22×C8×C73C2211yescharacteristic
29#11924028—21no—
30#11924028—21no—
31#11924028—21no—
32#11924028—21no—
33C2×Dic146C2×C411yescharacteristic
34C2×D292C2×C411yescharacteristic
35C2×C22⋊D73—21no—
36C22×Dic73—21no—
37C2×C4×D73—21no—
38#11924018—22no—
39#11924016—22no—
40#11924015—22no—
41#11924013—22no—
42#11924012—21no—
43#11924012—21no—
44C2×#10596831—21no—
45C2×#10596831—21no—
46C2×#10596831—21no—
47C2×#10596831C2×C411yescharacteristic
48C2×#10596831C2×C411yescharacteristic
49C4×Dic73—21no—
50C4×Dic73—21no—
51#41×C73—21no—
52#41×C73—21no—
53#41×C73D412yes—
54#41×C73D412yes—
55C2×Q8×C73C2×C411yescharacteristic
56C2×D4×C73—21no—
57C2×D4×C73C2×C411yescharacteristic
58C22×C4×C73—21no—
59C22×C4×C73C2311yescharacteristic
60M16×C73—24no—
61M16×C73—21no—
62M16×C73D412yes—
63C2×C8×C73—24no—
64C2×C8×C73—21no—
65C2×C8×C73—21no—
66C2×C8×C73—21no—
67C2×C8×C73D411yescharacteristic
68C2×C8×C73D411yescharacteristic
69C23×C73—21no—
70C23×C73#4111yescharacteristic
71C22×D73—21no—
72Q8×C73—21no—
73Q8×C73C22⋊C412yes—
74D4×C73—22no—
75D4×C73—22no—
76D4×C73—21no—
77D4×C73C22⋊C412yes—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73C22×C411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C22⋊D73—41no—
88C22⋊D73—41no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—41no—
92C2×Dic73—41no—
93D292—21no—
94D292—21no—
95C4×D73—41no—
96C4×D73—41no—
97Dic146—21no—
98Dic146—21no—
99C8×C73—21no—
100C8×C73—22no—
101C8×C73—21no—
102#10596831—21no—
103#10596831—21no—
104#10596831—41no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73—22no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73C4×D411yescharacteristic
111C22×C73#12111yescharacteristic
112C22×C73#12311yescharacteristic
113C2×D73—41no—
114C2×D73—41no—
115C2×D73—41no—
116C4×C73—22no—
117C4×C73C2×C22⋊C411yescharacteristic
118C4×C73C4×D411yescharacteristic
119C4×C73#12011yescharacteristic
120C4×C73#12111yescharacteristic
121Dic73—42no—
122Dic73—41no—
123C2×C73—21no—
124C2×C73—21no—
125C2×C73—42no—
126C2×C73#38611yescharacteristic
127C2×C73#44311yescharacteristic
128C2×C73#44411yescharacteristic
129D73—81no—
130#1876—731nomaximal, Sylow
131C73#187611yescharacteristic, complemented, Sylow
132C2×#135—731no—
133C2×#131D7311yescharacteristic, complemented
134C2×#104—731no—
135C2×#104—731no—
136#408—731no—
137#341—731no—
138#336—731no—
139C2×#41—731no—
140C2×#41C2×D7311yescharacteristic
141#135—1462no—
142#135—1462no—
143C2×Q16—731no—
144C2×SD16—731no—
145C2×SD16—731no—
146C2×D8—731no—
147#131—22no—
148#131—22no—
149C2×M16—21no—
150C2×M16—731no—
151C2×M16C2×D7311yescharacteristic
152C22×C8—21no—
153C22×C8—731no—
154C22×C8C2×D7311yescharacteristic
155C2×C42—731no—
156#104—1462no—
157#104—1462no—
158C22⋊C8—1461no—
159C22⋊C8—1461no—
160#41—21no—
161#41—21no—
162#41—1461no—
163#41—1461no—
164#41—1461no—
165#41—1461no—
166#41D29212yes—
167#41C22⋊D7312yes—
168C2×Q8—731no—
169C2×Q8C4×D7311yescharacteristic
170C2×D4—21no—
171C2×D4—731no—
172C2×D4—1461no—
173C2×D4C4×D7311yescharacteristic
174C22×C4—21no—
175C22×C4—1461no—
176C22×C4—1461no—
177C22×C4C22×D7311yescharacteristic
178Q16—1462no—
179SD16—1462no—
180SD16—1462no—
181D8—1462no—
182M16—24no—
183M16—21no—
184M16—1461no—
185M16—1461no—
186M16C22⋊D7312yes—
187C2×C8—24no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—731no—
192C2×C8—731no—
193C2×C8—1461no—
194C2×C8—1461no—
195C2×C8—1461no—
196C2×C8C22⋊D7311yescharacteristic
197C2×C8C22⋊D7311yescharacteristic
198C42—1461no—
199C42—1461no—
200C23—21no—
201C23—1461no—
202C23#1192402811yescharacteristic
203Q8—21no—
204Q8—1461no—
205Q8—1461no—
206Q8#1192400512yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—2921no—
211D4—2921no—
212D4—1461no—
213D4—1461no—
214D4#1192400512yes—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—2921no—
219C2×C4—2921no—
220C2×C4—2921no—
221C2×C4—2921no—
222C2×C4—1462no—
223C2×C4—1461no—
224C2×C4C2×C4×D7311yescharacteristic
225C2×C4C2×C22⋊D7311yescharacteristic
226C2×C4C2×C22⋊D7311yescharacteristic
227C2×C4C2×C22⋊D7311yescharacteristic
228C2×C4C2×D29211yescharacteristic
229C2×C4#1192402811yescharacteristic
230C8—21no—
231C8—22no—
232C8—21no—
233C8—2921no—
234C8—1461no—
235C8—1461no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—2921no—
242C22—2921no—
243C22—2921no—
244C22C4×C22⋊D7311yescharacteristic
245C22#1455656511yescharacteristic
246C22#1455657411yescharacteristic
247C4—22no—
248C4—2922no—
249C4—2921no—
250C4C2×#1192400511yescharacteristic
251C4C4×C22⋊D7311yescharacteristic
252C4#1455656011yescharacteristic
253C4#1455656511yescharacteristic
254C2—21no—
255C2—21no—
256C2—42no—
257C2—5841no—
258C2#1798846611yescharacteristic
259C2#1798870211yescharacteristic
260C2#1798870711yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
FittingC2×#131×C73C2
socleC22×C73C4×D4
hypercenterC2×#131D73
hypocenterC73#1876
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. C2×#14556518C2semidirect
3. C2×#14556517C2semidirect
4. #17988553C2semidirect
5. #17988351C2semidirect
6. #17988341C2semidirect
7. C2×#131×C73C2semidirect
11. C2×#11924018C4semidirect
12. C2×#11924016C4semidirect
13. C2×#11924015C4semidirect
14. C2×#11924013C4semidirect
131. C73#1876semidirect
133. C2×#131D73semidirect