Finite Group Databasebeta

← #22610823

Subgroups — #22610823

Order 9344.

292 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14556526C211yesmaximal, characteristic, complemented
3C2×#14556518C211yesmaximal, characteristic, complemented
4C2×#14556517C211yesmaximal, characteristic, complemented
5#17988553C211yesmaximal, characteristic, complemented
6C2×#14556501C211yesmaximal, characteristic, complemented
7#408×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#14556526—22no—
19#14556518—22no—
20#14556517—22no—
21#14556503—22no—
22#14556501—22no—
23C2×#41×C73C2211yescharacteristic
24C2×M16×C73C2211yescharacteristic
25C22×C8×C73C2211yescharacteristic
26C22⋊C8×C73—22no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30#11924028—21no—
31C2×Dic146C2×C411yescharacteristic
32C2×D292C2×C411yescharacteristic
33C2×C22⋊D73—21no—
34C22×Dic73—21no—
35C2×C4×D73—21no—
36#11924018—22no—
37#11924016—22no—
38#11924015—22no—
39#11924013—22no—
40#11924012—21no—
41#11924012—21no—
42C2×#10596831—21no—
43C2×#10596831C2×C411yescharacteristic
44C2×#10596831C2×C411yescharacteristic
45C2×#10596831D412yes—
46C2×#10596831D412yes—
47C4×Dic73—21no—
48C4×Dic73D412yes—
49#41×C73—21no—
50#41×C73—21no—
51#41×C73—21no—
52#41×C73—21no—
53C2×Q8×C73C2×C411yescharacteristic
54C2×D4×C73—21no—
55C2×D4×C73C2×C411yescharacteristic
56C22×C4×C73—21no—
57C22×C4×C73C2311yescharacteristic
58M16×C73—21no—
59M16×C73—21no—
60C2×C8×C73—21no—
61C2×C8×C73—21no—
62C2×C8×C73—21no—
63C2×C8×C73D412yes—
64C23×C73—21no—
65C23×C73#4111yescharacteristic
66C22×D73—21no—
67Q8×C73—21no—
68Q8×C73—21no—
69D4×C73—21no—
70D4×C73—21no—
71D4×C73—41no—
72D4×C73—41no—
73C2×C4×C73—21no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73C22×C411yescharacteristic
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73#4111yescharacteristic
82C22⋊D73—41no—
83C22⋊D73—41no—
84C2×Dic73—21no—
85C2×Dic73—22no—
86C2×Dic73—42no—
87D292—21no—
88D292—21no—
89C4×D73—41no—
90C4×D73—41no—
91Dic146—21no—
92Dic146—21no—
93C8×C73—22no—
94C8×C73—41no—
95#10596831—41no—
96#10596831C22⋊C412yes—
97#10596831C22⋊C412yes—
98C22×C73—22no—
99C22×C73—41no—
100C22×C73—42no—
101C22×C73C4×D411yescharacteristic
102C22×C73#12111yescharacteristic
103C22×C73#12411yescharacteristic
104C2×D73—41no—
105C2×D73—42no—
106C4×C73—41no—
107C4×C73C2×C22⋊C411yescharacteristic
108C4×C73C4×D411yescharacteristic
109C4×C73#12111yescharacteristic
110C4×C73#12711yescharacteristic
111Dic73—42no—
112Dic73—41no—
113C2×C73—21no—
114C2×C73—21no—
115C2×C73—81no—
116C2×C73#39011yescharacteristic
117C2×C73#44412yes—
118D73—81no—
119#1975—731nomaximal, Sylow
120C73#197511yescharacteristic, complemented, Sylow
121C2×#135—731no—
122C2×#108—731no—
123C2×#104—731no—
124C2×#104—731no—
125#408—731no—
126#408D7311yescharacteristic, complemented
127C2×#97—731no—
128C2×#41—731no—
129C2×#41C2×D7311yescharacteristic
130#135—1462no—
131#135—1462no—
132C2×Q16—731no—
133C2×SD16—731no—
134C2×SD16—731no—
135C2×D8—731no—
136C2×M16—731no—
137C2×M16C2×D7311yescharacteristic
138C22×C8—731no—
139C22×C8C2×D7311yescharacteristic
140C2×C42—731no—
141#108—1462no—
142#104—1462no—
143#104—1462no—
144C22⋊C8—22no—
145C22⋊C8—1462no—
146#97—1462no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—1461no—
152#41—1461no—
153#41—1461no—
154#41—1461no—
155C2×Q8—731no—
156C2×Q8C4×D7311yescharacteristic
157C2×D4—21no—
158C2×D4—731no—
159C2×D4—1461no—
160C2×D4C4×D7311yescharacteristic
161C22×C4—21no—
162C22×C4—1461no—
163C22×C4—1461no—
164C22×C4C22×D7311yescharacteristic
165Q16—1462no—
166SD16—1462no—
167SD16—1462no—
168D8—1462no—
169M16—21no—
170M16—21no—
171M16—1461no—
172M16—1461no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—731no—
177C2×C8—731no—
178C2×C8—732no—
179C2×C8—732no—
180C2×C8—1461no—
181C2×C8C22⋊D7312yes—
182C42—732no—
183C42—1461no—
184C23—21no—
185C23—1461no—
186C23#1192402811yescharacteristic
187Q8—21no—
188Q8—21no—
189Q8—1461no—
190Q8—1461no—
191D4—21no—
192D4—21no—
193D4—41no—
194D4—41no—
195D4—2921no—
196D4—2921no—
197D4—1461no—
198D4—1461no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—2922no—
203C2×C4—2921no—
204C2×C4—2921no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4C2×C4×D7311yescharacteristic
208C2×C4D4×D7311yescharacteristic
209C2×C4D4×D7311yescharacteristic
210C2×C4D4×D7311yescharacteristic
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4#1192402711yescharacteristic
213C8—22no—
214C8—41no—
215C8—2921no—
216C8—732no—
217C8—732no—
218C22—22no—
219C22—42no—
220C22—41no—
221C22—2922no—
222C22—2921no—
223C22C4×C22⋊D7311yescharacteristic
224C22#1455656411yescharacteristic
225C22#1455657711yescharacteristic
226C4—41no—
227C4—2922no—
228C4—2921no—
229C4C22⋊C4×D7311yescharacteristic
230C4#1455655111yescharacteristic
231C4#1455656311yescharacteristic
232C4#1455658711yescharacteristic
233C2—21no—
234C2—21no—
235C2—81no—
236C2—5841no—
237C2#1798848711yescharacteristic
238C2#1798870712yes—
subgroupG/H
centerC2×C4C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#408×C73C2
socleC22×C73C4×D4
hypercenter#408D73
hypocenterC73#1975
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #408

Complements

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

NH ≅ G/Ntype
2. C2×#14556526C2semidirect
3. C2×#14556518C2semidirect
4. C2×#14556517C2semidirect
5. #17988553C2semidirect
6. C2×#14556501C2semidirect
7. #408×C73C2semidirect
11. C2×#11924018C4semidirect
12. C2×#11924016C4semidirect
13. C2×#11924015C4semidirect
14. C2×#11924013C4semidirect
120. C73#1975semidirect
126. #408D73semidirect