Finite Group Databasebeta

← #22611147

Subgroups — #22611147

Order 9344.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#17989158C211yesmaximal, characteristic
2#17988629C211yesmaximal, characteristic, complemented
3#17988588C211yesmaximal, characteristic
4C2×#14556509C211yesmaximal, characteristic, complemented
5#17988493C211yesmaximal, characteristic, complemented
6#17988347C211yesmaximal, characteristic, complemented
7C2×#104×C73C211yesmaximal, characteristic
8C22×Dic146C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10#14556589—21no—
11#14556578—21no—
12#14556572—22no—
13#14556570—21no—
14#14556570—21no—
15#14556550C2211yescharacteristic
16C2×C4⋊Dic73C2211yescharacteristic
17#14556525—21no—
18#14556523—21no—
19#14556515—21no—
20#14556512—21no—
21#14556509—22no—
22#14556498—22no—
23C2×#41×C73C2211yescharacteristic
24C2×M16×C73C2211yescharacteristic
25C2×C42×C73C2211yescharacteristic
26#104×C73—22no—
27C2×Dic146—21no—
28C2×Dic146—21no—
29C2×Dic146—21no—
30C2×Dic146—21no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C22×Dic73—21no—
34C22×Dic73D412yes—
35#11924012—21no—
36#11924012—21no—
37C2×#10596831—21no—
38C4⋊Dic73—21no—
39C4⋊Dic73—21no—
40C4⋊Dic73D411yescharacteristic
41C4⋊Dic73D411yescharacteristic
42#11924007—22no—
43#11924007—22no—
44C22⋊Dic73—22no—
45C22⋊Dic73—22no—
46C22⋊Dic73—21no—
47C4×Dic73—21no—
48#41×C73—21no—
49#41×C73—21no—
50#41×C73—21no—
51#41×C73—21no—
52C2×Q8×C73D411yescharacteristic
53C2×D4×C73—21no—
54C2×D4×C73D411yescharacteristic
55C22×C4×C73—21no—
56C22×C4×C73—21no—
57C22×C4×C73C2311yescharacteristic
58M16×C73—21no—
59M16×C73D412yes—
60C2×C8×C73—21no—
61C42×C73—21no—
62C42×C73—21no—
63C23×C73—21no—
64C23×C73C2×D411yescharacteristic
65Q8×C73—21no—
66Q8×C73—21no—
67D4×C73—21no—
68D4×C73—21no—
69D4×C73—41no—
70D4×C73—41no—
71C2×C4×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—41no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73—41no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73#4111yescharacteristic
81C2×C4×C73#4111yescharacteristic
82C2×C4×C73#4111yescharacteristic
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—22no—
88C2×Dic73—42no—
89C2×Dic73—41no—
90Dic146—41no—
91Dic146—41no—
92Dic146—41no—
93Dic146—41no—
94C8×C73—22no—
95#10596831—41no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73#12011yescharacteristic
102C22×C73#12111yescharacteristic
103C22×C73#12311yescharacteristic
104C4×C73—42no—
105C4×C73—41no—
106C4×C73#12111yescharacteristic
107C4×C73#12111yescharacteristic
108C4×C73#12311yescharacteristic
109C4×C73#12411yescharacteristic
110Dic73—42no—
111Dic73—41no—
112Dic73—41no—
113Dic73—81no—
114C2×C73—21no—
115C2×C73—21no—
116C2×C73—81no—
117C2×C73#39411yescharacteristic
118C2×C73#45411yescharacteristic
119C2×C73#45611yescharacteristic
120#2038—731nomaximal, Sylow
121C73#203811yescharacteristic, complemented, Sylow
122#536—731no—
123#428—731no—
124C2×#104D7311yescharacteristic
125#417—731no—
126C2×#101—731no—
127#391—731no—
128#339—731no—
129C2×#41C2×D7311yescharacteristic
130C22×Q8—731no—
131C2×M16—731no—
132C2×M16C2×D7311yescharacteristic
133C4⋊Q8—1461no—
134#124—1461no—
135#123—1462no—
136C22⋊Q8—1461no—
137C22⋊Q8—1461no—
138#117—731no—
139C2×C4⋊C4—731no—
140C2×C42C2×D7311yescharacteristic
141#107—1461no—
142#106—1461no—
143#104—22no—
144#103—1461no—
145#102—1461no—
146#101—1462no—
147#95—1462no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—1461no—
153C2×Q8—1461no—
154C2×Q8—1461no—
155C2×Q8—1461no—
156C2×Q8—1461no—
157C2×Q8—1461no—
158C2×Q8D29211yescharacteristic
159C2×D4—21no—
160C2×D4D29211yescharacteristic
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—732no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166M16—21no—
167M16—1461no—
168M16—1461no—
169M16C22⋊D7312yes—
170C2×C8—21no—
171C2×C8—1461no—
172C4⋊C4—731no—
173C4⋊C4—731no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1461no—
177C4⋊C4—1461no—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C22⋊C4—1461no—
181C42—21no—
182C42—21no—
183C42—1461no—
184C23—21no—
185C23D4×D7311yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—2921no—
189Q8—2921no—
190Q8—2921no—
191Q8—2921no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—2922no—
203C2×C4—2921no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4D4×D7311yescharacteristic
210C2×C4C2×C22⋊D7311yescharacteristic
211C2×C4C2×D29211yescharacteristic
212C2×C4#1192402711yescharacteristic
213C2×C4#1192402711yescharacteristic
214C2×C4#1192402811yescharacteristic
215C8—22no—
216C8—2921no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1455656111yescharacteristic
223C22#1455656211yescharacteristic
224C22#1455657311yescharacteristic
225C4—42no—
226C4—41no—
227C4—2922no—
228C4—2921no—
229C4—2921no—
230C4—5841no—
231C4#1455656311yescharacteristic
232C4#1455656511yescharacteristic
233C4#1455657511yescharacteristic
234C4#1455657711yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1798850311yescharacteristic
239C2#1798876111yescharacteristic
240C2#1798877111yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
FittingC2×#104×C73C2
socleC22×C73#120
hypercenterC2×#104D73
hypocenterC73#2038
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #17988629C2semidirect
4. C2×#14556509C2semidirect
5. #17988493C2semidirect
6. #17988347C2semidirect
121. C73#2038semidirect