Finite Group Databasebeta

← #22611150

Subgroups — #22611150

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#17989163C211yesmaximal, characteristic
2C2×#14556517C211yesmaximal, characteristic
3#17988586C211yesmaximal, characteristic
4C2×#14556509C211yesmaximal, characteristic, complemented
5#17988492C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#428×C73C211yesmaximal, characteristic, complemented
8C2×#11924028C2211yescharacteristic
9C22×Dic146C2211yescharacteristic
10C2×#11924012C2211yescharacteristic
11#14556591—21no—
12#14556579—21no—
13#14556575—22no—
14#14556571—21no—
15#14556571—21no—
16C2×C4×Dic73C2211yescharacteristic
17#14556517—22no—
18#14556514—21no—
19#14556511—21no—
20#14556509—22no—
21#14556498—22no—
22C2×M16×C73C2211yescharacteristic
23#117×C73C2211yescharacteristic
24C2×C4⋊C4×C73C2211yescharacteristic
25#107×C73—21no—
26#106×C73—21no—
27#11924028—21no—
28#11924028—21no—
29#11924028—21no—
30#11924028—21no—
31C2×Dic146—21no—
32C2×Dic146—21no—
33C2×Dic146—21no—
34C2×Dic146—21no—
35C2×Dic146—21no—
36C2×Dic146—21no—
37C2×Dic146D411yescharacteristic
38C2×D292D411yescharacteristic
39C2×C22⋊D73—21no—
40C22×Dic73—21no—
41C22×Dic73D412yes—
42C2×C4×D73—21no—
43#11924012—21no—
44#11924012—21no—
45C2×#10596831—21no—
46C4⋊Dic73—22no—
47C4⋊Dic73—22no—
48#11924005—22no—
49#11924005—22no—
50C4×Dic73—21no—
51C4×Dic73—21no—
52C22×C4×C73—21no—
53C22×C4×C73C2311yescharacteristic
54M16×C73—21no—
55M16×C73D412yes—
56C2×C8×C73—21no—
57C4⋊C4×C73—21no—
58C4⋊C4×C73—21no—
59C4⋊C4×C73D411yescharacteristic
60C4⋊C4×C73D411yescharacteristic
61C22⋊C4×C73—21no—
62C42×C73—21no—
63C23×C73C2×D411yescharacteristic
64C22×D73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—42no—
68C2×C4×C73—41no—
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73#4111yescharacteristic
73C2×C4×C73#4111yescharacteristic
74C2×C4×C73#4111yescharacteristic
75C22⋊D73—41no—
76C22⋊D73—41no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—21no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84D292—21no—
85D292—21no—
86C4×D73—41no—
87C4×D73—41no—
88Dic146—21no—
89Dic146—21no—
90Dic146—41no—
91Dic146—41no—
92Dic146—41no—
93Dic146—41no—
94C8×C73—22no—
95#10596831—41no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73#12011yescharacteristic
99C22×C73#12111yescharacteristic
100C22×C73#12311yescharacteristic
101C2×D73—41no—
102C2×D73—41no—
103C2×D73—41no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73—81no—
107C4×C73#12111yescharacteristic
108C4×C73#12111yescharacteristic
109C4×C73#12311yescharacteristic
110C4×C73#12411yescharacteristic
111Dic73—42no—
112Dic73—41no—
113Dic73—42no—
114C2×C73—21no—
115C2×C73—21no—
116C2×C73#39411yescharacteristic
117C2×C73#45411yescharacteristic
118C2×C73#45611yescharacteristic
119D73—81no—
120#2038—731nomaximal, Sylow
121C73#203811yescharacteristic, complemented, Sylow
122#536—731no—
123#428D7311yescharacteristic, complemented
124C2×#104—731no—
125#417—731no—
126C2×#101—731no—
127#391—731no—
128#339—731no—
129C2×#41—731no—
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#117C2×D7311yescharacteristic
139C2×C4⋊C4C2×D7311yescharacteristic
140C2×C42—731no—
141#107—21no—
142#106—21no—
143#104—1462no—
144#103—1461no—
145#102—1461no—
146#101—1462no—
147#95—1462no—
148#41—1461no—
149#41—1461no—
150#41—1461no—
151#41—1461no—
152C2×Q8—731no—
153C2×Q8—1461no—
154C2×Q8—1461no—
155C2×Q8—1461no—
156C2×Q8—1461no—
157C2×Q8—1461no—
158C2×Q8—1461no—
159C2×D4—731no—
160C2×D4—1461no—
161C22×C4—21no—
162C22×C4—732no—
163C22×C4—1461no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166M16—21no—
167M16—1461no—
168M16—1461no—
169M16D29212yes—
170C2×C8—21no—
171C2×C8—1461no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4C22⋊D7311yescharacteristic
177C4⋊C4C22⋊D7311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1462no—
180C22⋊C4—1462no—
181C42—21no—
182C42—1461no—
183C42—1461no—
184C23—1461no—
185C23D4×D7311yescharacteristic
186Q8—2921no—
187Q8—2921no—
188Q8—2921no—
189Q8—2921no—
190Q8—1461no—
191Q8—1461no—
192D4—2921no—
193D4—2921no—
194D4—1461no—
195D4—1461no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—2921no—
201C2×C4—2921no—
202C2×C4—2921no—
203C2×C4—2921no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4—1461no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4D4×D7311yescharacteristic
210C2×C4C2×C22⋊D7311yescharacteristic
211C2×C4C2×D29211yescharacteristic
212C2×C4#1192402811yescharacteristic
213C2×C4#1192402911yescharacteristic
214C2×C4#1192402911yescharacteristic
215C8—22no—
216C8—2921no—
217C22—21no—
218C22—21no—
219C22—2921no—
220C22—2921no—
221C22—2921no—
222C22#1455655911yescharacteristic
223C22#1455656611yescharacteristic
224C22#1455657611yescharacteristic
225C4—41no—
226C4—41no—
227C4—81no—
228C4—2922no—
229C4—2921no—
230C4—2922no—
231C4#1455656511yescharacteristic
232C4#1455656611yescharacteristic
233C4#1455657611yescharacteristic
234C4#1455658011yescharacteristic
235C2—21no—
236C2—21no—
237C2—5841no—
238C2#1798850411yescharacteristic
239C2#1798875811yescharacteristic
240C2#1798876811yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#428×C73C2
socleC22×C73#120
hypercenter#428D73
hypocenterC73#2038
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
4. C2×#14556509C2semidirect
5. #17988492C2semidirect
6. #17988346C2semidirect
7. #428×C73C2semidirect
121. C73#2038semidirect
123. #428D73semidirect