Finite Group Databasebeta

← #22619902

Subgroups — #22619902

Order 9344.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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
2#17989068C211yesmaximal, characteristic
3#17988931C212yesmaximal, complemented
4#17988930C212yesmaximal, complemented
5#17988924C212yesmaximal, complemented
6#17988919C212yesmaximal, complemented
7#17988623C211yesmaximal, characteristic, complemented
8#17988597C211yesmaximal, characteristic, complemented
9C2×#14556514C211yesmaximal, characteristic, complemented
10#17988555C211yesmaximal, characteristic
11#428×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15#14556591—21no—
16#14556579—21no—
17#14556575—22no—
18#14556571C2212yes—
19#14556571C2212yes—
20#14556556—21no—
21#14556553—21no—
22C4×C22⋊D73—22no—
23#14556550C2211yescharacteristic
24#14556549C2212yes—
25C4⋊C4×D73C2212yes—
26#14556524C2211yescharacteristic
27#14556524C2211yescharacteristic
28#14556522C2211yescharacteristic
29#14556522C2211yescharacteristic
30#14556516C2212yes—
31#14556516C2212yes—
32#14556514C2212yes—
33#14556514C2212yes—
34#14556503C2212yes—
35#14556503C2212yes—
36C2×M16×C73C2211yescharacteristic
37#117×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#107×C73C2212yes—
40#106×C73C2212yes—
41#11924028—22no—
42#11924028—22no—
43C2×Dic146—22no—
44C2×Dic146—22no—
45C2×Dic146—21no—
46C2×Dic146D411yescharacteristic
47C2×Dic146C2312yes—
48C2×D292D411yescharacteristic
49C2×C22⋊D73D412yes—
50C22×Dic73—21no—
51C2×C4×D73—22no—
52C2×C4×D73C2312yes—
53C2×#10596831—22no—
54C2×#10596831C2311yescharacteristic
55C2×#10596831C2311yescharacteristic
56C4⋊Dic73—22no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2311yescharacteristic
59C4⋊Dic73C2311yescharacteristic
60#11924007—22no—
61C22⋊Dic73—21no—
62#11924005—22no—
63#11924005—22no—
64#11924005—22no—
65C4×Dic73—21no—
66C4×Dic73—22no—
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69M16×C73—22no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73—21no—
72C4⋊C4×C73C2311yescharacteristic
73C4⋊C4×C73C2312yes—
74C4⋊C4×C73C2311yescharacteristic
75C22⋊C4×C73—21no—
76C42×C73—21no—
77C23×C73C2×D411yescharacteristic
78C22×D73C2×D412yes—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—81no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73#4112yes—
85C2×C4×C73#4112yes—
86C2×C4×C73C2411yescharacteristic
87C22⋊D73—24no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—42no—
92C2×Dic73C2×D412yes—
93D292—22no—
94C4×D73—22no—
95C4×D73—22no—
96C4×D73—82no—
97Dic146—22no—
98Dic146—22no—
99Dic146—22no—
100Dic146—42no—
101C8×C73—22no—
102#10596831—21no—
103#10596831—21no—
104C22×C73—21no—
105C22×C73—21no—
106C22×C73#12312yes—
107C22×C73C22×D411yescharacteristic
108C2×D73—22no—
109C2×D73—22no—
110C2×D73—22no—
111C4×C73—42no—
112C4×C73—41no—
113C4×C73—41no—
114C4×C73#12312yes—
115C4×C73C2×#4111yescharacteristic
116C4×C73C2×#4111yescharacteristic
117Dic73—22no—
118Dic73—42no—
119Dic73—41no—
120Dic73—41no—
121C2×C73—22no—
122C2×C73C2×#12311yescharacteristic
123C2×C73#57711yescharacteristic
124C2×C73#57811yescharacteristic
125D73—42no—
126#3097—731nomaximal, Sylow
127C73#309711yescharacteristic, complemented, Sylow
128#536—731no—
129#520—731no—
130#485—732no—
131#485—732no—
132#484—732no—
133#483—732no—
134#428D7311yescharacteristic, complemented
135#427—731no—
136#419—731no—
137C2×#103—731no—
138#408—731no—
139C2×#41—731no—
140C22×Q8—731no—
141C2×M16C2×D7311yescharacteristic
142C22×C8—731no—
143C4⋊Q8—1461no—
144#124—1461no—
145#123—1462no—
146C22⋊Q8—732no—
147C22⋊Q8—732no—
148C4×Q8—1461no—
149C4×D4—1461no—
150C4×D4—1462no—
151#117—731no—
152#117—732no—
153#117C2×D7311yescharacteristic
154C2×C4⋊C4—732no—
155C2×C4⋊C4C2×D7311yescharacteristic
156#107—731no—
157#107—731no—
158#107C2×D7312yes—
159#106—731no—
160#106—731no—
161#106C2×D7312yes—
162#103—732no—
163#103—732no—
164#103—732no—
165#103—732no—
166C22⋊C8—732no—
167C22⋊C8—732no—
168#41—1462no—
169#41—1462no—
170C2×Q8—731no—
171C2×Q8—732no—
172C2×Q8—1462no—
173C2×Q8—1462no—
174C2×Q8—1461no—
175C2×D4—732no—
176C2×D4—731no—
177C22×C4—21no—
178C22×C4—732no—
179C22×C4—1462no—
180C22×C4—1461no—
181C22×C4C22×D7311yescharacteristic
182M16—22no—
183C2×C8—731no—
184C2×C8—731no—
185C2×C8—1462no—
186C2×C8C22×D7312yes—
187C4⋊C4—21no—
188C4⋊C4—731no—
189C4⋊C4—731no—
190C4⋊C4—1462no—
191C4⋊C4—1462no—
192C4⋊C4—1462no—
193C4⋊C4C22×D7312yes—
194C4⋊C4C22×D7311yescharacteristic
195C4⋊C4C22×D7311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1462no—
198C22⋊C4—1462no—
199C22⋊C4—1462no—
200C22⋊C4—1461no—
201C42—21no—
202C42—1462no—
203C42—1461no—
204C23—732no—
205C23D4×D7311yescharacteristic
206Q8—2922no—
207Q8—1462no—
208Q8—1462no—
209Q8—1462no—
210D4—1464no—
211D4—1462no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—81no—
216C2×C4—2922no—
217C2×C4—5842no—
218C2×C4—732no—
219C2×C4—1461no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4D4×D7311yescharacteristic
225C2×C4#1192402812yes—
226C2×C4#1192402912yes—
227C2×C4C23×D7311yescharacteristic
228C8—22no—
229C8—1461no—
230C8—1461no—
231C22—21no—
232C22—21no—
233C22—1462no—
234C22—1462no—
235C22—1462no—
236C22#1455657612yes—
237C22C2×D4×D7311yescharacteristic
238C4—42no—
239C4—41no—
240C4—41no—
241C4—2921no—
242C4—2921no—
243C4—2922no—
244C4—1462no—
245C4#1455657612yes—
246C4C2×#1192402811yescharacteristic
247C4C2×#1192402911yescharacteristic
248C2—22no—
249C2—2922no—
250C2C2×#1455657611yescharacteristic
251C2#1798939711yescharacteristic
252C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3097
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. #17988931C2semidirect
4. #17988930C2semidirect
5. #17988924C2semidirect
6. #17988919C2semidirect
7. #17988623C2semidirect
8. #17988597C2semidirect
9. C2×#14556514C2semidirect
11. #428×C73C2semidirect
127. C73#3097semidirect
134. #428D73semidirect