Finite Group Databasebeta

← #22619595

Subgroups — #22619595

Order 9344.

484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14556614C211yesmaximal, characteristic, complemented
2C2×#14556599C211yesmaximal, characteristic, complemented
3#17989167C212yesmaximal, complemented
4#17988842C211yesmaximal, characteristic, complemented
5#17988841C211yesmaximal, characteristic, complemented
6#17988840C211yesmaximal, characteristic, complemented
7#17988819C212yesmaximal, complemented
8#17988818C212yesmaximal, complemented
9#106×D73C211yesmaximal, characteristic, complemented
10#17988587C212yesmaximal, complemented
11#470×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2212yes—
13C2×#11924028C2211yescharacteristic
14#14556614—24no—
15C2×#11924015C2212yes—
16C2×D584C2211yescharacteristic
17#14556599—24no—
18C2×#11924011C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C22×#10596831C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23#14556569—22no—
24#14556567C2212yes—
25#14556566—22no—
26#14556566C2212yes—
27#14556565C2212yes—
28#14556564—22no—
29#14556564—22no—
30C4⋊C4×D73C2212yes—
31#14556523C2211yescharacteristic
32#14556522C2212yes—
33#14556515C2212yes—
34#14556513C2212yes—
35#14556511C2212yes—
36C2×Q16×C73C2211yescharacteristic
37C2×M16×C73C2211yescharacteristic
38C22⋊Q8×C73C2212yes—
39#106×C73C2211yescharacteristic
40#103×C73C2212yes—
41#11924029—24no—
42#11924029—24no—
43#11924028—22no—
44#11924028—22no—
45C2×Dic146D411yescharacteristic
46C2×D292—22no—
47C2×D292—22no—
48C2×D292D411yescharacteristic
49C2×D292C2312yes—
50C2×C22⋊D73—22no—
51C2×C22⋊D73D411yescharacteristic
52C2×C22⋊D73D411yescharacteristic
53C2×C4×D73—22no—
54C2×C4×D73—22no—
55C2×C4×D73C2311yescharacteristic
56C2×C4×D73C2311yescharacteristic
57#11924015—24no—
58D584—22no—
59#11924011—22no—
60#11924011—22no—
61C2×#10596831—22no—
62C2×#10596831C2311yescharacteristic
63C2×#10596831C2311yescharacteristic
64C8×D73—22no—
65C8×D73D414yescomplemented
66C4⋊Dic73C2312yes—
67#11924007—22no—
68#11924007—22no—
69#11924005—22no—
70#11924005—22no—
71#11924005—22no—
72C2×Q8×C73C2312yes—
73C22×C4×C73C2311yescharacteristic
74Q16×C73—22no—
75M16×C73—22no—
76C2×C8×C73C2311yescharacteristic
77C2×C8×C73C2311yescharacteristic
78C4⋊C4×C73—22no—
79C4⋊C4×C73C2312yes—
80C22⋊C4×C73—22no—
81C23×C73C2×D411yescharacteristic
82C22×D73—22no—
83C22×D73C2×D411yescharacteristic
84C22×D73C2×D411yescharacteristic
85Q8×C73—22no—
86Q8×C73—22no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2411yescharacteristic
93C22⋊D73—22no—
94C22⋊D73—22no—
95C22⋊D73—82no—
96C2×Dic73—22no—
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99D292—22no—
100D292—22no—
101D292—22no—
102D292—44no—
103D292—82no—
104C4×D73—21no—
105C4×D73—21no—
106C4×D73—44no—
107C4×D73—82no—
108C4×D73C2×D412yes—
109C4×D73#4112yes—
110Dic146—22no—
111C8×C73—21no—
112C8×C73C2×D412yes—
113#10596831—21no—
114#10596831C2×D412yes—
115C22×C73—21no—
116C22×C73—22no—
117C22×C73C22×D411yescharacteristic
118C2×D73—22no—
119C2×D73—21no—
120C2×D73—22no—
121C2×D73—42no—
122C2×D73—42no—
123C2×D73—42no—
124C2×D73#12112yes—
125C4×C73—21no—
126C4×C73—42no—
127C4×C73—42no—
128C4×C73C22×D411yescharacteristic
129C4×C73C2×#4111yescharacteristic
130Dic73—21no—
131Dic73—42no—
132Dic73#12112yes—
133C2×C73—41no—
134C2×C73C2×#12111yescharacteristic
135C2×C73#57712yes—
136D73—22no—
137D73—41no—
138D73—82no—
139#3060—731nomaximal, Sylow
140C73#306011yescharacteristic, complemented, Sylow
141C2×#135—731no—
142C2×#131—731no—
143#537—732no—
144#470—731no—
145#470D7311yescharacteristic, complemented
146#469—731no—
147#469—731no—
148#465—732no—
149#465—732no—
150C2×#106—731no—
151#417—732no—
152C2×#41—731no—
153C2×#41—732no—
154#135—1464no—
155C2×Q16C2×D7311yescharacteristic
156C2×SD16—732no—
157C2×D8—731no—
158#131—1464no—
159C2×M16—731no—
160C2×M16—731no—
161C2×M16C2×D7311yescharacteristic
162C22×C8—731no—
163C22×C8—731no—
164C22×C8—731no—
165C22⋊Q8—732no—
166C22⋊Q8—1462no—
167C22⋊Q8C2×D7312yes—
168#121—732no—
169#121—732no—
170#121—1462no—
171#121—1462no—
172#121—1462no—
173C2×C4⋊C4—732no—
174#106—731no—
175#106—732no—
176#106C2×D7311yescharacteristic
177#103—732no—
178#103C2×D7312yes—
179#102—732no—
180#102—732no—
181#41—1462no—
182#41—1462no—
183#41—1464no—
184#41—1464no—
185C2×Q8—731no—
186C2×Q8C22×D7312yes—
187C2×D4—731no—
188C2×D4—731no—
189C2×D4—731no—
190C2×D4—732no—
191C2×D4—1462no—
192C2×D4—1462no—
193C2×D4—1462no—
194C22×C4—731no—
195C22×C4—731no—
196C22×C4—1462no—
197C22×C4—1462no—
198C22×C4C22×D7311yescharacteristic
199Q16—22no—
200SD16—1464no—
201D8—1462no—
202M16—22no—
203M16—1462no—
204M16—1462no—
205C2×C8—731no—
206C2×C8—734no—
207C2×C8—731no—
208C2×C8—1462no—
209C2×C8—1462no—
210C2×C8C22×D7311yescharacteristic
211C2×C8C22×D7311yescharacteristic
212C4⋊C4—22no—
213C4⋊C4—732no—
214C4⋊C4—1462no—
215C4⋊C4—1462no—
216C4⋊C4C22×D7312yes—
217C22⋊C4—22no—
218C22⋊C4—1462no—
219C22⋊C4—1462no—
220C22⋊C4—1462no—
221C23—731no—
222C23—731no—
223C23—1462no—
224C23D4×D7311yescharacteristic
225Q8—22no—
226Q8—22no—
227Q8—1462no—
228D4—2924no—
229D4—5842no—
230D4—5842no—
231D4—1462no—
232D4—1462no—
233D4—1462no—
234D4—1462no—
235D4—1462no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—2924no—
241C2×C4—5842no—
242C2×C4—731no—
243C2×C4—732no—
244C2×C4—732no—
245C2×C4—731no—
246C2×C4—1462no—
247C2×C4—1461no—
248C2×C4—1461no—
249C2×C4D4×D7311yescharacteristic
250C2×C4C23×D7311yescharacteristic
251C8—21no—
252C8—732no—
253C8—1461no—
254C8D4×D7312yes—
255C22—22no—
256C22—21no—
257C22—2922no—
258C22—2922no—
259C22—2922no—
260C22—732no—
261C22—1462no—
262C22—1461no—
263C22—1462no—
264C22C2×D4×D7311yescharacteristic
265C4—21no—
266C4—42no—
267C4—42no—
268C4—2922no—
269C4—732no—
270C4—1461no—
271C4C2×D4×D7311yescharacteristic
272C4#41×D7311yescharacteristic
273C2—41no—
274C2—2921no—
275C2—5842no—
276C2—1462no—
277C2#121×D7311yescharacteristic
278C2#1798939612yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3060
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. C2×#14556614C2semidirect
2. C2×#14556599C2semidirect
3. #17989167C2semidirect
4. #17988842C2semidirect
5. #17988841C2semidirect
6. #17988840C2semidirect
7. #17988819C2semidirect
8. #17988818C2semidirect
9. #106×D73C2semidirect
10. #17988587C2semidirect
11. #470×C73C2semidirect
65. C8×D73D4semidirect
140. C73#3060semidirect
145. #470D73semidirect