Finite Group Databasebeta

← #22619855

Subgroups — #22619855

Order 9344.

458 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989100C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988921C212yesmaximal, complemented
4#17988915C211yesmaximal, characteristic, complemented
5#17988907C212yesmaximal, complemented
6#17988901C211yesmaximal, characteristic, complemented
7#17988900C211yesmaximal, characteristic, complemented
8#17988626C212yesmaximal, complemented
9#17988587C212yesmaximal, complemented
10#17988549C211yesmaximal, characteristic, complemented
11#483×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2211yescharacteristic
13C22×C4×D73—21no—
14C22×C4×D73C2211yescharacteristic
15C2×#11924011C2212yes—
16#14556576—21no—
17#14556567C2211yescharacteristic
18#14556566C2211yescharacteristic
19#14556565C2211yescharacteristic
20#14556561—21no—
21#14556553—21no—
22#14556551—21no—
23#14556549C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C2×#11924007—21no—
26C4⋊C4×D73—21no—
27C4⋊C4×D73—21no—
28C4⋊C4×D73C2212yes—
29C4⋊C4×D73C2212yes—
30#14556525C2212yescomplemented
31#14556524C2212yescomplemented
32#14556522C2212yescomplemented
33#14556515C2212yescomplemented
34#14556513C2212yescomplemented
35#14556511C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic
37#14556503C2212yes—
38C22⋊Q8×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#106×C73C2212yescomplemented
41#103×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic
43C23×D73D411yescharacteristic
44#11924029—24no—
45C2×D292—21no—
46C2×D292—21no—
47C2×D292C2311yescharacteristic
48C2×C22⋊D73—21no—
49C22×Dic73—21no—
50C22×Dic73D411yescharacteristic
51C2×C4×D73—24no—
52C2×C4×D73—22no—
53C2×C4×D73—22no—
54C2×C4×D73—21no—
55C2×C4×D73—44no—
56C2×C4×D73D411yescharacteristic
57C2×C4×D73D411yescharacteristic
58C2×C4×D73C2311yescharacteristic
59C2×C4×D73C2311yescharacteristic
60#11924011—24no—
61C2×#10596831C2312yes—
62C4⋊Dic73—21no—
63C4⋊Dic73C2312yes—
64C4⋊Dic73C2311yescharacteristic
65#11924007—22no—
66#11924007—22no—
67#11924007—21no—
68#11924005—21no—
69#11924005—21no—
70#11924005—21no—
71#11924005—21no—
72C4×Dic73—21no—
73C2×Q8×C73C2311yescharacteristic
74C22×C4×C73—21no—
75C22×C4×C73C2311yescharacteristic
76C2×C8×C73C2312yes—
77C4⋊C4×C73—21no—
78C4⋊C4×C73—21no—
79C4⋊C4×C73C2312yes—
80C4⋊C4×C73C2311yescharacteristic
81C22⋊C4×C73—21no—
82C23×C73C2×D411yescharacteristic
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—21no—
87C22×D73C2×D411yescharacteristic
88C22×D73C2×D411yescharacteristic
89Q8×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—42no—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2411yescharacteristic
97C22⋊D73—42no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—42no—
102C2×Dic73C2×D411yescharacteristic
103C2×Dic73C2×D411yescharacteristic
104D292—22no—
105D292—42no—
106D292—42no—
107C4×D73—22no—
108C4×D73—22no—
109C4×D73—22no—
110C4×D73—44no—
111C4×D73—44no—
112C4×D73—42no—
113C4×D73#4114yes—
114C8×C73—22no—
115#10596831—22no—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73AGL(1,ℤ/8)12yes—
119C22×C73C22×D411yescharacteristic
120C2×D73—28no—
121C2×D73—21no—
122C2×D73—21no—
123C2×D73—21no—
124C2×D73—21no—
125C2×D73—41no—
126C2×D73—41no—
127C2×D73—41no—
128C2×D73#12312yes—
129C2×D73#13712yes—
130C4×C73—21no—
131C4×C73—41no—
132C4×C73—42no—
133C4×C73—41no—
134C4×C73C2×#4112yes—
135Dic73—21no—
136Dic73—42no—
137Dic73—41no—
138Dic73#12312yes—
139C2×C73—22no—
140C2×C73C2×#12311yescharacteristic
141C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C73C2×#13711yescharacteristic
143D73—22no—
144D73—22no—
145D73—81no—
146#3092—731nomaximal, Sylow
147C73#309211yescharacteristic, complemented, Sylow
148#525—731no—
149C22×C4⋊C4—731no—
150#484—732no—
151#483—731no—
152#483D7311yescharacteristic, complemented
153#481—732no—
154#480—731no—
155#480—731no—
156#428—732no—
157#417—732no—
158#407—731no—
159C2×#41—731no—
160C23×C4—731no—
161C23×C4—1461no—
162C2×M16—732no—
163#123—1461no—
164C22⋊Q8—731no—
165C22⋊Q8C2×D7311yescharacteristic
166#121—731no—
167#121—731no—
168#120—1461no—
169C4×D4—1461no—
170C4×D4—1461no—
171#117—731no—
172C2×C4⋊C4—731no—
173C2×C4⋊C4—732no—
174C2×C4⋊C4—732no—
175C2×C4⋊C4—1461no—
176C2×C4⋊C4—1461no—
177C2×C4⋊C4—1461no—
178C2×C4⋊C4C2×D7311yescharacteristic
179#107—732no—
180#107—732no—
181#106—732no—
182#106C2×D7312yescomplemented
183#103—732no—
184#103C2×D7312yescomplemented
185#102—732no—
186#102—732no—
187C22⋊C8—731no—
188C22⋊C8—732no—
189C22⋊C8C2×D7311yescharacteristic
190C24—731no—
191#41—1464no—
192C2×Q8C22×D7311yescharacteristic
193C2×D4—731no—
194C2×D4—1461no—
195C2×D4—1461no—
196C2×D4—1461no—
197C22×C4—21no—
198C22×C4—2924no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—731no—
202C22×C4—731no—
203C22×C4—731no—
204C22×C4—1461no—
205C22×C4—1462no—
206C22×C4—1462no—
207C22×C4—1464no—
208C22×C4—1461no—
209C22×C4C22×D7311yescharacteristic
210M16—1464no—
211C2×C8—732no—
212C2×C8C22×D7312yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—732no—
216C4⋊C4—731no—
217C4⋊C4—1462no—
218C4⋊C4—1462no—
219C4⋊C4—1461no—
220C4⋊C4—1461no—
221C4⋊C4C22×D7312yes—
222C4⋊C4C22×D7311yescharacteristic
223C22⋊C4—21no—
224C22⋊C4—1461no—
225C22⋊C4—1461no—
226C22⋊C4—1461no—
227C22⋊C4—1461no—
228C42—1461no—
229C23—731no—
230C23—731no—
231C23—1462no—
232C23—1462no—
233C23—1461no—
234C23—1462no—
235C23D4×D7311yescharacteristic
236Q8—22no—
237D4—2922no—
238D4—2922no—
239D4—2922no—
240D4—1462no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—2924no—
247C2×C4—2924no—
248C2×C4—2922no—
249C2×C4—2922no—
250C2×C4—731no—
251C2×C4—734no—
252C2×C4—731no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1461no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4D4×D7311yescharacteristic
260C2×C4C23×D7311yescharacteristic
261C8—22no—
262C8—1462no—
263C22—21no—
264C22—21no—
265C22—2921no—
266C22—2921no—
267C22—2921no—
268C22—732no—
269C22—732no—
270C22—1468no—
271C22—1461no—
272C22—1461no—
273C22—1461no—
274C22—1461no—
275C22#1455661812yes—
276C22C2×D4×D7311yescharacteristic
277C4—21no—
278C4—41no—
279C4—41no—
280C4—42no—
281C4—2922no—
282C4—2921no—
283C4—732no—
284C4—1461no—
285C4#41×D7312yes—
286C2—22no—
287C2—5841no—
288C2—1462no—
289C2—1462no—
290C2#123×D7311yescharacteristic
291C2C2×#1455661811yescharacteristic
292C2#137×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#483×C73C2
socleC22×C73C22×D4
hypercenter#483D73
hypocenterC73#3092
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988921C2semidirect
4. #17988915C2semidirect
5. #17988907C2semidirect
6. #17988901C2semidirect
7. #17988900C2semidirect
8. #17988626C2semidirect
9. #17988587C2semidirect
10. #17988549C2semidirect
11. #483×C73C2semidirect
30. #14556525C22semidirect
31. #14556524C22semidirect
32. #14556522C22semidirect
33. #14556515C22semidirect
34. #14556513C22semidirect
35. #14556511C22semidirect
40. #106×C73C22semidirect
41. #103×C73C22semidirect
147. C73#3092semidirect
152. #483D73semidirect
182. #106C2×D73semidirect
184. #103C2×D73semidirect