Finite Group Databasebeta

← #22619748

Subgroups — #22619748

Order 9344.

384 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#125×D73C211yesmaximal, characteristic, complemented
2C4×#11924027C211yesmaximal, characteristic
3#17988897C211yesmaximal, characteristic, complemented
4#17988895C211yesmaximal, characteristic, complemented
5#17988893C211yesmaximal, characteristic, complemented
6#17988891C211yesmaximal, characteristic, complemented
7#17988889C211yesmaximal, characteristic, complemented
8#17988887C211yesmaximal, characteristic, complemented
9#17988885C211yesmaximal, characteristic, complemented
10#17988628C211yesmaximal, characteristic, complemented
11#17988626C211yesmaximal, characteristic, complemented
12#17988609C211yesmaximal, characteristic, complemented
13#17988585C211yesmaximal, characteristic
14#17988585C211yesmaximal, characteristic
15#478×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×#11924011C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19#14556583C2211yescharacteristic
20#14556582C2211yescharacteristic
21#14556582C2211yescharacteristic
22#14556581—21no—
23#14556581—21no—
24C4×Dic146C2211yescharacteristic
25#14556556C2211yescharacteristic
26D4×Dic73C2211yescharacteristic
27C4×C22⋊D73—21no—
28#14556551—21no—
29#14556549C2211yescharacteristic
30#14556547—21no—
31C4⋊C4×D73—21no—
32C4⋊C4×D73—21no—
33C4⋊C4×D73C2211yescharacteristic
34C4⋊C4×D73C2211yescharacteristic
35C2×C4×Dic73—21no—
36C42×D73C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556523C2211yescharacteristic
41#14556522C2211yescharacteristic
42#14556522C2211yescharacteristic
43C4⋊#10596831C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556520C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556514C2211yescharacteristic
49#14556514C2211yescharacteristic
50#14556512C2211yescharacteristic
51#14556512C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—22no—
60#11924027Q814yes—
61C2×Dic146C2311yescharacteristic
62C2×C22⋊D73—21no—
63C22×Dic73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73D411yescharacteristic
68C2×C4×D73D411yescharacteristic
69C2×C4×D73C2311yescharacteristic
70#11924011—22no—
71#11924011—22no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73—21no—
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78C4⋊Dic73C2311yescharacteristic
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924007—21no—
87C22⋊Dic73—21no—
88#11924005—21no—
89C4×Dic73—21no—
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73D411yescharacteristic
93C4×Dic73D411yescharacteristic
94C4×Dic73C2311yescharacteristic
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73—21no—
97C2×C8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C4⋊C4×C73—21no—
100C4⋊C4×C73—21no—
101C4⋊C4×C73C2311yescharacteristic
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C42×C73C2311yescharacteristic
106C23×C73—21no—
107C22×D73C2×D411yescharacteristic
108D4×C73—21no—
109D4×C73C2×Q812yes—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—42no—
114C2×C4×C73C2×D411yescharacteristic
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2411yescharacteristic
117C22⋊D73—24no—
118C2×Dic73—21no—
119C2×Dic73—24no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—42no—
124C2×Dic73C2×D411yescharacteristic
125C2×Dic73C2×D411yescharacteristic
126C2×Dic73C2×D411yescharacteristic
127C4×D73—41no—
128C4×D73—41no—
129C4×D73—42no—
130C4×D73—42no—
131C4×D73C2×Q812yes—
132C4×D73#4112yes—
133Dic146—21no—
134Dic146C2×Q812yes—
135C8×C73—21no—
136C8×C73—21no—
137#10596831—21no—
138#10596831—21no—
139C22×C73—22no—
140C22×C73—41no—
141C22×C73—41no—
142C22×C73C22×D411yescharacteristic
143C2×D73—21no—
144C2×D73—21no—
145C2×D73C22⋊Q812yes—
146C4×C73—21no—
147C4×C73—21no—
148C4×C73—41no—
149C4×C73—41no—
150C4×C73—41no—
151C4×C73C22×Q811yescharacteristic
152C4×C73C2×#4111yescharacteristic
153Dic73—22no—
154Dic73—21no—
155Dic73—21no—
156Dic73—41no—
157Dic73—41no—
158Dic73—41no—
159Dic73C22⋊Q812yes—
160C2×C73—42no—
161C2×C73C2×C22⋊Q811yescharacteristic
162C2×C73#57511yescharacteristic
163C2×C73#57511yescharacteristic
164D73—22no—
165#3080—731nomaximal, Sylow
166C73#308011yescharacteristic, complemented, Sylow
167C2×#125—731no—
168C4×#41—731no—
169#479—731no—
170#479—731no—
171#479—731no—
172#479—731no—
173#478—731no—
174#478—731no—
175#478—731no—
176#478D7311yescharacteristic, complemented
177#428—731no—
178#428—731no—
179#423—731no—
180#417—731no—
181#417—731no—
182C2×#41—731no—
183C2×M16—731no—
184C2×M16—731no—
185#125—731no—
186#125—731no—
187#125—731no—
188#125—1461no—
189#125—1461no—
190#125C2×D7311yescharacteristic
191C4×Q8—731no—
192C4×Q8—731no—
193C4×D4—731no—
194C4×D4—1461no—
195C4×D4—1461no—
196C4×D4C2×D7311yescharacteristic
197#117—731no—
198#117—1461no—
199C2×C4⋊C4—731no—
200C2×C4⋊C4—731no—
201C2×C4⋊C4—1461no—
202C2×C4⋊C4—1461no—
203C2×C42—731no—
204C2×C42—1461no—
205#107—731no—
206#107—731no—
207#107—731no—
208#107C2×D7311yescharacteristic
209#106—731no—
210#106—731no—
211#106—731no—
212#106C2×D7311yescharacteristic
213C4⋊C8—731no—
214C4⋊C8—731no—
215C4⋊C8—731no—
216C4⋊C8C2×D7311yescharacteristic
217#103—731no—
218#103—731no—
219#103—731no—
220#103—731no—
221#102—731no—
222#102—731no—
223#102C2×D7311yescharacteristic
224#102C2×D7311yescharacteristic
225#41—734no—
226#41—1462no—
227C2×Q8—731no—
228C2×D4—1461no—
229C2×D4C22×D7311yescharacteristic
230C22×C4—21no—
231C22×C4—731no—
232C22×C4—731no—
233C22×C4—731no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4—1461no—
237C22×C4—1461no—
238M16—1462no—
239M16—1462no—
240C2×C8—731no—
241C2×C8—731no—
242C2×C8C22×D7311yescharacteristic
243C2×C8C22×D7311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—731no—
247C4⋊C4—731no—
248C4⋊C4—731no—
249C4⋊C4—1461no—
250C4⋊C4—1461no—
251C4⋊C4—1461no—
252C4⋊C4—1461no—
253C4⋊C4—1461no—
254C4⋊C4—1461no—
255C4⋊C4—1461no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4C22×D7311yescharacteristic
260C4⋊C4C22×D7311yescharacteristic
261C4⋊C4C22×D7311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—1461no—
264C22⋊C4—1461no—
265C42—731no—
266C42—731no—
267C42—731no—
268C42—1461no—
269C42—1461no—
270C42—1461no—
271C42C22×D7311yescharacteristic
272C23—21no—
273C23—731no—
274Q8—732no—
275Q8—1461no—
276D4—21no—
277D4—1464no—
278D4Q8×D7312yes—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2922no—
286C2×C4—2922no—
287C2×C4—2922no—
288C2×C4—731no—
289C2×C4—732no—
290C2×C4—732no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—1461no—
294C2×C4—1461no—
295C2×C4—1461no—
296C2×C4—1464no—
297C2×C4—1461no—
298C2×C4D4×D7311yescharacteristic
299C2×C4D4×D7311yescharacteristic
300C2×C4C23×D7311yescharacteristic
301C8—21no—
302C8—21no—
303C8—1461no—
304C8—1461no—
305C22—22no—
306C22—41no—
307C22—41no—
308C22—732no—
309C22—1461no—
310C22—1461no—
311C22C2×D4×D7311yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—2921no—
318C4—2921no—
319C4—2921no—
320C4—732no—
321C4—1461no—
322C4—1461no—
323C4—1462no—
324C4C2×Q8×D7311yescharacteristic
325C4#41×D7311yescharacteristic
326C2—42no—
327C2—1462no—
328C2C22⋊Q8×D7311yescharacteristic
329C2#1798938311yescharacteristic
330C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3080
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #125×D73C2semidirect
3. #17988897C2semidirect
4. #17988895C2semidirect
5. #17988893C2semidirect
6. #17988891C2semidirect
7. #17988889C2semidirect
8. #17988887C2semidirect
9. #17988885C2semidirect
10. #17988628C2semidirect
11. #17988626C2semidirect
12. #17988609C2semidirect
15. #478×C73C2semidirect
166. C73#3080semidirect
176. #478D73semidirect