Finite Group Databasebeta

← #22622366

Subgroups — #22622366

Order 9344.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989271C211yesmaximal, characteristic, complemented
2#17989237C211yesmaximal, characteristic
3#17988995C211yesmaximal, characteristic, complemented
4#17988920C211yesmaximal, characteristic, complemented
5#17988916C211yesmaximal, characteristic, complemented
6#17988908C211yesmaximal, characteristic, complemented
7#17988899C211yesmaximal, characteristic, complemented
8#17988889C211yesmaximal, characteristic, complemented
9#17988880C211yesmaximal, characteristic, complemented
10#17988813C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12#17988656C211yesmaximal, characteristic, complemented
13#17988629C211yesmaximal, characteristic, complemented
14#107×D73C211yesmaximal, characteristic, complemented
15#468×C73C211yesmaximal, characteristic, complemented
16C2×#11924027—21no—
17C2×C8×D73C2211yescharacteristic
18#14556590C2211yescharacteristic
19#14556584—21no—
20#14556582C2211yescharacteristic
21#14556581—21no—
22#14556573—21no—
23#14556573—21no—
24#14556572—21no—
25#14556568—21no—
26#14556567C2211yescharacteristic
27#14556562C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30C4×C22⋊D73C2211yescharacteristic
31#14556550C2211yescharacteristic
32#14556549—21no—
33C2×C4⋊Dic73C2211yescharacteristic
34C4⋊C4×D73C2211yescharacteristic
35C4⋊C4×D73C2211yescharacteristic
36#14556525C2211yescharacteristic
37#14556525C2211yescharacteristic
38#14556524C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556524C2211yescharacteristic
41#14556523C2211yescharacteristic
42#14556523C2211yescharacteristic
43#14556522C2211yescharacteristic
44#14556520C2211yescharacteristic
45#14556515C2211yescharacteristic
46#14556515C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic
52C2×SD16×C73C2211yescharacteristic
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55#121×C73C2211yescharacteristic
56#107×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59#11924027—44no—
60C2×Dic146—21no—
61C2×C22⋊D73—21no—
62C2×C22⋊D73D411yescharacteristic
63C22×Dic73—21no—
64C22×Dic73—21no—
65C2×C4×D73—21no—
66C2×C4×D73—21no—
67C2×C4×D73C2311yescharacteristic
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C8×D73—22no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73C2311yescharacteristic
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84C22⋊Dic73—21no—
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87C22⋊Dic73D411yescharacteristic
88#11924005—21no—
89#11924005D411yescharacteristic
90C4×Dic73—21no—
91C4×Dic73—21no—
92C4×Dic73C2311yescharacteristic
93C2×Q8×C73C2311yescharacteristic
94C2×D4×C73—21no—
95C2×D4×C73C2311yescharacteristic
96C22×C4×C73C2311yescharacteristic
97SD16×C73—22no—
98M16×C73—22no—
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
102C4⋊C4×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C22⋊C4×C73—21no—
105C22⋊C4×C73—21no—
106C23×C73—21no—
107C23×C73C2×D411yescharacteristic
108C22×D73C2×D411yescharacteristic
109Q8×C73—21no—
110Q8×C73—21no—
111D4×C73—21no—
112D4×C73—21no—
113D4×C73—42no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2411yescharacteristic
121C22⋊D73—22no—
122C22⋊D73—42no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—42no—
128C2×Dic73—42no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132C4×D73—21no—
133C4×D73—21no—
134C4×D73—42no—
135C4×D73—42no—
136Dic146—42no—
137C8×C73—21no—
138C8×C73#4112yescomplemented
139#10596831—21no—
140#10596831—21no—
141C22×C73—21no—
142C22×C73—21no—
143C22×C73—21no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73—41no—
147C22×C73C22×D411yescharacteristic
148C2×D73—21no—
149C2×D73—21no—
150C2×D73AGL(1,ℤ/8)12yes—
151C4×C73—21no—
152C4×C73—41no—
153C4×C73—41no—
154C4×C73—41no—
155C4×C73C2×#4111yescharacteristic
156C4×C732−1+411yescharacteristic
157Dic73—21no—
158Dic73—21no—
159Dic73—21no—
160Dic73—41no—
161Dic73—41no—
162Dic73—41no—
163Dic73—41no—
164C2×C73—41no—
165C2×C73—81no—
166C2×C73#54711yescharacteristic
167C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C73#57811yescharacteristic
169D73—22no—
170#3343—731nomaximal, Sylow
171C73#334311yescharacteristic, complemented, Sylow
172#552—731no—
173#547—731no—
174#501—731no—
175#484—731no—
176#483—731no—
177#482—731no—
178#480—731no—
179#478—731no—
180#477—731no—
181#468D7311yescharacteristic, complemented
182#465—731no—
183#440—731no—
184#435—731no—
185#428—731no—
186C2×#107—731no—
187C2×#41—1461no—
188C2×SD16C2×D7311yescharacteristic
189C2×M16C2×D7311yescharacteristic
190C22×C8—731no—
191C4⋊Q8—731no—
192#126—1461no—
193#125—731no—
194#125—1461no—
195#123—1461no—
196#123—1461no—
197#123—1461no—
198C22⋊Q8—731no—
199C22⋊Q8—1461no—
200C22⋊Q8C2×D7311yescharacteristic
201#121—731no—
202#121C2×D7311yescharacteristic
203C4×Q8—731no—
204C4×D4—731no—
205C4×D4—731no—
206#117—731no—
207#117—1461no—
208C2×C4⋊C4—731no—
209C2×C4⋊C4—731no—
210C2×C4⋊C4—731no—
211#107—731no—
212#107—731no—
213#107—731no—
214#107—731no—
215#107—731no—
216#107C2×D7311yescharacteristic
217#106—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221#103—731no—
222#103—731no—
223#103C2×D7311yescharacteristic
224#102—731no—
225#102—731no—
226#102C2×D7311yescharacteristic
227C22⋊C8—731no—
228C22⋊C8—731no—
229#97—731no—
230#41—2924no—
231C2×Q8—1461no—
232C2×Q8C22×D7311yescharacteristic
233C2×D4—21no—
234C2×D4—731no—
235C2×D4—1461no—
236C2×D4C22×D7311yescharacteristic
237C22×C4—731no—
238C22×C4—1461no—
239C22×C4—1461no—
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4C22×D7311yescharacteristic
243SD16—22no—
244M16—22no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—1462no—
248C2×C8C22×D7311yescharacteristic
249C2×C8C22×D7311yescharacteristic
250C4⋊C4—21no—
251C4⋊C4—731no—
252C4⋊C4—731no—
253C4⋊C4—731no—
254C4⋊C4—731no—
255C4⋊C4—731no—
256C4⋊C4—1461no—
257C4⋊C4—1461no—
258C4⋊C4—1461no—
259C4⋊C4—1461no—
260C4⋊C4—1461no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4C22×D7311yescharacteristic
265C4⋊C4C22×D7311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—731no—
269C22⋊C4—731no—
270C22⋊C4—1461no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C42—731no—
275C42—1461no—
276C42—1461no—
277C23—21no—
278C23—731no—
279C23D4×D7311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—2922no—
283D4—21no—
284D4—21no—
285D4—42no—
286D4—2922no—
287D4—1462no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—2922no—
294C2×C4—2922no—
295C2×C4—2922no—
296C2×C4—2922no—
297C2×C4—731no—
298C2×C4—731no—
299C2×C4—731no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4D4×D7311yescharacteristic
307C2×C4C23×D7311yescharacteristic
308C8—21no—
309C8—1461no—
310C8—1461no—
311C8#1192402712yescomplemented
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22—732no—
319C22—1461no—
320C22—1461no—
321C22C2×D4×D7311yescharacteristic
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—2921no—
327C4—2921no—
328C4—2921no—
329C4—2921no—
330C4—1461no—
331C4—1461no—
332C4—1461no—
333C4C2×#1192402711yescharacteristic
334C4#1455663811yescharacteristic
335C2—41no—
336C2—81no—
337C2—1462no—
338C2#1798923711yescharacteristic
339C2AGL(1,ℤ/8)×D7311yescharacteristic
340C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#468×C73C2
socleC22×C73C22×D4
hypercenter#468D73
hypocenterC73#3343
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #17989271C2semidirect
3. #17988995C2semidirect
4. #17988920C2semidirect
5. #17988916C2semidirect
6. #17988908C2semidirect
7. #17988899C2semidirect
8. #17988889C2semidirect
9. #17988880C2semidirect
10. #17988813C2semidirect
11. #17988688C2semidirect
12. #17988656C2semidirect
13. #17988629C2semidirect
14. #107×D73C2semidirect
15. #468×C73C2semidirect
138. C8×C73#41semidirect
171. C73#3343semidirect
181. #468D73semidirect
311. C8#11924027semidirect