Finite Group Databasebeta

← #22620224

Subgroups — #22620224

Order 9344.

382 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989193C211yesmaximal, characteristic
2#17989063C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988891C211yesmaximal, characteristic, complemented
6#17988788C211yesmaximal, characteristic, complemented
7#17988787C211yesmaximal, characteristic, complemented
8#17988727C211yesmaximal, characteristic, complemented
9#17988727C211yesmaximal, characteristic, complemented
10#17988690C211yesmaximal, characteristic, complemented
11#17988686C211yesmaximal, characteristic, complemented
12#17988674C211yesmaximal, characteristic, complemented
13#17988672C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#479×C73C211yesmaximal, characteristic, complemented
16C2×Q8×D73C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924015C2211yescharacteristic
20C2×#11924015C2211yescharacteristic
21#14556588C2211yescharacteristic
22#14556576—21no—
23#14556576—21no—
24#14556566—21no—
25#14556566—21no—
26#14556566C2211yescharacteristic
27#14556566C2211yescharacteristic
28Q8×Dic73C2211yescharacteristic
29C4×Dic146—21no—
30C4×Dic146C2211yescharacteristic
31#14556556—21no—
32#14556556C2211yescharacteristic
33#14556553C2211yescharacteristic
34#14556553C2211yescharacteristic
35#14556549—21no—
36#14556549C2211yescharacteristic
37#14556548—21no—
38#14556548C2211yescharacteristic
39#14556524C2211yescharacteristic
40#14556522C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic
42#14556514C2211yescharacteristic
43#14556514C2211yescharacteristic
44#14556513C2211yescharacteristic
45#14556513C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic
51C8×Dic73C2211yescharacteristic
52#125×C73C2211yescharacteristic
53C4×Q8×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic
55#106×C73C2211yescharacteristic
56C4⋊C8×C73C2211yescharacteristic
57#103×C73C2211yescharacteristic
58#103×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61Q8×D73—22no—
62Q8×D73—22no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73C2311yescharacteristic
73#11924017—22no—
74#11924017—22no—
75#11924015—22no—
76#11924015—22no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81#11924007—21no—
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005D411yescharacteristic
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73C2311yescharacteristic
98C2×C8×C73C2311yescharacteristic
99C2×C8×C73C2311yescharacteristic
100C4⋊C4×C73—21no—
101C4⋊C4×C73—21no—
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C42×C73—21no—
107C42×C73C2311yescharacteristic
108C22×D73—21no—
109C22×D73—21no—
110C22×D73C2×D411yescharacteristic
111Q8×C73—21no—
112Q8×C73#4112yes—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2411yescharacteristic
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73C2×D411yescharacteristic
123C2×Dic73C2×D411yescharacteristic
124C2×Dic73C2×D411yescharacteristic
125D292—21no—
126D292—21no—
127D292—21no—
128D292—21no—
129D292—81no—
130D292—81no—
131D292—81no—
132D292—81no—
133C4×D73—24no—
134C4×D73—21no—
135C4×D73—21no—
136C4×D73—81no—
137C4×D73—81no—
138Dic146—24no—
139Dic146—21no—
140Dic146#4112yes—
141C8×C73—21no—
142C8×C73—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73C22×D411yescharacteristic
146C2×D73—21no—
147C2×D73—21no—
148C2×D73—21no—
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—22no—
156C4×C73—21no—
157C4×C73—21no—
158C4×C73—41no—
159C4×C73—41no—
160C4×C73—41no—
161C4×C73C2×#4111yescharacteristic
162C4×C73C2×#4111yescharacteristic
163Dic73—21no—
164Dic73—22no—
165Dic73—21no—
166Dic73—21no—
167Dic73—41no—
168C2×C73#52511yescharacteristic
169C2×C73#57711yescharacteristic
170C2×C73#57711yescharacteristic
171D73—41no—
172D73—81no—
173D73—81no—
174#3126—731nomaximal, Sylow
175C73#312611yescharacteristic, complemented, Sylow
176#540—731no—
177#519—731no—
178#482—731no—
179#482—731no—
180#479—731no—
181#479D7311yescharacteristic, complemented
182#460—731no—
183#460—731no—
184#448—731no—
185#448—731no—
186#440—731no—
187#440—731no—
188C4×SD16—731no—
189C4×SD16—731no—
190#433—731no—
191C22×Q8—731no—
192C2×SD16—731no—
193C2×SD16—731no—
194C2×SD16—731no—
195C2×SD16—731no—
196#127—731no—
197#125C2×D7311yescharacteristic
198#123—1461no—
199#123—1461no—
200#121—731no—
201#121—731no—
202#121—1461no—
203#121—1461no—
204C4×Q8—731no—
205C4×Q8—731no—
206C4×Q8—731no—
207C4×Q8—1461no—
208C4×Q8—1461no—
209C4×Q8C2×D7311yescharacteristic
210C4×D4—731no—
211C4×D4—731no—
212#117—731no—
213#117—731no—
214#117—1461no—
215#117—1461no—
216#107—731no—
217#107C2×D7311yescharacteristic
218#106—731no—
219#106C2×D7311yescharacteristic
220C4⋊C8—731no—
221C4⋊C8C2×D7311yescharacteristic
222#103—731no—
223#103—731no—
224#103C2×D7311yescharacteristic
225#103C2×D7311yescharacteristic
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230C22⋊C8—731no—
231C22⋊C8—731no—
232#97—731no—
233C4×C8—731no—
234C2×Q8—731no—
235C2×Q8—1461no—
236C2×Q8—1462no—
237C2×Q8—1462no—
238C2×Q8C22×D7311yescharacteristic
239C2×D4—731no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4—1461no—
243C2×D4—1461no—
244C2×D4—1461no—
245C22×C4—731no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249SD16—1462no—
250SD16—1462no—
251SD16—1462no—
252SD16—1462no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8C22×D7311yescharacteristic
256C2×C8C22×D7311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—731no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4C22×D7311yescharacteristic
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—731no—
270C22⋊C4—731no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C42—21no—
277C42—731no—
278C42—1461no—
279C42—1461no—
280C42—1461no—
281C42—1461no—
282C42C22×D7311yescharacteristic
283C23—731no—
284C23—1461no—
285C23—1461no—
286Q8—21no—
287Q8—732no—
288Q8—1464no—
289Q8—1461no—
290Q8#1192402912yes—
291D4—5841no—
292D4—5841no—
293D4—5841no—
294D4—5841no—
295D4—1461no—
296D4—1461no—
297D4—1461no—
298D4—1461no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—5841no—
304C2×C4—5841no—
305C2×C4—731no—
306C2×C4—731no—
307C2×C4—731no—
308C2×C4—1464no—
309C2×C4—1461no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4D4×D7311yescharacteristic
314C2×C4D4×D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—21no—
317C8—21no—
318C8—1461no—
319C8—1461no—
320C22—2921no—
321C22—2921no—
322C22—2921no—
323C22—2921no—
324C22—2921no—
325C22—2921no—
326C22—1461no—
327C22—1461no—
328C22—1461no—
329C22C2×D4×D7311yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—2921no—
337C4—1461no—
338C4—1461no—
339C4—1461no—
340C4—1462no—
341C4#41×D7311yescharacteristic
342C4C2×#1192402911yescharacteristic
343C2—2921no—
344C2—5841no—
345C2—5841no—
346C2#1798910011yescharacteristic
347C2#1798939411yescharacteristic
348C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#479×C73C2
socleC22×C73C22×D4
hypercenter#479D73
hypocenterC73#3126
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
2. #17989063C2semidirect
3. #17988914C2semidirect
4. #17988913C2semidirect
5. #17988891C2semidirect
6. #17988788C2semidirect
7. #17988787C2semidirect
8. #17988727C2semidirect
9. #17988727C2semidirect
10. #17988690C2semidirect
11. #17988686C2semidirect
12. #17988674C2semidirect
13. #17988672C2semidirect
14. #17988647C2semidirect
15. #479×C73C2semidirect
175. C73#3126semidirect
181. #479D73semidirect