Finite Group Databasebeta

← #22620208

Subgroups — #22620208

Order 9344.

384 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#17989208C211yesmaximal, characteristic, complemented
2#17988917C211yesmaximal, characteristic, complemented
3#17988905C211yesmaximal, characteristic, complemented
4#17988877C211yesmaximal, characteristic, complemented
5#17988872C211yesmaximal, characteristic, complemented
6#17988809C211yesmaximal, characteristic, complemented
7#17988802C211yesmaximal, characteristic, complemented
8#17988749C211yesmaximal, characteristic, complemented
9#17988732C211yesmaximal, characteristic
10#17988697C211yesmaximal, characteristic, complemented
11#17988692C211yesmaximal, characteristic, complemented
12C4×#11924015C211yesmaximal, characteristic, complemented
13C4×#11924016C211yesmaximal, characteristic, complemented
14#17988648C211yesmaximal, characteristic, complemented
15#520×C73C211yesmaximal, characteristic, complemented
16C2×#11924018C2211yescharacteristic
17C2×#11924016C2211yescharacteristic
18C2×#11924015C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20#14556591C2211yescharacteristic
21#14556586—21no—
22#14556579C2211yescharacteristic
23#14556577—21no—
24#14556573—21no—
25#14556570C2211yescharacteristic
26#14556569—21no—
27#14556565C2211yescharacteristic
28C4×Dic146C2211yescharacteristic
29C4×D292C2211yescharacteristic
30#14556522C2211yescharacteristic
31#14556522C2211yescharacteristic
32#14556522C2211yescharacteristic
33#14556522C2211yescharacteristic
34C4⋊#10596831C2211yescharacteristic
35C4⋊#10596831C2211yescharacteristic
36#14556515C2211yescharacteristic
37#14556515C2211yescharacteristic
38#14556514C2211yescharacteristic
39#14556514C2211yescharacteristic
40#14556512C2211yescharacteristic
41#14556512C2211yescharacteristic
42#14556511C2211yescharacteristic
43#14556511C2211yescharacteristic
44C22⋊#10596831C2211yescharacteristic
45C22⋊#10596831C2211yescharacteristic
46#14556502C2211yescharacteristic
47C4×#10596831C2211yescharacteristic
48C2×#41×C73C2211yescharacteristic
49C4×Q8×C73C2211yescharacteristic
50C4×Q8×C73C2211yescharacteristic
51C4×D4×C73—21no—
52C4×D4×C73—21no—
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55#117×C73—21no—
56#117×C73C2211yescharacteristic
57C2×C4⋊C4×C73—21no—
58C2×C4⋊C4×C73C2211yescharacteristic
59C2×Dic146—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C4×D73—21no—
64#11924018—22no—
65#11924016—22no—
66#11924015—22no—
67#11924013—22no—
68C2×#10596831C2311yescharacteristic
69C2×#10596831C2311yescharacteristic
70C2×#10596831C2311yescharacteristic
71C2×#10596831C2311yescharacteristic
72C4⋊Dic73—21no—
73C4⋊Dic73C2311yescharacteristic
74C4⋊Dic73C2311yescharacteristic
75#11924007—21no—
76#11924007—21no—
77C22⋊Dic73—21no—
78#11924005—21no—
79#11924005—21no—
80#11924005—21no—
81#11924005—21no—
82C4×Dic73—21no—
83#41×C73—22no—
84#41×C73—22no—
85C2×Q8×C73C2311yescharacteristic
86C2×D4×C73—21no—
87C2×D4×C73C2311yescharacteristic
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—21no—
91C22×C4×C73—21no—
92C22×C4×C73C2311yescharacteristic
93C4⋊C4×C73—21no—
94C4⋊C4×C73—21no—
95C4⋊C4×C73—21no—
96C4⋊C4×C73D411yescharacteristic
97C4⋊C4×C73D411yescharacteristic
98C4⋊C4×C73C2311yescharacteristic
99C4⋊C4×C73C2311yescharacteristic
100C22⋊C4×C73—21no—
101C22⋊C4×C73—21no—
102C22⋊C4×C73D411yescharacteristic
103C22⋊C4×C73D411yescharacteristic
104C42×C73—21no—
105C42×C73—21no—
106C42×C73C2311yescharacteristic
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73C2×D411yescharacteristic
110C22×D73—21no—
111Q8×C73—21no—
112Q8×C73#4112yes—
113D4×C73—24no—
114D4×C73—21no—
115D4×C73#4112yes—
116C2×C4×C73—24no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73—81no—
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2×D411yescharacteristic
127C2×C4×C73C2×D411yescharacteristic
128C2×C4×C73C2×D411yescharacteristic
129C2×C4×C73C2×D411yescharacteristic
130C2×C4×C73C2411yescharacteristic
131C22⋊D73—81no—
132C2×Dic73—21no—
133C2×Dic73—21no—
134C2×Dic73—21no—
135D292—21no—
136D292—21no—
137C4×D73—81no—
138Dic146—21no—
139Dic146—21no—
140Dic146—81no—
141#10596831—21no—
142#10596831—21no—
143#10596831—21no—
144#10596831—21no—
145C22×C73—21no—
146C22×C73—22no—
147C22×C73—21no—
148C22×C73—21no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C4×C73—21no—
156C4×C73—22no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—41no—
162C4×C73—41no—
163C4×C73C2×#4111yescharacteristic
164C4×C73C2×#4111yescharacteristic
165Dic73—41no—
166Dic73—41no—
167Dic73—41no—
168C2×C73—41no—
169C2×C73—42no—
170C2×C73#52511yescharacteristic
171C2×C73#57711yescharacteristic
172C2×C73#57711yescharacteristic
173D73—81no—
174#3125—731nomaximal, Sylow
175C73#312511yescharacteristic, complemented, Sylow
176#542—731no—
177#520D7311yescharacteristic, complemented
178#483—731no—
179#481—731no—
180#476—731no—
181#475—731no—
182#464—731no—
183#463—731no—
184#452—731no—
185#449—731no—
186#442—731no—
187#441—731no—
188C4×SD16—731no—
189C4×SD16—731no—
190#433—731no—
191C2×#41C2×D7311yescharacteristic
192C2×Q16—731no—
193C2×SD16—731no—
194C2×SD16—731no—
195C2×D8—731no—
196C4⋊Q8—731no—
197#126—1461no—
198#124—731no—
199#124—1461no—
200#123—1461no—
201C22⋊Q8—731no—
202C22⋊Q8—1461no—
203#121—731no—
204C4×Q8—731no—
205C4×Q8C2×D7311yescharacteristic
206C4×Q8C2×D7311yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—731no—
210C4×D4C2×D7311yescharacteristic
211C4×D4C2×D7311yescharacteristic
212#117—21no—
213#117C2×D7311yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D7311yescharacteristic
216#106—731no—
217#106—731no—
218#106—731no—
219#106—731no—
220C4⋊C8—731no—
221C4⋊C8—731no—
222#103—731no—
223#103—731no—
224#103—731no—
225#103—731no—
226#102—731no—
227#102—731no—
228#102—731no—
229#102—731no—
230C22⋊C8—731no—
231C22⋊C8—731no—
232#97—731no—
233C4×C8—731no—
234#41—22no—
235#41—22no—
236C2×Q8—731no—
237C2×Q8—1461no—
238C2×Q8C22×D7311yescharacteristic
239C2×D4—21no—
240C2×D4—731no—
241C2×D4—1461no—
242C2×D4C22×D7311yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1461no—
248C22×C4C22×D7311yescharacteristic
249Q16—1462no—
250SD16—1462no—
251SD16—1462no—
252D8—1462no—
253C2×C8—731no—
254C2×C8—731no—
255C2×C8—731no—
256C2×C8—731no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—731no—
261C4⋊C4—731no—
262C4⋊C4—1461no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4C22⋊D7311yescharacteristic
266C4⋊C4C22⋊D7311yescharacteristic
267C4⋊C4C22×D7311yescharacteristic
268C4⋊C4C22×D7311yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1461no—
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4C22⋊D7311yescharacteristic
277C22⋊C4C22⋊D7311yescharacteristic
278C42—21no—
279C42—21no—
280C42—1461no—
281C42C22×D7311yescharacteristic
282C42C22×D7311yescharacteristic
283C23—21no—
284C23—1461no—
285C23C2×C22⋊D7311yescharacteristic
286Q8—21no—
287Q8—5841no—
288Q8—1461no—
289Q8—1461no—
290Q8#1192402812yes—
291D4—24no—
292D4—21no—
293D4—5841no—
294D4—1461no—
295D4—1461no—
296D4#1192402812yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—5841no—
307C2×C4—1461no—
308C2×C4—1461no—
309C2×C4—1461no—
310C2×C4C2×C22⋊D7311yescharacteristic
311C2×C4C2×C22⋊D7311yescharacteristic
312C2×C4C2×C22⋊D7311yescharacteristic
313C2×C4C2×C22⋊D7311yescharacteristic
314C2×C4C2×C22⋊D7311yescharacteristic
315C2×C4C23×D7311yescharacteristic
316C8—1461no—
317C8—1461no—
318C8—1461no—
319C8—1461no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—2921no—
327C22—2921no—
328C22—2921no—
329C22C22×C22⋊D7311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—2921no—
339C4—2921no—
340C4—2921no—
341C4C2×#1192402811yescharacteristic
342C4C2×#1192402811yescharacteristic
343C2—41no—
344C2—42no—
345C2—5841no—
346C2#1798909811yescharacteristic
347C2#1798939511yescharacteristic
348C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#520×C73C2
socleC22×C73C22×D4
hypercenter#520D73
hypocenterC73#3125
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #17989208C2semidirect
2. #17988917C2semidirect
3. #17988905C2semidirect
4. #17988877C2semidirect
5. #17988872C2semidirect
6. #17988809C2semidirect
7. #17988802C2semidirect
8. #17988749C2semidirect
10. #17988697C2semidirect
11. #17988692C2semidirect
12. C4×#11924015C2semidirect
13. C4×#11924016C2semidirect
14. #17988648C2semidirect
15. #520×C73C2semidirect
175. C73#3125semidirect
177. #520D73semidirect