Finite Group Databasebeta

← #22622999

Subgroups — #22622999

Order 9344.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989322C211yesmaximal, characteristic, complemented
2#17989310C211yesmaximal, characteristic, complemented
3#17988981C211yesmaximal, characteristic, complemented
4#17988976C211yesmaximal, characteristic
5#17988971C211yesmaximal, characteristic, complemented
6#17988810C211yesmaximal, characteristic, complemented
7#17988810C211yesmaximal, characteristic, complemented
8#17988803C211yesmaximal, characteristic, complemented
9#17988803C211yesmaximal, characteristic, complemented
10#17988793C211yesmaximal, characteristic, complemented
11#17988788C211yesmaximal, characteristic, complemented
12#17988700C211yesmaximal, characteristic, complemented
13#17988695C211yesmaximal, characteristic, complemented
14C4×#11924017C211yesmaximal, characteristic, complemented
15#446×C73C211yesmaximal, characteristic, complemented
16C2×Dic292C2211yescharacteristic
17C2×Dic292C2211yescharacteristic
18C2×#11924017C2211yescharacteristic
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic
21C2×#11924017C2211yescharacteristic
22C2×#11924017C2211yescharacteristic
23C2×D584C2211yescharacteristic
24C2×D584C2211yescharacteristic
25#14556591C2211yescharacteristic
26#14556588C2211yescharacteristic
27#14556586—21no—
28#14556586—21no—
29#14556580—21no—
30#14556579C2211yescharacteristic
31#14556579C2211yescharacteristic
32#14556579C2211yescharacteristic
33#14556579C2211yescharacteristic
34#14556576—21no—
35#14556576—21no—
36#14556567—21no—
37C4×Dic146C2211yescharacteristic
38C4×Dic146C2211yescharacteristic
39C4×Dic146C2211yescharacteristic
40C4×D292C2211yescharacteristic
41C4×D292C2211yescharacteristic
42C4×D292C2211yescharacteristic
43#14556553—21no—
44#14556549—21no—
45#14556523C2211yescharacteristic
46#14556516C2211yescharacteristic
47#14556516C2211yescharacteristic
48#14556516C2211yescharacteristic
49#14556513C2211yescharacteristic
50#14556513C2211yescharacteristic
51#14556513C2211yescharacteristic
52C4×Q8×C73C2211yescharacteristic
53C4⋊C8×C73C2211yescharacteristic
54C4⋊C8×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic
56#97×C73C2211yescharacteristic
57#97×C73C2211yescharacteristic
58C4×C8×C73C2211yescharacteristic
59C2×Dic146C2311yescharacteristic
60C2×Dic146C2311yescharacteristic
61C2×Dic146C2311yescharacteristic
62C2×D292—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C4×D73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70Dic292—22no—
71Dic292—41no—
72#11924017—22no—
73#11924017—41no—
74#11924017—41no—
75#11924017—41no—
76#11924017—41no—
77D584—22no—
78D584—41no—
79C4⋊Dic73—21no—
80C4⋊Dic73—21no—
81C4⋊Dic73C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007—21no—
84#11924007—21no—
85#11924007—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C4×Dic73—21no—
100C2×Q8×C73D411yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C2×C8×C73C2311yescharacteristic
104C2×C8×C73C2311yescharacteristic
105C4⋊C4×C73D411yescharacteristic
106C4⋊C4×C73D411yescharacteristic
107C4⋊C4×C73D411yescharacteristic
108C42×C73C2311yescharacteristic
109C42×C73C2311yescharacteristic
110C42×C73C2311yescharacteristic
111C22×D73—21no—
112C22×D73—21no—
113C22×D73—21no—
114Q8×C73—41no—
115C2×C4×C73C2×D411yescharacteristic
116C2×C4×C73C2×D411yescharacteristic
117C2×C4×C73C2×D411yescharacteristic
118C2×C4×C73C2×D411yescharacteristic
119C2×C4×C73C2×D411yescharacteristic
120C2×C4×C73C2×D411yescharacteristic
121C2×C4×C73C2411yescharacteristic
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127D292—21no—
128D292—21no—
129D292—21no—
130D292—21no—
131D292—21no—
132D292—21no—
133D292—42no—
134D292—81no—
135C4×D73—42no—
136C4×D73—81no—
137C4×D73—81no—
138Dic146—21no—
139Dic146—21no—
140Dic146—21no—
141Dic146—21no—
142Dic146—21no—
143Dic146—21no—
144C8×C73—21no—
145C8×C73—21no—
146C8×C73—21no—
147C8×C73#4112yes—
148C22×C73C22×D411yescharacteristic
149C2×D73—41no—
150C2×D73—41no—
151C2×D73—41no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C2×D73—41no—
157C2×D73—41no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—21no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73C2×#4111yescharacteristic
165C4×C73H(5,𝔽2)11yescharacteristic
166Dic73—41no—
167Dic73—41no—
168Dic73—41no—
169Dic73—41no—
170Dic73—41no—
171C2×C73#55011yescharacteristic
172C2×C73#57511yescharacteristic
173C2×C73#57711yescharacteristic
174D73—81no—
175D73—81no—
176D73—81no—
177#3401—731nomaximal, Sylow
178C73#340111yescharacteristic, complemented, Sylow
179#559—731no—
180#556—731no—
181#497—731no—
182#496—731no—
183#495—731no—
184#464—731no—
185#464—731no—
186#463—731no—
187#463—731no—
188#461—731no—
189#460—731no—
190#446D7311yescharacteristic, complemented
191#442—731no—
192#441—731no—
193C4×SD16—731no—
194C2×Q16—731no—
195C2×Q16—731no—
196C2×SD16—731no—
197C2×SD16—731no—
198C2×SD16—731no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×D8—731no—
202C2×D8—731no—
203C4⋊Q8—731no—
204#127—731no—
205#126—1461no—
206#126—1461no—
207#124—731no—
208#124—731no—
209#124—731no—
210#124—731no—
211#124—1461no—
212#123—1461no—
213#123—1461no—
214C22⋊Q8—1461no—
215C4×Q8—731no—
216C4×Q8—731no—
217C4×Q8—731no—
218C4×Q8C2×D7311yescharacteristic
219C4×D4—731no—
220C4×D4—731no—
221C4×D4—731no—
222C4×D4—1461no—
223#117—1461no—
224#106—731no—
225C4⋊C8C2×D7311yescharacteristic
226C4⋊C8C2×D7311yescharacteristic
227C4⋊C8C2×D7311yescharacteristic
228#103—731no—
229#103—731no—
230#103—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#97C2×D7311yescharacteristic
235#97C2×D7311yescharacteristic
236C4×C8C2×D7311yescharacteristic
237C2×Q8—731no—
238C2×Q8—731no—
239C2×Q8—731no—
240C2×Q8D29211yescharacteristic
241C2×D4—731no—
242C2×D4—731no—
243C2×D4—731no—
244C2×D4—1461no—
245C2×D4—1461no—
246C22×C4—1461no—
247C22×C4—1461no—
248C22×C4—1461no—
249Q16—2921no—
250Q16—1462no—
251SD16—2921no—
252SD16—2921no—
253SD16—2921no—
254SD16—2921no—
255SD16—1462no—
256D8—2921no—
257D8—1462no—
258C2×C8C22×D7311yescharacteristic
259C2×C8C22×D7311yescharacteristic
260C2×C8C22×D7311yescharacteristic
261C2×C8C22×D7311yescharacteristic
262C4⋊C4—731no—
263C4⋊C4—731no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C4⋊C4—1461no—
268C4⋊C4—1461no—
269C4⋊C4D29211yescharacteristic
270C4⋊C4D29211yescharacteristic
271C4⋊C4D29211yescharacteristic
272C22⋊C4—1461no—
273C22⋊C4—1461no—
274C22⋊C4—1461no—
275C22⋊C4—1461no—
276C22⋊C4—1461no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C42—1461no—
284C42—1461no—
285C42—1461no—
286C42C22×D7311yescharacteristic
287C42C22×D7311yescharacteristic
288C42C22×D7311yescharacteristic
289C23—1461no—
290C23—1461no—
291C23—1461no—
292Q8—41no—
293Q8—1461no—
294Q8—1461no—
295Q8—1461no—
296Q8—1461no—
297Q8—1461no—
298Q8—1461no—
299D4—2922no—
300D4—5841no—
301D4—1461no—
302D4—1461no—
303D4—1461no—
304D4—1461no—
305D4—1461no—
306D4—1461no—
307C2×C4—2922no—
308C2×C4—5841no—
309C2×C4—5841no—
310C2×C4—1461no—
311C2×C4—1461no—
312C2×C4—1461no—
313C2×C4—1461no—
314C2×C4—1461no—
315C2×C4C2×D29211yescharacteristic
316C2×C4C2×D29211yescharacteristic
317C2×C4C2×D29211yescharacteristic
318C2×C4C2×D29211yescharacteristic
319C2×C4C2×D29211yescharacteristic
320C2×C4C2×D29211yescharacteristic
321C2×C4C23×D7311yescharacteristic
322C8—21no—
323C8—21no—
324C8—21no—
325C8#1192402912yes—
326C22—2921no—
327C22—2921no—
328C22—2921no—
329C22—2921no—
330C22—2921no—
331C22—2921no—
332C22—2921no—
333C22—2921no—
334C22—2921no—
335C22C22×D29211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—2921no—
343C4—2921no—
344C4—2921no—
345C4—2921no—
346C4—2921no—
347C4C2×#1192402911yescharacteristic
348C4#1455663711yescharacteristic
349C2—5841no—
350C2—5841no—
351C2—5841no—
352C2#1798925911yescharacteristic
353C2#1798938711yescharacteristic
354C2#1798939911yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#446×C73C2
socleC22×C73C22×D4
hypercenter#446D73
hypocenterC73#3401
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #17989322C2semidirect
2. #17989310C2semidirect
3. #17988981C2semidirect
5. #17988971C2semidirect
6. #17988810C2semidirect
7. #17988810C2semidirect
8. #17988803C2semidirect
9. #17988803C2semidirect
10. #17988793C2semidirect
11. #17988788C2semidirect
12. #17988700C2semidirect
13. #17988695C2semidirect
14. C4×#11924017C2semidirect
15. #446×C73C2semidirect
178. C73#3401semidirect
190. #446D73semidirect