Finite Group Databasebeta

← #22624040

Subgroups — #22624040

Order 9344.

1030 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#17989320C213yesmaximal, complemented
2#17989313C211yesmaximal, characteristic, complemented
3#17989300C213yesmaximal, complemented
4#17989287C213yesmaximal, complemented
5#17989276C213yesmaximal, complemented
6#17989256C211yesmaximal, characteristic, complemented
7#17989249C211yesmaximal, characteristic, complemented
8#17989244C211yesmaximal, characteristic, complemented
9#17989202C213yesmaximal, complemented
10#17989188C213yesmaximal, complemented
11#17989121C213yesmaximal, complemented
12#17989121C213yesmaximal, complemented
13#17989069C211yesmaximal, characteristic, complemented
14#17989063C211yesmaximal, characteristic, complemented
15C4×#41×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18#14556590C2213yes—
19#14556587C2213yes—
20#14556585C2211yescharacteristic
21#14556585C2213yes—
22#14556584C2216yes—
23#14556583C2213yes—
24#14556583C2213yes—
25#14556582C2213yes—
26#14556579C2213yes—
27#14556579C2213yes—
28#14556578C2213yes—
29#14556577C2216yes—
30#14556574C2216yes—
31#14556574C2213yes—
32#14556574C2213yes—
33#14556573C2216yes—
34#14556571C2213yes—
35#14556570C2213yes—
36#14556570C2213yes—
37#14556566C2213yes—
38#14556565C2213yes—
39#14556565C2213yes—
40#14556564C2216yes—
41#14556562C2213yes—
42#14556562C2213yes—
43Q8×Dic73C2211yescharacteristic
44Q8×Dic73C2211yescharacteristic
45C4×Dic146C2213yes—
46C4×Dic146C2213yes—
47#14556556C2213yes—
48C4×D292C2213yes—
49C4×D292C2213yes—
50#14556553C2213yes—
51C4×C22⋊D73C2213yes—
52C4×C22⋊D73C2213yes—
53C4×C22⋊D73C2216yes—
54#14556549C2213yes—
55#14556548C2213yes—
56#14556548C2213yes—
57#14556548C2216yes—
58C4⋊C4×D73C2213yes—
59C2×#41×C73C2211yescharacteristic
60C4×Q8×C73C2211yescharacteristic
61C4×Q8×C73C2211yescharacteristic
62C4×D4×C73C2213yes—
63C4×D4×C73C2213yes—
64#117×C73C2213yes—
65C2×C42×C73C2213yes—
66#11924029—24no—
67C2×Dic146C2313yes—
68C2×Dic146C2313yes—
69Q8×D73—24no—
70C2×D292C2313yes—
71C2×D292C2313yes—
72C2×C22⋊D73C2313yes—
73C2×C22⋊D73C2316yes—
74C2×C22⋊D73C2313yes—
75C2×C4×D73C2313yes—
76C2×C4×D73C2313yes—
77C2×C4×D73C2316yes—
78C4⋊Dic73C2313yes—
79C4⋊Dic73C2313yes—
80C4⋊Dic73C2313yes—
81C4⋊Dic73C2313yes—
82#11924007C2313yes—
83#11924007C2311yescharacteristic
84#11924007C2313yes—
85#11924007C2313yes—
86#11924007C2313yes—
87#11924007C2316yes—
88#11924007C2311yescharacteristic
89#11924007C2313yes—
90#11924007C2311yescharacteristic
91C22⋊Dic73C2313yes—
92C22⋊Dic73C2316yes—
93C22⋊Dic73C2313yes—
94#11924005C2311yescharacteristic
95#11924005C2313yes—
96#11924005C2313yes—
97#11924005C2313yes—
98#11924005C2313yes—
99#11924005C2316yes—
100#11924005C2311yescharacteristic
101#11924005C2313yes—
102#11924005C2311yescharacteristic
103C4×Dic73C2316yes—
104C4×Dic73C2313yes—
105C4×Dic73C2313yes—
106#41×C73—24no—
107C2×Q8×C73C2311yescharacteristic
108C2×D4×C73C2313yes—
109C22×C4×C73C2313yes—
110C22×C4×C73C2313yes—
111C22×C4×C73C2313yes—
112C4⋊C4×C73C2313yes—
113C4⋊C4×C73C2313yes—
114C22⋊C4×C73C2316yes—
115C42×C73C2311yescharacteristic
116C42×C73C2313yes—
117C42×C73C2313yes—
118C42×C73C2313yes—
119C23×C73C2413yes—
120C22×D73C2411yescharacteristic
121C22×D73C2413yes—
122Q8×C73#4114yes—
123D4×C73—26no—
124C2×C4×C73—26no—
125C2×C4×C73—43no—
126C2×C4×C73—43no—
127C2×C4×C73C2411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C2×C4×C73C2411yescharacteristic
130C2×C4×C73C2413yes—
131C2×C4×C73C2413yes—
132C2×C4×C73C2413yes—
133C22⋊D73—46no—
134C22⋊D73—43no—
135C22⋊D73—43no—
136C2×Dic73C2411yescharacteristic
137C2×Dic73C2413yes—
138C2×Dic73C2411yescharacteristic
139C2×Dic73C2413yes—
140C2×Dic73C2413yes—
141C2×Dic73C2411yescharacteristic
142D292—26no—
143D292—43no—
144C4×D73—26no—
145C4×D73—26no—
146C4×D73—46no—
147Dic146—26no—
148Dic146—43no—
149C22×C73—23no—
150C22×C73—23no—
151C22×C73—23no—
152C22×C73C2511yescharacteristic
153C2×D73—21no—
154C2×D73—23no—
155C2×D73—23no—
156C2×D73—21no—
157C2×D73—23no—
158C2×D73—21no—
159C4×C73—21no—
160C4×C73—23no—
161C4×C73—23no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73C2×#4116yes—
165Dic73—23no—
166Dic73—21no—
167Dic73—21no—
168Dic73—23no—
169Dic73—23no—
170Dic73—21no—
171C2×C73—43no—
172C2×C73C22×#4111yescharacteristic
173C2×C73#58511yescharacteristic
174C2×C73#58511yescharacteristic
175D73—41no—
176D73—43no—
177#3524—731nomaximal, Sylow
178C73#352411yescharacteristic, complemented, Sylow
179#559—733no—
180#557—731no—
181#555—733no—
182#553—733no—
183#552—733no—
184#550—731no—
185#548—731no—
186#548—731no—
187#542—733no—
188#540—733no—
189#529—733no—
190#529—733no—
191#520—731no—
192#519—731no—
193C4×#41D7311yescharacteristic, complemented
194C2×#41—731no—
195C2×#41C2×D7311yescharacteristic
196C22×Q8—731no—
197C4⋊Q8—733no—
198#127—733no—
199#126—736no—
200#126—731no—
201#126—733no—
202#125—733no—
203#125—733no—
204#125—733no—
205#124—733no—
206#124—736no—
207#124—733no—
208#124—733no—
209#123—736no—
210#123—733no—
211#123—733no—
212#123—736no—
213C22⋊Q8—733no—
214C22⋊Q8—733no—
215C22⋊Q8—733no—
216#121—733no—
217#121—733no—
218#121—733no—
219#121—733no—
220#121—733no—
221#121—736no—
222C4×Q8—731no—
223C4×Q8—731no—
224C4×Q8—733no—
225C4×Q8—733no—
226C4×Q8—733no—
227C4×Q8C2×D7311yescharacteristic
228C4×Q8C2×D7311yescharacteristic
229C4×D4—733no—
230C4×D4—733no—
231C4×D4—736no—
232C4×D4—733no—
233C4×D4—733no—
234C4×D4—733no—
235C4×D4C2×D7313yes—
236C4×D4C2×D7313yes—
237#117—733no—
238#117—733no—
239#117—733no—
240#117—736no—
241#117C2×D7313yes—
242C2×C4⋊C4—733no—
243C2×C42C2×D7313yes—
244#41—24no—
245#41—1464no—
246C2×Q8—733no—
247C2×Q8—733no—
248C2×Q8—1464no—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—733no—
251C2×D4—736no—
252C2×D4—733no—
253C2×D4—733no—
254C2×D4—733no—
255C2×D4C22×D7313yes—
256C22×C4—736no—
257C22×C4—733no—
258C22×C4—733no—
259C22×C4C22×D7313yes—
260C22×C4C22×D7313yes—
261C22×C4C22×D7313yes—
262C4⋊C4—733no—
263C4⋊C4—731no—
264C4⋊C4—733no—
265C4⋊C4—733no—
266C4⋊C4—733no—
267C4⋊C4—736no—
268C4⋊C4—731no—
269C4⋊C4—733no—
270C4⋊C4—731no—
271C4⋊C4—733no—
272C4⋊C4—733no—
273C4⋊C4—733no—
274C4⋊C4—733no—
275C4⋊C4C22×D7313yes—
276C4⋊C4C22×D7313yes—
277C22⋊C4—733no—
278C22⋊C4—736no—
279C22⋊C4—733no—
280C22⋊C4—731no—
281C22⋊C4—733no—
282C22⋊C4—733no—
283C22⋊C4—733no—
284C22⋊C4—733no—
285C22⋊C4—736no—
286C22⋊C4—731no—
287C22⋊C4—733no—
288C22⋊C4—731no—
289C22⋊C4C22×D7316yes—
290C42—736no—
291C42—733no—
292C42—733no—
293C42C22×D7311yescharacteristic
294C42C22×D7313yes—
295C42C22×D7313yes—
296C42C22×D7313yes—
297C23—731no—
298C23—733no—
299C23C23×D7313yes—
300Q8—2923no—
301Q8—1466no—
302Q8#1192402814yes—
303D4—26no—
304D4—2923no—
305D4—2923no—
306D4—2923no—
307D4—2926no—
308D4—1466no—
309C2×C4—26no—
310C2×C4—43no—
311C2×C4—43no—
312C2×C4—2926no—
313C2×C4—731no—
314C2×C4—733no—
315C2×C4—731no—
316C2×C4—733no—
317C2×C4—733no—
318C2×C4—731no—
319C2×C4—1466no—
320C2×C4—1466no—
321C2×C4C23×D7313yes—
322C2×C4C23×D7311yescharacteristic
323C2×C4C23×D7311yescharacteristic
324C2×C4C23×D7311yescharacteristic
325C2×C4C23×D7313yes—
326C2×C4C23×D7313yes—
327C22—23no—
328C22—23no—
329C22—23no—
330C22—1461no—
331C22—1463no—
332C22—1463no—
333C22—1461no—
334C22—1463no—
335C22—1461no—
336C22C24×D7311yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—23no—
342C4—1461no—
343C4—1463no—
344C4—1463no—
345C4—1461no—
346C4—1463no—
347C4—1461no—
348C4C2×#1192402816yes—
349C2—43no—
350C2—2921no—
351C2—2923no—
352C2C22×#1192402811yescharacteristic
353C2#1798942311yescharacteristic
354C2#1798942311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
FittingC4×#41×C73C2
hypercenterC4×#41D73
hypocenterC73#3524
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #17989320C2semidirect
2. #17989313C2semidirect
3. #17989300C2semidirect
4. #17989287C2semidirect
5. #17989276C2semidirect
6. #17989256C2semidirect
7. #17989249C2semidirect
8. #17989244C2semidirect
9. #17989202C2semidirect
10. #17989188C2semidirect
11. #17989121C2semidirect
12. #17989121C2semidirect
13. #17989069C2semidirect
14. #17989063C2semidirect
15. C4×#41×C73C2semidirect
178. C73#3524semidirect
193. C4×#41D73semidirect