Finite Group Databasebeta

← #22623924

Subgroups — #22623924

Order 9344.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989313C211yesmaximal, characteristic, complemented
2#17989309C213yesmaximal, complemented
3#17989292C213yesmaximal, complemented
4#17989285C213yesmaximal, complemented
5#17989278C213yesmaximal, complemented
6Q8×C22⋊D73C211yesmaximal, characteristic, complemented
7#17989249C211yesmaximal, characteristic, complemented
8#17989248C211yesmaximal, characteristic, complemented
9#17989209C213yesmaximal, complemented
10#17989195C213yesmaximal, complemented
11#17989121C213yesmaximal, complemented
12#17989121C213yesmaximal, complemented
13#17989069C211yesmaximal, characteristic, complemented
14#17989063C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18#14556590C2213yes—
19#14556589C2213yes—
20#14556586C2216yes—
21#14556585C2216yes—
22#14556585C2213yes—
23#14556585C2213yes—
24#14556583C2213yes—
25#14556583C2213yes—
26#14556582C2213yes—
27#14556581C2216yes—
28#14556580C2213yes—
29#14556579C2213yes—
30#14556579C2213yes—
31#14556576C2216yes—
32#14556574C2211yescharacteristic
33#14556574C2213yes—
34#14556571C2213yes—
35#14556570C2213yes—
36#14556570C2213yes—
37#14556569C2216yes—
38#14556567C2213yes—
39#14556567C2213yes—
40#14556566C2213yes—
41#14556565C2213yes—
42#14556565C2213yes—
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—
59C22×Q8×C73C2211yescharacteristic
60C4×Q8×C73C2213yes—
61C4×Q8×C73C2211yescharacteristic
62C4×Q8×C73C2213yes—
63C4×Q8×C73C2211yescharacteristic
64C2×C4⋊C4×C73C2213yes—
65C2×C42×C73C2213yes—
66#11924029—24no—
67C2×Dic146C2313yes—
68C2×Dic146C2313yes—
69Q8×D73—24no—
70C2×D292C2313yes—
71C2×D292C2313yes—
72C2×C22⋊D73C2313yes—
73C2×C22⋊D73C2311yescharacteristic
74C2×C4×D73C2313yes—
75C2×C4×D73C2313yes—
76C2×C4×D73C2316yes—
77C4⋊Dic73C2313yes—
78C4⋊Dic73C2313yes—
79C4⋊Dic73C2313yes—
80C4⋊Dic73C2313yes—
81#11924007C2313yes—
82#11924007C2311yescharacteristic
83#11924007C2313yes—
84#11924007C2313yes—
85#11924007C2313yes—
86#11924007C2316yes—
87#11924007C2313yes—
88#11924007C2316yes—
89#11924007C2313yes—
90#11924007C2311yescharacteristic
91C22⋊Dic73C2311yescharacteristic
92C22⋊Dic73C2313yes—
93#11924005C2311yescharacteristic
94#11924005C2313yes—
95#11924005C2313yes—
96#11924005C2313yes—
97#11924005C2313yes—
98#11924005C2316yes—
99#11924005C2316yes—
100#11924005C2313yes—
101#11924005C2313yes—
102#11924005C2311yescharacteristic
103C4×Dic73C2316yes—
104C4×Dic73C2313yes—
105C4×Dic73C2313yes—
106C2×Q8×C73—24no—
107C2×Q8×C73C2313yes—
108C2×Q8×C73C2311yescharacteristic
109C22×C4×C73C2311yescharacteristic
110C22×C4×C73C2313yes—
111C22×C4×C73C2313yes—
112C4⋊C4×C73C2313yes—
113C4⋊C4×C73C2313yes—
114C4⋊C4×C73C2316yes—
115C42×C73C2313yes—
116C42×C73C2313yes—
117C42×C73C2313yes—
118C42×C73C2313yes—
119C23×C73C2411yescharacteristic
120C22×D73C2411yescharacteristic
121C22×D73C2413yes—
122Q8×C73—26no—
123Q8×C73#4114yes—
124C2×C4×C73—22no—
125C2×C4×C73—26no—
126C2×C4×C73—43no—
127C2×C4×C73C2411yescharacteristic
128C2×C4×C73C2411yescharacteristic
129C2×C4×C73C2413yes—
130C2×C4×C73C2413yes—
131C2×C4×C73C2413yes—
132C2×C4×C73C2413yes—
133C22⋊D73—26no—
134C22⋊D73—22no—
135C2×Dic73C2411yescharacteristic
136C2×Dic73C2413yes—
137C2×Dic73C2411yescharacteristic
138C2×Dic73C2413yes—
139C2×Dic73C2413yes—
140C2×Dic73C2411yescharacteristic
141D292—26no—
142D292—43no—
143C4×D73—26no—
144C4×D73—26no—
145C4×D73—46no—
146Dic146—26no—
147Dic146—43no—
148C22×C73—21no—
149C22×C73—21no—
150C22×C732−1+412yes—
151C22×C73C2511yescharacteristic
152C2×D73—21no—
153C2×D73—23no—
154C2×D73—21no—
155C2×D73—23no—
156C2×D73—23no—
157C2×D73—21no—
158C4×C73—23no—
159C4×C73—21no—
160C4×C73—21no—
161C4×C73—23no—
162C4×C73—23no—
163C4×C73C2×#4116yes—
164Dic73—23no—
165Dic73—21no—
166Dic73—23no—
167Dic73—21no—
168Dic73—21no—
169Dic73—23no—
170C2×C73—22no—
171C2×C73C22×#4111yescharacteristic
172C2×C73C2×2−1+411yescharacteristic
173C2×C73#58511yescharacteristic
174D73—41no—
175D73—43no—
176#3516—731nomaximal, Sylow
177C73#351611yescharacteristic, complemented, Sylow
178#557—731no—
179#556—733no—
180#554—733no—
181#553—733no—
182#552—733no—
183D4×Q8—731no—
184#548—731no—
185#548—731no—
186#542—733no—
187#541—733no—
188#529—733no—
189#529—733no—
190#520—731no—
191#519—731no—
192C2×C4×Q8D7311yescharacteristic, complemented
193C2×#41—731no—
194C22×Q8—731no—
195C22×Q8C2×D7311yescharacteristic
196C4⋊Q8—733no—
197C4⋊Q8—733no—
198#126—736no—
199#126—736no—
200#126—733no—
201#126—733no—
202#125—736no—
203#125—733no—
204#125—733no—
205#125—733no—
206#124—733no—
207#124—733no—
208#124—733no—
209#123—731no—
210#123—733no—
211#123—736no—
212C22⋊Q8—733no—
213C22⋊Q8—733no—
214C22⋊Q8—733no—
215C22⋊Q8—733no—
216C22⋊Q8—733no—
217C22⋊Q8—736no—
218#121—733no—
219#121—733no—
220#121—733no—
221C4×Q8—731no—
222C4×Q8—731no—
223C4×Q8—733no—
224C4×Q8—733no—
225C4×Q8—733no—
226C4×Q8C2×D7311yescharacteristic
227C4×Q8C2×D7313yes—
228C4×Q8C2×D7311yescharacteristic
229C4×Q8C2×D7313yes—
230C4×D4—733no—
231C4×D4—733no—
232C4×D4—736no—
233C4×D4—733no—
234C4×D4—733no—
235C4×D4—733no—
236#117—733no—
237#117—733no—
238#117—733no—
239#117—736no—
240C2×C4⋊C4—733no—
241C2×C4⋊C4C2×D7313yes—
242C2×C42C2×D7313yes—
243#41—1464no—
244C2×Q8—24no—
245C2×Q8—733no—
246C2×Q8—733no—
247C2×Q8—1464no—
248C2×Q8C22×D7313yes—
249C2×Q8C22×D7311yescharacteristic
250C2×D4—733no—
251C2×D4—731no—
252C2×D4—733no—
253C2×D4—733no—
254C22×C4—736no—
255C22×C4—733no—
256C22×C4—733no—
257C22×C4C22×D7311yescharacteristic
258C22×C4C22×D7313yes—
259C22×C4C22×D7313yes—
260C4⋊C4—733no—
261C4⋊C4—731no—
262C4⋊C4—733no—
263C4⋊C4—733no—
264C4⋊C4—733no—
265C4⋊C4—736no—
266C4⋊C4—733no—
267C4⋊C4—736no—
268C4⋊C4—733no—
269C4⋊C4—731no—
270C4⋊C4—733no—
271C4⋊C4—733no—
272C4⋊C4—733no—
273C4⋊C4—733no—
274C4⋊C4C22×D7313yes—
275C4⋊C4C22×D7313yes—
276C4⋊C4C22×D7316yes—
277C22⋊C4—731no—
278C22⋊C4—733no—
279C22⋊C4—733no—
280C22⋊C4—731no—
281C22⋊C4—733no—
282C22⋊C4—733no—
283C22⋊C4—733no—
284C22⋊C4—736no—
285C22⋊C4—731no—
286C22⋊C4—736no—
287C22⋊C4—733no—
288C22⋊C4—733no—
289C42—736no—
290C42—733no—
291C42—733no—
292C42C22×D7313yes—
293C42C22×D7313yes—
294C42C22×D7313yes—
295C42C22×D7313yes—
296C23—731no—
297C23—733no—
298C23C23×D7311yescharacteristic
299Q8—26no—
300Q8—2923no—
301Q8—1466no—
302Q8#1192402814yes—
303D4—2923no—
304D4—1466no—
305D4—1462no—
306D4—1466no—
307C2×C4—22no—
308C2×C4—26no—
309C2×C4—43no—
310C2×C4—2926no—
311C2×C4—731no—
312C2×C4—733no—
313C2×C4—731no—
314C2×C4—733no—
315C2×C4—733no—
316C2×C4—731no—
317C2×C4—1466no—
318C2×C4—1466no—
319C2×C4C23×D7313yes—
320C2×C4C23×D7311yescharacteristic
321C2×C4C23×D7311yescharacteristic
322C2×C4C23×D7313yes—
323C2×C4C23×D7313yes—
324C2×C4C23×D7313yes—
325C22—21no—
326C22—21no—
327C22—1461no—
328C22—1463no—
329C22—1461no—
330C22—1463no—
331C22—1463no—
332C22—1461no—
333C22#1455663912yes—
334C22C24×D7311yescharacteristic
335C4—23no—
336C4—21no—
337C4—21no—
338C4—23no—
339C4—23no—
340C4—1461no—
341C4—1463no—
342C4—1463no—
343C4—1461no—
344C4—1463no—
345C4—1461no—
346C4C2×#1192402816yes—
347C2—22no—
348C2—2921no—
349C2—2923no—
350C2C22×#1192402811yescharacteristic
351C2C2×#1455663911yescharacteristic
352C2#1798942311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D73
commutator, socleC22×C73C25
FittingC2×C4×Q8×C73C2
hypercenterC2×C4×Q8D73
hypocenterC73#3516
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #17989313C2semidirect
2. #17989309C2semidirect
3. #17989292C2semidirect
4. #17989285C2semidirect
5. #17989278C2semidirect
6. Q8×C22⋊D73C2semidirect
7. #17989249C2semidirect
8. #17989248C2semidirect
9. #17989209C2semidirect
10. #17989195C2semidirect
11. #17989121C2semidirect
12. #17989121C2semidirect
13. #17989069C2semidirect
14. #17989063C2semidirect
15. C2×C4×Q8×C73C2semidirect
177. C73#3516semidirect
192. C2×C4×Q8D73semidirect