Finite Group Databasebeta

← #23777490

Subgroups — #23777490

Order 10112.

992 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099291C213yesmaximal, complemented
2#19099289C211yesmaximal, characteristic, complemented
3#19099281C213yesmaximal, complemented
4#19099254C213yesmaximal, complemented
5#19099252C213yesmaximal, complemented
6Q8×D316C211yesmaximal, characteristic, complemented
7Q8×C22⋊D79C211yesmaximal, characteristic, complemented
8Q8×C22⋊D79C211yesmaximal, characteristic, complemented
9#19099175C213yesmaximal, complemented
10#19099171C213yesmaximal, complemented
11#19099117C213yesmaximal, complemented
12#19099091C213yesmaximal
13#19099039C211yesmaximal, characteristic, complemented
14C4×Q8×D79C211yesmaximal, characteristic, complemented
15#519×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18#14579161C2213yes—
19#14579160C2213yes—
20#14579159C2213yes—
21#14579159C2213yes—
22#14579156C2213yes—
23#14579155C2216yes—
24#14579154C2213yes—
25#14579154C2216yes—
26#14579153C2216yes—
27#14579153C2213yes—
28#14579152C2213yes—
29#14579151C2216yes—
30#14579151C2216yes—
31#14579151C2213yes—
32#14579147C2213yes—
33#14579146C2213yes—
34#14579143C2213yes—
35#14579141C2213yes—
36#14579141C2213yes—
37#14579140C2213yes—
38#14579140C2213yes—
39#14579139C2213yes—
40#14579137C2213yes—
41#14579137C2213yes—
42#14579134C2211yescharacteristic
43Q8×Dic79C2211yescharacteristic
44Q8×Dic79C2211yescharacteristic
45C4×Dic158C2213yes—
46C4×Dic158C2213yes—
47C4×Dic158C2216yes—
48C4×Dic158C2213yes—
49#14579126C2213yes—
50#14579126C2213yes—
51C4×D316C2213yes—
52C4×C22⋊D79C2213yes—
53C4×C22⋊D79C2213yes—
54#14579119C2213yes—
55#14579118C2213yes—
56#14579118C2216yes—
57C4⋊C4×D79C2213yes—
58C42×D79C2213yes—
59C22×Q8×C79C2211yescharacteristic
60C4×Q8×C79C2213yes—
61C4×Q8×C79C2211yescharacteristic
62C4×Q8×C79C2213yes—
63C4×Q8×C79C2211yescharacteristic
64#117×C79C2213yes—
65#117×C79C2213yes—
66C2×Dic158C2313yes—
67C2×Dic158C2313yes—
68C2×Dic158C2313yes—
69Q8×D79—24no—
70Q8×D79—24no—
71C2×D316C2311yescharacteristic
72C2×C22⋊D79C2311yescharacteristic
73C2×C22⋊D79C2311yescharacteristic
74C2×C4×D79C2313yes—
75C2×C4×D79C2313yes—
76C2×C4×D79C2311yescharacteristic
77C2×C4×D79C2313yes—
78C4⋊Dic79C2313yes—
79C4⋊Dic79C2313yes—
80C4⋊Dic79C2313yes—
81C4⋊Dic79C2316yes—
82C4⋊Dic79C2313yes—
83Dic79⋊C4C2316yes—
84Dic79⋊C4C2313yes—
85Dic79⋊C4C2313yes—
86Dic79⋊C4C2316yes—
87Dic79⋊C4C2316yes—
88Dic79⋊C4C2313yes—
89Dic79⋊C4C2313yes—
90Dic79⋊C4C2311yescharacteristic
91Dic79⋊C4C2316yes—
92Dic79⋊C4C2313yes—
93C22⋊Dic79C2313yes—
94C22⋊Dic79C2313yes—
95(C2×D79)⋊C4C2311yescharacteristic
96(C2×D79)⋊C4C2313yes—
97(C2×D79)⋊C4C2313yes—
98(C2×D79)⋊C4C2313yes—
99(C2×D79)⋊C4C2313yes—
100(C2×D79)⋊C4C2313yes—
101C4×Dic79C2313yes—
102C4×Dic79C2313yes—
103C4×Dic79C2313yes—
104C4×Dic79C2316yes—
105C4×Dic79C2313yes—
106C2×Q8×C79—24no—
107C2×Q8×C79C2313yes—
108C2×Q8×C79C2311yescharacteristic
109C22×C4×C79C2313yes—
110C4⋊C4×C79C2313yes—
111C4⋊C4×C79C2313yes—
112C4⋊C4×C79C2313yes—
113C4⋊C4×C79C2313yes—
114C22⋊C4×C79C2311yescharacteristic
115C22⋊C4×C79C2313yes—
116C42×C79C2313yes—
117C42×C79C2316yes—
118C42×C79C2313yes—
119C23×C79C2411yescharacteristic
120C22×D79C2411yescharacteristic
121C22×D79C2411yescharacteristic
122Q8×C79—26no—
123Q8×C79#4114yes—
124C2×C4×C79—26no—
125C2×C4×C79C2413yes—
126C2×C4×C79C2411yescharacteristic
127C2×C4×C79C2413yes—
128C2×C4×C79C2413yes—
129C2×C4×C79C2411yescharacteristic
130C2×C4×C79C2413yes—
131C22⋊D79—22no—
132C22⋊D79—22no—
133C2×Dic79C2413yes—
134C2×Dic79C2411yescharacteristic
135C2×Dic79C2413yes—
136C2×Dic79C2413yes—
137C2×Dic79C2413yes—
138C2×Dic79C2411yescharacteristic
139D316—22no—
140C4×D79—26no—
141C4×D79—26no—
142C4×D79—26no—
143C4×D79—22no—
144Dic158—26no—
145Dic158—26no—
146Dic158—26no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79C2511yescharacteristic
151C2×D79—21no—
152C2×D79—21no—
153C2×D79—21no—
154C2×D79—21no—
155C2×D79—21no—
156C2×D792−1+412yes—
157C4×C79—23no—
158C4×C79—23no—
159C4×C79—23no—
160C4×C79—21no—
161C4×C79—21no—
162C4×C79C2×#4116yes—
163Dic79—23no—
164Dic79—23no—
165Dic79—21no—
166Dic79—23no—
167Dic79—23no—
168Dic792−1+412yes—
169C2×C79—41no—
170C2×C79C22×#4111yescharacteristic
171C2×C79C2×2−1+411yescharacteristic
172C2×C79C2×2−1+411yescharacteristic
173D79—22no—
174D79—41no—
175#3523—791nomaximal, Sylow
176C79#352311yescharacteristic, complemented, Sylow
177#557—791no—
178#557—793no—
179#556—793no—
180#552—793no—
181#552—793no—
182D4×Q8—791no—
183D4×Q8—791no—
184D4×Q8—791no—
185#541—793no—
186#541—793no—
187#533—793no—
188#529—793no—
189#519—791no—
190#519D7911yescharacteristic, complemented
191C2×C4×Q8—791no—
192C22×Q8—791no—
193C22×Q8—791no—
194C22×Q8C2×D7911yescharacteristic
195C4⋊Q8—793no—
196C4⋊Q8—793no—
197C4⋊Q8—793no—
198C4⋊Q8—793no—
199#126—793no—
200#126—793no—
201#126—796no—
202#126—796no—
203#125—793no—
204#125—796no—
205#125—796no—
206#125—793no—
207#125—796no—
208#125—793no—
209#124—793no—
210#123—793no—
211#123—793no—
212C22⋊Q8—793no—
213C22⋊Q8—793no—
214C22⋊Q8—793no—
215C22⋊Q8—793no—
216C22⋊Q8—793no—
217C22⋊Q8—793no—
218C22⋊Q8—793no—
219#121—791no—
220C4×Q8—791no—
221C4×Q8—791no—
222C4×Q8—793no—
223C4×Q8—793no—
224C4×Q8—793no—
225C4×Q8—793no—
226C4×Q8—793no—
227C4×Q8—796no—
228C4×Q8C2×D7911yescharacteristic
229C4×Q8C2×D7913yes—
230C4×Q8C2×D7911yescharacteristic
231C4×Q8C2×D7913yes—
232C4×D4—793no—
233C4×D4—793no—
234C4×D4—793no—
235#117—793no—
236#117—793no—
237#117—796no—
238#117C2×D7913yes—
239#117C2×D7913yes—
240C2×C4⋊C4—793no—
241C2×C42—793no—
242C2×Q8—24no—
243C2×Q8—793no—
244C2×Q8—793no—
245C2×Q8—793no—
246C2×Q8—1584no—
247C2×Q8—1584no—
248C2×Q8C22×D7913yes—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—791no—
251C2×D4—791no—
252C2×D4—791no—
253C22×C4—791no—
254C22×C4—793no—
255C22×C4—793no—
256C22×C4—793no—
257C22×C4C22×D7913yes—
258C4⋊C4—796no—
259C4⋊C4—793no—
260C4⋊C4—793no—
261C4⋊C4—796no—
262C4⋊C4—796no—
263C4⋊C4—793no—
264C4⋊C4—793no—
265C4⋊C4—791no—
266C4⋊C4—796no—
267C4⋊C4—793no—
268C4⋊C4—793no—
269C4⋊C4—793no—
270C4⋊C4—793no—
271C4⋊C4—796no—
272C4⋊C4—793no—
273C4⋊C4C22×D7913yes—
274C4⋊C4C22×D7913yes—
275C4⋊C4C22×D7913yes—
276C4⋊C4C22×D7913yes—
277C22⋊C4—793no—
278C22⋊C4—793no—
279C22⋊C4—791no—
280C22⋊C4—793no—
281C22⋊C4—793no—
282C22⋊C4—793no—
283C22⋊C4—793no—
284C22⋊C4—793no—
285C22⋊C4C22×D7911yescharacteristic
286C22⋊C4C22×D7913yes—
287C42—793no—
288C42—793no—
289C42—793no—
290C42—796no—
291C42—793no—
292C42C22×D7913yes—
293C42C22×D7916yes—
294C42C22×D7913yes—
295C23—791no—
296C23—791no—
297C23C23×D7911yescharacteristic
298Q8—26no—
299Q8—1586no—
300Q8—1586no—
301Q8—1586no—
302Q8#1192962414yes—
303D4—1582no—
304D4—1582no—
305D4—1582no—
306C2×C4—26no—
307C2×C4—791no—
308C2×C4—793no—
309C2×C4—791no—
310C2×C4—793no—
311C2×C4—793no—
312C2×C4—793no—
313C2×C4—1582no—
314C2×C4—1586no—
315C2×C4—1586no—
316C2×C4—1586no—
317C2×C4C23×D7913yes—
318C2×C4C23×D7911yescharacteristic
319C2×C4C23×D7913yes—
320C2×C4C23×D7911yescharacteristic
321C2×C4C23×D7913yes—
322C2×C4C23×D7913yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—792no—
327C22—1581no—
328C22—1581no—
329C22—1581no—
330C22—1581no—
331C22—1581no—
332C22C24×D7911yescharacteristic
333C4—21no—
334C4—23no—
335C4—21no—
336C4—23no—
337C4—23no—
338C4—792no—
339C4—1583no—
340C4—1581no—
341C4—1583no—
342C4—1583no—
343C4—1583no—
344C4C2×#1192962416yes—
345C2—41no—
346C2—3161no—
347C2—1582no—
348C2C22×#1192962411yescharacteristic
349C22−1+4×D7911yescharacteristic
350C22−1+4×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#519×C79C2
prime radical#14579134C22
hypercenter#519D79
hypocenterC79#3523
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #519

Complements

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

NH ≅ G/Ntype
1. #19099291C2semidirect
2. #19099289C2semidirect
3. #19099281C2semidirect
4. #19099254C2semidirect
5. #19099252C2semidirect
6. Q8×D316C2semidirect
7. Q8×C22⋊D79C2semidirect
8. Q8×C22⋊D79C2semidirect
9. #19099175C2semidirect
10. #19099171C2semidirect
11. #19099117C2semidirect
13. #19099039C2semidirect
14. C4×Q8×D79C2semidirect
15. #519×C79C2semidirect
176. C79#3523semidirect
190. #519D79semidirect