Finite Group Databasebeta

← #23777487

Subgroups — #23777487

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#19099289C211yesmaximal, characteristic, complemented
2#19099288C213yesmaximal, complemented
3#19099284C213yesmaximal, complemented
4#19099255C213yesmaximal, complemented
5#19099253C213yesmaximal, complemented
6Q8×C22⋊D79C211yesmaximal, characteristic, complemented
7Q8×C22⋊D79C211yesmaximal, characteristic, complemented
8#19099174C213yesmaximal, complemented
9#19099173C213yesmaximal, complemented
10#19099115C213yesmaximal, complemented
11#19099093C213yesmaximal
12#19099041C211yesmaximal, characteristic, complemented
13#19099039C211yesmaximal, characteristic, complemented
14C2×Q8×Dic79C211yesmaximal, characteristic, complemented
15D4×Q8×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17#14579160C2213yes—
18#14579159C2213yes—
19#14579159C2213yes—
20#14579156C2213yes—
21#14579156C2216yes—
22#14579154C2213yes—
23#14579154C2216yes—
24#14579153C2213yes—
25#14579152C2216yes—
26#14579152C2213yes—
27#14579151C2216yes—
28#14579151C2216yes—
29#14579151C2213yes—
30#14579147C2213yes—
31#14579145C2213yes—
32#14579142C2213yes—
33#14579140C2213yes—
34#14579140C2213yes—
35#14579138C2213yes—
36#14579137C2213yes—
37#14579137C2213yes—
38#14579133C2211yescharacteristic
39Q8×Dic79C2213yes—
40Q8×Dic79C2213yes—
41Q8×Dic79C2211yescharacteristic
42Q8×Dic79C2211yescharacteristic
43Q8×Dic79C2213yes—
44Q8×Dic79C2213yes—
45Q8×Dic79C2211yescharacteristic
46C4×Dic158C2213yes—
47C4×Dic158C2213yes—
48#14579126C2213yes—
49#14579126C2216yes—
50C4×C22⋊D79C2213yes—
51C4×C22⋊D79C2213yes—
52#14579120C2213yes—
53#14579120C2213yes—
54#14579119C2213yes—
55#14579118C2213yes—
56#14579117C2216yes—
57C2×C4⋊Dic79C2213yes—
58C2×C4×Dic79C2213yes—
59C22×Q8×C79C2211yescharacteristic
60C22×Q8×C79C2211yescharacteristic
61C4⋊Q8×C79C2213yes—
62C22⋊Q8×C79C2213yes—
63C22⋊Q8×C79C2213yes—
64C4×Q8×C79C2211yescharacteristic
65C4×D4×C79C2213yes—
66C2×Dic158C2313yes—
67C2×Dic158C2313yes—
68Q8×D79—24no—
69C2×C22⋊D79C2311yescharacteristic
70C2×C22⋊D79C2311yescharacteristic
71C22×Dic79C2311yescharacteristic
72C22×Dic79C2313yes—
73C2×C4×D79C2313yes—
74C4⋊Dic79C2313yes—
75C4⋊Dic79C2313yes—
76C4⋊Dic79C2316yes—
77C4⋊Dic79C2313yes—
78C4⋊Dic79C2313yes—
79C4⋊Dic79C2313yes—
80C4⋊Dic79C2313yes—
81Dic79⋊C4C2316yes—
82Dic79⋊C4C2316yes—
83Dic79⋊C4C2313yes—
84Dic79⋊C4C2313yes—
85Dic79⋊C4C2313yes—
86Dic79⋊C4C2313yes—
87Dic79⋊C4C2316yes—
88Dic79⋊C4C2311yescharacteristic
89Dic79⋊C4C2313yes—
90C22⋊Dic79C2313yes—
91C22⋊Dic79C2311yescharacteristic
92C22⋊Dic79C2313yes—
93C22⋊Dic79C2313yes—
94(C2×D79)⋊C4C2311yescharacteristic
95(C2×D79)⋊C4C2313yes—
96(C2×D79)⋊C4C2313yes—
97(C2×D79)⋊C4C2313yes—
98C4×Dic79C2313yes—
99C4×Dic79C2313yes—
100C4×Dic79C2313yes—
101C4×Dic79C2313yes—
102C4×Dic79C2316yes—
103C4×Dic79C2316yes—
104C4×Dic79C2313yes—
105C2×Q8×C79—24no—
106C2×Q8×C79—24no—
107C2×Q8×C79C2313yes—
108C2×Q8×C79C2313yes—
109C2×Q8×C79C2311yescharacteristic
110C2×D4×C79C2311yescharacteristic
111C22×C4×C79C2313yes—
112C22×C4×C79C2313yes—
113C4⋊C4×C79C2313yes—
114C4⋊C4×C79C2313yes—
115C4⋊C4×C79C2316yes—
116C22⋊C4×C79C2313yes—
117C22⋊C4×C79C2313yes—
118C42×C79C2313yes—
119C23×C79C2411yescharacteristic
120C23×C79C2411yescharacteristic
121C22×D79C2411yescharacteristic
122Q8×C79—26no—
123Q8×C79—26no—
124Q8×C79#4114yes—
125D4×C79—22no—
126C2×C4×C79—26no—
127C2×C4×C79—26no—
128C2×C4×C79C2413yes—
129C2×C4×C79C2413yes—
130C2×C4×C79C2413yes—
131C2×C4×C79C2411yescharacteristic
132C2×C4×C79C2413yes—
133C22⋊D79—22no—
134C22⋊D79—22no—
135C2×Dic79—26no—
136C2×Dic79—22no—
137C2×Dic79C2411yescharacteristic
138C2×Dic79C2413yes—
139C2×Dic79C2413yes—
140C2×Dic79C2411yescharacteristic
141C2×Dic79C2413yes—
142C2×Dic79C2413yes—
143C2×Dic79C2411yescharacteristic
144C4×D79—26no—
145Dic158—26no—
146Dic158—26no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C792−1+412yes—
153C22×C79C2511yescharacteristic
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—21no—
157C4×C79—23no—
158C4×C79—23no—
159C4×C79—21no—
160C4×C79—23no—
161C4×C79C2×#4116yes—
162Dic79—23no—
163Dic79—21no—
164Dic79—23no—
165Dic79—21no—
166Dic79—23no—
167Dic79—23no—
168Dic792−1+412yes—
169C2×C79—22no—
170C2×C79—41no—
171C2×C79C22×#4111yescharacteristic
172C2×C79C2×2−1+411yescharacteristic
173C2×C79C2×2−1+411yescharacteristic
174D79—41no—
175#3523—791nomaximal, Sylow
176C79#352311yescharacteristic, complemented, Sylow
177#557—793no—
178#557—791no—
179#556—793no—
180#552—793no—
181#552—793no—
182D4×Q8—791no—
183D4×Q8—791no—
184D4×Q8D7911yescharacteristic, complemented
185#541—793no—
186#541—793no—
187#533—793no—
188#529—793no—
189#519—791no—
190#519—791no—
191C2×C4×Q8—791no—
192C22×Q8—791no—
193C22×Q8C2×D7911yescharacteristic
194C22×Q8C2×D7911yescharacteristic
195C4⋊Q8—793no—
196C4⋊Q8—793no—
197C4⋊Q8—793no—
198C4⋊Q8C2×D7913yes—
199#126—793no—
200#126—796no—
201#126—793no—
202#126—796no—
203#125—793no—
204#125—796no—
205#125—796no—
206#125—796no—
207#125—793no—
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⋊Q8C2×D7913yes—
218C22⋊Q8C2×D7913yes—
219#121—791no—
220C4×Q8—791no—
221C4×Q8—793no—
222C4×Q8—791no—
223C4×Q8—793no—
224C4×Q8—793no—
225C4×Q8—791no—
226C4×Q8—793no—
227C4×Q8—793no—
228C4×Q8—796no—
229C4×Q8—793no—
230C4×Q8—793no—
231C4×Q8C2×D7911yescharacteristic
232C4×D4—793no—
233C4×D4—793no—
234C4×D4C2×D7913yes—
235#117—793no—
236#117—793no—
237#117—793no—
238#117—796no—
239#117—793no—
240C2×C4⋊C4—793no—
241C2×C42—793no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—793no—
245C2×Q8—793no—
246C2×Q8—1584no—
247C2×Q8C22×D7913yes—
248C2×Q8C22×D7913yes—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—791no—
251C2×D4—791no—
252C2×D4C22×D7911yescharacteristic
253C22×C4—791no—
254C22×C4—793no—
255C22×C4—793no—
256C22×C4C22×D7913yes—
257C22×C4C22×D7913yes—
258C4⋊C4—793no—
259C4⋊C4—793no—
260C4⋊C4—796no—
261C4⋊C4—796no—
262C4⋊C4—793no—
263C4⋊C4—793no—
264C4⋊C4—791no—
265C4⋊C4—796no—
266C4⋊C4—793no—
267C4⋊C4—793no—
268C4⋊C4—793no—
269C4⋊C4—796no—
270C4⋊C4—793no—
271C4⋊C4—793no—
272C4⋊C4—793no—
273C4⋊C4—793no—
274C4⋊C4C22×D7913yes—
275C4⋊C4C22×D7913yes—
276C4⋊C4C22×D7916yes—
277C22⋊C4—791no—
278C22⋊C4—793no—
279C22⋊C4—793no—
280C22⋊C4—793no—
281C22⋊C4—791no—
282C22⋊C4—793no—
283C22⋊C4—793no—
284C22⋊C4—793no—
285C22⋊C4C22×D7913yes—
286C22⋊C4C22×D7913yes—
287C42—793no—
288C42—793no—
289C42—793no—
290C42—793no—
291C42—796no—
292C42—796no—
293C42—793no—
294C42C22×D7913yes—
295C23—791no—
296C23C23×D7911yescharacteristic
297C23C23×D7911yescharacteristic
298Q8—26no—
299Q8—26no—
300Q8—1586no—
301Q8—1586no—
302Q8#1192962314yes—
303D4—22no—
304D4—1582no—
305D4—1582no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—791no—
309C2×C4—791no—
310C2×C4—793no—
311C2×C4—793no—
312C2×C4—791no—
313C2×C4—793no—
314C2×C4—793no—
315C2×C4—1582no—
316C2×C4—1586no—
317C2×C4—1586no—
318C2×C4C23×D7913yes—
319C2×C4C23×D7913yes—
320C2×C4C23×D7913yes—
321C2×C4C23×D7911yescharacteristic
322C2×C4C23×D7913yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—1581no—
329C22—1581no—
330C22—1581no—
331C22#1457920912yes—
332C22C24×D7911yescharacteristic
333C4—23no—
334C4—21no—
335C4—23no—
336C4—23no—
337C4—792no—
338C4—1581no—
339C4—1583no—
340C4—1583no—
341C4—1583no—
342C4—1581no—
343C4—1583no—
344C4C2×#1192962316yes—
345C2—22no—
346C2—41no—
347C2—3161no—
348C2C22×#1192962311yescharacteristic
349C22−1+4×D7911yescharacteristic
350C2C2×#1457920911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
FittingD4×Q8×C79C2
prime radical#14579133C22
hypercenterD4×Q8D79
hypocenterC79#3523
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #19099289C2semidirect
2. #19099288C2semidirect
3. #19099284C2semidirect
4. #19099255C2semidirect
5. #19099253C2semidirect
6. Q8×C22⋊D79C2semidirect
7. Q8×C22⋊D79C2semidirect
8. #19099174C2semidirect
9. #19099173C2semidirect
10. #19099115C2semidirect
12. #19099041C2semidirect
13. #19099039C2semidirect
14. C2×Q8×Dic79C2semidirect
15. D4×Q8×C79C2semidirect
176. C79#3523semidirect
184. D4×Q8D79semidirect