Finite Group Databasebeta

← #23777016

Subgroups — #23777016

Order 10112.

1094 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099289C211yesmaximal, characteristic, complemented
2#19099282C213yesmaximal, complemented
3#19099253C213yesmaximal, complemented
4#19099247C213yesmaximal, complemented
5Q8×C22⋊D79C211yesmaximal, characteristic, complemented
6#19099220C211yesmaximal, characteristic, complemented
7#19099213C213yesmaximal, complemented
8#19099115C213yesmaximal, complemented
9#19099094C213yesmaximal, complemented
10#19099092C213yesmaximal, complemented
11#41×Dic79C211yesmaximal, characteristic, complemented
12C4×#11929623C213yesmaximal, complemented
13C2×Q8×Dic79C211yesmaximal, characteristic, complemented
14C4×Q8×D79C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2213yes—
17C2×Q8×D79C2211yescharacteristic
18#14579160C2213yes—
19#14579159C2213yes—
20#14579154C2216yes—
21#14579154C2216yes—
22#14579153C2213yes—
23#14579152C2213yes—
24#14579151C2216yes—
25#14579148C2213yes—
26#14579143C2216yes—
27#14579142C2216yes—
28#14579140C2213yes—
29#14579140C2213yes—
30#14579138C2216yes—
31#14579137C2213yes—
32#14579132C2213yes—
33Q8×Dic79C2211yescharacteristic
34Q8×Dic79C2211yescharacteristic
35Q8×Dic79C2213yes—
36Q8×Dic79C2211yescharacteristic
37Q8×Dic79C2213yes—
38C4×Dic158C2213yes—
39C4×Dic158C2213yes—
40#14579126C2213yes—
41#14579126C2213yes—
42D4×Dic79C2213yes—
43D4×Dic79C2213yes—
44D4×Dic79C2213yes—
45C4×C22⋊D79C2213yes—
46C4×C22⋊D79C2213yes—
47(C22⋊D79)⋊C4C2211yescharacteristic
48(C22⋊D79)⋊C4C2213yes—
49#14579120C2213yes—
50#14579119C2213yes—
51#14579117C2213yes—
52#14579117C2213yes—
53#14579117C2216yes—
54C2×C4⋊Dic79C2213yes—
55C4⋊C4×D79C2213yes—
56C2×C4×Dic79C2213yes—
57C2×C4×Dic79C2213yes—
58C42×D79C2213yes—
59C2×#41×C79C2211yescharacteristic
60C22×Q8×C79C2211yescharacteristic
61#124×C79C2213yes—
62C22⋊Q8×C79C2213yes—
63#121×C79C2213yes—
64C4×Q8×C79C2211yescharacteristic
65C4×D4×C79C2213yes—
66#11929623—212no—
67C2×Dic158C2313yes—
68C2×Dic158C2313yes—
69Q8×D79—24no—
70C2×C22⋊D79C2313yes—
71C2×C22⋊D79C2311yescharacteristic
72C22×Dic79C2313yes—
73C22×Dic79C2313yes—
74C22×Dic79C2311yescharacteristic
75C22×Dic79C2313yes—
76C2×C4×D79C2313yes—
77C2×C4×D79C2313yes—
78C2×C4×D79C2311yescharacteristic
79C4⋊Dic79C2313yes—
80C4⋊Dic79C2313yes—
81C4⋊Dic79C2316yes—
82C4⋊Dic79C2313yes—
83C4⋊Dic79C2313yes—
84Dic79⋊C4C2316yes—
85Dic79⋊C4C2311yescharacteristic
86Dic79⋊C4C2313yes—
87Dic79⋊C4C2313yes—
88Dic79⋊C4C2313yes—
89Dic79⋊C4C2316yes—
90Dic79⋊C4C2316yes—
91C22⋊Dic79C2313yes—
92C22⋊Dic79C2313yes—
93C22⋊Dic79C2316yes—
94C22⋊Dic79C2316yes—
95(C2×D79)⋊C4C2311yescharacteristic
96(C2×D79)⋊C4C2313yes—
97C4×Dic79C2313yes—
98C4×Dic79C2313yes—
99C4×Dic79C2313yes—
100C4×Dic79C2311yescharacteristic
101C4×Dic79C2313yes—
102C4×Dic79C2313yes—
103C4×Dic79C2313yes—
104C4×Dic79C2313yes—
105C4×Dic79C2313yes—
106#41×C79—24no—
107C2×Q8×C79—24no—
108C2×Q8×C79C2313yes—
109C2×Q8×C79C2311yescharacteristic
110C2×D4×C79C2313yes—
111C2×D4×C79C2313yes—
112C22×C4×C79C2313yes—
113C22×C4×C79C2313yes—
114C4⋊C4×C79C2313yes—
115C4⋊C4×C79C2313yes—
116C22⋊C4×C79C2311yescharacteristic
117C22⋊C4×C79C2313yes—
118C22⋊C4×C79C2316yes—
119C42×C79C2313yes—
120C23×C79C2413yes—
121C23×C79C2411yescharacteristic
122C22×D79C2411yescharacteristic
123Q8×C79—26no—
124Q8×C79#4114yescomplemented
125D4×C79—26no—
126D4×C79—26no—
127C2×C4×C79—26no—
128C2×C4×C79—26no—
129C2×C4×C79C2411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C2×C4×C79C2413yes—
132C2×C4×C79C2413yes—
133C2×C4×C79C2413yes—
134C22⋊D79—26no—
135C22⋊D79#4114yescomplemented
136C2×Dic79—26no—
137C2×Dic79—26no—
138C2×Dic79—22no—
139C2×Dic79—26no—
140C2×Dic79C2411yescharacteristic
141C2×Dic79C2413yes—
142C2×Dic79C2413yes—
143C2×Dic79C2413yes—
144C2×Dic79C2413yes—
145C2×Dic79C2411yescharacteristic
146C2×Dic79C2411yescharacteristic
147C4×D79—26no—
148C4×D79—26no—
149C4×D79—22no—
150Dic158—26no—
151Dic158—26no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—23no—
155C22×C79—23no—
156C22×C79—23no—
157C22×C79C2×#4112yes—
158C22×C79C2511yescharacteristic
159C2×D79—21no—
160C2×D79—21no—
161C2×D79C2×#4112yes—
162C4×C79—21no—
163C4×C79—23no—
164C4×C79—23no—
165C4×C79—21no—
166C4×C79C2×#4116yes—
167Dic79—23no—
168Dic79—23no—
169Dic79—23no—
170Dic79—21no—
171Dic79—23no—
172Dic79C2×#4112yes—
173Dic792−1+412yes—
174C2×C79—22no—
175C2×C79—43no—
176C2×C79C22×#4111yescharacteristic
177C2×C79C22×#4111yescharacteristic
178C2×C79C2×2−1+411yescharacteristic
179D79—22no—
180#3482—791nomaximal, Sylow
181C79#348211yescharacteristic, complemented, Sylow
182#557—791no—
183#556—793no—
184#552—793no—
185#552—793no—
186D4×Q8—791no—
187#548—791no—
188#548D7911yescharacteristic, complemented
189#547—793no—
190#533—793no—
191#529—793no—
192#529—793no—
193C4×#41—791no—
194C4×#41—793no—
195C2×C4×Q8—791no—
196C2×C4×Q8—791no—
197C2×#41—793no—
198C2×#41C2×D7911yescharacteristic
199C22×Q8—791no—
200C22×Q8C2×D7911yescharacteristic
201C4⋊Q8—793no—
202C4⋊Q8—793no—
203#126—796no—
204#126—796no—
205#125—793no—
206#125—796no—
207#125—793no—
208#124—793no—
209#124C2×D7913yes—
210#123—796no—
211#123—796no—
212C22⋊Q8—793no—
213C22⋊Q8—793no—
214C22⋊Q8—793no—
215C22⋊Q8—796no—
216C22⋊Q8C2×D7913yes—
217#121—793no—
218#121C2×D7913yes—
219C4×Q8—791no—
220C4×Q8—793no—
221C4×Q8—791no—
222C4×Q8—793no—
223C4×Q8—791no—
224C4×Q8—793no—
225C4×Q8—793no—
226C4×Q8—793no—
227C4×Q8—793no—
228C4×Q8C2×D7911yescharacteristic
229C4×D4—793no—
230C4×D4—793no—
231C4×D4—793no—
232C4×D4—793no—
233C4×D4—793no—
234C4×D4—791no—
235C4×D4—793no—
236C4×D4C2×D7913yes—
237#117—793no—
238#117—793no—
239#117—793no—
240#117—793no—
241#117—796no—
242C2×C4⋊C4—793no—
243C2×C4⋊C4—793no—
244C2×C42—793no—
245C2×C42—793no—
246C2×C42—793no—
247#41—24no—
248#41—15812no—
249C2×Q8—24no—
250C2×Q8—793no—
251C2×Q8—793no—
252C2×Q8—1584no—
253C2×Q8C22×D7913yes—
254C2×Q8C22×D7911yescharacteristic
255C2×D4—791no—
256C2×D4—793no—
257C2×D4C22×D7913yes—
258C2×D4C22×D7913yes—
259C22×C4—791no—
260C22×C4—793no—
261C22×C4—793no—
262C22×C4—793no—
263C22×C4—791no—
264C22×C4—793no—
265C22×C4—793no—
266C22×C4C22×D7913yes—
267C22×C4C22×D7913yes—
268C4⋊C4—796no—
269C4⋊C4—791no—
270C4⋊C4—793no—
271C4⋊C4—793no—
272C4⋊C4—793no—
273C4⋊C4—796no—
274C4⋊C4—796no—
275C4⋊C4—793no—
276C4⋊C4—793no—
277C4⋊C4—796no—
278C4⋊C4—793no—
279C4⋊C4—793no—
280C4⋊C4C22×D7913yes—
281C4⋊C4C22×D7913yes—
282C22⋊C4—793no—
283C22⋊C4—796no—
284C22⋊C4—793no—
285C22⋊C4—796no—
286C22⋊C4—791no—
287C22⋊C4—793no—
288C22⋊C4C22×D7911yescharacteristic
289C22⋊C4C22×D7913yes—
290C22⋊C4C22×D7916yes—
291C42—791no—
292C42—793no—
293C42—793no—
294C42—793no—
295C42—793no—
296C42—793no—
297C42—793no—
298C42—793no—
299C42—793no—
300C42C22×D7913yes—
301C23—791no—
302C23C23×D7913yes—
303C23C23×D7911yescharacteristic
304Q8—26no—
305Q8—1586no—
306Q8—1586no—
307Q8#1192962314yescomplemented
308D4—26no—
309D4—26no—
310D4—794no—
311D4—1586no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—793no—
318C2×C4—793no—
319C2×C4—793no—
320C2×C4—793no—
321C2×C4—1582no—
322C2×C4—1586no—
323C2×C4—1586no—
324C2×C4—1582no—
325C2×C4—1586no—
326C2×C4—1586no—
327C2×C4—1586no—
328C2×C4C23×D7911yescharacteristic
329C2×C4C23×D7911yescharacteristic
330C2×C4C23×D7913yes—
331C2×C4C23×D7913yes—
332C2×C4C23×D7913yes—
333C22—21no—
334C22—21no—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—792no—
339C22—1581no—
340C22—1581no—
341C22#41×D7912yes—
342C22C24×D7911yescharacteristic
343C4—21no—
344C4—23no—
345C4—21no—
346C4—23no—
347C4—792no—
348C4—792no—
349C4—1581no—
350C4—1583no—
351C4—1583no—
352C4—1583no—
353C4—1583no—
354C4C2×#1192962316yes—
355C2—22no—
356C2—43no—
357C2—1582no—
358C2C2×#41×D7911yescharacteristic
359C2C22×#1192962311yescharacteristic
360C22−1+4×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D79
commutator, socle, cosocleC22×C79C25
Fitting#548×C79C2
hypercenter#548D79
hypocenterC79#3482
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #19099289C2semidirect
2. #19099282C2semidirect
3. #19099253C2semidirect
4. #19099247C2semidirect
5. Q8×C22⋊D79C2semidirect
6. #19099220C2semidirect
7. #19099213C2semidirect
8. #19099115C2semidirect
9. #19099094C2semidirect
10. #19099092C2semidirect
11. #41×Dic79C2semidirect
12. C4×#11929623C2semidirect
13. C2×Q8×Dic79C2semidirect
14. C4×Q8×D79C2semidirect
15. #548×C79C2semidirect
124. Q8×C79#41semidirect
135. C22⋊D79#41semidirect
181. C79#3482semidirect
188. #548D79semidirect
307. Q8#11929623semidirect