Finite Group Databasebeta

← #23776998

Subgroups — #23776998

Order 10112.

1112 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099296C213yesmaximal, complemented
2#19099289C211yesmaximal, characteristic, complemented
3#19099281C213yesmaximal, complemented
4#19099263C213yesmaximal, complemented
5#19099257C213yesmaximal, complemented
6#19099232C211yesmaximal, characteristic, complemented
7#19099225C211yesmaximal, characteristic, complemented
8#19099220C211yesmaximal, characteristic, complemented
9#19099110C213yesmaximal, complemented
10#19099097C213yesmaximal, complemented
11#19099095C213yesmaximal, complemented
12C4×#11929625C211yesmaximal, characteristic, complemented
13C4×#11929624C213yesmaximal, complemented
14C4×Q8×D79C211yesmaximal, characteristic, complemented
15C4×#41×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929624C2213yes—
18C2×Q8×D79C2211yescharacteristic
19#14579160C2213yes—
20#14579157C2213yes—
21#14579155C2216yes—
22#14579154C2216yes—
23#14579153C2213yes—
24#14579152C2213yes—
25#14579149C2213yes—
26#14579148C2213yes—
27#14579147C2216yes—
28#14579144C2216yes—
29#14579143C2216yes—
30#14579141C2213yes—
31#14579140C2213yes—
32#14579136C2213yes—
33#14579135C2213yes—
34#14579134C2216yes—
35#14579132C2213yes—
36#14579132C2213yes—
37Q8×Dic79C2211yescharacteristic
38Q8×Dic79C2211yescharacteristic
39C4×Dic158C2213yes—
40C4×Dic158C2213yes—
41C4×Dic158C2213yes—
42#14579126C2213yes—
43C4×D316C2213yes—
44C4×D316C2213yes—
45C4×D316C2213yes—
46#14579123C2213yes—
47C4×C22⋊D79C2213yes—
48C4×C22⋊D79C2213yes—
49C4×C22⋊D79C2213yes—
50C4×C22⋊D79C2213yes—
51C4×C22⋊D79C2216yes—
52#14579120C2213yes—
53#14579119C2213yes—
54#14579118C2211yescharacteristic
55#14579118C2213yes—
56C4⋊C4×D79C2213yes—
57C42×D79C2213yes—
58C42×D79C2213yes—
59C2×#41×C79C2211yescharacteristic
60C4×Q8×C79C2211yescharacteristic
61C4×Q8×C79C2211yescharacteristic
62C4×D4×C79C2213yes—
63C4×D4×C79C2213yes—
64#117×C79C2213yes—
65C2×C42×C79C2213yes—
66#11929625—24no—
67#11929624—212no—
68C2×Dic158C2313yes—
69C2×Dic158C2313yes—
70Q8×D79—24no—
71C2×D316C2313yes—
72C2×D316C2313yes—
73C2×C22⋊D79C2313yes—
74C2×C22⋊D79C2313yes—
75C2×C22⋊D79C2316yes—
76C2×C4×D79C2313yes—
77C2×C4×D79C2313yes—
78C2×C4×D79C2313yes—
79C2×C4×D79C2313yes—
80C2×C4×D79C2313yes—
81C2×C4×D79C2311yescharacteristic
82C4⋊Dic79C2313yes—
83C4⋊Dic79C2313yes—
84C4⋊Dic79C2313yes—
85C4⋊Dic79C2313yes—
86Dic79⋊C4C2316yes—
87Dic79⋊C4C2311yescharacteristic
88Dic79⋊C4C2311yescharacteristic
89Dic79⋊C4C2313yes—
90Dic79⋊C4C2313yes—
91Dic79⋊C4C2316yes—
92C22⋊Dic79C2313yes—
93C22⋊Dic79C2313yes—
94C22⋊Dic79C2316yes—
95(C2×D79)⋊C4C2311yescharacteristic
96(C2×D79)⋊C4C2311yescharacteristic
97(C2×D79)⋊C4C2313yes—
98(C2×D79)⋊C4C2313yes—
99(C2×D79)⋊C4C2316yes—
100(C2×D79)⋊C4C2316yes—
101C4×Dic79C2311yescharacteristic
102C4×Dic79C2313yes—
103C4×Dic79C2313yes—
104C4×Dic79C2313yes—
105C4×Dic79C2313yes—
106C4×Dic79C2313yes—
107#41×C79—24no—
108C2×Q8×C79C2311yescharacteristic
109C2×D4×C79C2313yes—
110C22×C4×C79C2313yes—
111C22×C4×C79C2313yes—
112C22×C4×C79C2313yes—
113C4⋊C4×C79C2313yes—
114C4⋊C4×C79C2313yes—
115C22⋊C4×C79C2316yes—
116C42×C79C2311yescharacteristic
117C42×C79C2313yes—
118C42×C79C2313yes—
119C42×C79C2313yes—
120C23×C79C2413yes—
121C22×D79C2413yes—
122C22×D79C2411yescharacteristic
123Q8×C79#4114yescomplemented
124D4×C79—26no—
125C2×C4×C79—26no—
126C2×C4×C79—26no—
127C2×C4×C79—43no—
128C2×C4×C79C2413yes—
129C2×C4×C79C2411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C2×C4×C79C2413yes—
132C2×C4×C79C2413yes—
133C2×C4×C79C2411yescharacteristic
134C22⋊D79—26no—
135C22⋊D79—26no—
136C22⋊D79—46no—
137C2×Dic79C2411yescharacteristic
138C2×Dic79C2411yescharacteristic
139C2×Dic79C2413yes—
140C2×Dic79C2413yes—
141C2×Dic79C2413yes—
142C2×Dic79C2411yescharacteristic
143D316—26no—
144D316—26no—
145C4×D79—26no—
146C4×D79—26no—
147C4×D79—26no—
148C4×D79—43no—
149C4×D79—43no—
150C4×D79#4114yescomplemented
151Dic158—26no—
152Dic158—26no—
153C22×C79—23no—
154C22×C79—23no—
155C22×C79—23no—
156C22×C79C2511yescharacteristic
157C2×D79—21no—
158C2×D79—21no—
159C2×D79—23no—
160C2×D79—23no—
161C2×D79—23no—
162C2×D79C2×#4112yes—
163C4×C79—21no—
164C4×C79—23no—
165C4×C79—21no—
166C4×C79—23no—
167C4×C79C2×#4112yes—
168C4×C79C2×#4116yes—
169Dic79—23no—
170Dic79—23no—
171Dic79—21no—
172Dic79—23no—
173Dic79—21no—
174Dic79C2×#4112yes—
175C2×C79—43no—
176C2×C79C22×#4111yescharacteristic
177C2×C79C22×#4111yescharacteristic
178C2×C79#58511yescharacteristic
179D79—22no—
180D79—43no—
181#3480—791nomaximal, Sylow
182C79#348011yescharacteristic, complemented, Sylow
183#559—793no—
184#557—791no—
185#556—793no—
186#553—793no—
187#553—793no—
188#550—791no—
189#548—791no—
190#548—791no—
191#532—793no—
192#529—793no—
193#529—793no—
194C4×#41—791no—
195C4×#41—793no—
196C4×#41D7911yescharacteristic, complemented
197C2×C4×Q8—791no—
198C2×#41—791no—
199C2×#41—793no—
200C2×#41C2×D7911yescharacteristic
201C22×Q8—791no—
202C4⋊Q8—793no—
203#127—793no—
204#126—796no—
205#126—796no—
206#125—793no—
207#125—793no—
208#124—793no—
209#124—796no—
210#124—793no—
211#123—796no—
212#123—796no—
213C22⋊Q8—793no—
214C22⋊Q8—793no—
215#121—793no—
216#121—793no—
217#121—793no—
218#121—793no—
219#121—796no—
220C4×Q8—791no—
221C4×Q8—791no—
222C4×Q8—793no—
223C4×Q8—793no—
224C4×Q8—793no—
225C4×Q8—793no—
226C4×Q8C2×D7911yescharacteristic
227C4×Q8C2×D7911yescharacteristic
228C4×D4—793no—
229C4×D4—793no—
230C4×D4—793no—
231C4×D4—793no—
232C4×D4—796no—
233C4×D4—793no—
234C4×D4—793no—
235C4×D4—793no—
236C4×D4—793no—
237C4×D4C2×D7913yes—
238C4×D4C2×D7913yes—
239#117—793no—
240#117—793no—
241#117—791no—
242#117—793no—
243#117C2×D7913yes—
244C2×C4⋊C4—793no—
245C2×C42—793no—
246C2×C42—793no—
247C2×C42C2×D7913yes—
248#41—24no—
249#41—15812no—
250#41—1584no—
251C2×Q8—793no—
252C2×Q8—793no—
253C2×Q8—1584no—
254C2×Q8C22×D7911yescharacteristic
255C2×D4—796no—
256C2×D4—793no—
257C2×D4—793no—
258C2×D4—793no—
259C2×D4—793no—
260C2×D4C22×D7913yes—
261C22×C4—793no—
262C22×C4—793no—
263C22×C4—791no—
264C22×C4—793no—
265C22×C4—793no—
266C22×C4—793no—
267C22×C4C22×D7913yes—
268C22×C4C22×D7913yes—
269C22×C4C22×D7913yes—
270C4⋊C4—796no—
271C4⋊C4—791no—
272C4⋊C4—791no—
273C4⋊C4—793no—
274C4⋊C4—793no—
275C4⋊C4—796no—
276C4⋊C4—793no—
277C4⋊C4—793no—
278C4⋊C4—793no—
279C4⋊C4—793no—
280C4⋊C4C22×D7913yes—
281C4⋊C4C22×D7913yes—
282C22⋊C4—793no—
283C22⋊C4—793no—
284C22⋊C4—796no—
285C22⋊C4—791no—
286C22⋊C4—791no—
287C22⋊C4—793no—
288C22⋊C4—796no—
289C22⋊C4—793no—
290C22⋊C4—796no—
291C22⋊C4C22×D7916yes—
292C42—793no—
293C42—793no—
294C42—793no—
295C42—793no—
296C42—791no—
297C42—793no—
298C42C22×D7913yes—
299C42C22×D7913yes—
300C42C22×D7913yes—
301C42C22×D7911yescharacteristic
302C23—791no—
303C23—793no—
304C23C23×D7913yes—
305Q8—1586no—
306Q8—1586no—
307Q8#1192962414yescomplemented
308D4—26no—
309D4—3166no—
310D4—1586no—
311D4—1586no—
312D4—1586no—
313D4—1586no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—3163no—
318C2×C4—3163no—
319C2×C4—791no—
320C2×C4—794no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—793no—
324C2×C4—793no—
325C2×C4—793no—
326C2×C4—1586no—
327C2×C4—1586no—
328C2×C4—1586no—
329C2×C4C23×D7913yes—
330C2×C4C23×D7911yescharacteristic
331C2×C4C23×D7911yescharacteristic
332C2×C4C23×D7913yes—
333C2×C4C23×D7913yes—
334C2×C4C23×D7911yescharacteristic
335C22—23no—
336C22—23no—
337C22—23no—
338C22—792no—
339C22—1583no—
340C22—1583no—
341C22—1583no—
342C22—1581no—
343C22—1581no—
344C22C24×D7911yescharacteristic
345C4—21no—
346C4—23no—
347C4—23no—
348C4—21no—
349C4—792no—
350C4—1581no—
351C4—1583no—
352C4—1583no—
353C4—1581no—
354C4—1583no—
355C4#41×D7912yes—
356C4C2×#1192962416yes—
357C2—43no—
358C2—3163no—
359C2—1582no—
360C2C2×#41×D7911yescharacteristic
361C2C22×#1192962411yescharacteristic
362C2#1909939911yescharacteristic
subgroupG/H
centerC2×C4C23×D79
commutator, socle, cosocleC22×C79C25
FrattiniC22C24×D79
FittingC4×#41×C79C2
hypercenterC4×#41D79
hypocenterC79#3480
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #19099296C2semidirect
2. #19099289C2semidirect
3. #19099281C2semidirect
4. #19099263C2semidirect
5. #19099257C2semidirect
6. #19099232C2semidirect
7. #19099225C2semidirect
8. #19099220C2semidirect
9. #19099110C2semidirect
10. #19099097C2semidirect
11. #19099095C2semidirect
12. C4×#11929625C2semidirect
13. C4×#11929624C2semidirect
14. C4×Q8×D79C2semidirect
15. C4×#41×C79C2semidirect
123. Q8×C79#41semidirect
150. C4×D79#41semidirect
182. C79#3480semidirect
196. C4×#41D79semidirect
307. Q8#11929624semidirect