Finite Group Databasebeta

← #23775526

Subgroups — #23775526

Order 10112.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2#19098927C211yesmaximal, characteristic, complemented
3#19098884C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098870C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098760C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14#19098559C211yesmaximal, characteristic, complemented
15#550×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21#14579154—21no—
22#14579153C2211yescharacteristic
23#14579151—21no—
24#14579142—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27C4×Dic158C2211yescharacteristic
28#14579120C2211yescharacteristic
29#14579117—21no—
30C2×C4⋊Dic79C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C2×#41×C79C2211yescharacteristic
50#127×C79—21no—
51#127×C79C2211yescharacteristic
52#121×C79—21no—
53#121×C79—21no—
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79—21no—
58C4×D4×C79C2211yescharacteristic
59C2×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61#11929614—22no—
62#11929612—41no—
63#11929612—41no—
64#11929608—41no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79—21no—
71C4⋊Dic79C2311yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C4×Dic79—21no—
83C4×Dic79—21no—
84#41×C79—22no—
85#41×C79—22no—
86#41×C79—41no—
87#41×C79—41no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79—21no—
94C2×D4×C79—21no—
95C2×D4×C79D411yescharacteristic
96C2×D4×C79C2311yescharacteristic
97C2×D4×C79C2311yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79—21no—
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79D411yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C23×C79C2×D411yescharacteristic
115Q8×C79—21no—
116Q8×C79#4112yes—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—41no—
122D4×C79—42no—
123D4×C79—42no—
124D4×C79—42no—
125D4×C79—81no—
126D4×C79—81no—
127D4×C79—81no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—42no—
135C2×C4×C79—42no—
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2411yescharacteristic
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146Dic158—21no—
147Dic158—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79C22×D411yescharacteristic
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—22no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79C2×#4111yescharacteristic
172C4×C79H(5,𝔽2)11yescharacteristic
173Dic79—41no—
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79—81no—
181C2×C79#54611yescharacteristic
182C2×C79#57511yescharacteristic
183C2×C79#57711yescharacteristic
184#3317—791nomaximal, Sylow
185C79#331711yescharacteristic, complemented, Sylow
186#552—791no—
187#550D7911yescharacteristic
188#490—791no—
189#482—791no—
190#481—791no—
191#479—791no—
192#468—791no—
193#465—791no—
194#460—791no—
195#452—791no—
196#452—791no—
197#441—791no—
198#435—791no—
199#417—791no—
200#416—791no—
201C2×#41C2×D7911yescharacteristic
202C2×#41C2×D7911yescharacteristic
203C2×Q16—791no—
204C2×SD16—791no—
205C2×SD16—791no—
206C2×M16—791no—
207C22×C8—791no—
208#127—21no—
209#127C2×D7911yescharacteristic
210#126—1581no—
211#125—791no—
212#125—1581no—
213#123—1581no—
214C22⋊Q8—791no—
215C22⋊Q8—791no—
216#121—21no—
217#121—21no—
218#121C2×D7911yescharacteristic
219#121C2×D7911yescharacteristic
220C4×Q8—791no—
221C4×Q8C2×D7911yescharacteristic
222C4×D4—21no—
223C4×D4C2×D7911yescharacteristic
224#117—791no—
225#117—1581no—
226C2×C4⋊C4—791no—
227#107—791no—
228#106—791no—
229#106—791no—
230C4⋊C8—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241C22⋊C8—791no—
242C22⋊C8—791no—
243#97—791no—
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8—791no—
249C2×Q8C22×D7911yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4C22⋊D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C2×D4C22×D7911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264Q16—1582no—
265SD16—3161no—
266SD16—3161no—
267M16—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—791no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4—1581no—
283C4⋊C4C22⋊D7911yescharacteristic
284C4⋊C4C22×D7911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4C22⋊D7911yescharacteristic
291C22⋊C4C22⋊D7911yescharacteristic
292C42—21no—
293C42—1581no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×C22⋊D7911yescharacteristic
299C23C2×C22⋊D7911yescharacteristic
300Q8—21no—
301Q8—1581no—
302Q8—1581no—
303Q8#1192962312yes—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—81no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—3162no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4C2×C22⋊D7911yescharacteristic
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C23×D7911yescharacteristic
333C8—1581no—
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×C22⋊D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4C2×#1192962311yescharacteristic
361C4#1457920611yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2#1909920711yescharacteristic
367C2#1909936111yescharacteristic
368C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#550×C79C2
socleC22×C79C22×D4
hypercenter#550D79
hypocenterC79#3317
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
2. #19098927C2semidirect
3. #19098884C2semidirect
4. #19098879C2semidirect
5. #19098870C2semidirect
6. #19098807C2semidirect
7. #19098790C2semidirect
8. #19098760C2semidirect
9. #19098725C2semidirect
10. #19098725C2semidirect
11. #19098668C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. #19098559C2semidirect
185. C79#3317semidirect