Finite Group Databasebeta

← #23775302

Subgroups — #23775302

Order 10112.

398 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#19099259C211yesmaximal, characteristic, complemented
2#19098917C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098879C211yesmaximal, characteristic, complemented
5#19098870C211yesmaximal, characteristic, complemented
6#19098797C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098775C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic, complemented
10#19098702C211yesmaximal, characteristic, complemented
11C4×#11929611C211yesmaximal, characteristic, complemented
12D4×C79⋊C8C211yesmaximal, characteristic, complemented
13#19098559C211yesmaximal, characteristic, complemented
14C2×#14579085C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19C22×C79⋊C8C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21#14579156—21no—
22#14579153C2211yescharacteristic
23#14579143—21no—
24#14579135C2211yescharacteristic
25#14579135C2211yescharacteristic
26#14579133—21no—
27C4×D316C2211yescharacteristic
28(C22⋊D79)⋊C4—21no—
29#14579120C2211yescharacteristic
30C2×C4⋊Dic79C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52C22⋊Q8×C79—21no—
53C22⋊Q8×C79C2211yescharacteristic
54#121×C79—21no—
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79—21no—
58C4×D4×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C22×Dic79—21no—
63C2×C4×D79—21no—
64#11929611—22no—
65#11929611—41no—
66#11929609—41no—
67C2×C79⋊C8—41no—
68C2×C79⋊C8—41no—
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C4⋊Dic79—21no—
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83C4×Dic79—21no—
84#41×C79—22no—
85#41×C79—41no—
86C2×Q8×C79—21no—
87C2×Q8×C79—22no—
88C2×Q8×C79—41no—
89C2×Q8×C79C2311yescharacteristic
90C2×Q8×C79C2311yescharacteristic
91C2×D4×C79—21no—
92C2×D4×C79—21no—
93C2×D4×C79D411yescharacteristic
94C2×D4×C79C2311yescharacteristic
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79D411yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114C22×D79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—42no—
119Q8×C79#4112yes—
120D4×C79—22no—
121D4×C79—21no—
122D4×C79—21no—
123D4×C79—42no—
124D4×C79—42no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—42no—
133C2×C4×C79—42no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2411yescharacteristic
139C22⋊D79—42no—
140C22⋊D79—81no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—81no—
145D316—21no—
146D316—21no—
147C4×D79—81no—
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—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79#13512yes—
161C22×C79C22×D411yescharacteristic
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—22no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79C2×#4111yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—22no—
178C2×C79—41no—
179C2×C79—81no—
180C2×C79#54611yescharacteristic
181C2×C79C2×#13511yescharacteristic
182C2×C79#57711yescharacteristic
183D79—81no—
184#3301—791nomaximal, Sylow
185C79#330111yescharacteristic, complemented, Sylow
186#553—791no—
187#548D7911yescharacteristic, complemented
188#488—791no—
189#485—791no—
190#481—791no—
191#479—791no—
192#466—791no—
193#465—791no—
194#463—791no—
195#449—791no—
196#448—791no—
197C4×SD16—791no—
198C8×D4—791no—
199#416—791no—
200C2×#103—791no—
201C2×#41C2×D7911yescharacteristic
202C22×Q8C2×D7911yescharacteristic
203C2×SD16—791no—
204C2×SD16—791no—
205C2×D8—791no—
206C22×C8—791no—
207C22×C8—791no—
208#126—1581no—
209#125—791no—
210#124—21no—
211#124C2×D7911yescharacteristic
212#123—1581no—
213C22⋊Q8—21no—
214C22⋊Q8C2×D7911yescharacteristic
215#121—21no—
216#121—791no—
217#121—791no—
218#121—1581no—
219#121C2×D7911yescharacteristic
220C4×Q8C2×D7911yescharacteristic
221C4×D4—21no—
222C4×D4—791no—
223C4×D4—1581no—
224C4×D4C2×D7911yescharacteristic
225#117—791no—
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#103—791no—
236#103—791no—
237#102—791no—
238#102—791no—
239#102—791no—
240#102—791no—
241C22⋊C8—791no—
242C22⋊C8—791no—
243C4×C8—791no—
244#41—22no—
245#41—41no—
246C2×Q8—21no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8C22×D7911yescharacteristic
250C2×Q8C22×D7911yescharacteristic
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—791no—
254C2×D4—1581no—
255C2×D4—1581no—
256C2×D4C22⋊D7911yescharacteristic
257C2×D4C22×D7911yescharacteristic
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264SD16—3161no—
265SD16—1582no—
266D8—3161no—
267C2×C8—3161no—
268C2×C8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—791no—
276C4⋊C4—791no—
277C4⋊C4—791no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4C22⋊D7911yescharacteristic
282C4⋊C4C22×D7911yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4C22⋊D7911yescharacteristic
292C22⋊C4C22⋊D7911yescharacteristic
293C42—21no—
294C42—1581no—
295C42C22×D7911yescharacteristic
296C23—21no—
297C23—1581no—
298C23C2×C22⋊D7911yescharacteristic
299C23C2×C22⋊D7911yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—42no—
304Q8#1192962312yes—
305D4—22no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—42no—
310D4—3162no—
311D4—6321no—
312D4—1581no—
313D4—1581no—
314C2×C4—21no—
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—6321no—
324C2×C4—6321no—
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—41no—
343C22—41no—
344C22—41no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22#1457918112yes—
349C22C22×C22⋊D7911yescharacteristic
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—41no—
356C4—41no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4C2×#1192962311yescharacteristic
361C4#1457920611yescharacteristic
362C2—22no—
363C2—41no—
364C2—81no—
365C2—6321no—
366C2#1909920711yescharacteristic
367C2C2×#1457918111yescharacteristic
368C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3301
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #19099259C2semidirect
2. #19098917C2semidirect
3. #19098901C2semidirect
4. #19098879C2semidirect
5. #19098870C2semidirect
6. #19098797C2semidirect
7. #19098794C2semidirect
8. #19098775C2semidirect
9. #19098708C2semidirect
10. #19098702C2semidirect
11. C4×#11929611C2semidirect
12. D4×C79⋊C8C2semidirect
13. #19098559C2semidirect
14. C2×#14579085C2semidirect
15. #548×C79C2semidirect
185. C79#3301semidirect
187. #548D79semidirect