Finite Group Databasebeta

← #23773592

Subgroups — #23773592

Order 10112.

396 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#19099166C211yesmaximal, characteristic, complemented
2#19099046C211yesmaximal, characteristic, complemented
3#19098879C211yesmaximal, characteristic, complemented
4#19098877C211yesmaximal, characteristic, complemented
5#19098872C211yesmaximal, characteristic, complemented
6#19098861C211yesmaximal, characteristic, complemented
7#19098761C211yesmaximal, characteristic, complemented
8#19098756C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic, complemented
10#19098672C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12#19098648C211yesmaximal, characteristic, complemented
13D8×Dic79C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929609C2211yescharacteristic
18#14579157C2211yescharacteristic
19#14579152C2211yescharacteristic
20#14579145—21no—
21#14579143—21no—
22#14579135C2211yescharacteristic
23#14579133—21no—
24#14579132—21no—
25Q8×Dic79C2211yescharacteristic
26Q8×Dic79C2211yescharacteristic
27D4×Dic79—21no—
28D4×Dic79—21no—
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32#14579123C2211yescharacteristic
33#14579120—21no—
34#14579120C2211yescharacteristic
35C2×C4⋊Dic79—21no—
36C2×C4⋊Dic79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579092C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68#11929611—22no—
69#11929609—22no—
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79D411yescharacteristic
77C4⋊Dic79D411yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79D411yescharacteristic
86C22⋊Dic79D411yescharacteristic
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93#41×C79—22no—
94#41×C79—22no—
95C2×Q8×C79C2311yescharacteristic
96C2×D4×C79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101C22×C4×C79C2311yescharacteristic
102SD16×C79—22no—
103D8×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79C2×D411yescharacteristic
111C22×D79—21no—
112Q8×C79—21no—
113Q8×C79#4112yes—
114D4×C79—24no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—81no—
119D4×C79#4112yes—
120C2×C4×C79—24no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—81no—
128C22⋊D79—81no—
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79—81no—
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141D316—21no—
142D316—21no—
143C4×D79—81no—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—21no—
149C22×C79—22no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79C22×D411yescharacteristic
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C4×C79—21no—
162C4×C79—22no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C79C2×#4111yescharacteristic
166Dic79—21no—
167Dic79—21no—
168Dic79—21no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173C2×C79—41no—
174C2×C79—42no—
175C2×C79—81no—
176C2×C79#52511yescharacteristic
177C2×C79#57611yescharacteristic
178C2×C79#57711yescharacteristic
179D79—81no—
180#3119—791nomaximal, Sylow
181C79#311911yescharacteristic, complemented, Sylow
182#540—791no—
183#520—791no—
184#481—791no—
185#480—791no—
186#479—791no—
187#478—791no—
188#460—791no—
189#459—791no—
190#449—791no—
191#449D7911yescharacteristic, complemented
192#442—791no—
193#440—791no—
194C4×SD16—791no—
195C4×D8—791no—
196#433—791no—
197C2×#41C2×D7911yescharacteristic
198C2×SD16—791no—
199C2×SD16C2×D7911yescharacteristic
200C2×D8—791no—
201C2×D8C2×D7911yescharacteristic
202#127—791no—
203#125—791no—
204#123—1581no—
205#123—1581no—
206#121—791no—
207#121—1581no—
208#121—1581no—
209#121C2×D7911yescharacteristic
210C4×Q8—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—1581no—
217C4×D4—1581no—
218#117—791no—
219#117—1581no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—1581no—
222#107—791no—
223#107—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227C4⋊C8—791no—
228#103—791no—
229#103C2×D7911yescharacteristic
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236C22⋊C8—791no—
237C22⋊C8C2×D7911yescharacteristic
238#97—791no—
239C4×C8—791no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D7911yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—791no—
246C2×D4—1581no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—21no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258SD16—22no—
259SD16—1582no—
260D8—22no—
261D8—1582no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—791no—
279C22⋊C4—791no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C42—791no—
286C42—791no—
287C42—1581no—
288C42—1581no—
289C23—21no—
290C23—21no—
291C23—1581no—
292C23D4×D7911yescharacteristic
293Q8—21no—
294Q8#1192962312yes—
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—6321no—
301D4—6321no—
302D4—6321no—
303D4—1581no—
304D4—1581no—
305D4#1192962312yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—791no—
312C2×C4—791no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—6321no—
316C2×C4—6321no—
317C2×C4—6321no—
318C2×C4—6321no—
319C2×C4—6321no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4D4×D7911yescharacteristic
324C2×C4C23×D7911yescharacteristic
325C8—21no—
326C8—21no—
327C8—1581no—
328C8—1581no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3161no—
339C22—3161no—
340C22—3161no—
341C22C2×D4×D7911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—1581no—
349C4—1581no—
350C4—1581no—
351C4—1581no—
352C4C2×#1192962311yescharacteristic
353C4C2×#1192962311yescharacteristic
354C2—41no—
355C2—42no—
356C2—81no—
357C2—6321no—
358C2#1909906911yescharacteristic
359C2#1909936511yescharacteristic
360C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3119
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099166C2semidirect
2. #19099046C2semidirect
3. #19098879C2semidirect
4. #19098877C2semidirect
5. #19098872C2semidirect
6. #19098861C2semidirect
7. #19098761C2semidirect
8. #19098756C2semidirect
9. #19098708C2semidirect
10. #19098672C2semidirect
11. #19098664C2semidirect
12. #19098648C2semidirect
13. D8×Dic79C2semidirect
14. #19098621C2semidirect
15. #449×C79C2semidirect
181. C79#3119semidirect
191. #449D79semidirect