Finite Group Databasebeta

← #23773453

Subgroups — #23773453

Order 10112.

434 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099108C211yesmaximal, characteristic, complemented
2#41×Dic79C211yesmaximal, characteristic, complemented
3#19098888C211yesmaximal, characteristic, complemented
4#19098884C211yesmaximal, characteristic, complemented
5#19098856C211yesmaximal, characteristic, complemented
6#19098851C211yesmaximal, characteristic, complemented
7#19098761C211yesmaximal, characteristic, complemented
8#19098756C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic, complemented
10SD16×Dic79C211yesmaximal, characteristic, complemented
11#19098648C211yesmaximal, characteristic, complemented
12D8×Dic79C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14#19098613C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929611C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19#14579160C2211yescharacteristic
20#14579157C2211yescharacteristic
21#14579147—21no—
22#14579135C2211yescharacteristic
23#14579133—21no—
24Q8×Dic79C2211yescharacteristic
25Q8×Dic79C2211yescharacteristic
26D4×Dic79—21no—
27D4×Dic79—21no—
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31#14579123C2211yescharacteristic
32(C22⋊D79)⋊C4—21no—
33#14579120—21no—
34#14579120C2211yescharacteristic
35C2×C4×Dic79—21no—
36C2×C4×Dic79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50C8×Dic79C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79D411yescharacteristic
69C22×Dic79D411yescharacteristic
70C2×C4×D79—21no—
71#11929611—22no—
72#11929609—22no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88C4×Dic79—21no—
89C4×Dic79—21no—
90C4×Dic79D411yescharacteristic
91C4×Dic79D411yescharacteristic
92C4×Dic79C2311yescharacteristic
93C4×Dic79C2311yescharacteristic
94#41×C79—22no—
95#41×C79—22no—
96C2×Q8×C79C2311yescharacteristic
97C2×D4×C79—21no—
98C2×D4×C79—21no—
99C2×D4×C79C2311yescharacteristic
100C2×D4×C79C2311yescharacteristic
101C22×C4×C79—21no—
102C22×C4×C79C2311yescharacteristic
103SD16×C79—22no—
104D8×C79—22no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C22⋊C4×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79—21no—
113Q8×C79—21no—
114Q8×C79#4112yescomplemented
115D4×C79—24no—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—21no—
119D4×C79—42no—
120D4×C79#4112yescomplemented
121C2×C4×C79—24no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—42no—
129C22⋊D79—42no—
130C22⋊D79—42no—
131C2×Dic79—22no—
132C2×Dic79—22no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—42no—
137C2×Dic79—42no—
138C2×Dic79—42no—
139C2×Dic79C2×D411yescharacteristic
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143D316—21no—
144D316—21no—
145C4×D79—42no—
146Dic158—42no—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—22no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79C22×D411yescharacteristic
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C4×C79—21no—
165C4×C79—22no—
166C4×C79—41no—
167C4×C79C2×#4111yescharacteristic
168C4×C79C2×#4111yescharacteristic
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174Dic79#13512yes—
175Dic79AGL(1,ℤ/8)12yes—
176C2×C79—41no—
177C2×C79—42no—
178C2×C79—81no—
179C2×C79#52511yescharacteristic
180C2×C79C2×#13511yescharacteristic
181C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
182D79—81no—
183#3106—791nomaximal, Sylow
184C79#310611yescharacteristic, complemented, Sylow
185#532—791no—
186C4×#41—791no—
187#482—791no—
188#482—791no—
189#477—791no—
190#476—791no—
191#460—791no—
192#459—791no—
193#449—791no—
194#449D7911yescharacteristic, complemented
195C4×SD16—791no—
196C4×SD16—791no—
197C4×D8—791no—
198C4×D8—791no—
199#431—791no—
200C2×#41—1581no—
201C2×#41C2×D7911yescharacteristic
202C2×SD16—791no—
203C2×SD16C2×D7911yescharacteristic
204C2×D8—791no—
205C2×D8C2×D7911yescharacteristic
206C4⋊Q8—791no—
207#127—791no—
208#124—1581no—
209#121—791no—
210#121—1581no—
211#121C2×D7911yescharacteristic
212C4×Q8—791no—
213C4×Q8—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4—791no—
218C4×D4—1581no—
219C4×D4—1581no—
220C4×D4—1581no—
221#117—791no—
222#117—1581no—
223C2×C42—791no—
224C2×C42—1581no—
225#107—791no—
226#107—791no—
227#106—791no—
228#106—791no—
229C4⋊C8—791no—
230C4⋊C8—791no—
231#103—791no—
232#103C2×D7911yescharacteristic
233#102—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237#102—791no—
238#102C2×D7911yescharacteristic
239C22⋊C8—791no—
240C22⋊C8C2×D7911yescharacteristic
241C4×C8—791no—
242C4×C8—791no—
243#41—22no—
244#41—22no—
245#41—3164no—
246C2×Q8—1581no—
247C2×Q8C22×D7911yescharacteristic
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4—1581no—
253C2×D4—1581no—
254C2×D4C22×D7911yescharacteristic
255C2×D4C22×D7911yescharacteristic
256C22×C4—21no—
257C22×C4—791no—
258C22×C4—791no—
259C22×C4—1581no—
260C22×C4—1581no—
261C22×C4—1581no—
262C22×C4—1581no—
263C22×C4C22×D7911yescharacteristic
264SD16—22no—
265SD16—1582no—
266D8—22no—
267D8—1582no—
268C2×C8—791no—
269C2×C8—791no—
270C2×C8C22×D7911yescharacteristic
271C2×C8C22×D7911yescharacteristic
272C4⋊C4—791no—
273C4⋊C4—791no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4C22×D7911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C42—791no—
288C42—791no—
289C42—791no—
290C42—1581no—
291C42—1581no—
292C42—1581no—
293C23—21no—
294C23—21no—
295C23—1581no—
296C23D4×D7911yescharacteristic
297Q8—21no—
298Q8—3162no—
299Q8#1192962312yescomplemented
300D4—24no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—42no—
305D4—3162no—
306D4—3162no—
307D4—3162no—
308D4—1581no—
309D4—1581no—
310D4#1192962312yescomplemented
311C2×C4—24no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—3162no—
317C2×C4—3162no—
318C2×C4—3162no—
319C2×C4—3162no—
320C2×C4—791no—
321C2×C4—791no—
322C2×C4—791no—
323C2×C4—791no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1582no—
328C2×C4—1582no—
329C2×C4D4×D7911yescharacteristic
330C2×C4C23×D7911yescharacteristic
331C8—21no—
332C8—21no—
333C8—1581no—
334C8—1581no—
335C22—21no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22C2×D4×D7911yescharacteristic
348C4—21no—
349C4—22no—
350C4—41no—
351C4—3161no—
352C4—3161no—
353C4—3161no—
354C4—792no—
355C4—792no—
356C4—1581no—
357C4—1581no—
358C4C2×#1192962311yescharacteristic
359C4C2×#1192962311yescharacteristic
360C2—41no—
361C2—42no—
362C2—81no—
363C2—6321no—
364C2#1909906911yescharacteristic
365C2#135×D7911yescharacteristic
366C2AGL(1,ℤ/8)×D7911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3106
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. #19099108C2semidirect
2. #41×Dic79C2semidirect
3. #19098888C2semidirect
4. #19098884C2semidirect
5. #19098856C2semidirect
6. #19098851C2semidirect
7. #19098761C2semidirect
8. #19098756C2semidirect
9. #19098708C2semidirect
10. SD16×Dic79C2semidirect
11. #19098648C2semidirect
12. D8×Dic79C2semidirect
13. #19098643C2semidirect
14. #19098613C2semidirect
15. #449×C79C2semidirect
114. Q8×C79#41semidirect
120. D4×C79#41semidirect
184. C79#3106semidirect
194. #449D79semidirect
299. Q8#11929623semidirect
310. D4#11929623semidirect