Finite Group Databasebeta

← #23775384

Subgroups — #23775384

Order 10112.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099220C211yesmaximal, characteristic, complemented
2#19099213C211yesmaximal, characteristic, complemented
3#19098921C211yesmaximal, characteristic, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098875C211yesmaximal, characteristic, complemented
6#19098856C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098796C211yesmaximal, characteristic, complemented
9#19098776C211yesmaximal, characteristic, complemented
10#19098700C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12#19098637C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14#103×D79C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×Q8×D79C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579148—21no—
23#14579148C2211yescharacteristic
24#14579143—21no—
25#14579142—21no—
26#14579140—21no—
27#14579140C2211yescharacteristic
28#14579138—21no—
29#14579132—21no—
30#14579132C2211yescharacteristic
31#14579132C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic
33D4×Dic79C2211yescharacteristic
34C4×C22⋊D79—21no—
35C4×C22⋊D79C2211yescharacteristic
36C2×C4⋊Dic79C2211yescharacteristic
37C4⋊C4×D79C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49#14579082C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
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×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63Q8×D79—22no—
64Q8×D79—41no—
65C2×C22⋊D79—21no—
66C2×C22⋊D79—21no—
67C2×C22⋊D79D411yescharacteristic
68C22×Dic79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71C2×C4×D79—21no—
72C2×C4×D79C2311yescharacteristic
73#11929612—41no—
74#11929608—41no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C8×D79—41no—
78C4⋊Dic79—21no—
79C4⋊Dic79—21no—
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93C22⋊Dic79D411yescharacteristic
94(C2×D79)⋊C4D411yescharacteristic
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79—21no—
102C2×D4×C79C2311yescharacteristic
103C2×D4×C79C2311yescharacteristic
104C22×C4×C79—21no—
105C22×C4×C79C2311yescharacteristic
106SD16×C79—22no—
107D8×C79—41no—
108C2×C8×C79C2311yescharacteristic
109C2×C8×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C22⋊C4×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79C2×D411yescharacteristic
115C22×D79C2×D411yescharacteristic
116Q8×C79—21no—
117Q8×C79#4112yescomplemented
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121D4×C79—21no—
122D4×C79—42no—
123D4×C79—42no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—42no—
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C22⋊D79—22no—
132C22⋊D79—42no—
133C22⋊D79—42no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—42no—
139C2×Dic79—42no—
140C2×Dic79C2×D411yescharacteristic
141C2×Dic79C2×D411yescharacteristic
142C2×Dic79C2×D411yescharacteristic
143C4×D79—21no—
144C4×D79—21no—
145C4×D79—42no—
146C4×D79—42no—
147Dic158—21no—
148Dic158—21no—
149Dic158—42no—
150Dic158—42no—
151C8×C79—21no—
152C8×C79—21no—
153C79⋊C8—21no—
154C79⋊C8—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
165C2×D79—21no—
166C2×D79—21no—
167C2×D79AGL(1,ℤ/8)12yes—
168C4×C79—21no—
169C4×C79—22no—
170C4×C79—41no—
171C4×C79C2×#4111yescharacteristic
172C4×C79H(5,𝔽2)11yescharacteristic
173Dic79—21no—
174Dic79—21no—
175Dic79—21no—
176Dic79—41no—
177Dic79—41no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—41no—
181C2×C79—81no—
182C2×C79—81no—
183C2×C79#54611yescharacteristic
184C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C79#57811yescharacteristic
186D79—22no—
187#3308—791nomaximal, Sylow
188C79#330811yescharacteristic, complemented, Sylow
189#548—791no—
190#547—791no—
191#489—791no—
192#484—791no—
193#480—791no—
194#477—791no—
195#468—791no—
196#466—791no—
197#463—791no—
198#449D7911yescharacteristic, complemented
199#448—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#103—791no—
204C2×#41—1581no—
205C2×#41C2×D7911yescharacteristic
206C22×Q8—791no—
207C2×SD16—791no—
208C2×SD16C2×D7911yescharacteristic
209C2×D8C2×D7911yescharacteristic
210C2×M16—791no—
211C22×C8—791no—
212C4⋊Q8—791no—
213#124—791no—
214#124—1581no—
215#123—1581no—
216#123—1581no—
217C22⋊Q8—791no—
218C22⋊Q8—1581no—
219C22⋊Q8—1581no—
220#121—791no—
221#121—791no—
222#121—1581no—
223#121C2×D7911yescharacteristic
224C4×Q8—791no—
225C4×D4—791no—
226C4×D4—791no—
227C4×D4—1581no—
228C2×C4⋊C4—791no—
229C2×C4⋊C4—791no—
230#107—791no—
231#107—791no—
232#107—791no—
233C4⋊C8—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#103—791no—
238#103—791no—
239#103C2×D7911yescharacteristic
240#102—791no—
241#102—791no—
242#102—791no—
243#102C2×D7911yescharacteristic
244C22⋊C8—791no—
245C22⋊C8C2×D7911yescharacteristic
246#97—791no—
247#41—22no—
248#41—41no—
249#41—3164no—
250C2×Q8—3161no—
251C2×Q8—791no—
252C2×Q8—1581no—
253C2×Q8—1581no—
254C2×Q8—1582no—
255C2×Q8C22×D7911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—791no—
259C2×D4—1581no—
260C2×D4—1581no—
261C2×D4C22×D7911yescharacteristic
262C2×D4C22×D7911yescharacteristic
263C22×C4—21no—
264C22×C4—791no—
265C22×C4—1581no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4—1581no—
269C22×C4C22×D7911yescharacteristic
270SD16—22no—
271SD16—3161no—
272D8—41no—
273M16—3161no—
274C2×C8—3161no—
275C2×C8—791no—
276C2×C8—791no—
277C2×C8C22×D7911yescharacteristic
278C2×C8C22×D7911yescharacteristic
279C4⋊C4—791no—
280C4⋊C4—791no—
281C4⋊C4—791no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4—1581no—
286C4⋊C4—1581no—
287C4⋊C4—1581no—
288C4⋊C4C22×D7911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—791no—
291C22⋊C4—791no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4—1581no—
297C22⋊C4—1581no—
298C42—791no—
299C42—1581no—
300C23—21no—
301C23—21no—
302C23—791no—
303C23D4×D7911yescharacteristic
304Q8—21no—
305Q8—3162no—
306Q8—3162no—
307Q8—1581no—
308Q8—1581no—
309Q8#1192962312yescomplemented
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—3162no—
317D4—3162no—
318D4—1582no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—3162no—
325C2×C4—3162no—
326C2×C4—3162no—
327C2×C4—3162no—
328C2×C4—791no—
329C2×C4—791no—
330C2×C4—791no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4D4×D7911yescharacteristic
338C2×C4C23×D7911yescharacteristic
339C8—21no—
340C8—21no—
341C8—1581no—
342C8—1581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—792no—
353C22—1581no—
354C22—1581no—
355C22C2×D4×D7911yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—3161no—
360C4—3161no—
361C4—3161no—
362C4—3161no—
363C4—1581no—
364C4—1581no—
365C4—1581no—
366C4C2×#1192962311yescharacteristic
367C4#1457920611yescharacteristic
368C2—41no—
369C2—81no—
370C2—81no—
371C2—1582no—
372C2#1909920011yescharacteristic
373C2AGL(1,ℤ/8)×D7911yescharacteristic
374C2#1909937711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3308
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. #19099220C2semidirect
2. #19099213C2semidirect
3. #19098921C2semidirect
4. #19098899C2semidirect
5. #19098875C2semidirect
6. #19098856C2semidirect
7. #19098807C2semidirect
8. #19098796C2semidirect
9. #19098776C2semidirect
10. #19098700C2semidirect
11. #19098664C2semidirect
12. #19098637C2semidirect
13. #19098564C2semidirect
14. #103×D79C2semidirect
15. #449×C79C2semidirect
117. Q8×C79#41semidirect
188. C79#3308semidirect
198. #449D79semidirect
309. Q8#11929623semidirect