Finite Group Databasebeta

← #23775385

Subgroups — #23775385

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#19099222C211yesmaximal, characteristic, complemented
2#19098925C211yesmaximal, characteristic, complemented
3#19098898C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098855C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098797C211yesmaximal, characteristic, complemented
8#19098778C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic, complemented
10#19098701C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14C2×#14579084C211yesmaximal, characteristic, complemented
15#547×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579147—21no—
25#14579140C2211yescharacteristic
26#14579139—21no—
27#14579135C2211yescharacteristic
28#14579133—21no—
29C4×Dic158C2211yescharacteristic
30(C22⋊D79)⋊C4—21no—
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579084C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79—21no—
49C4⋊Q8×C79C2211yescharacteristic
50#123×C79—21no—
51#123×C79—21no—
52C22⋊Q8×C79—21no—
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57C2×C4⋊C4×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—41no—
61C2×Dic158—22no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158C2311yescharacteristic
65C2×Dic158C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71#11929612—22no—
72#11929612—41no—
73#11929609—41no—
74#11929608—41no—
75C2×C79⋊C8—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88#41×C79—44no—
89C2×Q8×C79—21no—
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79D411yescharacteristic
93C2×D4×C79C2311yescharacteristic
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79D411yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79D411yescharacteristic
110C22⋊C4×C79D411yescharacteristic
111C42×C79C2311yescharacteristic
112C23×C79—21no—
113C23×C79C2×D411yescharacteristic
114C23×C79C2×D411yescharacteristic
115C22×D79—21no—
116Q8×C79—42no—
117D4×C79—22no—
118D4×C79—21no—
119D4×C79—21no—
120D4×C79—42no—
121D4×C79—42no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—42no—
130C2×C4×C79—42no—
131C2×C4×C79—42no—
132C2×C4×C79C2×D411yescharacteristic
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2411yescharacteristic
137C22⋊D79—42no—
138C22⋊D79—42no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—42no—
143D316—21no—
144D316—21no—
145C4×D79—42no—
146Dic158—21no—
147Dic158—21no—
148Dic158—21no—
149Dic158—42no—
150Dic158#4112yescomplemented
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C79⋊C8—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79AGL(1,ℤ/8)12yes—
164C22×C79C22×D411yescharacteristic
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C4×C79—21no—
169C4×C79—21no—
170C4×C79—21no—
171C4×C79—21no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79C2×#4111yescharacteristic
176C4×C79H(5,𝔽2)11yescharacteristic
177Dic79—22no—
178Dic79—41no—
179Dic79—41no—
180C2×C79—22no—
181C2×C79—41no—
182C2×C79—81no—
183C2×C79#54611yescharacteristic
184C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C79#57811yescharacteristic
186D79—81no—
187#3308—791nomaximal, Sylow
188C79#330811yescharacteristic, complemented, Sylow
189#548—791no—
190#547D7911yescharacteristic, complemented
191#489—791no—
192#484—791no—
193#480—791no—
194#477—791no—
195#468—791no—
196#466—791no—
197#463—791no—
198#449—791no—
199#448—791no—
200#440—791no—
201#435—791no—
202#417—791no—
203C2×#103—791no—
204C2×#41—21no—
205C2×#41—791no—
206C22×Q8—791no—
207C2×SD16—791no—
208C2×SD16—791no—
209C2×D8—791no—
210C2×M16—791no—
211C22×C8—791no—
212C4⋊Q8C2×D7911yescharacteristic
213#124—791no—
214#124—1581no—
215#123—21no—
216#123—21no—
217C22⋊Q8—21no—
218C22⋊Q8—791no—
219C22⋊Q8—1581no—
220#121—791no—
221#121—1581no—
222#121C2×D7911yescharacteristic
223#121C2×D7911yescharacteristic
224C4×Q8—791no—
225C4×D4—1581no—
226C4×D4C2×D7911yescharacteristic
227C4×D4C2×D7911yescharacteristic
228C2×C4⋊C4C2×D7911yescharacteristic
229C2×C4⋊C4C2×D7911yescharacteristic
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#103—791no—
240#102—791no—
241#102—791no—
242#102—791no—
243#102—791no—
244C22⋊C8—791no—
245C22⋊C8—791no—
246#97—791no—
247#41—44no—
248#41—3161no—
249#41—1582no—
250C2×Q8—21no—
251C2×Q8—3161no—
252C2×Q8—791no—
253C2×Q8—791no—
254C2×Q8—1582no—
255C2×Q8—1581no—
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—21no—
265C22×C4—21no—
266C22×C4—1581no—
267C22×C4—1581no—
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270SD16—3161no—
271SD16—1582no—
272D8—3161no—
273M16—3161no—
274C2×C8—3161no—
275C2×C8—791no—
276C2×C8—791no—
277C2×C8—791no—
278C2×C8—791no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—791no—
283C4⋊C4—1581no—
284C4⋊C4—1581no—
285C4⋊C4C22⋊D7911yescharacteristic
286C4⋊C4C22×D7911yescharacteristic
287C4⋊C4C22×D7911yescharacteristic
288C4⋊C4C22×D7911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1581no—
293C22⋊C4—1581no—
294C22⋊C4—1581no—
295C22⋊C4—1581no—
296C22⋊C4C22⋊D7911yescharacteristic
297C22⋊C4C22⋊D7911yescharacteristic
298C42—1581no—
299C42C22×D7911yescharacteristic
300C23—21no—
301C23—1581no—
302C23C2×C22⋊D7911yescharacteristic
303C23C2×C22⋊D7911yescharacteristic
304Q8—42no—
305Q8—3162no—
306Q8—792no—
307Q8—1581no—
308Q8—1581no—
309Q8—1581no—
310D4—22no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—42no—
315D4—3162no—
316D4—3162no—
317D4—1581no—
318D4—1581no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—3162no—
330C2×C4—3162no—
331C2×C4—1581no—
332C2×C4—1581no—
333C2×C4—1581no—
334C2×C4C2×C22⋊D7911yescharacteristic
335C2×C4C2×C22⋊D7911yescharacteristic
336C2×C4C2×C22⋊D7911yescharacteristic
337C2×C4C2×C22⋊D7911yescharacteristic
338C2×C4C23×D7911yescharacteristic
339C8—1581no—
340C8—1581no—
341C8—1581no—
342C8—1581no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—3161no—
352C22—3161no—
353C22—3161no—
354C22#1457918712yes—
355C22C22×C22⋊D7911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—41no—
363C4—3161no—
364C4—3161no—
365C4—1582no—
366C4#41×D7911yescharacteristic
367C4#1457920711yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—6321no—
372C2#1909920111yescharacteristic
373C2C2×#1457918711yescharacteristic
374C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#547×C79C2
socleC22×C79C22×D4
hypercenter#547D79
hypocenterC79#3308
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19099222C2semidirect
2. #19098925C2semidirect
3. #19098898C2semidirect
4. #19098876C2semidirect
5. #19098855C2semidirect
6. #19098807C2semidirect
7. #19098797C2semidirect
8. #19098778C2semidirect
9. #19098706C2semidirect
10. #19098701C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. C2×#14579084C2semidirect
15. #547×C79C2semidirect
150. Dic158#41semidirect
188. C79#3308semidirect
190. #547D79semidirect