Finite Group Databasebeta

← #23775513

Subgroups — #23775513

Order 10112.

388 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#19099270C211yesmaximal, characteristic, complemented
2#19099222C211yesmaximal, characteristic
3#19098923C211yesmaximal, characteristic, complemented
4#19098894C211yesmaximal, characteristic, complemented
5#19098882C211yesmaximal, characteristic, complemented
6#19098849C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098786C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098721C211yesmaximal, characteristic, complemented
12#19098671C211yesmaximal, characteristic, complemented
13#19098565C211yesmaximal, characteristic, complemented
14C2×#14579086C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×Dic316C2211yescharacteristic
19C2×Dic316C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21#14579161C2211yescharacteristic
22#14579152—21no—
23#14579149C2211yescharacteristic
24#14579147—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27#14579140C2211yescharacteristic
28#14579139—21no—
29#14579138—21no—
30#14579138—21no—
31#14579135C2211yescharacteristic
32#14579133—21no—
33C4×Dic158C2211yescharacteristic
34C4×Dic158C2211yescharacteristic
35D4×Dic79—21no—
36(C22⋊D79)⋊C4—21no—
37C2×C4⋊Dic79C2211yescharacteristic
38C2×C4⋊Dic79C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579093C2211yescharacteristic
41#14579093C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579086C2211yescharacteristic
47#14579086C2211yescharacteristic
48#14579086C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—41no—
61C2×Dic158—22no—
62C2×Dic158—21no—
63C2×Dic158—21no—
64C2×Dic158—41no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79—21no—
71C22×Dic79—21no—
72C22×Dic79—21no—
73C22×Dic79—21no—
74C2×C4×D79—21no—
75Dic316—22no—
76Dic316—41no—
77#11929613—41no—
78C4⋊Dic79—21no—
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82C4⋊Dic79C2311yescharacteristic
83C4⋊Dic79C2311yescharacteristic
84C4⋊Dic79C2311yescharacteristic
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92C22⋊Dic79—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C2×D4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101M16×C79—41no—
102C2×C8×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114D4×C79—22no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2411yescharacteristic
124C22⋊D79—42no—
125C22⋊D79—42no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—42no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136D316—21no—
137D316—21no—
138C4×D79—42no—
139Dic158—21no—
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—21no—
144Dic158—42no—
145Dic158—81no—
146Dic158#4112yes—
147C8×C79—21no—
148C8×C79—21no—
149C8×C79—21no—
150C8×C79—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79#13712yes—
157C22×C79C22×D411yescharacteristic
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—21no—
165C4×C79C2×#4111yescharacteristic
166C4×C79H(5,𝔽2)11yescharacteristic
167Dic79—22no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79—41no—
176C2×C79#54611yescharacteristic
177C2×C79C2×#13711yescharacteristic
178C2×C79#57711yescharacteristic
179D79—81no—
180#3316—791nomaximal, Sylow
181C79#331611yescharacteristic, complemented, Sylow
182#554—791no—
183#548—791no—
184#489—791no—
185#483—791no—
186#481—791no—
187#475—791no—
188#470—791no—
189#465—791no—
190#464—791no—
191#452—791no—
192#451—791no—
193#441—791no—
194#435D7911yescharacteristic, complemented
195#417—791no—
196C2×#103—791no—
197C2×#41—791no—
198C22×Q8—791no—
199C2×Q16—791no—
200C2×Q16—791no—
201C2×SD16—791no—
202C2×M16C2×D7911yescharacteristic
203C22×C8C2×D7911yescharacteristic
204C4⋊Q8—791no—
205#125—1581no—
206#124—791no—
207#124—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212C22⋊Q8—1581no—
213C22⋊Q8—1581no—
214#121—791no—
215#121—1581no—
216C4×Q8—791no—
217C4×Q8—791no—
218C4×D4—1581no—
219C4×D4—1581no—
220C4×D4C2×D7911yescharacteristic
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8C2×D7911yescharacteristic
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#102—791no—
235#102—791no—
236#102—791no—
237C22⋊C8C2×D7911yescharacteristic
238C22⋊C8C2×D7911yescharacteristic
239#97C2×D7911yescharacteristic
240#41—3161no—
241#41—1582no—
242C2×Q8—3161no—
243C2×Q8—791no—
244C2×Q8—791no—
245C2×Q8—791no—
246C2×Q8—1582no—
247C2×Q8—1581no—
248C2×Q8—1581no—
249C2×D4—791no—
250C2×D4—1581no—
251C2×D4—1581no—
252C2×D4D31611yescharacteristic
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259Q16—3161no—
260Q16—1582no—
261SD16—3161no—
262M16—41no—
263C2×C8—41no—
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C2×C8C22×D7911yescharacteristic
267C2×C8C22×D7911yescharacteristic
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4—1581no—
280C4⋊C4D31611yescharacteristic
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4D31611yescharacteristic
288C22⋊C4D31611yescharacteristic
289C42—1581no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—1581no—
293C23C2×D31611yescharacteristic
294C23C2×D31611yescharacteristic
295Q8—3162no—
296Q8—792no—
297Q8—6321no—
298Q8—1581no—
299Q8—1581no—
300Q8—1581no—
301Q8—1581no—
302Q8—1581no—
303D4—22no—
304D4—3162no—
305D4—3162no—
306D4—1581no—
307D4—1581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—3162no—
313C2×C4—3162no—
314C2×C4—6321no—
315C2×C4—6321no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4C2×D31611yescharacteristic
324C2×C4C2×D31611yescharacteristic
325C2×C4C2×D31611yescharacteristic
326C2×C4C2×D31611yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—21no—
329C8—21no—
330C8—21no—
331C8—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22#1457919412yes—
341C22C22×D31611yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—3161no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—1582no—
353C4#41×D7911yescharacteristic
354C4#1457920611yescharacteristic
355C2—22no—
356C2—41no—
357C2—6321no—
358C2#1909920811yescharacteristic
359C2C2×#1457919411yescharacteristic
360C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
prime radical#19099222C2
hypercenter#435D79
hypocenterC79#3316
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #19099270C2semidirect
3. #19098923C2semidirect
4. #19098894C2semidirect
5. #19098882C2semidirect
6. #19098849C2semidirect
7. #19098821C2semidirect
8. #19098792C2semidirect
9. #19098786C2semidirect
10. #19098727C2semidirect
11. #19098721C2semidirect
12. #19098671C2semidirect
13. #19098565C2semidirect
14. C2×#14579086C2semidirect
15. #435×C79C2semidirect
181. C79#3316semidirect
194. #435D79semidirect