Finite Group Databasebeta

← #23775505

Subgroups — #23775505

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#19099222C211yesmaximal, characteristic
2#19098925C211yesmaximal, characteristic, complemented
3#19098893C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098845C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098794C211yesmaximal, characteristic, complemented
8#19098785C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098562C211yesmaximal, characteristic, complemented
14C2×#14579084C211yesmaximal, characteristic, complemented
15#554×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
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#14579092C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#125×C79—21no—
50C22⋊Q8×C79—21no—
51C22⋊Q8×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79—21no—
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#11929614—22no—
72#11929614—41no—
73#11929611—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—
88C2×Q8×C79—21no—
89C2×Q8×C79C2311yescharacteristic
90C2×D4×C79D411yescharacteristic
91C22×C4×C79—21no—
92C22×C4×C79—21no—
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79D411yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C4⋊C4×C79C2311yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—81no—
117D4×C79—22no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—81no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C22⋊D79—42no—
134C22⋊D79—42no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—42no—
139D316—21no—
140D316—21no—
141C4×D79—42no—
142Dic158—21no—
143Dic158—21no—
144Dic158—21no—
145Dic158—42no—
146Dic158#4112yes—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—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×C79—41no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79C2×#4111yescharacteristic
170C4×C79H(5,𝔽2)11yescharacteristic
171Dic79—22no—
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#554D7911yescharacteristic, complemented
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#435—791no—
195#417—791no—
196C2×#103—791no—
197C2×#41—791no—
198C22×Q8—791no—
199C2×Q16—791no—
200C2×Q16—791no—
201C2×SD16—791no—
202C2×M16—791no—
203C22×C8—791no—
204C4⋊Q8C2×D7911yescharacteristic
205#125—21no—
206#124—791no—
207#124—1581no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212C22⋊Q8C2×D7911yescharacteristic
213C22⋊Q8C2×D7911yescharacteristic
214#121—791no—
215#121—1581no—
216C4×Q8—791no—
217C4×Q8C2×D7911yescharacteristic
218C4×D4—21no—
219C4×D4—1581no—
220C4×D4C2×D7911yescharacteristic
221C2×C4⋊C4C2×D7911yescharacteristic
222C2×C4⋊C4C2×D7911yescharacteristic
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
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⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240#41—3161no—
241#41—1582no—
242C2×Q8—21no—
243C2×Q8—3161no—
244C2×Q8—791no—
245C2×Q8—791no—
246C2×Q8—1582no—
247C2×Q8—1581no—
248C2×Q8C22×D7911yescharacteristic
249C2×D4—791no—
250C2×D4—1581no—
251C2×D4—1581no—
252C2×D4C22⋊D7911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259Q16—3161no—
260Q16—1582no—
261SD16—3161no—
262M16—3161no—
263C2×C8—3161no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8—791no—
267C2×C8—791no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—791no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22⋊D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4C22⋊D7911yescharacteristic
288C22⋊C4C22⋊D7911yescharacteristic
289C42—21no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—1581no—
293C23C2×C22⋊D7911yescharacteristic
294C23C2×C22⋊D7911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—81no—
298Q8—3162no—
299Q8—792no—
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—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—3162no—
319C2×C4—3162no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4C2×C22⋊D7911yescharacteristic
324C2×C4C2×C22⋊D7911yescharacteristic
325C2×C4C2×C22⋊D7911yescharacteristic
326C2×C4C2×C22⋊D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—1581no—
329C8—1581no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3161no—
338C22—3161no—
339C22—3161no—
340C22#1457919212yes—
341C22C22×C22⋊D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—3161no—
351C4—3161no—
352C4—1582no—
353C4#41×D7911yescharacteristic
354C4#1457920711yescharacteristic
355C2—22no—
356C2—41no—
357C2—6321no—
358C2#1909920111yescharacteristic
359C2C2×#1457919211yescharacteristic
360C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#554×C79C2
socleC22×C79C22×D4
prime radical#19099222C2
hypercenter#554D79
hypocenterC79#3316
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19098925C2semidirect
3. #19098893C2semidirect
4. #19098881C2semidirect
5. #19098845C2semidirect
6. #19098819C2semidirect
7. #19098794C2semidirect
8. #19098785C2semidirect
9. #19098723C2semidirect
10. #19098718C2semidirect
11. #19098668C2semidirect
12. #19098635C2semidirect
13. #19098562C2semidirect
14. C2×#14579084C2semidirect
15. #554×C79C2semidirect
181. C79#3316semidirect
182. #554D79semidirect