Finite Group Databasebeta

← #23775834

Subgroups — #23775834

Order 10112.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2#19098969C211yesmaximal, characteristic, complemented
3#19098898C211yesmaximal, characteristic, complemented
4#19098893C211yesmaximal, characteristic, complemented
5#19098884C211yesmaximal, characteristic, complemented
6#19098874C211yesmaximal, characteristic, complemented
7#19098863C211yesmaximal, characteristic, complemented
8#19098855C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098790C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098603C211yesmaximal, characteristic, complemented
14C2×#14579094C211yesmaximal, characteristic, complemented
15#547×C79C211yesmaximal, characteristic
16C2×#11929612C2211yescharacteristic
17C2×#11929608C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19#14579154—21no—
20#14579153C2211yescharacteristic
21#14579151—21no—
22#14579142—21no—
23#14579140C2211yescharacteristic
24#14579140C2211yescharacteristic
25C4×Dic158C2211yescharacteristic
26#14579120C2211yescharacteristic
27#14579117—21no—
28C2×C4⋊Dic79C2211yescharacteristic
29#14579094C2211yescharacteristic
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579094C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579092C2211yescharacteristic
37#14579092C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
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
59C2×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61#11929612—22no—
62#11929608—22no—
63C2×C79⋊C8—22no—
64C2×C79⋊C8C2311yescharacteristic
65C2×C79⋊C8C2311yescharacteristic
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C4⋊Dic79—21no—
69C4⋊Dic79C2311yescharacteristic
70C4⋊Dic79C2311yescharacteristic
71C4⋊Dic79C2311yescharacteristic
72Dic79⋊C4—21no—
73Dic79⋊C4—21no—
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77C22⋊Dic79—21no—
78C22⋊Dic79—21no—
79C22⋊Dic79—21no—
80C4×Dic79—21no—
81C4×Dic79—21no—
82#41×C79—44no—
83C2×Q8×C79—21no—
84C2×D4×C79—21no—
85C2×D4×C79—21no—
86C2×D4×C79D411yescharacteristic
87C2×D4×C79C2311yescharacteristic
88C22×C4×C79—21no—
89C22×C4×C79—21no—
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79D411yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C4⋊C4×C79C2311yescharacteristic
99C4⋊C4×C79C2311yescharacteristic
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C42×C79C2311yescharacteristic
106C23×C79—21no—
107C23×C79C2×D411yescharacteristic
108C23×C79C2×D411yescharacteristic
109Q8×C79—42no—
110D4×C79—22no—
111D4×C79—21no—
112D4×C79—21no—
113D4×C79—42no—
114D4×C79—42no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—42no—
123C2×C4×C79—42no—
124C2×C4×C79—42no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—42no—
135Dic158—21no—
136Dic158—21no—
137C79⋊C8—21no—
138C79⋊C8—21no—
139C79⋊C8—21no—
140C79⋊C8#4112yescomplemented
141C22×C79—21no—
142C22×C79—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79AGL(1,ℤ/8)12yes—
150C22×C79C22×D411yescharacteristic
151C4×C79—21no—
152C4×C79—21no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79C2×#4111yescharacteristic
159C4×C792−1+411yescharacteristic
160Dic79—41no—
161Dic79—41no—
162Dic79—41no—
163Dic79—41no—
164C2×C79—22no—
165C2×C79—41no—
166C2×C79—81no—
167C2×C79#54711yescharacteristic
168C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
169C2×C79#57811yescharacteristic
170#3343—791nomaximal, Sylow
171C79#334311yescharacteristic, complemented, Sylow
172#552—791no—
173#547D7911yescharacteristic
174#501—791no—
175#484—791no—
176#483—791no—
177#482—791no—
178#480—791no—
179#478—791no—
180#477—791no—
181#468—791no—
182#465—791no—
183#440—791no—
184#435—791no—
185#428—791no—
186C2×#107—791no—
187C2×#41—21no—
188C2×SD16—791no—
189C2×M16—791no—
190C22×C8—791no—
191C4⋊Q8C2×D7911yescharacteristic
192#126—1581no—
193#125—791no—
194#125—1581no—
195#123—21no—
196#123—21no—
197#123—1581no—
198C22⋊Q8—21no—
199C22⋊Q8—791no—
200C22⋊Q8—791no—
201#121C2×D7911yescharacteristic
202#121C2×D7911yescharacteristic
203C4×Q8—791no—
204C4×D4C2×D7911yescharacteristic
205C4×D4C2×D7911yescharacteristic
206#117—791no—
207#117—1581no—
208C2×C4⋊C4—791no—
209C2×C4⋊C4C2×D7911yescharacteristic
210C2×C4⋊C4C2×D7911yescharacteristic
211#107—791no—
212#107—791no—
213#107—791no—
214#107—791no—
215#107—791no—
216#107—791no—
217#106—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221#103—791no—
222#103—791no—
223#103—791no—
224#102—791no—
225#102—791no—
226#102—791no—
227C22⋊C8—791no—
228C22⋊C8—791no—
229#97—791no—
230#41—44no—
231C2×Q8—21no—
232C2×Q8—791no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊D7911yescharacteristic
236C2×D4C22×D7911yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—1581no—
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243SD16—1582no—
244M16—1582no—
245C2×C8—791no—
246C2×C8—791no—
247C2×C8—791no—
248C2×C8—791no—
249C2×C8—1582no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—791no—
254C4⋊C4—791no—
255C4⋊C4—791no—
256C4⋊C4—1581no—
257C4⋊C4—1581no—
258C4⋊C4—1581no—
259C4⋊C4—1581no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4C22⋊D7911yescharacteristic
263C4⋊C4C22×D7911yescharacteristic
264C4⋊C4C22×D7911yescharacteristic
265C4⋊C4C22×D7911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—1581no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4C22⋊D7911yescharacteristic
273C22⋊C4C22⋊D7911yescharacteristic
274C42—1581no—
275C42—1581no—
276C42C22×D7911yescharacteristic
277C23—21no—
278C23C2×C22⋊D7911yescharacteristic
279C23C2×C22⋊D7911yescharacteristic
280Q8—42no—
281Q8—1581no—
282Q8—1581no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—3162no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4C2×C22⋊D7911yescharacteristic
304C2×C4C2×C22⋊D7911yescharacteristic
305C2×C4C2×C22⋊D7911yescharacteristic
306C2×C4C2×C22⋊D7911yescharacteristic
307C2×C4C23×D7911yescharacteristic
308C8—792no—
309C8—1581no—
310C8—1581no—
311C8—1581no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1457918712yes—
321C22C22×C22⋊D7911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—3161no—
330C4—3161no—
331C4—3161no—
332C4—3161no—
333C4#41×D7911yescharacteristic
334C4#1457920811yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2#1909921211yescharacteristic
339C2C2×#1457918711yescharacteristic
340C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#547×C79C2
socleC22×C79C22×D4
hypercenter#547D79
hypocenterC79#3343
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. #19099253C2semidirect
2. #19098969C2semidirect
3. #19098898C2semidirect
4. #19098893C2semidirect
5. #19098884C2semidirect
6. #19098874C2semidirect
7. #19098863C2semidirect
8. #19098855C2semidirect
9. #19098807C2semidirect
10. #19098790C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098603C2semidirect
14. C2×#14579094C2semidirect
140. C79⋊C8#41semidirect
171. C79#3343semidirect