Finite Group Databasebeta

← #23775840

Subgroups — #23775840

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#19099217C211yesmaximal, characteristic
2#19098973C211yesmaximal, characteristic, complemented
3#19098896C211yesmaximal, characteristic, complemented
4#19098891C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098876C211yesmaximal, characteristic, complemented
7#19098860C211yesmaximal, characteristic, complemented
8#19098858C211yesmaximal, characteristic, complemented
9#19098811C211yesmaximal, characteristic, complemented
10#19098794C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098606C211yesmaximal, characteristic, complemented
14C2×#14579094C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929611C2211yescharacteristic
18C2×#11929608C2211yescharacteristic
19C22×C79⋊C8C2211yescharacteristic
20#14579161C2211yescharacteristic
21#14579145—21no—
22#14579145—21no—
23#14579141—21no—
24#14579135C2211yescharacteristic
25#14579135C2211yescharacteristic
26C4×D316C2211yescharacteristic
27C2×C4⋊Dic79C2211yescharacteristic
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#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C22×Dic79—21no—
66C2×C4×D79—21no—
67#11929611—22no—
68#11929608—22no—
69C2×C79⋊C8—22no—
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83C2×Q8×C79C2311yescharacteristic
84C2×D4×C79D411yescharacteristic
85C22×C4×C79—21no—
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C4⋊C4×C79—21no—
89C4⋊C4×C79—21no—
90C4⋊C4×C79—21no—
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79D411yescharacteristic
95C4⋊C4×C79C2311yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79D411yescharacteristic
102C22⋊C4×C79D411yescharacteristic
103C42×C79—21no—
104C42×C79—21no—
105C42×C79C2311yescharacteristic
106C23×C79C2×D411yescharacteristic
107C23×C79C2×D411yescharacteristic
108C22×D79—21no—
109Q8×C79—21no—
110Q8×C79—21no—
111D4×C79—22no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—42no—
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C22⋊D79—42no—
127C22⋊D79—42no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—42no—
132C2×Dic79—42no—
133D316—21no—
134D316—21no—
135C4×D79—42no—
136Dic158—42no—
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×C79AGL(1,ℤ/8)12yes—
147C22×C79C22×D411yescharacteristic
148C2×D79—41no—
149C2×D79—41no—
150C2×D79—41no—
151C4×C79—21no—
152C4×C79—21no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C792−1+411yescharacteristic
161Dic79—41no—
162Dic79—41no—
163Dic79—41no—
164C2×C79—22no—
165C2×C79—41no—
166C2×C79#54711yescharacteristic
167C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
168C2×C79#57811yescharacteristic
169D79—81no—
170#3343—791nomaximal, Sylow
171C79#334311yescharacteristic, complemented, Sylow
172#552D7911yescharacteristic, complemented
173#547—791no—
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—1581no—
188C2×SD16—791no—
189C2×M16—791no—
190C22×C8—791no—
191C4⋊Q8—791no—
192#126—21no—
193#125—21no—
194#125C2×D7911yescharacteristic
195#123—21no—
196#123—1581no—
197#123—1581no—
198C22⋊Q8—1581no—
199C22⋊Q8C2×D7911yescharacteristic
200C22⋊Q8C2×D7911yescharacteristic
201#121—791no—
202#121—791no—
203C4×Q8C2×D7911yescharacteristic
204C4×D4—791no—
205C4×D4C2×D7911yescharacteristic
206#117—21no—
207#117C2×D7911yescharacteristic
208C2×C4⋊C4—791no—
209C2×C4⋊C4—791no—
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—3164no—
231C2×Q8—1581no—
232C2×Q8C22×D7911yescharacteristic
233C2×D4—791no—
234C2×D4—1581no—
235C2×D4—1581no—
236C2×D4C22⋊D7911yescharacteristic
237C22×C4—21no—
238C22×C4—1581no—
239C22×C4—1581no—
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—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—791no—
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—21no—
275C42—21no—
276C42C22×D7911yescharacteristic
277C23—1581no—
278C23C2×C22⋊D7911yescharacteristic
279C23C2×C22⋊D7911yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—3162no—
283D4—22no—
284D4—3162no—
285D4—3162no—
286D4—1581no—
287D4—1581no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—3162no—
298C2×C4—3162no—
299C2×C4—3162no—
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—3161no—
318C22—3161no—
319C22—3161no—
320C22#1457918612yes—
321C22C22×C22⋊D7911yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—3161no—
331C4—3161no—
332C4—3161no—
333C4#41×D7911yescharacteristic
334C4#1457920811yescharacteristic
335C2—22no—
336C2—41no—
337C2—6321no—
338C2#1909921211yescharacteristic
339C2C2×#1457918611yescharacteristic
340C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radical#19099217C2
hypercenter#552D79
hypocenterC79#3343
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098973C2semidirect
3. #19098896C2semidirect
4. #19098891C2semidirect
5. #19098887C2semidirect
6. #19098876C2semidirect
7. #19098860C2semidirect
8. #19098858C2semidirect
9. #19098811C2semidirect
10. #19098794C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098606C2semidirect
14. C2×#14579094C2semidirect
15. #552×C79C2semidirect
140. C79⋊C8#41semidirect
171. C79#3343semidirect
172. #552D79semidirect