Finite Group Databasebeta

← #23770276

Subgroups — #23770276

Order 10112.

472 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579141C211yesmaximal, characteristic
2#19098502C211yesmaximal, characteristic, complemented
3#19098498C211yesmaximal, characteristic
4#19098493C211yesmaximal, characteristic, complemented
5#19098485C211yesmaximal, characteristic
6#19098483C211yesmaximal, characteristic, complemented
7#19098483C211yesmaximal, characteristic, complemented
8#19098461C211yesmaximal, characteristic, complemented
9#19098454C211yesmaximal, characteristic
10#19098453C211yesmaximal, characteristic
11#19098449C211yesmaximal, characteristic, complemented
12#19098434C211yesmaximal, characteristic
13#19098434C211yesmaximal, characteristic
14#19098432C211yesmaximal, characteristic, complemented
15C2×#125×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18#14579141—24no—
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45#125×C79—24no—
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C4⋊C4×C79C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—41no—
56C2×Dic158—41no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C2×C4×D79—22no—
65C2×C4×D79—41no—
66C2×C4×D79—41no—
67C4⋊Dic79—22no—
68C4⋊Dic79—22no—
69C4⋊Dic79—22no—
70Dic79⋊C4—41no—
71Dic79⋊C4—41no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75Dic79⋊C4—41no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—41no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4Q814yescomplemented
82C4×Dic79—22no—
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C4⋊C4×C79—22no—
91C4⋊C4×C79—22no—
92C4⋊C4×C79—22no—
93C4⋊C4×C79—22no—
94C4⋊C4×C79—22no—
95C4⋊C4×C79D414yes—
96C42×C79—22no—
97C23×C79C2411yescharacteristic
98C22×D79—21no—
99C22×D79—21no—
100C22×D79—21no—
101C22×D79—21no—
102C22×D79—21no—
103C22×D79—21no—
104C22×D79C2×Q812yes—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
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—21no—
121C2×C4×C79—21no—
122C2×C4×C79C2×D412yes—
123C2×C4×C79C2×D412yes—
124C2×C4×C79C2×D412yes—
125C2×C4×C79C2×Q812yes—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79C2×Q812yes—
146C2×Dic79#4112yes—
147C4×D79—44no—
148Dic158—44no—
149C22×C79C22×D411yescharacteristic
150C22×C79C22×Q811yescharacteristic
151C22×C79C2×#4111yescharacteristic
152C22×C79H(5,𝔽2)11yescharacteristic
153C22×C79H(5,𝔽2)11yescharacteristic
154C22×C792−1+411yescharacteristic
155C22×C792−1+411yescharacteristic
156C2×D79—22no—
157C2×D79—22no—
158C2×D79—22no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C4×C79—22no—
164C4×C79—22no—
165C4×C79—22no—
166C4×C79—22no—
167C4×C79—41no—
168C4×C79—41no—
169C4×C79—41no—
170Dic79—22no—
171Dic79—22no—
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79#53511yescharacteristic
178C2×C79#53911yescharacteristic
179C2×C79#54411yescharacteristic
180C2×C79#54711yescharacteristic
181C2×C79D4×Q811yescharacteristic
182C2×C79#55411yescharacteristic
183C2×C79#56311yescharacteristic
184D79—42no—
185#2720—791nomaximal, Sylow
186C79#272011yescharacteristic, complemented, Sylow
187C2×#125D7911yescharacteristic, complemented
188C2×C22⋊Q8—791no—
189#400—791no—
190#399—791no—
191#398—791no—
192#396—791no—
193#395—791no—
194#395—791no—
195#389—791no—
196#388—791no—
197#388—791no—
198#387—791no—
199#385—791no—
200#385—791no—
201#384—791no—
202C22×Q8—791no—
203C23×C4—791no—
204#125—24no—
205C22⋊Q8—1584no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4—791no—
209C2×C4⋊C4—791no—
210C2×C4⋊C4—791no—
211C2×C4⋊C4—791no—
212C2×C4⋊C4—791no—
213C2×C4⋊C4—791no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4C2×D7911yescharacteristic
216C2×C4⋊C4C2×D7911yescharacteristic
217C2×C4⋊C4C2×D7911yescharacteristic
218C2×C4⋊C4C2×D7911yescharacteristic
219C2×C4⋊C4C2×D7911yescharacteristic
220C2×C4⋊C4C2×D7911yescharacteristic
221C2×C22⋊C4—791no—
222C2×C22⋊C4—791no—
223C2×C22⋊C4—791no—
224C2×C22⋊C4—791no—
225C2×C22⋊C4—791no—
226C2×C22⋊C4—791no—
227C2×C42—791no—
228C2×C42C2×D7911yescharacteristic
229#95—791no—
230#95—791no—
231#95—791no—
232#95—791no—
233#95—791no—
234#95—791no—
235#95—791no—
236#95—791no—
237#95—791no—
238#95—791no—
239C24—791no—
240C2×Q8—3161no—
241C2×Q8—3161no—
242C2×Q8—1582no—
243C22×C4—3161no—
244C22×C4—3161no—
245C22×C4—791no—
246C22×C4—791no—
247C22×C4—791no—
248C22×C4—791no—
249C22×C4—791no—
250C22×C4—791no—
251C22×C4—791no—
252C22×C4—1582no—
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255C22×C4C22×D7911yescharacteristic
256C22×C4C22×D7911yescharacteristic
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259C22×C4C22×D7911yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—3161no—
266C4⋊C4—3161no—
267C4⋊C4—3161no—
268C4⋊C4—3161no—
269C4⋊C4—3161no—
270C4⋊C4—3161no—
271C4⋊C4—1582no—
272C4⋊C4—1582no—
273C4⋊C4—1582no—
274C4⋊C4C22⋊D7914yes—
275C22⋊C4—3161no—
276C22⋊C4—3161no—
277C22⋊C4—794no—
278C22⋊C4—1582no—
279C22⋊C4—1582no—
280C22⋊C4—1582no—
281C42—22no—
282C42—1582no—
283C23—792no—
284C23—1581no—
285C23—1581no—
286C23—1581no—
287C23—1581no—
288C23—1581no—
289C23—1581no—
290C23C23×D7911yescharacteristic
291Q8—3164no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3164no—
310C2×C4—792no—
311C2×C4—792no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4C2×C22⋊D7912yes—
332C2×C4C2×C22⋊D7912yes—
333C2×C4C2×C22⋊D7912yes—
334C2×C4Q8×D7912yes—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22—1582no—
340C22—1582no—
341C22—1582no—
342C22C22×C22⋊D7911yescharacteristic
343C22C2×Q8×D7911yescharacteristic
344C22#41×D7911yescharacteristic
345C22#1457920711yescharacteristic
346C22#1457920711yescharacteristic
347C22#1457920811yescharacteristic
348C22#1457920911yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—3161no—
360C4—3161no—
361C4—1582no—
362C4—1582no—
363C2—3162no—
364C2#1909912711yescharacteristic
365C2#1909916111yescharacteristic
366C2#1909919311yescharacteristic
367C2#1909921211yescharacteristic
368C2Q8×C22⋊D7911yescharacteristic
369C2#1909926911yescharacteristic
370C2#1909931711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#125×C79C2
prime radicalC23×D79C23
hypercenterC2×#125D79
hypocenterC79#2720
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #19098502C2semidirect
4. #19098493C2semidirect
6. #19098483C2semidirect
7. #19098483C2semidirect
8. #19098461C2semidirect
11. #19098449C2semidirect
14. #19098432C2semidirect
15. C2×#125×C79C2semidirect
81. (C2×D79)⋊C4Q8semidirect
186. C79#2720semidirect
187. C2×#125D79semidirect