Finite Group Databasebeta

← #23767484

Subgroups — #23767484

Order 10112.

470 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
1C2×#14579156C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic, complemented
3#19098485C211yesmaximal, characteristic
4#19098484C211yesmaximal, characteristic, complemented
5#19098476C211yesmaximal, characteristic
6#19098459C211yesmaximal, characteristic, complemented
7#19098455C211yesmaximal, characteristic
8#19098452C211yesmaximal, characteristic
9#19098452C211yesmaximal, characteristic
10#19098452C211yesmaximal, characteristic
11#19098450C211yesmaximal, characteristic, complemented
12#19098450C211yesmaximal, characteristic, complemented
13#19098446C211yesmaximal, characteristic, complemented
14#19098414C211yesmaximal, characteristic, complemented
15#400×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17#14579156—24no—
18#14579126—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×(C2×D79)⋊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
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C2×C4×Dic79C2211yescharacteristic
38C2×C4×Dic79C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—22no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C4⋊Dic79—22no—
65C4⋊Dic79—22no—
66C4⋊Dic79—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4D414yes—
72(C2×D79)⋊C4—22no—
73(C2×D79)⋊C4—22no—
74(C2×D79)⋊C4—22no—
75(C2×D79)⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—22no—
78(C2×D79)⋊C4—22no—
79C4×Dic79—22no—
80C4×Dic79—22no—
81C4×Dic79—22no—
82C4×Dic79—22no—
83C4×Dic79—22no—
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C4⋊C4×C79—22no—
92C4⋊C4×C79—22no—
93C23×C79C2411yescharacteristic
94C22×D79—21no—
95C22×D79—21no—
96C22×D79—21no—
97C22×D79—21no—
98C22×D79—21no—
99C22×D79—21no—
100C22×D79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
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×C79C2×D412yes—
121C2×C4×C79#4112yes—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
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×Dic79C2×D412yes—
139C2×Dic79C2×D412yes—
140C2×Dic79#4112yes—
141C2×Dic79#4112yes—
142C2×Dic79#4112yes—
143Dic158—28no—
144C22×C79C22×D411yescharacteristic
145C22×C79C2×#4111yescharacteristic
146C22×C79C2×#4111yescharacteristic
147C22×C79C2×#4111yescharacteristic
148C22×C79C2×#4111yescharacteristic
149C22×C792−1+411yescharacteristic
150C22×C792−1+411yescharacteristic
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C4×C79—22no—
159C4×C79—22no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79—41no—
165Dic79—22no—
166Dic79—22no—
167Dic79—22no—
168Dic79—22no—
169Dic79—22no—
170Dic79—41no—
171Dic79—41no—
172C2×C79#52511yescharacteristic
173C2×C79#52911yescharacteristic
174C2×C79#54111yescharacteristic
175C2×C79#54711yescharacteristic
176C2×C79#54811yescharacteristic
177C2×C79#55611yescharacteristic
178C2×C79#55611yescharacteristic
179D79—81no—
180#2469—791nomaximal, Sylow
181C79#246911yescharacteristic, complemented, Sylow
182C2×#126—791no—
183C2×C4×Q8—791no—
184#400D7911yescharacteristic, complemented
185#396—791no—
186#395—791no—
187#393—791no—
188#389—791no—
189#388—791no—
190#388—791no—
191#388—791no—
192#388—791no—
193#387—791no—
194#387—791no—
195#387—791no—
196C4×C4⋊C4—791no—
197C22×Q8—791no—
198#126—1584no—
199C4×Q8—1584no—
200C2×C4⋊C4—791no—
201C2×C4⋊C4—791no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4—791no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4C2×D7911yescharacteristic
209C2×C4⋊C4C2×D7911yescharacteristic
210C2×C22⋊C4—791no—
211C2×C22⋊C4—791no—
212C2×C22⋊C4—791no—
213C2×C22⋊C4—791no—
214C2×C22⋊C4—791no—
215C2×C22⋊C4—791no—
216C2×C22⋊C4—791no—
217C2×C42—791no—
218C2×C42—791no—
219C2×C42—791no—
220C2×C42—791no—
221C2×C42—791no—
222#95—791no—
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95C2×D7911yescharacteristic
230#95C2×D7911yescharacteristic
231#95C2×D7911yescharacteristic
232#95C2×D7911yescharacteristic
233#95C2×D7911yescharacteristic
234C24—791no—
235C2×Q8—1582no—
236C2×Q8—1582no—
237C2×Q8—1582no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4C22×D7911yescharacteristic
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—794no—
255C4⋊C4—1582no—
256C4⋊C4—1582no—
257C4⋊C4—1582no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C4⋊C4—1582no—
262C22⋊C4—1582no—
263C22⋊C4—1582no—
264C22⋊C4—1582no—
265C22⋊C4—1582no—
266C22⋊C4—1582no—
267C22⋊C4—1582no—
268C22⋊C4—1582no—
269C42—1582no—
270C42—1582no—
271C42—1582no—
272C42—1582no—
273C42—1582no—
274C23—1581no—
275C23—1581no—
276C23—1581no—
277C23—1581no—
278C23—1581no—
279C23—1581no—
280C23—1581no—
281C23C23×D7911yescharacteristic
282Q8—1588no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—792no—
303C2×C4—792no—
304C2×C4—792no—
305C2×C4—792no—
306C2×C4—792no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
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×C4D4×D7912yes—
324C2×C4#1192962512yes—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22—3161no—
330C22—3161no—
331C22—3161no—
332C22C2×D4×D7911yescharacteristic
333C22#41×D7911yescharacteristic
334C22#41×D7911yescharacteristic
335C22#41×D7911yescharacteristic
336C22C2×#1192962511yescharacteristic
337C22#1457920811yescharacteristic
338C22#1457920811yescharacteristic
339C4—22no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3161no—
347C4—3161no—
348C4—1582no—
349C4—1582no—
350C4—1582no—
351C4—1582no—
352C4—1582no—
353C2—6321no—
354C2#1909907611yescharacteristic
355C2#1909909811yescharacteristic
356C2#1909917611yescharacteristic
357C2#1909921111yescharacteristic
358C2#1909922111yescharacteristic
359C2#1909928011yescharacteristic
360C2#1909928011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC23×D79C23
hypercenter#400D79
hypocenterC79#2469
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#14579126C2semidirect
4. #19098484C2semidirect
6. #19098459C2semidirect
11. #19098450C2semidirect
12. #19098450C2semidirect
13. #19098446C2semidirect
14. #19098414C2semidirect
15. #400×C79C2semidirect
181. C79#2469semidirect
184. #400D79semidirect