Finite Group Databasebeta

← #23769232

Subgroups — #23769232

Order 10112.

472 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579151C211yesmaximal, characteristic, complemented
2C2×#14579119C211yesmaximal, characteristic
3#19098497C211yesmaximal, characteristic, complemented
4#19098496C211yesmaximal, characteristic, complemented
5#19098495C211yesmaximal, characteristic, complemented
6#19098487C211yesmaximal, characteristic
7#19098485C211yesmaximal, characteristic
8#19098485C211yesmaximal, characteristic
9#19098485C211yesmaximal, characteristic
10#19098460C211yesmaximal, characteristic, complemented
11#19098458C211yesmaximal, characteristic, complemented
12#19098432C211yesmaximal, characteristic, complemented
13#19098422C211yesmaximal, characteristic
14#19098422C211yesmaximal, characteristic
15#398×C79C211yesmaximal, characteristic, complemented
16C22×C4×D79C2211yescharacteristic
17#14579151—24no—
18#14579119—24no—
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×Dic79⋊C4C2211yescharacteristic
31C2×Dic79⋊C4C2211yescharacteristic
32C2×Dic79⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×(C2×D79)⋊C4C2211yescharacteristic
37C2×(C2×D79)⋊C4C2211yescharacteristic
38C2×(C2×D79)⋊C4C2211yescharacteristic
39C2×C4×Dic79C2211yescharacteristic
40C2×C4×Dic79C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C2×C4×D79—22no—
62C2×C4×D79—22no—
63C2×C4×D79Q814yes—
64C4⋊Dic79—22no—
65C4⋊Dic79—22no—
66C4⋊Dic79—41no—
67C4⋊Dic79—41no—
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—41no—
75Dic79⋊C4—41no—
76Dic79⋊C4—41no—
77Dic79⋊C4—41no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4—41no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84C4×Dic79—22no—
85C4×Dic79D414yes—
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—22no—
94C4⋊C4×C79—22no—
95C4⋊C4×C79—41no—
96C4⋊C4×C79—41no—
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×C79—21no—
123C2×C4×C79—21no—
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×Dic79C2×D412yes—
144C2×Dic79C2×D412yes—
145C2×Dic79C2×Q812yes—
146C2×Dic79#4112yes—
147C4×D79—28no—
148C22×C79C22×D411yescharacteristic
149C22×C79C22×Q811yescharacteristic
150C22×C79C2×#4111yescharacteristic
151C22×C79H(5,𝔽2)11yescharacteristic
152C22×C79H(5,𝔽2)11yescharacteristic
153C22×C792−1+411yescharacteristic
154C22×C792−1+411yescharacteristic
155C2×D79—22no—
156C2×D79—22no—
157C2×D79—22no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C4×C79—22no—
163C4×C79—22no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79—41no—
169Dic79—22no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174Dic79—41no—
175Dic79C22⋊Q814yes—
176C2×C79C2×C22⋊Q811yescharacteristic
177C2×C79#53711yescharacteristic
178C2×C79#53711yescharacteristic
179C2×C79#54011yescharacteristic
180C2×C79#54111yescharacteristic
181C2×C79#54411yescharacteristic
182C2×C79#54411yescharacteristic
183D79—42no—
184#2629—791nomaximal, Sylow
185C79#262911yescharacteristic, complemented, Sylow
186C2×#125—791no—
187C2×#117—791no—
188#398—791no—
189#398—791no—
190#398—791no—
191#398D7911yescharacteristic, complemented
192#396—791no—
193#396—791no—
194#396—791no—
195#396—791no—
196#389—791no—
197#389—791no—
198#384—791no—
199#380—791no—
200#380—791no—
201C23×C4—791no—
202#125—1584no—
203#117—1584no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4—791no—
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⋊C4—791no—
216C2×C4⋊C4—791no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4C2×D7911yescharacteristic
219C2×C4⋊C4C2×D7911yescharacteristic
220C2×C4⋊C4C2×D7911yescharacteristic
221C2×C4⋊C4C2×D7911yescharacteristic
222C2×C22⋊C4—791no—
223C2×C22⋊C4—791no—
224C2×C22⋊C4—791no—
225C2×C22⋊C4—791no—
226C2×C22⋊C4—791no—
227C2×C22⋊C4—791no—
228C2×C42—791no—
229C2×C42—791no—
230#95—791no—
231#95—791no—
232#95—791no—
233#95—791no—
234#95—791no—
235#95C2×D7911yescharacteristic
236#95C2×D7911yescharacteristic
237#95C2×D7911yescharacteristic
238C24—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—794no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4—791no—
245C22×C4—791no—
246C22×C4—791no—
247C22×C4—1582no—
248C22×C4—1582no—
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252C22×C4C22×D7911yescharacteristic
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255C22×C4C22×D7911yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—3161no—
261C4⋊C4—3161no—
262C4⋊C4—3161no—
263C4⋊C4—3161no—
264C4⋊C4—3161no—
265C4⋊C4—3161no—
266C4⋊C4—1582no—
267C4⋊C4—1582no—
268C4⋊C4—1582no—
269C4⋊C4—1582no—
270C4⋊C4—1582no—
271C4⋊C4—1582no—
272C4⋊C4—1582no—
273C4⋊C4—1582no—
274C22⋊C4—3161no—
275C22⋊C4—3161no—
276C22⋊C4—3161no—
277C22⋊C4—3161no—
278C22⋊C4—1582no—
279C22⋊C4—1582no—
280C42—794no—
281C42—1582no—
282C23—792no—
283C23—1581no—
284C23—1581no—
285C23—1581no—
286C23—1581no—
287C23—1581no—
288C23—1581no—
289C23C23×D7911yescharacteristic
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—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—792no—
310C2×C4—792no—
311C2×C4—792no—
312C2×C4—792no—
313C2×C4—1588no—
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×C4D4×D7912yes—
332C2×C4Q8×D7912yes—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—1582no—
338C22—1582no—
339C22—1582no—
340C22C2×D4×D7911yescharacteristic
341C22C2×Q8×D7911yescharacteristic
342C22#41×D7911yescharacteristic
343C22#1457920611yescharacteristic
344C22#1457920711yescharacteristic
345C22#1457920811yescharacteristic
346C22#1457920911yescharacteristic
347C4—22no—
348C4—22no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—3161no—
355C4—3161no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4—794no—
360C4—1582no—
361C2—3162no—
362C2C22⋊Q8×D7911yescharacteristic
363C2#1909914011yescharacteristic
364C2#1909914311yescharacteristic
365C2#1909916511yescharacteristic
366C2#1909917211yescharacteristic
367C2#1909919011yescharacteristic
368C2#1909919311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC23×D79C23
hypercenter#398D79
hypocenterC79#2629
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14579151C2semidirect
3. #19098497C2semidirect
4. #19098496C2semidirect
5. #19098495C2semidirect
10. #19098460C2semidirect
11. #19098458C2semidirect
12. #19098432C2semidirect
15. #398×C79C2semidirect
185. C79#2629semidirect
191. #398D79semidirect