Finite Group Databasebeta

← #23771339

Subgroups — #23771339

Order 10112.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098491C211yesmaximal, characteristic, complemented
2#19098477C211yesmaximal, characteristic, complemented
3#19098477C211yesmaximal, characteristic, complemented
4#19098477C211yesmaximal, characteristic, complemented
5#19098477C211yesmaximal, characteristic, complemented
6#19098466C211yesmaximal, characteristic, complemented
7#19098466C211yesmaximal, characteristic, complemented
8#19098460C211yesmaximal, characteristic, complemented
9#19098457C211yesmaximal, characteristic, complemented
10#19098457C211yesmaximal, characteristic, complemented
11#19098456C211yesmaximal, characteristic, complemented
12#19098456C211yesmaximal, characteristic, complemented
13#19098451C211yesmaximal, characteristic, complemented
14#19098450C211yesmaximal, characteristic, complemented
15#392×C79C211yesmaximal, characteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C22⋊Dic79C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C22⋊Dic79C2211yescharacteristic
32C2×C22⋊Dic79C2211yescharacteristic
33C2×C22⋊Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C22×D4×C79C2211yescharacteristic
45C22×D4×C79C2211yescharacteristic
46C22×D4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C22×Dic79C2311yescharacteristic
52C22×Dic79C2311yescharacteristic
53C22×Dic79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C4⋊Dic79—41no—
60C4⋊Dic79—41no—
61Dic79⋊C4—22no—
62Dic79⋊C4—22no—
63Dic79⋊C4—41no—
64Dic79⋊C4—41no—
65C22⋊Dic79—22no—
66C22⋊Dic79—22no—
67C22⋊Dic79—22no—
68C22⋊Dic79—41no—
69C22⋊Dic79—41no—
70C22⋊Dic79—41no—
71C22⋊Dic79—41no—
72C22⋊Dic79—41no—
73C22⋊Dic79—41no—
74C22⋊Dic79—41no—
75C22⋊Dic79—41no—
76C22⋊Dic79—41no—
77C4×Dic79—41no—
78C4×Dic79—41no—
79C4×Dic79—41no—
80C24×C79C2311yescharacteristic
81C24×C79C2311yescharacteristic
82C24×C79C2311yescharacteristic
83C2×D4×C79—22no—
84C2×D4×C79—22no—
85C2×D4×C79—41no—
86C2×D4×C79—41no—
87C2×D4×C79—41no—
88C2×D4×C79—41no—
89C2×D4×C79—41no—
90C2×D4×C79—41no—
91C2×D4×C79—41no—
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C22⋊C4×C79—22no—
97C22⋊C4×C79—22no—
98C22⋊C4×C79—41no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79—21no—
106C23×C79—21no—
107C23×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79—21no—
112C23×C79—21no—
113C23×C79—21no—
114C23×C79—21no—
115C23×C79—21no—
116C23×C79—21no—
117C23×C79—21no—
118C23×C79—21no—
119C23×C79—21no—
120C23×C79C2411yescharacteristic
121D4×C79—44no—
122D4×C79—44no—
123D4×C79—44no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79#4112yes—
135C2×C4×C79#4112yes—
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×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158C2×Dic79—21no—
159C2×Dic79#4112yes—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79—41no—
163C22×C79—41no—
164C22×C79—41no—
165C22×C79—41no—
166C22×C79—41no—
167C22×C79—41no—
168C22×C79—41no—
169C22×C79—41no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79C2×#4111yescharacteristic
182C22×C79C2×#4111yescharacteristic
183C22×C79C2×#4111yescharacteristic
184C22×C79H(5,𝔽2)11yescharacteristic
185C22×C79H(5,𝔽2)11yescharacteristic
186C22×C79H(5,𝔽2)11yescharacteristic
187C22×C79H(5,𝔽2)11yescharacteristic
188C4×C79—22no—
189C4×C79—22no—
190C4×C79—41no—
191C4×C79—41no—
192Dic79—22no—
193Dic79—41no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200C2×C79—81no—
201C2×C79—81no—
202C2×C79—81no—
203C2×C79#53811yescharacteristic
204C2×C79#53811yescharacteristic
205C2×C79#54011yescharacteristic
206C2×C79#55311yescharacteristic
207C2×C79#55511yescharacteristic
208C2×C79#55911yescharacteristic
209C2×C79#56011yescharacteristic
210#2803—791nomaximal, Sylow
211C79#280311yescharacteristic, complemented, Sylow
212#397—791no—
213#394—791no—
214#394—791no—
215#394—791no—
216#394—791no—
217#392D7911yescharacteristic
218#390—791no—
219#390—791no—
220#389—791no—
221#388—791no—
222#388—791no—
223#388—791no—
224#388—791no—
225#388—791no—
226#387—791no—
227C22×D4C2×D7911yescharacteristic
228C22×D4C2×D7911yescharacteristic
229C22×D4C2×D7911yescharacteristic
230C2×C4⋊C4—791no—
231C2×C4⋊C4—791no—
232C2×C4⋊C4—791no—
233C2×C4⋊C4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C22⋊C4—791no—
237C2×C22⋊C4—791no—
238C2×C22⋊C4—791no—
239C2×C22⋊C4—791no—
240C2×C22⋊C4—791no—
241C2×C22⋊C4—791no—
242C2×C22⋊C4—791no—
243C2×C22⋊C4—791no—
244C2×C22⋊C4—791no—
245C2×C22⋊C4—791no—
246C2×C22⋊C4—791no—
247C2×C22⋊C4—791no—
248C2×C22⋊C4C2×D7911yescharacteristic
249C2×C22⋊C4C2×D7911yescharacteristic
250C2×C22⋊C4C2×D7911yescharacteristic
251C2×C42—791no—
252C2×C42—791no—
253C2×C42—791no—
254#95—791no—
255#95—791no—
256#95—791no—
257#95—791no—
258#95—791no—
259#95—791no—
260#95—791no—
261#95C2×D7911yescharacteristic
262C24C22×D7911yescharacteristic
263C24C22×D7911yescharacteristic
264C24C22×D7911yescharacteristic
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—791no—
275C22×C4—791no—
276C22×C4—791no—
277C22×C4—791no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4—791no—
282C22×C4C22×D7911yescharacteristic
283C22×C4C22×D7911yescharacteristic
284C22×C4C22×D7911yescharacteristic
285C22×C4C22×D7911yescharacteristic
286C4⋊C4—3161no—
287C4⋊C4—3161no—
288C4⋊C4—3161no—
289C4⋊C4—3161no—
290C4⋊C4—1582no—
291C4⋊C4—1582no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—3161no—
296C22⋊C4—3161no—
297C22⋊C4—3161no—
298C22⋊C4—3161no—
299C22⋊C4—3161no—
300C22⋊C4—3161no—
301C22⋊C4—3161no—
302C22⋊C4—3161no—
303C22⋊C4—3161no—
304C22⋊C4—1582no—
305C22⋊C4—1582no—
306C22⋊C4—1582no—
307C42—3161no—
308C42—3161no—
309C42—3161no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23C23×D7911yescharacteristic
332D4—44no—
333D4—44no—
334D4—44no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—792no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4—1581no—
351C2×C4—1581no—
352C2×C4—1581no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4—1581no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4#1192962312yes—
370C2×C4#1192962312yes—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#41×D7911yescharacteristic
393C22C2×#1192962311yescharacteristic
394C22C2×#1192962311yescharacteristic
395C22#1457920611yescharacteristic
396C22#1457920611yescharacteristic
397C22#1457920611yescharacteristic
398C22#1457920611yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—3161no—
404C4—3161no—
405C4—3161no—
406C4—3161no—
407C4—3161no—
408C4—3161no—
409C4—3161no—
410C4—1582no—
411C2—81no—
412C2—81no—
413C2—81no—
414C2#1909914811yescharacteristic
415C2#1909914811yescharacteristic
416C2#1909916311yescharacteristic
417C2#1909926011yescharacteristic
418C2#1909927711yescharacteristic
419C2#1909929911yescharacteristic
420C2#1909930211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting, prime radical#392×C79C2
hypercenter#392D79
hypocenterC79#2803
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #19098491C2semidirect
2. #19098477C2semidirect
3. #19098477C2semidirect
4. #19098477C2semidirect
5. #19098477C2semidirect
6. #19098466C2semidirect
7. #19098466C2semidirect
8. #19098460C2semidirect
9. #19098457C2semidirect
10. #19098457C2semidirect
11. #19098456C2semidirect
12. #19098456C2semidirect
13. #19098451C2semidirect
14. #19098450C2semidirect
211. C79#2803semidirect