Finite Group Databasebeta

← #23770682

Subgroups — #23770682

Order 10112.

484 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098504C211yesmaximal, characteristic, complemented
2#19098488C211yesmaximal, characteristic, complemented
3#19098479C211yesmaximal, characteristic, complemented
4#19098477C211yesmaximal, characteristic, complemented
5#19098471C211yesmaximal, characteristic
6#19098463C211yesmaximal, characteristic, complemented
7#19098457C211yesmaximal, characteristic, complemented
8#19098456C211yesmaximal, characteristic, complemented
9#19098456C211yesmaximal, characteristic, complemented
10#19098455C211yesmaximal, characteristic, complemented
11#19098439C211yesmaximal, characteristic, complemented
12#19098439C211yesmaximal, characteristic, complemented
13#19098434C211yesmaximal, characteristic, complemented
14#19098428C211yesmaximal, characteristic, complemented
15#394×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C22×C22⋊D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×C22⋊Dic79C2211yescharacteristic
24C2×C22⋊Dic79C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C22×D4×C79C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C23×D79C2311yescharacteristic
52C2×C22⋊D79—22no—
53C2×C22⋊D79—22no—
54C2×C22⋊D79—22no—
55C2×C22⋊D79—41no—
56C2×C22⋊D79—41no—
57C2×C22⋊D79—41no—
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C2×C4×D79—41no—
66C2×C4×D79—41no—
67C2×C4×D79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70Dic79⋊C4—41no—
71Dic79⋊C4—41no—
72C22⋊Dic79—22no—
73C22⋊Dic79—41no—
74C22⋊Dic79—41no—
75C22⋊Dic79—41no—
76C22⋊Dic79—41no—
77C22⋊Dic79—41no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4—41no—
82C4×Dic79—22no—
83C4×Dic79—41no—
84C24×C79C2311yescharacteristic
85C24×C79C2311yescharacteristic
86C2×D4×C79—41no—
87C2×D4×C79—41no—
88C2×D4×C79—41no—
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—41no—
95C22⋊C4×C79—22no—
96C22⋊C4×C79—22no—
97C22⋊C4×C79—41no—
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×C79C2411yescharacteristic
114C22×D79—21no—
115C22×D79—21no—
116C22×D79—21no—
117C22×D79—21no—
118C22×D79—21no—
119C22×D79—21no—
120C22×D79#4112yes—
121D4×C79—44no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
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—21no—
135C2×C4×C79—21no—
136C2×C4×C79#4112yes—
137C22⋊D79—44no—
138C22⋊D79—44no—
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—
160C4×D79—44no—
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×C79C2×#4111yescharacteristic
176C22×C79C2×#4111yescharacteristic
177C22×C79C2×#4111yescharacteristic
178C22×C79H(5,𝔽2)11yescharacteristic
179C22×C79H(5,𝔽2)11yescharacteristic
180C22×C79H(5,𝔽2)11yescharacteristic
181C22×C79H(5,𝔽2)11yescharacteristic
182C2×D79—22no—
183C2×D79—22no—
184C2×D79—22no—
185C2×D79—41no—
186C2×D79—41no—
187C2×D79—41no—
188C2×D79—41no—
189C4×C79—22no—
190C4×C79—41no—
191C4×C79—41no—
192C4×C79—41no—
193C4×C79—41no—
194Dic79—22no—
195Dic79—41no—
196Dic79—41no—
197Dic79—41no—
198Dic79—41no—
199Dic79—41no—
200Dic79—41no—
201C2×C79—81no—
202C2×C79—81no—
203C2×C79#53811yescharacteristic
204C2×C79#54011yescharacteristic
205C2×C79#54011yescharacteristic
206C2×C79#55111yescharacteristic
207C2×C79#55311yescharacteristic
208C2×C79#55311yescharacteristic
209C2×C79H(3,𝔽4)11yescharacteristic
210D79—42no—
211#2753—791nomaximal, Sylow
212C79#275311yescharacteristic, complemented, Sylow
213#400—791no—
214#397—791no—
215#394—791no—
216#394—791no—
217#394D7911yescharacteristic, complemented
218#392—791no—
219#390—791no—
220#388—791no—
221#388—791no—
222#388—791no—
223#388—791no—
224#386—791no—
225#386—791no—
226#385—791no—
227#382—791no—
228C22×D4—791no—
229C22×D4—791no—
230C22×D4C2×D7911yescharacteristic
231C23×C4—791no—
232C2×C4⋊C4—791no—
233C2×C4⋊C4—791no—
234C2×C4⋊C4—791no—
235C2×C4⋊C4—791no—
236C2×C4⋊C4C2×D7911yescharacteristic
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⋊C4C2×D7911yescharacteristic
248C2×C22⋊C4C2×D7911yescharacteristic
249C2×C22⋊C4C2×D7911yescharacteristic
250C2×C22⋊C4C2×D7911yescharacteristic
251C2×C42—791no—
252C2×C42—791no—
253#95—791no—
254#95—791no—
255#95—791no—
256#95—791no—
257#95—791no—
258#95—791no—
259#95—791no—
260#95—791no—
261#95—791no—
262#95C2×D7911yescharacteristic
263C24—791no—
264C24C22×D7911yescharacteristic
265C24C22×D7911yescharacteristic
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—3161no—
270C2×D4—3161no—
271C2×D4—3161no—
272C2×D4—1582no—
273C2×D4—1582no—
274C2×D4—1582no—
275C22×C4—3161no—
276C22×C4—3161no—
277C22×C4—3161no—
278C22×C4—791no—
279C22×C4—791no—
280C22×C4—791no—
281C22×C4—791no—
282C22×C4—791no—
283C22×C4—791no—
284C22×C4—791no—
285C22×C4C22×D7911yescharacteristic
286C22×C4C22×D7911yescharacteristic
287C22×C4C22×D7911yescharacteristic
288C22×C4C22×D7911yescharacteristic
289C22×C4C22×D7911yescharacteristic
290C4⋊C4—41no—
291C4⋊C4—3161no—
292C4⋊C4—3161no—
293C4⋊C4—3161no—
294C4⋊C4—3161no—
295C22⋊C4—22no—
296C22⋊C4—22no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C22⋊C4—3161no—
300C22⋊C4—3161no—
301C22⋊C4—3161no—
302C22⋊C4—3161no—
303C22⋊C4—3161no—
304C22⋊C4—3161no—
305C22⋊C4—3161no—
306C22⋊C4—1582no—
307C22⋊C4—1582no—
308C22⋊C4—1582no—
309C42—3161no—
310C42—1582no—
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—792no—
326C23—1581no—
327C23—1581no—
328C23—1581no—
329C23—1581no—
330C23—1581no—
331C23—1581no—
332C23C23×D7911yescharacteristic
333D4—44no—
334D4—3164no—
335D4—3164no—
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—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—3164no—
351C2×C4—792no—
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—1581no—
370C2×C4—1581no—
371C2×C4—1581no—
372C2×C4#1192962312yes—
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—3161no—
388C22—3161no—
389C22—3161no—
390C22—3161no—
391C22—1582no—
392C22—1582no—
393C22—1582no—
394C22#41×D7911yescharacteristic
395C22#41×D7911yescharacteristic
396C22C2×#1192962311yescharacteristic
397C22#1457920611yescharacteristic
398C22#1457920611yescharacteristic
399C22#1457920611yescharacteristic
400C22#1457920711yescharacteristic
401C4—22no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—41no—
406C4—3161no—
407C4—3161no—
408C4—3161no—
409C4—3161no—
410C4—3161no—
411C4—3161no—
412C4—1582no—
413C2—81no—
414C2—81no—
415C2—3162no—
416C2#1909914711yescharacteristic
417C2#1909916511yescharacteristic
418C2#1909916611yescharacteristic
419C2#1909924111yescharacteristic
420C2#1909925611yescharacteristic
421C2#1909926011yescharacteristic
422C2#1909930611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radical#19098471C2
hypercenter#394D79
hypocenterC79#2753
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #19098504C2semidirect
2. #19098488C2semidirect
3. #19098479C2semidirect
4. #19098477C2semidirect
6. #19098463C2semidirect
7. #19098457C2semidirect
8. #19098456C2semidirect
9. #19098456C2semidirect
10. #19098455C2semidirect
11. #19098439C2semidirect
12. #19098439C2semidirect
13. #19098434C2semidirect
14. #19098428C2semidirect
15. #394×C79C2semidirect
212. C79#2753semidirect
217. #394D79semidirect