Finite Group Databasebeta

← #23774907

Subgroups — #23774907

Order 10112.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579193C211yesmaximal, characteristic, complemented
2C22×#11929613C211yesmaximal, characteristic, complemented
3#19099226C211yesmaximal, characteristic, complemented
4#19099204C211yesmaximal, characteristic
5#19098956C211yesmaximal, characteristic, complemented
6#19098810C211yesmaximal, characteristic, complemented
7#19098788C211yesmaximal, characteristic, complemented
8#19098767C211yesmaximal, characteristic, complemented
9#19098728C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11#19098713C211yesmaximal, characteristic, complemented
12#19098703C211yesmaximal, characteristic, complemented
13#19098662C211yesmaximal, characteristic, complemented
14#19098634C211yesmaximal, characteristic, complemented
15#467×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×Q8×D79C2211yescharacteristic, complemented
19C22×D316C2211yescharacteristic
20#14579193—24no—
21C2×#11929614C2211yescharacteristic, complemented
22C2×#11929614C2211yescharacteristic, complemented
23C2×#11929613—24no—
24C2×#11929613C2211yescharacteristic
25C2×#11929613C2211yescharacteristic
26C2×#11929613C2211yescharacteristic
27C2×#11929613C2211yescharacteristic
28C2×#11929611C2211yescharacteristic
29C2×#11929611C2211yescharacteristic
30C2×#11929607C2211yescharacteristic, complemented
31#14579160—21no—
32#14579159C2211yescharacteristic, complemented
33#14579150C2211yescharacteristic
34#14579146—21no—
35#14579141C2211yescharacteristic, complemented
36#14579139—21no—
37#14579138—21no—
38#14579136—21no—
39#14579136C2211yescharacteristic
40#14579131—21no—
41#14579126C2211yescharacteristic, complemented
42#14579123C2211yescharacteristic
43C4×C22⋊D79C2211yescharacteristic
44(C22⋊D79)⋊C4—21no—
45C22⋊C4×D79—21no—
46Dic79⋊C8C2211yescharacteristic, complemented
47#14579084C2211yescharacteristic, complemented
48#14579084C2211yescharacteristic, complemented
49#14579081C2211yescharacteristic
50#14579081C2211yescharacteristic
51C22⋊(C79⋊C8)C2211yescharacteristic
52(C2×D79)⋊C8C2211yescharacteristic, complemented
53#14579071C2211yescharacteristic, complemented
54C2×Q16×C79C2211yescharacteristic, complemented
55C22×C8×C79C2211yescharacteristic
56C22⋊Q8×C79C2211yescharacteristic
57C22⋊Q8×C79C2211yescharacteristic
58#107×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#103×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929625—22no—
63#11929625—41no—
64C2×Dic158—22no—
65C2×Dic158—21no—
66C2×Dic158—21no—
67C2×Dic158—41no—
68C2×Dic158C2311yescharacteristic
69C2×Dic158C2311yescharacteristic
70Q8×D79—22no—
71Q8×D79—41no—
72C2×D316—21no—
73C2×D316—21no—
74C2×D316—22no—
75C2×D316—21no—
76C2×D316—41no—
77C2×D316C2311yescharacteristic
78C2×D316C2311yescharacteristic
79C2×C22⋊D79D411yescharacteristic
80C22×Dic79—21no—
81C2×C4×D79—21no—
82C2×C4×D79—21no—
83C2×C4×D79—21no—
84C2×C4×D79C2311yescharacteristic
85#11929614—22no—
86#11929614—41no—
87#11929613—22no—
88#11929613—22no—
89#11929613—22no—
90#11929613D414yescomplemented
91#11929611—22no—
92#11929611—41no—
93#11929607—22no—
94C2×C79⋊C8C2311yescharacteristic
95C2×C79⋊C8C2311yescharacteristic
96C4⋊Dic79—21no—
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100Dic79⋊C4D411yescharacteristic
101C22⋊Dic79D411yescharacteristic
102(C2×D79)⋊C4—21no—
103(C2×D79)⋊C4—21no—
104(C2×D79)⋊C4—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4D411yescharacteristic
108C4×Dic79—21no—
109C4×Dic79C2311yescharacteristic
110C2×Q8×C79C2311yescharacteristic
111C2×Q8×C79C2311yescharacteristic
112C22×C4×C79C2311yescharacteristic
113Q16×C79—22no—
114C2×C8×C79—22no—
115C2×C8×C79C2311yescharacteristic
116C2×C8×C79C2311yescharacteristic
117C4⋊C4×C79—21no—
118C4⋊C4×C79—21no—
119C4⋊C4×C79C2311yescharacteristic
120C4⋊C4×C79C2311yescharacteristic
121C22⋊C4×C79—21no—
122C22⋊C4×C79—21no—
123C23×C79C2×D411yescharacteristic
124C22×D79—21no—
125C22×D79—21no—
126C22×D79—42no—
127C22×D79—42no—
128C22×D79—81no—
129C22×D79C2×D411yescharacteristic
130Q8×C79—21no—
131Q8×C79—21no—
132Q8×C79—21no—
133Q8×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79C2×D411yescharacteristic
141C2×C4×C79C2411yescharacteristic
142C22⋊D79—22no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—42no—
146C2×Dic79C2×D411yescharacteristic
147C2×Dic79C2×D411yescharacteristic
148C2×Dic79C2×D411yescharacteristic
149D316—21no—
150D316—21no—
151D316—21no—
152D316—42no—
153D316—42no—
154D316—81no—
155D316C2×D412yes—
156C4×D79—21no—
157C4×D79—21no—
158C4×D79—42no—
159C4×D79—42no—
160C4×D79—81no—
161Dic158—21no—
162Dic158—21no—
163Dic158—21no—
164Dic158—42no—
165Dic158—42no—
166Dic158C2×D412yes—
167C8×C79—21no—
168C8×C79C2×D412yes—
169C79⋊C8—21no—
170C79⋊C8—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79#13712yescomplemented
174C22×C79C22×D411yescharacteristic
175C2×D79—22no—
176C2×D79—21no—
177C2×D79—21no—
178C2×D79—21no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—84no—
185C4×C79—21no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79—41no—
190C4×C79C22×D411yescharacteristic
191C4×C79H(5,𝔽2)11yescharacteristic
192Dic79—22no—
193Dic79—21no—
194Dic79—21no—
195Dic79—21no—
196Dic79—41no—
197C2×C79—22no—
198C2×C79D4211yescharacteristic
199C2×C79C2×#13711yescharacteristic
200C2×C79#57711yescharacteristic
201D79—41no—
202D79—42no—
203D79—81no—
204#3266—791nomaximal, Sylow
205C79#326611yescharacteristic, complemented, Sylow
206C2×#137—791no—
207C22×SD16—791no—
208D4×Q8—791no—
209#546—791no—
210#497—791no—
211#468—791no—
212#467D7911yescharacteristic, complemented
213#464—791no—
214#461—791no—
215#452—791no—
216#451—791no—
217#450—791no—
218#448—791no—
219#440—791no—
220#435—791no—
221C2×#41—791no—
222C22×Q8—791no—
223C22×Q8—791no—
224C22×D4—791no—
225#137—1584no—
226C2×Q16—791no—
227C2×Q16—791no—
228C2×Q16C2×D7911yescharacteristic, complemented
229C2×SD16—791no—
230C2×SD16—791no—
231C2×SD16—791no—
232C2×SD16—791no—
233C2×SD16—791no—
234C2×SD16—791no—
235C2×SD16—1584no—
236C2×M16—791no—
237C22×C8C2×D7911yescharacteristic
238C4⋊Q8—791no—
239C4⋊Q8—1581no—
240#124—791no—
241#123—1581no—
242C22⋊Q8—791no—
243C22⋊Q8—1581no—
244C22⋊Q8—1581no—
245C22⋊Q8C2×D7911yescharacteristic
246C22⋊Q8C2×D7911yescharacteristic
247#121—791no—
248#121—1581no—
249#120—1581no—
250C4×Q8—791no—
251C4×D4—791no—
252C4×D4—791no—
253C4×D4—1581no—
254C2×C22⋊C4—1581no—
255#107C2×D7911yescharacteristic, complemented
256C4⋊C8—791no—
257#103—791no—
258#103—791no—
259#103C2×D7911yescharacteristic, complemented
260#103C2×D7911yescharacteristic, complemented
261#102—791no—
262#102—791no—
263C22⋊C8—791no—
264C22⋊C8—791no—
265#97—791no—
266C24—1581no—
267#41—3161no—
268#41—1582no—
269C2×Q8—3161no—
270C2×Q8—3161no—
271C2×Q8—791no—
272C2×Q8—791no—
273C2×Q8—1582no—
274C2×Q8—1581no—
275C2×Q8—1582no—
276C2×Q8—1581no—
277C2×Q8C22×D7911yescharacteristic
278C2×Q8C22×D7911yescharacteristic
279C2×D4—3161no—
280C2×D4—791no—
281C2×D4—791no—
282C2×D4—791no—
283C2×D4—1581no—
284C2×D4—1582no—
285C2×D4—1581no—
286C2×D4—1581no—
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4—1581no—
292C22×C4C22×D7911yescharacteristic
293Q16—22no—
294Q16—3161no—
295Q16—1582no—
296SD16—3161no—
297SD16—794no—
298SD16—1582no—
299SD16—1582no—
300SD16—1582no—
301SD16—1582no—
302M16—1582no—
303C2×C8—22no—
304C2×C8—791no—
305C2×C8—791no—
306C2×C8C22×D7911yescharacteristic
307C2×C8C22×D7911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—791no—
311C4⋊C4—1581no—
312C4⋊C4—1581no—
313C4⋊C4—1581no—
314C4⋊C4—1581no—
315C4⋊C4C22×D7911yescharacteristic
316C4⋊C4C22×D7911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—791no—
320C22⋊C4—791no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4—1581no—
325C22⋊C4—1581no—
326C42—791no—
327C42—1581no—
328C23—3162no—
329C23—3162no—
330C23—791no—
331C23—6321no—
332C23—1581no—
333C23—1581no—
334C23D4×D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—3162no—
340Q8—3162no—
341Q8—792no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345D4—3162no—
346D4—3162no—
347D4—792no—
348D4—6321no—
349D4—1582no—
350D4—1581no—
351D4—1581no—
352D4—1581no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—3162no—
360C2×C4—3162no—
361C2×C4—3162no—
362C2×C4—791no—
363C2×C4—791no—
364C2×C4—791no—
365C2×C4—6321no—
366C2×C4—1581no—
367C2×C4—1581no—
368C2×C4—1581no—
369C2×C4—1581no—
370C2×C4D4×D7911yescharacteristic
371C2×C4C23×D7911yescharacteristic
372C8—21no—
373C8—1581no—
374C8—1581no—
375C8D4×D7912yes—
376C22—21no—
377C22—21no—
378C22—3161no—
379C22—3161no—
380C22—3161no—
381C22—3161no—
382C22—3161no—
383C22—6324no—
384C22—1581no—
385C22—1582no—
386C22—1581no—
387C22—1581no—
388C22#1457919312yescomplemented
389C22C2×D4×D7911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—3161no—
396C4—1581no—
397C4—1582no—
398C4—1581no—
399C4—1581no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920711yescharacteristic
402C2—22no—
403C2—3162no—
404C2—3161no—
405C2—6321no—
406C2#1909919711yescharacteristic
407C2C2×#1457919311yescharacteristic
408C2#1909937011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#467×C79C2
socleC22×C79C22×D4
prime radical#19099204C2
hypercenter#467D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. C2×#14579193C2semidirect
2. C22×#11929613C2semidirect
3. #19099226C2semidirect
5. #19098956C2semidirect
6. #19098810C2semidirect
7. #19098788C2semidirect
8. #19098767C2semidirect
9. #19098728C2semidirect
10. #19098718C2semidirect
11. #19098713C2semidirect
12. #19098703C2semidirect
13. #19098662C2semidirect
14. #19098634C2semidirect
15. #467×C79C2semidirect
18. C2×Q8×D79C22semidirect
21. C2×#11929614C22semidirect
22. C2×#11929614C22semidirect
30. C2×#11929607C22semidirect
32. #14579159C22semidirect
35. #14579141C22semidirect
41. #14579126C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579084C22semidirect
52. (C2×D79)⋊C8C22semidirect
53. #14579071C22semidirect
54. C2×Q16×C79C22semidirect
58. #107×C79C22semidirect
59. #103×C79C22semidirect
60. #103×C79C22semidirect
90. #11929613D4semidirect
173. C22×C79#137semidirect
205. C79#3266semidirect
212. #467D79semidirect
228. C2×Q16C2×D79semidirect
255. #107C2×D79semidirect
259. #103C2×D79semidirect
260. #103C2×D79semidirect
388. C22#14579193semidirect