Finite Group Databasebeta

← #23774917

Subgroups — #23774917

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×#14579194C211yesmaximal, characteristic, complemented
2C2×SD16×D79C211yesmaximal, characteristic, complemented
3#19099226C211yesmaximal, characteristic, complemented
4#19099210C211yesmaximal, characteristic
5#19098954C211yesmaximal, characteristic, complemented
6#19098805C211yesmaximal, characteristic, complemented
7#19098784C211yesmaximal, characteristic, complemented
8#19098767C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098720C211yesmaximal, characteristic, complemented
11#19098715C211yesmaximal, characteristic, complemented
12#19098701C211yesmaximal, characteristic, complemented
13#19098662C211yesmaximal, characteristic, complemented
14#19098632C211yesmaximal, characteristic, complemented
15#468×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic, complemented
18C2×Q8×D79C2211yescharacteristic
19C2×D4×D79C2211yescharacteristic
20#14579194—24no—
21C2×Dic316C2211yescharacteristic, complemented
22C2×Dic316C2211yescharacteristic, complemented
23C2×#11929614C2211yescharacteristic, complemented
24C2×#11929613C2211yescharacteristic
25C2×#11929613C2211yescharacteristic
26C2×#11929612C2211yescharacteristic
27C2×#11929612C2211yescharacteristic
28C2×#11929611C2211yescharacteristic
29SD16×D79—24no—
30C2×C8×D79C2211yescharacteristic
31#14579160—21no—
32#14579159C2211yescharacteristic, complemented
33#14579148C2211yescharacteristic
34#14579143—21no—
35#14579141C2211yescharacteristic
36#14579141C2211yescharacteristic
37#14579139—21no—
38#14579138—21no—
39#14579132—21no—
40#14579129—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#14579084C2211yescharacteristic, complemented
50#14579081C2211yescharacteristic
51C22⋊(C79⋊C8)C2211yescharacteristic, complemented
52(C2×D79)⋊C8C2211yescharacteristic
53#14579071C2211yescharacteristic, complemented
54C2×SD16×C79C2211yescharacteristic
55C2×M16×C79C2211yescharacteristic, complemented
56C22⋊Q8×C79C2211yescharacteristic, complemented
57#121×C79C2211yescharacteristic
58#107×C79C2211yescharacteristic, complemented
59#103×C79C2211yescharacteristic, complemented
60#102×C79C2211yescharacteristic
61C23×D79—21no—
62#11929624—22no—
63#11929624—41no—
64C2×Dic158—22no—
65C2×Dic158—21no—
66C2×Dic158—21no—
67C2×Dic158—41no—
68C2×Dic158C2311yescharacteristic
69C2×Dic158C2311yescharacteristic
70C2×Dic158C2311yescharacteristic
71Q8×D79—22no—
72Q8×D79—41no—
73C2×D316C2311yescharacteristic
74C2×C22⋊D79—21no—
75C2×C22⋊D79—21no—
76C2×C22⋊D79D411yescharacteristic
77D4×D79—22no—
78D4×D79—41no—
79C22×Dic79—21no—
80C2×C4×D79—21no—
81C2×C4×D79—21no—
82C2×C4×D79—21no—
83C2×C4×D79C2311yescharacteristic
84Dic316—22no—
85Dic316—22no—
86#11929614—41no—
87#11929613—22no—
88#11929613D414yescomplemented
89#11929612—22no—
90#11929612—41no—
91#11929611—22no—
92C2×C79⋊C8C2311yescharacteristic
93C2×C79⋊C8C2311yescharacteristic
94C8×D79—22no—
95C4⋊Dic79—21no—
96C4⋊Dic79—21no—
97Dic79⋊C4—21no—
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100Dic79⋊C4D411yescharacteristic
101C22⋊Dic79—21no—
102C22⋊Dic79—21no—
103C22⋊Dic79D411yescharacteristic
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×D4×C79—21no—
112C2×D4×C79C2311yescharacteristic
113C22×C4×C79C2311yescharacteristic
114SD16×C79—22no—
115M16×C79—22no—
116C2×C8×C79C2311yescharacteristic
117C2×C8×C79C2311yescharacteristic
118C4⋊C4×C79—21no—
119C4⋊C4×C79C2311yescharacteristic
120C4⋊C4×C79C2311yescharacteristic
121C22⋊C4×C79—21no—
122C22⋊C4×C79—21no—
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—42no—
127C22×D79—42no—
128C22×D79—81no—
129C22×D79C2×D411yescharacteristic
130Q8×C79—21no—
131Q8×C79—21no—
132D4×C79—21no—
133D4×C79—21no—
134D4×C79—81no—
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—
143C22⋊D79—42no—
144C22⋊D79—42no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—42no—
149C2×Dic79C2×D411yescharacteristic
150C2×Dic79C2×D411yescharacteristic
151C2×Dic79C2×D411yescharacteristic
152D316—21no—
153D316C2×D412yes—
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—42no—
157C4×D79—42no—
158C4×D79—81no—
159Dic158—21no—
160Dic158—21no—
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—21no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79—41no—
177C22×C79C22×D411yescharacteristic
178C2×D79—21no—
179C2×D79—21no—
180C2×D79—22no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—84no—
184C2×D79#13712yescomplemented
185C4×C79—21no—
186C4×C79—41no—
187C4×C79—41no—
188C4×C79—41no—
189C4×C79C22×D411yescharacteristic
190C4×C79H(5,𝔽2)11yescharacteristic
191Dic79—21no—
192Dic79—22no—
193Dic79—21no—
194Dic79—21no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—41no—
198C2×C79—81no—
199C2×C79D4211yescharacteristic
200C2×C79C2×#13711yescharacteristic
201C2×C79#57711yescharacteristic
202D79—22no—
203D79—42no—
204#3266—791nomaximal, Sylow
205C79#326611yescharacteristic, complemented, Sylow
206C2×#137—791no—
207C22×SD16—791no—
208D4×Q8—791no—
209#546—791no—
210#497—791no—
211#468D7911yescharacteristic, complemented
212#467—791no—
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×Q16—791no—
229C2×SD16—791no—
230C2×SD16—791no—
231C2×SD16—791no—
232C2×SD16—791no—
233C2×SD16—791no—
234C2×SD16—1584no—
235C2×SD16C2×D7911yescharacteristic
236C2×M16C2×D7911yescharacteristic, complemented
237C22×C8—791no—
238C4⋊Q8—791no—
239C4⋊Q8—1581no—
240#124—791no—
241#123—1581no—
242C22⋊Q8—791no—
243C22⋊Q8—791no—
244C22⋊Q8—1581no—
245C22⋊Q8—1581no—
246C22⋊Q8C2×D7911yescharacteristic, complemented
247#121—1581no—
248#121C2×D7911yescharacteristic
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#103—791no—
260#103C2×D7911yescharacteristic, complemented
261#102—791no—
262#102C2×D7911yescharacteristic
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—791no—
274C2×Q8—1582no—
275C2×Q8—1581no—
276C2×Q8—1582no—
277C2×Q8—1581no—
278C2×Q8C22×D7911yescharacteristic
279C2×D4—21no—
280C2×D4—3161no—
281C2×D4—791no—
282C2×D4—791no—
283C2×D4—1581no—
284C2×D4—1582no—
285C2×D4—1581no—
286C2×D4C22×D7911yescharacteristic
287C22×C4—791no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4—1581no—
292C22×C4C22×D7911yescharacteristic
293Q16—3161no—
294Q16—1582no—
295Q16—1582no—
296SD16—22no—
297SD16—3161no—
298SD16—794no—
299SD16—1582no—
300SD16—1582no—
301SD16—1582no—
302M16—22no—
303C2×C8—791no—
304C2×C8—791no—
305C2×C8—1582no—
306C2×C8C22×D7911yescharacteristic
307C2×C8C22×D7911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—791no—
310C4⋊C4—1581no—
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—21no—
329C23—3162no—
330C23—3162no—
331C23—791no—
332C23—6321no—
333C23—1581no—
334C23D4×D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—3162no—
338Q8—3162no—
339Q8—792no—
340Q8—1581no—
341Q8—1581no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345D4—21no—
346D4—21no—
347D4—81no—
348D4—3162no—
349D4—3162no—
350D4—792no—
351D4—1582no—
352D4—1581no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—3162no—
359C2×C4—3162no—
360C2×C4—3162no—
361C2×C4—791no—
362C2×C4—791no—
363C2×C4—791no—
364C2×C4—6321no—
365C2×C4—1581no—
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—21no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—3161no—
383C22—3161no—
384C22—792no—
385C22—6324no—
386C22—1582no—
387C22—1581no—
388C22—1581no—
389C22C2×D4×D7911yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—3161no—
395C4—3161no—
396C4—1582no—
397C4—1581no—
398C4—1581no—
399C4—1581no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920711yescharacteristic
402C2—41no—
403C2—81no—
404C2—3162no—
405C2—1582no—
406C2#1909919711yescharacteristic
407C2#137×D7911yescharacteristic
408C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#468×C79C2
socleC22×C79C22×D4
prime radical#19099210C2
hypercenter#468D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#14579194C2semidirect
2. C2×SD16×D79C2semidirect
3. #19099226C2semidirect
5. #19098954C2semidirect
6. #19098805C2semidirect
7. #19098784C2semidirect
8. #19098767C2semidirect
9. #19098723C2semidirect
10. #19098720C2semidirect
11. #19098715C2semidirect
12. #19098701C2semidirect
13. #19098662C2semidirect
14. #19098632C2semidirect
15. #468×C79C2semidirect
17. C22×Dic158C22semidirect
21. C2×Dic316C22semidirect
22. C2×Dic316C22semidirect
23. C2×#11929614C22semidirect
32. #14579159C22semidirect
41. #14579126C22semidirect
46. Dic79⋊C8C22semidirect
47. #14579084C22semidirect
48. #14579084C22semidirect
49. #14579084C22semidirect
51. C22⋊(C79⋊C8)C22semidirect
53. #14579071C22semidirect
55. C2×M16×C79C22semidirect
56. C22⋊Q8×C79C22semidirect
58. #107×C79C22semidirect
59. #103×C79C22semidirect
88. #11929613D4semidirect
184. C2×D79#137semidirect
205. C79#3266semidirect
211. #468D79semidirect
236. C2×M16C2×D79semidirect
246. C22⋊Q8C2×D79semidirect
255. #107C2×D79semidirect
260. #103C2×D79semidirect