Finite Group Databasebeta

← #23774915

Subgroups — #23774915

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
2C22×#11929613C211yesmaximal, characteristic, complemented
3D4×Dic158C211yesmaximal, characteristic, complemented
4#19099209C211yesmaximal, characteristic
5#19098957C211yesmaximal, characteristic, complemented
6#19098809C211yesmaximal, characteristic, complemented
7#19098804C211yesmaximal, characteristic, complemented
8#19098786C211yesmaximal, characteristic, complemented
9#19098769C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098721C211yesmaximal, characteristic, complemented
12#19098716C211yesmaximal, characteristic, complemented
13#19098704C211yesmaximal, characteristic, complemented
14#19098665C211yesmaximal, characteristic, complemented
15#435×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C22×Dic158C2211yescharacteristic, complemented
19C22×D316C2211yescharacteristic
20#14579194—24no—
21C2×Dic316C2211yescharacteristic, complemented
22C2×Dic316C2211yescharacteristic, complemented
23C2×Dic316C2211yescharacteristic, complemented
24C2×#11929613—24no—
25C2×#11929613C2211yescharacteristic
26C2×#11929613C2211yescharacteristic
27C2×#11929613C2211yescharacteristic
28C2×#11929613C2211yescharacteristic
29C2×#11929613C2211yescharacteristic
30C2×#11929613C2211yescharacteristic
31#14579161C2211yescharacteristic, complemented
32#14579160—21no—
33#14579149C2211yescharacteristic
34#14579146—21no—
35#14579140C2211yescharacteristic
36#14579140C2211yescharacteristic
37#14579140C2211yescharacteristic, complemented
38#14579138—21no—
39#14579138—21no—
40#14579135C2211yescharacteristic
41#14579134—21no—
42#14579129—21no—
43C4×Dic158C2211yescharacteristic, complemented
44C4×D316C2211yescharacteristic
45D4×Dic79—21no—
46C22⋊C4×D79—21no—
47#14579095C2211yescharacteristic, complemented
48#14579086C2211yescharacteristic, complemented
49#14579086C2211yescharacteristic, complemented
50#14579086C2211yescharacteristic, complemented
51#14579086C2211yescharacteristic, complemented
52#14579083C2211yescharacteristic
53#14579083C2211yescharacteristic
54C2×M16×C79C2211yescharacteristic, complemented
55C22×C8×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57C4⋊C8×C79C2211yescharacteristic, complemented
58C22⋊C8×C79C2211yescharacteristic
59C22⋊C8×C79C2211yescharacteristic, complemented
60#97×C79C2211yescharacteristic, complemented
61C23×D79—21no—
62#11929624—22no—
63#11929624—41no—
64C2×Dic158—22no—
65C2×Dic158—22no—
66C2×Dic158—21no—
67C2×Dic158—21no—
68C2×Dic158—41no—
69C2×Dic158—41no—
70C2×Dic158C2311yescharacteristic
71C2×Dic158C2311yescharacteristic
72C2×Dic158C2311yescharacteristic
73C2×Dic158C2311yescharacteristic
74C2×D316—22no—
75C2×D316—21no—
76C2×D316—41no—
77C2×D316C2311yescharacteristic
78C2×D316C2311yescharacteristic
79C2×C22⋊D79—21no—
80C2×C22⋊D79—21no—
81C22×Dic79—21no—
82C22×Dic79—21no—
83C2×C4×D79—21no—
84C2×C4×D79—21no—
85Dic316—22no—
86Dic316—22no—
87Dic316—41no—
88#11929613—22no—
89#11929613—22no—
90#11929613—22no—
91#11929613—22no—
92#11929613—41no—
93#11929613D414yescomplemented
94C4⋊Dic79—21no—
95C4⋊Dic79—21no—
96C4⋊Dic79C2311yescharacteristic
97C4⋊Dic79C2311yescharacteristic
98Dic79⋊C4—21no—
99Dic79⋊C4—21no—
100Dic79⋊C4—21no—
101Dic79⋊C4—21no—
102C22⋊Dic79—21no—
103C22⋊Dic79—21no—
104C22⋊Dic79—21no—
105(C2×D79)⋊C4—21no—
106(C2×D79)⋊C4—21no—
107(C2×D79)⋊C4—21no—
108(C2×D79)⋊C4—21no—
109C4×Dic79—21no—
110C2×D4×C79D411yescharacteristic
111C22×C4×C79C2311yescharacteristic
112C22×C4×C79C2311yescharacteristic
113M16×C79—22no—
114C2×C8×C79—22no—
115C2×C8×C79C2311yescharacteristic
116C2×C8×C79C2311yescharacteristic
117C2×C8×C79C2311yescharacteristic
118C2×C8×C79C2311yescharacteristic
119C4⋊C4×C79D411yescharacteristic
120C22⋊C4×C79D411yescharacteristic
121C22⋊C4×C79D411yescharacteristic
122C42×C79C2311yescharacteristic
123C23×C79C2×D411yescharacteristic
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—42no—
128C22×D79—42no—
129C22×D79—81no—
130D4×C79—22no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—42no—
141C22⋊D79—81no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—42no—
149C2×Dic79—42no—
150D316—21no—
151D316—21no—
152D316—21no—
153D316—42no—
154D316C2×D412yes—
155C4×D79—42no—
156C4×D79—81no—
157Dic158—21no—
158Dic158—21no—
159Dic158—21no—
160Dic158—21no—
161Dic158—21no—
162Dic158—21no—
163Dic158—21no—
164Dic158—42no—
165Dic158—42no—
166Dic158C2×D412yes—
167C8×C79—21no—
168C8×C79—21no—
169C8×C79—21no—
170C8×C79C2×D412yes—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—21no—
175C22×C79—21no—
176C22×C79#13712yescomplemented
177C22×C79C22×D411yescharacteristic
178C2×D79—22no—
179C2×D79—41no—
180C2×D79—41no—
181C2×D79—41no—
182C2×D79—41no—
183C2×D79—41no—
184C2×D79—84no—
185C4×C79—21no—
186C4×C79—21no—
187C4×C79—21no—
188C4×C79—21no—
189C4×C79C22×D411yescharacteristic
190C4×C79H(5,𝔽2)11yescharacteristic
191Dic79—22no—
192Dic79—41no—
193Dic79—41no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—22no—
198C2×C79—41no—
199C2×C79D4211yescharacteristic
200C2×C79C2×#13711yescharacteristic
201C2×C79#57711yescharacteristic
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#467—791no—
213#464—791no—
214#461—791no—
215#452—791no—
216#451—791no—
217#450—791no—
218#448—791no—
219#440—791no—
220#435D7911yescharacteristic, complemented
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—791no—
235C2×SD16—1584no—
236C2×M16C2×D7911yescharacteristic, complemented
237C22×C8C2×D7911yescharacteristic
238C4⋊Q8—791no—
239C4⋊Q8—1581no—
240#124—791no—
241#123—1581no—
242C22⋊Q8—791no—
243C22⋊Q8—791no—
244C22⋊Q8—791no—
245C22⋊Q8—1581no—
246C22⋊Q8—1581no—
247#121—791no—
248#121—1581no—
249#120—1581no—
250C4×Q8—791no—
251C4×D4—791no—
252C4×D4—1581no—
253C4×D4C2×D7911yescharacteristic
254C2×C22⋊C4—1581no—
255#107—791no—
256C4⋊C8C2×D7911yescharacteristic, complemented
257#103—791no—
258#103—791no—
259#103—791no—
260#103—791no—
261#102—791no—
262#102—791no—
263C22⋊C8C2×D7911yescharacteristic
264C22⋊C8C2×D7911yescharacteristic, complemented
265#97C2×D7911yescharacteristic, complemented
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—791no—
275C2×Q8—1582no—
276C2×Q8—1582no—
277C2×Q8—1581no—
278C2×Q8—1581no—
279C2×D4—3161no—
280C2×D4—791no—
281C2×D4—791no—
282C2×D4—1582no—
283C2×D4—1581no—
284C2×D4—1581no—
285C2×D4—1581no—
286C2×D4D31611yescharacteristic
287C22×C4—1581no—
288C22×C4—1581no—
289C22×C4—1581no—
290C22×C4—1581no—
291C22×C4C22×D7911yescharacteristic
292C22×C4C22×D7911yescharacteristic
293Q16—3161no—
294Q16—1582no—
295Q16—1582no—
296SD16—3161no—
297SD16—794no—
298SD16—1582no—
299SD16—1582no—
300SD16—1582no—
301SD16—1582no—
302M16—22no—
303C2×C8—22no—
304C2×C8C22×D7911yescharacteristic
305C2×C8C22×D7911yescharacteristic
306C2×C8C22×D7911yescharacteristic
307C2×C8C22×D7911yescharacteristic
308C4⋊C4—791no—
309C4⋊C4—791no—
310C4⋊C4—1581no—
311C4⋊C4—1581no—
312C4⋊C4—1581no—
313C4⋊C4—1581no—
314C4⋊C4—1581no—
315C4⋊C4—1581no—
316C4⋊C4D31611yescharacteristic
317C22⋊C4—1581no—
318C22⋊C4—1581no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4D31611yescharacteristic
325C22⋊C4D31611yescharacteristic
326C42—1581no—
327C42C22×D7911yescharacteristic
328C23—3162no—
329C23—3162no—
330C23—6321no—
331C23—1581no—
332C23—1581no—
333C23C2×D31611yescharacteristic
334C23C2×D31611yescharacteristic
335Q8—3162no—
336Q8—3162no—
337Q8—792no—
338Q8—1581no—
339Q8—1581no—
340Q8—1581no—
341Q8—1581no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345D4—22no—
346D4—3162no—
347D4—3162no—
348D4—792no—
349D4—6321no—
350D4—1581no—
351D4—1581no—
352D4—1581no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—3162no—
358C2×C4—3162no—
359C2×C4—3162no—
360C2×C4—6321no—
361C2×C4—1581no—
362C2×C4—1581no—
363C2×C4—1581no—
364C2×C4—1581no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4C2×D31611yescharacteristic
368C2×C4C2×D31611yescharacteristic
369C2×C4C2×D31611yescharacteristic
370C2×C4C2×D31611yescharacteristic
371C2×C4C23×D7911yescharacteristic
372C8—21no—
373C8—21no—
374C8—21no—
375C8D4×D7912yes—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—3161no—
382C22—3161no—
383C22—3161no—
384C22—3161no—
385C22—3161no—
386C22—6324no—
387C22—1582no—
388C22#1457919412yescomplemented
389C22C22×D31611yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—3161no—
395C4—3161no—
396C4—3161no—
397C4—3161no—
398C4—3161no—
399C4—1582no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920711yescharacteristic
402C2—22no—
403C2—41no—
404C2—3162no—
405C2—6321no—
406C2D4×D31611yescharacteristic
407C2C2×#1457919411yescharacteristic
408C2#1909937511yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#435×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenter#435D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#14579194C2semidirect
2. C22×#11929613C2semidirect
3. D4×Dic158C2semidirect
5. #19098957C2semidirect
6. #19098809C2semidirect
7. #19098804C2semidirect
8. #19098786C2semidirect
9. #19098769C2semidirect
10. #19098727C2semidirect
11. #19098721C2semidirect
12. #19098716C2semidirect
13. #19098704C2semidirect
14. #19098665C2semidirect
15. #435×C79C2semidirect
18. C22×Dic158C22semidirect
21. C2×Dic316C22semidirect
22. C2×Dic316C22semidirect
23. C2×Dic316C22semidirect
31. #14579161C22semidirect
37. #14579140C22semidirect
43. C4×Dic158C22semidirect
47. #14579095C22semidirect
48. #14579086C22semidirect
49. #14579086C22semidirect
50. #14579086C22semidirect
51. #14579086C22semidirect
54. C2×M16×C79C22semidirect
57. C4⋊C8×C79C22semidirect
59. C22⋊C8×C79C22semidirect
60. #97×C79C22semidirect
93. #11929613D4semidirect
176. C22×C79#137semidirect
205. C79#3266semidirect
220. #435D79semidirect
236. C2×M16C2×D79semidirect
256. C4⋊C8C2×D79semidirect
264. C22⋊C8C2×D79semidirect
265. #97C2×D79semidirect
388. C22#14579194semidirect