Finite Group Databasebeta

← #23774911

Subgroups — #23774911

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×#14579192C211yesmaximal, characteristic, complemented
2C22×#11929611C211yesmaximal, characteristic, complemented
3#19099209C211yesmaximal, characteristic
4#19098955C211yesmaximal, characteristic, complemented
5#19098811C211yesmaximal, characteristic, complemented
6#19098802C211yesmaximal, characteristic, complemented
7#19098785C211yesmaximal, characteristic, complemented
8#19098765C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098719C211yesmaximal, characteristic, complemented
11#19098713C211yesmaximal, characteristic, complemented
12#19098702C211yesmaximal, characteristic, complemented
13#19098661C211yesmaximal, characteristic, complemented
14#19098635C211yesmaximal, characteristic, complemented
15D4×Q8×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×D316C2211yescharacteristic
18#14579192—24no—
19C2×#11929614C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929614C2211yescharacteristic, complemented
22C2×#11929611—24no—
23C2×#11929611C2211yescharacteristic
24C2×#11929611C2211yescharacteristic
25C2×#11929611C2211yescharacteristic
26C2×#11929611C2211yescharacteristic
27C2×#11929611C2211yescharacteristic
28C2×#11929611C2211yescharacteristic
29C2×#11929608C2211yescharacteristic, complemented
30C22×C79⋊C8C2211yescharacteristic
31#14579149C2211yescharacteristic
32#14579146—21no—
33#14579140C2211yescharacteristic
34#14579135C2211yescharacteristic
35#14579134—21no—
36#14579129—21no—
37C4×D316C2211yescharacteristic
38C22⋊C4×D79—21no—
39#14579094C2211yescharacteristic, complemented
40C4⋊(C79⋊C8)C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579085C2211yescharacteristic, complemented
43#14579085C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579081C2211yescharacteristic
46#14579081C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C22⋊(C79⋊C8)C2211yescharacteristic, complemented
49#14579072C2211yescharacteristic, complemented
50C22×Q8×C79C2211yescharacteristic
51C22×Q8×C79C2211yescharacteristic, complemented
52C4⋊Q8×C79—21no—
53C4⋊Q8×C79C2211yescharacteristic, complemented
54C22⋊Q8×C79—21no—
55C22⋊Q8×C79—21no—
56C22⋊Q8×C79C2211yescharacteristic
57C22⋊Q8×C79C2211yescharacteristic, complemented
58C4×Q8×C79C2211yescharacteristic, complemented
59C4×D4×C79—21no—
60C4×D4×C79C2211yescharacteristic
61C23×D79—21no—
62#11929624—22no—
63#11929624—41no—
64C2×Dic158C2311yescharacteristic
65C2×D316—22no—
66C2×D316—21no—
67C2×D316—41no—
68C2×D316C2311yescharacteristic
69C2×D316C2311yescharacteristic
70C2×C22⋊D79—21no—
71C2×C22⋊D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74#11929614—22no—
75#11929614—22no—
76#11929614—41no—
77#11929611—22no—
78#11929611—22no—
79#11929611—22no—
80#11929611—22no—
81#11929611—41no—
82#11929611D414yescomplemented
83#11929608—22no—
84C2×C79⋊C8—22no—
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C2×C79⋊C8C2311yescharacteristic
88C2×C79⋊C8C2311yescharacteristic
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96C2×Q8×C79—21no—
97C2×Q8×C79—21no—
98C2×Q8×C79—22no—
99C2×Q8×C79—22no—
100C2×Q8×C79—41no—
101C2×Q8×C79—41no—
102C2×Q8×C79C2311yescharacteristic
103C2×Q8×C79C2311yescharacteristic
104C2×Q8×C79C2311yescharacteristic
105C2×D4×C79D411yescharacteristic
106C22×C4×C79—21no—
107C22×C4×C79—21no—
108C22×C4×C79C2311yescharacteristic
109C22×C4×C79C2311yescharacteristic
110C4⋊C4×C79—21no—
111C4⋊C4×C79—21no—
112C4⋊C4×C79—21no—
113C4⋊C4×C79—21no—
114C4⋊C4×C79—21no—
115C4⋊C4×C79D411yescharacteristic
116C4⋊C4×C79C2311yescharacteristic
117C22⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C22⋊C4×C79D411yescharacteristic
120C22⋊C4×C79D411yescharacteristic
121C42×C79—21no—
122C42×C79C2311yescharacteristic
123C23×C79C2×D411yescharacteristic
124C23×C79C2×D411yescharacteristic
125C22×D79—21no—
126C22×D79—21no—
127C22×D79—42no—
128C22×D79—42no—
129C22×D79—81no—
130Q8×C79—21no—
131Q8×C79—21no—
132Q8×C79—21no—
133Q8×C79—21no—
134Q8×C79—21no—
135Q8×C79—42no—
136Q8×C79—42no—
137Q8×C79C2×D412yes—
138D4×C79—22no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—21no—
143C2×C4×C79—21no—
144C2×C4×C79—21no—
145C2×C4×C79—21no—
146C2×C4×C79—21no—
147C2×C4×C79—42no—
148C2×C4×C79—42no—
149C2×C4×C79C2×D411yescharacteristic
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2×D411yescharacteristic
152C2×C4×C79C2×D411yescharacteristic
153C2×C4×C79C2411yescharacteristic
154C22⋊D79—42no—
155C22⋊D79—81no—
156C2×Dic79—21no—
157C2×Dic79—21no—
158D316—21no—
159D316—21no—
160D316—21no—
161D316—42no—
162D316C2×D412yes—
163C4×D79—42no—
164C4×D79—81no—
165Dic158—21no—
166Dic158—21no—
167C79⋊C8—21no—
168C79⋊C8—21no—
169C79⋊C8—21no—
170C79⋊C8C2×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—22no—
188C4×C79—21no—
189C4×C79—21no—
190C4×C79—41no—
191C4×C79—41no—
192C4×C79—41no—
193C4×C79C22×D411yescharacteristic
194C4×C79H(5,𝔽2)11yescharacteristic
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×Q8D7911yescharacteristic, complemented
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#435—791no—
221C2×#41—791no—
222C22×Q8C2×D7911yescharacteristic
223C22×Q8C2×D7911yescharacteristic, complemented
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×M16—791no—
237C22×C8—791no—
238C4⋊Q8—21no—
239C4⋊Q8C2×D7911yescharacteristic, complemented
240#124—791no—
241#123—1581no—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C22⋊Q8—791no—
245C22⋊Q8C2×D7911yescharacteristic
246C22⋊Q8C2×D7911yescharacteristic, complemented
247#121—791no—
248#121—1581no—
249#120—1581no—
250C4×Q8C2×D7911yescharacteristic, complemented
251C4×D4—21no—
252C4×D4—791no—
253C4×D4C2×D7911yescharacteristic
254C2×C22⋊C4—1581no—
255#107—791no—
256C4⋊C8—791no—
257#103—791no—
258#103—791no—
259#103—791no—
260#103—791no—
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—21no—
270C2×Q8—21no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—791no—
276C2×Q8C22×D7911yescharacteristic
277C2×Q8C22×D7911yescharacteristic
278C2×Q8C22×D7911yescharacteristic
279C2×D4—3161no—
280C2×D4—791no—
281C2×D4—791no—
282C2×D4—1582no—
283C2×D4—1581no—
284C2×D4—1581no—
285C2×D4—1581no—
286C2×D4C22⋊D7911yescharacteristic
287C22×C4—21no—
288C22×C4—21no—
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—1582no—
303C2×C8—791no—
304C2×C8—791no—
305C2×C8—791no—
306C2×C8—791no—
307C2×C8—1582no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—791no—
314C4⋊C4—1581no—
315C4⋊C4C22⋊D7911yescharacteristic
316C4⋊C4C22×D7911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—1581no—
320C22⋊C4—1581no—
321C22⋊C4—1581no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4C22⋊D7911yescharacteristic
325C22⋊C4C22⋊D7911yescharacteristic
326C42—21no—
327C42C22×D7911yescharacteristic
328C23—3162no—
329C23—3162no—
330C23—6321no—
331C23—1581no—
332C23—1581no—
333C23C2×C22⋊D7911yescharacteristic
334C23C2×C22⋊D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8—42no—
342Q8—1581no—
343Q8—1581no—
344Q8D4×D7912yes—
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—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—3162no—
364C2×C4—6321no—
365C2×C4—1581no—
366C2×C4—1581no—
367C2×C4C2×C22⋊D7911yescharacteristic
368C2×C4C2×C22⋊D7911yescharacteristic
369C2×C4C2×C22⋊D7911yescharacteristic
370C2×C4C2×C22⋊D7911yescharacteristic
371C2×C4C23×D7911yescharacteristic
372C8—792no—
373C8—1581no—
374C8—1581no—
375C8—1581no—
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#1457919212yescomplemented
389C22C22×C22⋊D7911yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—21no—
394C4—21no—
395C4—41no—
396C4—41no—
397C4—41no—
398C4—3161no—
399C4—3161no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920611yescharacteristic
402C2—22no—
403C2—41no—
404C2—3162no—
405C2—6321no—
406C2D4×C22⋊D7911yescharacteristic
407C2C2×#1457919211yescharacteristic
408C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingD4×Q8×C79C2
socleC22×C79C22×D4
prime radical#19099209C2
hypercenterD4×Q8D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#14579192C2semidirect
2. C22×#11929611C2semidirect
4. #19098955C2semidirect
5. #19098811C2semidirect
6. #19098802C2semidirect
7. #19098785C2semidirect
8. #19098765C2semidirect
9. #19098723C2semidirect
10. #19098719C2semidirect
11. #19098713C2semidirect
12. #19098702C2semidirect
13. #19098661C2semidirect
14. #19098635C2semidirect
15. D4×Q8×C79C2semidirect
19. C2×#11929614C22semidirect
20. C2×#11929614C22semidirect
21. C2×#11929614C22semidirect
29. C2×#11929608C22semidirect
39. #14579094C22semidirect
40. C4⋊(C79⋊C8)C22semidirect
41. #14579085C22semidirect
42. #14579085C22semidirect
43. #14579085C22semidirect
44. #14579084C22semidirect
48. C22⋊(C79⋊C8)C22semidirect
49. #14579072C22semidirect
51. C22×Q8×C79C22semidirect
53. C4⋊Q8×C79C22semidirect
57. C22⋊Q8×C79C22semidirect
58. C4×Q8×C79C22semidirect
82. #11929611D4semidirect
176. C22×C79#137semidirect
205. C79#3266semidirect
208. D4×Q8D79semidirect
223. C22×Q8C2×D79semidirect
239. C4⋊Q8C2×D79semidirect
246. C22⋊Q8C2×D79semidirect
250. C4×Q8C2×D79semidirect
388. C22#14579192semidirect