Finite Group Databasebeta

← #23774970

Subgroups — #23774970

Order 10112.

472 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579193C211yesmaximal, characteristic, complemented
2Q8×C22⋊D79C211yesmaximal, characteristic, complemented
3#19099224C211yesmaximal, characteristic
4#19098956C211yesmaximal, characteristic, complemented
5#19098818C211yesmaximal, characteristic, complemented
6#19098792C211yesmaximal, characteristic, complemented
7#19098787C211yesmaximal, characteristic, complemented
8#19098771C211yesmaximal, characteristic, complemented
9#19098724C211yesmaximal, characteristic, complemented
10#19098719C211yesmaximal, characteristic, complemented
11#19098717C211yesmaximal, characteristic, complemented
12#19098702C211yesmaximal, characteristic, complemented
13#19098670C211yesmaximal, characteristic, complemented
14#19098634C211yesmaximal, characteristic, complemented
15C22×Q16×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18#14579193—24no—
19C2×#11929614C2211yescharacteristic
20C2×#11929614C2211yescharacteristic
21C2×#11929613C2211yescharacteristic
22C2×#11929611C2211yescharacteristic
23C2×#11929611C2211yescharacteristic
24C2×#11929607C2211yescharacteristic
25#14579159—21no—
26#14579159C2211yescharacteristic
27#14579150—21no—
28#14579150C2211yescharacteristic
29#14579140—21no—
30#14579140C2211yescharacteristic
31#14579137—21no—
32#14579137—21no—
33#14579137C2211yescharacteristic
34#14579137C2211yescharacteristic
35#14579135—21no—
36#14579135C2211yescharacteristic
37Q8×Dic79C2211yescharacteristic
38Q8×Dic79C2211yescharacteristic
39C4×C22⋊D79—21no—
40C4×C22⋊D79—21no—
41C4×C22⋊D79C2211yescharacteristic
42#14579093C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579085C2211yescharacteristic
48#14579085C2211yescharacteristic
49#14579083C2211yescharacteristic
50C22⋊(C79⋊C8)C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52#14579071C2211yescharacteristic
53C22×Q8×C79C2211yescharacteristic
54C22×Q8×C79C2211yescharacteristic
55C2×Q16×C79—24no—
56C2×Q16×C79C2211yescharacteristic
57C2×Q16×C79C2211yescharacteristic
58C2×Q16×C79C2211yescharacteristic
59C2×Q16×C79C2211yescharacteristic
60C22×C8×C79C2211yescharacteristic
61#11929625—22no—
62#11929625—41no—
63C2×Dic158—21no—
64C2×Dic158C2311yescharacteristic
65Q8×D79—22no—
66Q8×D79—41no—
67C2×D316—21no—
68C2×D316C2311yescharacteristic
69C2×C22⋊D79—21no—
70C2×C22⋊D79D411yescharacteristic
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74#11929614—22no—
75#11929614—41no—
76#11929613—22no—
77#11929611—22no—
78#11929611—41no—
79#11929607—22no—
80C2×C79⋊C8C2311yescharacteristic
81C2×C79⋊C8C2311yescharacteristic
82C4⋊Dic79—21no—
83C4⋊Dic79—21no—
84C4⋊Dic79C2311yescharacteristic
85C4⋊Dic79C2311yescharacteristic
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88Dic79⋊C4—21no—
89Dic79⋊C4—21no—
90Dic79⋊C4—21no—
91Dic79⋊C4D411yescharacteristic
92C22⋊Dic79—21no—
93C22⋊Dic79D411yescharacteristic
94(C2×D79)⋊C4—21no—
95(C2×D79)⋊C4—21no—
96(C2×D79)⋊C4—21no—
97(C2×D79)⋊C4—21no—
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4D411yescharacteristic
100C4×Dic79—21no—
101C4×Dic79—21no—
102C4×Dic79C2311yescharacteristic
103C2×Q8×C79—21no—
104C2×Q8×C79—21no—
105C2×Q8×C79—22no—
106C2×Q8×C79—22no—
107C2×Q8×C79—41no—
108C2×Q8×C79—41no—
109C2×Q8×C79C2311yescharacteristic
110C2×Q8×C79C2311yescharacteristic
111C2×Q8×C79C2311yescharacteristic
112C2×Q8×C79C2311yescharacteristic
113C22×C4×C79—21no—
114C22×C4×C79—21no—
115C22×C4×C79C2311yescharacteristic
116Q16×C79—22no—
117Q16×C79—22no—
118Q16×C79—22no—
119Q16×C79D414yescomplemented
120C2×C8×C79—22no—
121C2×C8×C79C2311yescharacteristic
122C2×C8×C79C2311yescharacteristic
123C23×C79C2×D411yescharacteristic
124C22×D79—21no—
125C22×D79C2×D411yescharacteristic
126Q8×C79—21no—
127Q8×C79—21no—
128Q8×C79—21no—
129Q8×C79—21no—
130Q8×C79—21no—
131Q8×C79—21no—
132Q8×C79—42no—
133Q8×C79—42no—
134Q8×C79C2×D412yes—
135Q8×C79C2×D412yes—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—21no—
142C2×C4×C79—42no—
143C2×C4×C79—42no—
144C2×C4×C79C2×D411yescharacteristic
145C2×C4×C79C2411yescharacteristic
146C22⋊D79—22no—
147C22⋊D79—42no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153C2×Dic79C2×D411yescharacteristic
154D316—21no—
155D316—21no—
156D316—42no—
157C4×D79—21no—
158C4×D79—21no—
159C4×D79—42no—
160C4×D79—42no—
161Dic158—21no—
162Dic158—21no—
163Dic158—42no—
164C8×C79—21no—
165C8×C79C2×D412yes—
166C79⋊C8—21no—
167C79⋊C8—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79#13712yescomplemented
171C22×C79C22×D411yescharacteristic
172C2×D79—21no—
173C2×D79—21no—
174C2×D79—21no—
175C2×D79—41no—
176C2×D79—41no—
177C2×D79—41no—
178C4×C79—21no—
179C4×C79—22no—
180C4×C79—22no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79C22×D411yescharacteristic
184C4×C79H(5,𝔽2)11yescharacteristic
185Dic79—21no—
186Dic79—21no—
187Dic79—21no—
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191C2×C79—22no—
192C2×C79D4211yescharacteristic
193C2×C79C2×#13711yescharacteristic
194C2×C79#57811yescharacteristic
195D79—41no—
196D79—81no—
197#3270—791nomaximal, Sylow
198C79#327011yescharacteristic, complemented, Sylow
199C2×#137—791no—
200C22×Q16D7911yescharacteristic, complemented
201D4×Q8—791no—
202#548—791no—
203#497—791no—
204#470—791no—
205#465—791no—
206#464—791no—
207#462—791no—
208#452—791no—
209#451—791no—
210#451—791no—
211#448—791no—
212#441—791no—
213#435—791no—
214C2×#41—791no—
215C22×Q8—791no—
216C22×Q8C2×D7911yescharacteristic
217C22×Q8C2×D7911yescharacteristic
218#137—1584no—
219C2×Q16—24no—
220C2×Q16—791no—
221C2×Q16—791no—
222C2×Q16C2×D7911yescharacteristic
223C2×Q16C2×D7911yescharacteristic
224C2×Q16C2×D7911yescharacteristic
225C2×Q16C2×D7911yescharacteristic
226C2×SD16—791no—
227C2×SD16—791no—
228C2×SD16—791no—
229C2×M16—791no—
230C22×C8C2×D7911yescharacteristic
231C4⋊Q8—791no—
232C4⋊Q8—1581no—
233#124—791no—
234#124—1581no—
235C22⋊Q8—791no—
236C22⋊Q8—791no—
237C22⋊Q8—791no—
238C22⋊Q8—1581no—
239C22⋊Q8—1581no—
240C22⋊Q8—1581no—
241#121—791no—
242#121—1581no—
243C4×Q8—791no—
244C4×Q8—791no—
245C4×D4—791no—
246C4×D4—1581no—
247C4×D4—1581no—
248#106—791no—
249C4⋊C8—791no—
250#103—791no—
251#103—791no—
252#103—791no—
253#103—791no—
254#103—791no—
255#102—791no—
256C22⋊C8—791no—
257C22⋊C8—791no—
258#97—791no—
259#41—3161no—
260#41—1582no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—22no—
264C2×Q8—22no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—3161no—
268C2×Q8—791no—
269C2×Q8—1581no—
270C2×Q8—1582no—
271C2×Q8C22×D7911yescharacteristic
272C2×Q8C22×D7911yescharacteristic
273C2×Q8C22×D7911yescharacteristic
274C2×Q8C22×D7911yescharacteristic
275C2×D4—791no—
276C2×D4—791no—
277C2×D4—1581no—
278C2×D4—1581no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—791no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4C22×D7911yescharacteristic
285Q16—22no—
286Q16—22no—
287Q16—22no—
288Q16—3161no—
289Q16—1582no—
290Q16C22⋊D7914yescomplemented
291SD16—3161no—
292SD16—1582no—
293SD16—1582no—
294M16—1582no—
295C2×C8—22no—
296C2×C8—791no—
297C2×C8—791no—
298C2×C8C22×D7911yescharacteristic
299C2×C8C22×D7911yescharacteristic
300C4⋊C4—791no—
301C4⋊C4—791no—
302C4⋊C4—791no—
303C4⋊C4—1581no—
304C4⋊C4—1581no—
305C4⋊C4—1581no—
306C4⋊C4—1581no—
307C4⋊C4—1581no—
308C4⋊C4—1581no—
309C4⋊C4—1581no—
310C22⋊C4—791no—
311C22⋊C4—791no—
312C22⋊C4—1581no—
313C22⋊C4—1581no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4—1581no—
317C22⋊C4—1581no—
318C42—791no—
319C42—1581no—
320C42—1581no—
321C23—791no—
322C23—1581no—
323C23D4×D7911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—42no—
331Q8—42no—
332Q8—3162no—
333Q8—1581no—
334Q8—1581no—
335Q8C2×C22⋊D7912yes—
336Q8C2×C22⋊D7912yes—
337D4—3162no—
338D4—3162no—
339D4—1582no—
340D4—1581no—
341D4—1581no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—3162no—
351C2×C4—3162no—
352C2×C4—791no—
353C2×C4—791no—
354C2×C4—791no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4—1581no—
358C2×C4—1581no—
359C2×C4—1581no—
360C2×C4D4×D7911yescharacteristic
361C2×C4C23×D7911yescharacteristic
362C8—21no—
363C8—1581no—
364C8—1581no—
365C8C2×C22⋊D7912yes—
366C22—21no—
367C22—21no—
368C22—3161no—
369C22—3161no—
370C22—3161no—
371C22—1581no—
372C22—1581no—
373C22—1581no—
374C22#1457919312yescomplemented
375C22C2×D4×D7911yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—1581no—
385C4—1581no—
386C4—1581no—
387C4C22×C22⋊D7911yescharacteristic
388C4#1457920611yescharacteristic
389C2—22no—
390C2—3161no—
391C2—6321no—
392C2D4×C22⋊D7911yescharacteristic
393C2C2×#1457919311yescharacteristic
394C2#1909937611yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC22×Q16×C79C2
socleC22×C79C22×D4
prime radical#19099224C2
hypercenterC22×Q16D79
hypocenterC79#3270
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#14579193C2semidirect
2. Q8×C22⋊D79C2semidirect
4. #19098956C2semidirect
5. #19098818C2semidirect
6. #19098792C2semidirect
7. #19098787C2semidirect
8. #19098771C2semidirect
9. #19098724C2semidirect
10. #19098719C2semidirect
11. #19098717C2semidirect
12. #19098702C2semidirect
13. #19098670C2semidirect
14. #19098634C2semidirect
15. C22×Q16×C79C2semidirect
119. Q16×C79D4semidirect
170. C22×C79#137semidirect
198. C79#3270semidirect
200. C22×Q16D79semidirect
290. Q16C22⋊D79semidirect
374. C22#14579193semidirect