Finite Group Databasebeta

← #23774964

Subgroups — #23774964

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×Q16×D79C211yesmaximal, characteristic, complemented
2Q8×C22⋊D79C211yesmaximal, characteristic, complemented
3#19099220C211yesmaximal, characteristic
4#19098954C211yesmaximal, characteristic, complemented
5#19098821C211yesmaximal, characteristic, complemented
6#19098789C211yesmaximal, characteristic, complemented
7#19098783C211yesmaximal, characteristic, complemented
8#19098771C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098719C211yesmaximal, characteristic, complemented
11#19098717C211yesmaximal, characteristic, complemented
12#19098700C211yesmaximal, characteristic, complemented
13#19098670C211yesmaximal, characteristic, complemented
14#19098632C211yesmaximal, characteristic, complemented
15C2×#137×C79C211yesmaximal, characteristic, complemented
16C2×Q8×D79C2211yescharacteristic
17C2×Q8×D79C2211yescharacteristic
18C2×Dic316C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929614C2211yescharacteristic
21C2×#11929614C2211yescharacteristic
22Q16×D79—24no—
23C2×#11929612C2211yescharacteristic
24C2×C8×D79C2211yescharacteristic
25#14579159—21no—
26#14579159C2211yescharacteristic
27#14579148—21no—
28#14579148C2211yescharacteristic
29#14579140—21no—
30#14579140—21no—
31#14579140C2211yescharacteristic
32#14579140C2211yescharacteristic
33#14579137—21no—
34#14579137C2211yescharacteristic
35#14579132—21no—
36#14579132C2211yescharacteristic
37Q8×Dic79C2211yescharacteristic
38Q8×Dic79C2211yescharacteristic
39C4×C22⋊D79—21no—
40C4×C22⋊D79—21no—
41C4×C22⋊D79C2211yescharacteristic
42#14579093C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579085C2211yescharacteristic
48#14579085C2211yescharacteristic
49#14579082C2211yescharacteristic
50C22⋊(C79⋊C8)C2211yescharacteristic
51(C2×D79)⋊C8C2211yescharacteristic
52#14579071C2211yescharacteristic
53C2×#41×C79C2211yescharacteristic
54C22×Q8×C79C2211yescharacteristic
55#137×C79—24no—
56C2×Q16×C79C2211yescharacteristic
57C2×Q16×C79C2211yescharacteristic
58C2×SD16×C79C2211yescharacteristic
59C2×SD16×C79C2211yescharacteristic
60C2×M16×C79C2211yescharacteristic
61C2×Dic158—21no—
62C2×Dic158—21no—
63C2×Dic158C2311yescharacteristic
64C2×Dic158C2311yescharacteristic
65Q8×D79—22no—
66Q8×D79—22no—
67Q8×D79—41no—
68Q8×D79—41no—
69C2×C22⋊D79—21no—
70C2×C22⋊D79D411yescharacteristic
71C2×C4×D79—21no—
72C2×C4×D79—21no—
73C2×C4×D79C2311yescharacteristic
74Dic316—22no—
75#11929614—22no—
76#11929614—22no—
77#11929614—41no—
78#11929612—41no—
79C2×C79⋊C8C2311yescharacteristic
80C2×C79⋊C8C2311yescharacteristic
81C8×D79—22no—
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⋊Dic79—21no—
94C22⋊Dic79—21no—
95C22⋊Dic79—21no—
96C22⋊Dic79—21no—
97C22⋊Dic79D411yescharacteristic
98(C2×D79)⋊C4—21no—
99(C2×D79)⋊C4D411yescharacteristic
100C4×Dic79—21no—
101C4×Dic79—21no—
102C4×Dic79C2311yescharacteristic
103#41×C79—22no—
104#41×C79—41no—
105C2×Q8×C79—21no—
106C2×Q8×C79—22no—
107C2×Q8×C79—41no—
108C2×Q8×C79C2311yescharacteristic
109C2×Q8×C79C2311yescharacteristic
110C2×Q8×C79C2311yescharacteristic
111C2×D4×C79—21no—
112C2×D4×C79C2311yescharacteristic
113C22×C4×C79—21no—
114C22×C4×C79—21no—
115C22×C4×C79C2311yescharacteristic
116Q16×C79—22no—
117Q16×C79D414yescomplemented
118SD16×C79—22no—
119SD16×C79—22no—
120M16×C79—22no—
121C2×C8×C79C2311yescharacteristic
122C2×C8×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C22×D79C2×D411yescharacteristic
126Q8×C79—21no—
127Q8×C79—21no—
128Q8×C79—21no—
129Q8×C79—21no—
130Q8×C79—42no—
131Q8×C79C2×D412yes—
132Q8×C79C2×D412yes—
133D4×C79—21no—
134D4×C79—21no—
135D4×C79—42no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—21no—
140C2×C4×C79—21no—
141C2×C4×C79—42no—
142C2×C4×C79—42no—
143C2×C4×C79C2×D411yescharacteristic
144C2×C4×C79C2411yescharacteristic
145C22⋊D79—22no—
146C22⋊D79—42no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79C2×D411yescharacteristic
152C2×Dic79C2×D411yescharacteristic
153C2×Dic79C2×D411yescharacteristic
154C4×D79—21no—
155C4×D79—21no—
156C4×D79—42no—
157C4×D79—42no—
158Dic158—21no—
159Dic158—21no—
160Dic158—21no—
161Dic158—21no—
162Dic158—42no—
163Dic158—42no—
164C8×C79—21no—
165C8×C79C2×D412yes—
166C79⋊C8—21no—
167C79⋊C8—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79—41no—
174C22×C79C22×D411yescharacteristic
175C2×D79—21no—
176C2×D79—21no—
177C2×D79#13712yescomplemented
178C4×C79—21no—
179C4×C79—22no—
180C4×C79—22no—
181C4×C79—41no—
182C4×C79C22×D411yescharacteristic
183C4×C79H(5,𝔽2)11yescharacteristic
184Dic79—21no—
185Dic79—21no—
186Dic79—21no—
187Dic79—41no—
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191C2×C79—41no—
192C2×C79—81no—
193C2×C79D4211yescharacteristic
194C2×C79C2×#13711yescharacteristic
195C2×C79#57811yescharacteristic
196D79—22no—
197#3270—791nomaximal, Sylow
198C79#327011yescharacteristic, complemented, Sylow
199C2×#137D7911yescharacteristic, complemented
200C22×Q16—791no—
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×#41C2×D7911yescharacteristic
215C22×Q8—791no—
216C22×Q8—791no—
217C22×Q8C2×D7911yescharacteristic
218#137—24no—
219C2×Q16—791no—
220C2×Q16—791no—
221C2×Q16—791no—
222C2×Q16—791no—
223C2×Q16—1584no—
224C2×Q16C2×D7911yescharacteristic
225C2×Q16C2×D7911yescharacteristic
226C2×SD16—791no—
227C2×SD16C2×D7911yescharacteristic
228C2×SD16C2×D7911yescharacteristic
229C2×M16C2×D7911yescharacteristic
230C22×C8—791no—
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—22no—
260#41—41no—
261C2×Q8—21no—
262C2×Q8—22no—
263C2×Q8—41no—
264C2×Q8—3161no—
265C2×Q8—3161no—
266C2×Q8—791no—
267C2×Q8—791no—
268C2×Q8—1581no—
269C2×Q8—1581no—
270C2×Q8—1582no—
271C2×Q8—1582no—
272C2×Q8C22×D7911yescharacteristic
273C2×Q8C22×D7911yescharacteristic
274C2×Q8C22×D7911yescharacteristic
275C2×D4—21no—
276C2×D4—791no—
277C2×D4—1581no—
278C2×D4C22×D7911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—791no—
282C22×C4—1581no—
283C22×C4—1581no—
284C22×C4C22×D7911yescharacteristic
285Q16—22no—
286Q16—3161no—
287Q16—1582no—
288Q16—1582no—
289Q16—1582no—
290Q16C22⋊D7914yescomplemented
291SD16—22no—
292SD16—22no—
293SD16—3161no—
294M16—22no—
295C2×C8—791no—
296C2×C8—791no—
297C2×C8—1582no—
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—21no—
322C23—791no—
323C23D4×D7911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—21no—
328Q8—42no—
329Q8—3162no—
330Q8—3162no—
331Q8—1581no—
332Q8—1581no—
333Q8—1581no—
334Q8—1581no—
335Q8C2×C22⋊D7912yes—
336Q8C2×C22⋊D7912yes—
337D4—21no—
338D4—21no—
339D4—42no—
340D4—3162no—
341D4—1582no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—3162no—
350C2×C4—3162no—
351C2×C4—791no—
352C2×C4—791no—
353C2×C4—791no—
354C2×C4—1581no—
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—21no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—792no—
373C22—1581no—
374C22—1581no—
375C22C2×D4×D7911yescharacteristic
376C4—21no—
377C4—22no—
378C4—22no—
379C4—41no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—1581no—
385C4—1581no—
386C4—1581no—
387C4C22×C22⋊D7911yescharacteristic
388C4#1457920611yescharacteristic
389C2—41no—
390C2—81no—
391C2—1582no—
392C2D4×C22⋊D7911yescharacteristic
393C2#137×D7911yescharacteristic
394C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#137×C79C2
socleC22×C79C22×D4
prime radical#19099220C2
hypercenterC2×#137D79
hypocenterC79#3270
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×Q16×D79C2semidirect
2. Q8×C22⋊D79C2semidirect
4. #19098954C2semidirect
5. #19098821C2semidirect
6. #19098789C2semidirect
7. #19098783C2semidirect
8. #19098771C2semidirect
9. #19098725C2semidirect
10. #19098719C2semidirect
11. #19098717C2semidirect
12. #19098700C2semidirect
13. #19098670C2semidirect
14. #19098632C2semidirect
15. C2×#137×C79C2semidirect
117. Q16×C79D4semidirect
177. C2×D79#137semidirect
198. C79#3270semidirect
199. C2×#137D79semidirect
290. Q16C22⋊D79semidirect