Finite Group Databasebeta

← #23774966

Subgroups — #23774966

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×#14579191C211yesmaximal, characteristic, complemented
2C22×#11929614C211yesmaximal, characteristic, complemented
3D4×Dic158C211yesmaximal, characteristic, complemented
4#19098958C211yesmaximal, characteristic, complemented
5#19098819C211yesmaximal, characteristic, complemented
6#19098790C211yesmaximal, characteristic, complemented
7#19098782C211yesmaximal, characteristic, complemented
8#19098773C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098719C211yesmaximal, characteristic, complemented
11#19098718C211yesmaximal, characteristic, complemented
12#19098701C211yesmaximal, characteristic, complemented
13#19098668C211yesmaximal, characteristic, complemented
14#19098635C211yesmaximal, characteristic, complemented
15#548×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18#14579191—24no—
19C2×#11929614—24no—
20C2×#11929614C2211yescharacteristic
21C2×#11929614C2211yescharacteristic
22C2×#11929614C2211yescharacteristic
23C2×#11929614C2211yescharacteristic
24C2×#11929614C2211yescharacteristic
25C2×#11929614C2211yescharacteristic
26C2×#11929612C2211yescharacteristic
27C2×#11929612C2211yescharacteristic
28C2×#11929612C2211yescharacteristic
29C2×#11929608C2211yescharacteristic
30C22×C79⋊C8C2211yescharacteristic
31#14579161C2211yescharacteristic
32#14579160—21no—
33#14579140C2211yescharacteristic
34#14579140C2211yescharacteristic
35#14579138—21no—
36#14579138—21no—
37C4×Dic158C2211yescharacteristic
38D4×Dic79—21no—
39#14579092C2211yescharacteristic
40C4⋊(C79⋊C8)C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579085C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579084C2211yescharacteristic
45#14579084C2211yescharacteristic
46#14579082C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C22⋊(C79⋊C8)C2211yescharacteristic
49#14579072C2211yescharacteristic
50C2×#41×C79C2211yescharacteristic
51C22×Q8×C79C2211yescharacteristic
52#124×C79—21no—
53#124×C79C2211yescharacteristic
54C22⋊Q8×C79—21no—
55C22⋊Q8×C79C2211yescharacteristic
56#121×C79—21no—
57#121×C79C2211yescharacteristic
58C4×Q8×C79C2211yescharacteristic
59C4×D4×C79—21no—
60C4×D4×C79C2211yescharacteristic
61C2×Dic158—22no—
62C2×Dic158—22no—
63C2×Dic158—21no—
64C2×Dic158—21no—
65C2×Dic158—41no—
66C2×Dic158—41no—
67C2×Dic158C2311yescharacteristic
68C2×Dic158C2311yescharacteristic
69C2×Dic158C2311yescharacteristic
70C22×Dic79—21no—
71C22×Dic79—21no—
72#11929614—22no—
73#11929614—22no—
74#11929614—22no—
75#11929614—22no—
76#11929614—41no—
77#11929614D414yescomplemented
78#11929612—22no—
79#11929612—22no—
80#11929612—41no—
81#11929608—22no—
82C2×C79⋊C8—22no—
83C2×C79⋊C8C2311yescharacteristic
84C2×C79⋊C8C2311yescharacteristic
85C2×C79⋊C8C2311yescharacteristic
86C2×C79⋊C8C2311yescharacteristic
87C4⋊Dic79—21no—
88C4⋊Dic79—21no—
89C4⋊Dic79C2311yescharacteristic
90Dic79⋊C4—21no—
91Dic79⋊C4—21no—
92Dic79⋊C4—21no—
93C22⋊Dic79—21no—
94C22⋊Dic79—21no—
95C4×Dic79—21no—
96#41×C79—22no—
97#41×C79—41no—
98C2×Q8×C79—21no—
99C2×Q8×C79—22no—
100C2×Q8×C79—41no—
101C2×Q8×C79C2311yescharacteristic
102C2×Q8×C79C2311yescharacteristic
103C2×D4×C79—21no—
104C2×D4×C79—21no—
105C2×D4×C79D411yescharacteristic
106C2×D4×C79C2311yescharacteristic
107C22×C4×C79—21no—
108C22×C4×C79—21no—
109C22×C4×C79C2311yescharacteristic
110C22×C4×C79C2311yescharacteristic
111C4⋊C4×C79—21no—
112C4⋊C4×C79—21no—
113C4⋊C4×C79D411yescharacteristic
114C4⋊C4×C79C2311yescharacteristic
115C22⋊C4×C79—21no—
116C22⋊C4×C79—21no—
117C22⋊C4×C79—21no—
118C22⋊C4×C79—21no—
119C22⋊C4×C79D411yescharacteristic
120C22⋊C4×C79D411yescharacteristic
121C42×C79—21no—
122C42×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79C2×D411yescharacteristic
125C23×C79C2×D411yescharacteristic
126Q8×C79—21no—
127Q8×C79—21no—
128Q8×C79—21no—
129Q8×C79—42no—
130Q8×C79C2×D412yes—
131D4×C79—22no—
132D4×C79—21no—
133D4×C79—21no—
134D4×C79—42no—
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—21no—
142C2×C4×C79—21no—
143C2×C4×C79—42no—
144C2×C4×C79—42no—
145C2×C4×C79C2×D411yescharacteristic
146C2×C4×C79C2×D411yescharacteristic
147C2×C4×C79C2×D411yescharacteristic
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2411yescharacteristic
150C2×Dic79—21no—
151C2×Dic79—21no—
152C2×Dic79—21no—
153C2×Dic79—21no—
154C2×Dic79—42no—
155C2×Dic79—42no—
156Dic158—21no—
157Dic158—21no—
158Dic158—21no—
159Dic158—21no—
160Dic158—21no—
161Dic158—42no—
162Dic158—42no—
163Dic158C2×D412yes—
164C79⋊C8—21no—
165C79⋊C8—21no—
166C79⋊C8—21no—
167C79⋊C8C2×D412yes—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—21no—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—41no—
174C22×C79—41no—
175C22×C79—41no—
176C22×C79#13712yescomplemented
177C22×C79C22×D411yescharacteristic
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—22no—
181C4×C79—21no—
182C4×C79—21no—
183C4×C79—41no—
184C4×C79—41no—
185C4×C79C22×D411yescharacteristic
186C4×C79H(5,𝔽2)11yescharacteristic
187Dic79—22no—
188Dic79—41no—
189Dic79—41no—
190Dic79—41no—
191C2×C79—22no—
192C2×C79—41no—
193C2×C79—81no—
194C2×C79D4211yescharacteristic
195C2×C79C2×#13711yescharacteristic
196C2×C79#57811yescharacteristic
197#3270—791nomaximal, Sylow
198C79#327011yescharacteristic, complemented, Sylow
199C2×#137—791no—
200C22×Q16—791no—
201D4×Q8—791no—
202#548D7911yescharacteristic
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—1584no—
219C2×Q16—791no—
220C2×Q16—791no—
221C2×Q16—791no—
222C2×Q16—791no—
223C2×Q16—791no—
224C2×Q16—791no—
225C2×Q16—1584no—
226C2×SD16—791no—
227C2×SD16—791no—
228C2×SD16—791no—
229C2×M16—791no—
230C22×C8—791no—
231C4⋊Q8—791no—
232C4⋊Q8—1581no—
233#124—21no—
234#124C2×D7911yescharacteristic
235C22⋊Q8—21no—
236C22⋊Q8—791no—
237C22⋊Q8—791no—
238C22⋊Q8—1581no—
239C22⋊Q8—1581no—
240C22⋊Q8C2×D7911yescharacteristic
241#121—21no—
242#121C2×D7911yescharacteristic
243C4×Q8—791no—
244C4×Q8C2×D7911yescharacteristic
245C4×D4—21no—
246C4×D4—1581no—
247C4×D4C2×D7911yescharacteristic
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—791no—
269C2×Q8—1582no—
270C2×Q8—1582no—
271C2×Q8—1581no—
272C2×Q8—1581no—
273C2×Q8C22×D7911yescharacteristic
274C2×Q8C22×D7911yescharacteristic
275C2×D4—21no—
276C2×D4—21no—
277C2×D4C22⋊D7911yescharacteristic
278C2×D4C22×D7911yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—1581no—
282C22×C4—1581no—
283C22×C4C22×D7911yescharacteristic
284C22×C4C22×D7911yescharacteristic
285Q16—3161no—
286Q16—794no—
287Q16—1582no—
288Q16—1582no—
289Q16—1582no—
290Q16—1582no—
291SD16—3161no—
292SD16—1582no—
293SD16—1582no—
294M16—1582no—
295C2×C8—791no—
296C2×C8—791no—
297C2×C8—791no—
298C2×C8—791no—
299C2×C8—1582no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—791no—
303C4⋊C4—1581no—
304C4⋊C4—1581no—
305C4⋊C4—1581no—
306C4⋊C4—1581no—
307C4⋊C4—1581no—
308C4⋊C4C22⋊D7911yescharacteristic
309C4⋊C4C22×D7911yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—21no—
314C22⋊C4—1581no—
315C22⋊C4—1581no—
316C22⋊C4C22⋊D7911yescharacteristic
317C22⋊C4C22⋊D7911yescharacteristic
318C42—21no—
319C42—1581no—
320C42C22×D7911yescharacteristic
321C23—21no—
322C23C2×C22⋊D7911yescharacteristic
323C23C2×C22⋊D7911yescharacteristic
324Q8—21no—
325Q8—21no—
326Q8—21no—
327Q8—42no—
328Q8—3162no—
329Q8—3162no—
330Q8—792no—
331Q8—1581no—
332Q8—1581no—
333Q8—1581no—
334Q8—1581no—
335Q8—1581no—
336Q8D4×D7912yes—
337D4—22no—
338D4—21no—
339D4—21no—
340D4—42no—
341D4—42no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—3162no—
352C2×C4—3162no—
353C2×C4—1581no—
354C2×C4—1581no—
355C2×C4—1581no—
356C2×C4—1581no—
357C2×C4C2×C22⋊D7911yescharacteristic
358C2×C4C2×C22⋊D7911yescharacteristic
359C2×C4C2×C22⋊D7911yescharacteristic
360C2×C4C2×C22⋊D7911yescharacteristic
361C2×C4C23×D7911yescharacteristic
362C8—792no—
363C8—1581no—
364C8—1581no—
365C8—1581no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22#1457919112yescomplemented
375C22C22×C22⋊D7911yescharacteristic
376C4—21no—
377C4—21no—
378C4—22no—
379C4—21no—
380C4—21no—
381C4—41no—
382C4—41no—
383C4—3161no—
384C4—3161no—
385C4—3161no—
386C4—1582no—
387C4C2×D4×D7911yescharacteristic
388C4#1457920611yescharacteristic
389C2—22no—
390C2—41no—
391C2—81no—
392C2D4×C22⋊D7911yescharacteristic
393C2C2×#1457919111yescharacteristic
394C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#548×C79C2
socleC22×C79C22×D4
hypercenter#548D79
hypocenterC79#3270
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#14579191C2semidirect
2. C22×#11929614C2semidirect
3. D4×Dic158C2semidirect
4. #19098958C2semidirect
5. #19098819C2semidirect
6. #19098790C2semidirect
7. #19098782C2semidirect
8. #19098773C2semidirect
9. #19098725C2semidirect
10. #19098719C2semidirect
11. #19098718C2semidirect
12. #19098701C2semidirect
13. #19098668C2semidirect
14. #19098635C2semidirect
77. #11929614D4semidirect
176. C22×C79#137semidirect
198. C79#3270semidirect
374. C22#14579191semidirect