Finite Group Databasebeta

← #23774906

Subgroups — #23774906

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×#14579191C211yesmaximal, characteristic, complemented
2C22×#11929612C211yesmaximal, characteristic, complemented
3D4×Dic158C211yesmaximal, characteristic, complemented
4#19098958C211yesmaximal, characteristic, complemented
5#19098807C211yesmaximal, characteristic, complemented
6#19098802C211yesmaximal, characteristic, complemented
7#19098782C211yesmaximal, characteristic, complemented
8#19098768C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11#19098714C211yesmaximal, characteristic, complemented
12#19098701C211yesmaximal, characteristic, complemented
13#19098663C211yesmaximal, characteristic, complemented
14#19098635C211yesmaximal, characteristic, complemented
15#546×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic, complemented
18#14579191—24no—
19C2×#11929614C2211yescharacteristic, complemented
20C2×#11929614C2211yescharacteristic, complemented
21C2×#11929614C2211yescharacteristic, complemented
22C2×#11929612—24no—
23C2×#11929612C2211yescharacteristic
24C2×#11929612C2211yescharacteristic
25C2×#11929612C2211yescharacteristic
26C2×#11929612C2211yescharacteristic
27C2×#11929612C2211yescharacteristic
28C2×#11929612C2211yescharacteristic
29C2×#11929608C2211yescharacteristic, complemented
30C22×C79⋊C8C2211yescharacteristic
31#14579161C2211yescharacteristic, complemented
32#14579160—21no—
33#14579140C2211yescharacteristic
34#14579140C2211yescharacteristic, complemented
35#14579138—21no—
36#14579138—21no—
37C4×Dic158C2211yescharacteristic, complemented
38D4×Dic79—21no—
39#14579094C2211yescharacteristic, complemented
40C4⋊(C79⋊C8)C2211yescharacteristic, complemented
41#14579085C2211yescharacteristic, complemented
42#14579084C2211yescharacteristic, complemented
43#14579084C2211yescharacteristic, complemented
44#14579084C2211yescharacteristic, complemented
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C22⋊(C79⋊C8)C2211yescharacteristic, complemented
49#14579072C2211yescharacteristic, complemented
50C2×#41×C79C2211yescharacteristic
51C22×D4×C79C2211yescharacteristic
52#124×C79C2211yescharacteristic
53#123×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79—21no—
56#121×C79C2211yescharacteristic
57#120×C79—21no—
58C4×D4×C79C2211yescharacteristic
59C4×D4×C79C2211yescharacteristic
60C2×C22⋊C4×C79—21no—
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—41no—
75#11929612—22no—
76#11929612—22no—
77#11929612—22no—
78#11929612—22no—
79#11929612—41no—
80#11929612D414yescomplemented
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—
96C24×C79—21no—
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—22no—
101C2×D4×C79—21no—
102C2×D4×C79—21no—
103C2×D4×C79—21no—
104C2×D4×C79—41no—
105C2×D4×C79D411yescharacteristic
106C2×D4×C79C2311yescharacteristic
107C2×D4×C79C2311yescharacteristic
108C22×C4×C79—21no—
109C22×C4×C79—21no—
110C22×C4×C79C2311yescharacteristic
111C22×C4×C79C2311yescharacteristic
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×C79—21no—
120C22⋊C4×C79D411yescharacteristic
121C22⋊C4×C79D411yescharacteristic
122C42×C79C2311yescharacteristic
123C23×C79—21no—
124C23×C79—21no—
125C23×C79—42no—
126C23×C79—42no—
127C23×C79—81no—
128C23×C79C2×D411yescharacteristic
129C23×C79C2×D411yescharacteristic
130Q8×C79—21no—
131Q8×C79—21no—
132D4×C79—22no—
133D4×C79—21no—
134D4×C79—21no—
135D4×C79—21no—
136D4×C79—42no—
137D4×C79—42no—
138D4×C79—81no—
139D4×C79C2×D412yes—
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—42no—
147C2×C4×C79—81no—
148C2×C4×C79C2×D411yescharacteristic
149C2×C4×C79C2×D411yescharacteristic
150C2×C4×C79C2×D411yescharacteristic
151C2×C4×C79C2×D411yescharacteristic
152C2×C4×C79C2411yescharacteristic
153C2×Dic79—21no—
154C2×Dic79—21no—
155C2×Dic79—21no—
156C2×Dic79—21no—
157C2×Dic79—42no—
158C2×Dic79—42no—
159Dic158—21no—
160Dic158—21no—
161Dic158—21no—
162Dic158—21no—
163Dic158—21no—
164Dic158—42no—
165Dic158—42no—
166Dic158C2×D412yes—
167C79⋊C8—21no—
168C79⋊C8—21no—
169C79⋊C8—21no—
170C79⋊C8C2×D412yes—
171C22×C79—21no—
172C22×C79—21no—
173C22×C79—21no—
174C22×C79—22no—
175C22×C79—21no—
176C22×C79—21no—
177C22×C79—41no—
178C22×C79—41no—
179C22×C79—41no—
180C22×C79—41no—
181C22×C79—41no—
182C22×C79—84no—
183C22×C79#13712yescomplemented
184C22×C79C22×D411yescharacteristic
185C4×C79—21no—
186C4×C79—21no—
187C4×C79—21no—
188C4×C79—21no—
189C4×C79—41no—
190C4×C79—41no—
191C4×C79C22×D411yescharacteristic
192C4×C79H(5,𝔽2)11yescharacteristic
193Dic79—22no—
194Dic79—41no—
195Dic79—41no—
196Dic79—41no—
197C2×C79—22no—
198C2×C79—41no—
199C2×C79—42no—
200C2×C79—81no—
201C2×C79D4211yescharacteristic
202C2×C79C2×#13711yescharacteristic
203C2×C79#57711yescharacteristic
204#3266—791nomaximal, Sylow
205C79#326611yescharacteristic, complemented, Sylow
206C2×#137—791no—
207C22×SD16—791no—
208D4×Q8—791no—
209#546D7911yescharacteristic
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×#41C2×D7911yescharacteristic
222C22×Q8—791no—
223C22×Q8—791no—
224C22×D4C2×D7911yescharacteristic
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—791no—
239C4⋊Q8—1581no—
240#124C2×D7911yescharacteristic
241#123—21no—
242C22⋊Q8—791no—
243C22⋊Q8—791no—
244C22⋊Q8—1581no—
245C22⋊Q8—1581no—
246C22⋊Q8C2×D7911yescharacteristic
247#121—21no—
248#121C2×D7911yescharacteristic
249#120—21no—
250C4×Q8—791no—
251C4×D4—1581no—
252C4×D4C2×D7911yescharacteristic
253C4×D4C2×D7911yescharacteristic
254C2×C22⋊C4—21no—
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—21no—
267#41—22no—
268#41—41no—
269C2×Q8—3161no—
270C2×Q8—3161no—
271C2×Q8—791no—
272C2×Q8—791no—
273C2×Q8—791no—
274C2×Q8—1582no—
275C2×Q8—1582no—
276C2×Q8—1581no—
277C2×Q8—1581no—
278C2×Q8C22×D7911yescharacteristic
279C2×D4—22no—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C2×D4C22⋊D7911yescharacteristic
285C2×D4C22×D7911yescharacteristic
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—791no—
310C4⋊C4—1581no—
311C4⋊C4—1581no—
312C4⋊C4—1581no—
313C4⋊C4—1581no—
314C4⋊C4—1581no—
315C4⋊C4C22⋊D7911yescharacteristic
316C4⋊C4C22×D7911yescharacteristic
317C22⋊C4—21no—
318C22⋊C4—21no—
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—1581no—
323C22⋊C4—1581no—
324C22⋊C4C22⋊D7911yescharacteristic
325C22⋊C4C22⋊D7911yescharacteristic
326C42—1581no—
327C42C22×D7911yescharacteristic
328C23—21no—
329C23—21no—
330C23—42no—
331C23—42no—
332C23—81no—
333C23C2×C22⋊D7911yescharacteristic
334C23C2×C22⋊D7911yescharacteristic
335Q8—21no—
336Q8—21no—
337Q8—3162no—
338Q8—3162no—
339Q8—792no—
340Q8—1581no—
341Q8—1581no—
342Q8—1581no—
343Q8—1581no—
344Q8—1581no—
345D4—22no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—42no—
350D4—42no—
351D4—81no—
352D4D4×D7912yes—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—42no—
360C2×C4—81no—
361C2×C4—3162no—
362C2×C4—3162no—
363C2×C4—1581no—
364C2×C4—1581no—
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—22no—
380C22—21no—
381C22—21no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—84no—
388C22#1457919112yescomplemented
389C22C22×C22⋊D7911yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—3161no—
397C4—3161no—
398C4—3161no—
399C4—1582no—
400C4C2×D4×D7911yescharacteristic
401C4#1457920611yescharacteristic
402C2—22no—
403C2—41no—
404C2—42no—
405C2—81no—
406C2D4×C22⋊D7911yescharacteristic
407C2C2×#1457919111yescharacteristic
408C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#546×C79C2
socleC22×C79C22×D4
hypercenter#546D79
hypocenterC79#3266
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14579191C2semidirect
2. C22×#11929612C2semidirect
3. D4×Dic158C2semidirect
4. #19098958C2semidirect
5. #19098807C2semidirect
6. #19098802C2semidirect
7. #19098782C2semidirect
8. #19098768C2semidirect
9. #19098725C2semidirect
10. #19098718C2semidirect
11. #19098714C2semidirect
12. #19098701C2semidirect
13. #19098663C2semidirect
14. #19098635C2semidirect
17. C22×Dic158C22semidirect
19. C2×#11929614C22semidirect
20. C2×#11929614C22semidirect
21. C2×#11929614C22semidirect
29. C2×#11929608C22semidirect
31. #14579161C22semidirect
34. #14579140C22semidirect
37. C4×Dic158C22semidirect
39. #14579094C22semidirect
40. C4⋊(C79⋊C8)C22semidirect
41. #14579085C22semidirect
42. #14579084C22semidirect
43. #14579084C22semidirect
44. #14579084C22semidirect
48. C22⋊(C79⋊C8)C22semidirect
49. #14579072C22semidirect
80. #11929612D4semidirect
183. C22×C79#137semidirect
205. C79#3266semidirect
388. C22#14579191semidirect