Finite Group Databasebeta

← #23776450

Subgroups — #23776450

Order 10112.

362 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099295C211yesmaximal, characteristic
2#19099288C211yesmaximal, characteristic, complemented
3#19098956C211yesmaximal, characteristic, complemented
4#19098934C211yesmaximal, characteristic
5#19098787C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098771C211yesmaximal, characteristic, complemented
8#19098766C211yesmaximal, characteristic, complemented
9#19098765C211yesmaximal, characteristic, complemented
10#19098761C211yesmaximal, characteristic
11#19098691C211yesmaximal, characteristic, complemented
12#19098665C211yesmaximal, characteristic, complemented
13#19098664C211yesmaximal, characteristic, complemented
14Q16×Dic79C211yesmaximal, characteristic, complemented
15#497×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929613C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21#14579159C2211yescharacteristic
22#14579159C2211yescharacteristic
23#14579157C2211yescharacteristic
24#14579152—21no—
25#14579151—21no—
26#14579151—21no—
27#14579150C2211yescharacteristic
28#14579147—21no—
29#14579145—21no—
30#14579143—21no—
31Q8×Dic79C2211yescharacteristic
32Q8×Dic79C2211yescharacteristic
33Q8×Dic79C2211yescharacteristic
34C4×Dic158C2211yescharacteristic
35C4×Dic158C2211yescharacteristic
36#14579126—21no—
37C4×D316C2211yescharacteristic
38D4×Dic79C2211yescharacteristic
39(C22⋊D79)⋊C4—21no—
40#14579095C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43Dic79⋊C8C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579085C2211yescharacteristic
47#14579085C2211yescharacteristic
48#14579083C2211yescharacteristic
49#14579082C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×Q16×C79C2211yescharacteristic
53C2×Q16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55C2×SD16×C79C2211yescharacteristic
56C4⋊Q8×C79C2211yescharacteristic
57#124×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59C2×Dic158D411yescharacteristic
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C2×C4×D79—21no—
66#11929614—41no—
67#11929613—22no—
68#11929612—41no—
69#11929611—41no—
70#11929611—41no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C4⋊Dic79—21no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79D411yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4D411yescharacteristic
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87(C2×D79)⋊C4—21no—
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
90C4×Dic79—21no—
91C4×Dic79—21no—
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C4×Dic79C2311yescharacteristic
96C2×Q8×C79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C2×Q8×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100Q16×C79—22no—
101Q16×C79—41no—
102SD16×C79—22no—
103SD16×C79—41no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79—21no—
107C4⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C22×D79—21no—
113Q8×C79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118Q8×C79—21no—
119D4×C79—21no—
120D4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—42no—
128C22⋊D79—81no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—81no—
133C2×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139C4×D79—81no—
140Dic158—22no—
141Dic158—21no—
142Dic158—21no—
143C8×C79—21no—
144C8×C79#4112yes—
145C79⋊C8—21no—
146C79⋊C8—21no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79C22×D411yescharacteristic
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79H(5,𝔽2)11yescharacteristic
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—41no—
165Dic79—41no—
166Dic79—41no—
167Dic79#13712yes—
168C2×C79—81no—
169C2×C79#55011yescharacteristic
170C2×C79C2×#13711yescharacteristic
171C2×C79#57711yescharacteristic
172D79—81no—
173#3400—791nomaximal, Sylow
174C79#340011yescharacteristic, complemented, Sylow
175#559—791no—
176#557—791no—
177#497—791no—
178#497D7911yescharacteristic, complemented
179#492—791no—
180#464—791no—
181#464—791no—
182#462—791no—
183#461—791no—
184#461—791no—
185#460—791no—
186#446—791no—
187#440—791no—
188#440—791no—
189C4×Q16—791no—
190C2×Q16—791no—
191C2×Q16C2×D7911yescharacteristic
192C2×Q16C2×D7911yescharacteristic
193C2×SD16—791no—
194C2×SD16—791no—
195C2×SD16—791no—
196C2×SD16—791no—
197C2×SD16C2×D7911yescharacteristic
198C2×SD16C2×D7911yescharacteristic
199C4⋊Q8—791no—
200C4⋊Q8—791no—
201C4⋊Q8C2×D7911yescharacteristic
202#127—791no—
203#125—1581no—
204#125—1581no—
205#125—1581no—
206#124—791no—
207#124—1581no—
208#124C2×D7911yescharacteristic
209#123—1581no—
210#123—1581no—
211C4×Q8—791no—
212C4×Q8—791no—
213C4×Q8—791no—
214C4×Q8—791no—
215C4×Q8—791no—
216C4×Q8—1581no—
217C4×D4—791no—
218C4×D4—791no—
219C4×D4—1581no—
220#107—791no—
221C4⋊C8—791no—
222C4⋊C8—791no—
223C4⋊C8—791no—
224#103—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#102—791no—
229#102—791no—
230#97—791no—
231#97C2×D7911yescharacteristic
232C4×C8—791no—
233C2×Q8—791no—
234C2×Q8—791no—
235C2×Q8C22×D7911yescharacteristic
236C2×Q8C22×D7911yescharacteristic
237C2×Q8C22×D7911yescharacteristic
238C2×D4—791no—
239C2×D4—1581no—
240C2×D4—1581no—
241C2×D4C22×D7911yescharacteristic
242C22×C4—1581no—
243C22×C4—1581no—
244Q16—22no—
245Q16—41no—
246Q16—3161no—
247SD16—22no—
248SD16—41no—
249SD16—3161no—
250SD16—3161no—
251SD16—3161no—
252SD16—1582no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C42—791no—
279C42—791no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C42—1581no—
284C42C22×D7911yescharacteristic
285C23—21no—
286C23—1581no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—1582no—
294Q8—1581no—
295Q8—1581no—
296D4—21no—
297D4—21no—
298D4—3162no—
299D4—6321no—
300D4—1581no—
301D4—1581no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—6321no—
310C2×C4—6321no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4D4×D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—21no—
318C8—1581no—
319C8—1581no—
320C8#1192962312yes—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22C2×D4×D7911yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3161no—
334C4—3161no—
335C4—3161no—
336C4—792no—
337C4—1581no—
338C4—1581no—
339C4—1581no—
340C4C2×#1192962311yescharacteristic
341C4#1457920611yescharacteristic
342C2—81no—
343C2—6321no—
344C2#1909923311yescharacteristic
345C2#137×D7911yescharacteristic
346C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#497×C79C2
socleC22×C79C22×D4
prime radical#14579157C22
hypercenter#497D79
hypocenterC79#3400
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
2. #19099288C2semidirect
3. #19098956C2semidirect
5. #19098787C2semidirect
6. #19098782C2semidirect
7. #19098771C2semidirect
8. #19098766C2semidirect
9. #19098765C2semidirect
11. #19098691C2semidirect
12. #19098665C2semidirect
13. #19098664C2semidirect
14. Q16×Dic79C2semidirect
15. #497×C79C2semidirect
174. C79#3400semidirect
178. #497D79semidirect