Finite Group Databasebeta

← #23775879

Subgroups — #23775879

Order 10112.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099259C211yesmaximal, characteristic
2#19098969C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098896C211yesmaximal, characteristic, complemented
5#19098881C211yesmaximal, characteristic, complemented
6#19098876C211yesmaximal, characteristic, complemented
7#19098870C211yesmaximal, characteristic, complemented
8#19098840C211yesmaximal, characteristic, complemented
9#19098811C211yesmaximal, characteristic, complemented
10#19098794C211yesmaximal, characteristic, complemented
11#19098661C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098603C211yesmaximal, characteristic, complemented
14C2×#14579094C211yesmaximal, characteristic, complemented
15#554×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929608C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19#14579156—21no—
20#14579153C2211yescharacteristic
21#14579143—21no—
22#14579135C2211yescharacteristic
23#14579135C2211yescharacteristic
24#14579133—21no—
25C4×D316C2211yescharacteristic
26(C22⋊D79)⋊C4—21no—
27#14579120C2211yescharacteristic
28C2×C4⋊Dic79C2211yescharacteristic
29#14579094C2211yescharacteristic
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579094C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579092C2211yescharacteristic
37#14579092C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#125×C79—21no—
50C22⋊Q8×C79—21no—
51C22⋊Q8×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79—21no—
56C4×D4×C79C2211yescharacteristic
57C2×C4⋊C4×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C22×Dic79—21no—
63C2×C4×D79—21no—
64#11929611—22no—
65#11929608—22no—
66C2×C79⋊C8—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C4⋊Dic79—21no—
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77C22⋊Dic79—21no—
78(C2×D79)⋊C4—21no—
79(C2×D79)⋊C4—21no—
80(C2×D79)⋊C4—21no—
81C4×Dic79—21no—
82C2×Q8×C79—21no—
83C2×Q8×C79C2311yescharacteristic
84C2×D4×C79D411yescharacteristic
85C22×C4×C79—21no—
86C22×C4×C79—21no—
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C4⋊C4×C79—21no—
90C4⋊C4×C79—21no—
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79D411yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C4⋊C4×C79C2311yescharacteristic
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79D411yescharacteristic
102C22⋊C4×C79D411yescharacteristic
103C42×C79—21no—
104C42×C79C2311yescharacteristic
105C23×C79C2×D411yescharacteristic
106C23×C79C2×D411yescharacteristic
107C22×D79—21no—
108Q8×C79—21no—
109Q8×C79—21no—
110Q8×C79—81no—
111D4×C79—22no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—81no—
121C2×C4×C79—81no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2×D411yescharacteristic
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—
133D316—21no—
134D316—21no—
135C4×D79—81no—
136C79⋊C8—21no—
137C79⋊C8—21no—
138C79⋊C8—21no—
139C79⋊C8#4112yes—
140C22×C79—21no—
141C22×C79—21no—
142C22×C79—21no—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79#13712yes—
146C22×C79C22×D411yescharacteristic
147C2×D79—41no—
148C2×D79—41no—
149C2×D79—41no—
150C4×C79—21no—
151C4×C79—21no—
152C4×C79—21no—
153C4×C79—21no—
154C4×C79—41no—
155C4×C79—41no—
156C4×C79—41no—
157C4×C79—41no—
158C4×C79C2×#4111yescharacteristic
159C4×C792−1+411yescharacteristic
160Dic79—41no—
161Dic79—41no—
162Dic79—41no—
163C2×C79—22no—
164C2×C79—41no—
165C2×C79#54711yescharacteristic
166C2×C79C2×#13711yescharacteristic
167C2×C79#57611yescharacteristic
168D79—81no—
169#3346—791nomaximal, Sylow
170C79#334611yescharacteristic, complemented, Sylow
171#554D7911yescharacteristic, complemented
172#553—791no—
173#501—791no—
174#485—791no—
175#484—791no—
176#481—791no—
177#480—791no—
178#479—791no—
179#474—791no—
180#468—791no—
181#465—791no—
182#440—791no—
183#435—791no—
184#428—791no—
185C2×#107—791no—
186C2×SD16—791no—
187C2×M16—791no—
188C22×C8—791no—
189C4⋊Q8C2×D7911yescharacteristic
190#126—1581no—
191#125—21no—
192#125—791no—
193#123—1581no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C22⋊Q8C2×D7911yescharacteristic
197C22⋊Q8C2×D7911yescharacteristic
198#121—791no—
199#121—791no—
200#121—1581no—
201C4×Q8C2×D7911yescharacteristic
202C4×D4—21no—
203C4×D4—791no—
204C4×D4—1581no—
205C4×D4C2×D7911yescharacteristic
206#117—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4C2×D7911yescharacteristic
209C2×C4⋊C4C2×D7911yescharacteristic
210#107—791no—
211#107—791no—
212#107—791no—
213#107—791no—
214#107—791no—
215#107—791no—
216#106—791no—
217#106—791no—
218#106—791no—
219C4⋊C8—791no—
220#103—791no—
221#103—791no—
222#103—791no—
223#102—791no—
224#102—791no—
225#102—791no—
226C22⋊C8—791no—
227C22⋊C8—791no—
228#97—791no—
229C2×Q8—21no—
230C2×Q8C22×D7911yescharacteristic
231C2×D4—791no—
232C2×D4—1581no—
233C2×D4—1581no—
234C2×D4C22⋊D7911yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—1581no—
238C22×C4—1581no—
239C22×C4C22×D7911yescharacteristic
240C22×C4C22×D7911yescharacteristic
241SD16—1582no—
242M16—1582no—
243C2×C8—791no—
244C2×C8—791no—
245C2×C8—791no—
246C2×C8—791no—
247C2×C8—1582no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—791no—
255C4⋊C4—791no—
256C4⋊C4—791no—
257C4⋊C4—1581no—
258C4⋊C4—1581no—
259C4⋊C4—1581no—
260C4⋊C4C22⋊D7911yescharacteristic
261C4⋊C4C22×D7911yescharacteristic
262C4⋊C4C22×D7911yescharacteristic
263C4⋊C4C22×D7911yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—1581no—
267C22⋊C4—1581no—
268C22⋊C4—1581no—
269C22⋊C4—1581no—
270C22⋊C4C22⋊D7911yescharacteristic
271C22⋊C4C22⋊D7911yescharacteristic
272C42—21no—
273C42—1581no—
274C42C22×D7911yescharacteristic
275C23—1581no—
276C23C2×C22⋊D7911yescharacteristic
277C23C2×C22⋊D7911yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—3162no—
283D4—6321no—
284D4—1581no—
285D4—1581no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—6321no—
297C2×C4—6321no—
298C2×C4—1581no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4C2×C22⋊D7911yescharacteristic
302C2×C4C2×C22⋊D7911yescharacteristic
303C2×C4C2×C22⋊D7911yescharacteristic
304C2×C4C2×C22⋊D7911yescharacteristic
305C2×C4C23×D7911yescharacteristic
306C8—792no—
307C8—1581no—
308C8—1581no—
309C8—1581no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—3161no—
316C22—3161no—
317C22—3161no—
318C22#1457919212yes—
319C22C22×C22⋊D7911yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—3161no—
329C4—3161no—
330C4—3161no—
331C4#41×D7911yescharacteristic
332C4#1457920811yescharacteristic
333C2—22no—
334C2—41no—
335C2—6321no—
336C2#1909921211yescharacteristic
337C2C2×#1457919211yescharacteristic
338C2#1909936611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#554×C79C2
socleC22×C79C22×D4
prime radical#19099259C2
hypercenter#554D79
hypocenterC79#3346
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #19098969C2semidirect
3. #19098901C2semidirect
4. #19098896C2semidirect
5. #19098881C2semidirect
6. #19098876C2semidirect
7. #19098870C2semidirect
8. #19098840C2semidirect
9. #19098811C2semidirect
10. #19098794C2semidirect
11. #19098661C2semidirect
12. #19098635C2semidirect
13. #19098603C2semidirect
14. C2×#14579094C2semidirect
15. #554×C79C2semidirect
170. C79#3346semidirect
171. #554D79semidirect