Finite Group Databasebeta

← #23776475

Subgroups — #23776475

Order 10112.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099286C211yesmaximal, characteristic, complemented
2#19098958C211yesmaximal, characteristic, complemented
3#19098955C211yesmaximal, characteristic, complemented
4#19098945C211yesmaximal, characteristic
5#19098785C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098778C211yesmaximal, characteristic
8#19098775C211yesmaximal, characteristic
9#19098773C211yesmaximal, characteristic, complemented
10#19098770C211yesmaximal, characteristic, complemented
11#19098694C211yesmaximal, characteristic, complemented
12#19098663C211yesmaximal, characteristic, complemented
13#19098661C211yesmaximal, characteristic, complemented
14C4×#11929614C211yesmaximal, characteristic, complemented
15#556×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929612C2211yescharacteristic
22C2×#11929611C2211yescharacteristic
23C2×#11929611C2211yescharacteristic
24C2×#11929609C2211yescharacteristic
25#14579161C2211yescharacteristic
26#14579156—21no—
27#14579156—21no—
28#14579149C2211yescharacteristic
29#14579149C2211yescharacteristic
30#14579137—21no—
31C4×Dic158C2211yescharacteristic
32C4×Dic158C2211yescharacteristic
33C4×D316C2211yescharacteristic
34#14579119—21no—
35#14579094C2211yescharacteristic
36C4⋊(C79⋊C8)C2211yescharacteristic
37C4⋊(C79⋊C8)C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579084C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579081C2211yescharacteristic
45#14579072C2211yescharacteristic
46#14579072C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#126×C79—21no—
50#126×C79—21no—
51#124×C79C2211yescharacteristic
52#124×C79C2211yescharacteristic
53C22⋊Q8×C79—21no—
54C4×Q8×C79C2211yescharacteristic
55C4×Q8×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58#117×C79—21no—
59C2×Dic158C2311yescharacteristic
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C4×D79—21no—
63#11929614—22no—
64#11929614—41no—
65#11929614—41no—
66#11929614—41no—
67#11929612—22no—
68#11929612—41no—
69#11929611—22no—
70#11929611—41no—
71#11929609—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86C4×Dic79—21no—
87C4×Dic79—21no—
88C2×Q8×C79D411yescharacteristic
89C2×Q8×C79C2311yescharacteristic
90C2×Q8×C79C2311yescharacteristic
91C2×D4×C79C2311yescharacteristic
92C22×C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79D411yescharacteristic
98C4⋊C4×C79D411yescharacteristic
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C42×C79—21no—
107C42×C79—21no—
108C42×C79C2311yescharacteristic
109C42×C79C2311yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C22×D79—21no—
113Q8×C79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—41no—
118D4×C79—21no—
119D4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—42no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2411yescharacteristic
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134D316—21no—
135D316—21no—
136C4×D79—42no—
137Dic158—21no—
138Dic158—21no—
139Dic158—21no—
140Dic158—21no—
141C79⋊C8—21no—
142C79⋊C8—21no—
143C79⋊C8—21no—
144C79⋊C8#4112yes—
145C22×C79—41no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79C22×D411yescharacteristic
149C2×D79—41no—
150C2×D79—41no—
151C2×D79—41no—
152C4×C79—21no—
153C4×C79—21no—
154C4×C79—21no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79C2×#4111yescharacteristic
162C4×C79H(5,𝔽2)11yescharacteristic
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79—81no—
167C2×C79#55011yescharacteristic
168C2×C79#57511yescharacteristic
169C2×C79#57811yescharacteristic
170D79—81no—
171#3402—791nomaximal, Sylow
172C79#340211yescharacteristic, complemented, Sylow
173#556—791no—
174#556D7911yescharacteristic, complemented
175#497—791no—
176#497—791no—
177#495—791no—
178#464—791no—
179#464—791no—
180#463—791no—
181#463—791no—
182#462—791no—
183#462—791no—
184#446—791no—
185#440—791no—
186#440—791no—
187C4×Q16—791no—
188C2×Q16—791no—
189C2×Q16—791no—
190C2×Q16—791no—
191C2×Q16—791no—
192C2×SD16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×SD16—791no—
196C2×D8—791no—
197C4⋊Q8—791no—
198C4⋊Q8C2×D7911yescharacteristic
199#126—21no—
200#126—21no—
201#126—1581no—
202#126—1581no—
203#124—791no—
204#124—791no—
205#124C2×D7911yescharacteristic
206#124C2×D7911yescharacteristic
207C22⋊Q8—21no—
208C22⋊Q8—1581no—
209C4×Q8—791no—
210C4×Q8—791no—
211C4×Q8C2×D7911yescharacteristic
212C4×Q8C2×D7911yescharacteristic
213C4×Q8C2×D7911yescharacteristic
214C4×D4—791no—
215C4×D4C2×D7911yescharacteristic
216#117—21no—
217#117—1581no—
218#107—791no—
219C4⋊C8—791no—
220C4⋊C8—791no—
221C4⋊C8—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#102—791no—
227#102—791no—
228#97—791no—
229#97—791no—
230C4×C8—791no—
231C2×Q8—791no—
232C2×Q8—791no—
233C2×Q8C22⋊D7911yescharacteristic
234C2×Q8C22×D7911yescharacteristic
235C2×Q8C22×D7911yescharacteristic
236C2×D4—791no—
237C2×D4C22×D7911yescharacteristic
238C22×C4—21no—
239C22×C4—1581no—
240Q16—3161no—
241Q16—3161no—
242Q16—3161no—
243Q16—1582no—
244SD16—3161no—
245SD16—3161no—
246SD16—1582no—
247SD16—1582no—
248D8—3161no—
249C2×C8—791no—
250C2×C8—791no—
251C2×C8—791no—
252C2×C8—791no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—791no—
258C4⋊C4—1581no—
259C4⋊C4—1581no—
260C4⋊C4—1581no—
261C4⋊C4—1581no—
262C4⋊C4C22⋊D7911yescharacteristic
263C4⋊C4C22⋊D7911yescharacteristic
264C4⋊C4C22⋊D7911yescharacteristic
265C4⋊C4C22×D7911yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C42—21no—
277C42—21no—
278C42—1581no—
279C42—1581no—
280C42C22×D7911yescharacteristic
281C42C22×D7911yescharacteristic
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—1581no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—41no—
290Q8—1581no—
291Q8—1581no—
292Q8—1581no—
293Q8—1581no—
294D4—21no—
295D4—21no—
296D4—1581no—
297D4—1581no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—3162no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4C2×C22⋊D7911yescharacteristic
307C2×C4C2×C22⋊D7911yescharacteristic
308C2×C4C2×C22⋊D7911yescharacteristic
309C2×C4C2×C22⋊D7911yescharacteristic
310C2×C4C2×C22⋊D7911yescharacteristic
311C2×C4C2×C22⋊D7911yescharacteristic
312C2×C4C23×D7911yescharacteristic
313C8—792no—
314C8—1581no—
315C8—1581no—
316C8—1581no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—3161no—
321C22—3161no—
322C22—3161no—
323C22C22×C22⋊D7911yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—3161no—
334C4—3161no—
335C4—3161no—
336C4#41×D7911yescharacteristic
337C4#1457920711yescharacteristic
338C2—81no—
339C2—6321no—
340C2#1909923211yescharacteristic
341C2#1909936111yescharacteristic
342C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#556×C79C2
socleC22×C79C22×D4
prime radicalC2×#11929609C22
hypercenter#556D79
hypocenterC79#3402
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #19099286C2semidirect
2. #19098958C2semidirect
3. #19098955C2semidirect
5. #19098785C2semidirect
6. #19098782C2semidirect
9. #19098773C2semidirect
10. #19098770C2semidirect
11. #19098694C2semidirect
12. #19098663C2semidirect
13. #19098661C2semidirect
14. C4×#11929614C2semidirect
15. #556×C79C2semidirect
172. C79#3402semidirect
174. #556D79semidirect