Finite Group Databasebeta

← #23774011

Subgroups — #23774011

Order 10112.

362 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19098959C211yesmaximal, characteristic, complemented
3#19098945C211yesmaximal, characteristic, complemented
4#19098925C211yesmaximal, characteristic, complemented
5#19098922C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098814C211yesmaximal, characteristic
8#19098794C211yesmaximal, characteristic, complemented
9#19098790C211yesmaximal, characteristic, complemented
10#19098673C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12C4×#11929611C211yesmaximal, characteristic, complemented
13C4×#11929612C211yesmaximal, characteristic, complemented
14#19098519C211yesmaximal, characteristic, complemented
15#542×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929608C2211yescharacteristic
21C22×C79⋊C8C2211yescharacteristic
22#14579161C2211yescharacteristic
23#14579156—21no—
24#14579149C2211yescharacteristic
25#14579147—21no—
26#14579143—21no—
27#14579140C2211yescharacteristic
28#14579139—21no—
29#14579135C2211yescharacteristic
30C4×Dic158C2211yescharacteristic
31C4×D316C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579072C2211yescharacteristic
45#14579072C2211yescharacteristic
46C4×C79⋊C8C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#126×C79—21no—
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52#123×C79—21no—
53C22⋊Q8×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58#117×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C4×D79—21no—
64#11929614—22no—
65#11929612—22no—
66#11929611—22no—
67#11929609—22no—
68#11929608—22no—
69C2×C79⋊C8—22no—
70C2×C79⋊C8C2311yescharacteristic
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C4⋊Dic79—21no—
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84C4×Dic79—21no—
85C2×Q8×C79—21no—
86C2×Q8×C79C2311yescharacteristic
87C2×D4×C79—21no—
88C2×D4×C79C2311yescharacteristic
89C22×C4×C79—21no—
90C22×C4×C79C2311yescharacteristic
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79D411yescharacteristic
95C4⋊C4×C79D411yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C42×C79—21no—
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113Q8×C79—81no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—81no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—81no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133D316—21no—
134D316—21no—
135C4×D79—81no—
136Dic158—21no—
137Dic158—21no—
138Dic158—81no—
139C79⋊C8—21no—
140C79⋊C8—21no—
141C79⋊C8#4112yes—
142C79⋊C8#4112yes—
143C22×C79—21no—
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79C22×D411yescharacteristic
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
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×C79C2×#4111yescharacteristic
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79—41no—
167C2×C79—81no—
168C2×C79#53211yescharacteristic
169C2×C79#57711yescharacteristic
170C2×C79#57711yescharacteristic
171D79—81no—
172#3173—791nomaximal, Sylow
173C79#317311yescharacteristic, complemented, Sylow
174#542—791no—
175#542D7911yescharacteristic, complemented
176#498—791no—
177#495—791no—
178#489—791no—
179#489—791no—
180#470—791no—
181#469—791no—
182#465—791no—
183#465—791no—
184#442—791no—
185#441—791no—
186C4×SD16—791no—
187C4×SD16—791no—
188#405—791no—
189C2×Q16—791no—
190C2×SD16—791no—
191C2×SD16—791no—
192C2×D8—791no—
193C2×M16—791no—
194C22×C8—791no—
195C4⋊Q8—791no—
196C4⋊Q8C2×D7911yescharacteristic
197#126—21no—
198#126—1581no—
199#124—21no—
200#124—791no—
201#124—1581no—
202#124C2×D7911yescharacteristic
203#123—21no—
204#123—1581no—
205C22⋊Q8—21no—
206C22⋊Q8—791no—
207C22⋊Q8—1581no—
208C22⋊Q8C2×D7911yescharacteristic
209#121—791no—
210#121C2×D7911yescharacteristic
211C4×Q8—791no—
212C4×Q8C2×D7911yescharacteristic
213C4×D4—791no—
214C4×D4C2×D7911yescharacteristic
215#117C2×D7911yescharacteristic
216#106—791no—
217#106—791no—
218#106—791no—
219#106—791no—
220#103—791no—
221#103—791no—
222#103—791no—
223#103—791no—
224#102—791no—
225#102—791no—
226#102—791no—
227#102—791no—
228#97—791no—
229#97—791no—
230C4×C8—791no—
231C4×C8—791no—
232C2×Q8—21no—
233C2×Q8—791no—
234C2×Q8—1581no—
235C2×Q8C22×D7911yescharacteristic
236C2×D4—21no—
237C2×D4—791no—
238C2×D4—1581no—
239C2×D4C22×D7911yescharacteristic
240C22×C4—21no—
241C22×C4—1581no—
242C22×C4C22×D7911yescharacteristic
243Q16—1582no—
244SD16—1582no—
245SD16—1582no—
246D8—1582no—
247M16—1582no—
248C2×C8—791no—
249C2×C8—791no—
250C2×C8—791no—
251C2×C8—791no—
252C2×C8—1582no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—791no—
257C4⋊C4—791no—
258C4⋊C4—1581no—
259C4⋊C4—1581no—
260C4⋊C4—1581no—
261C4⋊C4C22⋊D7911yescharacteristic
262C4⋊C4C22⋊D7911yescharacteristic
263C4⋊C4C22×D7911yescharacteristic
264C4⋊C4C22×D7911yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4C22⋊D7911yescharacteristic
276C22⋊C4C22⋊D7911yescharacteristic
277C42—21no—
278C42—1581no—
279C42C22×D7911yescharacteristic
280C42C22×D7911yescharacteristic
281C23—21no—
282C23—1581no—
283C23C2×C22⋊D7911yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—81no—
287Q8—6321no—
288Q8—1581no—
289Q8—1581no—
290D4—21no—
291D4—21no—
292D4—81no—
293D4—6321no—
294D4—1581no—
295D4—1581no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—81no—
302C2×C4—6321no—
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×C4C23×D7911yescharacteristic
312C8—792no—
313C8—792no—
314C8—1581no—
315C8—1581no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—3161no—
323C22—3161no—
324C22—3161no—
325C22C22×C22⋊D7911yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4#41×D7911yescharacteristic
338C4#41×D7911yescharacteristic
339C2—41no—
340C2—81no—
341C2—6321no—
342C2#1909910911yescharacteristic
343C2#1909937111yescharacteristic
344C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#542×C79C2
socleC22×C79C22×D4
prime radical#19098814C2
hypercenter#542D79
hypocenterC79#3173
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19098959C2semidirect
3. #19098945C2semidirect
4. #19098925C2semidirect
5. #19098922C2semidirect
6. #19098819C2semidirect
8. #19098794C2semidirect
9. #19098790C2semidirect
10. #19098673C2semidirect
11. #19098668C2semidirect
12. C4×#11929611C2semidirect
13. C4×#11929612C2semidirect
14. #19098519C2semidirect
15. #542×C79C2semidirect
173. C79#3173semidirect
175. #542D79semidirect