Finite Group Databasebeta

← #23773418

Subgroups — #23773418

Order 10112.

396 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099097C211yesmaximal, characteristic, complemented
2#19098904C211yesmaximal, characteristic, complemented
3#19098887C211yesmaximal, characteristic, complemented
4#19098870C211yesmaximal, characteristic, complemented
5#19098863C211yesmaximal, characteristic, complemented
6#19098785C211yesmaximal, characteristic, complemented
7#19098778C211yesmaximal, characteristic, complemented
8#19098725C211yesmaximal, characteristic, complemented
9#19098708C211yesmaximal, characteristic
10C4×#11929614C211yesmaximal, characteristic, complemented
11C4×#11929611C211yesmaximal, characteristic, complemented
12C4×#11929612C211yesmaximal, characteristic, complemented
13C4×#11929609C211yesmaximal, characteristic, complemented
14#19098616C211yesmaximal, characteristic, complemented
15C4×#41×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929611C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20#14579155—21no—
21#14579153C2211yescharacteristic
22#14579149C2211yescharacteristic
23#14579144—21no—
24#14579140C2211yescharacteristic
25#14579135C2211yescharacteristic
26C4×Dic158C2211yescharacteristic
27C4×D316C2211yescharacteristic
28C4×C22⋊D79—21no—
29#14579118—21no—
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35C4⋊(C79⋊C8)C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C4×C79⋊C8C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C4×Q8×C79C2211yescharacteristic
50C4×Q8×C79C2211yescharacteristic
51C4×D4×C79—21no—
52C4×D4×C79—21no—
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55#117×C79—21no—
56#117×C79C2211yescharacteristic
57C2×C42×C79—21no—
58C2×C42×C79C2211yescharacteristic
59C2×Dic158C2311yescharacteristic
60C2×D316C2311yescharacteristic
61C2×C22⋊D79—21no—
62C2×C4×D79—21no—
63#11929614—22no—
64#11929612—22no—
65#11929611—22no—
66#11929609—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C4⋊Dic79C2311yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73Dic79⋊C4—21no—
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77C22⋊Dic79—21no—
78(C2×D79)⋊C4—21no—
79(C2×D79)⋊C4—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82C4×Dic79—21no—
83#41×C79—22no—
84#41×C79—22no—
85C2×Q8×C79C2311yescharacteristic
86C2×D4×C79—21no—
87C2×D4×C79C2311yescharacteristic
88C22×C4×C79—21no—
89C22×C4×C79—21no—
90C22×C4×C79—21no—
91C22×C4×C79D411yescharacteristic
92C22×C4×C79D411yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C42×C79—21no—
102C42×C79—21no—
103C42×C79—21no—
104C42×C79D411yescharacteristic
105C42×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79#4112yes—
113D4×C79—24no—
114D4×C79—21no—
115D4×C79#4112yes—
116C2×C4×C79—24no—
117C2×C4×C79—21no—
118C2×C4×C79—22no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—41no—
124C2×C4×C79—42no—
125C2×C4×C79—42no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2411yescharacteristic
132C22⋊D79—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136D316—21no—
137D316—21no—
138C4×D79—42no—
139Dic158—21no—
140Dic158—21no—
141C79⋊C8—21no—
142C79⋊C8—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—22no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79C22×D411yescharacteristic
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—21no—
156C4×C79—22no—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79#13512yes—
163C4×C79C2×#4111yescharacteristic
164C4×C79C2×#4111yescharacteristic
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79—42no—
170C2×C79#52511yescharacteristic
171C2×C79C2×#13511yescharacteristic
172C2×C79#57511yescharacteristic
173D79—81no—
174#3102—791nomaximal, Sylow
175C79#310211yescharacteristic, complemented, Sylow
176#529—791no—
177C4×#41D7911yescharacteristic, complemented
178#485—791no—
179#482—791no—
180#479—791no—
181#478—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186C4×Q16—791no—
187C4×SD16—791no—
188C4×SD16—791no—
189C4×D8—791no—
190#431—791no—
191C2×#41C2×D7911yescharacteristic
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8—791no—
196#126—1581no—
197#125—791no—
198#124—791no—
199#123—1581no—
200C22⋊Q8—791no—
201#121—791no—
202C4×Q8—791no—
203C4×Q8C2×D7911yescharacteristic
204C4×Q8C2×D7911yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4—791no—
208C4×D4—1581no—
209C4×D4C2×D7911yescharacteristic
210C4×D4C2×D7911yescharacteristic
211#117—21no—
212#117—1581no—
213#117C2×D7911yescharacteristic
214C2×C42—21no—
215C2×C42C2×D7911yescharacteristic
216#107—791no—
217#107—791no—
218#106—791no—
219#106—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#102—791no—
229#102—791no—
230C22⋊C8—791no—
231C22⋊C8—791no—
232C4×C8—791no—
233C4×C8—791no—
234#41—22no—
235#41—22no—
236C2×Q8—791no—
237C2×Q8C22×D7911yescharacteristic
238C2×D4—21no—
239C2×D4—791no—
240C2×D4—1581no—
241C2×D4C22×D7911yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—1581no—
246C22×C4C22⋊D7911yescharacteristic
247C22×C4C22⋊D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249Q16—1582no—
250SD16—1582no—
251SD16—1582no—
252D8—1582no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8—791no—
256C2×C8—791no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—1581no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4C22×D7911yescharacteristic
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—1581no—
271C22⋊C4—1581no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—1581no—
279C42C22⋊D7911yescharacteristic
280C42C22⋊D7911yescharacteristic
281C42C22×D7911yescharacteristic
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—1581no—
285C23C2×C22⋊D7911yescharacteristic
286Q8—21no—
287Q8—1581no—
288Q8—1581no—
289Q8#1192962412yes—
290D4—24no—
291D4—21no—
292D4—3162no—
293D4—1581no—
294D4—1581no—
295D4#1192962412yes—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—3162no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4C2×C22⋊D7911yescharacteristic
311C2×C4C2×C22⋊D7911yescharacteristic
312C2×C4C2×C22⋊D7911yescharacteristic
313C2×C4C2×C22⋊D7911yescharacteristic
314C2×C4C2×C22⋊D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—1581no—
317C8—1581no—
318C8—1581no—
319C8—1581no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22C22×C22⋊D7911yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—3161no—
338C4—3161no—
339C4—3161no—
340C4#1457918112yes—
341C4C2×#1192962411yescharacteristic
342C4C2×#1192962411yescharacteristic
343C2—41no—
344C2—42no—
345C2—6321no—
346C2#1909907411yescharacteristic
347C2C2×#1457918111yescharacteristic
348C2#1909936111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC4×#41×C79C2
socleC22×C79C22×D4
prime radical#19098708C2
hypercenterC4×#41D79
hypocenterC79#3102
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
1. #19099097C2semidirect
2. #19098904C2semidirect
3. #19098887C2semidirect
4. #19098870C2semidirect
5. #19098863C2semidirect
6. #19098785C2semidirect
7. #19098778C2semidirect
8. #19098725C2semidirect
10. C4×#11929614C2semidirect
11. C4×#11929611C2semidirect
12. C4×#11929612C2semidirect
13. C4×#11929609C2semidirect
14. #19098616C2semidirect
15. C4×#41×C79C2semidirect
175. C79#3102semidirect
177. C4×#41D79semidirect