Finite Group Databasebeta

← #23775565

Subgroups — #23775565

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×Dic158C211yesmaximal, characteristic, complemented
2#19098933C211yesmaximal, characteristic, complemented
3#19098904C211yesmaximal, characteristic, complemented
4#19098898C211yesmaximal, characteristic, complemented
5#19098867C211yesmaximal, characteristic, complemented
6#19098807C211yesmaximal, characteristic, complemented
7#19098790C211yesmaximal, characteristic, complemented
8#19098768C211yesmaximal, characteristic, complemented
9#19098701C211yesmaximal, characteristic, complemented
10#19098701C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098571C211yesmaximal, characteristic, complemented
14C2×#14579084C211yesmaximal, characteristic, complemented
15#553×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929612C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579161C2211yescharacteristic
24#14579160—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27#14579138—21no—
28#14579138—21no—
29C4×Dic158C2211yescharacteristic
30D4×Dic79—21no—
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579084C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579084C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579082C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79C2211yescharacteristic
50#123×C79—21no—
51#121×C79—21no—
52#121×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×D4×C79—21no—
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59C2×Dic158—22no—
60C2×Dic158—22no—
61C2×Dic158—21no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158—41no—
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67C2×Dic158C2311yescharacteristic
68C22×Dic79—21no—
69C22×Dic79—21no—
70#11929612—22no—
71#11929612—41no—
72#11929612—41no—
73#11929608—41no—
74C2×C79⋊C8—41no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C4⋊Dic79—21no—
80C4⋊Dic79—21no—
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C4×Dic79—21no—
88C2×D4×C79—21no—
89C2×D4×C79—21no—
90C2×D4×C79D411yescharacteristic
91C2×D4×C79C2311yescharacteristic
92C22×C4×C79—21no—
93C22×C4×C79—21no—
94C22×C4×C79C2311yescharacteristic
95C22×C4×C79C2311yescharacteristic
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114D4×C79—22no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—42no—
118D4×C79—81no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—81no—
127C2×C4×C79—81no—
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2×D411yescharacteristic
130C2×C4×C79C2×D411yescharacteristic
131C2×C4×C79C2×D411yescharacteristic
132C2×C4×C79C2411yescharacteristic
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—42no—
138C2×Dic79—42no—
139Dic158—21no—
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—21no—
144Dic158—42no—
145Dic158—42no—
146Dic158#4112yes—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79#13712yes—
160C22×C79C22×D411yescharacteristic
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—21no—
164C4×C79—21no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79—41no—
168C4×C79C2×#4111yescharacteristic
169C4×C79H(5,𝔽2)11yescharacteristic
170Dic79—22no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79—41no—
176C2×C79—81no—
177C2×C79#54611yescharacteristic
178C2×C79C2×#13711yescharacteristic
179C2×C79#57711yescharacteristic
180#3320—791nomaximal, Sylow
181C79#332011yescharacteristic, complemented, Sylow
182#553D7911yescharacteristic
183D4×Q8—791no—
184#491—791no—
185#485—791no—
186#484—791no—
187#479—791no—
188#468—791no—
189#465—791no—
190#461—791no—
191#448—791no—
192#448—791no—
193#440—791no—
194#435—791no—
195#419—791no—
196C2×#103—791no—
197C22×Q8—791no—
198C22×Q8—791no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×SD16—791no—
202C2×M16—791no—
203C22×C8—791no—
204C4⋊Q8—791no—
205C4⋊Q8—1581no—
206#126—21no—
207#125C2×D7911yescharacteristic
208#123—21no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212C22⋊Q8—1581no—
213#121—21no—
214#121C2×D7911yescharacteristic
215#121C2×D7911yescharacteristic
216C4×Q8—791no—
217C4×D4—21no—
218C4×D4—1581no—
219C4×D4C2×D7911yescharacteristic
220C4×D4C2×D7911yescharacteristic
221#117C2×D7911yescharacteristic
222C2×C4⋊C4C2×D7911yescharacteristic
223#107—791no—
224#107—791no—
225#106—791no—
226C4⋊C8—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#102—791no—
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240C2×Q8—3161no—
241C2×Q8—3161no—
242C2×Q8—791no—
243C2×Q8—791no—
244C2×Q8—791no—
245C2×Q8—1582no—
246C2×Q8—1582no—
247C2×Q8—1581no—
248C2×Q8—1581no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4C22⋊D7911yescharacteristic
252C2×D4C22×D7911yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258C22×C4C22×D7911yescharacteristic
259SD16—3161no—
260SD16—3161no—
261SD16—1582no—
262M16—3161no—
263C2×C8—3161no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8—791no—
267C2×C8—791no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—791no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22⋊D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C4⋊C4C22×D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4C22⋊D7911yescharacteristic
288C22⋊C4C22⋊D7911yescharacteristic
289C42—21no—
290C42—1581no—
291C42C22×D7911yescharacteristic
292C23—21no—
293C23C2×C22⋊D7911yescharacteristic
294C23C2×C22⋊D7911yescharacteristic
295Q8—3162no—
296Q8—3162no—
297Q8—792no—
298Q8—1581no—
299Q8—1581no—
300Q8—1581no—
301Q8—1581no—
302Q8—1581no—
303D4—22no—
304D4—21no—
305D4—21no—
306D4—42no—
307D4—81no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—3162no—
318C2×C4—3162no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4C2×C22⋊D7911yescharacteristic
324C2×C4C2×C22⋊D7911yescharacteristic
325C2×C4C2×C22⋊D7911yescharacteristic
326C2×C4C2×C22⋊D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—1581no—
329C8—1581no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22#1457919112yes—
341C22C22×C22⋊D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3161no—
350C4—3161no—
351C4—3161no—
352C4—1582no—
353C4#41×D7911yescharacteristic
354C4#1457920711yescharacteristic
355C2—22no—
356C2—41no—
357C2—81no—
358C2#1909920111yescharacteristic
359C2C2×#1457919111yescharacteristic
360C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#553×C79C2
socleC22×C79C22×D4
hypercenter#553D79
hypocenterC79#3320
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. D4×Dic158C2semidirect
2. #19098933C2semidirect
3. #19098904C2semidirect
4. #19098898C2semidirect
5. #19098867C2semidirect
6. #19098807C2semidirect
7. #19098790C2semidirect
8. #19098768C2semidirect
9. #19098701C2semidirect
10. #19098701C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098571C2semidirect
14. C2×#14579084C2semidirect
181. C79#3320semidirect