Finite Group Databasebeta

← #23774509

Subgroups — #23774509

Order 10112.

376 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099184C211yesmaximal, characteristic, complemented
2#19098955C211yesmaximal, characteristic, complemented
3#19098945C211yesmaximal, characteristic, complemented
4#19098922C211yesmaximal, characteristic, complemented
5#19098913C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098770C211yesmaximal, characteristic, complemented
9#19098765C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098719C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic
13#19098702C211yesmaximal, characteristic, complemented
14#19098624C211yesmaximal, characteristic, complemented
15#536×C79C211yesmaximal, characteristic, complemented
16C2×#11929614C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21C2×#11929611C2211yescharacteristic
22C2×#11929611C2211yescharacteristic
23C2×#11929609C2211yescharacteristic
24#14579161C2211yescharacteristic
25#14579156—21no—
26#14579149C2211yescharacteristic
27#14579147—21no—
28#14579143—21no—
29#14579140C2211yescharacteristic
30#14579139—21no—
31#14579135C2211yescharacteristic
32C4×Dic158C2211yescharacteristic
33C4×D316C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35C4⋊(C79⋊C8)C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579085C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46#14579072C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50C4⋊Q8×C79C2211yescharacteristic
51C4⋊Q8×C79C2211yescharacteristic
52#124×C79C2211yescharacteristic
53#124×C79C2211yescharacteristic
54#123×C79—21no—
55#123×C79—21no—
56C22⋊Q8×C79—21no—
57C22⋊Q8×C79—21no—
58#117×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C2×D316C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C4×D79—21no—
64#11929614—41no—
65#11929614—41no—
66#11929614—41no—
67#11929612—41no—
68#11929611—41no—
69#11929611—41no—
70#11929611—41no—
71#11929609—41no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81C22⋊Dic79—21no—
82(C2×D79)⋊C4—21no—
83(C2×D79)⋊C4—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86C4×Dic79—21no—
87#41×C79—41no—
88#41×C79—41no—
89C2×Q8×C79—21no—
90C2×Q8×C79—41no—
91C2×Q8×C79—41no—
92C2×Q8×C79C2311yescharacteristic
93C2×Q8×C79C2311yescharacteristic
94C2×Q8×C79C2311yescharacteristic
95C2×D4×C79—21no—
96C2×D4×C79C2311yescharacteristic
97C22×C4×C79—21no—
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79—21no—
103C4⋊C4×C79—21no—
104C4⋊C4×C79D411yescharacteristic
105C4⋊C4×C79D411yescharacteristic
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C22⋊C4×C79D411yescharacteristic
111C22⋊C4×C79D411yescharacteristic
112C42×C79C2311yescharacteristic
113C42×C79C2311yescharacteristic
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C22×D79—21no—
117Q8×C79—21no—
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122Q8×C79—21no—
123Q8×C79—42no—
124D4×C79—21no—
125D4×C79—21no—
126D4×C79—42no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—42no—
133C2×C4×C79—42no—
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2×D411yescharacteristic
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2411yescharacteristic
140C22⋊D79—81no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144D316—21no—
145D316—21no—
146C4×D79—81no—
147Dic158—21no—
148Dic158—21no—
149Dic158—81no—
150C79⋊C8—21no—
151C79⋊C8—21no—
152C79⋊C8—21no—
153C79⋊C8—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—21no—
157C22×C79—41no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79C22×D411yescharacteristic
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C4×C79—21no—
165C4×C79—21no—
166C4×C79—21no—
167C4×C79—21no—
168C4×C79—21no—
169C4×C79—41no—
170C4×C79—41no—
171C4×C79—41no—
172C4×C79H(5,𝔽2)11yescharacteristic
173C4×C79H(5,𝔽2)11yescharacteristic
174Dic79—41no—
175Dic79—41no—
176Dic79—41no—
177C2×C79—41no—
178C2×C79—81no—
179C2×C79#53511yescharacteristic
180C2×C79#57711yescharacteristic
181C2×C79#57811yescharacteristic
182D79—81no—
183#3225—791nomaximal, Sylow
184C79#322511yescharacteristic, complemented, Sylow
185#542—791no—
186#536D7911yescharacteristic, complemented
187#497—791no—
188#495—791no—
189#489—791no—
190#487—791no—
191#464—791no—
192#463—791no—
193#462—791no—
194#461—791no—
195#452—791no—
196#451—791no—
197#449—791no—
198#448—791no—
199#433—791no—
200C2×#41C2×D7911yescharacteristic
201C22×Q8C2×D7911yescharacteristic
202C2×Q16—791no—
203C2×Q16—791no—
204C2×Q16—791no—
205C2×SD16—791no—
206C2×SD16—791no—
207C2×SD16—791no—
208C2×SD16—791no—
209C2×D8—791no—
210C4⋊Q8—791no—
211C4⋊Q8C2×D7911yescharacteristic
212C4⋊Q8C2×D7911yescharacteristic
213#126—1581no—
214#124—791no—
215#124—1581no—
216#124C2×D7911yescharacteristic
217#124C2×D7911yescharacteristic
218#123—21no—
219#123—21no—
220#123—1581no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—791no—
224C22⋊Q8—1581no—
225#121—791no—
226C4×Q8—791no—
227C4×D4—791no—
228#117C2×D7911yescharacteristic
229C4⋊C8—791no—
230C4⋊C8—791no—
231#103—791no—
232#103—791no—
233#103—791no—
234#103—791no—
235#103—791no—
236#103—791no—
237#102—791no—
238#102—791no—
239C22⋊C8—791no—
240C22⋊C8—791no—
241#97—791no—
242C4×C8—791no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—791no—
249C2×Q8—1581no—
250C2×Q8C22×D7911yescharacteristic
251C2×Q8C22×D7911yescharacteristic
252C2×Q8C22×D7911yescharacteristic
253C2×D4—21no—
254C2×D4—791no—
255C2×D4—1581no—
256C2×D4C22×D7911yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—1581no—
260C22×C4C22×D7911yescharacteristic
261Q16—3161no—
262Q16—3161no—
263Q16—3161no—
264SD16—3161no—
265SD16—3161no—
266SD16—3161no—
267SD16—3161no—
268D8—3161no—
269C2×C8—791no—
270C2×C8—791no—
271C2×C8—791no—
272C2×C8—791no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—791no—
278C4⋊C4—791no—
279C4⋊C4—1581no—
280C4⋊C4—1581no—
281C4⋊C4—1581no—
282C4⋊C4C22⋊D7911yescharacteristic
283C4⋊C4C22⋊D7911yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—1581no—
289C22⋊C4—1581no—
290C22⋊C4—1581no—
291C22⋊C4—1581no—
292C22⋊C4—1581no—
293C22⋊C4C22⋊D7911yescharacteristic
294C22⋊C4C22⋊D7911yescharacteristic
295C42—1581no—
296C42C22×D7911yescharacteristic
297C42C22×D7911yescharacteristic
298C23—21no—
299C23—1581no—
300C23C2×C22⋊D7911yescharacteristic
301Q8—21no—
302Q8—21no—
303Q8—21no—
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—6321no—
309Q8—1581no—
310Q8—1581no—
311D4—21no—
312D4—21no—
313D4—42no—
314D4—6321no—
315D4—1581no—
316D4—1581no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—6321no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4C2×C22⋊D7911yescharacteristic
329C2×C4C2×C22⋊D7911yescharacteristic
330C2×C4C2×C22⋊D7911yescharacteristic
331C2×C4C2×C22⋊D7911yescharacteristic
332C2×C4C2×C22⋊D7911yescharacteristic
333C2×C4C23×D7911yescharacteristic
334C8—1581no—
335C8—1581no—
336C8—1581no—
337C8—1581no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22C22×C22⋊D7911yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—3161no—
357C4—3161no—
358C4—3161no—
359C4#1457920611yescharacteristic
360C4#1457920611yescharacteristic
361C2—41no—
362C2—81no—
363C2—6321no—
364C2#1909913011yescharacteristic
365C2#1909937111yescharacteristic
366C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#536×C79C2
socleC22×C79C22×D4
prime radical#19098708C2
hypercenter#536D79
hypocenterC79#3225
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #19099184C2semidirect
2. #19098955C2semidirect
3. #19098945C2semidirect
4. #19098922C2semidirect
5. #19098913C2semidirect
6. #19098782C2semidirect
7. #19098775C2semidirect
8. #19098770C2semidirect
9. #19098765C2semidirect
10. #19098725C2semidirect
11. #19098719C2semidirect
13. #19098702C2semidirect
14. #19098624C2semidirect
15. #536×C79C2semidirect
184. C79#3225semidirect
186. #536D79semidirect