Finite Group Databasebeta

← #23773596

Subgroups — #23773596

Order 10112.

396 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
1#19099167C211yesmaximal, characteristic, complemented
2#19099042C211yesmaximal, characteristic, complemented
3#19098880C211yesmaximal, characteristic, complemented
4#19098875C211yesmaximal, characteristic, complemented
5#19098871C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098760C211yesmaximal, characteristic, complemented
8#19098705C211yesmaximal, characteristic, complemented
9#19098705C211yesmaximal, characteristic, complemented
10#19098675C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098654C211yesmaximal, characteristic, complemented
13D8×Dic79C211yesmaximal, characteristic, complemented
14#19098623C211yesmaximal, characteristic, complemented
15#459×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19#14579153C2211yescharacteristic
20#14579142—21no—
21#14579142—21no—
22#14579133—21no—
23#14579133—21no—
24#14579132C2211yescharacteristic
25#14579132C2211yescharacteristic
26C4×Dic158C2211yescharacteristic
27#14579126C2211yescharacteristic
28D4×Dic79C2211yescharacteristic
29D4×Dic79C2211yescharacteristic
30D4×Dic79C2211yescharacteristic
31C4×C22⋊D79—21no—
32(C22⋊D79)⋊C4—21no—
33#14579118C2211yescharacteristic
34#14579117—21no—
35C2×Dic79⋊C4—21no—
36C4⋊C4×D79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41C4⋊(C79⋊C8)C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579082C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48(C2×D79)⋊C8C2211yescharacteristic
49(C2×D79)⋊C8C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C2×D8×C79C2211yescharacteristic
54#127×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56C4⋊C8×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—22no—
61C2×Dic158C2311yescharacteristic
62C2×C22⋊D79—21no—
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C22×Dic79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79—21no—
69C2×C4×D79—21no—
70C2×C4×D79C2311yescharacteristic
71#11929612—22no—
72#11929612—22no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4D411yescharacteristic
84Dic79⋊C4D411yescharacteristic
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90(C2×D79)⋊C4D411yescharacteristic
91(C2×D79)⋊C4D411yescharacteristic
92C4×Dic79—21no—
93C4×Dic79—21no—
94C4×Dic79C2311yescharacteristic
95C2×D4×C79—21no—
96C2×D4×C79—21no—
97C2×D4×C79C2311yescharacteristic
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101D8×C79—22no—
102D8×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C22⋊C4×C79—21no—
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C22×D79C2×D411yescharacteristic
112D4×C79—21no—
113D4×C79—21no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—81no—
118D4×C79—81no—
119D4×C79#4112yes—
120C2×C4×C79—21no—
121C2×C4×C79—81no—
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2411yescharacteristic
125C22⋊D79—24no—
126C22⋊D79—81no—
127C22⋊D79—81no—
128C2×Dic79—24no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134C2×Dic79—81no—
135C2×Dic79—81no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—81no—
142Dic158—21no—
143Dic158#4112yes—
144C8×C79—21no—
145C8×C79—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C22×C79—22no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79C22×D411yescharacteristic
158C2×D79—21no—
159C2×D79—21no—
160C2×D79—21no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C79C2×#4111yescharacteristic
166Dic79—22no—
167Dic79—21no—
168Dic79—21no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173C2×C79—42no—
174C2×C79—81no—
175C2×C79—81no—
176C2×C79#52511yescharacteristic
177C2×C79#57611yescharacteristic
178C2×C79#57711yescharacteristic
179D79—41no—
180#3119—791nomaximal, Sylow
181C79#311911yescharacteristic, complemented, Sylow
182#540—791no—
183#520—791no—
184#481—791no—
185#480—791no—
186#479—791no—
187#478—791no—
188#460—791no—
189#459D7911yescharacteristic, complemented
190#449—791no—
191#449—791no—
192#442—791no—
193#440—791no—
194C4×SD16—791no—
195C4×D8—791no—
196#433—791no—
197C2×#41—791no—
198C2×SD16—791no—
199C2×SD16—791no—
200C2×D8C2×D7911yescharacteristic
201C2×D8C2×D7911yescharacteristic
202#127C2×D7911yescharacteristic
203#125—791no—
204#123—1581no—
205#123—1581no—
206#121—791no—
207#121—791no—
208#121—1581no—
209#121—1581no—
210C4×Q8—791no—
211C4×Q8—791no—
212C4×D4—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—1581no—
216C4×D4—1581no—
217C4×D4C2×D7911yescharacteristic
218#117—791no—
219#117—1581no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—1581no—
222#107—791no—
223#107—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227C4⋊C8C2×D7911yescharacteristic
228#103—791no—
229#103—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102C2×D7911yescharacteristic
235#102C2×D7911yescharacteristic
236C22⋊C8—791no—
237C22⋊C8—791no—
238#97—791no—
239C4×C8—791no—
240#41—1582no—
241#41—1582no—
242C2×Q8—791no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—1581no—
246C2×D4—1581no—
247C2×D4—1581no—
248C2×D4C22×D7911yescharacteristic
249C2×D4C22×D7911yescharacteristic
250C2×D4C22×D7911yescharacteristic
251C22×C4—21no—
252C22×C4—791no—
253C22×C4—1581no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258SD16—1582no—
259SD16—1582no—
260D8—22no—
261D8—22no—
262C2×C8—791no—
263C2×C8—791no—
264C2×C8C22×D7911yescharacteristic
265C2×C8C22×D7911yescharacteristic
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—791no—
279C22⋊C4—791no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C42—791no—
286C42—1581no—
287C42—1581no—
288C42C22×D7911yescharacteristic
289C23—21no—
290C23—21no—
291C23—21no—
292C23—791no—
293Q8—792no—
294Q8—1581no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—6321no—
303D4—6321no—
304D4—1584no—
305D4#1192962312yes—
306C2×C4—21no—
307C2×C4—81no—
308C2×C4—791no—
309C2×C4—791no—
310C2×C4—791no—
311C2×C4—6321no—
312C2×C4—6321no—
313C2×C4—6321no—
314C2×C4—6321no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1584no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4D4×D7911yescharacteristic
323C2×C4D4×D7911yescharacteristic
324C2×C4C23×D7911yescharacteristic
325C8—21no—
326C8—21no—
327C8—1581no—
328C8—1581no—
329C22—22no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—1581no—
339C22—1581no—
340C22—1581no—
341C22C2×D4×D7911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—1581no—
349C4—1582no—
350C4—1581no—
351C4—1581no—
352C4#41×D7911yescharacteristic
353C4C2×#1192962311yescharacteristic
354C2—42no—
355C2—81no—
356C2—81no—
357C2—3161no—
358C2#1909907311yescharacteristic
359C2#1909936411yescharacteristic
360C2#1909937311yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#459×C79C2
socleC22×C79C22×D4
hypercenter#459D79
hypocenterC79#3119
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #19099167C2semidirect
2. #19099042C2semidirect
3. #19098880C2semidirect
4. #19098875C2semidirect
5. #19098871C2semidirect
6. #19098863C2semidirect
7. #19098760C2semidirect
8. #19098705C2semidirect
9. #19098705C2semidirect
10. #19098675C2semidirect
11. #19098660C2semidirect
12. #19098654C2semidirect
13. D8×Dic79C2semidirect
14. #19098623C2semidirect
15. #459×C79C2semidirect
181. C79#3119semidirect
189. #459D79semidirect