Finite Group Databasebeta

← #23776108

Subgroups — #23776108

Order 10112.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099272C211yesmaximal, characteristic, complemented
2#19099234C211yesmaximal, characteristic, complemented
3#19098928C211yesmaximal, characteristic, complemented
4#19098926C211yesmaximal, characteristic, complemented
5#19098908C211yesmaximal, characteristic, complemented
6#19098863C211yesmaximal, characteristic, complemented
7#19098862C211yesmaximal, characteristic, complemented
8#19098852C211yesmaximal, characteristic, complemented
9#19098758C211yesmaximal, characteristic, complemented
10#19098756C211yesmaximal, characteristic, complemented
11#19098756C211yesmaximal, characteristic, complemented
12#19098691C211yesmaximal, characteristic, complemented
13#19098672C211yesmaximal, characteristic, complemented
14#19098643C211yesmaximal, characteristic, complemented
15#442×C79C211yesmaximal, characteristic, complemented
16C2×#11929624—21no—
17C2×#11929609C2211yescharacteristic
18C2×#11929609C2211yescharacteristic
19#14579160C2211yescharacteristic
20#14579158C2211yescharacteristic
21#14579157C2211yescharacteristic
22#14579157C2211yescharacteristic
23#14579153C2211yescharacteristic
24#14579152C2211yescharacteristic
25#14579140—21no—
26#14579138—21no—
27#14579138—21no—
28#14579135—21no—
29#14579134—21no—
30#14579134—21no—
31C4×Dic158C2211yescharacteristic
32D4×Dic79C2211yescharacteristic
33D4×Dic79C2211yescharacteristic
34#14579123C2211yescharacteristic
35#14579123C2211yescharacteristic
36C2×Dic79⋊C4—21no—
37#14579094C2211yescharacteristic
38#14579092C2211yescharacteristic
39C4⋊(C79⋊C8)C2211yescharacteristic
40Dic79⋊C8C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42#14579083C2211yescharacteristic
43#14579083C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579081C2211yescharacteristic
49#14579081C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C4×D4×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55#106×C79C2211yescharacteristic
56#102×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#97×C79C2211yescharacteristic
59#11929624—44no—
60C2×Dic158—21no—
61C2×Dic158D411yescharacteristic
62C2×D316—21no—
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×D316C2311yescharacteristic
66C2×C22⋊D79—21no—
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C22×Dic79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73C2×C4×D79—21no—
74#11929609—22no—
75#11929609—22no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C4⋊Dic79—21no—
79C4⋊Dic79D411yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81C4⋊Dic79C2311yescharacteristic
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4D411yescharacteristic
87Dic79⋊C4D411yescharacteristic
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92C4×Dic79C2311yescharacteristic
93C4×Dic79C2311yescharacteristic
94C2×D4×C79C2311yescharacteristic
95C2×D4×C79C2311yescharacteristic
96C22×C4×C79—21no—
97C22×C4×C79—21no—
98D8×C79—22no—
99C2×C8×C79C2311yescharacteristic
100C2×C8×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C42×C79C2311yescharacteristic
106C23×C79—21no—
107C23×C79—21no—
108C22×D79—21no—
109C22×D79—21no—
110D4×C79—21no—
111D4×C79—21no—
112D4×C79—21no—
113D4×C79#4112yescomplemented
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—42no—
117C2×C4×C79—81no—
118C2×C4×C79C2×D411yescharacteristic
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2411yescharacteristic
121C22⋊D79—42no—
122C22⋊D79—42no—
123C22⋊D79—81no—
124C22⋊D79—81no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—42no—
128C2×Dic79—81no—
129C2×Dic79C2×D411yescharacteristic
130C2×Dic79C2×D411yescharacteristic
131C2×Dic79C2×D411yescharacteristic
132C2×Dic79C2×D411yescharacteristic
133D316—21no—
134D316—21no—
135D316—21no—
136D316—21no—
137D316—42no—
138D316—81no—
139C4×D79—42no—
140C4×D79—42no—
141Dic158—22no—
142Dic158—81no—
143C8×C79—21no—
144C8×C79—21no—
145C79⋊C8—21no—
146C79⋊C8—21no—
147C22×C79—22no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79C22×D411yescharacteristic
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C2×D79—41no—
160C4×C79—21no—
161C4×C79—21no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C792−1+411yescharacteristic
166Dic79—21no—
167Dic79—21no—
168Dic79—21no—
169Dic79—41no—
170Dic79—41no—
171Dic79AGL(1,ℤ/8)12yes—
172C2×C79—42no—
173C2×C79—81no—
174C2×C79#54811yescharacteristic
175C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C79#57611yescharacteristic
177D79—81no—
178D79—81no—
179#3366—791nomaximal, Sylow
180C79#336611yescharacteristic, complemented, Sylow
181#554—791no—
182#550—791no—
183#490—791no—
184#490—791no—
185#486—791no—
186#478—791no—
187#478—791no—
188#476—791no—
189#459—791no—
190#459—791no—
191#459—791no—
192#446—791no—
193#442—791no—
194#442D7911yescharacteristic, complemented
195C4×D8—791no—
196C2×#41—1581no—
197C2×D8—791no—
198C2×D8—791no—
199C2×D8C2×D7911yescharacteristic
200C4⋊Q8—791no—
201#127—791no—
202#127—791no—
203#127—791no—
204#125—791no—
205#125—791no—
206C22⋊Q8—1581no—
207C22⋊Q8—1581no—
208C22⋊Q8—1581no—
209#121—1581no—
210#121—1581no—
211#121—1581no—
212C4×Q8—791no—
213C4×D4—791no—
214C4×D4—791no—
215C4×D4—791no—
216C4×D4—791no—
217C4×D4C2×D7911yescharacteristic
218C4×D4C2×D7911yescharacteristic
219C2×C4⋊C4—1581no—
220#107—791no—
221#106—791no—
222#106C2×D7911yescharacteristic
223C4⋊C8—791no—
224C4⋊C8—791no—
225C4⋊C8—791no—
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102C2×D7911yescharacteristic
235#102C2×D7911yescharacteristic
236#97—791no—
237#97C2×D7911yescharacteristic
238C4×C8—791no—
239#41—3164no—
240C2×Q8—791no—
241C2×Q8—1581no—
242C2×D4—791no—
243C2×D4—791no—
244C2×D4—1581no—
245C2×D4—1581no—
246C2×D4—1581no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4—1581no—
250C2×D4C22×D7911yescharacteristic
251C2×D4C22×D7911yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4—1581no—
258D8—22no—
259D8—1582no—
260D8—1582no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8C22×D7911yescharacteristic
264C2×C8C22×D7911yescharacteristic
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C42—791no—
284C42—791no—
285C42C22×D7911yescharacteristic
286C23—21no—
287C23—21no—
288C23—1581no—
289C23—1581no—
290Q8—6321no—
291Q8—1582no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—3162no—
296D4—3162no—
297D4—3162no—
298D4—6321no—
299D4—6321no—
300D4—6321no—
301D4—1581no—
302D4—1581no—
303D4—1581no—
304D4—1581no—
305D4#1192962412yescomplemented
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—3162no—
311C2×C4—3162no—
312C2×C4—3162no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—791no—
317C2×C4—6321no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4D4×D7911yescharacteristic
321C2×C4D4×D7911yescharacteristic
322C2×C4C23×D7911yescharacteristic
323C8—21no—
324C8—21no—
325C8—1581no—
326C8—1581no—
327C22—22no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3161no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—3161no—
338C22—3161no—
339C22C2×D4×D7911yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—3161no—
345C4—3161no—
346C4—792no—
347C4—1581no—
348C4—1581no—
349C4—1581no—
350C4C2×#1192962411yescharacteristic
351C4#1457920811yescharacteristic
352C2—42no—
353C2—81no—
354C2—6321no—
355C2—6321no—
356C2#1909922211yescharacteristic
357C2AGL(1,ℤ/8)×D7911yescharacteristic
358C2#1909936711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#442×C79C2
socleC22×C79C22×D4
hypercenter#442D79
hypocenterC79#3366
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #19099272C2semidirect
2. #19099234C2semidirect
3. #19098928C2semidirect
4. #19098926C2semidirect
5. #19098908C2semidirect
6. #19098863C2semidirect
7. #19098862C2semidirect
8. #19098852C2semidirect
9. #19098758C2semidirect
10. #19098756C2semidirect
11. #19098756C2semidirect
12. #19098691C2semidirect
13. #19098672C2semidirect
14. #19098643C2semidirect
15. #442×C79C2semidirect
113. D4×C79#41semidirect
180. C79#3366semidirect
194. #442D79semidirect
305. D4#11929624semidirect