Finite Group Databasebeta

← #23775870

Subgroups — #23775870

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099259C211yesmaximal, characteristic, complemented
2#19098969C211yesmaximal, characteristic, complemented
3#19098884C211yesmaximal, characteristic, complemented
4#19098881C211yesmaximal, characteristic, complemented
5#19098879C211yesmaximal, characteristic, complemented
6#19098876C211yesmaximal, characteristic, complemented
7#19098863C211yesmaximal, characteristic, complemented
8#19098850C211yesmaximal, characteristic, complemented
9#19098814C211yesmaximal, characteristic, complemented
10#19098797C211yesmaximal, characteristic, complemented
11#19098673C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098603C211yesmaximal, characteristic, complemented
14C2×#14579092C211yesmaximal, characteristic, complemented
15#547×C79C211yesmaximal, characteristic, complemented
16C2×#11929609C2211yescharacteristic
17C2×#11929608C2211yescharacteristic
18C22×C79⋊C8C2211yescharacteristic
19#14579156—21no—
20#14579153C2211yescharacteristic
21#14579143—21no—
22#14579135C2211yescharacteristic
23#14579135C2211yescharacteristic
24#14579133—21no—
25C4×D316C2211yescharacteristic
26(C22⋊D79)⋊C4—21no—
27#14579120C2211yescharacteristic
28C2×C4⋊Dic79C2211yescharacteristic
29#14579094C2211yescharacteristic
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579092C2211yescharacteristic
37#14579092C2211yescharacteristic
38C4⋊(C79⋊C8)C2211yescharacteristic
39#14579082C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79—21no—
49C4⋊Q8×C79C2211yescharacteristic
50#123×C79—21no—
51#123×C79—21no—
52C22⋊Q8×C79—21no—
53#121×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56C4×D4×C79C2211yescharacteristic
57C2×C4⋊C4×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C22×Dic79—21no—
63C2×C4×D79—21no—
64#11929609—22no—
65#11929608—22no—
66C2×C79⋊C8—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C2×C79⋊C8C2311yescharacteristic
71C4⋊Dic79—21no—
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77C22⋊Dic79—21no—
78(C2×D79)⋊C4—21no—
79(C2×D79)⋊C4—21no—
80(C2×D79)⋊C4—21no—
81C4×Dic79—21no—
82#41×C79—44no—
83C2×Q8×C79—21no—
84C2×D4×C79—21no—
85C2×D4×C79—21no—
86C2×D4×C79D411yescharacteristic
87C2×D4×C79C2311yescharacteristic
88C22×C4×C79—21no—
89C22×C4×C79—21no—
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79D411yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C4⋊C4×C79C2311yescharacteristic
99C4⋊C4×C79C2311yescharacteristic
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C42×C79C2311yescharacteristic
106C23×C79—21no—
107C23×C79C2×D411yescharacteristic
108C23×C79C2×D411yescharacteristic
109C22×D79—21no—
110Q8×C79—42no—
111D4×C79—22no—
112D4×C79—21no—
113D4×C79—21no—
114D4×C79—42no—
115D4×C79—42no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—42no—
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×C79C2411yescharacteristic
131C22⋊D79—42no—
132C22⋊D79—81no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—81no—
137D316—21no—
138D316—21no—
139C4×D79—81no—
140C79⋊C8—21no—
141C79⋊C8—21no—
142C79⋊C8—21no—
143C79⋊C8#4112yescomplemented
144C22×C79—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79AGL(1,ℤ/8)12yes—
153C22×C79C22×D411yescharacteristic
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79—21no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C792−1+411yescharacteristic
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169C2×C79—22no—
170C2×C79—41no—
171C2×C79—81no—
172C2×C79#54711yescharacteristic
173C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
174C2×C79#57711yescharacteristic
175D79—81no—
176#3345—791nomaximal, Sylow
177C79#334511yescharacteristic, complemented, Sylow
178#553—791no—
179#547D7911yescharacteristic, complemented
180#501—791no—
181#482—791no—
182#481—791no—
183#481—791no—
184#480—791no—
185#478—791no—
186#476—791no—
187#469—791no—
188#466—791no—
189#442—791no—
190#435—791no—
191#428—791no—
192C2×#106—791no—
193C2×#41—21no—
194C2×D8—791no—
195C2×M16—791no—
196C22×C8—791no—
197C4⋊Q8C2×D7911yescharacteristic
198#126—1581no—
199#125—791no—
200#123—21no—
201#123—21no—
202#123—1581no—
203C22⋊Q8—21no—
204#121—791no—
205#121—791no—
206#121—1581no—
207#121C2×D7911yescharacteristic
208#121C2×D7911yescharacteristic
209C4×D4—791no—
210C4×D4—1581no—
211C4×D4C2×D7911yescharacteristic
212C4×D4C2×D7911yescharacteristic
213#117—791no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4C2×D7911yescharacteristic
216C2×C4⋊C4C2×D7911yescharacteristic
217#107—791no—
218#107—791no—
219#107—791no—
220#106—791no—
221#106—791no—
222#106—791no—
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230#102—791no—
231#102—791no—
232#102—791no—
233C22⋊C8—791no—
234C22⋊C8—791no—
235#97—791no—
236#41—44no—
237C2×Q8—21no—
238C2×D4—21no—
239C2×D4—21no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4—1581no—
243C2×D4C22⋊D7911yescharacteristic
244C2×D4C22×D7911yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—1581no—
249C22×C4—1581no—
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252D8—1582no—
253M16—1582no—
254C2×C8—791no—
255C2×C8—791no—
256C2×C8—791no—
257C2×C8—791no—
258C2×C8—1582no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—791no—
263C4⋊C4—791no—
264C4⋊C4—791no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4C22⋊D7911yescharacteristic
269C4⋊C4C22×D7911yescharacteristic
270C4⋊C4C22×D7911yescharacteristic
271C4⋊C4C22×D7911yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4C22⋊D7911yescharacteristic
280C22⋊C4C22⋊D7911yescharacteristic
281C42—1581no—
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—1581no—
285C23C2×C22⋊D7911yescharacteristic
286C23C2×C22⋊D7911yescharacteristic
287Q8—42no—
288D4—22no—
289D4—21no—
290D4—21no—
291D4—42no—
292D4—42no—
293D4—3162no—
294D4—6321no—
295D4—1581no—
296D4—1581no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4C2×C22⋊D7911yescharacteristic
313C2×C4C2×C22⋊D7911yescharacteristic
314C2×C4C2×C22⋊D7911yescharacteristic
315C2×C4C2×C22⋊D7911yescharacteristic
316C2×C4C23×D7911yescharacteristic
317C8—792no—
318C8—1581no—
319C8—1581no—
320C8—1581no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—3161no—
330C22—3161no—
331C22—3161no—
332C22#1457918712yes—
333C22C22×C22⋊D7911yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—3161no—
342C4—3161no—
343C4—3161no—
344C4#41×D7911yescharacteristic
345C4#1457920811yescharacteristic
346C2—22no—
347C2—41no—
348C2—81no—
349C2—6321no—
350C2#1909921211yescharacteristic
351C2C2×#1457918711yescharacteristic
352C2#1909937111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#547×C79C2
socleC22×C79C22×D4
hypercenter#547D79
hypocenterC79#3345
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19099259C2semidirect
2. #19098969C2semidirect
3. #19098884C2semidirect
4. #19098881C2semidirect
5. #19098879C2semidirect
6. #19098876C2semidirect
7. #19098863C2semidirect
8. #19098850C2semidirect
9. #19098814C2semidirect
10. #19098797C2semidirect
11. #19098673C2semidirect
12. #19098635C2semidirect
13. #19098603C2semidirect
14. C2×#14579092C2semidirect
15. #547×C79C2semidirect
143. C79⋊C8#41semidirect
177. C79#3345semidirect
179. #547D79semidirect