Finite Group Databasebeta

← #23773990

Subgroups — #23773990

Order 10112.

408 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099108C211yesmaximal, characteristic, complemented
2#19099094C211yesmaximal, characteristic, complemented
3#19098970C211yesmaximal, characteristic, complemented
4#19098951C211yesmaximal, characteristic, complemented
5#19098926C211yesmaximal, characteristic, complemented
6#19098921C211yesmaximal, characteristic, complemented
7#19098814C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098807C211yesmaximal, characteristic, complemented
10#19098654C211yesmaximal, characteristic, complemented
11#19098650C211yesmaximal, characteristic, complemented
12D8×Dic79C211yesmaximal, characteristic, complemented
13#19098643C211yesmaximal, characteristic, complemented
14M16×Dic79C211yesmaximal, characteristic, complemented
15#469×C79C211yesmaximal, characteristic, complemented
16C2×#11929623—21no—
17C2×#11929613C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929609C2211yescharacteristic
20C2×#11929608C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579157C2211yescharacteristic
23#14579154—21no—
24#14579152C2211yescharacteristic
25#14579148C2211yescharacteristic
26#14579147—21no—
27#14579142—21no—
28#14579140C2211yescharacteristic
29#14579135C2211yescharacteristic
30#14579133—21no—
31#14579126C2211yescharacteristic
32D4×Dic79—21no—
33D4×Dic79C2211yescharacteristic
34D4×Dic79C2211yescharacteristic
35#14579123C2211yescharacteristic
36(C22⋊D79)⋊C4—21no—
37#14579117—21no—
38C2×C4×Dic79C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579092C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579084C2211yescharacteristic
44#14579083C2211yescharacteristic
45#14579082C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579071C2211yescharacteristic
49#14579071C2211yescharacteristic
50C8×Dic79C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×D8×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54#121×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#106×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—44no—
60C2×Dic158—21no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C22×Dic79—21no—
67C22×Dic79—21no—
68C22×Dic79D411yescharacteristic
69C22×Dic79D411yescharacteristic
70C2×C4×D79—21no—
71#11929613—22no—
72#11929612—22no—
73#11929609—22no—
74#11929608—22no—
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89(C2×D79)⋊C4—21no—
90(C2×D79)⋊C4—21no—
91C4×Dic79—21no—
92C4×Dic79D411yescharacteristic
93C4×Dic79D411yescharacteristic
94C4×Dic79C2311yescharacteristic
95C4×Dic79C2311yescharacteristic
96C2×D4×C79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101D8×C79—22no—
102M16×C79—22no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C4⋊C4×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C22⋊C4×C79—21no—
109C23×C79—21no—
110C23×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79—21no—
113D4×C79—21no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—42no—
118D4×C79—42no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2411yescharacteristic
125C22⋊D79—42no—
126C22⋊D79—42no—
127C22⋊D79—42no—
128C2×Dic79—22no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—41no—
133C2×Dic79—42no—
134C2×Dic79—42no—
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139D316—21no—
140D316—21no—
141C4×D79—42no—
142Dic158—21no—
143Dic158—21no—
144Dic158—42no—
145C8×C79—21no—
146C8×C79#4112yescomplemented
147C79⋊C8—21no—
148C79⋊C8#4112yescomplemented
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C2×D79—41no—
160C2×D79—41no—
161C2×D79—41no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79C2×#4111yescharacteristic
166C4×C79C2×#4111yescharacteristic
167Dic79—21no—
168Dic79—21no—
169Dic79—21no—
170Dic79—41no—
171Dic79—41no—
172Dic79—41no—
173Dic79AGL(1,ℤ/8)12yes—
174C2×C79—41no—
175C2×C79—81no—
176C2×C79—81no—
177C2×C79#53211yescharacteristic
178C2×C79C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C79#57511yescharacteristic
180D79—81no—
181#3171—791nomaximal, Sylow
182C79#317111yescharacteristic, complemented, Sylow
183#532—791no—
184#529—791no—
185#501—791no—
186#496—791no—
187#490—791no—
188#489—791no—
189#469—791no—
190#469D7911yescharacteristic, complemented
191#468—791no—
192#468—791no—
193C4×SD16—791no—
194C4×SD16—791no—
195C4×D8—791no—
196C4×D8—791no—
197C4×M16—791no—
198C2×#41—1581no—
199C2×SD16—791no—
200C2×SD16—791no—
201C2×D8—791no—
202C2×D8C2×D7911yescharacteristic
203C2×M16—791no—
204C2×M16C2×D7911yescharacteristic
205C4⋊Q8—791no—
206#127—791no—
207#126—1581no—
208#125—791no—
209#124—791no—
210#124—1581no—
211#123—1581no—
212C22⋊Q8—791no—
213#121—791no—
214#121—1581no—
215#121C2×D7911yescharacteristic
216#121C2×D7911yescharacteristic
217C4×Q8—791no—
218C4×D4—791no—
219C4×D4—791no—
220C4×D4—791no—
221C4×D4—1581no—
222C4×D4—1581no—
223#117—1581no—
224C2×C42—791no—
225#107—791no—
226#107—791no—
227#106—791no—
228#106C2×D7911yescharacteristic
229#103—791no—
230#103—791no—
231#102—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235#102C2×D7911yescharacteristic
236#102C2×D7911yescharacteristic
237#97—791no—
238#97—791no—
239C4×C8—791no—
240C4×C8—791no—
241#41—3164no—
242C2×Q8—791no—
243C2×Q8—1581no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4—1581no—
250C2×D4C22×D7911yescharacteristic
251C2×D4C22×D7911yescharacteristic
252C22×C4—791no—
253C22×C4—791no—
254C22×C4—1581no—
255C22×C4—1581no—
256C22×C4—1581no—
257C22×C4C22×D7911yescharacteristic
258SD16—1582no—
259SD16—1582no—
260D8—22no—
261D8—1582no—
262M16—22no—
263M16—1582no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8C22×D7911yescharacteristic
267C2×C8C22×D7911yescharacteristic
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—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—791no—
287C42—791no—
288C42—791no—
289C42—791no—
290C42—1581no—
291C23—21no—
292C23—21no—
293C23—1581no—
294C23D4×D7911yescharacteristic
295Q8—3162no—
296Q8—1581no—
297Q8—1581no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—42no—
304D4—3162no—
305D4—3162no—
306D4—3162no—
307D4—1581no—
308D4—1581no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—3162no—
314C2×C4—3162no—
315C2×C4—3162no—
316C2×C4—3161no—
317C2×C4—791no—
318C2×C4—791no—
319C2×C4—791no—
320C2×C4—791no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1582no—
325C2×C4D4×D7911yescharacteristic
326C2×C4C23×D7911yescharacteristic
327C8—21no—
328C8—792no—
329C8—1581no—
330C8#1192962312yescomplemented
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—3161no—
341C22—3161no—
342C22—3161no—
343C22C2×D4×D7911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—792no—
351C4—1581no—
352C4—1581no—
353C4—1581no—
354C4#41×D7911yescharacteristic
355C4C2×#1192962311yescharacteristic
356C2—41no—
357C2—81no—
358C2—81no—
359C2—6321no—
360C2#1909910811yescharacteristic
361C2AGL(1,ℤ/8)×D7911yescharacteristic
362C2#1909935911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#469×C79C2
socleC22×C79C22×D4
hypercenter#469D79
hypocenterC79#3171
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #19099108C2semidirect
2. #19099094C2semidirect
3. #19098970C2semidirect
4. #19098951C2semidirect
5. #19098926C2semidirect
6. #19098921C2semidirect
7. #19098814C2semidirect
8. #19098809C2semidirect
9. #19098807C2semidirect
10. #19098654C2semidirect
11. #19098650C2semidirect
12. D8×Dic79C2semidirect
13. #19098643C2semidirect
14. M16×Dic79C2semidirect
15. #469×C79C2semidirect
146. C8×C79#41semidirect
148. C79⋊C8#41semidirect
182. C79#3171semidirect
190. #469D79semidirect
330. C8#11929623semidirect