Finite Group Databasebeta

← #23775497

Subgroups — #23775497

Order 10112.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099248C211yesmaximal, characteristic, complemented
2#19099212C211yesmaximal, characteristic
3#19098930C211yesmaximal, characteristic, complemented
4#19098902C211yesmaximal, characteristic, complemented
5#19098898C211yesmaximal, characteristic, complemented
6#19098865C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098803C211yesmaximal, characteristic, complemented
9#19098772C211yesmaximal, characteristic, complemented
10#19098726C211yesmaximal, characteristic, complemented
11#19098725C211yesmaximal, characteristic, complemented
12#19098660C211yesmaximal, characteristic, complemented
13#19098632C211yesmaximal, characteristic, complemented
14#19098556C211yesmaximal, characteristic, complemented
15#417×C79C211yesmaximal, characteristic, complemented
16C2×#11929623C2211yescharacteristic
17C2×Dic316C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929612C2211yescharacteristic
20C2×C8×D79C2211yescharacteristic
21#14579159C2211yescharacteristic
22#14579156—21no—
23#14579152C2211yescharacteristic
24#14579151—21no—
25#14579144—21no—
26#14579144—21no—
27#14579142—21no—
28#14579141C2211yescharacteristic
29#14579140C2211yescharacteristic
30#14579140C2211yescharacteristic
31#14579137C2211yescharacteristic
32#14579133—21no—
33#14579126C2211yescharacteristic
34D4×Dic79C2211yescharacteristic
35C4×C22⋊D79C2211yescharacteristic
36#14579120—21no—
37#14579119C2211yescharacteristic
38C2×Dic79⋊C4—21no—
39#14579094C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579093C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579084C2211yescharacteristic
47#14579084C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54C2×C4⋊C4×C79C2211yescharacteristic
55#103×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58#102×C79C2211yescharacteristic
59#11929623—22no—
60#11929623—41no—
61C2×Dic158C2311yescharacteristic
62C2×Dic158C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79D411yescharacteristic
65C22×Dic79—21no—
66C22×Dic79—21no—
67C2×C4×D79C2311yescharacteristic
68Dic316—41no—
69#11929614—41no—
70#11929612—22no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C8×D79—41no—
74C4⋊Dic79—21no—
75C4⋊Dic79—21no—
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87C22⋊Dic79—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79D411yescharacteristic
90(C2×D79)⋊C4—21no—
91(C2×D79)⋊C4—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4D411yescharacteristic
94C4×Dic79—21no—
95C4×Dic79—21no—
96C4×Dic79C2311yescharacteristic
97#41×C79—22no—
98#41×C79—41no—
99C2×Q8×C79C2311yescharacteristic
100C2×D4×C79—21no—
101C2×D4×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79—21no—
104C22×C4×C79C2311yescharacteristic
105M16×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C22×D79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116D4×C79—21no—
117D4×C79—42no—
118D4×C79#4112yes—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—42no—
125C2×C4×C79—42no—
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2411yescharacteristic
128C22⋊D79—41no—
129C22⋊D79—42no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—42no—
135C2×Dic79—42no—
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138C2×Dic79C2×D411yescharacteristic
139C4×D79—21no—
140C4×D79—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—21no—
144Dic158—21no—
145C8×C79—21no—
146C8×C79—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—22no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79C22×D411yescharacteristic
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—21no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79C2×#4111yescharacteristic
164C4×C79H(5,𝔽2)11yescharacteristic
165Dic79—21no—
166Dic79—21no—
167Dic79—21no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172C2×C79—41no—
173C2×C79—42no—
174C2×C79#54611yescharacteristic
175C2×C79#57511yescharacteristic
176C2×C79#57811yescharacteristic
177D79—41no—
178#3315—791nomaximal, Sylow
179C79#331511yescharacteristic, complemented, Sylow
180#552—791no—
181#547—791no—
182#491—791no—
183#485—791no—
184#484—791no—
185#478—791no—
186#470—791no—
187#467—791no—
188#462—791no—
189#452—791no—
190#452—791no—
191#440—791no—
192#435—791no—
193#417D7911yescharacteristic, complemented
194#416—791no—
195C2×#41—791no—
196C2×#41C2×D7911yescharacteristic
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×M16C2×D7911yescharacteristic
201C22×C8—791no—
202C4⋊Q8—791no—
203#126—1581no—
204#125—791no—
205#125—1581no—
206#123—1581no—
207#123—1581no—
208#123—1581no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—791no—
212C22⋊Q8—791no—
213#121—1581no—
214C4×Q8—791no—
215C4×D4—791no—
216C4×D4—791no—
217#117—791no—
218#117—1581no—
219C2×C4⋊C4—1581no—
220C2×C4⋊C4C2×D7911yescharacteristic
221#107—791no—
222#107—791no—
223#106—791no—
224C4⋊C8—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103C2×D7911yescharacteristic
231#103C2×D7911yescharacteristic
232#102—791no—
233#102C2×D7911yescharacteristic
234#102C2×D7911yescharacteristic
235C22⋊C8—791no—
236C22⋊C8—791no—
237#97—791no—
238#41—22no—
239#41—41no—
240#41—3161no—
241#41—1582no—
242C2×Q8—791no—
243C2×Q8—791no—
244C2×Q8C22×D7911yescharacteristic
245C2×D4—21no—
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4C22×D7911yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—791no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4C22×D7911yescharacteristic
255Q16—3161no—
256Q16—3161no—
257SD16—1582no—
258M16—41no—
259C2×C8—3161no—
260C2×C8—791no—
261C2×C8—791no—
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—791no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
270C4⋊C4—1581no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22×D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C22⋊C4—791no—
280C22⋊C4—791no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C42—791no—
288C42—1581no—
289C42—1581no—
290C23—21no—
291C23—791no—
292C23D4×D7911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—1581no—
296Q8—1581no—
297Q8—1581no—
298Q8—1581no—
299D4—21no—
300D4—42no—
301D4—3162no—
302D4—3161no—
303D4#1192962412yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—3162no—
312C2×C4—3162no—
313C2×C4—791no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4—1581no—
322C2×C4D4×D7911yescharacteristic
323C2×C4C23×D7911yescharacteristic
324C8—21no—
325C8—21no—
326C8—1581no—
327C8—1581no—
328C22—21no—
329C22—22no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—1581no—
335C22—1581no—
336C22—1581no—
337C22C2×D4×D7911yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3161no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—1581no—
347C4—1581no—
348C4—1581no—
349C4C2×#1192962411yescharacteristic
350C4#1457920611yescharacteristic
351C2—41no—
352C2—42no—
353C2—3161no—
354C2#1909920311yescharacteristic
355C2#1909935911yescharacteristic
356C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#417×C79C2
socleC22×C79C22×D4
prime radical#19099212C2
hypercenter#417D79
hypocenterC79#3315
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #19099248C2semidirect
3. #19098930C2semidirect
4. #19098902C2semidirect
5. #19098898C2semidirect
6. #19098865C2semidirect
7. #19098821C2semidirect
8. #19098803C2semidirect
9. #19098772C2semidirect
10. #19098726C2semidirect
11. #19098725C2semidirect
12. #19098660C2semidirect
13. #19098632C2semidirect
14. #19098556C2semidirect
15. #417×C79C2semidirect
179. C79#3315semidirect
193. #417D79semidirect