Finite Group Databasebeta

← #23775670

Subgroups — #23775670

Order 10112.

380 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#19099253C211yesmaximal, characteristic, complemented
2#19099222C211yesmaximal, characteristic
3#19098918C211yesmaximal, characteristic, complemented
4#19098899C211yesmaximal, characteristic, complemented
5#19098888C211yesmaximal, characteristic, complemented
6#19098871C211yesmaximal, characteristic, complemented
7#19098821C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098786C211yesmaximal, characteristic, complemented
10#19098727C211yesmaximal, characteristic, complemented
11#19098721C211yesmaximal, characteristic, complemented
12C4×Dic316C211yesmaximal, characteristic, complemented
13#19098573C211yesmaximal, characteristic, complemented
14#19098565C211yesmaximal, characteristic, complemented
15#436×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×Dic316C2211yescharacteristic
19C2×Dic316C2211yescharacteristic
20C2×#11929613C2211yescharacteristic
21#14579154—21no—
22#14579153C2211yescharacteristic
23#14579151—21no—
24#14579149C2211yescharacteristic
25#14579147—21no—
26#14579142—21no—
27#14579140C2211yescharacteristic
28#14579140C2211yescharacteristic
29#14579140C2211yescharacteristic
30#14579139—21no—
31#14579135C2211yescharacteristic
32#14579133—21no—
33C4×Dic158C2211yescharacteristic
34C4×Dic158C2211yescharacteristic
35(C22⋊D79)⋊C4—21no—
36#14579120C2211yescharacteristic
37#14579117—21no—
38C2×C4⋊Dic79C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579095C2211yescharacteristic
41#14579093C2211yescharacteristic
42#14579086C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579086C2211yescharacteristic
46#14579086C2211yescharacteristic
47#14579086C2211yescharacteristic
48#14579086C2211yescharacteristic
49#14579083C2211yescharacteristic
50#14579083C2211yescharacteristic
51#14579083C2211yescharacteristic
52C2×M16×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54C4×D4×C79C2211yescharacteristic
55C4⋊C8×C79C2211yescharacteristic
56C22⋊C8×C79C2211yescharacteristic
57C22⋊C8×C79C2211yescharacteristic
58C4×C8×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—41no—
61C2×Dic158—22no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158C2311yescharacteristic
65C2×Dic158C2311yescharacteristic
66C2×Dic158C2311yescharacteristic
67C2×D316C2311yescharacteristic
68C2×C22⋊D79—21no—
69C2×C22⋊D79—21no—
70C22×Dic79—21no—
71C22×Dic79—21no—
72C2×C4×D79—21no—
73Dic316—22no—
74Dic316—41no—
75#11929613—41no—
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4—21no—
86Dic79⋊C4—21no—
87Dic79⋊C4—21no—
88C22⋊Dic79—21no—
89C22⋊Dic79—21no—
90C22⋊Dic79—21no—
91C22⋊Dic79—21no—
92(C2×D79)⋊C4—21no—
93(C2×D79)⋊C4—21no—
94(C2×D79)⋊C4—21no—
95C4×Dic79—21no—
96C4×Dic79—21no—
97C4×Dic79—21no—
98C2×D4×C79D411yescharacteristic
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101M16×C79—41no—
102M16×C79—41no—
103C2×C8×C79C2311yescharacteristic
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79D411yescharacteristic
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114D4×C79—41no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79C2×D411yescharacteristic
120C2×C4×C79C2×D411yescharacteristic
121C2×C4×C79C2×D411yescharacteristic
122C2×C4×C79C2×D411yescharacteristic
123C2×C4×C79C2411yescharacteristic
124C22⋊D79—42no—
125C22⋊D79—42no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—42no—
134C2×Dic79—42no—
135D316—21no—
136D316—21no—
137C4×D79—42no—
138Dic158—21no—
139Dic158—21no—
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—42no—
144Dic158#4112yes—
145C8×C79—21no—
146C8×C79—21no—
147C8×C79—21no—
148C8×C79—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79C22×D411yescharacteristic
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C4×C79—21no—
160C4×C79—21no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79C2×#4111yescharacteristic
164C4×C79H(5,𝔽2)11yescharacteristic
165Dic79—22no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172C2×C79—41no—
173C2×C79—41no—
174C2×C79#54611yescharacteristic
175C2×C79#57511yescharacteristic
176C2×C79#57811yescharacteristic
177D79—81no—
178#3327—791nomaximal, Sylow
179C79#332711yescharacteristic, complemented, Sylow
180#552—791no—
181#548—791no—
182#488—791no—
183#484—791no—
184#482—791no—
185#479—791no—
186#470—791no—
187#468—791no—
188#464—791no—
189#452—791no—
190#451—791no—
191C4×Q16—791no—
192#436D7911yescharacteristic, complemented
193#419—791no—
194#417—791no—
195C2×#41—791no—
196C22×Q8—791no—
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×M16C2×D7911yescharacteristic
201C2×M16C2×D7911yescharacteristic
202#126—1581no—
203#125—791no—
204#125—1581no—
205#124—791no—
206#124—1581no—
207#123—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212#121—791no—
213#121—1581no—
214C4×Q8—791no—
215C4×Q8—791no—
216C4×D4—1581no—
217C4×D4C2×D7911yescharacteristic
218#117—791no—
219#117—1581no—
220C2×C4⋊C4—791no—
221#107—791no—
222#107—791no—
223#106—791no—
224C4⋊C8C2×D7911yescharacteristic
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235C22⋊C8C2×D7911yescharacteristic
236C22⋊C8C2×D7911yescharacteristic
237C4×C8C2×D7911yescharacteristic
238#41—3161no—
239#41—1582no—
240C2×Q8—3161no—
241C2×Q8—791no—
242C2×Q8—791no—
243C2×Q8—791no—
244C2×Q8—1582no—
245C2×Q8—1581no—
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4D31611yescharacteristic
250C22×C4—1581no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255Q16—3161no—
256Q16—1582no—
257SD16—3161no—
258M16—41no—
259M16—41no—
260C2×C8C22×D7911yescharacteristic
261C2×C8C22×D7911yescharacteristic
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C4⋊C4—791no—
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⋊C4D31611yescharacteristic
277C22⋊C4—1581no—
278C22⋊C4—1581no—
279C22⋊C4—1581no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4D31611yescharacteristic
285C22⋊C4D31611yescharacteristic
286C42—1581no—
287C42—1581no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—1581no—
291C23C2×D31611yescharacteristic
292C23C2×D31611yescharacteristic
293Q8—3162no—
294Q8—792no—
295Q8—1581no—
296Q8—1581no—
297Q8—1581no—
298Q8—1581no—
299Q8—1581no—
300D4—41no—
301D4—3162no—
302D4—3162no—
303D4—1581no—
304D4—1581no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—3162no—
310C2×C4—3162no—
311C2×C4—3162no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4C2×D31611yescharacteristic
320C2×C4C2×D31611yescharacteristic
321C2×C4C2×D31611yescharacteristic
322C2×C4C2×D31611yescharacteristic
323C2×C4C23×D7911yescharacteristic
324C8—21no—
325C8—21no—
326C8—21no—
327C8—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22C22×D31611yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—3161no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—1582no—
349C4#41×D7911yescharacteristic
350C4#1457920611yescharacteristic
351C2—41no—
352C2—41no—
353C2—6321no—
354C2#1909920811yescharacteristic
355C2#1909936311yescharacteristic
356C2#1909938011yescharacteristic
subgroupG/H
centerC22C22×D316
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#436×C79C2
socleC22×C79C22×D4
prime radical#19099222C2
hypercenter#436D79
hypocenterC79#3327
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
3. #19098918C2semidirect
4. #19098899C2semidirect
5. #19098888C2semidirect
6. #19098871C2semidirect
7. #19098821C2semidirect
8. #19098809C2semidirect
9. #19098786C2semidirect
10. #19098727C2semidirect
11. #19098721C2semidirect
12. C4×Dic316C2semidirect
13. #19098573C2semidirect
14. #19098565C2semidirect
15. #436×C79C2semidirect
179. C79#3327semidirect
192. #436D79semidirect