Finite Group Databasebeta

← #23775662

Subgroups — #23775662

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#19099222C211yesmaximal, characteristic
2#19098920C211yesmaximal, characteristic, complemented
3#19098898C211yesmaximal, characteristic, complemented
4#19098887C211yesmaximal, characteristic, complemented
5#19098867C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098785C211yesmaximal, characteristic, complemented
9#19098723C211yesmaximal, characteristic, complemented
10#19098718C211yesmaximal, characteristic, complemented
11C4×#11929614C211yesmaximal, characteristic, complemented
12#19098641C211yesmaximal, characteristic, complemented
13#19098571C211yesmaximal, characteristic, complemented
14#19098562C211yesmaximal, characteristic, complemented
15#552×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929614C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C2×#11929608C2211yescharacteristic
23#14579149C2211yescharacteristic
24#14579147—21no—
25#14579140C2211yescharacteristic
26#14579139—21no—
27#14579135C2211yescharacteristic
28#14579133—21no—
29C4×Dic158C2211yescharacteristic
30(C22⋊D79)⋊C4—21no—
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579084C2211yescharacteristic
37#14579084C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44#14579081C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48#126×C79—21no—
49#125×C79—21no—
50#125×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53C22⋊Q8×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79C2211yescharacteristic
56#117×C79—21no—
57#117×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—41no—
61C2×Dic158—22no—
62C2×Dic158—21no—
63C2×Dic158—41no—
64C2×Dic158C2311yescharacteristic
65C2×Dic158C2311yescharacteristic
66C2×D316C2311yescharacteristic
67C2×C22⋊D79—21no—
68C2×C22⋊D79—21no—
69C22×Dic79—21no—
70C2×C4×D79—21no—
71#11929614—22no—
72#11929614—41no—
73#11929611—41no—
74#11929608—41no—
75#11929608—41no—
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C2×C79⋊C8C2311yescharacteristic
79C2×C79⋊C8C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87C4×Dic79—21no—
88C2×Q8×C79C2311yescharacteristic
89C2×D4×C79D411yescharacteristic
90C22×C4×C79—21no—
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
96C4⋊C4×C79—21no—
97C4⋊C4×C79—21no—
98C4⋊C4×C79—21no—
99C4⋊C4×C79D411yescharacteristic
100C4⋊C4×C79C2311yescharacteristic
101C4⋊C4×C79C2311yescharacteristic
102C4⋊C4×C79C2311yescharacteristic
103C22⋊C4×C79—21no—
104C22⋊C4×C79—21no—
105C22⋊C4×C79—21no—
106C22⋊C4×C79D411yescharacteristic
107C22⋊C4×C79D411yescharacteristic
108C42×C79—21no—
109C42×C79—21no—
110C42×C79C2311yescharacteristic
111C23×C79C2×D411yescharacteristic
112C23×C79C2×D411yescharacteristic
113C22×D79—21no—
114Q8×C79—21no—
115Q8×C79—21no—
116D4×C79—41no—
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—21no—
124C2×C4×C79—21no—
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—42no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—42no—
137D316—21no—
138D316—21no—
139C4×D79—42no—
140Dic158—21no—
141Dic158—21no—
142Dic158—21no—
143Dic158—42no—
144Dic158#4112yes—
145C79⋊C8—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C79⋊C8—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×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79—41no—
167C4×C79C2×#4111yescharacteristic
168C4×C79H(5,𝔽2)11yescharacteristic
169Dic79—22no—
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#552D7911yescharacteristic, complemented
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#436—791no—
193#419—791no—
194#417—791no—
195C2×#41—791no—
196C22×Q8—791no—
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×M16—791no—
201C2×M16—791no—
202#126—21no—
203#125—21no—
204#125C2×D7911yescharacteristic
205#124—791no—
206#124—1581no—
207#123—21no—
208C22⋊Q8—791no—
209C22⋊Q8—1581no—
210C22⋊Q8C2×D7911yescharacteristic
211C22⋊Q8C2×D7911yescharacteristic
212#121—791no—
213#121—1581no—
214C4×Q8—791no—
215C4×Q8C2×D7911yescharacteristic
216C4×D4—1581no—
217C4×D4C2×D7911yescharacteristic
218#117—21no—
219#117C2×D7911yescharacteristic
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#103—791no—
231#103—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235C22⋊C8—791no—
236C22⋊C8—791no—
237C4×C8—791no—
238#41—3161no—
239#41—1582no—
240C2×Q8—3161no—
241C2×Q8—791no—
242C2×Q8—791no—
243C2×Q8—1582no—
244C2×Q8—1581no—
245C2×Q8C22×D7911yescharacteristic
246C2×D4—791no—
247C2×D4—1581no—
248C2×D4—1581no—
249C2×D4C22⋊D7911yescharacteristic
250C22×C4—21no—
251C22×C4—1581no—
252C22×C4—1581no—
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255Q16—3161no—
256Q16—1582no—
257SD16—3161no—
258M16—3161no—
259M16—3161no—
260C2×C8—791no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8—791no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4C22⋊D7911yescharacteristic
274C4⋊C4C22×D7911yescharacteristic
275C4⋊C4C22×D7911yescharacteristic
276C4⋊C4C22×D7911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4C22⋊D7911yescharacteristic
285C22⋊C4C22⋊D7911yescharacteristic
286C42—21no—
287C42—21no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—1581no—
291C23C2×C22⋊D7911yescharacteristic
292C23C2×C22⋊D7911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—3162no—
296Q8—792no—
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—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—3162no—
315C2×C4—3162no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4C2×C22⋊D7911yescharacteristic
320C2×C4C2×C22⋊D7911yescharacteristic
321C2×C4C2×C22⋊D7911yescharacteristic
322C2×C4C2×C22⋊D7911yescharacteristic
323C2×C4C23×D7911yescharacteristic
324C8—1581no—
325C8—1581no—
326C8—1581no—
327C8—1581no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22C22×C22⋊D7911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—3161no—
347C4—3161no—
348C4—1582no—
349C4#41×D7911yescharacteristic
350C4#1457920711yescharacteristic
351C2—41no—
352C2—41no—
353C2—6321no—
354C2#1909920111yescharacteristic
355C2#1909936111yescharacteristic
356C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#552×C79C2
socleC22×C79C22×D4
prime radical#19099222C2
hypercenter#552D79
hypocenterC79#3327
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
2. #19098920C2semidirect
3. #19098898C2semidirect
4. #19098887C2semidirect
5. #19098867C2semidirect
6. #19098819C2semidirect
7. #19098811C2semidirect
8. #19098785C2semidirect
9. #19098723C2semidirect
10. #19098718C2semidirect
11. C4×#11929614C2semidirect
12. #19098641C2semidirect
13. #19098571C2semidirect
14. #19098562C2semidirect
15. #552×C79C2semidirect
179. C79#3327semidirect
180. #552D79semidirect