Finite Group Databasebeta

← #23775664

Subgroups — #23775664

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#19099252C211yesmaximal, characteristic, complemented
2#19099224C211yesmaximal, characteristic
3#19098919C211yesmaximal, characteristic, complemented
4#19098897C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098872C211yesmaximal, characteristic, complemented
7#19098820C211yesmaximal, characteristic, complemented
8#19098809C211yesmaximal, characteristic, complemented
9#19098788C211yesmaximal, characteristic, complemented
10#19098728C211yesmaximal, characteristic, complemented
11#19098719C211yesmaximal, characteristic, complemented
12#19098655C211yesmaximal, characteristic, complemented
13#19098639C211yesmaximal, characteristic, complemented
14#19098563C211yesmaximal, characteristic, complemented
15#419×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929607C2211yescharacteristic
21#14579154—21no—
22#14579153—21no—
23#14579152C2211yescharacteristic
24#14579150—21no—
25#14579150C2211yescharacteristic
26#14579143—21no—
27#14579141C2211yescharacteristic
28#14579140C2211yescharacteristic
29#14579137—21no—
30#14579137C2211yescharacteristic
31#14579135—21no—
32#14579135C2211yescharacteristic
33Q8×Dic79C2211yescharacteristic
34#14579126C2211yescharacteristic
35C4×C22⋊D79—21no—
36C4×C22⋊D79C2211yescharacteristic
37#14579118—21no—
38C4⋊C4×D79C2211yescharacteristic
39#14579095C2211yescharacteristic
40#14579094C2211yescharacteristic
41#14579092C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic
53C2×M16×C79C2211yescharacteristic
54#117×C79C2211yescharacteristic
55#103×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic
59#11929625—22no—
60#11929625—41no—
61C2×Dic158C2311yescharacteristic
62C2×D316—21no—
63C2×D316C2311yescharacteristic
64C2×C22⋊D79—21no—
65C2×C22⋊D79D411yescharacteristic
66C2×C4×D79—21no—
67C2×C4×D79—21no—
68C2×C4×D79C2311yescharacteristic
69#11929614—22no—
70#11929614—41no—
71#11929613—41no—
72#11929607—41no—
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79—21no—
76C4⋊Dic79—21no—
77C4⋊Dic79—21no—
78C4⋊Dic79C2311yescharacteristic
79C4⋊Dic79C2311yescharacteristic
80Dic79⋊C4—21no—
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83Dic79⋊C4—21no—
84Dic79⋊C4—21no—
85Dic79⋊C4D411yescharacteristic
86C22⋊Dic79—21no—
87C22⋊Dic79D411yescharacteristic
88(C2×D79)⋊C4—21no—
89(C2×D79)⋊C4—21no—
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
97C2×Q8×C79—21no—
98C2×Q8×C79—22no—
99C2×Q8×C79—41no—
100C2×Q8×C79C2311yescharacteristic
101C2×Q8×C79C2311yescharacteristic
102C22×C4×C79—21no—
103C22×C4×C79C2311yescharacteristic
104M16×C79—41no—
105C2×C8×C79C2311yescharacteristic
106C2×C8×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C4⋊C4×C79C2311yescharacteristic
109C22⋊C4×C79—21no—
110C42×C79—21no—
111C23×C79C2×D411yescharacteristic
112C22×D79—21no—
113C22×D79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—42no—
118Q8×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—21no—
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×Dic79C2×D411yescharacteristic
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136D316—21no—
137D316—21no—
138D316—42no—
139C4×D79—21no—
140C4×D79—21no—
141C4×D79—42no—
142C4×D79—42no—
143Dic158—21no—
144Dic158—21no—
145C8×C79—21no—
146C8×C79—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—21no—
152C22×C79C22×D411yescharacteristic
153C2×D79—21no—
154C2×D79—21no—
155C2×D79—21no—
156C2×D79—41no—
157C2×D79—41no—
158C2×D79—41no—
159C4×C79—21no—
160C4×C79—22no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164C4×C79C2×#4111yescharacteristic
165C4×C79H(5,𝔽2)11yescharacteristic
166Dic79—21no—
167Dic79—21no—
168Dic79—21no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172C2×C79—41no—
173C2×C79#54611yescharacteristic
174C2×C79#57511yescharacteristic
175C2×C79#57811yescharacteristic
176D79—41no—
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#436—791no—
193#419D7911yescharacteristic, complemented
194#417—791no—
195C2×#41—791no—
196C22×Q8C2×D7911yescharacteristic
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×M16—791no—
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—791no—
217C4×D4—1581no—
218#117—1581no—
219#117C2×D7911yescharacteristic
220C2×C4⋊C4—791no—
221#107—791no—
222#107—791no—
223#106—791no—
224C4⋊C8—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103C2×D7911yescharacteristic
229#103C2×D7911yescharacteristic
230#103C2×D7911yescharacteristic
231#103C2×D7911yescharacteristic
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—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—791no—
244C2×Q8C22×D7911yescharacteristic
245C2×Q8C22×D7911yescharacteristic
246C2×D4—791no—
247C2×D4—791no—
248C2×D4—1581no—
249C2×D4—1581no—
250C22×C4—21no—
251C22×C4—791no—
252C22×C4—1581no—
253C22×C4—1581no—
254C22×C4C22×D7911yescharacteristic
255Q16—3161no—
256Q16—1582no—
257SD16—3161no—
258M16—41no—
259M16—3161no—
260C2×C8—791no—
261C2×C8—791no—
262C2×C8C22×D7911yescharacteristic
263C2×C8C22×D7911yescharacteristic
264C4⋊C4—791no—
265C4⋊C4—791no—
266C4⋊C4—791no—
267C4⋊C4—1581no—
268C4⋊C4—1581no—
269C4⋊C4—1581no—
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—791no—
279C22⋊C4—791no—
280C22⋊C4—1581no—
281C22⋊C4—1581no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C42—21no—
287C42—791no—
288C42—1581no—
289C42—1581no—
290C23—791no—
291C23—1581no—
292C23D4×D7911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—1581no—
298Q8—1581no—
299Q8#1192962412yes—
300D4—3162no—
301D4—3162no—
302D4—3161no—
303D4—1581no—
304D4—1581no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—3162no—
313C2×C4—3162no—
314C2×C4—791no—
315C2×C4—791no—
316C2×C4—791no—
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—21no—
330C22—21no—
331C22—3161no—
332C22—3161no—
333C22—3161no—
334C22—1581no—
335C22—1581no—
336C22—1581no—
337C22C2×D4×D7911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—1581no—
347C4—1581no—
348C4—1581no—
349C4C2×#1192962411yescharacteristic
350C4#1457920611yescharacteristic
351C2—41no—
352C2—3161no—
353C2—6321no—
354C2#1909920311yescharacteristic
355C2#1909936211yescharacteristic
356C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#419×C79C2
socleC22×C79C22×D4
prime radical#19099224C2
hypercenter#419D79
hypocenterC79#3327
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #19099252C2semidirect
3. #19098919C2semidirect
4. #19098897C2semidirect
5. #19098887C2semidirect
6. #19098872C2semidirect
7. #19098820C2semidirect
8. #19098809C2semidirect
9. #19098788C2semidirect
10. #19098728C2semidirect
11. #19098719C2semidirect
12. #19098655C2semidirect
13. #19098639C2semidirect
14. #19098563C2semidirect
15. #419×C79C2semidirect
179. C79#3327semidirect
193. #419D79semidirect