Finite Group Databasebeta

← #23775507

Subgroups — #23775507

Order 10112.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099268C211yesmaximal, characteristic, complemented
2#19099224C211yesmaximal, characteristic
3#19098924C211yesmaximal, characteristic, complemented
4#19098892C211yesmaximal, characteristic, complemented
5#19098881C211yesmaximal, characteristic, complemented
6#19098846C211yesmaximal, characteristic, complemented
7#19098820C211yesmaximal, characteristic, complemented
8#19098792C211yesmaximal, characteristic, complemented
9#19098788C211yesmaximal, characteristic, complemented
10#19098728C211yesmaximal, characteristic, complemented
11#19098719C211yesmaximal, characteristic, complemented
12#19098667C211yesmaximal, characteristic, complemented
13#19098634C211yesmaximal, characteristic, complemented
14#19098563C211yesmaximal, characteristic, complemented
15C2×#103×C79C211yesmaximal, characteristic, complemented
16C2×#11929625C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929613C2211yescharacteristic
20C2×#11929607C2211yescharacteristic
21#14579160C2211yescharacteristic
22#14579151—21no—
23#14579150—21no—
24#14579150C2211yescharacteristic
25#14579141C2211yescharacteristic
26#14579140—21no—
27#14579140C2211yescharacteristic
28#14579139—21no—
29#14579137—21no—
30#14579137C2211yescharacteristic
31#14579135—21no—
32#14579135C2211yescharacteristic
33Q8×Dic79C2211yescharacteristic
34#14579126C2211yescharacteristic
35C4×C22⋊D79—21no—
36C4×C22⋊D79—21no—
37C4×C22⋊D79C2211yescharacteristic
38C4⋊C4×D79C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41#14579092C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579081C2211yescharacteristic
48#14579081C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50(C2×D79)⋊C8C2211yescharacteristic
51#14579071C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic
53C22×C8×C79C2211yescharacteristic
54C2×C4⋊C4×C79C2211yescharacteristic
55#103×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58#103×C79C2211yescharacteristic
59#11929625—22no—
60#11929625—41no—
61C2×Dic158—21no—
62C2×Dic158C2311yescharacteristic
63C2×D316—21no—
64C2×D316C2311yescharacteristic
65C2×C22⋊D79—21no—
66C2×C22⋊D79D411yescharacteristic
67C2×C4×D79—21no—
68C2×C4×D79—21no—
69C2×C4×D79C2311yescharacteristic
70#11929614—22no—
71#11929614—41no—
72#11929613—41no—
73#11929607—41no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
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×C79—21no—
104C22×C4×C79C2311yescharacteristic
105C2×C8×C79—41no—
106C2×C8×C79C2311yescharacteristic
107C2×C8×C79C2311yescharacteristic
108C4⋊C4×C79—21no—
109C4⋊C4×C79C2311yescharacteristic
110C4⋊C4×C79C2311yescharacteristic
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×C79—81no—
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—22no—
130C22⋊D79—42no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137D316—21no—
138D316—21no—
139D316—42no—
140C4×D79—21no—
141C4×D79—21no—
142C4×D79—42no—
143C4×D79—81no—
144Dic158—21no—
145Dic158—21no—
146Dic158—81no—
147C8×C79—21no—
148C8×C79—21no—
149C79⋊C8—21no—
150C79⋊C8—21no—
151C22×C79—21no—
152C22×C79—21no—
153C22×C79#13712yes—
154C22×C79C22×D411yescharacteristic
155C2×D79—21no—
156C2×D79—21no—
157C2×D79—21no—
158C2×D79—41no—
159C2×D79—41no—
160C2×D79—41no—
161C4×C79—21no—
162C4×C79—22no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79H(5,𝔽2)11yescharacteristic
168Dic79—21no—
169Dic79—21no—
170Dic79—21no—
171Dic79—41no—
172Dic79—41no—
173Dic79—41no—
174C2×C79—22no—
175C2×C79#54611yescharacteristic
176C2×C79C2×#13711yescharacteristic
177C2×C79#57711yescharacteristic
178D79—41no—
179D79—81no—
180#3316—791nomaximal, Sylow
181C79#331611yescharacteristic, complemented, Sylow
182#554—791no—
183#548—791no—
184#489—791no—
185#483—791no—
186#481—791no—
187#475—791no—
188#470—791no—
189#465—791no—
190#464—791no—
191#452—791no—
192#451—791no—
193#441—791no—
194#435—791no—
195#417—791no—
196C2×#103D7911yescharacteristic, complemented
197C2×#41—791no—
198C22×Q8C2×D7911yescharacteristic
199C2×Q16—791no—
200C2×Q16—791no—
201C2×SD16—791no—
202C2×M16—791no—
203C22×C8C2×D7911yescharacteristic
204C4⋊Q8—791no—
205#125—1581no—
206#124—791no—
207#124—1581no—
208C22⋊Q8—791no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8—1581no—
212C22⋊Q8—1581no—
213C22⋊Q8—1581no—
214#121—791no—
215#121—1581no—
216C4×Q8—791no—
217C4×Q8—791no—
218C4×D4—791no—
219C4×D4—1581no—
220C4×D4—1581no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4C2×D7911yescharacteristic
223#106—791no—
224#106—791no—
225#106—791no—
226C4⋊C8—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103C2×D7911yescharacteristic
231#103C2×D7911yescharacteristic
232#103C2×D7911yescharacteristic
233#103C2×D7911yescharacteristic
234#102—791no—
235#102—791no—
236#102—791no—
237C22⋊C8—791no—
238C22⋊C8—791no—
239#97—791no—
240#41—3161no—
241#41—1582no—
242C2×Q8—21no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—791no—
246C2×Q8—1581no—
247C2×Q8C22×D7911yescharacteristic
248C2×Q8C22×D7911yescharacteristic
249C2×D4—791no—
250C2×D4—791no—
251C2×D4—1581no—
252C2×D4—1581no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—791no—
256C22×C4—1581no—
257C22×C4—1581no—
258C22×C4C22×D7911yescharacteristic
259Q16—3161no—
260Q16—1582no—
261SD16—3161no—
262M16—3161no—
263C2×C8—41no—
264C2×C8—791no—
265C2×C8—791no—
266C2×C8C22×D7911yescharacteristic
267C2×C8C22×D7911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—791no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4—1581no—
278C4⋊C4—1581no—
279C4⋊C4C22×D7911yescharacteristic
280C4⋊C4C22×D7911yescharacteristic
281C22⋊C4—791no—
282C22⋊C4—791no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4—1581no—
286C22⋊C4—1581no—
287C22⋊C4—1581no—
288C22⋊C4—1581no—
289C42—791no—
290C42—1581no—
291C42—1581no—
292C23—791no—
293C23—1581no—
294C23D4×D7911yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—42no—
299Q8—6321no—
300Q8—1581no—
301Q8—1581no—
302Q8#1192962412yes—
303D4—3162no—
304D4—3162no—
305D4—1582no—
306D4—1581no—
307D4—1581no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—3162no—
317C2×C4—791no—
318C2×C4—791no—
319C2×C4—791no—
320C2×C4—6321no—
321C2×C4—1581no—
322C2×C4—1581no—
323C2×C4—1581no—
324C2×C4—1581no—
325C2×C4—1581no—
326C2×C4D4×D7911yescharacteristic
327C2×C4C23×D7911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1581no—
331C8—1581no—
332C22—21no—
333C22—21no—
334C22—3161no—
335C22—3161no—
336C22—3161no—
337C22—1581no—
338C22—1581no—
339C22—1581no—
340C22#1457919312yes—
341C22C2×D4×D7911yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—3161no—
348C4—3161no—
349C4—3161no—
350C4—1581no—
351C4—1581no—
352C4—1581no—
353C4C2×#1192962411yescharacteristic
354C4#1457920611yescharacteristic
355C2—22no—
356C2—3161no—
357C2—6321no—
358C2#1909920311yescharacteristic
359C2C2×#1457919311yescharacteristic
360C2#1909936911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
FittingC2×#103×C79C2
socleC22×C79C22×D4
prime radical#19099224C2
hypercenterC2×#103D79
hypocenterC79#3316
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #19099268C2semidirect
3. #19098924C2semidirect
4. #19098892C2semidirect
5. #19098881C2semidirect
6. #19098846C2semidirect
7. #19098820C2semidirect
8. #19098792C2semidirect
9. #19098788C2semidirect
10. #19098728C2semidirect
11. #19098719C2semidirect
12. #19098667C2semidirect
13. #19098634C2semidirect
14. #19098563C2semidirect
15. C2×#103×C79C2semidirect
181. C79#3316semidirect
196. C2×#103D79semidirect