Finite Group Databasebeta

← #23773671

Subgroups — #23773671

Order 10112.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099043C211yesmaximal, characteristic, complemented
2#19098891C211yesmaximal, characteristic, complemented
3#19098879C211yesmaximal, characteristic, complemented
4#19098850C211yesmaximal, characteristic, complemented
5#19098845C211yesmaximal, characteristic, complemented
6#19098782C211yesmaximal, characteristic, complemented
7#19098775C211yesmaximal, characteristic, complemented
8#19098723C211yesmaximal, characteristic, complemented
9#19098706C211yesmaximal, characteristic
10#19098673C211yesmaximal, characteristic, complemented
11#19098668C211yesmaximal, characteristic, complemented
12C4×#11929611C211yesmaximal, characteristic, complemented
13C4×#11929612C211yesmaximal, characteristic, complemented
14#19098624C211yesmaximal, characteristic, complemented
15#542×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C4×Dic158C2211yescharacteristic
22C4×Dic158C2211yescharacteristic
23C4×D316C2211yescharacteristic
24C4×D316C2211yescharacteristic
25(C22⋊D79)⋊C4—21no—
26(C22⋊D79)⋊C4—21no—
27#14579119—21no—
28C2×C4⋊Dic79C2211yescharacteristic
29C4⋊C4×D79—21no—
30#14579092C2211yescharacteristic
31#14579092C2211yescharacteristic
32#14579092C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35C4⋊(C79⋊C8)C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46#14579072C2211yescharacteristic
47C4×C79⋊C8C2211yescharacteristic
48C4⋊Q8×C79C2211yescharacteristic
49#126×C79—21no—
50#124×C79—21no—
51#124×C79C2211yescharacteristic
52#123×C79—21no—
53C22⋊Q8×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56C4×Q8×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58#117×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C22×Dic79—21no—
65C2×C4×D79—21no—
66C2×C4×D79—21no—
67C2×C4×D79—21no—
68#11929614—22no—
69#11929612—22no—
70#11929611—22no—
71#11929609—22no—
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C4⋊Dic79—21no—
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80Dic79⋊C4—21no—
81(C2×D79)⋊C4—21no—
82(C2×D79)⋊C4—21no—
83C4×Dic79—21no—
84C4×Dic79—21no—
85C2×Q8×C79—21no—
86C2×Q8×C79C2311yescharacteristic
87C2×D4×C79—21no—
88C2×D4×C79C2311yescharacteristic
89C22×C4×C79—21no—
90C22×C4×C79C2311yescharacteristic
91C4⋊C4×C79—21no—
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79D411yescharacteristic
95C4⋊C4×C79D411yescharacteristic
96C4⋊C4×C79C2311yescharacteristic
97C4⋊C4×C79C2311yescharacteristic
98C22⋊C4×C79—21no—
99C22⋊C4×C79—21no—
100C22⋊C4×C79—21no—
101C22⋊C4×C79—21no—
102C22⋊C4×C79—21no—
103C22⋊C4×C79D411yescharacteristic
104C22⋊C4×C79D411yescharacteristic
105C42×C79—21no—
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113Q8×C79—81no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—81no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—81no—
123C2×C4×C79C2×D411yescharacteristic
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2411yescharacteristic
129C22⋊D79—24no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134D316—21no—
135D316#4112yes—
136C4×D79—24no—
137C4×D79—81no—
138C4×D79—81no—
139Dic158—21no—
140Dic158#4112yes—
141C79⋊C8—21no—
142C79⋊C8—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—21no—
147C22×C79—21no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79C22×D411yescharacteristic
152C2×D79—22no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—21no—
156C4×C79—21no—
157C4×C79—21no—
158C4×C79—21no—
159C4×C79—21no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79C2×#4111yescharacteristic
164C4×C79C2×#4111yescharacteristic
165Dic79—22no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79—81no—
170C2×C79#52511yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57711yescharacteristic
173D79—42no—
174#3125—791nomaximal, Sylow
175C79#312511yescharacteristic, complemented, Sylow
176#542D7911yescharacteristic, complemented
177#520—791no—
178#483—791no—
179#481—791no—
180#476—791no—
181#475—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186#442—791no—
187#441—791no—
188C4×SD16—791no—
189C4×SD16—791no—
190#433—791no—
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8—791no—
196C4⋊Q8C2×D7911yescharacteristic
197#126—21no—
198#124—21no—
199#124C2×D7911yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C2×D7911yescharacteristic
203#121C2×D7911yescharacteristic
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8C2×D7911yescharacteristic
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—1581no—
210C4×D4—1581no—
211C4×D4C2×D7911yescharacteristic
212#117—1581no—
213#117C2×D7911yescharacteristic
214C2×C4⋊C4—791no—
215C2×C4⋊C4—1581no—
216#106—791no—
217#106—791no—
218#106—791no—
219#106—791no—
220C4⋊C8—791no—
221C4⋊C8—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103—791no—
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230C22⋊C8—791no—
231C22⋊C8—791no—
232#97—791no—
233C4×C8—791no—
234#41—1582no—
235#41—1582no—
236C2×Q8—21no—
237C2×Q8—791no—
238C2×Q8C22×D7911yescharacteristic
239C2×D4—21no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4C22×D7911yescharacteristic
243C22×C4—21no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249Q16—1582no—
250SD16—1582no—
251SD16—1582no—
252D8—1582no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8—791no—
256C2×C8—791no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4C22⋊D7911yescharacteristic
266C4⋊C4C22⋊D7911yescharacteristic
267C4⋊C4C22×D7911yescharacteristic
268C4⋊C4C22×D7911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4C22⋊D7911yescharacteristic
277C22⋊C4C22⋊D7911yescharacteristic
278C42—21no—
279C42—1581no—
280C42—1581no—
281C42C22×D7911yescharacteristic
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—1581no—
285C23C2×C22⋊D7911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—81no—
289Q8—792no—
290Q8—1581no—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—792no—
295D4—1584no—
296D4—1581no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—6321no—
304C2×C4—6321no—
305C2×C4—6321no—
306C2×C4—1584no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4C2×C22⋊D7911yescharacteristic
311C2×C4C2×C22⋊D7911yescharacteristic
312C2×C4C2×C22⋊D7911yescharacteristic
313C2×C4C2×C22⋊D7911yescharacteristic
314C2×C4C2×C22⋊D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—1581no—
317C8—1581no—
318C8—1581no—
319C8—1581no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3161no—
327C22—3161no—
328C22—1582no—
329C22C22×C22⋊D7911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—3161no—
339C4—3161no—
340C4—1582no—
341C4#41×D7911yescharacteristic
342C4#41×D7911yescharacteristic
343C2—41no—
344C2—81no—
345C2—3162no—
346C2#1909907011yescharacteristic
347C2#1909937111yescharacteristic
348C2#1909937411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#542×C79C2
socleC22×C79C22×D4
prime radical#19098706C2
hypercenter#542D79
hypocenterC79#3125
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #19099043C2semidirect
2. #19098891C2semidirect
3. #19098879C2semidirect
4. #19098850C2semidirect
5. #19098845C2semidirect
6. #19098782C2semidirect
7. #19098775C2semidirect
8. #19098723C2semidirect
10. #19098673C2semidirect
11. #19098668C2semidirect
12. C4×#11929611C2semidirect
13. C4×#11929612C2semidirect
14. #19098624C2semidirect
15. #542×C79C2semidirect
175. C79#3125semidirect
176. #542D79semidirect