Finite Group Databasebeta

← #23773503

Subgroups — #23773503

Order 10112.

392 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
1C4×#11929624C211yesmaximal, characteristic, complemented
2#19098901C211yesmaximal, characteristic, complemented
3#19098884C211yesmaximal, characteristic, complemented
4#19098867C211yesmaximal, characteristic, complemented
5#19098860C211yesmaximal, 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
12#19098663C211yesmaximal, characteristic, complemented
13#19098661C211yesmaximal, characteristic, complemented
14#19098620C211yesmaximal, characteristic, complemented
15#529×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C4×Dic158C2211yescharacteristic
22C4×Dic158C2211yescharacteristic
23C4×D316C2211yescharacteristic
24C4×D316C2211yescharacteristic
25C4×C22⋊D79—21no—
26C4×C22⋊D79—21no—
27#14579120C2211yescharacteristic
28#14579118—21no—
29C42×D79—21no—
30#14579094C2211yescharacteristic
31#14579094C2211yescharacteristic
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
47#14579072C2211yescharacteristic
48#126×C79—21no—
49#125×C79C2211yescharacteristic
50#124×C79C2211yescharacteristic
51#123×C79—21no—
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79C2211yescharacteristic
54C4×Q8×C79C2211yescharacteristic
55C4×D4×C79—21no—
56C4×D4×C79C2211yescharacteristic
57#117×C79—21no—
58C2×C42×C79C2211yescharacteristic
59#11929624—22no—
60#11929624—22no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C4×D79—21no—
65C2×C4×D79—21no—
66C2×C4×D79—21no—
67#11929614—22no—
68#11929612—22no—
69#11929611—22no—
70#11929609—22no—
71C2×C79⋊C8C2311yescharacteristic
72C2×C79⋊C8C2311yescharacteristic
73C2×C79⋊C8C2311yescharacteristic
74C2×C79⋊C8C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80(C2×D79)⋊C4—21no—
81(C2×D79)⋊C4—21no—
82C4×Dic79—21no—
83C4×Dic79—21no—
84C4×Dic79—21no—
85C2×Q8×C79C2311yescharacteristic
86C2×D4×C79—21no—
87C2×D4×C79C2311yescharacteristic
88C22×C4×C79—21no—
89C22×C4×C79D411yescharacteristic
90C22×C4×C79D411yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C4⋊C4×C79—21no—
93C4⋊C4×C79—21no—
94C4⋊C4×C79—21no—
95C4⋊C4×C79—21no—
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—
103C42×C79—21no—
104C42×C79D411yescharacteristic
105C42×C79D411yescharacteristic
106C42×C79C2311yescharacteristic
107C42×C79C2311yescharacteristic
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—21no—
112Q8×C79—21no—
113D4×C79—21no—
114D4×C79—21no—
115D4×C79—42no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—41no—
122C2×C4×C79—41no—
123C2×C4×C79—42no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2×D411yescharacteristic
127C2×C4×C79C2×D411yescharacteristic
128C2×C4×C79C2×D411yescharacteristic
129C2×C4×C79C2411yescharacteristic
130C22⋊D79—24no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134D316—21no—
135D316#4112yes—
136C4×D79—24no—
137C4×D79—42no—
138C4×D79—42no—
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#57511yescharacteristic
172C2×C79#57511yescharacteristic
173D79—42no—
174#3111—791nomaximal, Sylow
175C79#311111yescharacteristic, complemented, Sylow
176#529D7911yescharacteristic, complemented
177C4×#41—791no—
178#485—791no—
179#482—791no—
180#479—791no—
181#478—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449—791no—
186#442—791no—
187#441—791no—
188#440—791no—
189#440—791no—
190#432—791no—
191C2×#41—791no—
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16—791no—
195C2×D8—791no—
196#126—21no—
197#125C2×D7911yescharacteristic
198#124C2×D7911yescharacteristic
199#123—21no—
200C22⋊Q8C2×D7911yescharacteristic
201#121C2×D7911yescharacteristic
202C4×Q8—791no—
203C4×Q8—791no—
204C4×Q8C2×D7911yescharacteristic
205C4×D4—21no—
206C4×D4—791no—
207C4×D4—791no—
208C4×D4—1581no—
209C4×D4—1581no—
210C4×D4C2×D7911yescharacteristic
211#117—21no—
212#117—791no—
213#117—1581no—
214C2×C42—1581no—
215C2×C42C2×D7911yescharacteristic
216#107—791no—
217#107—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—
233#97—791no—
234#41—1582no—
235#41—1582no—
236C2×Q8—791no—
237C2×Q8C22×D7911yescharacteristic
238C2×D4—21no—
239C2×D4—791no—
240C2×D4—1581no—
241C2×D4C22×D7911yescharacteristic
242C22×C4—21no—
243C22×C4—1581no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4C22⋊D7911yescharacteristic
247C22×C4C22⋊D7911yescharacteristic
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—21no—
261C4⋊C4—791no—
262C4⋊C4—791no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4C22×D7911yescharacteristic
266C4⋊C4C22×D7911yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C42—21no—
276C42—1581no—
277C42—1581no—
278C42—1581no—
279C42C22⋊D7911yescharacteristic
280C42C22⋊D7911yescharacteristic
281C42C22×D7911yescharacteristic
282C42C22×D7911yescharacteristic
283C23—21no—
284C23—1581no—
285C23C2×C22⋊D7911yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—792no—
289Q8—1581no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—792no—
294D4—1584no—
295D4—1581no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—3162no—
305C2×C4—3162no—
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#1909936111yescharacteristic
348C2#1909936111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#529×C79C2
socleC22×C79C22×D4
prime radical#19098706C2
hypercenter#529D79
hypocenterC79#3111
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C4×#11929624C2semidirect
2. #19098901C2semidirect
3. #19098884C2semidirect
4. #19098867C2semidirect
5. #19098860C2semidirect
6. #19098782C2semidirect
7. #19098775C2semidirect
8. #19098723C2semidirect
10. #19098673C2semidirect
11. #19098668C2semidirect
12. #19098663C2semidirect
13. #19098661C2semidirect
14. #19098620C2semidirect
15. #529×C79C2semidirect
175. C79#3111semidirect
176. #529D79semidirect