Finite Group Databasebeta

← #23774297

Subgroups — #23774297

Order 10112.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099141C211yesmaximal, characteristic, complemented
2#19098898C211yesmaximal, characteristic, complemented
3#19098896C211yesmaximal, characteristic, complemented
4#19098876C211yesmaximal, characteristic, complemented
5#19098874C211yesmaximal, characteristic, complemented
6#19098811C211yesmaximal, characteristic, complemented
7#19098807C211yesmaximal, characteristic, complemented
8#19098802C211yesmaximal, characteristic, complemented
9#19098797C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098723C211yesmaximal, characteristic, complemented
12#19098708C211yesmaximal, characteristic, complemented
13#19098706C211yesmaximal, characteristic, complemented
14#19098530C211yesmaximal, characteristic, complemented
15#537×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929609C2211yescharacteristic
21C2×#11929608C2211yescharacteristic
22C22×C79⋊C8C2211yescharacteristic
23#14579140C2211yescharacteristic
24#14579140C2211yescharacteristic
25#14579137—21no—
26#14579135C2211yescharacteristic
27#14579135C2211yescharacteristic
28#14579133—21no—
29#14579133—21no—
30#14579132—21no—
31C2×C4⋊Dic79C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579094C2211yescharacteristic
34#14579094C2211yescharacteristic
35#14579094C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579084C2211yescharacteristic
39#14579084C2211yescharacteristic
40#14579082C2211yescharacteristic
41#14579082C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C2×#41×C79C2211yescharacteristic
50C22⋊Q8×C79—21no—
51C22⋊Q8×C79C2211yescharacteristic
52C22⋊Q8×C79C2211yescharacteristic
53#121×C79—21no—
54#121×C79—21no—
55#121×C79—21no—
56#121×C79C2211yescharacteristic
57#121×C79C2211yescharacteristic
58C2×C4⋊C4×C79C2211yescharacteristic
59#11929624—41no—
60#11929624—41no—
61C2×Dic158C2311yescharacteristic
62C2×D316C2311yescharacteristic
63C2×C22⋊D79—21no—
64C2×C22⋊D79—21no—
65C2×C22⋊D79—21no—
66C22×Dic79—21no—
67C2×C4×D79—21no—
68#11929614—41no—
69#11929612—41no—
70#11929611—41no—
71#11929609—41no—
72#11929608—41no—
73C2×C79⋊C8—41no—
74C2×C79⋊C8C2311yescharacteristic
75C2×C79⋊C8C2311yescharacteristic
76C2×C79⋊C8C2311yescharacteristic
77C2×C79⋊C8C2311yescharacteristic
78C4⋊Dic79—21no—
79C4⋊Dic79C2311yescharacteristic
80C4⋊Dic79C2311yescharacteristic
81Dic79⋊C4—21no—
82Dic79⋊C4—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85(C2×D79)⋊C4—21no—
86(C2×D79)⋊C4—21no—
87#41×C79—41no—
88#41×C79—41no—
89#41×C79—41no—
90#41×C79—41no—
91C2×Q8×C79D411yescharacteristic
92C2×Q8×C79C2311yescharacteristic
93C2×D4×C79—21no—
94C2×D4×C79—21no—
95C2×D4×C79—21no—
96C2×D4×C79D411yescharacteristic
97C2×D4×C79D411yescharacteristic
98C2×D4×C79D411yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101C22×C4×C79—21no—
102C22×C4×C79C2311yescharacteristic
103C22×C4×C79C2311yescharacteristic
104C22×C4×C79C2311yescharacteristic
105C4⋊C4×C79—21no—
106C4⋊C4×C79—21no—
107C4⋊C4×C79—21no—
108C4⋊C4×C79C2311yescharacteristic
109C4⋊C4×C79C2311yescharacteristic
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C22⋊C4×C79—21no—
114C23×C79—21no—
115C23×C79C2×D411yescharacteristic
116C23×C79C2×D411yescharacteristic
117C23×C79C2×D411yescharacteristic
118C22×D79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—41no—
122D4×C79—21no—
123D4×C79—21no—
124D4×C79—41no—
125D4×C79—41no—
126D4×C79—41no—
127D4×C79—42no—
128D4×C79—81no—
129D4×C79—81no—
130C2×C4×C79—21no—
131C2×C4×C79—21no—
132C2×C4×C79—21no—
133C2×C4×C79—21no—
134C2×C4×C79—21no—
135C2×C4×C79—21no—
136C2×C4×C79—21no—
137C2×C4×C79—21no—
138C2×C4×C79—21no—
139C2×C4×C79—42no—
140C2×C4×C79—81no—
141C2×C4×C79C2×D411yescharacteristic
142C2×C4×C79C2×D411yescharacteristic
143C2×C4×C79C2×D411yescharacteristic
144C2×C4×C79C2411yescharacteristic
145C22⋊D79—42no—
146C22⋊D79—81no—
147C22⋊D79—81no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79—21no—
151C2×Dic79—81no—
152D316—21no—
153D316—21no—
154C4×D79—42no—
155Dic158—21no—
156Dic158—21no—
157C79⋊C8—21no—
158C79⋊C8—21no—
159C79⋊C8—21no—
160C79⋊C8—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79—21no—
168C22×C79—21no—
169C22×C79—21no—
170C22×C79—41no—
171C22×C79—41no—
172C22×C79—41no—
173C22×C79C22×D411yescharacteristic
174C2×D79—41no—
175C2×D79—41no—
176C2×D79—41no—
177C4×C79—21no—
178C4×C79—21no—
179C4×C79—21no—
180C4×C79—41no—
181C4×C79—41no—
182C4×C79—41no—
183C4×C79H(5,𝔽2)11yescharacteristic
184C4×C79H(5,𝔽2)11yescharacteristic
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79—41no—
189C2×C79—41no—
190C2×C79—41no—
191C2×C79—81no—
192C2×C79#53411yescharacteristic
193C2×C79#57611yescharacteristic
194C2×C79#57811yescharacteristic
195D79—81no—
196#3203—791nomaximal, Sylow
197C79#320311yescharacteristic, complemented, Sylow
198#537—791no—
199#537D7911yescharacteristic, complemented
200#484—791no—
201#484—791no—
202#480—791no—
203#480—791no—
204#468—791no—
205#468—791no—
206#467—791no—
207#466—791no—
208#452—791no—
209#452—791no—
210#449—791no—
211#449—791no—
212#408—791no—
213C2×#41—791no—
214C2×#41C2×D7911yescharacteristic
215C2×#41C2×D7911yescharacteristic
216C2×Q16—791no—
217C2×SD16—791no—
218C2×SD16—791no—
219C2×D8—791no—
220C2×M16—791no—
221C22×C8—791no—
222C22⋊Q8—21no—
223C22⋊Q8—791no—
224C22⋊Q8—791no—
225C22⋊Q8—1581no—
226C22⋊Q8C2×D7911yescharacteristic
227C22⋊Q8C2×D7911yescharacteristic
228#121—21no—
229#121—21no—
230#121—21no—
231#121—791no—
232#121—791no—
233#121—1581no—
234#121—1581no—
235#121—1581no—
236#121C2×D7911yescharacteristic
237#121C2×D7911yescharacteristic
238C2×C4⋊C4—791no—
239C2×C4⋊C4C2×D7911yescharacteristic
240#107—791no—
241#107—791no—
242#107—791no—
243#107—791no—
244#103—791no—
245#103—791no—
246#103—791no—
247#103—791no—
248#102—791no—
249#102—791no—
250#102—791no—
251#102—791no—
252C22⋊C8—791no—
253C22⋊C8—791no—
254C22⋊C8—791no—
255C22⋊C8—791no—
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—3161no—
261#41—3161no—
262C2×Q8—791no—
263C2×Q8C22⋊D7911yescharacteristic
264C2×Q8C22×D7911yescharacteristic
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—791no—
269C2×D4—1581no—
270C2×D4—1581no—
271C2×D4—1581no—
272C2×D4C22⋊D7911yescharacteristic
273C2×D4C22⋊D7911yescharacteristic
274C2×D4C22⋊D7911yescharacteristic
275C2×D4C22×D7911yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—1581no—
279C22×C4—1581no—
280C22×C4C22×D7911yescharacteristic
281C22×C4C22×D7911yescharacteristic
282C22×C4C22×D7911yescharacteristic
283Q16—3161no—
284SD16—3161no—
285SD16—3161no—
286D8—3161no—
287M16—3161no—
288C2×C8—3161no—
289C2×C8—791no—
290C2×C8—791no—
291C2×C8—791no—
292C2×C8—791no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—791no—
297C4⋊C4—791no—
298C4⋊C4—1581no—
299C4⋊C4—1581no—
300C4⋊C4—1581no—
301C4⋊C4C22×D7911yescharacteristic
302C4⋊C4C22×D7911yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—1581no—
308C22⋊C4—1581no—
309C22⋊C4—1581no—
310C22⋊C4—1581no—
311C23—21no—
312C23—1581no—
313C23C2×C22⋊D7911yescharacteristic
314C23C2×C22⋊D7911yescharacteristic
315C23C2×C22⋊D7911yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—41no—
319Q8—1581no—
320Q8—1581no—
321D4—21no—
322D4—21no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—3162no—
330D4—6321no—
331D4—6321no—
332D4—1581no—
333D4—1581no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—81no—
345C2×C4—3162no—
346C2×C4—6321no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4C2×C22⋊D7911yescharacteristic
351C2×C4C2×C22⋊D7911yescharacteristic
352C2×C4C2×C22⋊D7911yescharacteristic
353C2×C4C23×D7911yescharacteristic
354C8—1581no—
355C8—1581no—
356C8—1581no—
357C8—1581no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—3161no—
371C22—3161no—
372C22—3161no—
373C22C22×C22⋊D7911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4#1457920611yescharacteristic
384C4#1457920611yescharacteristic
385C2—41no—
386C2—41no—
387C2—41no—
388C2—81no—
389C2—6321no—
390C2#1909912211yescharacteristic
391C2#1909936611yescharacteristic
392C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#537×C79C2
socleC22×C79C22×D4
hypercenter#537D79
hypocenterC79#3203
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #19099141C2semidirect
2. #19098898C2semidirect
3. #19098896C2semidirect
4. #19098876C2semidirect
5. #19098874C2semidirect
6. #19098811C2semidirect
7. #19098807C2semidirect
8. #19098802C2semidirect
9. #19098797C2semidirect
10. #19098725C2semidirect
11. #19098723C2semidirect
12. #19098708C2semidirect
13. #19098706C2semidirect
14. #19098530C2semidirect
15. #537×C79C2semidirect
197. C79#3203semidirect
199. #537D79semidirect