Finite Group Databasebeta

← #23774282

Subgroups — #23774282

Order 10112.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099141C211yesmaximal, characteristic
2#19098904C211yesmaximal, characteristic, complemented
3#19098896C211yesmaximal, characteristic, complemented
4#19098891C211yesmaximal, characteristic, complemented
5#19098887C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098811C211yesmaximal, characteristic, complemented
8#19098802C211yesmaximal, characteristic, complemented
9#19098794C211yesmaximal, characteristic, complemented
10#19098723C211yesmaximal, characteristic, complemented
11#19098723C211yesmaximal, characteristic, complemented
12#19098719C211yesmaximal, characteristic, complemented
13#19098702C211yesmaximal, characteristic, complemented
14#19098530C211yesmaximal, characteristic, complemented
15#536×C79C211yesmaximal, characteristic, complemented
16C2×#11929624C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929614C2211yescharacteristic
19C2×#11929611C2211yescharacteristic
20C2×#11929611C2211yescharacteristic
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#14579092C2211yescharacteristic
35#14579092C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579084C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579081C2211yescharacteristic
43#14579081C2211yescharacteristic
44C22⋊(C79⋊C8)C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47C22⋊(C79⋊C8)C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C22×Q8×C79C2211yescharacteristic
50C4⋊Q8×C79—21no—
51#124×C79—21no—
52#123×C79—21no—
53#123×C79—21no—
54C22⋊Q8×C79C2211yescharacteristic
55C22⋊Q8×C79C2211yescharacteristic
56C22⋊Q8×C79C2211yescharacteristic
57C22⋊Q8×C79C2211yescharacteristic
58#117×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#11929614—41no—
70#11929611—41no—
71#11929611—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—
89C2×Q8×C79—21no—
90C2×Q8×C79—41no—
91C2×Q8×C79—41no—
92C2×Q8×C79D411yescharacteristic
93C2×Q8×C79C2311yescharacteristic
94C2×Q8×C79C2311yescharacteristic
95C2×D4×C79D411yescharacteristic
96C2×D4×C79D411yescharacteristic
97C2×D4×C79D411yescharacteristic
98C22×C4×C79—21no—
99C22×C4×C79C2311yescharacteristic
100C22×C4×C79C2311yescharacteristic
101C22×C4×C79C2311yescharacteristic
102C4⋊C4×C79—21no—
103C4⋊C4×C79—21no—
104C4⋊C4×C79—21no—
105C4⋊C4×C79—21no—
106C4⋊C4×C79C2311yescharacteristic
107C4⋊C4×C79C2311yescharacteristic
108C22⋊C4×C79—21no—
109C22⋊C4×C79—21no—
110C22⋊C4×C79—21no—
111C22⋊C4×C79—21no—
112C22⋊C4×C79—21no—
113C42×C79—21no—
114C23×C79C2×D411yescharacteristic
115C23×C79C2×D411yescharacteristic
116C23×C79C2×D411yescharacteristic
117C22×D79—21no—
118Q8×C79—21no—
119Q8×C79—21no—
120Q8×C79—21no—
121Q8×C79—21no—
122Q8×C79—41no—
123Q8×C79—42no—
124D4×C79—41no—
125D4×C79—41no—
126D4×C79—41no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
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—42no—
138C2×C4×C79C2×D411yescharacteristic
139C2×C4×C79C2×D411yescharacteristic
140C2×C4×C79C2×D411yescharacteristic
141C2×C4×C79C2411yescharacteristic
142C22⋊D79—42no—
143C22⋊D79—81no—
144C22⋊D79—81no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—81no—
149D316—21no—
150D316—21no—
151C4×D79—42no—
152Dic158—21no—
153Dic158—21no—
154C79⋊C8—21no—
155C79⋊C8—21no—
156C79⋊C8—21no—
157C79⋊C8—21no—
158C22×C79—21no—
159C22×C79—21no—
160C22×C79—21no—
161C22×C79—21no—
162C22×C79—21no—
163C22×C79—21no—
164C22×C79—21no—
165C22×C79—21no—
166C22×C79—21no—
167C22×C79C22×D411yescharacteristic
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C4×C79—21no—
172C4×C79—21no—
173C4×C79—21no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178C4×C79H(5,𝔽2)11yescharacteristic
179C4×C79H(5,𝔽2)11yescharacteristic
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183C2×C79—41no—
184C2×C79—41no—
185C2×C79—41no—
186C2×C79#53411yescharacteristic
187C2×C79#57711yescharacteristic
188C2×C79#57811yescharacteristic
189D79—81no—
190#3201—791nomaximal, Sylow
191C79#320111yescharacteristic, complemented, Sylow
192#537—791no—
193#536D7911yescharacteristic, complemented
194#485—791no—
195#484—791no—
196#483—791no—
197#482—791no—
198#470—791no—
199#468—791no—
200#467—791no—
201#465—791no—
202#452—791no—
203#452—791no—
204#451—791no—
205#448—791no—
206#408—791no—
207C2×#41—791no—
208C2×#41C2×D7911yescharacteristic
209C22×Q8C2×D7911yescharacteristic
210C2×Q16—791no—
211C2×Q16—791no—
212C2×SD16—791no—
213C2×SD16—791no—
214C2×M16—791no—
215C22×C8—791no—
216C4⋊Q8—21no—
217#124—21no—
218#123—21no—
219#123—21no—
220C22⋊Q8—791no—
221C22⋊Q8—791no—
222C22⋊Q8—1581no—
223C22⋊Q8C2×D7911yescharacteristic
224C22⋊Q8C2×D7911yescharacteristic
225C22⋊Q8C2×D7911yescharacteristic
226C22⋊Q8C2×D7911yescharacteristic
227#121—791no—
228#121—791no—
229#121—1581no—
230#121—1581no—
231#121—1581no—
232#117C2×D7911yescharacteristic
233C2×C4⋊C4—791no—
234#107—791no—
235#107—791no—
236#106—791no—
237#106—791no—
238#103—791no—
239#103—791no—
240#103—791no—
241#103—791no—
242#103—791no—
243#103—791no—
244#102—791no—
245#102—791no—
246C22⋊C8—791no—
247C22⋊C8—791no—
248C22⋊C8—791no—
249C22⋊C8—791no—
250#41—41no—
251#41—41no—
252#41—3161no—
253#41—3161no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—791no—
258C2×Q8C22⋊D7911yescharacteristic
259C2×Q8C22×D7911yescharacteristic
260C2×Q8C22×D7911yescharacteristic
261C2×D4—791no—
262C2×D4—1581no—
263C2×D4—1581no—
264C2×D4—1581no—
265C2×D4C22⋊D7911yescharacteristic
266C2×D4C22⋊D7911yescharacteristic
267C2×D4C22⋊D7911yescharacteristic
268C22×C4—21no—
269C22×C4—1581no—
270C22×C4—1581no—
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C22×C4C22×D7911yescharacteristic
274Q16—3161no—
275Q16—3161no—
276SD16—3161no—
277SD16—3161no—
278M16—3161no—
279C2×C8—3161no—
280C2×C8—791no—
281C2×C8—791no—
282C2×C8—791no—
283C2×C8—791no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—791no—
289C4⋊C4—791no—
290C4⋊C4—1581no—
291C4⋊C4—1581no—
292C4⋊C4—1581no—
293C4⋊C4C22×D7911yescharacteristic
294C4⋊C4C22×D7911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1581no—
301C22⋊C4—1581no—
302C22⋊C4—1581no—
303C22⋊C4—1581no—
304C42—21no—
305C23—1581no—
306C23C2×C22⋊D7911yescharacteristic
307C23C2×C22⋊D7911yescharacteristic
308C23C2×C22⋊D7911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—21no—
312Q8—21no—
313Q8—41no—
314Q8—42no—
315Q8—1581no—
316Q8—1581no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—3162no—
321D4—6321no—
322D4—6321no—
323D4—1581no—
324D4—1581no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—3162no—
337C2×C4—6321no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4C2×C22⋊D7911yescharacteristic
342C2×C4C2×C22⋊D7911yescharacteristic
343C2×C4C2×C22⋊D7911yescharacteristic
344C2×C4C23×D7911yescharacteristic
345C8—1581no—
346C8—1581no—
347C8—1581no—
348C8—1581no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—3161no—
359C22—3161no—
360C22—3161no—
361C22C22×C22⋊D7911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3161no—
370C4—3161no—
371C4—3161no—
372C4#1457920611yescharacteristic
373C4#1457920611yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—6321no—
378C2#1909912211yescharacteristic
379C2#1909937111yescharacteristic
380C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#536×C79C2
socleC22×C79C22×D4
prime radical#19099141C2
hypercenter#536D79
hypocenterC79#3201
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #19098904C2semidirect
3. #19098896C2semidirect
4. #19098891C2semidirect
5. #19098887C2semidirect
6. #19098819C2semidirect
7. #19098811C2semidirect
8. #19098802C2semidirect
9. #19098794C2semidirect
10. #19098723C2semidirect
11. #19098723C2semidirect
12. #19098719C2semidirect
13. #19098702C2semidirect
14. #19098530C2semidirect
15. #536×C79C2semidirect
191. C79#3201semidirect
193. #536D79semidirect