Finite Group Databasebeta

← #23775496

Subgroups — #23775496

Order 10112.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19099253C211yesmaximal, characteristic, complemented
2#19098931C211yesmaximal, characteristic, complemented
3#19098901C211yesmaximal, characteristic, complemented
4#19098896C211yesmaximal, characteristic, complemented
5#19098863C211yesmaximal, characteristic, complemented
6#19098819C211yesmaximal, characteristic, complemented
7#19098802C211yesmaximal, characteristic, complemented
8#19098770C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098725C211yesmaximal, characteristic, complemented
11#19098663C211yesmaximal, characteristic, complemented
12#19098635C211yesmaximal, characteristic, complemented
13#19098564C211yesmaximal, characteristic, complemented
14#19098559C211yesmaximal, characteristic, complemented
15#547×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic
17C2×#11929614C2211yescharacteristic
18C2×#11929612C2211yescharacteristic
19C2×#11929608C2211yescharacteristic
20C22×C79⋊C8C2211yescharacteristic
21#14579154—21no—
22#14579153C2211yescharacteristic
23#14579151—21no—
24#14579142—21no—
25#14579140C2211yescharacteristic
26#14579140C2211yescharacteristic
27C4×Dic158C2211yescharacteristic
28#14579120C2211yescharacteristic
29#14579117—21no—
30C2×C4⋊Dic79C2211yescharacteristic
31#14579094C2211yescharacteristic
32#14579094C2211yescharacteristic
33#14579092C2211yescharacteristic
34C4⋊(C79⋊C8)C2211yescharacteristic
35#14579085C2211yescharacteristic
36#14579085C2211yescharacteristic
37#14579085C2211yescharacteristic
38#14579085C2211yescharacteristic
39#14579085C2211yescharacteristic
40#14579085C2211yescharacteristic
41#14579084C2211yescharacteristic
42#14579082C2211yescharacteristic
43#14579082C2211yescharacteristic
44#14579082C2211yescharacteristic
45C22⋊(C79⋊C8)C2211yescharacteristic
46C22⋊(C79⋊C8)C2211yescharacteristic
47#14579072C2211yescharacteristic
48C2×#41×C79C2211yescharacteristic
49C2×#41×C79C2211yescharacteristic
50C4⋊Q8×C79C2211yescharacteristic
51#123×C79—21no—
52#123×C79—21no—
53C22⋊Q8×C79C2211yescharacteristic
54C22⋊Q8×C79C2211yescharacteristic
55#121×C79—21no—
56C4×D4×C79C2211yescharacteristic
57C4×D4×C79C2211yescharacteristic
58C2×C4⋊C4×C79—21no—
59C2×Dic158C2311yescharacteristic
60C22×Dic79—21no—
61#11929614—41no—
62#11929614—41no—
63#11929612—22no—
64#11929608—41no—
65C2×C79⋊C8—41no—
66C2×C79⋊C8C2311yescharacteristic
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C2×C79⋊C8C2311yescharacteristic
70C4⋊Dic79—21no—
71C4⋊Dic79C2311yescharacteristic
72C4⋊Dic79C2311yescharacteristic
73C4⋊Dic79C2311yescharacteristic
74Dic79⋊C4—21no—
75Dic79⋊C4—21no—
76Dic79⋊C4—21no—
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79C22⋊Dic79—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C4×Dic79—21no—
83C4×Dic79—21no—
84#41×C79—22no—
85#41×C79—22no—
86#41×C79—41no—
87#41×C79—41no—
88C2×Q8×C79C2311yescharacteristic
89C2×Q8×C79C2311yescharacteristic
90C2×D4×C79—21no—
91C2×D4×C79—21no—
92C2×D4×C79D411yescharacteristic
93C2×D4×C79C2311yescharacteristic
94C22×C4×C79—21no—
95C22×C4×C79—21no—
96C22×C4×C79—21no—
97C22×C4×C79C2311yescharacteristic
98C22×C4×C79C2311yescharacteristic
99C4⋊C4×C79—21no—
100C4⋊C4×C79—21no—
101C4⋊C4×C79—21no—
102C4⋊C4×C79—21no—
103C4⋊C4×C79D411yescharacteristic
104C4⋊C4×C79C2311yescharacteristic
105C22⋊C4×C79—21no—
106C22⋊C4×C79—21no—
107C22⋊C4×C79—21no—
108C22⋊C4×C79D411yescharacteristic
109C22⋊C4×C79D411yescharacteristic
110C42×C79C2311yescharacteristic
111C23×C79—21no—
112C23×C79C2×D411yescharacteristic
113C23×C79C2×D411yescharacteristic
114Q8×C79—21no—
115Q8×C79—21no—
116Q8×C79—21no—
117Q8×C79—21no—
118D4×C79—21no—
119D4×C79—41no—
120D4×C79—42no—
121D4×C79—42no—
122D4×C79#4112yes—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79—21no—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79—21no—
129C2×C4×C79—21no—
130C2×C4×C79—42no—
131C2×C4×C79—42no—
132C2×C4×C79—42no—
133C2×C4×C79C2×D411yescharacteristic
134C2×C4×C79C2×D411yescharacteristic
135C2×C4×C79C2×D411yescharacteristic
136C2×C4×C79C2×D411yescharacteristic
137C2×C4×C79C2411yescharacteristic
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—42no—
143Dic158—21no—
144Dic158—21no—
145C79⋊C8—21no—
146C79⋊C8—21no—
147C79⋊C8—21no—
148C79⋊C8—21no—
149C22×C79—21no—
150C22×C79—21no—
151C22×C79—22no—
152C22×C79—21no—
153C22×C79—21no—
154C22×C79—21no—
155C22×C79—21no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C22×D411yescharacteristic
159C4×C79—21no—
160C4×C79—21no—
161C4×C79—21no—
162C4×C79—21no—
163C4×C79—41no—
164C4×C79—41no—
165C4×C79—41no—
166C4×C79C2×#4111yescharacteristic
167C4×C79H(5,𝔽2)11yescharacteristic
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171Dic79—41no—
172C2×C79—41no—
173C2×C79—41no—
174C2×C79—42no—
175C2×C79#54611yescharacteristic
176C2×C79#57511yescharacteristic
177C2×C79#57811yescharacteristic
178#3315—791nomaximal, Sylow
179C79#331511yescharacteristic, complemented, Sylow
180#552—791no—
181#547D7911yescharacteristic
182#491—791no—
183#485—791no—
184#484—791no—
185#478—791no—
186#470—791no—
187#467—791no—
188#462—791no—
189#452—791no—
190#452—791no—
191#440—791no—
192#435—791no—
193#417—791no—
194#416—791no—
195C2×#41C2×D7911yescharacteristic
196C2×#41C2×D7911yescharacteristic
197C2×Q16—791no—
198C2×Q16—791no—
199C2×SD16—791no—
200C2×M16—791no—
201C22×C8—791no—
202C4⋊Q8C2×D7911yescharacteristic
203#126—1581no—
204#125—791no—
205#125—1581no—
206#123—21no—
207#123—21no—
208#123—1581no—
209C22⋊Q8—791no—
210C22⋊Q8—791no—
211C22⋊Q8C2×D7911yescharacteristic
212C22⋊Q8C2×D7911yescharacteristic
213#121—21no—
214C4×Q8—791no—
215C4×D4C2×D7911yescharacteristic
216C4×D4C2×D7911yescharacteristic
217#117—791no—
218#117—1581no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—791no—
221#107—791no—
222#107—791no—
223#106—791no—
224C4⋊C8—791no—
225#103—791no—
226#103—791no—
227#103—791no—
228#103—791no—
229#103—791no—
230#103—791no—
231#103—791no—
232#102—791no—
233#102—791no—
234#102—791no—
235C22⋊C8—791no—
236C22⋊C8—791no—
237#97—791no—
238#41—22no—
239#41—22no—
240#41—41no—
241#41—41no—
242C2×Q8—791no—
243C2×Q8C22×D7911yescharacteristic
244C2×Q8C22×D7911yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4C22⋊D7911yescharacteristic
248C2×D4C22×D7911yescharacteristic
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1581no—
253C22×C4C22×D7911yescharacteristic
254C22×C4C22×D7911yescharacteristic
255Q16—3161no—
256Q16—3161no—
257SD16—1582no—
258M16—3161no—
259C2×C8—3161no—
260C2×C8—791no—
261C2×C8—791no—
262C2×C8—791no—
263C2×C8—791no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—791no—
269C4⋊C4—791no—
270C4⋊C4—791no—
271C4⋊C4—1581no—
272C4⋊C4—1581no—
273C4⋊C4—1581no—
274C4⋊C4—1581no—
275C4⋊C4—1581no—
276C4⋊C4—1581no—
277C4⋊C4C22⋊D7911yescharacteristic
278C4⋊C4C22×D7911yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—1581no—
283C22⋊C4—1581no—
284C22⋊C4—1581no—
285C22⋊C4C22⋊D7911yescharacteristic
286C22⋊C4C22⋊D7911yescharacteristic
287C42—1581no—
288C42—1581no—
289C42C22×D7911yescharacteristic
290C23—21no—
291C23C2×C22⋊D7911yescharacteristic
292C23C2×C22⋊D7911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—1581no—
298Q8—1581no—
299D4—21no—
300D4—41no—
301D4—42no—
302D4—42no—
303D4#1192962312yes—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—3162no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4C2×C22⋊D7911yescharacteristic
320C2×C4C2×C22⋊D7911yescharacteristic
321C2×C4C2×C22⋊D7911yescharacteristic
322C2×C4C2×C22⋊D7911yescharacteristic
323C2×C4C23×D7911yescharacteristic
324C8—1581no—
325C8—1581no—
326C8—1581no—
327C8—1581no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22C22×C22⋊D7911yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—3161no—
349C4C2×#1192962311yescharacteristic
350C4#1457920611yescharacteristic
351C2—41no—
352C2—41no—
353C2—42no—
354C2#1909920711yescharacteristic
355C2#1909936111yescharacteristic
356C2#1909937811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#547×C79C2
socleC22×C79C22×D4
hypercenter#547D79
hypocenterC79#3315
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #19099253C2semidirect
2. #19098931C2semidirect
3. #19098901C2semidirect
4. #19098896C2semidirect
5. #19098863C2semidirect
6. #19098819C2semidirect
7. #19098802C2semidirect
8. #19098770C2semidirect
9. #19098725C2semidirect
10. #19098725C2semidirect
11. #19098663C2semidirect
12. #19098635C2semidirect
13. #19098564C2semidirect
14. #19098559C2semidirect
179. C79#3315semidirect