Finite Group Databasebeta

← #23773655

Subgroups — #23773655

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#19099180C211yesmaximal, characteristic, complemented
2#19099046C211yesmaximal, characteristic, complemented
3#19098899C211yesmaximal, characteristic, complemented
4#19098874C211yesmaximal, characteristic, complemented
5#19098856C211yesmaximal, characteristic, complemented
6#19098841C211yesmaximal, characteristic, complemented
7#19098783C211yesmaximal, characteristic, complemented
8#19098776C211yesmaximal, characteristic, complemented
9#19098725C211yesmaximal, characteristic, complemented
10#19098664C211yesmaximal, characteristic, complemented
11#19098660C211yesmaximal, characteristic, complemented
12#19098655C211yesmaximal, characteristic, complemented
13D8×Dic79C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#449×C79C211yesmaximal, characteristic
16C2×#11929614C2211yescharacteristic
17C2×#11929612C2211yescharacteristic
18#14579160C2211yescharacteristic
19#14579154—21no—
20#14579148—21no—
21#14579148C2211yescharacteristic
22#14579142—21no—
23#14579140C2211yescharacteristic
24#14579138—21no—
25Q8×Dic79C2211yescharacteristic
26Q8×Dic79C2211yescharacteristic
27#14579126C2211yescharacteristic
28D4×Dic79—21no—
29D4×Dic79—21no—
30D4×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32D4×Dic79C2211yescharacteristic
33#14579120—21no—
34#14579120C2211yescharacteristic
35C2×C4⋊Dic79—21no—
36C2×C4⋊Dic79C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579095C2211yescharacteristic
39#14579094C2211yescharacteristic
40#14579094C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579086C2211yescharacteristic
44#14579086C2211yescharacteristic
45#14579085C2211yescharacteristic
46#14579082C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C2×#41×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×D8×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#102×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×Dic158—21no—
60C2×Dic158C2311yescharacteristic
61C22×Dic79—21no—
62C22×Dic79—21no—
63C22×Dic79—21no—
64C22×Dic79—21no—
65#11929614—22no—
66#11929612—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C4⋊Dic79—21no—
70C4⋊Dic79—21no—
71C4⋊Dic79—21no—
72C4⋊Dic79D411yescharacteristic
73C4⋊Dic79D411yescharacteristic
74C4⋊Dic79C2311yescharacteristic
75C4⋊Dic79C2311yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77Dic79⋊C4—21no—
78Dic79⋊C4—21no—
79Dic79⋊C4—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79—21no—
83C22⋊Dic79—21no—
84C22⋊Dic79—21no—
85C22⋊Dic79—21no—
86C22⋊Dic79D411yescharacteristic
87C22⋊Dic79D411yescharacteristic
88C4×Dic79—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93#41×C79—22no—
94#41×C79—22no—
95C2×Q8×C79C2311yescharacteristic
96C2×D4×C79—21no—
97C2×D4×C79—21no—
98C2×D4×C79C2311yescharacteristic
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101C22×C4×C79C2311yescharacteristic
102SD16×C79—22no—
103D8×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—21no—
109C23×C79—21no—
110C23×C79C2×D411yescharacteristic
111Q8×C79—21no—
112Q8×C79#4112yes—
113D4×C79—24no—
114D4×C79—21no—
115D4×C79—21no—
116D4×C79—21no—
117D4×C79—81no—
118D4×C79#4112yes—
119C2×C4×C79—24no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79C2×D411yescharacteristic
125C2×C4×C79C2411yescharacteristic
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—81no—
131C2×Dic79—81no—
132C2×Dic79—81no—
133C2×Dic79—81no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138Dic158—21no—
139Dic158—21no—
140Dic158—81no—
141C8×C79—21no—
142C8×C79—21no—
143C79⋊C8—21no—
144C79⋊C8—21no—
145C22×C79—21no—
146C22×C79—22no—
147C22×C79—21no—
148C22×C79—21no—
149C22×C79—41no—
150C22×C79—41no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79C22×D411yescharacteristic
155C4×C79—21no—
156C4×C79—22no—
157C4×C79—41no—
158C4×C79C2×#4111yescharacteristic
159C4×C79C2×#4111yescharacteristic
160Dic79—21no—
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—41no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79—42no—
170C2×C79—81no—
171C2×C79#52511yescharacteristic
172C2×C79#57611yescharacteristic
173C2×C79#57811yescharacteristic
174#3124—791nomaximal, Sylow
175C79#312411yescharacteristic, complemented, Sylow
176#542—791no—
177#520—791no—
178#484—791no—
179#480—791no—
180#477—791no—
181#474—791no—
182#464—791no—
183#463—791no—
184#452—791no—
185#449D7911yescharacteristic
186#440—791no—
187#440—791no—
188C4×Q16—791no—
189C4×D8—791no—
190#433—791no—
191C2×#41C2×D7911yescharacteristic
192C2×Q16—791no—
193C2×SD16—791no—
194C2×SD16C2×D7911yescharacteristic
195C2×D8C2×D7911yescharacteristic
196C4⋊Q8—791no—
197#126—1581no—
198#124—791no—
199#124—1581no—
200#123—1581no—
201C22⋊Q8—791no—
202C22⋊Q8—1581no—
203#121C2×D7911yescharacteristic
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×D4—791no—
208C4×D4—791no—
209C4×D4—791no—
210C4×D4—1581no—
211C4×D4—1581no—
212#117—791no—
213#117—1581no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4—1581no—
216#107—791no—
217#107—791no—
218#107—791no—
219#107—791no—
220C4⋊C8—791no—
221C4⋊C8—791no—
222#103—791no—
223#103—791no—
224#103—791no—
225#103C2×D7911yescharacteristic
226#102—791no—
227#102—791no—
228#102—791no—
229#102C2×D7911yescharacteristic
230C22⋊C8—791no—
231C22⋊C8C2×D7911yescharacteristic
232#97—791no—
233C4×C8—791no—
234#41—22no—
235#41—22no—
236C2×Q8—791no—
237C2×Q8—1581no—
238C2×Q8C22×D7911yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C22×D7911yescharacteristic
242C2×D4C22×D7911yescharacteristic
243C22×C4—21no—
244C22×C4—1581no—
245C22×C4—1581no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249Q16—1582no—
250SD16—22no—
251SD16—1582no—
252D8—22no—
253C2×C8—791no—
254C2×C8—791no—
255C2×C8C22×D7911yescharacteristic
256C2×C8C22×D7911yescharacteristic
257C4⋊C4—791no—
258C4⋊C4—791no—
259C4⋊C4—791no—
260C4⋊C4—791no—
261C4⋊C4—791no—
262C4⋊C4—1581no—
263C4⋊C4—1581no—
264C4⋊C4—1581no—
265C4⋊C4—1581no—
266C4⋊C4—1581no—
267C4⋊C4—1581no—
268C4⋊C4C22×D7911yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—791no—
271C22⋊C4—791no—
272C22⋊C4—1581no—
273C22⋊C4—1581no—
274C22⋊C4—1581no—
275C22⋊C4—1581no—
276C22⋊C4—1581no—
277C22⋊C4—1581no—
278C42—791no—
279C42—791no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C23—21no—
284C23—21no—
285C23D4×D7911yescharacteristic
286Q8—21no—
287Q8—6321no—
288Q8—1581no—
289Q8—1581no—
290Q8#1192962312yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#1192962312yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—791no—
303C2×C4—791no—
304C2×C4—791no—
305C2×C4—791no—
306C2×C4—6321no—
307C2×C4—6321no—
308C2×C4—6321no—
309C2×C4—6321no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4D4×D7911yescharacteristic
315C2×C4C23×D7911yescharacteristic
316C8—21no—
317C8—21no—
318C8—1581no—
319C8—1581no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C2×D4×D7911yescharacteristic
330C4—21no—
331C4—22no—
332C4—41no—
333C4—3161no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—1581no—
338C4—1581no—
339C4—1581no—
340C4—1581no—
341C4C2×#1192962311yescharacteristic
342C4C2×#1192962311yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2#1909906911yescharacteristic
347C2#1909936711yescharacteristic
348C2#1909937711yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting, prime radical#449×C79C2
socleC22×C79C22×D4
hypercenter#449D79
hypocenterC79#3124
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #19099180C2semidirect
2. #19099046C2semidirect
3. #19098899C2semidirect
4. #19098874C2semidirect
5. #19098856C2semidirect
6. #19098841C2semidirect
7. #19098783C2semidirect
8. #19098776C2semidirect
9. #19098725C2semidirect
10. #19098664C2semidirect
11. #19098660C2semidirect
12. #19098655C2semidirect
13. D8×Dic79C2semidirect
14. #19098621C2semidirect
175. C79#3124semidirect