Finite Group Databasebeta

← #23773685

Subgroups — #23773685

Order 10112.

382 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#19099166C211yesmaximal, characteristic
2#19099041C211yesmaximal, characteristic, complemented
3#19098888C211yesmaximal, characteristic, complemented
4#19098884C211yesmaximal, characteristic, complemented
5#19098872C211yesmaximal, characteristic, complemented
6#19098868C211yesmaximal, characteristic, complemented
7#19098761C211yesmaximal, characteristic, complemented
8#19098761C211yesmaximal, characteristic, complemented
9#19098702C211yesmaximal, characteristic, complemented
10#19098666C211yesmaximal, characteristic, complemented
11#19098664C211yesmaximal, characteristic, complemented
12SD16×Dic79C211yesmaximal, characteristic, complemented
13#19098648C211yesmaximal, characteristic, complemented
14#19098621C211yesmaximal, characteristic, complemented
15#448×C79C211yesmaximal, characteristic, complemented
16C2×#11929611C2211yescharacteristic
17C2×#11929611C2211yescharacteristic
18#14579157C2211yescharacteristic
19#14579152C2211yescharacteristic
20#14579145—21no—
21#14579143—21no—
22#14579135C2211yescharacteristic
23#14579133—21no—
24#14579132—21no—
25Q8×Dic79—21no—
26Q8×Dic79—21no—
27Q8×Dic79C2211yescharacteristic
28Q8×Dic79C2211yescharacteristic
29Q8×Dic79C2211yescharacteristic
30Q8×Dic79C2211yescharacteristic
31D4×Dic79C2211yescharacteristic
32#14579123C2211yescharacteristic
33#14579120—21no—
34#14579120—21no—
35#14579120C2211yescharacteristic
36#14579120C2211yescharacteristic
37#14579095C2211yescharacteristic
38#14579094C2211yescharacteristic
39#14579093C2211yescharacteristic
40#14579092C2211yescharacteristic
41Dic79⋊C8C2211yescharacteristic
42Dic79⋊C8C2211yescharacteristic
43#14579085C2211yescharacteristic
44#14579085C2211yescharacteristic
45#14579083C2211yescharacteristic
46#14579083C2211yescharacteristic
47#14579082C2211yescharacteristic
48#14579082C2211yescharacteristic
49C22⋊(C79⋊C8)C2211yescharacteristic
50#14579071C2211yescharacteristic
51C8×Dic79C2211yescharacteristic
52C22×Q8×C79C2211yescharacteristic
53C2×SD16×C79C2211yescharacteristic
54C2×SD16×C79C2211yescharacteristic
55#121×C79C2211yescharacteristic
56#103×C79C2211yescharacteristic
57#103×C79C2211yescharacteristic
58C22⋊C8×C79C2211yescharacteristic
59C2×D316C2311yescharacteristic
60C2×C22⋊D79—21no—
61C2×C22⋊D79—21no—
62C2×C22⋊D79—21no—
63C22×Dic79—21no—
64C2×C4×D79—21no—
65#11929611—22no—
66#11929611—22no—
67C2×C79⋊C8C2311yescharacteristic
68C2×C79⋊C8C2311yescharacteristic
69C4⋊Dic79—21no—
70C4⋊Dic79—21no—
71C4⋊Dic79—21no—
72C4⋊Dic79—21no—
73C4⋊Dic79—21no—
74C4⋊Dic79D411yescharacteristic
75C4⋊Dic79D411yescharacteristic
76C4⋊Dic79C2311yescharacteristic
77C4⋊Dic79C2311yescharacteristic
78C4⋊Dic79C2311yescharacteristic
79Dic79⋊C4—21no—
80C22⋊Dic79—21no—
81C22⋊Dic79—21no—
82C22⋊Dic79D411yescharacteristic
83C22⋊Dic79D411yescharacteristic
84(C2×D79)⋊C4—21no—
85(C2×D79)⋊C4—21no—
86C4×Dic79—21no—
87C4×Dic79—21no—
88C4×Dic79—21no—
89C4×Dic79—21no—
90C4×Dic79—21no—
91C4×Dic79C2311yescharacteristic
92C4×Dic79C2311yescharacteristic
93C2×Q8×C79—22no—
94C2×Q8×C79—22no—
95C2×Q8×C79—21no—
96C2×Q8×C79C2311yescharacteristic
97C2×Q8×C79C2311yescharacteristic
98C2×D4×C79—21no—
99C2×D4×C79C2311yescharacteristic
100C22×C4×C79—21no—
101C22×C4×C79C2311yescharacteristic
102SD16×C79—22no—
103SD16×C79—22no—
104C2×C8×C79C2311yescharacteristic
105C2×C8×C79C2311yescharacteristic
106C4⋊C4×C79C2311yescharacteristic
107C22⋊C4×C79—21no—
108C23×C79—21no—
109C23×C79C2×D411yescharacteristic
110C22×D79—21no—
111Q8×C79—24no—
112Q8×C79—21no—
113Q8×C79—21no—
114Q8×C79#4112yes—
115Q8×C79#4112yes—
116D4×C79—21no—
117D4×C79—21no—
118D4×C79—81no—
119C2×C4×C79—24no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
123C2×C4×C79—21no—
124C2×C4×C79—21no—
125C2×C4×C79C2×D411yescharacteristic
126C2×C4×C79C2411yescharacteristic
127C22⋊D79—81no—
128C22⋊D79—81no—
129C22⋊D79—81no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—81no—
134C2×Dic79C2×D411yescharacteristic
135C2×Dic79C2×D411yescharacteristic
136C2×Dic79C2×D411yescharacteristic
137C2×Dic79C2×D411yescharacteristic
138D316—21no—
139D316—21no—
140C4×D79—81no—
141C8×C79—21no—
142C8×C79—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—41no—
153C2×D79—41no—
154C2×D79—41no—
155C4×C79—22no—
156C4×C79—22no—
157C4×C79—21no—
158C4×C79—41no—
159C4×C79C2×#4111yescharacteristic
160C4×C79C2×#4111yescharacteristic
161Dic79—21no—
162Dic79—21no—
163Dic79—21no—
164Dic79—21no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168C2×C79—41no—
169C2×C79—81no—
170C2×C79#52511yescharacteristic
171C2×C79#57711yescharacteristic
172C2×C79#57711yescharacteristic
173D79—81no—
174#3126—791nomaximal, Sylow
175C79#312611yescharacteristic, complemented, Sylow
176#540—791no—
177#519—791no—
178#482—791no—
179#482—791no—
180#479—791no—
181#479—791no—
182#460—791no—
183#460—791no—
184#448—791no—
185#448D7911yescharacteristic, complemented
186#440—791no—
187#440—791no—
188C4×SD16—791no—
189C4×SD16—791no—
190#433—791no—
191C22×Q8C2×D7911yescharacteristic
192C2×SD16—791no—
193C2×SD16—791no—
194C2×SD16C2×D7911yescharacteristic
195C2×SD16C2×D7911yescharacteristic
196#127—791no—
197#125—791no—
198#123—1581no—
199#123—1581no—
200#121—791no—
201#121—1581no—
202#121—1581no—
203#121C2×D7911yescharacteristic
204C4×Q8—791no—
205C4×Q8—791no—
206C4×Q8—791no—
207C4×Q8—791no—
208C4×Q8—1581no—
209C4×Q8—1581no—
210C4×D4—791no—
211C4×D4—791no—
212#117—791no—
213#117—791no—
214#117—1581no—
215#117—1581no—
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#103C2×D7911yescharacteristic
225#103C2×D7911yescharacteristic
226#102—791no—
227#102—791no—
228#102—791no—
229#102—791no—
230C22⋊C8—791no—
231C22⋊C8C2×D7911yescharacteristic
232#97—791no—
233C4×C8—791no—
234C2×Q8—22no—
235C2×Q8—22no—
236C2×Q8—21no—
237C2×Q8C22×D7911yescharacteristic
238C2×Q8C22×D7911yescharacteristic
239C2×D4—21no—
240C2×D4—791no—
241C2×D4—1581no—
242C2×D4—1581no—
243C2×D4—1581no—
244C2×D4C22×D7911yescharacteristic
245C22×C4—21no—
246C22×C4—1581no—
247C22×C4—1581no—
248C22×C4C22×D7911yescharacteristic
249SD16—22no—
250SD16—22no—
251SD16—1582no—
252SD16—1582no—
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—
276C42—791no—
277C42—791no—
278C42—1581no—
279C42—1581no—
280C42—1581no—
281C42—1581no—
282C42—1581no—
283C23—21no—
284C23—1581no—
285C23D4×D7911yescharacteristic
286Q8—24no—
287Q8—21no—
288Q8—21no—
289Q8#1192962312yes—
290Q8#1192962312yes—
291D4—21no—
292D4—21no—
293D4—81no—
294D4—6321no—
295D4—6321no—
296D4—6321no—
297D4—1581no—
298D4—1581no—
299C2×C4—24no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—791no—
306C2×C4—791no—
307C2×C4—791no—
308C2×C4—791no—
309C2×C4—6321no—
310C2×C4—6321no—
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—21no—
322C22—21no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22C2×D4×D7911yescharacteristic
330C4—22no—
331C4—22no—
332C4—21no—
333C4—41no—
334C4—3161no—
335C4—3161no—
336C4—3161no—
337C4—1581no—
338C4—1581no—
339C4—1581no—
340C4—1581no—
341C4C2×#1192962311yescharacteristic
342C4C2×#1192962311yescharacteristic
343C2—41no—
344C2—81no—
345C2—6321no—
346C2#1909906911yescharacteristic
347C2#1909936911yescharacteristic
348C2#1909937211yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#448×C79C2
socleC22×C79C22×D4
prime radical#19099166C2
hypercenter#448D79
hypocenterC79#3126
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #19099041C2semidirect
3. #19098888C2semidirect
4. #19098884C2semidirect
5. #19098872C2semidirect
6. #19098868C2semidirect
7. #19098761C2semidirect
8. #19098761C2semidirect
9. #19098702C2semidirect
10. #19098666C2semidirect
11. #19098664C2semidirect
12. SD16×Dic79C2semidirect
13. #19098648C2semidirect
14. #19098621C2semidirect
15. #448×C79C2semidirect
175. C79#3126semidirect
185. #448D79semidirect