Finite Group Databasebeta

← #23770612

Subgroups — #23770612

Order 10112.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098500C211yesmaximal, characteristic, complemented
2#19098498C211yesmaximal, characteristic, complemented
3#19098496C211yesmaximal, characteristic, complemented
4#19098485C211yesmaximal, characteristic, complemented
5#19098485C211yesmaximal, characteristic, complemented
6#19098464C211yesmaximal, characteristic
7#19098450C211yesmaximal, characteristic, complemented
8#19098446C211yesmaximal, characteristic, complemented
9#19098441C211yesmaximal, characteristic
10#19098441C211yesmaximal, characteristic
11#19098434C211yesmaximal, characteristic, complemented
12#19098434C211yesmaximal, characteristic, complemented
13#19098422C211yesmaximal, characteristic, complemented
14#19098420C211yesmaximal, characteristic, complemented
15#398×C79C211yesmaximal, characteristic, complemented
16C22×D316C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×(C2×D79)⋊C4C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×(C2×D79)⋊C4C2211yescharacteristic
35C2×(C2×D79)⋊C4C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C2×C4⋊C4×C79C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C23×D79C2311yescharacteristic
52C23×D79C2311yescharacteristic
53C2×D316—41no—
54C2×D316—41no—
55C2×D316Q814yes—
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C2×C4×D79—22no—
63C2×C4×D79—22no—
64C2×C4×D79—41no—
65C2×C4×D79—41no—
66C2×C4×D79—41no—
67C2×C4×D79—41no—
68C4⋊Dic79—22no—
69C4⋊Dic79—41no—
70C4⋊Dic79—41no—
71Dic79⋊C4—22no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75(C2×D79)⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—41no—
78(C2×D79)⋊C4—41no—
79(C2×D79)⋊C4—41no—
80(C2×D79)⋊C4—41no—
81(C2×D79)⋊C4—41no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84(C2×D79)⋊C4—41no—
85C4×Dic79—41no—
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C4⋊C4×C79—41no—
94C4⋊C4×C79—41no—
95C4⋊C4×C79—41no—
96C4⋊C4×C79—41no—
97C23×C79C2411yescharacteristic
98C22×D79—21no—
99C22×D79—21no—
100C22×D79—21no—
101C22×D79—21no—
102C22×D79—21no—
103C22×D79—21no—
104C22×D79—21no—
105C22×D79—21no—
106C22×D79—21no—
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79C2×Q812yes—
111C22×D79C2×Q812yes—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79—21no—
116C2×C4×C79—21no—
117C2×C4×C79—21no—
118C2×C4×C79—21no—
119C2×C4×C79—21no—
120C2×C4×C79—21no—
121C2×C4×C79—21no—
122C2×C4×C79—21no—
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—21no—
131C2×C4×C79C2×Q812yes—
132C2×C4×C79#4112yes—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—21no—
140C2×Dic79—21no—
141C2×Dic79—21no—
142C2×Dic79—21no—
143C2×Dic79—21no—
144C2×Dic79—21no—
145C2×Dic79—21no—
146C2×Dic79—21no—
147C2×Dic79—21no—
148C2×Dic79—21no—
149C2×Dic79—21no—
150C2×Dic79#4112yes—
151D316—44no—
152C4×D79—44no—
153C4×D79—44no—
154C22×C79C22×Q811yescharacteristic
155C22×C79C2×#4111yescharacteristic
156C22×C79C2×#4111yescharacteristic
157C22×C79H(5,𝔽2)11yescharacteristic
158C22×C79H(5,𝔽2)11yescharacteristic
159C22×C79H(5,𝔽2)11yescharacteristic
160C22×C79H(5,𝔽2)11yescharacteristic
161C2×D79—22no—
162C2×D79—22no—
163C2×D79—22no—
164C2×D79—22no—
165C2×D79—22no—
166C2×D79—22no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C4×C79—22no—
176C4×C79—22no—
177C4×C79—41no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182Dic79—22no—
183Dic79—41no—
184Dic79—41no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188C2×C79#54011yescharacteristic
189C2×C79#54011yescharacteristic
190C2×C79#54311yescharacteristic
191C2×C79#55111yescharacteristic
192C2×C79#55411yescharacteristic
193C2×C79#55411yescharacteristic
194C2×C79#56011yescharacteristic
195D79—42no—
196D79—42no—
197#2748—791nomaximal, Sylow
198C79#274811yescharacteristic, complemented, Sylow
199#399—791no—
200#399—791no—
201#398—791no—
202#398D7911yescharacteristic, complemented
203#396—791no—
204#396—791no—
205#390—791no—
206#387—791no—
207#387—791no—
208#386—791no—
209#386—791no—
210#385—791no—
211#385—791no—
212#380—791no—
213#380—791no—
214C22×D4—791no—
215C23×C4—791no—
216C23×C4—791no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4C2×D7911yescharacteristic
225C2×C4⋊C4C2×D7911yescharacteristic
226C2×C4⋊C4C2×D7911yescharacteristic
227C2×C4⋊C4C2×D7911yescharacteristic
228C2×C22⋊C4—791no—
229C2×C22⋊C4—791no—
230C2×C22⋊C4—791no—
231C2×C22⋊C4—791no—
232C2×C22⋊C4—791no—
233C2×C22⋊C4—791no—
234C2×C22⋊C4—791no—
235C2×C22⋊C4—791no—
236C2×C22⋊C4—791no—
237C2×C22⋊C4—791no—
238C2×C42—791no—
239#95—791no—
240#95—791no—
241#95—791no—
242#95—791no—
243#95—791no—
244#95—791no—
245#95—791no—
246#95C2×D7911yescharacteristic
247#95C2×D7911yescharacteristic
248#95C2×D7911yescharacteristic
249C24—791no—
250C24—791no—
251C2×D4—3161no—
252C2×D4—3161no—
253C2×D4—794no—
254C22×C4—3161no—
255C22×C4—3161no—
256C22×C4—3161no—
257C22×C4—3161no—
258C22×C4—791no—
259C22×C4—791no—
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—1582no—
265C22×C4—1582no—
266C22×C4C22×D7911yescharacteristic
267C22×C4C22×D7911yescharacteristic
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—3161no—
278C4⋊C4—3161no—
279C4⋊C4—3161no—
280C4⋊C4—3161no—
281C4⋊C4—3161no—
282C4⋊C4—1582no—
283C4⋊C4—1582no—
284C22⋊C4—3161no—
285C22⋊C4—3161no—
286C22⋊C4—3161no—
287C22⋊C4—3161no—
288C22⋊C4—3161no—
289C22⋊C4—3161no—
290C22⋊C4—3161no—
291C22⋊C4—3161no—
292C22⋊C4—1582no—
293C22⋊C4—1582no—
294C42—3161no—
295C23—792no—
296C23—792no—
297C23—1581no—
298C23—1581no—
299C23—1581no—
300C23—1581no—
301C23—1581no—
302C23—1581no—
303C23—1581no—
304C23—1581no—
305C23—1581no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23C23×D7911yescharacteristic
310D4—3164no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—3164no—
331C2×C4—3164no—
332C2×C4—792no—
333C2×C4—1581no—
334C2×C4—1581no—
335C2×C4—1581no—
336C2×C4—1581no—
337C2×C4—1581no—
338C2×C4—1581no—
339C2×C4—1581no—
340C2×C4—1581no—
341C2×C4—1581no—
342C2×C4—1581no—
343C2×C4—1581no—
344C2×C4—1581no—
345C2×C4—1581no—
346C2×C4—1581no—
347C2×C4—1581no—
348C2×C4—1581no—
349C2×C4—1581no—
350C2×C4Q8×D7912yes—
351C2×C4#1192962512yes—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—3161no—
356C22—3161no—
357C22—3161no—
358C22—3161no—
359C22—3161no—
360C22—1582no—
361C22—1582no—
362C22—1582no—
363C22—1582no—
364C22—1582no—
365C22—1582no—
366C22C2×Q8×D7911yescharacteristic
367C22#41×D7911yescharacteristic
368C22C2×#1192962511yescharacteristic
369C22#1457920611yescharacteristic
370C22#1457920611yescharacteristic
371C22#1457920711yescharacteristic
372C22#1457920711yescharacteristic
373C4—22no—
374C4—22no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—3161no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4—1582no—
386C2—3162no—
387C2—3162no—
388C2#1909916511yescharacteristic
389C2#1909916911yescharacteristic
390C2#1909918811yescharacteristic
391C2#1909924011yescharacteristic
392C2#1909926911yescharacteristic
393C2#1909927411yescharacteristic
394C2#1909930111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC22×D316C22
hypercenter#398D79
hypocenterC79#2748
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #19098500C2semidirect
2. #19098498C2semidirect
3. #19098496C2semidirect
4. #19098485C2semidirect
5. #19098485C2semidirect
7. #19098450C2semidirect
8. #19098446C2semidirect
11. #19098434C2semidirect
12. #19098434C2semidirect
13. #19098422C2semidirect
14. #19098420C2semidirect
15. #398×C79C2semidirect
198. C79#2748semidirect
202. #398D79semidirect