Finite Group Databasebeta

← #23766549

Subgroups — #23766549

Order 10112.

512 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579143C211yesmaximal, characteristic
2#19098463C211yesmaximal, characteristic
3#19098459C211yesmaximal, characteristic, complemented
4#19098458C211yesmaximal, characteristic, complemented
5#19098456C211yesmaximal, characteristic, complemented
6#19098453C211yesmaximal, characteristic, complemented
7#19098452C211yesmaximal, characteristic, complemented
8#19098451C211yesmaximal, characteristic, complemented
9#19098450C211yesmaximal, characteristic, complemented
10#19098448C211yesmaximal, characteristic, complemented
11#19098442C211yesmaximal, characteristic
12#19098436C211yesmaximal, characteristic, complemented
13#19098422C211yesmaximal, characteristic, complemented
14#19098420C211yesmaximal, characteristic, complemented
15#385×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18#14579143C418yescomplemented
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C2×(C2×D79)⋊C4C2211yescharacteristic
32C2×(C2×D79)⋊C4C2211yescharacteristic
33C2×(C2×D79)⋊C4C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C23×C4×C79C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C22⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52C23×D79C2311yescharacteristic
53C2×C22⋊D79—41no—
54C2×C22⋊D79—41no—
55C2×C22⋊D79C2×C414yes—
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C2×C4×D79—41no—
64C2×C4×D79—41no—
65C2×C4×D79C2×C414yescomplemented
66C4⋊Dic79—41no—
67C4⋊Dic79C2×C414yescomplemented
68Dic79⋊C4—41no—
69Dic79⋊C4—41no—
70Dic79⋊C4—41no—
71Dic79⋊C4—41no—
72Dic79⋊C4C2×C414yescomplemented
73C22⋊Dic79—41no—
74C22⋊Dic79—41no—
75C22⋊Dic79C2×C414yes—
76(C2×D79)⋊C4—41no—
77(C2×D79)⋊C4—41no—
78(C2×D79)⋊C4—41no—
79(C2×D79)⋊C4—41no—
80(C2×D79)⋊C4C2×C414yescomplemented
81C4×Dic79—41no—
82C4×Dic79—41no—
83C4×Dic79—41no—
84C24×C79C2311yescharacteristic
85C22×C4×C79—41no—
86C22×C4×C79—41no—
87C22×C4×C79—41no—
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C22×C4×C79C2311yescharacteristic
93C22×C4×C79C2311yescharacteristic
94C4⋊C4×C79—41no—
95C4⋊C4×C79—41no—
96C22⋊C4×C79—41no—
97C22⋊C4×C79C2×C414yes—
98C23×C79—21no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79C22×C412yes—
105C23×C79C2411yescharacteristic
106C22×D79—21no—
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79C22×C412yes—
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—44no—
130C2×C4×C79C22×C412yes—
131C2×C4×C79C22×C412yes—
132C22⋊D79—44no—
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—21no—
151C2×Dic79C22×C412yes—
152C2×Dic79C22×C412yes—
153C2×Dic79C22×C412yes—
154C4×D79—44no—
155C22×C79—22no—
156C22×C79—22no—
157C22×C79—22no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79C23×C411yescharacteristic
163C22×C79H(5,𝔽2)11yescharacteristic
164C22×C79H(5,𝔽2)11yescharacteristic
165C22×C79H(5,𝔽2)11yescharacteristic
166C22×C79H(5,𝔽2)11yescharacteristic
167C22×C792−1+411yescharacteristic
168C22×C792−1+411yescharacteristic
169C2×D79—22no—
170C2×D79—22no—
171C2×D79—22no—
172C2×D79—41no—
173C2×D79—41no—
174C2×D79—41no—
175C2×D79—41no—
176C4×C79—22no—
177C4×C79—22no—
178C4×C79—41no—
179C4×C79—41no—
180C4×C79—41no—
181C4×C79—41no—
182Dic79—22no—
183Dic79—22no—
184Dic79—22no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—42no—
190C2×C79#51811yescharacteristic
191C2×C79#52011yescharacteristic
192C2×C79#52011yescharacteristic
193C2×C79#56011yescharacteristic
194C2×C79#56211yescharacteristic
195C2×C79#56211yescharacteristic
196C2×C79#56311yescharacteristic
197D79—42no—
198#2376—791nomaximal, Sylow
199C79#237611yescharacteristic, complemented, Sylow
200C2×#123—791no—
201#390—791no—
202#389—791no—
203#389—791no—
204#388—791no—
205#388—791no—
206#388—791no—
207#388—791no—
208#387—791no—
209#387—791no—
210#386—791no—
211#385—791no—
212#385D7911yescharacteristic, complemented
213#380—791no—
214#380—791no—
215C22×D4—791no—
216C23×C4—791no—
217C23×C4C2×D7911yescharacteristic
218#123—798no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4—791no—
221C2×C4⋊C4—791no—
222C2×C4⋊C4—791no—
223C2×C4⋊C4—791no—
224C2×C4⋊C4—791no—
225C2×C4⋊C4—791no—
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⋊C4C2×D7911yescharacteristic
237C2×C22⋊C4C2×D7911yescharacteristic
238C2×C42—791no—
239C2×C42—791no—
240C2×C42—791no—
241#95—791no—
242#95—791no—
243#95—791no—
244#95—791no—
245#95—791no—
246#95—791no—
247#95—791no—
248#95—791no—
249#95C2×D7911yescharacteristic
250#95C2×D7911yescharacteristic
251C24—791no—
252C24C22×D7911yescharacteristic
253C2×D4—3161no—
254C2×D4—3161no—
255C2×D4—794no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—3161no—
260C22×C4—3161no—
261C22×C4—794no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—791no—
267C22×C4—791no—
268C22×C4—791no—
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C22×C4C22×D7911yescharacteristic
274C22×C4C22×D7911yescharacteristic
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—3161no—
278C4⋊C4—3161no—
279C4⋊C4—3161no—
280C4⋊C4—3161no—
281C4⋊C4—3161no—
282C4⋊C4—794no—
283C4⋊C4—794no—
284C22⋊C4—41no—
285C22⋊C4—3161no—
286C22⋊C4—3161no—
287C22⋊C4—3161no—
288C22⋊C4—3161no—
289C22⋊C4—3161no—
290C22⋊C4—3161no—
291C22⋊C4—794no—
292C22⋊C4—794no—
293C22⋊C4C4×D7914yes—
294C42—3161no—
295C42—3161no—
296C42—3161no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—792no—
304C23—1581no—
305C23—1581no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23—1581no—
310C23C2×C4×D7912yes—
311C23C23×D7911yescharacteristic
312D4—3164no—
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—44no—
330C2×C4—3164no—
331C2×C4—792no—
332C2×C4—792no—
333C2×C4—792no—
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×C4—1581no—
351C2×C4—1581no—
352C2×C4C2×C4×D7912yes—
353C2×C4C2×C4×D7912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—1582no—
366C22—1582no—
367C22—1582no—
368C22C22×C4×D7911yescharacteristic
369C22#1457920611yescharacteristic
370C22#1457920611yescharacteristic
371C22#1457920611yescharacteristic
372C22#1457920711yescharacteristic
373C22#1457920811yescharacteristic
374C22#1457920911yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4—1582no—
386C4—1582no—
387C4—1582no—
388C2—42no—
389C2—3162no—
390C2#1909903511yescharacteristic
391C2#1909904211yescharacteristic
392C2#1909904411yescharacteristic
393C2#1909930211yescharacteristic
394C2#1909930911yescharacteristic
395C2#1909931011yescharacteristic
396C2#1909931411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#385×C79C2
socle, cosocleC23×C79C24
prime radicalC22×C22⋊D79C22
hypercenter#385D79
hypocenterC79#2376
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #19098459C2semidirect
4. #19098458C2semidirect
5. #19098456C2semidirect
6. #19098453C2semidirect
7. #19098452C2semidirect
8. #19098451C2semidirect
9. #19098450C2semidirect
10. #19098448C2semidirect
12. #19098436C2semidirect
13. #19098422C2semidirect
14. #19098420C2semidirect
15. #385×C79C2semidirect
18. #14579143C4semidirect
65. C2×C4×D79C2×C4semidirect
67. C4⋊Dic79C2×C4semidirect
72. Dic79⋊C4C2×C4semidirect
80. (C2×D79)⋊C4C2×C4semidirect
199. C79#2376semidirect
212. #385D79semidirect