Finite Group Databasebeta

← #23770244

Subgroups — #23770244

Order 10112.

490 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×#14579145C211yesmaximal, characteristic
2#19098502C211yesmaximal, characteristic, complemented
3#19098498C211yesmaximal, characteristic, complemented
4#19098493C211yesmaximal, characteristic, complemented
5#19098485C211yesmaximal, characteristic, complemented
6#19098478C211yesmaximal, characteristic
7#19098478C211yesmaximal, characteristic
8#19098461C211yesmaximal, characteristic, complemented
9#19098456C211yesmaximal, characteristic, complemented
10#19098454C211yesmaximal, characteristic, complemented
11#19098453C211yesmaximal, characteristic, complemented
12#19098435C211yesmaximal, characteristic, complemented
13#19098435C211yesmaximal, characteristic, complemented
14#19098432C211yesmaximal, characteristic, complemented
15C2×#126×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18#14579145—24no—
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
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
44C79⋊#95C2211yescharacteristic
45#126×C79—24no—
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C22⋊C4×C79C2211yescharacteristic
50C2×C22⋊C4×C79C2211yescharacteristic
51C2×C22⋊C4×C79C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C2×C22⋊D79—22no—
55C2×C22⋊D79—41no—
56C2×C22⋊D79—41no—
57C22×Dic79—22no—
58C22×Dic79—41no—
59C22×Dic79—41no—
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C4⋊Dic79—22no—
68C4⋊Dic79—22no—
69C4⋊Dic79—22no—
70Dic79⋊C4—41no—
71Dic79⋊C4—41no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75Dic79⋊C4—41no—
76C22⋊Dic79—22no—
77C22⋊Dic79—22no—
78(C2×D79)⋊C4—22no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—22no—
81(C2×D79)⋊C4—22no—
82(C2×D79)⋊C4—41no—
83(C2×D79)⋊C4—41no—
84C4×Dic79—22no—
85C24×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C22×C4×C79C2311yescharacteristic
92C4⋊C4×C79—22no—
93C4⋊C4×C79—22no—
94C4⋊C4×C79—22no—
95C22⋊C4×C79—22no—
96C22⋊C4×C79—22no—
97C22⋊C4×C79D414yes—
98C42×C79—22no—
99C23×C79—21no—
100C23×C79—21no—
101C23×C79—21no—
102C23×C79—21no—
103C23×C79—21no—
104C23×C79—21no—
105C23×C79C2×D412yes—
106C23×C79C2411yescharacteristic
107C22×D79—21no—
108C22×D79—21no—
109C22×D79—21no—
110C22×D79—21no—
111C22×D79—21no—
112C22×D79—21no—
113C22×D79—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×C79C2×D412yes—
131C2×C4×C79C2×D412yes—
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×Dic79—21no—
152C2×Dic79—44no—
153C2×Dic79#4112yes—
154C2×Dic79#4112yes—
155C22×C79—22no—
156C22×C79—22no—
157C22×C79—22no—
158C22×C79—41no—
159C22×C79—41no—
160C22×C79—41no—
161C22×C79—41no—
162C22×C79C22×D411yescharacteristic
163C22×C79C2×#4111yescharacteristic
164C22×C79C2×#4111yescharacteristic
165C22×C79H(5,𝔽2)11yescharacteristic
166C22×C79H(5,𝔽2)11yescharacteristic
167C22×C792−1+411yescharacteristic
168C22×C792−1+411yescharacteristic
169C2×D79—41no—
170C2×D79—41no—
171C2×D79—41no—
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—41no—
185Dic79—41no—
186Dic79—41no—
187Dic79—41no—
188Dic79—41no—
189C2×C79—42no—
190C2×C79#53511yescharacteristic
191C2×C79#53911yescharacteristic
192C2×C79#54211yescharacteristic
193C2×C79#54711yescharacteristic
194C2×C79#54711yescharacteristic
195C2×C79#55311yescharacteristic
196C2×C79#56311yescharacteristic
197D79—81no—
198#2718—791nomaximal, Sylow
199C79#271811yescharacteristic, complemented, Sylow
200C2×#126D7911yescharacteristic, complemented
201C2×#123—791no—
202#400—791no—
203#399—791no—
204#398—791no—
205#396—791no—
206#394—791no—
207#394—791no—
208#389—791no—
209#388—791no—
210#388—791no—
211#388—791no—
212#385—791no—
213#385—791no—
214#384—791no—
215C22×D4—791no—
216C23×C4—791no—
217#126—24no—
218#123—1584no—
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⋊C4—791no—
227C2×C4⋊C4—791no—
228C2×C4⋊C4C2×D7911yescharacteristic
229C2×C4⋊C4C2×D7911yescharacteristic
230C2×C4⋊C4C2×D7911yescharacteristic
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×C22⋊C4—791no—
239C2×C22⋊C4C2×D7911yescharacteristic
240C2×C22⋊C4C2×D7911yescharacteristic
241C2×C22⋊C4C2×D7911yescharacteristic
242C2×C42—791no—
243C2×C42C2×D7911yescharacteristic
244#95—791no—
245#95—791no—
246#95—791no—
247#95—791no—
248#95—791no—
249#95—791no—
250#95—791no—
251#95—791no—
252C24—791no—
253C24C22×D7911yescharacteristic
254C2×D4—3161no—
255C2×D4—3161no—
256C2×D4—1582no—
257C22×C4—3161no—
258C22×C4—3161no—
259C22×C4—791no—
260C22×C4—791no—
261C22×C4—791no—
262C22×C4—791no—
263C22×C4—791no—
264C22×C4—791no—
265C22×C4—791no—
266C22×C4—1582no—
267C22×C4C22×D7911yescharacteristic
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—3161no—
277C4⋊C4—3161no—
278C4⋊C4—3161no—
279C4⋊C4—3161no—
280C4⋊C4—3161no—
281C4⋊C4—3161no—
282C4⋊C4—1582no—
283C4⋊C4—1582no—
284C4⋊C4—1582no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—3161no—
288C22⋊C4—3161no—
289C22⋊C4—1582no—
290C22⋊C4—1582no—
291C22⋊C4—1582no—
292C22⋊C4—1582no—
293C22⋊C4—1582no—
294C22⋊C4—1582no—
295C22⋊C4C22⋊D7914yes—
296C42—22no—
297C42—1582no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—1581no—
305C23—1581no—
306C23—1581no—
307C23—1581no—
308C23—1581no—
309C23—1581no—
310C23—1581no—
311C23C2×C22⋊D7912yes—
312C23C23×D7911yescharacteristic
313D4—3164no—
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—792no—
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×C4—1581no—
351C2×C4—1581no—
352C2×C4C2×C22⋊D7912yes—
353C2×C4C2×C22⋊D7912yes—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—3161no—
362C22—3161no—
363C22—3161no—
364C22—3161no—
365C22—3161no—
366C22—3161no—
367C22—3161no—
368C22C22×C22⋊D7911yescharacteristic
369C22#41×D7911yescharacteristic
370C22#41×D7911yescharacteristic
371C22#1457920711yescharacteristic
372C22#1457920711yescharacteristic
373C22#1457920811yescharacteristic
374C22#1457920811yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—3161no—
382C4—3161no—
383C4—3161no—
384C4—3161no—
385C4—3161no—
386C4—1582no—
387C4—1582no—
388C2—42no—
389C2—6321no—
390C2#1909912711yescharacteristic
391C2#1909915411yescharacteristic
392C2#1909917911yescharacteristic
393C2#1909921211yescharacteristic
394C2#1909921211yescharacteristic
395C2#1909926411yescharacteristic
396C2#1909931511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#126×C79C2
prime radicalC22×C22⋊D79C22
hypercenterC2×#126D79
hypocenterC79#2718
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
2. #19098502C2semidirect
3. #19098498C2semidirect
4. #19098493C2semidirect
5. #19098485C2semidirect
8. #19098461C2semidirect
9. #19098456C2semidirect
10. #19098454C2semidirect
11. #19098453C2semidirect
12. #19098435C2semidirect
13. #19098435C2semidirect
14. #19098432C2semidirect
15. C2×#126×C79C2semidirect
199. C79#2718semidirect
200. C2×#126D79semidirect