Finite Group Databasebeta

← #23769352

Subgroups — #23769352

Order 10112.

462 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79⋊#401C211yesmaximal, characteristic, complemented
2#19098505C211yesmaximal, characteristic, complemented
3#19098504C211yesmaximal, characteristic, complemented
4#19098502C211yesmaximal, characteristic, complemented
5#19098491C211yesmaximal, characteristic, complemented
6#19098488C211yesmaximal, characteristic, complemented
7#19098486C211yesmaximal, characteristic, complemented
8#19098439C211yesmaximal, characteristic
9#19098439C211yesmaximal, characteristic
10#19098439C211yesmaximal, characteristic
11#19098437C211yesmaximal, characteristic, complemented
12#19098437C211yesmaximal, characteristic, complemented
13#19098434C211yesmaximal, characteristic, complemented
14#95×D79C211yesmaximal, characteristic, complemented
15#397×C79C211yesmaximal, characteristic, complemented
16C22×C22⋊D79C2211yescharacteristic
17C22×C4×D79C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C22×C4×D79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C22⋊Dic79C2211yescharacteristic
27C2×C22⋊Dic79C2211yescharacteristic
28C2×(C2×D79)⋊C4C2211yescharacteristic
29C2×(C2×D79)⋊C4C2211yescharacteristic
30C2×(C2×D79)⋊C4C2211yescharacteristic
31C79⋊#95C2211yescharacteristic
32C79⋊#95C2211yescharacteristic
33C79⋊#95C2211yescharacteristic
34C79⋊#95C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C2×C4⋊C4×C79C2211yescharacteristic
45C2×C22⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C23×D79C2311yescharacteristic
52C2×C22⋊D79—22no—
53C2×C22⋊D79—22no—
54C2×C22⋊D79—22no—
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C2×C4×D79—22no—
63C2×C4×D79—22no—
64C2×C4×D79—22no—
65C2×C4×D79—41no—
66C2×C4×D79—41no—
67C2×C4×D79—41no—
68C2×C4×D79—41no—
69C2×C4×D79—41no—
70C2×C4×D79—41no—
71C4⋊Dic79—41no—
72C4⋊Dic79—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75Dic79⋊C4—41no—
76C22⋊Dic79—41no—
77C22⋊Dic79—41no—
78C22⋊Dic79—41no—
79(C2×D79)⋊C4—22no—
80(C2×D79)⋊C4—22no—
81(C2×D79)⋊C4—22no—
82C24×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C4⋊C4×C79—41no—
90C22⋊C4×C79—41no—
91C22⋊C4×C79—41no—
92C22⋊C4×C79—41no—
93C23×C79—21no—
94C23×C79—21no—
95C23×C79—21no—
96C23×C79—21no—
97C23×C79—21no—
98C23×C79—21no—
99C23×C79—21no—
100C23×C79C2411yescharacteristic
101C22×D79—21no—
102C22×D79—21no—
103C22×D79—21no—
104C22×D79—21no—
105C22×D79#4112yes—
106C22×D79#4112yes—
107C22×D79#4112yes—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
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—
126C22⋊D79—44no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
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—
148C4×D79—44no—
149C4×D79—44no—
150C4×D79—44no—
151C22×C79—41no—
152C22×C79—41no—
153C22×C79—41no—
154C22×C79—41no—
155C22×C79—41no—
156C22×C79—41no—
157C22×C79—41no—
158C22×C79C2×#4111yescharacteristic
159C22×C79C2×#4111yescharacteristic
160C22×C79C2×#4111yescharacteristic
161C22×C79H(5,𝔽2)11yescharacteristic
162C22×C79H(5,𝔽2)11yescharacteristic
163C22×C79H(5,𝔽2)11yescharacteristic
164C22×C792−1+411yescharacteristic
165C2×D79—22no—
166C2×D79—22no—
167C2×D79—22no—
168C2×D79—22no—
169C2×D79—22no—
170C2×D79—22no—
171C2×D79#12614yes—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178Dic79—41no—
179Dic79—41no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183Dic79—41no—
184Dic79—41no—
185C2×C79—81no—
186C2×C79C2×#12611yescharacteristic
187C2×C79#53811yescharacteristic
188C2×C79#53811yescharacteristic
189C2×C79#53811yescharacteristic
190C2×C79#53911yescharacteristic
191C2×C79#53911yescharacteristic
192C2×C79#53911yescharacteristic
193D79—24no—
194#2643—791nomaximal, Sylow
195C79#264311yescharacteristic, complemented, Sylow
196#401—791no—
197#400—791no—
198#400—791no—
199#400—791no—
200#397—791no—
201#397—791no—
202#397D7911yescharacteristic, complemented
203#396—791no—
204#386—791no—
205#386—791no—
206#386—791no—
207#385—791no—
208#385—791no—
209#385—791no—
210C2×#95—791no—
211C22×D4—791no—
212C23×C4—791no—
213C23×C4—791no—
214C23×C4—791no—
215C2×C4⋊C4—791no—
216C2×C4⋊C4—791no—
217C2×C4⋊C4—791no—
218C2×C4⋊C4—791no—
219C2×C4⋊C4—791no—
220C2×C4⋊C4C2×D7911yescharacteristic
221C2×C22⋊C4—791no—
222C2×C22⋊C4—791no—
223C2×C22⋊C4—791no—
224C2×C22⋊C4—791no—
225C2×C22⋊C4—791no—
226C2×C22⋊C4—791no—
227C2×C22⋊C4C2×D7911yescharacteristic
228C2×C22⋊C4C2×D7911yescharacteristic
229C2×C22⋊C4C2×D7911yescharacteristic
230#95—791no—
231#95—791no—
232#95—791no—
233#95—791no—
234#95—791no—
235#95—791no—
236#95—791no—
237#95—791no—
238#95—791no—
239#95—791no—
240#95—791no—
241#95—791no—
242#95—791no—
243#95C2×D7911yescharacteristic
244#95C2×D7911yescharacteristic
245#95C2×D7911yescharacteristic
246C24—791no—
247C24C22×D7911yescharacteristic
248C2×D4—1582no—
249C2×D4—1582no—
250C2×D4—1582no—
251C22×C4—3161no—
252C22×C4—3161no—
253C22×C4—3161no—
254C22×C4—3161no—
255C22×C4—3161no—
256C22×C4—3161no—
257C22×C4—791no—
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×C4—1582no—
267C22×C4C22×D7911yescharacteristic
268C22×C4C22×D7911yescharacteristic
269C22×C4C22×D7911yescharacteristic
270C22×C4C22×D7911yescharacteristic
271C22×C4C22×D7911yescharacteristic
272C22×C4C22×D7911yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—3161no—
275C4⋊C4—3161no—
276C4⋊C4—3161no—
277C4⋊C4—3161no—
278C4⋊C4—3161no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—3161no—
283C22⋊C4—3161no—
284C22⋊C4—3161no—
285C22⋊C4—1582no—
286C22⋊C4—1582no—
287C22⋊C4—1582no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—792no—
296C23—792no—
297C23—792no—
298C23—1581no—
299C23—1581no—
300C23—1581no—
301C23—1581no—
302C23C23×D7911yescharacteristic
303D4—3164no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
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—3164no—
323C2×C4—3164no—
324C2×C4—3164no—
325C2×C4—1581no—
326C2×C4—1581no—
327C2×C4—1581no—
328C2×C4—1581no—
329C2×C4—1581no—
330C2×C4—1581no—
331C2×C4—1581no—
332C2×C4—1581no—
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—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—794no—
354C22—1582no—
355C22—1582no—
356C22—1582no—
357C22—1582no—
358C22—1582no—
359C22—1582no—
360C22#41×D7911yescharacteristic
361C22#41×D7911yescharacteristic
362C22#41×D7911yescharacteristic
363C22#1457920611yescharacteristic
364C22#1457920611yescharacteristic
365C22#1457920711yescharacteristic
366C22#1457920811yescharacteristic
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—3161no—
377C4—3161no—
378C4—3161no—
379C4—3161no—
380C2—81no—
381C2—1584no—
382C2#126×D7911yescharacteristic
383C2#1909914511yescharacteristic
384C2#1909914711yescharacteristic
385C2#1909914911yescharacteristic
386C2#1909915411yescharacteristic
387C2#1909915611yescharacteristic
388C2#1909915611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#397D79
hypocenterC79#2643
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C79⋊#401C2semidirect
2. #19098505C2semidirect
3. #19098504C2semidirect
4. #19098502C2semidirect
5. #19098491C2semidirect
6. #19098488C2semidirect
7. #19098486C2semidirect
11. #19098437C2semidirect
12. #19098437C2semidirect
13. #19098434C2semidirect
14. #95×D79C2semidirect
15. #397×C79C2semidirect
195. C79#2643semidirect
202. #397D79semidirect