Finite Group Databasebeta

← #23770646

Subgroups — #23770646

Order 10112.

442 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098490C211yesmaximal, characteristic, complemented
2#19098490C211yesmaximal, characteristic, complemented
3#19098480C211yesmaximal, characteristic
4#19098476C211yesmaximal, characteristic, complemented
5#19098476C211yesmaximal, characteristic, complemented
6#19098467C211yesmaximal, characteristic, complemented
7#19098464C211yesmaximal, characteristic
8#19098455C211yesmaximal, characteristic, complemented
9#19098452C211yesmaximal, characteristic, complemented
10#19098449C211yesmaximal, characteristic, complemented
11#19098449C211yesmaximal, characteristic, complemented
12#19098441C211yesmaximal, characteristic
13#19098437C211yesmaximal, characteristic, complemented
14#19098425C211yesmaximal, characteristic, complemented
15#400×C79C211yesmaximal, characteristic, complemented
16C22×Dic158C2211yescharacteristic
17C22×D316C2211yescharacteristic
18C22×C4×D79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊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×C4×Dic79C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C2×C4⋊C4×C79C2211yescharacteristic
45C2×C4⋊C4×C79C2211yescharacteristic
46#95×C79C2211yescharacteristic
47#95×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C23×D79C2311yescharacteristic
52C23×D79C2311yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—41no—
55C2×Dic158—41no—
56C2×D316—22no—
57C2×D316—22no—
58C2×D316—41no—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C2×C4×D79—22no—
66C2×C4×D79—41no—
67C2×C4×D79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70Dic79⋊C4—41no—
71(C2×D79)⋊C4—22no—
72(C2×D79)⋊C4—22no—
73(C2×D79)⋊C4—22no—
74(C2×D79)⋊C4—41no—
75(C2×D79)⋊C4—41no—
76(C2×D79)⋊C4—41no—
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—
82C4×Dic79—41no—
83C4×Dic79—41no—
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C22×C4×C79C2311yescharacteristic
89C22×C4×C79C2311yescharacteristic
90C22×C4×C79C2311yescharacteristic
91C4⋊C4×C79—22no—
92C4⋊C4×C79—22no—
93C23×C79C2411yescharacteristic
94C22×D79—21no—
95C22×D79—21no—
96C22×D79—21no—
97C22×D79—21no—
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#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—
126C2×C4×C79—21no—
127C2×C4×C79—21no—
128C2×C4×C79#4112yes—
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#4112yes—
147D316—44no—
148C4×D79—44no—
149Dic158—44no—
150C22×C79C2×#4111yescharacteristic
151C22×C79C2×#4111yescharacteristic
152C22×C79C2×#4111yescharacteristic
153C22×C79H(5,𝔽2)11yescharacteristic
154C22×C79H(5,𝔽2)11yescharacteristic
155C22×C79H(5,𝔽2)11yescharacteristic
156C22×C792−1+411yescharacteristic
157C2×D79—22no—
158C2×D79—22no—
159C2×D79—22no—
160C2×D79—41no—
161C2×D79—41no—
162C2×D79—41no—
163C2×D79—41no—
164C2×D79—41no—
165C2×D79—41no—
166C2×D79—41no—
167C2×D79—41no—
168C2×D79—41no—
169C2×D79—41no—
170C2×D79—41no—
171C4×C79—22no—
172C4×C79—41no—
173C4×C79—41no—
174C4×C79—41no—
175C4×C79—41no—
176C4×C79—41no—
177C4×C79—41no—
178Dic79—22no—
179Dic79—41no—
180Dic79—41no—
181Dic79—41no—
182Dic79—41no—
183Dic79—41no—
184C2×C79#53811yescharacteristic
185C2×C79#53811yescharacteristic
186C2×C79#54211yescharacteristic
187C2×C79#55111yescharacteristic
188C2×C79#55211yescharacteristic
189C2×C79#55911yescharacteristic
190C2×C79#56211yescharacteristic
191D79—42no—
192D79—81no—
193#2751—791nomaximal, Sylow
194C79#275111yescharacteristic, complemented, Sylow
195#400D7911yescharacteristic, complemented
196#397—791no—
197#397—791no—
198#394—791no—
199#393—791no—
200#393—791no—
201#391—791no—
202#390—791no—
203#388—791no—
204#388—791no—
205#387—791no—
206#387—791no—
207#386—791no—
208#385—791no—
209#381—791no—
210C22×Q8—791no—
211C22×D4—791no—
212C23×C4—791no—
213C2×C4⋊C4—791no—
214C2×C4⋊C4—791no—
215C2×C4⋊C4—791no—
216C2×C4⋊C4C2×D7911yescharacteristic
217C2×C4⋊C4C2×D7911yescharacteristic
218C2×C22⋊C4—791no—
219C2×C22⋊C4—791no—
220C2×C22⋊C4—791no—
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⋊C4—791no—
228C2×C22⋊C4—791no—
229C2×C42—791no—
230C2×C42—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#95C2×D7911yescharacteristic
241#95C2×D7911yescharacteristic
242#95C2×D7911yescharacteristic
243#95C2×D7911yescharacteristic
244#95C2×D7911yescharacteristic
245C24—791no—
246C24—791no—
247C2×Q8—3161no—
248C2×Q8—3161no—
249C2×Q8—1582no—
250C2×D4—3161no—
251C2×D4—1582no—
252C2×D4—1582no—
253C22×C4—3161no—
254C22×C4—3161no—
255C22×C4—791no—
256C22×C4—791no—
257C22×C4—791no—
258C22×C4—791no—
259C22×C4—791no—
260C22×C4—791no—
261C22×C4—1582no—
262C22×C4C22×D7911yescharacteristic
263C22×C4C22×D7911yescharacteristic
264C22×C4C22×D7911yescharacteristic
265C22×C4C22×D7911yescharacteristic
266C22×C4C22×D7911yescharacteristic
267C22×C4C22×D7911yescharacteristic
268C22×C4C22×D7911yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—3161no—
272C4⋊C4—3161no—
273C4⋊C4—3161no—
274C22⋊C4—3161no—
275C22⋊C4—3161no—
276C22⋊C4—3161no—
277C22⋊C4—3161no—
278C22⋊C4—3161no—
279C22⋊C4—3161no—
280C22⋊C4—3161no—
281C22⋊C4—3161no—
282C22⋊C4—1582no—
283C22⋊C4—1582no—
284C22⋊C4—1582no—
285C42—3161no—
286C42—3161no—
287C23—792no—
288C23—1581no—
289C23—1581no—
290C23—1581no—
291C23—1581no—
292C23—1581no—
293C23—1581no—
294C23—1581no—
295C23—1581no—
296C23—1581no—
297C23—1581no—
298C23—1581no—
299C23—1581no—
300C23—1581no—
301C23C23×D7911yescharacteristic
302Q8—3164no—
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—21no—
323C2×C4—21no—
324C2×C4—3164no—
325C2×C4—792no—
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#1192962312yes—
344C22—3161no—
345C22—3161no—
346C22—3161no—
347C22—3161no—
348C22—3161no—
349C22—3161no—
350C22—3161no—
351C22—3161no—
352C22—3161no—
353C22—3161no—
354C22—3161no—
355C22—1582no—
356C22—1582no—
357C22—1582no—
358C22#41×D7911yescharacteristic
359C22#41×D7911yescharacteristic
360C22C2×#1192962311yescharacteristic
361C22#1457920711yescharacteristic
362C22#1457920711yescharacteristic
363C22#1457920711yescharacteristic
364C22#1457920911yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—3161no—
373C4—3161no—
374C4—3161no—
375C4—3161no—
376C4—3161no—
377C4—1582no—
378C2—3162no—
379C2—6321no—
380C2#1909915211yescharacteristic
381C2#1909915211yescharacteristic
382C2#1909918611yescharacteristic
383C2#1909923611yescharacteristic
384C2#1909924511yescharacteristic
385C2#1909929511yescharacteristic
386C2#1909931111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC22×D316C22
hypercenter#400D79
hypocenterC79#2751
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #19098490C2semidirect
2. #19098490C2semidirect
4. #19098476C2semidirect
5. #19098476C2semidirect
6. #19098467C2semidirect
8. #19098455C2semidirect
9. #19098452C2semidirect
10. #19098449C2semidirect
11. #19098449C2semidirect
13. #19098437C2semidirect
14. #19098425C2semidirect
15. #400×C79C2semidirect
194. C79#2751semidirect
195. #400D79semidirect