Finite Group Databasebeta

← #23769563

Subgroups — #23769563

Order 10112.

434 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579156C211yesmaximal, characteristic
2C2×#14579151C211yesmaximal, characteristic, complemented
3#19098505C211yesmaximal, characteristic, complemented
4#19098498C211yesmaximal, characteristic
5#19098497C211yesmaximal, characteristic, complemented
6#19098496C211yesmaximal, characteristic, complemented
7#19098494C211yesmaximal, characteristic, complemented
8#19098492C211yesmaximal, characteristic
9#19098487C211yesmaximal, characteristic
10#19098485C211yesmaximal, characteristic
11#19098458C211yesmaximal, characteristic, complemented
12#19098454C211yesmaximal, characteristic
13#19098453C211yesmaximal, characteristic
14C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
15#389×C79C211yesmaximal, characteristic, complemented
16#14579156—24no—
17#14579151—24no—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊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
37C2×C4×Dic79C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C79⋊#95C2211yescharacteristic
45C79⋊#95C2211yescharacteristic
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C42×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C23×D79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C4⋊Dic79—22no—
62C4⋊Dic79—22no—
63Dic79⋊C4—22no—
64Dic79⋊C4—22no—
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—41no—
72(C2×D79)⋊C4—22no—
73(C2×D79)⋊C4—22no—
74(C2×D79)⋊C4—22no—
75(C2×D79)⋊C4—22no—
76(C2×D79)⋊C4—22no—
77(C2×D79)⋊C4—41no—
78(C2×D79)⋊C4—41no—
79C4×Dic79—41no—
80C4×Dic79D414yes—
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C22×C4×C79C2311yescharacteristic
87C22×C4×C79C2311yescharacteristic
88C4⋊C4×C79—22no—
89C4⋊C4×C79—22no—
90C4⋊C4×C79—22no—
91C4⋊C4×C79—41no—
92C42×C79—41no—
93C23×C79C2411yescharacteristic
94C22×D79—21no—
95C22×D79—21no—
96C22×D79—21no—
97C22×D79—21no—
98C22×D79—21no—
99C22×D79—21no—
100C22×D79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
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×C79C2×D412yes—
121C2×C4×C79#4112yes—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
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×Dic79C2×D412yes—
141C2×Dic79C2×D412yes—
142C2×Dic79#4112yes—
143C22×C79C22×D411yescharacteristic
144C22×C79C2×#4111yescharacteristic
145C22×C79C2×#4111yescharacteristic
146C22×C79H(5,𝔽2)11yescharacteristic
147C22×C792−1+411yescharacteristic
148C22×C792−1+411yescharacteristic
149C22×C792−1+411yescharacteristic
150C2×D79—41no—
151C2×D79—41no—
152C2×D79—41no—
153C2×D79—41no—
154C2×D79—41no—
155C2×D79—41no—
156C2×D79—41no—
157C4×C79—22no—
158C4×C79—22no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163C4×C79—41no—
164Dic79—22no—
165Dic79—22no—
166Dic79—22no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79#53211yescharacteristic
172C2×C79#53611yescharacteristic
173C2×C79#53711yescharacteristic
174C2×C79#53911yescharacteristic
175C2×C79#53911yescharacteristic
176C2×C79#54111yescharacteristic
177C2×C79#54111yescharacteristic
178D79—81no—
179#2664—791nomaximal, Sylow
180C79#266411yescharacteristic, complemented, Sylow
181C2×#126—791no—
182C2×#125—791no—
183#400—791no—
184#399—791no—
185#398—791no—
186#398—791no—
187#398—791no—
188#397—791no—
189#396—791no—
190#396—791no—
191#389—791no—
192#389D7911yescharacteristic, complemented
193#388—791no—
194#388—791no—
195C4×C4⋊C4—791no—
196#126—1584no—
197#125—1584no—
198C2×C4⋊C4—791no—
199C2×C4⋊C4—791no—
200C2×C4⋊C4—791no—
201C2×C4⋊C4—791no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4—791no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4—791no—
209C2×C4⋊C4C2×D7911yescharacteristic
210C2×C4⋊C4C2×D7911yescharacteristic
211C2×C4⋊C4C2×D7911yescharacteristic
212C2×C4⋊C4C2×D7911yescharacteristic
213C2×C22⋊C4—791no—
214C2×C22⋊C4—791no—
215C2×C22⋊C4—791no—
216C2×C22⋊C4—791no—
217C2×C22⋊C4—791no—
218C2×C22⋊C4—791no—
219C2×C22⋊C4—791no—
220C2×C42—791no—
221C2×C42—791no—
222C2×C42C2×D7911yescharacteristic
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95—791no—
230#95—791no—
231#95C2×D7911yescharacteristic
232#95C2×D7911yescharacteristic
233C24—791no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243C22×C4C22×D7911yescharacteristic
244C22×C4C22×D7911yescharacteristic
245C22×C4C22×D7911yescharacteristic
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—3161no—
253C4⋊C4—1582no—
254C4⋊C4—1582no—
255C4⋊C4—1582no—
256C4⋊C4—1582no—
257C4⋊C4—1582no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C4⋊C4—1582no—
262C4⋊C4—1582no—
263C22⋊C4—3161no—
264C22⋊C4—3161no—
265C22⋊C4—1582no—
266C22⋊C4—1582no—
267C22⋊C4—1582no—
268C22⋊C4—1582no—
269C22⋊C4—1582no—
270C42—41no—
271C42—3161no—
272C42—794no—
273C23—1581no—
274C23—1581no—
275C23—1581no—
276C23—1581no—
277C23—1581no—
278C23—1581no—
279C23—1581no—
280C23C23×D7911yescharacteristic
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—792no—
301C2×C4—792no—
302C2×C4—792no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4D4×D7912yes—
322C2×C4#1192962412yes—
323C22—3161no—
324C22—3161no—
325C22—3161no—
326C22—3161no—
327C22—3161no—
328C22—3161no—
329C22—3161no—
330C22C2×D4×D7911yescharacteristic
331C22#41×D7911yescharacteristic
332C22C2×#1192962411yescharacteristic
333C22#1457920611yescharacteristic
334C22#1457920811yescharacteristic
335C22#1457920911yescharacteristic
336C22#1457920911yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—1582no—
349C4—1582no—
350C4—1582no—
351C2—6321no—
352C2#1909911011yescharacteristic
353C2#1909913811yescharacteristic
354C2#1909914011yescharacteristic
355C2#1909915911yescharacteristic
356C2#1909916011yescharacteristic
357C2#1909917111yescharacteristic
358C2#1909917211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#389×C79C2
prime radicalC23×D79C23
hypercenter#389D79
hypocenterC79#2664
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
2. C2×#14579151C2semidirect
3. #19098505C2semidirect
5. #19098497C2semidirect
6. #19098496C2semidirect
7. #19098494C2semidirect
11. #19098458C2semidirect
14. C4×Dic79⋊C4C2semidirect
15. #389×C79C2semidirect
180. C79#2664semidirect
192. #389D79semidirect