Finite Group Databasebeta

← #23770433

Subgroups — #23770433

Order 10112.

456 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579161C211yesmaximal, characteristic
2C2×#14579160C211yesmaximal, characteristic
3#19098497C211yesmaximal, characteristic
4#19098495C211yesmaximal, characteristic
5#19098484C211yesmaximal, characteristic
6#19098484C211yesmaximal, characteristic
7#19098484C211yesmaximal, characteristic
8#19098483C211yesmaximal, characteristic
9#19098467C211yesmaximal, characteristic
10#19098462C211yesmaximal, characteristic
11#19098460C211yesmaximal, characteristic
12#19098450C211yesmaximal, characteristic
13#19098449C211yesmaximal, characteristic
14#19098447C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C22×Dic158C2211yescharacteristic
19#14579161—24no—
20#14579160—24no—
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×C4⋊Dic79C2211yescharacteristic
24C2×C4⋊Dic79C2211yescharacteristic
25C2×C4⋊Dic79C2211yescharacteristic
26C2×C4⋊Dic79C2211yescharacteristic
27C2×C4⋊Dic79C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×Dic79⋊C4C2211yescharacteristic
31C2×Dic79⋊C4C2211yescharacteristic
32C2×Dic79⋊C4C2211yescharacteristic
33C2×Dic79⋊C4C2211yescharacteristic
34C2×C4×Dic79C2211yescharacteristic
35C2×C4×Dic79C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
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×C42×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—22no—
55C2×Dic158—41no—
56C2×Dic158—41no—
57C2×Dic158—41no—
58C2×Dic158—41no—
59C2×Dic158—41no—
60C2×Dic158—41no—
61C2×Dic158D414yes—
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C22×Dic79C2311yescharacteristic
68C22×Dic79C2311yescharacteristic
69C22×Dic79C2311yescharacteristic
70C4⋊Dic79—22no—
71C4⋊Dic79—22no—
72C4⋊Dic79—22no—
73C4⋊Dic79—22no—
74C4⋊Dic79—22no—
75C4⋊Dic79—41no—
76C4⋊Dic79—41no—
77Dic79⋊C4—22no—
78Dic79⋊C4—22no—
79Dic79⋊C4—41no—
80Dic79⋊C4—41no—
81Dic79⋊C4—41no—
82Dic79⋊C4Q814yescomplemented
83C4×Dic79—22no—
84C4×Dic79—41no—
85C22×C4×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×C79Q814yescomplemented
94C42×C79—22no—
95C23×C79C2411yescharacteristic
96C2×C4×C79—21no—
97C2×C4×C79—21no—
98C2×C4×C79—21no—
99C2×C4×C79—21no—
100C2×C4×C79—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×C79C2×D412yes—
113C2×C4×C79C2×Q812yes—
114C2×C4×C79C2×Q812yes—
115C2×C4×C79C2×Q812yes—
116C2×C4×C79C2×Q812yes—
117C2×Dic79—21no—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
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×Dic79C2×D412yes—
138C2×Dic79C2×D412yes—
139C2×Dic79C2×Q812yes—
140C2×Dic79C2×Q812yes—
141Dic158—44no—
142Dic158—44no—
143Dic158—44no—
144C22×C79C22×D411yescharacteristic
145C22×C79C22×Q811yescharacteristic
146C22×C79C22×Q811yescharacteristic
147C22×C79H(5,𝔽2)11yescharacteristic
148C22×C79H(5,𝔽2)11yescharacteristic
149C22×C792−1+411yescharacteristic
150C22×C792−1+411yescharacteristic
151C4×C79—22no—
152C4×C79—22no—
153C4×C79—22no—
154C4×C79—22no—
155C4×C79—22no—
156C4×C79—41no—
157C4×C79—41no—
158Dic79—22no—
159Dic79—22no—
160Dic79—22no—
161Dic79—22no—
162Dic79—41no—
163Dic79—41no—
164Dic79—41no—
165Dic79—41no—
166C2×C79#53411yescharacteristic
167C2×C79#54411yescharacteristic
168C2×C79#54411yescharacteristic
169C2×C79D4×Q811yescharacteristic
170C2×C79D4×Q811yescharacteristic
171C2×C79Q8211yescharacteristic
172C2×C79#56311yescharacteristic
173#2734—791nomaximal, Sylow
174C79#273411yescharacteristic, complemented, Sylow
175C2×C4⋊Q8—791no—
176C2×C4⋊Q8—791no—
177#398—791no—
178#398—791no—
179#395—791no—
180#395—791no—
181#395—791no—
182#395—791no—
183#391—791no—
184#389—791no—
185#389—791no—
186#387—791no—
187#387—791no—
188#387—791no—
189#387D7911yescharacteristic
190C22×Q8—791no—
191C22×Q8—791no—
192C22×Q8—791no—
193C4⋊Q8—1584no—
194C4⋊Q8—1584no—
195C2×C4⋊C4—791no—
196C2×C4⋊C4—791no—
197C2×C4⋊C4—791no—
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⋊C4C2×D7911yescharacteristic
209C2×C4⋊C4C2×D7911yescharacteristic
210C2×C42—791no—
211C2×C42—791no—
212C2×C42C2×D7911yescharacteristic
213#95—791no—
214#95—791no—
215#95—791no—
216#95—791no—
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95—791no—
222#95—791no—
223#95C2×D7911yescharacteristic
224#95C2×D7911yescharacteristic
225#95C2×D7911yescharacteristic
226#95C2×D7911yescharacteristic
227C2×Q8—3161no—
228C2×Q8—3161no—
229C2×Q8—3161no—
230C2×Q8—3161no—
231C2×Q8—3161no—
232C2×Q8—3161no—
233C2×Q8—794no—
234C2×Q8—1582no—
235C2×Q8—1582no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4C22×D7911yescharacteristic
245C22×C4C22×D7911yescharacteristic
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—3161no—
253C4⋊C4—3161no—
254C4⋊C4—3161no—
255C4⋊C4—3161no—
256C4⋊C4—3161no—
257C4⋊C4—794no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C4⋊C4—1582no—
262C4⋊C4—1582no—
263C4⋊C4—1582no—
264C4⋊C4—1582no—
265C4⋊C4Dic15814yescomplemented
266C42—22no—
267C42—3161no—
268C42—1582no—
269C23C23×D7911yescharacteristic
270Q8—3164no—
271Q8—3164no—
272Q8—3164no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
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—792no—
290C2×C4—792no—
291C2×C4—792no—
292C2×C4—792no—
293C2×C4—1581no—
294C2×C4—1581no—
295C2×C4—1581no—
296C2×C4—1581no—
297C2×C4—1581no—
298C2×C4—1581no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
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×C4D4×D7912yes—
314C2×C4Q8×D7912yes—
315C2×C4C2×Dic15812yes—
316C2×C4C2×Dic15812yes—
317C2×C4C2×Dic15812yes—
318C22C2×D4×D7911yescharacteristic
319C22C2×Q8×D7911yescharacteristic
320C22C22×Dic15811yescharacteristic
321C22#1457920711yescharacteristic
322C22#1457920711yescharacteristic
323C22#1457920811yescharacteristic
324C22#1457920811yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—22no—
329C4—22no—
330C4—41no—
331C4—41no—
332C4—3161no—
333C4—3161no—
334C4—3161no—
335C4—3161no—
336C4—1582no—
337C4—1582no—
338C4—1582no—
339C4—1582no—
340C2#1909912411yescharacteristic
341C2#1909919111yescharacteristic
342C2#1909919311yescharacteristic
343C2#1909922611yescharacteristic
344C2D4×Dic15811yescharacteristic
345C2Q8×Dic15811yescharacteristic
346C2#1909931511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#387×C79C2
hypercenter#387D79
hypocenterC79#2734
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
82. Dic79⋊C4Q8semidirect
93. C4⋊C4×C79Q8semidirect
174. C79#2734semidirect
265. C4⋊C4Dic158semidirect