Finite Group Databasebeta

← #23768810

Subgroups — #23768810

Order 10112.

412 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098495C211yesmaximal, characteristic
2#19098484C211yesmaximal, characteristic
3#19098484C211yesmaximal, characteristic
4#19098483C211yesmaximal, characteristic
5#19098469C211yesmaximal, characteristic
6#19098467C211yesmaximal, characteristic
7#19098467C211yesmaximal, characteristic
8#19098462C211yesmaximal, characteristic
9#19098460C211yesmaximal, characteristic
10#19098449C211yesmaximal, characteristic
11#19098446C211yesmaximal, characteristic
12#19098446C211yesmaximal, characteristic
13C4⋊C4×Dic79C211yesmaximal, characteristic
14C4×C4⋊Dic79C211yesmaximal, characteristic
15#387×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×C4⋊Dic79C2211yescharacteristic
23C2×C4⋊Dic79C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C2×C4×Dic79C2211yescharacteristic
30C2×C4×Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
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×C4⋊C4×C79C2211yescharacteristic
46C2×C42×C79C2211yescharacteristic
47#95×C79C2211yescharacteristic
48#95×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C2×Dic158—22no—
52C2×Dic158—22no—
53C2×Dic158—22no—
54C2×Dic158—41no—
55C2×Dic158—41no—
56C2×Dic158—41no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C4⋊Dic79—22no—
66C4⋊Dic79—22no—
67C4⋊Dic79—41no—
68C4⋊Dic79—41no—
69C4⋊Dic79—41no—
70C4⋊Dic79Q814yescomplemented
71Dic79⋊C4—22no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75C4×Dic79—22no—
76C4×Dic79—41no—
77C4×Dic79—41no—
78C4×Dic79—41no—
79C22×C4×C79C2311yescharacteristic
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C4⋊C4×C79—22no—
87C4⋊C4×C79Q814yescomplemented
88C42×C79—22no—
89C23×C79C2411yescharacteristic
90C2×C4×C79—21no—
91C2×C4×C79—21no—
92C2×C4×C79—21no—
93C2×C4×C79—21no—
94C2×C4×C79—21no—
95C2×C4×C79—21no—
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×C79C2×Q812yes—
107C2×C4×C79C2×Q812yes—
108C2×C4×C79C2×Q812yes—
109C2×C4×C79C2×Q812yes—
110C2×C4×C79#4112yes—
111C2×Dic79—21no—
112C2×Dic79—21no—
113C2×Dic79—21no—
114C2×Dic79—21no—
115C2×Dic79—21no—
116C2×Dic79—21no—
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×Dic79C2×Q812yes—
132C2×Dic79C2×Q812yes—
133C2×Dic79#4112yes—
134C2×Dic79#4112yes—
135Dic158—44no—
136Dic158—44no—
137C22×C79C22×Q811yescharacteristic
138C22×C79C22×Q811yescharacteristic
139C22×C79C2×#4111yescharacteristic
140C22×C79C2×#4111yescharacteristic
141C22×C79C2×#4111yescharacteristic
142C22×C79H(5,𝔽2)11yescharacteristic
143C22×C79H(5,𝔽2)11yescharacteristic
144C4×C79—22no—
145C4×C79—22no—
146C4×C79—22no—
147C4×C79—22no—
148C4×C79—22no—
149C4×C79—41no—
150C4×C79—41no—
151Dic79—22no—
152Dic79—22no—
153Dic79—22no—
154Dic79—22no—
155Dic79—41no—
156Dic79—41no—
157Dic79—41no—
158Dic79—41no—
159C2×C79#53311yescharacteristic
160C2×C79#53311yescharacteristic
161C2×C79#53811yescharacteristic
162C2×C79#55111yescharacteristic
163C2×C79#55411yescharacteristic
164C2×C79#55411yescharacteristic
165C2×C79Q8211yescharacteristic
166#2586—791nomaximal, Sylow
167C79#258611yescharacteristic, complemented, Sylow
168#398—791no—
169#395—791no—
170#395—791no—
171#395—791no—
172#391—791no—
173#391—791no—
174#391—791no—
175#389—791no—
176#389—791no—
177#387—791no—
178#387—791no—
179#387—791no—
180#387D7911yescharacteristic
181C4×C4⋊C4—791no—
182C4×C4⋊C4—791no—
183C22×Q8—791no—
184C22×Q8—791no—
185C2×C4⋊C4—791no—
186C2×C4⋊C4—791no—
187C2×C4⋊C4—791no—
188C2×C4⋊C4—791no—
189C2×C4⋊C4—791no—
190C2×C4⋊C4—791no—
191C2×C4⋊C4—791no—
192C2×C4⋊C4—791no—
193C2×C4⋊C4—791no—
194C2×C4⋊C4—791no—
195C2×C4⋊C4C2×D7911yescharacteristic
196C2×C4⋊C4C2×D7911yescharacteristic
197C2×C42—791no—
198C2×C42—791no—
199C2×C42—791no—
200C2×C42—791no—
201C2×C42C2×D7911yescharacteristic
202#95—791no—
203#95—791no—
204#95—791no—
205#95—791no—
206#95—791no—
207#95—791no—
208#95—791no—
209#95—791no—
210#95—791no—
211#95—791no—
212#95—791no—
213#95—791no—
214#95C2×D7911yescharacteristic
215#95C2×D7911yescharacteristic
216#95C2×D7911yescharacteristic
217#95C2×D7911yescharacteristic
218C2×Q8—3161no—
219C2×Q8—3161no—
220C2×Q8—3161no—
221C2×Q8—1582no—
222C2×Q8—1582no—
223C2×Q8—1582no—
224C22×C4—791no—
225C22×C4—791no—
226C22×C4—791no—
227C22×C4—791no—
228C22×C4—791no—
229C22×C4—791no—
230C22×C4—791no—
231C22×C4—791no—
232C22×C4C22×D7911yescharacteristic
233C22×C4C22×D7911yescharacteristic
234C22×C4C22×D7911yescharacteristic
235C22×C4C22×D7911yescharacteristic
236C22×C4C22×D7911yescharacteristic
237C22×C4C22×D7911yescharacteristic
238C22×C4C22×D7911yescharacteristic
239C4⋊C4—22no—
240C4⋊C4—3161no—
241C4⋊C4—3161no—
242C4⋊C4—3161no—
243C4⋊C4—3161no—
244C4⋊C4—3161no—
245C4⋊C4—3161no—
246C4⋊C4—794no—
247C4⋊C4—1582no—
248C4⋊C4—1582no—
249C4⋊C4—1582no—
250C4⋊C4Dic15814yescomplemented
251C42—22no—
252C42—3161no—
253C42—3161no—
254C42—3161no—
255C42—1582no—
256C23C23×D7911yescharacteristic
257Q8—3164no—
258Q8—3164no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—792no—
276C2×C4—792no—
277C2×C4—792no—
278C2×C4—792no—
279C2×C4—1581no—
280C2×C4—1581no—
281C2×C4—1581no—
282C2×C4—1581no—
283C2×C4—1581no—
284C2×C4—1581no—
285C2×C4—1581no—
286C2×C4—1581no—
287C2×C4—1581no—
288C2×C4—1581no—
289C2×C4—1581no—
290C2×C4—1581no—
291C2×C4—1581no—
292C2×C4—1581no—
293C2×C4—1581no—
294C2×C4—1581no—
295C2×C4—1581no—
296C2×C4—1581no—
297C2×C4—1581no—
298C2×C4—1581no—
299C2×C4Q8×D7912yes—
300C2×C4C2×Dic15812yes—
301C2×C4C2×Dic15812yes—
302C2×C4C2×Dic15812yes—
303C2×C4#1192962312yes—
304C22C2×Q8×D7911yescharacteristic
305C22C22×Dic15811yescharacteristic
306C22#41×D7911yescharacteristic
307C22#41×D7911yescharacteristic
308C22C2×#1192962311yescharacteristic
309C22#1457920711yescharacteristic
310C22#1457920711yescharacteristic
311C4—22no—
312C4—22no—
313C4—22no—
314C4—22no—
315C4—22no—
316C4—41no—
317C4—41no—
318C4—3161no—
319C4—3161no—
320C4—3161no—
321C4—3161no—
322C4—1582no—
323C4—1582no—
324C4—1582no—
325C4—1582no—
326C2#1909911511yescharacteristic
327C2#1909911611yescharacteristic
328C2#1909915211yescharacteristic
329C2#1909923611yescharacteristic
330C2#1909926911yescharacteristic
331C2#1909927011yescharacteristic
332C2Q8×Dic15811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#387×C79C2
hypercenter#387D79
hypocenterC79#2586
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
70. C4⋊Dic79Q8semidirect
87. C4⋊C4×C79Q8semidirect
167. C79#2586semidirect
250. C4⋊C4Dic158semidirect