Finite Group Databasebeta

← #23770177

Subgroups — #23770177

Order 10112.

432 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579160C211yesmaximal, characteristic
2#19098502C211yesmaximal, characteristic
3#19098501C211yesmaximal, characteristic
4#19098496C211yesmaximal, characteristic
5#19098493C211yesmaximal, characteristic
6#19098483C211yesmaximal, characteristic
7#19098483C211yesmaximal, characteristic
8#19098469C211yesmaximal, characteristic
9#19098468C211yesmaximal, characteristic
10#19098458C211yesmaximal, characteristic
11#19098449C211yesmaximal, characteristic
12#19098447C211yesmaximal, characteristic
13#19098444C211yesmaximal, characteristic
14#19098444C211yesmaximal, characteristic
15C2×#125×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C22×Dic158C2211yescharacteristic
18#14579160—24no—
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C79⋊#95C2211yescharacteristic
30C79⋊#95C2211yescharacteristic
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
44C79⋊#95C2211yescharacteristic
45#125×C79—24no—
46C2×C4⋊C4×C79C2211yescharacteristic
47C2×C4⋊C4×C79C2211yescharacteristic
48C2×C4⋊C4×C79C2211yescharacteristic
49C2×C4⋊C4×C79C2211yescharacteristic
50C2×C4⋊C4×C79C2211yescharacteristic
51C2×C4⋊C4×C79C2211yescharacteristic
52C2×C42×C79C2211yescharacteristic
53C2×Dic158—22no—
54C2×Dic158—22no—
55C2×Dic158—22no—
56C2×Dic158—22no—
57C2×Dic158—41no—
58C2×Dic158—41no—
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C22×Dic79C2311yescharacteristic
66C22×Dic79C2311yescharacteristic
67C4⋊Dic79—22no—
68C4⋊Dic79—41no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4Q814yescomplemented
75C4×Dic79—22no—
76C4×Dic79—41no—
77C22×C4×C79C2311yescharacteristic
78C22×C4×C79C2311yescharacteristic
79C22×C4×C79C2311yescharacteristic
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C4⋊C4×C79—22no—
85C4⋊C4×C79—22no—
86C4⋊C4×C79—22no—
87C4⋊C4×C79—22no—
88C4⋊C4×C79—22no—
89C4⋊C4×C79D414yes—
90C42×C79—22no—
91C23×C79C2411yescharacteristic
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×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79C2×D412yes—
110C2×C4×C79C2×D412yes—
111C2×C4×C79C2×D412yes—
112C2×C4×C79C2×Q812yes—
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×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79C2×Q812yes—
135C2×Dic79C2×Q812yes—
136C2×Dic79#4112yes—
137Dic158—44no—
138Dic158—44no—
139C22×C79C22×D411yescharacteristic
140C22×C79C22×Q811yescharacteristic
141C22×C79C2×#4111yescharacteristic
142C22×C79H(5,𝔽2)11yescharacteristic
143C22×C792−1+411yescharacteristic
144C22×C792−1+411yescharacteristic
145C22×C792−1+411yescharacteristic
146C4×C79—22no—
147C4×C79—22no—
148C4×C79—22no—
149C4×C79—22no—
150C4×C79—41no—
151C4×C79—41no—
152C4×C79—41no—
153Dic79—22no—
154Dic79—22no—
155Dic79—22no—
156Dic79—41no—
157Dic79—41no—
158Dic79—41no—
159Dic79—41no—
160Dic79—41no—
161C2×C79#53611yescharacteristic
162C2×C79#54111yescharacteristic
163C2×C79#54411yescharacteristic
164C2×C79#54611yescharacteristic
165C2×C79D4×Q811yescharacteristic
166C2×C79#55711yescharacteristic
167C2×C79#56311yescharacteristic
168#2713—791nomaximal, Sylow
169C79#271311yescharacteristic, complemented, Sylow
170C2×C4⋊Q8—791no—
171C2×#125D7911yescharacteristic
172#400—791no—
173#400—791no—
174#398—791no—
175#398—791no—
176#395—791no—
177#395—791no—
178#391—791no—
179#391—791no—
180#389—791no—
181#387—791no—
182#387—791no—
183#387—791no—
184#387—791no—
185C22×Q8—791no—
186C22×Q8—791no—
187C4⋊Q8—1584no—
188#125—24no—
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⋊C4—791no—
196C2×C4⋊C4—791no—
197C2×C4⋊C4C2×D7911yescharacteristic
198C2×C4⋊C4C2×D7911yescharacteristic
199C2×C4⋊C4C2×D7911yescharacteristic
200C2×C4⋊C4C2×D7911yescharacteristic
201C2×C4⋊C4C2×D7911yescharacteristic
202C2×C4⋊C4C2×D7911yescharacteristic
203C2×C42—791no—
204C2×C42—791no—
205C2×C42C2×D7911yescharacteristic
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#95—791no—
215#95—791no—
216#95—791no—
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95—791no—
222C2×Q8—3161no—
223C2×Q8—3161no—
224C2×Q8—1582no—
225C2×Q8—1582no—
226C2×Q8—1582no—
227C2×Q8—1582no—
228C22×C4—791no—
229C22×C4—791no—
230C22×C4—791no—
231C22×C4—791no—
232C22×C4—791no—
233C22×C4—791no—
234C22×C4—791no—
235C22×C4—791no—
236C22×C4C22×D7911yescharacteristic
237C22×C4C22×D7911yescharacteristic
238C22×C4C22×D7911yescharacteristic
239C22×C4C22×D7911yescharacteristic
240C22×C4C22×D7911yescharacteristic
241C22×C4C22×D7911yescharacteristic
242C22×C4C22×D7911yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—3161no—
249C4⋊C4—3161no—
250C4⋊C4—3161no—
251C4⋊C4—794no—
252C4⋊C4—1582no—
253C4⋊C4—1582no—
254C4⋊C4—1582no—
255C4⋊C4—1582no—
256C4⋊C4C22⋊D7914yes—
257C42—22no—
258C42—3161no—
259C42—1582no—
260C23C23×D7911yescharacteristic
261Q8—3164no—
262Q8—3164no—
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—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—792no—
281C2×C4—792no—
282C2×C4—792no—
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×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4C2×C22⋊D7912yes—
305C2×C4C2×C22⋊D7912yes—
306C2×C4C2×C22⋊D7912yes—
307C2×C4Q8×D7912yes—
308C22C22×C22⋊D7911yescharacteristic
309C22C2×Q8×D7911yescharacteristic
310C22#41×D7911yescharacteristic
311C22#1457920711yescharacteristic
312C22#1457920811yescharacteristic
313C22#1457920811yescharacteristic
314C22#1457920911yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—3161no—
323C4—3161no—
324C4—3161no—
325C4—3161no—
326C4—3161no—
327C4—1582no—
328C4—1582no—
329C4—1582no—
330C2#1909913411yescharacteristic
331C2#1909917211yescharacteristic
332C2#1909919311yescharacteristic
333C2#1909920111yescharacteristic
334C2Q8×C22⋊D7911yescharacteristic
335C2#1909929011yescharacteristic
336C2#1909931711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
FittingC2×#125×C79C2
hypercenterC2×#125D79
hypocenterC79#2713
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
74. Dic79⋊C4Q8semidirect
169. C79#2713semidirect