Finite Group Databasebeta

← #23768430

Subgroups — #23768430

Order 10112.

452 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14579151C211yesmaximal, characteristic
2C2×#14579151C211yesmaximal, characteristic
3#19098497C211yesmaximal, characteristic
4#19098496C211yesmaximal, characteristic
5#19098495C211yesmaximal, characteristic
6#19098460C211yesmaximal, characteristic
7#19098460C211yesmaximal, characteristic
8#19098458C211yesmaximal, characteristic
9#19098458C211yesmaximal, characteristic
10#19098432C211yesmaximal, characteristic
11#19098432C211yesmaximal, characteristic
12#19098432C211yesmaximal, characteristic
13#19098414C211yesmaximal, characteristic
14#19098414C211yesmaximal, characteristic
15#398×C79C211yesmaximal, characteristic
16#14579151—24no—
17#14579151—24no—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×Dic79⋊C4C2211yescharacteristic
29C2×Dic79⋊C4C2211yescharacteristic
30C2×Dic79⋊C4C2211yescharacteristic
31C2×Dic79⋊C4C2211yescharacteristic
32C2×Dic79⋊C4C2211yescharacteristic
33C2×Dic79⋊C4C2211yescharacteristic
34C2×Dic79⋊C4C2211yescharacteristic
35C2×Dic79⋊C4C2211yescharacteristic
36C2×C4×Dic79C2211yescharacteristic
37C2×C4×Dic79C2211yescharacteristic
38C2×C4×Dic79C2211yescharacteristic
39C2×C4×Dic79C2211yescharacteristic
40C2×C4×Dic79C2211yescharacteristic
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
50#95×C79C2211yescharacteristic
51#95×C79C2211yescharacteristic
52#95×C79C2211yescharacteristic
53C22×Dic79C2311yescharacteristic
54C22×Dic79C2311yescharacteristic
55C22×Dic79C2311yescharacteristic
56C22×Dic79C2311yescharacteristic
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C4⋊Dic79—22no—
62C4⋊Dic79—22no—
63C4⋊Dic79—41no—
64C4⋊Dic79—41no—
65Dic79⋊C4—22no—
66Dic79⋊C4—22no—
67Dic79⋊C4—22no—
68Dic79⋊C4—22no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—22no—
72Dic79⋊C4—22no—
73Dic79⋊C4—22no—
74Dic79⋊C4—22no—
75Dic79⋊C4—41no—
76Dic79⋊C4—41no—
77Dic79⋊C4D414yes—
78Dic79⋊C4Q814yes—
79C4×Dic79—22no—
80C4×Dic79—22no—
81C4×Dic79—22no—
82C4×Dic79—22no—
83C4×Dic79Q814yes—
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—
93C4⋊C4×C79—41no—
94C4⋊C4×C79—41no—
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×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79C2×D412yes—
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×Dic79C2×D412yes—
134C2×Dic79C2×D412yes—
135C2×Dic79C2×Q812yes—
136C2×Dic79C2×Q812yes—
137C2×Dic79C2×Q812yes—
138C2×Dic79C2×Q812yes—
139C2×Dic79#4112yes—
140C2×Dic79#4112yes—
141C22×C79C22×D411yescharacteristic
142C22×C79C22×Q811yescharacteristic
143C22×C79C22×Q811yescharacteristic
144C22×C79C2×#4111yescharacteristic
145C22×C79C2×#4111yescharacteristic
146C22×C79H(5,𝔽2)11yescharacteristic
147C22×C792−1+411yescharacteristic
148C4×C79—22no—
149C4×C79—22no—
150C4×C79—22no—
151C4×C79—41no—
152C4×C79—41no—
153C4×C79—41no—
154C4×C79—41no—
155Dic79—22no—
156Dic79—22no—
157Dic79—41no—
158Dic79—41no—
159Dic79—41no—
160Dic79—41no—
161Dic79#12514yescomplemented
162Dic79C4⋊Q814yes—
163C2×C79C2×#12511yescharacteristic
164C2×C79C2×C4⋊Q811yescharacteristic
165C2×C79#54411yescharacteristic
166C2×C79#54711yescharacteristic
167C2×C79#55011yescharacteristic
168C2×C79#55411yescharacteristic
169C2×C79#55711yescharacteristic
170#2552—791nomaximal, Sylow
171C79#255211yescharacteristic, complemented, Sylow
172C2×#125—791no—
173C2×#125—791no—
174#398—791no—
175#398—791no—
176#398—791no—
177#398D7911yescharacteristic
178#389—791no—
179#389—791no—
180#389—791no—
181#389—791no—
182#384—791no—
183#384—791no—
184#384—791no—
185C4×C4⋊C4—791no—
186C4×C4⋊C4—791no—
187#125—1584no—
188#125—1584no—
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⋊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⋊C4C2×D7911yescharacteristic
208C2×C4⋊C4C2×D7911yescharacteristic
209C2×C4⋊C4C2×D7911yescharacteristic
210C2×C4⋊C4C2×D7911yescharacteristic
211C2×C42—791no—
212C2×C42—791no—
213C2×C42—791no—
214C2×C42—791no—
215C2×C42—791no—
216#95—791no—
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95C2×D7911yescharacteristic
222#95C2×D7911yescharacteristic
223#95C2×D7911yescharacteristic
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—22no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—3161no—
244C4⋊C4—3161no—
245C4⋊C4—3161no—
246C4⋊C4—3161no—
247C4⋊C4—794no—
248C4⋊C4—794no—
249C4⋊C4—1582no—
250C4⋊C4—1582no—
251C4⋊C4—1582no—
252C4⋊C4—1582no—
253C4⋊C4—1582no—
254C4⋊C4—1582no—
255C4⋊C4—1582no—
256C4⋊C4—1582no—
257C4⋊C4—1582no—
258C4⋊C4—1582no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C42—794no—
262C42—1582no—
263C42—1582no—
264C42—1582no—
265C42—1582no—
266C23C23×D7911yescharacteristic
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—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—792no—
286C2×C4—792no—
287C2×C4—792no—
288C2×C4—792no—
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×C4D4×D7912yes—
310C2×C4Q8×D7912yes—
311C2×C4Q8×D7912yes—
312C22C2×D4×D7911yescharacteristic
313C22C2×Q8×D7911yescharacteristic
314C22C2×Q8×D7911yescharacteristic
315C22#41×D7911yescharacteristic
316C22#41×D7911yescharacteristic
317C22#1457920611yescharacteristic
318C22#1457920811yescharacteristic
319C4—22no—
320C4—22no—
321C4—22no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—3161no—
327C4—3161no—
328C4—3161no—
329C4—3161no—
330C4—794no—
331C4—794no—
332C4—1582no—
333C4—1582no—
334C2#125×D7911yescharacteristic
335C2C4⋊Q8×D7911yescharacteristic
336C2#1909919211yescharacteristic
337C2#1909921111yescharacteristic
338C2#1909923111yescharacteristic
339C2#1909926711yescharacteristic
340C2#1909929011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#398×C79C2
hypercenter#398D79
hypocenterC79#2552
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
161. Dic79#125semidirect
171. C79#2552semidirect