Finite Group Databasebeta

← #21427930

Subgroups — #21427930

Order 7552.

484 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×#14273726C211yesmaximal, characteristic
2C2×#14273692C211yesmaximal, characteristic
3#16837336C211yesmaximal, characteristic
4#16837322C211yesmaximal, characteristic
5#16837322C211yesmaximal, characteristic
6#16837307C211yesmaximal, characteristic
7#16837306C211yesmaximal, characteristic
8#16837306C211yesmaximal, characteristic
9#16837306C211yesmaximal, characteristic
10#16837297C211yesmaximal, characteristic
11#16837297C211yesmaximal, characteristic
12#16837289C211yesmaximal, characteristic
13#16837283C211yesmaximal, characteristic
14#16837253C211yesmaximal, characteristic
15C59×#398C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18C22×Dic118C2211yescharacteristic
19#14273726—24no—
20#14273692—24no—
21C2×C4⋊Dic59C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×Dic59⋊C4C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×Dic59⋊C4C2211yescharacteristic
28C2×Dic59⋊C4C2211yescharacteristic
29C2×Dic59⋊C4C2211yescharacteristic
30C2×C4×Dic59C2211yescharacteristic
31C2×C4×Dic59C2211yescharacteristic
32C2×C4×Dic59C2211yescharacteristic
33C2×C4×Dic59C2211yescharacteristic
34C2×C4×Dic59C2211yescharacteristic
35C59⋊#95C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C59⋊#95C2211yescharacteristic
46C2×C4⋊C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48C2×C4⋊C4×C59C2211yescharacteristic
49C2×C4⋊C4×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52#95×C59C2211yescharacteristic
53C22×C4×C59C2311yescharacteristic
54C22×C4×C59C2311yescharacteristic
55C22×C4×C59C2311yescharacteristic
56C22×C4×C59C2311yescharacteristic
57C22×C4×C59C2311yescharacteristic
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×Dic59C2311yescharacteristic
61C22×Dic59C2311yescharacteristic
62C22×Dic59C2311yescharacteristic
63C22×Dic59C2311yescharacteristic
64C22×Dic59C2311yescharacteristic
65C22×Dic59C2311yescharacteristic
66C22×Dic59C2311yescharacteristic
67C22×Dic59C2311yescharacteristic
68C2×Dic118—22no—
69C2×Dic118—22no—
70C2×Dic118—22no—
71C2×Dic118—22no—
72C2×Dic118—22no—
73C2×Dic118—22no—
74C2×Dic118—41no—
75C2×Dic118—41no—
76C2×Dic118Q814yescomplemented
77C4⋊C4×C59—22no—
78C4⋊C4×C59—22no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊Dic59—22no—
82Dic59⋊C4—22no—
83Dic59⋊C4—22no—
84Dic59⋊C4—22no—
85Dic59⋊C4—22no—
86Dic59⋊C4—41no—
87Dic59⋊C4—41no—
88Dic59⋊C4D414yes—
89Dic59⋊C4Q814yescomplemented
90C4×Dic59—22no—
91C4×Dic59—22no—
92C4×Dic59—22no—
93C4×Dic59—22no—
94C4×Dic59—22no—
95C23×C59C2411yescharacteristic
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59C2×D412yes—
115C2×C4×C59C2×Q812yes—
116C2×C4×C59C2×Q812yes—
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—21no—
132C2×Dic59—21no—
133C2×Dic59C2×D412yes—
134C2×Dic59C2×D412yes—
135C2×Dic59C2×Q812yes—
136C2×Dic59C2×Q812yes—
137C2×Dic59C2×Q812yes—
138C2×Dic59C2×Q812yes—
139C2×Dic59#4112yes—
140C2×Dic59#4112yes—
141Dic118—28no—
142Dic118—44no—
143Dic118—44no—
144C22×C59C22×D411yescharacteristic
145C22×C59C22×Q811yescharacteristic
146C22×C59C22×Q811yescharacteristic
147C22×C59C2×#4111yescharacteristic
148C22×C59C2×#4111yescharacteristic
149C22×C59H(5,𝔽2)11yescharacteristic
150C22×C592−1+411yescharacteristic
151C4×C59—22no—
152C4×C59—22no—
153C4×C59—22no—
154C4×C59—41no—
155C4×C59—41no—
156C4×C59—41no—
157C4×C59—41no—
158Dic59—22no—
159Dic59—22no—
160Dic59—22no—
161Dic59—22no—
162Dic59—22no—
163Dic59—41no—
164Dic59—41no—
165Dic59C22⋊Q814yes—
166#2451—591nomaximal, Sylow
167C2×C59C2×C22⋊Q811yescharacteristic
168C2×C59#53311yescharacteristic
169C2×C59#54211yescharacteristic
170C2×C59#54611yescharacteristic
171C2×C59D4×Q811yescharacteristic
172C2×C59#55711yescharacteristic
173C2×C59Q8211yescharacteristic
174C2×C4⋊Q8—591no—
175C2×C4×Q8—591no—
176#398—591no—
177#398D5911yescharacteristic
178#395—591no—
179#395—591no—
180#391—591no—
181#391—591no—
182#391—591no—
183#391—591no—
184#389—591no—
185#389—591no—
186#387—591no—
187#387—591no—
188C4×C4⋊C4—591no—
189C59#245111yescharacteristic, complemented, Sylow
190C22×Q8—591no—
191C22×Q8—591no—
192C22×Q8—591no—
193C4⋊Q8—1184no—
194C4×Q8—1184no—
195C2×C4⋊C4—591no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—591no—
201C2×C4⋊C4—591no—
202C2×C4⋊C4—591no—
203C2×C4⋊C4—591no—
204C2×C4⋊C4C2×D5911yescharacteristic
205C2×C4⋊C4C2×D5911yescharacteristic
206C2×C4⋊C4C2×D5911yescharacteristic
207C2×C4⋊C4C2×D5911yescharacteristic
208C2×C42—591no—
209C2×C42—591no—
210C2×C42—591no—
211C2×C42—591no—
212C2×C42—591no—
213#95—591no—
214#95—591no—
215#95—591no—
216#95—591no—
217#95—591no—
218#95—591no—
219#95—591no—
220#95—591no—
221#95—591no—
222#95—591no—
223#95—591no—
224#95C2×D5911yescharacteristic
225#95C2×D5911yescharacteristic
226#95C2×D5911yescharacteristic
227C2×Q8—594no—
228C2×Q8—1182no—
229C2×Q8—1182no—
230C2×Q8—1182no—
231C2×Q8—1182no—
232C2×Q8—1182no—
233C2×Q8—1182no—
234C2×Q8—2361no—
235C2×Q8—2361no—
236C22×C4—591no—
237C22×C4—591no—
238C22×C4—591no—
239C22×C4—591no—
240C22×C4—591no—
241C22×C4—591no—
242C22×C4—591no—
243C22×C4—591no—
244C22×C4C22×D5911yescharacteristic
245C22×C4C22×D5911yescharacteristic
246C22×C4C22×D5911yescharacteristic
247C22×C4C22×D5911yescharacteristic
248C22×C4C22×D5911yescharacteristic
249C22×C4C22×D5911yescharacteristic
250C22×C4C22×D5911yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—594no—
256C4⋊C4—594no—
257C4⋊C4—1182no—
258C4⋊C4—1182no—
259C4⋊C4—1182no—
260C4⋊C4—1182no—
261C4⋊C4—1182no—
262C4⋊C4—2361no—
263C4⋊C4—2361no—
264C42—1182no—
265C42—1182no—
266C42—1182no—
267C42—1182no—
268C42—1182no—
269C23C23×D5911yescharacteristic
270Q8—1188no—
271Q8—2364no—
272Q8—2364no—
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—21no—
290C2×C4—21no—
291C2×C4—592no—
292C2×C4—592no—
293C2×C4—592no—
294C2×C4—592no—
295C2×C4—592no—
296C2×C4—592no—
297C2×C4—592no—
298C2×C4—592no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—1181no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4D4×D5912yes—
316C2×C4Q8×D5912yes—
317C2×C4Q8×D5912yes—
318C22C2×D4×D5911yescharacteristic
319C22C2×Q8×D5911yescharacteristic
320C22C2×Q8×D5911yescharacteristic
321C22#41×D5911yescharacteristic
322C22#41×D5911yescharacteristic
323C22#1427377211yescharacteristic
324C22#1427377411yescharacteristic
325C4—22no—
326C4—22no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—594no—
333C4—1182no—
334C4—1182no—
335C4—1182no—
336C4—1182no—
337C4—1182no—
338C4—2361no—
339C4—2361no—
340C2C22⋊Q8×D5911yescharacteristic
341C2#1683795811yescharacteristic
342C2#1683802011yescharacteristic
343C2#1683804111yescharacteristic
344C2#1683806511yescharacteristic
345C2#1683812911yescharacteristic
346C2#1683813211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2451
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
76. C2×Dic118Q8semidirect
89. Dic59⋊C4Q8semidirect
189. C59#2451semidirect