Finite Group Databasebeta

← #21430883

Subgroups — #21430883

Order 7552.

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×#14273726C211yesmaximal, characteristic
2C2×#14273717C211yesmaximal, characteristic
3#16837344C211yesmaximal, characteristic
4#16837343C211yesmaximal, characteristic
5#16837335C211yesmaximal, characteristic
6#16837322C211yesmaximal, characteristic
7#16837322C211yesmaximal, characteristic
8#16837307C211yesmaximal, characteristic
9#16837306C211yesmaximal, characteristic
10#16837299C211yesmaximal, characteristic
11#16837289C211yesmaximal, characteristic
12#16837284C211yesmaximal, characteristic
13#16837283C211yesmaximal, characteristic
14#16837283C211yesmaximal, characteristic
15C59×#398C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C22×Dic118C2211yescharacteristic
18#14273726—24no—
19#14273717—24no—
20C2×C4⋊Dic59C2211yescharacteristic
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
33C59⋊#95C2211yescharacteristic
34C59⋊#95C2211yescharacteristic
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—41no—
73C2×Dic118—41no—
74C4⋊C4×C59—22no—
75C4⋊C4×C59—22no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊Dic59—22no—
79C4⋊Dic59—22no—
80Dic59⋊C4—22no—
81Dic59⋊C4—22no—
82Dic59⋊C4—22no—
83Dic59⋊C4—22no—
84Dic59⋊C4—22no—
85Dic59⋊C4—41no—
86Dic59⋊C4D414yes—
87Dic59⋊C4Q814yescomplemented
88C4×Dic59—22no—
89C4×Dic59—22no—
90C4×Dic59—41no—
91C23×C59C2411yescharacteristic
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
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×C59C2×D412yes—
112C2×C4×C59C2×Q812yes—
113C2×Dic59—21no—
114C2×Dic59—21no—
115C2×Dic59—21no—
116C2×Dic59—21no—
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×Dic59C2×D412yes—
133C2×Dic59C2×D412yes—
134C2×Dic59C2×Q812yes—
135C2×Dic59C2×Q812yes—
136C2×Dic59#4112yes—
137Dic118—44no—
138Dic118—44no—
139C22×C59C22×D411yescharacteristic
140C22×C59C22×Q811yescharacteristic
141C22×C59C2×#4111yescharacteristic
142C22×C59H(5,𝔽2)11yescharacteristic
143C22×C592−1+411yescharacteristic
144C22×C592−1+411yescharacteristic
145C22×C592−1+411yescharacteristic
146C4×C59—22no—
147C4×C59—22no—
148C4×C59—41no—
149C4×C59—41no—
150C4×C59—41no—
151C4×C59—41no—
152C4×C59—41no—
153Dic59—22no—
154Dic59—22no—
155Dic59—22no—
156Dic59—22no—
157Dic59—22no—
158Dic59—41no—
159Dic59—41no—
160Dic59—41no—
161#2713—591nomaximal, Sylow
162C2×C59#53611yescharacteristic
163C2×C59#54111yescharacteristic
164C2×C59#54411yescharacteristic
165C2×C59#54611yescharacteristic
166C2×C59D4×Q811yescharacteristic
167C2×C59#55711yescharacteristic
168C2×C59#56311yescharacteristic
169C2×C4⋊Q8—591no—
170C2×#125—591no—
171#400—591no—
172#400—591no—
173#398—591no—
174#398D5911yescharacteristic
175#395—591no—
176#395—591no—
177#391—591no—
178#391—591no—
179#389—591no—
180#387—591no—
181#387—591no—
182#387—591no—
183#387—591no—
184C59#271311yescharacteristic, complemented, Sylow
185C22×Q8—591no—
186C22×Q8—591no—
187C4⋊Q8—1184no—
188#125—1184no—
189C2×C4⋊C4—591no—
190C2×C4⋊C4—591no—
191C2×C4⋊C4—591no—
192C2×C4⋊C4—591no—
193C2×C4⋊C4—591no—
194C2×C4⋊C4—591no—
195C2×C4⋊C4—591no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4C2×D5911yescharacteristic
200C2×C4⋊C4C2×D5911yescharacteristic
201C2×C4⋊C4C2×D5911yescharacteristic
202C2×C4⋊C4C2×D5911yescharacteristic
203C2×C42—591no—
204C2×C42—591no—
205C2×C42—591no—
206#95—591no—
207#95—591no—
208#95—591no—
209#95—591no—
210#95—591no—
211#95—591no—
212#95—591no—
213#95—591no—
214#95—591no—
215#95—591no—
216#95—591no—
217#95—591no—
218#95—591no—
219#95C2×D5911yescharacteristic
220#95C2×D5911yescharacteristic
221#95C2×D5911yescharacteristic
222C2×Q8—1182no—
223C2×Q8—1182no—
224C2×Q8—1182no—
225C2×Q8—1182no—
226C2×Q8—2361no—
227C2×Q8—2361no—
228C22×C4—591no—
229C22×C4—591no—
230C22×C4—591no—
231C22×C4—591no—
232C22×C4—591no—
233C22×C4—591no—
234C22×C4—591no—
235C22×C4—591no—
236C22×C4C22×D5911yescharacteristic
237C22×C4C22×D5911yescharacteristic
238C22×C4C22×D5911yescharacteristic
239C22×C4C22×D5911yescharacteristic
240C22×C4C22×D5911yescharacteristic
241C22×C4C22×D5911yescharacteristic
242C22×C4C22×D5911yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—594no—
248C4⋊C4—594no—
249C4⋊C4—1182no—
250C4⋊C4—1182no—
251C4⋊C4—1182no—
252C4⋊C4—1182no—
253C4⋊C4—1182no—
254C4⋊C4—1182no—
255C4⋊C4—1182no—
256C4⋊C4—2361no—
257C42—1182no—
258C42—1182no—
259C42—2361no—
260C23C23×D5911yescharacteristic
261Q8—2364no—
262Q8—2364no—
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—21no—
281C2×C4—21no—
282C2×C4—592no—
283C2×C4—592no—
284C2×C4—592no—
285C2×C4—592no—
286C2×C4—592no—
287C2×C4—1181no—
288C2×C4—1181no—
289C2×C4—1181no—
290C2×C4—1181no—
291C2×C4—1181no—
292C2×C4—1181no—
293C2×C4—1181no—
294C2×C4—1181no—
295C2×C4—1181no—
296C2×C4—1181no—
297C2×C4—1181no—
298C2×C4—1181no—
299C2×C4—1181no—
300C2×C4—1181no—
301C2×C4—1181no—
302C2×C4—1181no—
303C2×C4—1181no—
304C2×C4—1181no—
305C2×C4—1181no—
306C2×C4D4×D5912yes—
307C2×C4Q8×D5912yes—
308C22C2×D4×D5911yescharacteristic
309C22C2×Q8×D5911yescharacteristic
310C22#41×D5911yescharacteristic
311C22#1427377211yescharacteristic
312C22#1427377411yescharacteristic
313C22#1427377411yescharacteristic
314C22#1427377511yescharacteristic
315C4—22no—
316C4—22no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1182no—
323C4—1182no—
324C4—1182no—
325C4—1182no—
326C4—1182no—
327C4—2361no—
328C4—2361no—
329C4—2361no—
330C2#1683797511yescharacteristic
331C2#1683801111yescharacteristic
332C2#1683802911yescharacteristic
333C2#1683804111yescharacteristic
334C2#1683806511yescharacteristic
335C2#1683812911yescharacteristic
336C2#1683815511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#398C2
hypercenter#398D59
hypocenterC59#2713
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
87. Dic59⋊C4Q8semidirect
184. C59#2713semidirect