Finite Group Databasebeta

← #21431069

Subgroups — #21431069

Order 7552.

512 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273706C211yesmaximal, characteristic, complemented
2C2×#14273705C211yesmaximal, characteristic, complemented
3#16837343C211yesmaximal, characteristic, complemented
4#16837341C211yesmaximal, characteristic, complemented
5#16837333C211yesmaximal, characteristic, complemented
6#16837330C211yesmaximal, characteristic, complemented
7#16837329C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic
9#16837306C211yesmaximal, characteristic, complemented
10#16837291C211yesmaximal, characteristic, complemented
11#16837290C211yesmaximal, characteristic, complemented
12#16837281C211yesmaximal, characteristic
13#16837278C211yesmaximal, characteristic
14#16837273C211yesmaximal, characteristic, complemented
15C59×#385C211yesmaximal, characteristic, complemented
16C22×Dic118C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19#14273706—24no—
20#14273705—24no—
21C2×C4⋊Dic59C2211yescharacteristic
22C2×Dic59⋊C4C2211yescharacteristic
23C2×Dic59⋊C4C2211yescharacteristic
24C2×Dic59⋊C4C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×C4×Dic59C2211yescharacteristic
36C59⋊#95C2211yescharacteristic
37C59⋊#95C2211yescharacteristic
38C59⋊#95C2211yescharacteristic
39C59⋊#95C2211yescharacteristic
40C59⋊#95C2211yescharacteristic
41C59⋊#95C2211yescharacteristic
42C59⋊#95C2211yescharacteristic
43C59⋊#95C2211yescharacteristic
44C59⋊#95C2211yescharacteristic
45C59⋊#95C2211yescharacteristic
46C23×C4×C59C2211yescharacteristic
47C2×C4⋊C4×C59C2211yescharacteristic
48C2×C4⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51#95×C59C2211yescharacteristic
52#95×C59C2211yescharacteristic
53C24×C59C2311yescharacteristic
54C23×D59C2311yescharacteristic
55C22×C4×C59—22no—
56C22×C4×C59—41no—
57C22×C4×C59—41no—
58C22×C4×C59C2311yescharacteristic
59C22×C4×C59C2311yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C2×C22⋊D59—22no—
65C2×C22⋊D59—22no—
66C2×C22⋊D59—41no—
67C22×Dic59C2311yescharacteristic
68C22×Dic59C2311yescharacteristic
69C22×Dic59C2311yescharacteristic
70C22×Dic59C2311yescharacteristic
71C22×Dic59C2311yescharacteristic
72C22×Dic59C2311yescharacteristic
73C22×Dic59C2311yescharacteristic
74C2×C4×D59—22no—
75C2×C4×D59—41no—
76C2×C4×D59—41no—
77C2×Dic118—41no—
78C2×Dic118—41no—
79C2×Dic118D414yescomplemented
80C4⋊C4×C59—22no—
81C4⋊C4×C59—41no—
82C22⋊C4×C59—22no—
83C22⋊C4×C59—41no—
84C22⋊Dic59—22no—
85C22⋊Dic59—22no—
86C22⋊Dic59—22no—
87(C2×D59)⋊C4—22no—
88(C2×D59)⋊C4—22no—
89(C2×D59)⋊C4—22no—
90(C2×D59)⋊C4—22no—
91(C2×D59)⋊C4—41no—
92C4⋊Dic59—22no—
93Dic59⋊C4—22no—
94Dic59⋊C4—22no—
95Dic59⋊C4—22no—
96Dic59⋊C4—22no—
97Dic59⋊C4—41no—
98C4×Dic59—41no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59—21no—
104C23×C59—21no—
105C23×C59#4112yes—
106C23×C59C2411yescharacteristic
107C22×D59—21no—
108C22×D59—21no—
109C22×D59—21no—
110C22×D59—21no—
111C22×D59—21no—
112C22×D59—21no—
113C22×D59#4112yes—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—44no—
132C2×C4×C59C2×D412yes—
133C22⋊D59—44no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—21no—
138C2×Dic59—21no—
139C2×Dic59—21no—
140C2×Dic59—21no—
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—21no—
149C2×Dic59—21no—
150C2×Dic59—21no—
151C2×Dic59—21no—
152C2×Dic59—21no—
153C2×Dic59C2×D412yes—
154C2×Dic59C2×D412yes—
155C4×D59—44no—
156Dic118—44no—
157C22×C59—22no—
158C22×C59—22no—
159C22×C59—22no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C22×C59C2×#4111yescharacteristic
166C22×C59C2×#4111yescharacteristic
167C22×C59H(5,𝔽2)11yescharacteristic
168C22×C59H(5,𝔽2)11yescharacteristic
169C22×C592−1+411yescharacteristic
170C22×C592−1+411yescharacteristic
171C2×D59—22no—
172C2×D59—22no—
173C2×D59—22no—
174C2×D59—41no—
175C2×D59—41no—
176C2×D59—41no—
177C2×D59—41no—
178C4×C59—22no—
179C4×C59—41no—
180C4×C59—41no—
181C4×C59—41no—
182C4×C59—41no—
183C4×C59—41no—
184Dic59—22no—
185Dic59—22no—
186Dic59—41no—
187Dic59—41no—
188Dic59—41no—
189Dic59—41no—
190Dic59—41no—
191#2728—591nomaximal, Sylow
192C2×C59—42no—
193C2×C59#53411yescharacteristic
194C2×C59#53911yescharacteristic
195C2×C59#53911yescharacteristic
196C2×C59#54811yescharacteristic
197C2×C59#54811yescharacteristic
198C2×C59#55111yescharacteristic
199C2×C59#56311yescharacteristic
200D59—42no—
201C2×C22⋊Q8—591no—
202C2×C22⋊Q8—591no—
203#400—591no—
204#400—591no—
205#398—591no—
206#397—591no—
207#397—591no—
208#394—591no—
209#391—591no—
210#388—591no—
211#388—591no—
212#386—591no—
213#386—591no—
214#385—591no—
215#385D5911yescharacteristic, complemented
216C59#272811yescharacteristic, complemented, Sylow
217C22×Q8—591no—
218C22×D4—591no—
219C23×C4—591no—
220C23×C4C2×D5911yescharacteristic
221C22⋊Q8—1184no—
222C22⋊Q8—1184no—
223C2×C4⋊C4—591no—
224C2×C4⋊C4—591no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—591no—
227C2×C4⋊C4—591no—
228C2×C4⋊C4—591no—
229C2×C4⋊C4C2×D5911yescharacteristic
230C2×C4⋊C4C2×D5911yescharacteristic
231C2×C22⋊C4—591no—
232C2×C22⋊C4—591no—
233C2×C22⋊C4—591no—
234C2×C22⋊C4—591no—
235C2×C22⋊C4—591no—
236C2×C22⋊C4—591no—
237C2×C22⋊C4—591no—
238C2×C22⋊C4—591no—
239C2×C22⋊C4C2×D5911yescharacteristic
240C2×C22⋊C4C2×D5911yescharacteristic
241C2×C42—591no—
242#95—591no—
243#95—591no—
244#95—591no—
245#95—591no—
246#95—591no—
247#95—591no—
248#95—591no—
249#95—591no—
250#95—591no—
251#95—591no—
252#95C2×D5911yescharacteristic
253#95C2×D5911yescharacteristic
254C24—591no—
255C24C22×D5911yescharacteristic
256C2×Q8—594no—
257C2×Q8—2361no—
258C2×Q8—2361no—
259C2×D4—1182no—
260C2×D4—1182no—
261C2×D4—2361no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—591no—
266C22×C4—591no—
267C22×C4—591no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—591no—
271C22×C4—591no—
272C22×C4—1182no—
273C22×C4—2361no—
274C22×C4—2361no—
275C22×C4C22×D5911yescharacteristic
276C22×C4C22×D5911yescharacteristic
277C22×C4C22×D5911yescharacteristic
278C22×C4C22×D5911yescharacteristic
279C22×C4C22×D5911yescharacteristic
280C22×C4C22×D5911yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—1182no—
284C4⋊C4—1182no—
285C4⋊C4—1182no—
286C4⋊C4—1182no—
287C4⋊C4—1182no—
288C4⋊C4—2361no—
289C22⋊C4—22no—
290C22⋊C4—41no—
291C22⋊C4—1182no—
292C22⋊C4—1182no—
293C22⋊C4—1182no—
294C22⋊C4—1182no—
295C22⋊C4—1182no—
296C22⋊C4—1182no—
297C22⋊C4—1182no—
298C22⋊C4—2361no—
299C42—2361no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—592no—
307C23—1181no—
308C23—1181no—
309C23—1181no—
310C23—1181no—
311C23—1181no—
312C23—1181no—
313C23#1174568512yes—
314C23C23×D5911yescharacteristic
315Q8—2364no—
316D4—2364no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—44no—
335C2×C4—592no—
336C2×C4—592no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—1181no—
341C2×C4—1181no—
342C2×C4—1181no—
343C2×C4—1181no—
344C2×C4—1181no—
345C2×C4—1181no—
346C2×C4—1181no—
347C2×C4—1181no—
348C2×C4—1181no—
349C2×C4—1181no—
350C2×C4—1181no—
351C2×C4—1181no—
352C2×C4—1181no—
353C2×C4—1181no—
354C2×C4—1181no—
355C2×C4—1181no—
356C2×C4—2364no—
357C2×C4D4×D5912yes—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—1182no—
366C22—1182no—
367C22—1182no—
368C22—2361no—
369C22—2361no—
370C22—2361no—
371C22—2361no—
372C22C2×D4×D5911yescharacteristic
373C22#41×D5911yescharacteristic
374C22C2×#1174568511yescharacteristic
375C22#1427377211yescharacteristic
376C22#1427377211yescharacteristic
377C22#1427377411yescharacteristic
378C22#1427377511yescharacteristic
379C4—22no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—1182no—
386C4—1182no—
387C4—2361no—
388C4—2361no—
389C4—2361no—
390C4—2361no—
391C4—2361no—
392C2—42no—
393C2—2362no—
394C2#1683796211yescharacteristic
395C2#1683799511yescharacteristic
396C2#1683799911yescharacteristic
397C2#1683806111yescharacteristic
398C2#1683806211yescharacteristic
399C2#1683808111yescharacteristic
400C2#1683815311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#385C2
hypercenter#385D59
hypocenterC59#2728
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14273706C2semidirect
2. C2×#14273705C2semidirect
3. #16837343C2semidirect
4. #16837341C2semidirect
5. #16837333C2semidirect
6. #16837330C2semidirect
7. #16837329C2semidirect
9. #16837306C2semidirect
10. #16837291C2semidirect
11. #16837290C2semidirect
14. #16837273C2semidirect
15. C59×#385C2semidirect
79. C2×Dic118D4semidirect
215. #385D59semidirect
216. C59#2728semidirect