Finite Group Databasebeta

← #21430893

Subgroups — #21430893

Order 7552.

598 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273722C211yesmaximal, characteristic, complemented
2C2×#14273701C211yesmaximal, characteristic, complemented
3#16837331C211yesmaximal, characteristic, complemented
4#16837320C211yesmaximal, characteristic, complemented
5#16837319C211yesmaximal, characteristic, complemented
6#16837312C211yesmaximal, characteristic, complemented
7#16837311C211yesmaximal, characteristic, complemented
8#16837311C211yesmaximal, characteristic, complemented
9#16837303C211yesmaximal, characteristic, complemented
10#16837302C211yesmaximal, characteristic, complemented
11#16837302C211yesmaximal, characteristic, complemented
12#16837292C211yesmaximal, characteristic, complemented
13#16837285C211yesmaximal, characteristic, complemented
14#16837281C211yesmaximal, characteristic, complemented
15C59×#385C211yesmaximal, characteristic, complemented
16C22×D236C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C22⋊D59C2211yescharacteristic
22#14273722—24no—
23#14273701—24no—
24C2×C4⋊Dic59C2211yescharacteristic
25C2×Dic59⋊C4C2211yescharacteristic
26C2×Dic59⋊C4C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic
40C2×C4×Dic59C2211yescharacteristic
41C2×C4×Dic59C2211yescharacteristic
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
55C23×D59C2311yescharacteristic
56C23×D59C2311yescharacteristic
57C22×C4×C59—22no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C22×C4×C59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C2×C22⋊D59—22no—
67C2×C22⋊D59—22no—
68C2×C22⋊D59—22no—
69C2×C22⋊D59—22no—
70C2×C22⋊D59—22no—
71C2×C22⋊D59—41no—
72C2×C22⋊D59—41no—
73C2×C22⋊D59—41no—
74C2×C22⋊D59—41no—
75C22×Dic59C2311yescharacteristic
76C22×Dic59C2311yescharacteristic
77C22×Dic59C2311yescharacteristic
78C22×Dic59C2311yescharacteristic
79C22×Dic59C2311yescharacteristic
80C2×D236—22no—
81C2×D236—22no—
82C2×D236—41no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C4⋊C4×C59—22no—
90C4⋊C4×C59—41no—
91C22⋊C4×C59—22no—
92C22⋊C4×C59—41no—
93C22⋊Dic59—41no—
94(C2×D59)⋊C4—22no—
95(C2×D59)⋊C4—22no—
96(C2×D59)⋊C4—22no—
97(C2×D59)⋊C4—22no—
98(C2×D59)⋊C4—22no—
99(C2×D59)⋊C4—22no—
100(C2×D59)⋊C4—41no—
101(C2×D59)⋊C4—41no—
102(C2×D59)⋊C4—41no—
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4—41no—
105(C2×D59)⋊C4—41no—
106C4⋊Dic59D414yescomplemented
107Dic59⋊C4—22no—
108Dic59⋊C4—41no—
109C4×Dic59—22no—
110C4×Dic59—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59#4112yes—
118C23×C59C2411yescharacteristic
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—21no—
125C22×D59—21no—
126C22×D59—21no—
127C22×D59—21no—
128C22×D59—21no—
129C22×D59—21no—
130C22×D59—21no—
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—21no—
138C22×D59—21no—
139C22×D59—21no—
140C2×C4×C59—21no—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—44no—
157C2×C4×C59C2×D412yes—
158C2×C4×C59#4112yes—
159C22⋊D59—44no—
160C22⋊D59—44no—
161C22⋊D59—44no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—21no—
165C2×Dic59—21no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C2×Dic59—21no—
174C2×Dic59—21no—
175C2×Dic59C2×D412yes—
176C2×Dic59C2×D412yes—
177D236—44no—
178D236—44no—
179D236—44no—
180C22×C59—22no—
181C22×C59—22no—
182C22×C59—22no—
183C22×C59—41no—
184C22×C59—41no—
185C22×C59—41no—
186C22×C59—41no—
187C22×C59C22×D411yescharacteristic
188C22×C59C2×#4111yescharacteristic
189C22×C59C2×#4111yescharacteristic
190C22×C59H(5,𝔽2)11yescharacteristic
191C22×C59H(5,𝔽2)11yescharacteristic
192C22×C59H(5,𝔽2)11yescharacteristic
193C22×C59H(5,𝔽2)11yescharacteristic
194C2×D59—41no—
195C2×D59—41no—
196C2×D59—41no—
197C2×D59—41no—
198C2×D59—41no—
199C2×D59—41no—
200C2×D59—41no—
201C2×D59—41no—
202C2×D59—41no—
203C2×D59—41no—
204C2×D59—41no—
205C2×D59—41no—
206C2×D59—41no—
207C2×D59—41no—
208C2×D59—41no—
209C2×D59—41no—
210C2×D59—41no—
211C2×D59—41no—
212C2×D59—41no—
213C2×D59—41no—
214C2×D59—41no—
215C4×C59—22no—
216C4×C59—22no—
217C4×C59—41no—
218C4×C59—41no—
219C4×C59—41no—
220C4×C59—41no—
221Dic59—22no—
222Dic59—22no—
223Dic59—41no—
224Dic59—41no—
225Dic59—41no—
226#2714—591nomaximal, Sylow
227C2×C59—42no—
228C2×C59#53511yescharacteristic
229C2×C59#53811yescharacteristic
230C2×C59#53811yescharacteristic
231C2×C59#54611yescharacteristic
232C2×C59#55011yescharacteristic
233C2×C59#55311yescharacteristic
234C2×C59#56011yescharacteristic
235D59—81no—
236D59—81no—
237D59—81no—
238C2×#126—591no—
239C2×#121—591no—
240#397—591no—
241#394—591no—
242#394—591no—
243#392—591no—
244#392—591no—
245#392—591no—
246#390—591no—
247#390—591no—
248#390—591no—
249#388—591no—
250#387—591no—
251#386—591no—
252#385D5911yescharacteristic, complemented
253C59#271411yescharacteristic, complemented, Sylow
254C22×D4—591no—
255C22×D4—591no—
256C22×D4—591no—
257C22×D4—591no—
258C22×D4—591no—
259C22×D4—591no—
260C23×C4C2×D5911yescharacteristic
261#126—1184no—
262#121—1184no—
263C2×C4⋊C4—591no—
264C2×C4⋊C4—591no—
265C2×C4⋊C4—591no—
266C2×C4⋊C4C2×D5911yescharacteristic
267C2×C4⋊C4C2×D5911yescharacteristic
268C2×C22⋊C4—591no—
269C2×C22⋊C4—591no—
270C2×C22⋊C4—591no—
271C2×C22⋊C4—591no—
272C2×C22⋊C4—591no—
273C2×C22⋊C4—591no—
274C2×C22⋊C4—591no—
275C2×C22⋊C4—591no—
276C2×C22⋊C4—591no—
277C2×C22⋊C4—591no—
278C2×C22⋊C4—591no—
279C2×C22⋊C4—591no—
280C2×C22⋊C4—591no—
281C2×C22⋊C4C2×D5911yescharacteristic
282C2×C22⋊C4C2×D5911yescharacteristic
283C2×C42—591no—
284C2×C42—591no—
285#95—591no—
286#95—591no—
287#95—591no—
288#95—591no—
289#95C2×D5911yescharacteristic
290#95C2×D5911yescharacteristic
291C24—591no—
292C24—591no—
293C24—591no—
294C24C22×D5911yescharacteristic
295C2×D4—1182no—
296C2×D4—1182no—
297C2×D4—1182no—
298C2×D4—1182no—
299C2×D4—1182no—
300C2×D4—1182no—
301C2×D4—1182no—
302C2×D4—2361no—
303C2×D4—2361no—
304C2×D4—2361no—
305C2×D4—2361no—
306C2×D4—2361no—
307C2×D4—2361no—
308C2×D4—2361no—
309C2×D4—2361no—
310C2×D4—2361no—
311C2×D4—2361no—
312C2×D4—2361no—
313C22×C4—22no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—591no—
317C22×C4—591no—
318C22×C4—591no—
319C22×C4—591no—
320C22×C4—591no—
321C22×C4C22×D5911yescharacteristic
322C22×C4C22×D5911yescharacteristic
323C22×C4C22×D5911yescharacteristic
324C22×C4C22×D5911yescharacteristic
325C22×C4C22×D5911yescharacteristic
326C22×C4C22×D5911yescharacteristic
327C4⋊C4—22no—
328C4⋊C4—41no—
329C4⋊C4—594no—
330C4⋊C4—1182no—
331C4⋊C4—2361no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—1182no—
335C22⋊C4—1182no—
336C22⋊C4—1182no—
337C22⋊C4—1182no—
338C22⋊C4—1182no—
339C22⋊C4—1182no—
340C22⋊C4—2361no—
341C22⋊C4—2361no—
342C22⋊C4—2361no—
343C22⋊C4—2361no—
344C22⋊C4—2361no—
345C22⋊C4—2361no—
346C22⋊C4—2361no—
347C42—1182no—
348C42—2361no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—1181no—
356C23—1181no—
357C23—1181no—
358C23—1181no—
359C23—1181no—
360C23—1181no—
361C23—1181no—
362C23—1181no—
363C23—1181no—
364C23—1181no—
365C23—1181no—
366C23—1181no—
367C23—1181no—
368C23—1181no—
369C23—1181no—
370C23—1181no—
371C23—1181no—
372C23—1181no—
373C23—1181no—
374C23—1181no—
375C23—1181no—
376C23#1174568912yes—
377C23C23×D5911yescharacteristic
378D4—2364no—
379D4—2364no—
380D4—2364no—
381D4—2364no—
382D4—2364no—
383D4—2364no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—44no—
401C2×C4—592no—
402C2×C4—592no—
403C2×C4—1181no—
404C2×C4—1181no—
405C2×C4—1181no—
406C2×C4—1181no—
407C2×C4—1181no—
408C2×C4—1181no—
409C2×C4—1181no—
410C2×C4—1181no—
411C2×C4—1181no—
412C2×C4—1181no—
413C2×C4—1181no—
414C2×C4—1181no—
415C2×C4—1181no—
416C2×C4#1174568512yes—
417C2×C4D4×D5912yes—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—2361no—
426C22—2361no—
427C22—2361no—
428C22—2361no—
429C22—2361no—
430C22—2361no—
431C22—2361no—
432C22—2361no—
433C22—2361no—
434C22—2361no—
435C22—2361no—
436C22—2361no—
437C22—2361no—
438C22—2361no—
439C22—2361no—
440C22—2361no—
441C22—2361no—
442C22—2361no—
443C22—2361no—
444C22—2361no—
445C22—2361no—
446C22C2×D4×D5911yescharacteristic
447C22C2×#1174568511yescharacteristic
448C22C2×#1174568911yescharacteristic
449C22#1427377211yescharacteristic
450C22#1427377211yescharacteristic
451C22#1427377311yescharacteristic
452C22#1427377311yescharacteristic
453C4—22no—
454C4—22no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—1182no—
460C4—1182no—
461C4—2361no—
462C4—2361no—
463C4—2361no—
464C2—42no—
465C2—4721no—
466C2—4721no—
467C2—4721no—
468C2#1683796711yescharacteristic
469C2#1683798511yescharacteristic
470C2#1683799211yescharacteristic
471C2#1683804311yescharacteristic
472C2#1683807311yescharacteristic
473C2#1683810011yescharacteristic
474C2#1683814211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#385C2
hypercenter#385D59
hypocenterC59#2714
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#14273722C2semidirect
2. C2×#14273701C2semidirect
3. #16837331C2semidirect
4. #16837320C2semidirect
5. #16837319C2semidirect
6. #16837312C2semidirect
7. #16837311C2semidirect
8. #16837311C2semidirect
9. #16837303C2semidirect
10. #16837302C2semidirect
11. #16837302C2semidirect
12. #16837292C2semidirect
13. #16837285C2semidirect
14. #16837281C2semidirect
15. C59×#385C2semidirect
106. C4⋊Dic59D4semidirect
252. #385D59semidirect
253. C59#2714semidirect