Finite Group Databasebeta

← #28615253

Subgroups — #28615253

Order 15104.

882 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427375C211yesmaximal, characteristic
2#21424394C211yesmaximal, characteristic, complemented
3#21424393C211yesmaximal, characteristic, complemented
4#21424393C211yesmaximal, characteristic, complemented
5#21424392C211yesmaximal, characteristic, complemented
6#21424391C211yesmaximal, characteristic, complemented
7#21424391C211yesmaximal, characteristic, complemented
8#21424390C211yesmaximal, characteristic, complemented
9#21424390C211yesmaximal, characteristic, complemented
10#21424387C211yesmaximal, characteristic, complemented
11#21424385C211yesmaximal, characteristic, complemented
12#21424385C211yesmaximal, characteristic, complemented
13#21424240C211yesmaximal, characteristic, complemented
14#21424240C211yesmaximal, characteristic, complemented
15C59×#1870C211yesmaximal, characteristic, complemented
16C22×#11745664C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×C22⋊D59C2211yescharacteristic
21C2×C4×C22⋊D59C2211yescharacteristic
22C2×C4×C22⋊D59C2211yescharacteristic
23C2×C4×C22⋊D59C2211yescharacteristic
24C2×C22⋊(C59⋊C8)C2211yescharacteristic
25C2×C22⋊(C59⋊C8)C2211yescharacteristic
26C2×C22⋊(C59⋊C8)C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33#16837338C411yescharacteristic
34#16837338C411yescharacteristic
35#16837337C411yescharacteristic
36#16837337C411yescharacteristic
37#16837311C411yescharacteristic
38#16837311C411yescharacteristic
39#16837310C411yescharacteristic
40#16837310C411yescharacteristic
41#16837248C2211yescharacteristic
42#16837157C2211yescharacteristic
43#16837157C2211yescharacteristic
44#16837156C2211yescharacteristic
45#16837156C2211yescharacteristic
46#16837156C2211yescharacteristic
47#16837156C2211yescharacteristic
48#16837156C2211yescharacteristic
49#16837156C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C22×M16×C59C2211yescharacteristic
53C2×C4×D4×C59C2211yescharacteristic
54C2×C22⋊C8×C59C2211yescharacteristic
55C2×C22⋊C8×C59C2211yescharacteristic
56C2×C22⋊C8×C59C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D236C2×C411yescharacteristic
60C22×C22⋊D59C2×C411yescharacteristic
61C22×C22⋊D59C2×C411yescharacteristic
62C22×C22⋊D59C2×C411yescharacteristic
63C22×C22⋊D59C2×C411yescharacteristic
64C22×C4×D59C2311yescharacteristic
65C22×C4×D59C2311yescharacteristic
66C2×#11745664—41no—
67C2×#11745664—41no—
68C2×#11745664—41no—
69C2×#11745659—41no—
70C2×#11745659—41no—
71C2×#11745659—41no—
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75C22×C59⋊C8C2311yescharacteristic
76C2×C8×D59—41no—
77C2×C8×D59—41no—
78C2×C8×D59—41no—
79C4×D236—41no—
80C4×D236—41no—
81C4×C22⋊D59—41no—
82C4×C22⋊D59—41no—
83C4×C22⋊D59—41no—
84C4×C22⋊D59—41no—
85C4×C22⋊D59—41no—
86C4×C22⋊D59—41no—
87C4×C22⋊D59—41no—
88C4×C22⋊D59—41no—
89C2×C4⋊Dic59C2×C411yescharacteristic
90C2×Dic59⋊C4C2×C411yescharacteristic
91C2×Dic59⋊C4C2×C411yescharacteristic
92C2×Dic59⋊C4C2×C411yescharacteristic
93C2×Dic59⋊C4C2×C411yescharacteristic
94C2×C22⋊Dic59C2×C411yescharacteristic
95C2×C22⋊Dic59C2×C411yescharacteristic
96C2×C22⋊Dic59C2×C411yescharacteristic
97C2×C22⋊Dic59C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×(C2×D59)⋊C4C2×C411yescharacteristic
100C2×(C2×D59)⋊C4C2×C411yescharacteristic
101C2×(C2×D59)⋊C4C2×C411yescharacteristic
102C2×(C2×D59)⋊C4C2×C411yescharacteristic
103C2×(C2×D59)⋊C4C2×C411yescharacteristic
104C2×C4×Dic59C2311yescharacteristic
105C2×C4×Dic59C2311yescharacteristic
106C22⋊(C59⋊C8)—41no—
107C22⋊(C59⋊C8)—41no—
108C22⋊(C59⋊C8)—41no—
109(C2×D59)⋊C8—41no—
110(C2×D59)⋊C8—41no—
111(C2×D59)⋊C8—41no—
112(C2×D59)⋊C8—41no—
113(C2×D59)⋊C8—41no—
114(C2×D59)⋊C8—41no—
115C59⋊#95C2×C411yescharacteristic
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C22×D4×C59C2×C411yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C2×M16×C59—41no—
123C2×M16×C59—41no—
124C2×M16×C59—41no—
125C22×C8×C59C2311yescharacteristic
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128C22×C8×C59C2311yescharacteristic
129C4×D4×C59—41no—
130C4×D4×C59—41no—
131C2×C4⋊C4×C59C2×C411yescharacteristic
132C2×C22⋊C4×C59C2×C411yescharacteristic
133C2×C22⋊C4×C59C2×C411yescharacteristic
134C2×C42×C59C2311yescharacteristic
135C22⋊C8×C59—41no—
136C22⋊C8×C59—41no—
137C22⋊C8×C59—41no—
138C24×C59C22×C411yescharacteristic
139C24×C59C22×C411yescharacteristic
140C23×D59C22×C411yescharacteristic
141C23×D59C22×C411yescharacteristic
142C2×D4×C59—41no—
143C2×D4×C59—41no—
144C2×D4×C59—41no—
145C22×C4×C59—21no—
146C22×C4×C59—21no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59C22×C411yescharacteristic
158C22×C4×C59C22×C411yescharacteristic
159C22×C4×C59C22×C411yescharacteristic
160C22×C4×C59C22×C411yescharacteristic
161C22×C4×C59C2411yescharacteristic
162C2×C22⋊D59—22no—
163C2×C22⋊D59—22no—
164C2×C22⋊D59—41no—
165C2×C22⋊D59—41no—
166C2×C22⋊D59—41no—
167C2×C22⋊D59—41no—
168C2×C22⋊D59—41no—
169C2×C22⋊D59—41no—
170C2×C22⋊D59—41no—
171C2×C22⋊D59—41no—
172C2×C22⋊D59—41no—
173C2×C22⋊D59—41no—
174C22×Dic59C22×C411yescharacteristic
175C22×Dic59C22×C411yescharacteristic
176C22×Dic59C22×C411yescharacteristic
177C22×Dic59C22×C411yescharacteristic
178C22×Dic59C22×C411yescharacteristic
179C22×Dic59C22×C411yescharacteristic
180C2×D236—22no—
181C2×D236—41no—
182C2×D236—41no—
183C2×C4×D59—21no—
184C2×C4×D59—21no—
185C2×C4×D59—21no—
186C2×C4×D59—21no—
187C2×C4×D59—21no—
188C2×C4×D59—21no—
189C2×C4×D59—21no—
190C2×C4×D59—21no—
191C2×C4×D59—21no—
192C2×C4×D59—21no—
193C2×C4×D59—21no—
194C2×C4×D59—21no—
195M16×C59—44no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59—21no—
199C2×C8×C59—21no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C2×C8×C59—21no—
204C2×C8×C59—21no—
205C2×C8×C59—21no—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C4⋊C4×C59—41no—
209C22⋊C4×C59—41no—
210C22⋊C4×C59—41no—
211C42×C59—21no—
212C42×C59—21no—
213C22⋊Dic59—41no—
214C22⋊Dic59—41no—
215C22⋊Dic59—41no—
216C22⋊Dic59—41no—
217(C2×D59)⋊C4—41no—
218(C2×D59)⋊C4—41no—
219(C2×D59)⋊C4—41no—
220(C2×D59)⋊C4—41no—
221(C2×D59)⋊C4—41no—
222(C2×D59)⋊C4—41no—
223C4⋊Dic59—41no—
224Dic59⋊C4—41no—
225Dic59⋊C4—41no—
226Dic59⋊C4—41no—
227Dic59⋊C4—41no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C4×Dic59—21no—
232#11745664—44no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245#11745659—44no—
246C8×D59—44no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59C23×C411yescharacteristic
262C22×D59—21no—
263C22×D59—21no—
264C22×D59—21no—
265C22×D59—21no—
266C22×D59—21no—
267C22×D59—21no—
268C22×D59—21no—
269C22×D59—21no—
270C22×D59—21no—
271C22×D59—21no—
272C22×D59—21no—
273C22×D59—21no—
274C22×D59—21no—
275C22×D59#13112yes—
276D4×C59—44no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—21no—
287C2×C4×C59—21no—
288C2×C4×C59—21no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—41no—
297C2×C4×C59H(5,𝔽2)11yescharacteristic
298C2×C4×C59H(5,𝔽2)11yescharacteristic
299C2×C4×C59H(5,𝔽2)11yescharacteristic
300C2×C4×C59H(5,𝔽2)11yescharacteristic
301C2×C4×C59H(5,𝔽2)11yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C22⋊D59—44no—
304C22⋊D59—44no—
305C22⋊D59—44no—
306C22⋊D59—44no—
307C2×Dic59—21no—
308C2×Dic59—21no—
309C2×Dic59—21no—
310C2×Dic59—21no—
311C2×Dic59—21no—
312C2×Dic59—21no—
313C2×Dic59—21no—
314C2×Dic59—21no—
315C2×Dic59—21no—
316C2×Dic59—21no—
317C2×Dic59—21no—
318C2×Dic59—21no—
319C2×Dic59—21no—
320C2×Dic59—21no—
321C2×Dic59—21no—
322C2×Dic59—21no—
323C2×Dic59—21no—
324C2×Dic59—21no—
325D236—44no—
326C4×D59—41no—
327C4×D59—41no—
328C4×D59—41no—
329C4×D59—41no—
330C4×D59—41no—
331C4×D59—41no—
332C4×D59—41no—
333C4×D59—41no—
334C8×C59—41no—
335C8×C59—41no—
336C8×C59—41no—
337C8×C59—41no—
338C59⋊C8—41no—
339C59⋊C8—41no—
340C59⋊C8—41no—
341C59⋊C8—41no—
342#23359—591nomaximal, Sylow
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—41no—
349C22×C59—41no—
350C22×C59—41no—
351C22×C59—41no—
352C22×C59—41no—
353C22×C59—41no—
354C22×C59—41no—
355C22×C59—41no—
356C22×C59—41no—
357C22×C59#51811yescharacteristic
358C22×C59#51811yescharacteristic
359C22×C59#51811yescharacteristic
360C22×C59C2×#13111yescharacteristic
361C22×C59#56811yescharacteristic
362C22×C59#56811yescharacteristic
363C22×C59#56811yescharacteristic
364C2×D59—22no—
365C2×D59—22no—
366C2×D59—22no—
367C2×D59—41no—
368C2×D59—41no—
369C2×D59—41no—
370C2×D59—41no—
371C2×D59—41no—
372C2×D59—41no—
373C2×D59—41no—
374C2×D59—41no—
375C2×D59—41no—
376C2×D59—41no—
377C2×D59—41no—
378C4×C59—41no—
379C4×C59—41no—
380C4×C59—41no—
381C4×C59—41no—
382C4×C59#56011yescharacteristic
383C4×C59#56011yescharacteristic
384C4×C59#56011yescharacteristic
385C4×C59#56011yescharacteristic
386Dic59—41no—
387Dic59—41no—
388Dic59—41no—
389Dic59—41no—
390Dic59—41no—
391Dic59—41no—
392#2397—591no—
393#1870—591no—
394#1870—591no—
395#1870—591no—
396#1870—591no—
397#1870—591no—
398#1870—591no—
399#1870—591no—
400#1870—591no—
401#1870D5911yescharacteristic, complemented
402#1869—591no—
403#1869—591no—
404#1869—591no—
405#1840—591no—
406#1840—591no—
407C2×C59—81no—
408C2×C59—81no—
409C2×C59#238011yescharacteristic
410C2×C59#297611yescharacteristic
411C2×C59#297611yescharacteristic
412C2×C59#297611yescharacteristic
413C2×C59#297811yescharacteristic
414C2×C59#297811yescharacteristic
415C2×C59#297811yescharacteristic
416D59—42no—
417D59—81no—
418C22×M16—591no—
419C22×M16—591no—
420C22×M16C2×D5911yescharacteristic
421C23×C8—591no—
422C2×C4×D4—591no—
423C2×C4×D4—591no—
424C2×C4×D4—591no—
425C2×C4×D4—591no—
426C2×C4×D4—591no—
427C2×C4×D4C2×D5911yescharacteristic
428C2×C22⋊C8—591no—
429C2×C22⋊C8—591no—
430C2×C22⋊C8—591no—
431C2×C22⋊C8—591no—
432C2×C22⋊C8—591no—
433C2×C22⋊C8—591no—
434C2×C22⋊C8—591no—
435C2×C22⋊C8—591no—
436C2×C22⋊C8—591no—
437C2×C22⋊C8C2×D5911yescharacteristic
438C2×C22⋊C8C2×D5911yescharacteristic
439C2×C22⋊C8C2×D5911yescharacteristic
440#399—591no—
441#399—591no—
442#399—591no—
443#399—591no—
444#392—591no—
445#392—591no—
446#392—591no—
447#392—591no—
448#376—591no—
449#336—591no—
450#336—591no—
451#336—591no—
452#336—591no—
453#336—591no—
454#336—591no—
455#336—591no—
456#336—591no—
457#336—591no—
458#336—591no—
459#336C2×D5911yescharacteristic
460#336C2×D5911yescharacteristic
461C59#2335911yescharacteristic, complemented, Sylow
462C22×D4—591no—
463C22×D4—591no—
464C22×D4—591no—
465C22×D4—591no—
466C22×D4—591no—
467C22×D4C4×D5911yescharacteristic
468C23×C4—591no—
469C23×C4—591no—
470C23×C4C22×D5911yescharacteristic
471C23×C4C22×D5911yescharacteristic
472C2×M16—41no—
473C2×M16—41no—
474C2×M16—41no—
475C2×M16—2361no—
476C2×M16—2361no—
477C2×M16—2361no—
478C2×M16—2361no—
479C2×M16—2361no—
480C2×M16—2361no—
481C22×C8—591no—
482C22×C8—591no—
483C22×C8—591no—
484C22×C8—591no—
485C22×C8—2361no—
486C22×C8—2361no—
487C22×C8—2361no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490C22×C8C22×D5911yescharacteristic
491C22×C8C22×D5911yescharacteristic
492C4×D4—41no—
493C4×D4—41no—
494C4×D4—2361no—
495C4×D4—2361no—
496C4×D4—2361no—
497C4×D4—2361no—
498C4×D4—2361no—
499C4×D4—2361no—
500C4×D4—2361no—
501C4×D4—2361no—
502C4×D4—2361no—
503C4×D4—2361no—
504C2×C4⋊C4—591no—
505C2×C4⋊C4—591no—
506C2×C4⋊C4—591no—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4C4×D5911yescharacteristic
510C2×C22⋊C4—591no—
511C2×C22⋊C4—591no—
512C2×C22⋊C4—591no—
513C2×C22⋊C4—591no—
514C2×C22⋊C4—591no—
515C2×C22⋊C4—591no—
516C2×C22⋊C4—591no—
517C2×C22⋊C4—591no—
518C2×C22⋊C4—591no—
519C2×C22⋊C4—591no—
520C2×C22⋊C4C4×D5911yescharacteristic
521C2×C22⋊C4C4×D5911yescharacteristic
522C2×C42—591no—
523C2×C42—591no—
524C2×C42C22×D5911yescharacteristic
525C22⋊C8—41no—
526C22⋊C8—41no—
527C22⋊C8—41no—
528C22⋊C8—2361no—
529C22⋊C8—2361no—
530C22⋊C8—2361no—
531C22⋊C8—2361no—
532C22⋊C8—2361no—
533C22⋊C8—2361no—
534C22⋊C8—2361no—
535C22⋊C8—2361no—
536C22⋊C8—2361no—
537#95—591no—
538#95—591no—
539#95—591no—
540#95—591no—
541C24—591no—
542C24—591no—
543C24C2×C4×D5911yescharacteristic
544C24C2×C4×D5911yescharacteristic
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—1182no—
549C2×D4—1182no—
550C2×D4—1182no—
551C2×D4—2361no—
552C2×D4—2361no—
553C2×D4—2361no—
554C2×D4—2361no—
555C2×D4—2361no—
556C2×D4—2361no—
557C2×D4—2361no—
558C2×D4—2361no—
559C2×D4—2361no—
560C2×D4—2361no—
561C2×D4—2361no—
562C2×D4—2361no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—591no—
576C22×C4—591no—
577C22×C4—591no—
578C22×C4—591no—
579C22×C4—591no—
580C22×C4—591no—
581C22×C4—1181no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—1181no—
588C22×C4—1181no—
589C22×C4—1181no—
590C22×C4—1181no—
591C22×C4—1181no—
592C22×C4—1181no—
593C22×C4C2×C4×D5911yescharacteristic
594C22×C4C2×C4×D5911yescharacteristic
595C22×C4C2×C4×D5911yescharacteristic
596C22×C4C2×C4×D5911yescharacteristic
597C22×C4C23×D5911yescharacteristic
598M16—44no—
599M16—2364no—
600M16—2364no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—1181no—
614C2×C8—1181no—
615C2×C8—1181no—
616C2×C8—1181no—
617C2×C8—1181no—
618C2×C8—1181no—
619C2×C8—1181no—
620C2×C8—1181no—
621C2×C8—1181no—
622C2×C8—1181no—
623C2×C8—1181no—
624C2×C8—1181no—
625C2×C8—2364no—
626C4⋊C4—41no—
627C4⋊C4—2361no—
628C4⋊C4—2361no—
629C4⋊C4—2361no—
630C4⋊C4—2361no—
631C4⋊C4—2361no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—2361no—
635C22⋊C4—2361no—
636C22⋊C4—2361no—
637C22⋊C4—2361no—
638C22⋊C4—2361no—
639C22⋊C4—2361no—
640C22⋊C4—2361no—
641C22⋊C4—2361no—
642C22⋊C4—2361no—
643C22⋊C4—2361no—
644C42—21no—
645C42—21no—
646C42—1181no—
647C42—1181no—
648C42—1181no—
649C42—1181no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—592no—
665C23—1181no—
666C23—1181no—
667C23—1181no—
668C23—1181no—
669C23—1181no—
670C23—1181no—
671C23—1181no—
672C23—1181no—
673C23—1181no—
674C23—1181no—
675C23—1181no—
676C23—1181no—
677C23—1181no—
678C23C22×C4×D5911yescharacteristic
679D4—44no—
680D4—2364no—
681D4—2364no—
682D4—2364no—
683D4—2364no—
684D4—2364no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—1181no—
706C2×C4—1181no—
707C2×C4—1181no—
708C2×C4—1181no—
709C2×C4—1181no—
710C2×C4—1181no—
711C2×C4—1181no—
712C2×C4—1181no—
713C2×C4—1181no—
714C2×C4—1181no—
715C2×C4—1181no—
716C2×C4—1181no—
717C2×C4—1181no—
718C2×C4—1181no—
719C2×C4—1181no—
720C2×C4—1181no—
721C2×C4—1181no—
722C2×C4—1181no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4—2361no—
731C2×C4#1427377211yescharacteristic
732C2×C4#1427377211yescharacteristic
733C2×C4#1427377211yescharacteristic
734C2×C4#1427377211yescharacteristic
735C2×C4#1427377311yescharacteristic
736C2×C4#1427377311yescharacteristic
737C8—41no—
738C8—41no—
739C8—41no—
740C8—41no—
741C8—2361no—
742C8—2361no—
743C8—2361no—
744C8—2361no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—1182no—
760C22—1182no—
761C22—1182no—
762C22—2361no—
763C22—2361no—
764C22—2361no—
765C22—2361no—
766C22—2361no—
767C22—2361no—
768C22—2361no—
769C22—2361no—
770C22—2361no—
771C22—2361no—
772C22—2361no—
773C22#1683787411yescharacteristic
774C22#1683787411yescharacteristic
775C22#1683787511yescharacteristic
776C22#131×D5911yescharacteristic
777C22#1683816711yescharacteristic
778C22#1683816811yescharacteristic
779C22#1683816811yescharacteristic
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—2361no—
785C4—2361no—
786C4—2361no—
787C4—2361no—
788C4—2361no—
789C4—2361no—
790C4#1683814011yescharacteristic
791C4#1683814011yescharacteristic
792C4#1683814111yescharacteristic
793C4#1683814211yescharacteristic
794C2—81no—
795C2—81no—
796C2—4721no—
797C2—2362no—
798C2#2142727111yescharacteristic
799C2#2143313911yescharacteristic
800C2#2143314011yescharacteristic
801C2#2143314311yescharacteristic
802C2#2143315311yescharacteristic
803C2#2143315511yescharacteristic
804C2#2143315611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1870C2
prime radical#21427375C2
cosocleC22×C4×C59C24
hypercenter#1870D59
hypocenterC59#23359
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. #21424394C2semidirect
3. #21424393C2semidirect
4. #21424393C2semidirect
5. #21424392C2semidirect
6. #21424391C2semidirect
7. #21424391C2semidirect
8. #21424390C2semidirect
9. #21424390C2semidirect
10. #21424387C2semidirect
11. #21424385C2semidirect
12. #21424385C2semidirect
13. #21424240C2semidirect
14. #21424240C2semidirect
15. C59×#1870C2semidirect
401. #1870D59semidirect
461. C59#23359semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214273752
#214243942
#214243932
#214243922
#214243912
#214243902
#214243872
#214243852
#214242402
C59×#18702
#2335959