Finite Group Databasebeta

← #28615030

Subgroups — #28615030

Order 15104.

776 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21427336C211yesmaximal, characteristic
2#21424894C211yesmaximal, characteristic, complemented
3#21424893C211yesmaximal, characteristic, complemented
4#21424709C211yesmaximal, characteristic, complemented
5#21424707C211yesmaximal, characteristic, complemented
6#21424662C211yesmaximal, characteristic, complemented
7#21424392C211yesmaximal, characteristic, complemented
8#21424392C211yesmaximal, characteristic, complemented
9#21424387C211yesmaximal, characteristic, complemented
10#21424387C211yesmaximal, characteristic, complemented
11#21424280C211yesmaximal, characteristic, complemented
12#21424272C211yesmaximal, characteristic, complemented
13#21424166C211yesmaximal, characteristic, complemented
14#21424079C211yesmaximal, characteristic, complemented
15C59×#1917C211yesmaximal, characteristic, complemented
16C22×#11745659C2211yescharacteristic
17C22×C8×D59C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×#14273684C2211yescharacteristic
22C2×C4⋊(C59⋊C8)C2211yescharacteristic
23C2×Dic59⋊C8C2211yescharacteristic
24C2×Dic59⋊C8C2211yescharacteristic
25C2×(C2×D59)⋊C8C2211yescharacteristic
26C2×(C2×D59)⋊C8C2211yescharacteristic
27C2×(C2×D59)⋊C8C2211yescharacteristic
28C2×(C2×D59)⋊C8C2211yescharacteristic
29C2×(C2×D59)⋊C8C2211yescharacteristic
30C2×(C2×D59)⋊C8C2211yescharacteristic
31C2×(C2×D59)⋊C8C2211yescharacteristic
32C2×(C2×D59)⋊C8C2211yescharacteristic
33C2×(C2×D59)⋊C8C2211yescharacteristic
34C2×(C2×D59)⋊C8C2211yescharacteristic
35C2×#14273638C2211yescharacteristic
36#16837334C411yescharacteristic
37#16837329C411yescharacteristic
38#16837324C411yescharacteristic
39#16837324C411yescharacteristic
40#16837320C411yescharacteristic
41#16837319C411yescharacteristic
42#16837319C411yescharacteristic
43#16837312C411yescharacteristic
44C4×(C2×D59)⋊C4C2211yescharacteristic
45C4×(C2×D59)⋊C4C2211yescharacteristic
46#16837157C2211yescharacteristic
47#16837157C2211yescharacteristic
48#16837157C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837156C2211yescharacteristic
51#16837156C2211yescharacteristic
52C2×C4⋊C8×C59C2211yescharacteristic
53C2×#97×C59C2211yescharacteristic
54C4×C4⋊C4×C59C2211yescharacteristic
55C59×#336C2211yescharacteristic
56C59×#336C2211yescharacteristic
57C59×#336C2211yescharacteristic
58C59×#336C2211yescharacteristic
59C22×D236C2×C411yescharacteristic
60C22×D236C2×C411yescharacteristic
61C22×D236C2×C411yescharacteristic
62C22×C4×D59C2311yescharacteristic
63C22×C4×D59C2311yescharacteristic
64C22×C4×D59C2311yescharacteristic
65C2×#11745659—41no—
66C2×#11745659—41no—
67C2×#11745659—41no—
68C22×C59⋊C8C2311yescharacteristic
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C2×C8×D59—41no—
73C2×C8×D59—41no—
74C2×C8×D59—41no—
75C4×D236—41no—
76C4×D236—41no—
77C4×D236—41no—
78C4×D236—41no—
79C4×D236—41no—
80C4×D236—41no—
81#14273684—41no—
82#14273684—41no—
83C2×C4⋊Dic59C2×C411yescharacteristic
84C2×C4⋊Dic59C2×C411yescharacteristic
85C2×C4⋊Dic59C2×C411yescharacteristic
86C2×Dic59⋊C4C2×C411yescharacteristic
87C2×Dic59⋊C4C2×C411yescharacteristic
88C2×(C2×D59)⋊C4C2×C411yescharacteristic
89C2×(C2×D59)⋊C4C2×C411yescharacteristic
90C2×(C2×D59)⋊C4C2×C411yescharacteristic
91C2×(C2×D59)⋊C4C2×C411yescharacteristic
92C2×(C2×D59)⋊C4C2×C411yescharacteristic
93C2×(C2×D59)⋊C4C2×C411yescharacteristic
94C2×(C2×D59)⋊C4C2×C411yescharacteristic
95C2×(C2×D59)⋊C4C2×C411yescharacteristic
96C2×(C2×D59)⋊C4C2×C411yescharacteristic
97C2×(C2×D59)⋊C4C2×C411yescharacteristic
98C2×(C2×D59)⋊C4C2×C411yescharacteristic
99C2×(C2×D59)⋊C4C2×C411yescharacteristic
100C2×C4×Dic59C2311yescharacteristic
101C4⋊(C59⋊C8)—41no—
102Dic59⋊C8—41no—
103Dic59⋊C8—41no—
104(C2×D59)⋊C8—41no—
105(C2×D59)⋊C8—41no—
106(C2×D59)⋊C8—41no—
107(C2×D59)⋊C8—41no—
108(C2×D59)⋊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#14273638—41no—
115C59⋊#95C2×C411yescharacteristic
116C59⋊#95C2×C411yescharacteristic
117C59⋊#95C2×C411yescharacteristic
118C59⋊#95C2×C411yescharacteristic
119C22×C8×C59C2311yescharacteristic
120C22×C8×C59C2311yescharacteristic
121C22×C8×C59C2311yescharacteristic
122C22×C8×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2×C411yescharacteristic
124C2×C4⋊C4×C59C2×C411yescharacteristic
125C2×C42×C59C2311yescharacteristic
126C2×C42×C59C2311yescharacteristic
127C2×C42×C59C2311yescharacteristic
128C4⋊C8×C59—41no—
129#97×C59—41no—
130#95×C59C2×C411yescharacteristic
131#95×C59C2×C411yescharacteristic
132C23×D59C22×C411yescharacteristic
133C23×D59C22×C411yescharacteristic
134C23×D59C22×C411yescharacteristic
135C22×C4×C59C22×C411yescharacteristic
136C22×C4×C59C22×C411yescharacteristic
137C22×C4×C59C22×C411yescharacteristic
138C22×C4×C59C22×C411yescharacteristic
139C22×C4×C59C22×C411yescharacteristic
140C22×C4×C59C22×C411yescharacteristic
141C22×C4×C59C2411yescharacteristic
142C22×Dic59C22×C411yescharacteristic
143C22×Dic59C22×C411yescharacteristic
144C22×Dic59C22×C411yescharacteristic
145C22×Dic59C22×C411yescharacteristic
146C22×Dic59C22×C411yescharacteristic
147C2×D236—22no—
148C2×D236—22no—
149C2×D236—41no—
150C2×D236—41no—
151C2×D236—41no—
152C2×D236—41no—
153C2×D236—41no—
154C2×D236—41no—
155C2×D236—41no—
156C2×C4×D59—21no—
157C2×C4×D59—21no—
158C2×C4×D59—21no—
159C2×C4×D59—21no—
160C2×C4×D59—21no—
161C2×C4×D59—21no—
162C2×C4×D59—21no—
163C2×C4×D59—21no—
164C2×C4×D59—21no—
165C2×C4×D59—21no—
166C2×C4×D59—21no—
167C2×C4×D59—21no—
168C2×C4×D59—21no—
169C2×C4×D59—21no—
170C2×C4×D59—21no—
171C2×C4×D59—21no—
172C2×C4×D59—21no—
173C2×C4×D59—21no—
174C2×C8×C59—21no—
175C2×C8×C59—21no—
176C2×C8×C59—21no—
177C2×C8×C59—21no—
178C2×C8×C59—21no—
179C2×C8×C59—21no—
180C2×C8×C59—21no—
181C2×C8×C59—21no—
182C2×C8×C59—21no—
183C2×C8×C59—21no—
184C2×C8×C59—21no—
185C2×C8×C59—21no—
186C4⋊C4×C59—41no—
187C4⋊C4×C59—41no—
188C42×C59—21no—
189C42×C59—21no—
190C42×C59—21no—
191C42×C59—21no—
192C42×C59—21no—
193C42×C59—21no—
194(C2×D59)⋊C4—22no—
195(C2×D59)⋊C4—41no—
196(C2×D59)⋊C4—41no—
197(C2×D59)⋊C4—41no—
198(C2×D59)⋊C4—41no—
199(C2×D59)⋊C4—41no—
200(C2×D59)⋊C4—41no—
201(C2×D59)⋊C4—41no—
202(C2×D59)⋊C4—41no—
203(C2×D59)⋊C4—41no—
204(C2×D59)⋊C4—41no—
205(C2×D59)⋊C4—41no—
206C4⋊Dic59—41no—
207C4⋊Dic59—41no—
208C4⋊Dic59—41no—
209Dic59⋊C4—41no—
210Dic59⋊C4—41no—
211C4×Dic59—21no—
212C4×Dic59—21no—
213C2×C59⋊C8—21no—
214C2×C59⋊C8—21no—
215C2×C59⋊C8—21no—
216C2×C59⋊C8—21no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—21no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225#11745659—44no—
226C8×D59—44no—
227C23×C59C23×C411yescharacteristic
228C22×D59—21no—
229C22×D59—21no—
230C22×D59—21no—
231C22×D59—21no—
232C22×D59—21no—
233C22×D59—21no—
234C22×D59—21no—
235C22×D59—21no—
236C22×D59—21no—
237C22×D59—21no—
238C22×D59—21no—
239C22×D59—21no—
240C22×D59—21no—
241C22×D59—21no—
242C22×D59—21no—
243C22×D59—21no—
244C22×D59—21no—
245C22×D59—21no—
246C22×D59—21no—
247C22×D59—21no—
248C22×D59#13112yes—
249C2×C4×C59—21no—
250C2×C4×C59—21no—
251C2×C4×C59—21no—
252C2×C4×C59—21no—
253C2×C4×C59—21no—
254C2×C4×C59—21no—
255C2×C4×C59—21no—
256C2×C4×C59—21no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—21no—
260C2×C4×C59—21no—
261C2×C4×C59—21no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—21no—
267C2×C4×C59H(5,𝔽2)11yescharacteristic
268C2×C4×C59H(5,𝔽2)11yescharacteristic
269C2×C4×C59H(5,𝔽2)11yescharacteristic
270C2×C4×C59H(5,𝔽2)11yescharacteristic
271C2×C4×C59H(5,𝔽2)11yescharacteristic
272C2×C4×C592−1+411yescharacteristic
273C2×Dic59—21no—
274C2×Dic59—21no—
275C2×Dic59—21no—
276C2×Dic59—21no—
277C2×Dic59—21no—
278C2×Dic59—21no—
279C2×Dic59—21no—
280C2×Dic59—21no—
281C2×Dic59—21no—
282C2×Dic59—21no—
283C2×Dic59—21no—
284C2×Dic59—21no—
285C2×Dic59—21no—
286C2×Dic59—21no—
287C2×Dic59—21no—
288D236—44no—
289D236—44no—
290D236—44no—
291C4×D59—41no—
292C4×D59—41no—
293C4×D59—41no—
294C4×D59—41no—
295C4×D59—41no—
296C4×D59—41no—
297C4×D59—41no—
298C4×D59—41no—
299C4×D59—41no—
300C4×D59—41no—
301C4×D59—41no—
302C4×D59—41no—
303C8×C59—41no—
304C8×C59—41no—
305C8×C59—41no—
306C8×C59—41no—
307C59⋊C8—41no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310C59⋊C8—41no—
311#23335—591nomaximal, Sylow
312C22×C59#51811yescharacteristic
313C22×C59#51811yescharacteristic
314C22×C59#52011yescharacteristic
315C22×C59C2×#13111yescharacteristic
316C22×C59#56811yescharacteristic
317C22×C59#56811yescharacteristic
318C22×C59#56811yescharacteristic
319C2×D59—22no—
320C2×D59—22no—
321C2×D59—22no—
322C2×D59—41no—
323C2×D59—41no—
324C2×D59—41no—
325C2×D59—41no—
326C2×D59—41no—
327C2×D59—41no—
328C2×D59—41no—
329C2×D59—41no—
330C2×D59—41no—
331C2×D59—41no—
332C2×D59—41no—
333C2×D59—41no—
334C2×D59—41no—
335C2×D59—41no—
336C2×D59—41no—
337C2×D59—41no—
338C2×D59—41no—
339C2×D59—41no—
340C4×C59—41no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—41no—
344C4×C59—41no—
345C4×C59—41no—
346C4×C59#56011yescharacteristic
347C4×C59#56011yescharacteristic
348C4×C59#56211yescharacteristic
349C4×C59#56211yescharacteristic
350Dic59—41no—
351Dic59—41no—
352Dic59—41no—
353Dic59—41no—
354Dic59—41no—
355#2392—591no—
356#1955—591no—
357#1955—591no—
358#1924—591no—
359#1924—591no—
360#1917—591no—
361#1917D5911yescharacteristic, complemented
362#1870—591no—
363#1870—591no—
364#1869—591no—
365#1869—591no—
366#1851—591no—
367#1850—591no—
368#1818—591no—
369#1798—591no—
370C2×C59#237711yescharacteristic
371C2×C59#297611yescharacteristic
372C2×C59#297611yescharacteristic
373C2×C59#297811yescharacteristic
374C2×C59#298011yescharacteristic
375C2×C59#299211yescharacteristic
376C2×C59#299511yescharacteristic
377D59—42no—
378D59—81no—
379D59—81no—
380C22×M16—591no—
381C23×C8—591no—
382C2×C4×D4—591no—
383C2×C4×D4—591no—
384C2×C4×D4—591no—
385C2×#117—591no—
386C2×C4⋊C8—591no—
387C2×C4⋊C8—591no—
388C2×C4⋊C8—591no—
389C2×C4⋊C8C2×D5911yescharacteristic
390C2×C22⋊C8—591no—
391C2×C22⋊C8—591no—
392C2×C22⋊C8—591no—
393C2×C22⋊C8—591no—
394C2×C22⋊C8—591no—
395C2×C22⋊C8—591no—
396C2×C22⋊C8—591no—
397C2×C22⋊C8—591no—
398C2×C22⋊C8—591no—
399C2×C22⋊C8—591no—
400C2×#97—591no—
401C2×#97C2×D5911yescharacteristic
402#398—591no—
403#397—591no—
404#396—591no—
405#396—591no—
406#394—591no—
407#394—591no—
408#394—591no—
409#392—591no—
410C4×C4⋊C4C2×D5911yescharacteristic
411C4×C22⋊C4—591no—
412C4×C22⋊C4—591no—
413#336—591no—
414#336—591no—
415#336—591no—
416#336—591no—
417#336—591no—
418#336—591no—
419#336C2×D5911yescharacteristic
420#336C2×D5911yescharacteristic
421#336C2×D5911yescharacteristic
422#336C2×D5911yescharacteristic
423C59#2333511yescharacteristic, complemented, Sylow
424C22×D4—591no—
425C22×D4—591no—
426C22×D4—591no—
427C23×C4—591no—
428C23×C4—591no—
429C23×C4—591no—
430C2×M16—2361no—
431C2×M16—2361no—
432C2×M16—2361no—
433C22×C8—591no—
434C22×C8—591no—
435C22×C8—591no—
436C22×C8—591no—
437C22×C8—2361no—
438C22×C8—2361no—
439C22×C8—2361no—
440C22×C8C22×D5911yescharacteristic
441C22×C8C22×D5911yescharacteristic
442C22×C8C22×D5911yescharacteristic
443C22×C8C22×D5911yescharacteristic
444C4×D4—2361no—
445C4×D4—2361no—
446C4×D4—2361no—
447C4×D4—2361no—
448C4×D4—2361no—
449C4×D4—2361no—
450#117—2361no—
451#117—2361no—
452C2×C4⋊C4—591no—
453C2×C4⋊C4—591no—
454C2×C4⋊C4—591no—
455C2×C4⋊C4—591no—
456C2×C4⋊C4—591no—
457C2×C4⋊C4C4×D5911yescharacteristic
458C2×C4⋊C4C4×D5911yescharacteristic
459C2×C22⋊C4—591no—
460C2×C22⋊C4—591no—
461C2×C22⋊C4—591no—
462C2×C22⋊C4—591no—
463C2×C22⋊C4—591no—
464C2×C22⋊C4—591no—
465C2×C22⋊C4—591no—
466C2×C22⋊C4—591no—
467C2×C22⋊C4—591no—
468C2×C22⋊C4—591no—
469C2×C22⋊C4—591no—
470C2×C22⋊C4—591no—
471C2×C42—591no—
472C2×C42C22×D5911yescharacteristic
473C2×C42C22×D5911yescharacteristic
474C2×C42C22×D5911yescharacteristic
475C4⋊C8—41no—
476C4⋊C8—2361no—
477C4⋊C8—2361no—
478C4⋊C8—2361no—
479C22⋊C8—2361no—
480C22⋊C8—2361no—
481C22⋊C8—2361no—
482C22⋊C8—2361no—
483C22⋊C8—2361no—
484C22⋊C8—2361no—
485C22⋊C8—2361no—
486C22⋊C8—2361no—
487C22⋊C8—2361no—
488C22⋊C8—2361no—
489#97—41no—
490#97—2361no—
491#95—591no—
492#95—591no—
493#95—591no—
494#95—591no—
495#95C4×D5911yescharacteristic
496#95C4×D5911yescharacteristic
497C24—591no—
498C24—591no—
499C24—591no—
500C2×D4—1182no—
501C2×D4—1182no—
502C2×D4—2361no—
503C2×D4—2361no—
504C2×D4—2361no—
505C2×D4—2361no—
506C2×D4—2361no—
507C2×D4—2361no—
508C2×D4—2361no—
509C22×C4—591no—
510C22×C4—591no—
511C22×C4—591no—
512C22×C4—591no—
513C22×C4—591no—
514C22×C4—1181no—
515C22×C4—1181no—
516C22×C4—1181no—
517C22×C4—1181no—
518C22×C4—1181no—
519C22×C4—1181no—
520C22×C4—1181no—
521C22×C4—1181no—
522C22×C4—1181no—
523C22×C4—1181no—
524C22×C4—1181no—
525C22×C4—1181no—
526C22×C4—1181no—
527C22×C4—1181no—
528C22×C4—1181no—
529C22×C4—1181no—
530C22×C4—1181no—
531C22×C4—1181no—
532C22×C4C2×C4×D5911yescharacteristic
533C22×C4C2×C4×D5911yescharacteristic
534C22×C4C2×C4×D5911yescharacteristic
535C22×C4C2×C4×D5911yescharacteristic
536C22×C4C2×C4×D5911yescharacteristic
537C22×C4C2×C4×D5911yescharacteristic
538C22×C4C23×D5911yescharacteristic
539M16—2364no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—1181no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C2×C8—1181no—
562C2×C8—1181no—
563C2×C8—1181no—
564C2×C8—2364no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—2361no—
568C4⋊C4—2361no—
569C4⋊C4—2361no—
570C4⋊C4—2361no—
571C4⋊C4—2361no—
572C22⋊C4—1182no—
573C22⋊C4—2361no—
574C22⋊C4—2361no—
575C22⋊C4—2361no—
576C22⋊C4—2361no—
577C22⋊C4—2361no—
578C22⋊C4—2361no—
579C22⋊C4—2361no—
580C22⋊C4—2361no—
581C22⋊C4—2361no—
582C22⋊C4—2361no—
583C22⋊C4—2361no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—1181no—
591C42—1181no—
592C23—592no—
593C23—1181no—
594C23—1181no—
595C23—1181no—
596C23—1181no—
597C23—1181no—
598C23—1181no—
599C23—1181no—
600C23—1181no—
601C23—1181no—
602C23—1181no—
603C23—1181no—
604C23—1181no—
605C23—1181no—
606C23—1181no—
607C23—1181no—
608C23—1181no—
609C23—1181no—
610C23—1181no—
611C23—1181no—
612C23—1181no—
613C23C22×C4×D5911yescharacteristic
614D4—2364no—
615D4—2364no—
616D4—2364no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—1181no—
636C2×C4—1181no—
637C2×C4—1181no—
638C2×C4—1181no—
639C2×C4—1181no—
640C2×C4—1181no—
641C2×C4—1181no—
642C2×C4—1181no—
643C2×C4—1181no—
644C2×C4—1181no—
645C2×C4—1181no—
646C2×C4—1181no—
647C2×C4—1181no—
648C2×C4—1181no—
649C2×C4—1181no—
650C2×C4—2361no—
651C2×C4—2361no—
652C2×C4—2361no—
653C2×C4—2361no—
654C2×C4—2361no—
655C2×C4—2361no—
656C2×C4—2361no—
657C2×C4—2361no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4#1427377211yescharacteristic
663C2×C4#1427377311yescharacteristic
664C2×C4#1427377311yescharacteristic
665C2×C4#1427377311yescharacteristic
666C2×C4#1427377311yescharacteristic
667C2×C4#1427377511yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—2361no—
673C8—2361no—
674C8—2361no—
675C8—2361no—
676C22—1182no—
677C22—1182no—
678C22—1182no—
679C22—2361no—
680C22—2361no—
681C22—2361no—
682C22—2361no—
683C22—2361no—
684C22—2361no—
685C22—2361no—
686C22—2361no—
687C22—2361no—
688C22—2361no—
689C22—2361no—
690C22—2361no—
691C22—2361no—
692C22—2361no—
693C22—2361no—
694C22—2361no—
695C22—2361no—
696C22—2361no—
697C22#1683787411yescharacteristic
698C22#1683787611yescharacteristic
699C22#1683788411yescharacteristic
700C22#131×D5911yescharacteristic
701C22#1683816711yescharacteristic
702C22#1683816811yescharacteristic
703C22#1683816811yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—2361no—
711C4—2361no—
712C4—2361no—
713C4—2361no—
714C4—2361no—
715C4#1683814211yescharacteristic
716C4#1683814311yescharacteristic
717C4#1683814811yescharacteristic
718C4#1683815011yescharacteristic
719C2—4721no—
720C2—4721no—
721C2—2362no—
722C2#2142725111yescharacteristic
723C2#2143314211yescharacteristic
724C2#2143314311yescharacteristic
725C2#2143315311yescharacteristic
726C2#2143316611yescharacteristic
727C2#2143323411yescharacteristic
728C2#2143326511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D59
commutator, socleC23×C59C23×C4
FittingC59×#1917C2
prime radical#16837312C4
cosocleC22×C4×C59C24
hypercenter#1917D59
hypocenterC59#23335
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ #1917

Complements

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

NH ≅ G/Ntype
2. #21424894C2semidirect
3. #21424893C2semidirect
4. #21424709C2semidirect
5. #21424707C2semidirect
6. #21424662C2semidirect
7. #21424392C2semidirect
8. #21424392C2semidirect
9. #21424387C2semidirect
10. #21424387C2semidirect
11. #21424280C2semidirect
12. #21424272C2semidirect
13. #21424166C2semidirect
14. #21424079C2semidirect
15. C59×#1917C2semidirect
361. #1917D59semidirect
423. C59#23335semidirect

Maximal subgroups

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

subgroupindex
#214273362
#214248942
#214248932
#214247092
#214247072
#214246622
#214243922
#214243872
#214242802
#214242722
#214241662
#214240792
C59×#19172
#2333559