Finite Group Databasebeta

← #28605009

Subgroups — #28605009

Order 15104.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838098C211yesmaximal, characteristic
2D4×C4⋊Dic59C211yesmaximal, characteristic, complemented
3#21425065C211yesmaximal, characteristic, complemented
4#21425051C211yesmaximal, characteristic, complemented
5#21424534C211yesmaximal, characteristic, complemented
6#21424524C211yesmaximal, characteristic, complemented
7#21424411C211yesmaximal, characteristic, complemented
8#21424411C211yesmaximal, characteristic, complemented
9#21424192C211yesmaximal, characteristic, complemented
10#21424187C211yesmaximal, characteristic, complemented
11#21424097C211yesmaximal, characteristic, complemented
12#21423922C211yesmaximal, characteristic, complemented
13#21423816C211yesmaximal, characteristic, complemented
14C2×#16837165C211yesmaximal, characteristic, complemented
15C2×C59×#435C211yesmaximal, characteristic, complemented
16#16838098—24no—
17#16838098C418yescomplemented
18C2×#14273722—21no—
19C2×#14273719C2211yescharacteristic
20C2×#14273709—21no—
21C2×#14273701C2211yescharacteristic
22C2×#14273701C2211yescharacteristic
23C2×#14273699—21no—
24C2×C4×D236C2211yescharacteristic
25C2×D4×Dic59—21no—
26C2×(C22⋊D59)⋊C4—21no—
27C2×#14273686C2211yescharacteristic
28C22×C4⋊Dic59C2211yescharacteristic
29C22×C4⋊Dic59C2211yescharacteristic
30C22×C4⋊Dic59C2211yescharacteristic
31C2×#14273649C2211yescharacteristic
32C2×#14273649C2211yescharacteristic
33C2×#14273649C2211yescharacteristic
34C2×#14273649C2211yescharacteristic
35#16837301—21no—
36#16837277—21no—
37#16837277—21no—
38#16837272C2211yescharacteristic
39#16837262C2211yescharacteristic
40#16837262C2211yescharacteristic
41C4×C4⋊Dic59C2211yescharacteristic
42#16837165C2211yescharacteristic
43#16837165C2211yescharacteristic
44#16837165C2211yescharacteristic
45#16837165C2211yescharacteristic
46#16837165C2211yescharacteristic
47#16837165C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837165C2211yescharacteristic
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837165C2211yescharacteristic
54C22×M16×C59C2211yescharacteristic
55C23×C8×C59C2211yescharacteristic
56C2×C4×D4×C59C2211yescharacteristic
57C59×#435—24no—
58C2×C4⋊C8×C59C2211yescharacteristic
59C2×C22⋊C8×C59C2211yescharacteristic
60C2×C22⋊C8×C59C2211yescharacteristic
61C2×#97×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C22⋊D59—21no—
65C23×Dic59—21no—
66C23×Dic59—21no—
67C23×Dic59—21no—
68C22×C4×D59—21no—
69#14273722—28no—
70#14273719—22no—
71#14273719C2×C414yescomplemented
72#14273709—28no—
73#14273701—22no—
74#14273701—22no—
75#14273701C2×C414yescomplemented
76#14273701C2×C414yescomplemented
77#14273699—28no—
78C4×D236—22no—
79C4×D236C2×C414yescomplemented
80D4×Dic59—44no—
81(C22⋊D59)⋊C4—28no—
82#14273686—22no—
83#14273686C2×C414yescomplemented
84C2×C4⋊Dic59—21no—
85C2×C4⋊Dic59—22no—
86C2×C4⋊Dic59—22no—
87C2×C4⋊Dic59—22no—
88C2×C4⋊Dic59—21no—
89C2×C4⋊Dic59—21no—
90C2×C4⋊Dic59—21no—
91C2×C4⋊Dic59—21no—
92C2×C4⋊Dic59—41no—
93C2×C4⋊Dic59—41no—
94C2×C4⋊Dic59C2×C414yescomplemented
95C2×C4⋊Dic59C2311yescharacteristic
96C2×C4⋊Dic59C2311yescharacteristic
97C2×C4⋊Dic59C2311yescharacteristic
98C2×C4⋊Dic59C2311yescharacteristic
99C2×C4⋊Dic59C2311yescharacteristic
100C2×C4⋊Dic59C2311yescharacteristic
101C2×C4⋊Dic59C2311yescharacteristic
102C2×Dic59⋊C4—21no—
103C2×Dic59⋊C4—21no—
104C2×C22⋊Dic59—21no—
105C2×C22⋊Dic59—21no—
106C2×C22⋊Dic59—21no—
107C2×(C2×D59)⋊C4—21no—
108C2×(C2×D59)⋊C4—21no—
109C2×(C2×D59)⋊C4—21no—
110C2×C4×Dic59—21no—
111C2×C4×Dic59—21no—
112#14273649—22no—
113#14273649—22no—
114#14273649—41no—
115#14273649—41no—
116C59⋊#95—21no—
117C59⋊#95—21no—
118C59⋊#95—21no—
119C22×D4×C59D411yescharacteristic
120C23×C4×C59C2311yescharacteristic
121C23×C4×C59C2311yescharacteristic
122C2×M16×C59—22no—
123C2×M16×C59—22no—
124C2×M16×C59—41no—
125C22×C8×C59—22no—
126C22×C8×C59—22no—
127C22×C8×C59—41no—
128C22×C8×C59C2311yescharacteristic
129C22×C8×C59C2311yescharacteristic
130C22×C8×C59C2311yescharacteristic
131C22×C8×C59C2311yescharacteristic
132C4×D4×C59C2×C414yes—
133C4×D4×C59D414yes—
134C2×C4⋊C4×C59D411yescharacteristic
135C2×C22⋊C4×C59D411yescharacteristic
136C2×C22⋊C4×C59D411yescharacteristic
137C2×C42×C59C2311yescharacteristic
138C4⋊C8×C59—22no—
139C22⋊C8×C59—22no—
140C22⋊C8×C59—22no—
141#97×C59—22no—
142C24×C59C2×D411yescharacteristic
143C24×C59C2×D411yescharacteristic
144C23×D59—21no—
145C2×D4×C59—22no—
146C2×D4×C59—22no—
147C2×D4×C59C22⋊C414yes—
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×C59C22×C412yes—
157C22×C4×C59C22×C412yes—
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D412yes—
163C22×C4×C59C2×D412yes—
164C22×C4×C59C2411yescharacteristic
165C2×C22⋊D59—24no—
166C2×C22⋊D59—24no—
167C2×C22⋊D59—42no—
168C2×C22⋊D59—42no—
169C2×C22⋊D59—81no—
170C2×C22⋊D59—81no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—24no—
176C22×Dic59—21no—
177C22×Dic59—21no—
178C22×Dic59—21no—
179C22×Dic59—42no—
180C22×Dic59—42no—
181C22×Dic59—42no—
182C22×Dic59—42no—
183C22×Dic59—81no—
184C22×Dic59—81no—
185C22×Dic59—81no—
186C22×Dic59—81no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236C22×C412yes—
193C2×C4×D59—24no—
194C2×C4×D59—81no—
195C2×C4×D59—81no—
196M16×C59—44no—
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—
208C2×C8×C59—44no—
209C2×C8×C59#4112yes—
210C4⋊C4×C59C22⋊C414yes—
211C22⋊C4×C59C22⋊C414yes—
212C22⋊C4×C59C22⋊C414yes—
213C42×C59C22×C412yes—
214C42×C59C2×D412yes—
215C22⋊Dic59—24no—
216C22⋊Dic59—42no—
217C22⋊Dic59—42no—
218(C2×D59)⋊C4—24no—
219(C2×D59)⋊C4—24no—
220(C2×D59)⋊C4—24no—
221C4⋊Dic59—24no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—21no—
231C4⋊Dic59—21no—
232C4⋊Dic59—42no—
233C4⋊Dic59—42no—
234C4⋊Dic59—42no—
235C4⋊Dic59—81no—
236C4⋊Dic59C22×C412yes—
237C4⋊Dic59C22×C412yes—
238C4⋊Dic59C22×C412yes—
239C4⋊Dic59#4112yes—
240Dic59⋊C4—24no—
241Dic59⋊C4—24no—
242C4×Dic59—24no—
243C4×Dic59—42no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59C2×C22⋊C412yes—
255C23×C59C2×C22⋊C412yes—
256C23×C59AGL(1,ℤ/8)12yes—
257C23×C59#13712yes—
258C23×C59C22×D411yescharacteristic
259C22×D59—22no—
260C22×D59—41no—
261C22×D59—41no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—41no—
266D4×C59—28no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—22no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59C2×C22⋊C412yes—
284C2×C4×C59C2×C22⋊C412yes—
285C2×C4×C59C2×C22⋊C412yes—
286C2×C4×C59C2×C22⋊C412yes—
287C2×C4×C59C23×C411yescharacteristic
288C2×C4×C59C22×D411yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59H(5,𝔽2)11yescharacteristic
292C2×C4×C592−1+411yescharacteristic
293C22⋊D59—48no—
294C22⋊D59—84no—
295C2×Dic59—22no—
296C2×Dic59—22no—
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—84no—
317C2×Dic59—84no—
318C2×Dic59—84no—
319D236—22no—
320D236—22no—
321D236—41no—
322D236—41no—
323C4×D59—84no—
324C8×C59—22no—
325C8×C59—41no—
326C8×C59—41no—
327C8×C59—41no—
328#22493—591nomaximal, Sylow
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—22no—
335C22×C59—22no—
336C22×C59—22no—
337C22×C59—22no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59#41714yes—
343C22×C59C22×C22⋊C411yescharacteristic
344C22×C59#54611yescharacteristic
345C22×C59#54711yescharacteristic
346C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C59C2×#13711yescharacteristic
348C22×C59#57611yescharacteristic
349C22×C59#57711yescharacteristic
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—81no—
354C2×D59—81no—
355C2×D59—81no—
356C2×D59—81no—
357C4×C59—22no—
358C4×C59—22no—
359C4×C59—22no—
360C4×C59—22no—
361C4×C59C4×#4111yescharacteristic
362C4×C59#52011yescharacteristic
363C4×C59#54611yescharacteristic
364C4×C59#54711yescharacteristic
365Dic59—42no—
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59—81no—
370Dic59—81no—
371Dic59—81no—
372C2×#553—591no—
373C2×#435D5911yescharacteristic, complemented
374D4×C4⋊C4—591no—
375#1992—591no—
376#1989—591no—
377#1895—591no—
378#1893—591no—
379#1874—591no—
380#1874—591no—
381#1825—591no—
382#1824—591no—
383#1802—591no—
384#1762—591no—
385#1736—591no—
386C2×#340—591no—
387C2×C59—24no—
388C2×C59—42no—
389C2×C59#233911yescharacteristic
390C2×C59C2×#41711yescharacteristic
391C2×C59#289711yescharacteristic
392C2×C59#331811yescharacteristic
393C2×C59#332011yescharacteristic
394C2×C59#334511yescharacteristic
395C2×C59#334611yescharacteristic
396D59—82no—
397C22×M16C2×D5911yescharacteristic
398C23×C8C2×D5911yescharacteristic
399#553—598no—
400#553—1184no—
401C2×#126—1181no—
402C2×#125—591no—
403C2×#123—1181no—
404C2×#121—591no—
405C2×#121—591no—
406C2×#121—1181no—
407C2×C4×D4—591no—
408C2×C4×D4—1181no—
409C2×C4×D4—1181no—
410C2×C4×D4C2×D5911yescharacteristic
411C2×#117—591no—
412C22×C4⋊C4—591no—
413C22×C4⋊C4—591no—
414C22×C4⋊C4—591no—
415#435—24no—
416C2×C4⋊C8C2×D5911yescharacteristic
417C2×#102—591no—
418C2×#102—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×C22⋊C8C2×D5911yescharacteristic
422C2×C22⋊C8C2×D5911yescharacteristic
423C2×#97C2×D5911yescharacteristic
424#389—1181no—
425#385—1181no—
426#385—1181no—
427#384—591no—
428#380—591no—
429#380—591no—
430C4×C4⋊C4—591no—
431#340—591no—
432#340—591no—
433#340—591no—
434#340—591no—
435#340—591no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#340—591no—
441#340—591no—
442#340—591no—
443C59#2249311yescharacteristic, complemented, Sylow
444C22×D4—591no—
445C22×D4—1181no—
446C22×D4—1181no—
447C22×D4D23611yescharacteristic
448C23×C4—1181no—
449C23×C4—1181no—
450C23×C4—1181no—
451C23×C4—1181no—
452C23×C4C22×D5911yescharacteristic
453C23×C4C22×D5911yescharacteristic
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—41no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—41no—
460C22×C8C22×D5911yescharacteristic
461C22×C8C22×D5911yescharacteristic
462C22×C8C22×D5911yescharacteristic
463C22×C8C22×D5911yescharacteristic
464#126—1188no—
465#125—594no—
466#125—1182no—
467#123—1188no—
468#121—594no—
469#121—594no—
470#121—1188no—
471#121—1182no—
472#121—1182no—
473C4×D4—594no—
474C4×D4—1188no—
475C4×D4—1182no—
476C4×D4—2364no—
477C4×D4C4×D5914yes—
478C4×D4C22⋊D5914yes—
479#117—594no—
480#117—1182no—
481C2×C4⋊C4—594no—
482C2×C4⋊C4—591no—
483C2×C4⋊C4—591no—
484C2×C4⋊C4—591no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—1182no—
490C2×C4⋊C4—1182no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4—1181no—
493C2×C4⋊C4—1181no—
494C2×C4⋊C4—1182no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4—1181no—
499C2×C4⋊C4—2361no—
500C2×C4⋊C4—2361no—
501C2×C4⋊C4D23611yescharacteristic
502C2×C22⋊C4—1181no—
503C2×C22⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4D23611yescharacteristic
509C2×C22⋊C4D23611yescharacteristic
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42C22×D5911yescharacteristic
513C4⋊C8—22no—
514#102—1182no—
515#102—1182no—
516#102—2361no—
517#102—2361no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520#97—22no—
521#95—1181no—
522#95—1181no—
523#95—1181no—
524C24—1181no—
525C24C2×D23611yescharacteristic
526C24C2×D23611yescharacteristic
527C2×D4—22no—
528C2×D4—22no—
529C2×D4—592no—
530C2×D4—1184no—
531C2×D4—1184no—
532C2×D4—1181no—
533C2×D4—1181no—
534C2×D4—1181no—
535C2×D4—1181no—
536C2×D4—1181no—
537C2×D4—4721no—
538C2×D4—4721no—
539C2×D4—2362no—
540C2×D4—2362no—
541C2×D4(C2×D59)⋊C414yes—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—1184no—
551C22×C4—1181no—
552C22×C4—1181no—
553C22×C4—1181no—
554C22×C4—1181no—
555C22×C4—1184no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—4721no—
560C22×C4—4721no—
561C22×C4—4721no—
562C22×C4—4721no—
563C22×C4—4721no—
564C22×C4—4721no—
565C22×C4—2362no—
566C22×C4—2362no—
567C22×C4—2362no—
568C22×C4—2362no—
569C22×C4C2×C4×D5912yes—
570C22×C4C2×C4×D5912yes—
571C22×C4C2×D23611yescharacteristic
572C22×C4C2×D23611yescharacteristic
573C22×C4C2×D23611yescharacteristic
574C22×C4C2×D23611yescharacteristic
575C22×C4C2×C22⋊D5912yes—
576C22×C4C2×C22⋊D5912yes—
577C22×C4C23×D5911yescharacteristic
578M16—44no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—44no—
591C2×C8#1174568712yes—
592C4⋊C4—592no—
593C4⋊C4—592no—
594C4⋊C4—592no—
595C4⋊C4—592no—
596C4⋊C4—1184no—
597C4⋊C4—1184no—
598C4⋊C4—1184no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—1181no—
607C4⋊C4—1181no—
608C4⋊C4—1181no—
609C4⋊C4—4721no—
610C4⋊C4—2362no—
611C4⋊C4—2362no—
612C4⋊C4—2362no—
613C4⋊C4(C2×D59)⋊C414yes—
614C22⋊C4—1184no—
615C22⋊C4—1184no—
616C22⋊C4—1184no—
617C22⋊C4—1184no—
618C22⋊C4—2362no—
619C22⋊C4—2362no—
620C22⋊C4(C2×D59)⋊C414yes—
621C22⋊C4(C2×D59)⋊C414yes—
622C42—1184no—
623C42—2362no—
624C42C2×C4×D5912yes—
625C42C2×C22⋊D5912yes—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—1182no—
637C23—2361no—
638C23—2361no—
639C23—2361no—
640C23—2361no—
641C23—2361no—
642C23—2361no—
643C23C2×(C2×D59)⋊C412yes—
644C23C2×(C2×D59)⋊C412yes—
645C23#1427375512yes—
646C23#1427376012yes—
647C23C22×D23611yescharacteristic
648D4—28no—
649D4—1182no—
650D4—1182no—
651D4—4724no—
652D4—2368no—
653D4—2361no—
654D4—2361no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—1182no—
672C2×C4—1182no—
673C2×C4—1182no—
674C2×C4—1182no—
675C2×C4—4724no—
676C2×C4—4724no—
677C2×C4—4724no—
678C2×C4—4724no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4—2361no—
682C2×C4—2361no—
683C2×C4—2361no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4—2361no—
696C2×C4C2×(C2×D59)⋊C412yes—
697C2×C4C2×(C2×D59)⋊C412yes—
698C2×C4C2×(C2×D59)⋊C412yes—
699C2×C4C2×(C2×D59)⋊C412yes—
700C2×C4C22×C4×D5911yescharacteristic
701C2×C4C22×C22⋊D5911yescharacteristic
702C2×C4#41×D5911yescharacteristic
703C2×C4C2×#1174568711yescharacteristic
704C2×C4#1427377211yescharacteristic
705C2×C4#1427377411yescharacteristic
706C8—22no—
707C8—41no—
708C8—41no—
709C8—41no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—4721no—
724C22—4721no—
725C22—4721no—
726C22—4721no—
727C22—2362no—
728C22—2362no—
729C22—2362no—
730C22#1683740414yes—
731C22C22×(C2×D59)⋊C411yescharacteristic
732C22#1683804711yescharacteristic
733C22#1683805611yescharacteristic
734C22C2×#1427375511yescharacteristic
735C22C2×#1427376011yescharacteristic
736C22#1683820711yescharacteristic
737C22#1683821411yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—4721no—
743C4—4721no—
744C4—4721no—
745C4—2362no—
746C4—2362no—
747C4—2362no—
748C4—2362no—
749C4C4×#1174568711yescharacteristic
750C4#1683788111yescharacteristic
751C4#1683804611yescharacteristic
752C4#1683805111yescharacteristic
753C2—24no—
754C2—42no—
755C2—4722no—
756C2#2142692111yescharacteristic
757C2C2×#1683740411yescharacteristic
758C2#2143262311yescharacteristic
759C2#2143623911yescharacteristic
760C2#2143626911yescharacteristic
761C2#2143656811yescharacteristic
762C2#2143658311yescharacteristic
subgroupG/H
centerC23C22×D236
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#435C2
socleC23×C59C22×D4
prime radicalC2×#16838098C2
cosocleC22×C4×C59C24
hypercenterC2×#435D59
hypocenterC59#22493
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. D4×C4⋊Dic59C2semidirect
3. #21425065C2semidirect
4. #21425051C2semidirect
5. #21424534C2semidirect
6. #21424524C2semidirect
7. #21424411C2semidirect
8. #21424411C2semidirect
9. #21424192C2semidirect
10. #21424187C2semidirect
11. #21424097C2semidirect
12. #21423922C2semidirect
13. #21423816C2semidirect
14. C2×#16837165C2semidirect
15. C2×C59×#435C2semidirect
17. #16838098C4semidirect
71. #14273719C2×C4semidirect
75. #14273701C2×C4semidirect
76. #14273701C2×C4semidirect
79. C4×D236C2×C4semidirect
83. #14273686C2×C4semidirect
94. C2×C4⋊Dic59C2×C4semidirect
373. C2×#435D59semidirect
443. C59#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#168380982
D4×C4⋊Dic592
#214250652
#214250512
#214245342
#214245242
#214244112
#214241922
#214241872
#214240972
#214239222
#214238162
C2×#168371652
C2×C59×#4352
#2249359