Finite Group Databasebeta

← #28556303

Subgroups — #28556303

Order 15104.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437831C211yesmaximal, characteristic
2#21426956C211yesmaximal, characteristic, complemented
3#21422674C211yesmaximal, characteristic, complemented
4#21422657C211yesmaximal, characteristic, complemented
5#21422653C211yesmaximal, characteristic, complemented
6#21422644C211yesmaximal, characteristic, complemented
7#21422635C211yesmaximal, characteristic, complemented
8#21422626C211yesmaximal, characteristic, complemented
9#21422622C211yesmaximal, characteristic, complemented
10#21422605C211yesmaximal, characteristic, complemented
11#21422601C211yesmaximal, characteristic, complemented
12#21422592C211yesmaximal, characteristic, complemented
13#21422583C211yesmaximal, characteristic, complemented
14C2×#16837137C211yesmaximal, characteristic, complemented
15C59×#2924C211yesmaximal, characteristic, complemented
16#16838115—21no—
17#16838100—21no—
18#16838096—21no—
19#16838076—21no—
20#16838076—21no—
21#16838053—21no—
22#16838042—21no—
23#16838042—21no—
24#16838030C411yescharacteristic, complemented
25#16838023C411yescharacteristic, complemented
26#16838023C411yescharacteristic, complemented
27#16838007C411yescharacteristic, complemented
28#16838007C411yescharacteristic, complemented
29#16837971C411yescharacteristic, complemented
30#16837952C2211yescharacteristic
31#16837952C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837936C2211yescharacteristic
34#16837913C2211yescharacteristic
35C2×#14273701C2211yescharacteristic
36#16837882C411yescharacteristic, complemented
37#16837876C411yescharacteristic, complemented
38#16837288—21no—
39#16837288—21no—
40#16837277—21no—
41#16837270C2211yescharacteristic, complemented
42#16837268C2211yescharacteristic, complemented
43#16837265C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic, complemented
45C22⋊C4×Dic59—21no—
46#16837248C2211yescharacteristic, complemented
47C2×C59⋊#95C2211yescharacteristic
48#16837140C2211yescharacteristic, complemented
49#16837140C2211yescharacteristic, complemented
50#16837140C2211yescharacteristic, complemented
51#16837140C2211yescharacteristic, complemented
52#16837137C2211yescharacteristic
53#16837137C2211yescharacteristic
54#16837137C2211yescharacteristic
55#16837137C2211yescharacteristic
56#16837137C2211yescharacteristic
57#16837137C2211yescharacteristic
58#16837137C2211yescharacteristic
59#16837137C2211yescharacteristic
60#16837137C2211yescharacteristic, complemented
61#16837137C2211yescharacteristic, complemented
62#16837137C2211yescharacteristic, complemented
63#16837137C2211yescharacteristic, complemented
64C2×#117×C59C2211yescharacteristic
65C59×#433—21no—
66C59×#433—21no—
67C59×#432C2211yescharacteristic, complemented
68C59×#432C2211yescharacteristic, complemented
69C59×#431C2211yescharacteristic, complemented
70C59×#431C2211yescharacteristic, complemented
71C59×#424—21no—
72C59×#407C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C59×#405—21no—
75C2×#11745685—21no—
76C2×#11745685—21no—
77C2×#11745685C2×C411yescharacteristic
78C22×D236C2×C411yescharacteristic
79C22×C22⋊D59—21no—
80C23×Dic59—21no—
81#14273727C2×C411yescharacteristic, complemented
82#14273727C2×C411yescharacteristic, complemented
83#14273726—21no—
84#14273724C2×C411yescharacteristic, complemented
85#14273724C2×C411yescharacteristic, complemented
86#14273722—21no—
87#14273722—21no—
88#14273721—21no—
89#14273721—21no—
90#14273719C2×C411yescharacteristic, complemented
91#14273719C2×C411yescharacteristic, complemented
92#14273718—21no—
93#14273715—21no—
94#14273715—21no—
95#14273715C2×C411yescharacteristic, complemented
96#14273715C2×C411yescharacteristic, complemented
97#14273713—21no—
98#14273713—21no—
99#14273712—21no—
100#14273712—21no—
101#14273712—21no—
102#14273712—21no—
103#14273710—21no—
104#14273710—21no—
105#14273710—21no—
106#14273709—21no—
107#14273709—21no—
108#14273706C2×C411yescharacteristic
109#14273706C2311yescharacteristic
110#14273705—21no—
111#14273705—21no—
112#14273704—21no—
113#14273704—21no—
114#14273702—21no—
115#14273702—21no—
116#14273701—21no—
117#14273701—21no—
118#14273701—21no—
119#14273701—21no—
120#14273701C2×C411yescharacteristic
121#14273701C2×C411yescharacteristic
122#14273701C2×C411yescharacteristic
123#14273701C2311yescharacteristic
124#14273701C2311yescharacteristic
125#14273701C2311yescharacteristic
126#14273700—21no—
127#14273700—21no—
128#14273700—21no—
129#14273700—21no—
130#14273697—21no—
131#14273697—21no—
132#14273696—21no—
133C4×Dic118C2×C411yescharacteristic, complemented
134C4×Dic118C2×C411yescharacteristic, complemented
135C4×D236—21no—
136C4×D236—21no—
137C4×D236C2×C411yescharacteristic, complemented
138C4×D236C2×C411yescharacteristic, complemented
139C4×D236C2×C411yescharacteristic, complemented
140C4×D236C2×C411yescharacteristic, complemented
141C4×D236C2×C411yescharacteristic, complemented
142C4×D236C2×C411yescharacteristic, complemented
143#14273689—21no—
144#14273689—21no—
145C4×C22⋊D59—21no—
146C4×C22⋊D59—21no—
147C4×C22⋊D59—21no—
148C4×C22⋊D59—21no—
149(C22⋊D59)⋊C4—21no—
150(C22⋊D59)⋊C4—21no—
151#14273686C2×C411yescharacteristic
152#14273685—21no—
153#14273684—21no—
154#14273684—21no—
155C2×C4⋊Dic59—21no—
156C2×C4⋊Dic59—21no—
157C2×C4⋊Dic59C2×C411yescharacteristic
158C4⋊C4×D59—21no—
159C2×C22⋊Dic59—21no—
160C2×(C2×D59)⋊C4—21no—
161C22⋊C4×D59—21no—
162C22⋊C4×D59—21no—
163C2×C4×Dic59—21no—
164C2×C4×Dic59—21no—
165C59⋊#95—21no—
166C59⋊#95—21no—
167C59⋊#95—21no—
168C59⋊#95—21no—
169C59⋊#95—21no—
170C59⋊#95—21no—
171C59⋊#95C2311yescharacteristic
172C59⋊#95C2311yescharacteristic
173C59⋊#95C2311yescharacteristic
174C59⋊#95C2311yescharacteristic
175C23×C4×C59C2311yescharacteristic
176C2×M16×C59—21no—
177C22×C8×C59—21no—
178#117×C59C2×C411yescharacteristic
179#117×C59C2×C411yescharacteristic
180#117×C59C2×C411yescharacteristic
181#117×C59C2×C411yescharacteristic
182#117×C59D411yescharacteristic
183#117×C59D411yescharacteristic
184#117×C59D411yescharacteristic
185#117×C59D411yescharacteristic
186C2×C4⋊C4×C59D411yescharacteristic
187C2×C4⋊C4×C59D411yescharacteristic
188C2×C22⋊C4×C59D411yescharacteristic
189C2×C22⋊C4×C59D411yescharacteristic
190C2×C42×C59C2311yescharacteristic
191C2×C42×C59C2311yescharacteristic
192C4⋊C8×C59—21no—
193C4⋊C8×C59—21no—
194C4⋊C8×C59—21no—
195C4⋊C8×C59—21no—
196C22⋊C8×C59—21no—
197C22⋊C8×C59—21no—
198C22⋊C8×C59C2311yescharacteristic
199C22⋊C8×C59C2311yescharacteristic
200C22⋊C8×C59C2311yescharacteristic
201C22⋊C8×C59C2311yescharacteristic
202#97×C59—21no—
203#97×C59—21no—
204C4×C8×C59—21no—
205C4×C8×C59—21no—
206C24×C59C2×D411yescharacteristic
207C23×D59—21no—
208C22×C4×C59—42no—
209C22×C4×C59C22×C411yescharacteristic
210C22×C4×C59C22×C411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59C2×D411yescharacteristic
216C22×C4×C59C2×D411yescharacteristic
217C22×C4×C59C2×D411yescharacteristic
218C22×C4×C59C2411yescharacteristic
219C2×C22⋊D59—21no—
220C2×C22⋊D59—21no—
221C2×C22⋊D59—21no—
222C2×C22⋊D59—21no—
223C2×C22⋊D59—21no—
224C2×C22⋊D59—21no—
225C2×C22⋊D59—21no—
226C2×C22⋊D59—81no—
227C2×C22⋊D59—81no—
228C22×Dic59—21no—
229C22×Dic59—21no—
230C22×Dic59—21no—
231C22×Dic59—21no—
232C22×Dic59—21no—
233C22×Dic59—42no—
234C22×Dic59—42no—
235C22×Dic59—81no—
236#11745685—42no—
237#11745685—81no—
238#11745685—81no—
239#11745685—81no—
240#11745685—81no—
241C2×D236—21no—
242C2×D236—21no—
243C2×D236—21no—
244C2×D236—21no—
245C2×D236—21no—
246C2×D236—42no—
247C2×D236C22×C411yescharacteristic
248C2×D236C22×C411yescharacteristic
249C2×D236C22×C411yescharacteristic
250C2×C4×D59—21no—
251C2×C4×D59—21no—
252C2×C4×D59—21no—
253C2×C4×D59—21no—
254C2×C4×D59—21no—
255C2×C4×D59—21no—
256C2×C4×D59—21no—
257C2×Dic118—21no—
258C2×Dic118—21no—
259C2×Dic118C22×C411yescharacteristic
260M16×C59—42no—
261C2×C8×C59—21no—
262C2×C8×C59—21no—
263C2×C8×C59—21no—
264C2×C8×C59—21no—
265C2×C8×C59—42no—
266C4⋊C4×C59C22⋊C411yescharacteristic
267C4⋊C4×C59C22⋊C411yescharacteristic
268C4⋊C4×C59C22⋊C411yescharacteristic
269C4⋊C4×C59C22⋊C411yescharacteristic
270C4⋊C4×C59C22⋊C411yescharacteristic
271C4⋊C4×C59C22⋊C411yescharacteristic
272C4⋊C4×C59C22⋊C411yescharacteristic
273C4⋊C4×C59C22⋊C411yescharacteristic
274C22⋊C4×C59C22⋊C411yescharacteristic
275C22⋊C4×C59C22⋊C411yescharacteristic
276C22⋊C4×C59C22⋊C411yescharacteristic
277C22⋊C4×C59C22⋊C411yescharacteristic
278C22⋊C4×C59C22⋊C411yescharacteristic
279C22⋊C4×C59C22⋊C411yescharacteristic
280C22⋊C4×C59C22⋊C411yescharacteristic
281C22⋊C4×C59C22⋊C411yescharacteristic
282C42×C59C22×C411yescharacteristic
283C42×C59C22×C411yescharacteristic
284C42×C59C22×C411yescharacteristic
285C42×C59C22×C411yescharacteristic
286C42×C59C2×D411yescharacteristic
287C42×C59C2×D411yescharacteristic
288C42×C59C2×D411yescharacteristic
289C42×C59C2×D411yescharacteristic
290C22⋊Dic59—21no—
291C22⋊Dic59—21no—
292C22⋊Dic59—21no—
293C22⋊Dic59—42no—
294(C2×D59)⋊C4—21no—
295(C2×D59)⋊C4—21no—
296(C2×D59)⋊C4—21no—
297(C2×D59)⋊C4—21no—
298(C2×D59)⋊C4—21no—
299(C2×D59)⋊C4—21no—
300(C2×D59)⋊C4—21no—
301(C2×D59)⋊C4—21no—
302(C2×D59)⋊C4—21no—
303(C2×D59)⋊C4—21no—
304(C2×D59)⋊C4—21no—
305(C2×D59)⋊C4—21no—
306(C2×D59)⋊C4—21no—
307(C2×D59)⋊C4—21no—
308(C2×D59)⋊C4—21no—
309(C2×D59)⋊C4—21no—
310C4⋊Dic59—21no—
311C4⋊Dic59—21no—
312C4⋊Dic59—21no—
313C4⋊Dic59—42no—
314C4⋊Dic59—81no—
315C4⋊Dic59C22×C411yescharacteristic
316C4⋊Dic59C22×C411yescharacteristic
317C4⋊Dic59C22×C411yescharacteristic
318C4⋊Dic59C22×C411yescharacteristic
319Dic59⋊C4—21no—
320Dic59⋊C4—21no—
321Dic59⋊C4—21no—
322Dic59⋊C4—21no—
323Dic59⋊C4—21no—
324Dic59⋊C4—21no—
325Dic59⋊C4—21no—
326Dic59⋊C4—21no—
327C4×Dic59—21no—
328C4×Dic59—21no—
329C4×Dic59—21no—
330C4×Dic59—42no—
331C4×Dic59—81no—
332C23×C59—21no—
333C23×C59—21no—
334C23×C59—22no—
335C23×C59—41no—
336C23×C59C2×C22⋊C411yescharacteristic
337C23×C59C2×C22⋊C411yescharacteristic
338C23×C59C22×D411yescharacteristic
339C22×D59—21no—
340C22×D59—21no—
341C22×D59—21no—
342C22×D59—42no—
343C22×D59—81no—
344C22×D59—81no—
345C2×C4×C59—21no—
346C2×C4×C59—21no—
347C2×C4×C59—21no—
348C2×C4×C59—21no—
349C2×C4×C59—22no—
350C2×C4×C59—22no—
351C2×C4×C59—41no—
352C2×C4×C59—41no—
353C2×C4×C59—41no—
354C2×C4×C59—41no—
355C2×C4×C59—41no—
356C2×C4×C59—41no—
357C2×C4×C59C2×C22⋊C411yescharacteristic
358C2×C4×C59C2×C22⋊C411yescharacteristic
359C2×C4×C59C2×C22⋊C411yescharacteristic
360C2×C4×C59C2×C22⋊C411yescharacteristic
361C2×C4×C59C2×C22⋊C411yescharacteristic
362C2×C4×C59C2×C22⋊C411yescharacteristic
363C2×C4×C59C2×C22⋊C411yescharacteristic
364C2×C4×C59C2×C22⋊C411yescharacteristic
365C2×C4×C59C2×C22⋊C411yescharacteristic
366C2×C4×C59C2×C22⋊C411yescharacteristic
367C2×C4×C59C23×C411yescharacteristic
368C2×C4×C59C22×D411yescharacteristic
369C22⋊D59—41no—
370C22⋊D59—41no—
371C22⋊D59—41no—
372C22⋊D59—41no—
373C22⋊D59—41no—
374C22⋊D59—41no—
375C22⋊D59—42no—
376C22⋊D59—81no—
377C22⋊D59—81no—
378C22⋊D59—81no—
379C2×Dic59—22no—
380C2×Dic59—21no—
381C2×Dic59—21no—
382C2×Dic59—21no—
383C2×Dic59—21no—
384C2×Dic59—21no—
385C2×Dic59—41no—
386C2×Dic59—41no—
387C2×Dic59—41no—
388C2×Dic59—41no—
389C2×Dic59—41no—
390C2×Dic59—41no—
391C2×Dic59—41no—
392C2×Dic59—41no—
393C2×Dic59—41no—
394C2×Dic59—41no—
395C2×Dic59—41no—
396C2×Dic59—81no—
397C2×Dic59—84no—
398D236—41no—
399D236—41no—
400D236—41no—
401D236—42no—
402D236—81no—
403D236—81no—
404D236—81no—
405D236—81no—
406C4×D59—42no—
407C4×D59—81no—
408C4×D59—81no—
409C4×D59—81no—
410C4×D59—81no—
411C4×D59—81no—
412C4×D59—81no—
413Dic118—41no—
414Dic118—81no—
415Dic118—81no—
416C8×C59—41no—
417C8×C59—41no—
418C8×C59—41no—
419C8×C59—41no—
420#17604—591nomaximal, Sylow
421C22×C59—21no—
422C22×C59—21no—
423C22×C59—21no—
424C22×C59—21no—
425C22×C59—21no—
426C22×C59—21no—
427C22×C59—21no—
428C22×C59—42no—
429C22×C59—42no—
430C22×C59#41012yes—
431C22×C59C22×C22⋊C411yescharacteristic
432C22×C59#57611yescharacteristic
433C22×C59#57711yescharacteristic
434C2×D59—41no—
435C2×D59—41no—
436C2×D59—41no—
437C2×D59—41no—
438C2×D59—41no—
439C2×D59—41no—
440C2×D59—41no—
441C2×D59—41no—
442C2×D59—41no—
443C2×D59—162no—
444C4×C59—21no—
445C4×C59—21no—
446C4×C59—21no—
447C4×C59—21no—
448C4×C59—21no—
449C4×C59—21no—
450C4×C59—21no—
451C4×C59—21no—
452C4×C59—21no—
453C4×C59—21no—
454C4×C59—21no—
455C4×C59—21no—
456Dic59—42no—
457Dic59—41no—
458Dic59—41no—
459Dic59—41no—
460Dic59—41no—
461Dic59—41no—
462Dic59—81no—
463Dic59—81no—
464Dic59—81no—
465#3494—591no—
466#2924D5911yescharacteristic, complemented
467#2343—591no—
468#1521—591no—
469#1517—591no—
470#1516—591no—
471#1514—591no—
472#1512—591no—
473#1510—591no—
474#1509—591no—
475#1505—591no—
476#1504—591no—
477#1502—591no—
478#1500—591no—
479C2×#327—591no—
480C2×C59—21no—
481C2×C59—21no—
482C2×C59—22no—
483C2×C59—41no—
484C2×C59C2×#41011yescharacteristic
485C2×C59#289711yescharacteristic
486C2×C59#290111yescharacteristic
487D59—81no—
488D59—81no—
489D59—81no—
490#555—1181no—
491#553—1181no—
492#553—1181no—
493#551—1181no—
494#551—1181no—
495#547—1181no—
496#546—1181no—
497#546—1181no—
498#544—591no—
499#542—591no—
500#542—591no—
501#540—591no—
502#540—591no—
503#535—591no—
504#532—591no—
505#532—591no—
506#529—591no—
507#529—591no—
508#525—591no—
509C2×#121—591no—
510#520—591no—
511#518—591no—
512C2×#117C2×D5911yescharacteristic
513#433—21no—
514#433—21no—
515#432C2×D5911yescharacteristic, complemented
516#432C2×D5911yescharacteristic, complemented
517#431C2×D5911yescharacteristic, complemented
518#431C2×D5911yescharacteristic, complemented
519#424—21no—
520#407C2×D5911yescharacteristic
521C2×C22⋊C8C2×D5911yescharacteristic
522#405—21no—
523#387—1181no—
524#387—1181no—
525#385—1181no—
526#383—591no—
527#382—591no—
528#381—591no—
529C4×C4⋊C4—591no—
530C4×C22⋊C4—1181no—
531#376—591no—
532C2×#95—591no—
533#328—591no—
534#328—591no—
535#328—591no—
536#328—591no—
537#327—591no—
538#327—591no—
539#327—591no—
540#327—591no—
541#327—591no—
542#327—591no—
543#327—591no—
544#327—591no—
545#327—591no—
546#327—591no—
547#327—591no—
548#327—591no—
549C59#1760411yescharacteristic, complemented, Sylow
550C2×#41—591no—
551C2×#41—1181no—
552C2×#41—1181no—
553C22×D4—591no—
554C22×D4—1181no—
555C23×C4—1181no—
556C23×C4C22×D5911yescharacteristic
557C2×M16—21no—
558C22×C8—21no—
559C4⋊Q8—591no—
560C4⋊Q8—591no—
561C4⋊Q8—1181no—
562#127—591no—
563#127—591no—
564#126—1181no—
565#126—1181no—
566#126—1181no—
567#126—1181no—
568#125—591no—
569#125—591no—
570#125—1181no—
571#124—591no—
572#124—591no—
573#124—1181no—
574#124—1181no—
575#124—1181no—
576#124—1181no—
577#123—1181no—
578#123—1181no—
579#123—1181no—
580#123—1181no—
581#123—1181no—
582#123—1181no—
583#123—1181no—
584#123—1181no—
585#123—1181no—
586C22⋊Q8—591no—
587C22⋊Q8—591no—
588C22⋊Q8—1181no—
589C22⋊Q8—1181no—
590C22⋊Q8—1181no—
591C22⋊Q8—1181no—
592#121—591no—
593#121—591no—
594#121—591no—
595#121—591no—
596#121—591no—
597#121—591no—
598#121—1181no—
599#121—1181no—
600#121—1181no—
601#121—1181no—
602#121—1181no—
603#121—1181no—
604#121—1181no—
605#121—1181no—
606#121—1181no—
607#121—1181no—
608#120—1181no—
609#120—1181no—
610#120—1181no—
611C4×Q8—591no—
612C4×Q8—591no—
613C4×D4—591no—
614C4×D4—591no—
615C4×D4—591no—
616C4×D4—591no—
617C4×D4—591no—
618C4×D4—591no—
619C4×D4—1181no—
620C4×D4—1181no—
621C4×D4—1181no—
622C4×D4—1181no—
623C4×D4—1181no—
624C4×D4—1181no—
625C4×D4—1181no—
626C4×D4—1181no—
627C4×D4—1181no—
628C4×D4—1181no—
629#117—591no—
630#117—1181no—
631#117—1181no—
632#117—1181no—
633#117C4×D5911yescharacteristic
634#117C4×D5911yescharacteristic
635#117C4×D5911yescharacteristic
636#117C4×D5911yescharacteristic
637#117C22⋊D5911yescharacteristic
638#117C22⋊D5911yescharacteristic
639#117C22⋊D5911yescharacteristic
640#117C22⋊D5911yescharacteristic
641C2×C4⋊C4—591no—
642C2×C4⋊C4—1181no—
643C2×C4⋊C4—1181no—
644C2×C4⋊C4—1181no—
645C2×C4⋊C4D23611yescharacteristic
646C2×C4⋊C4D23611yescharacteristic
647C2×C22⋊C4—1181no—
648C2×C22⋊C4—1181no—
649C2×C22⋊C4—1181no—
650C2×C22⋊C4—1181no—
651C2×C22⋊C4D23611yescharacteristic
652C2×C22⋊C4D23611yescharacteristic
653C2×C42—1181no—
654C2×C42—1181no—
655C2×C42C22×D5911yescharacteristic
656C2×C42C22×D5911yescharacteristic
657C4⋊C8—21no—
658C4⋊C8—21no—
659C4⋊C8—21no—
660C4⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8C22×D5911yescharacteristic
664C22⋊C8C22×D5911yescharacteristic
665C22⋊C8C22×D5911yescharacteristic
666C22⋊C8C22×D5911yescharacteristic
667#97—21no—
668#97—21no—
669C4×C8—21no—
670C4×C8—21no—
671#95—591no—
672#95—591no—
673#95—591no—
674#95—591no—
675#95—1181no—
676#95—1181no—
677#95—1181no—
678#95—1181no—
679#95—1181no—
680#95—1181no—
681C24—1181no—
682C24C2×D23611yescharacteristic
683#41—4721no—
684#41—4721no—
685#41—4721no—
686#41—4721no—
687#41—2362no—
688C2×Q8—591no—
689C2×Q8—1181no—
690C2×Q8—1181no—
691C2×D4—591no—
692C2×D4—591no—
693C2×D4—591no—
694C2×D4—1181no—
695C2×D4—1181no—
696C2×D4—1181no—
697C2×D4—1181no—
698C2×D4—1181no—
699C2×D4—1181no—
700C2×D4—1181no—
701C2×D4—1181no—
702C2×D4—1181no—
703C2×D4—1181no—
704C2×D4—1181no—
705C2×D4—1181no—
706C2×D4—4721no—
707C2×D4—4721no—
708C2×D4—2362no—
709C22×C4—42no—
710C22×C4—1181no—
711C22×C4—1181no—
712C22×C4—1181no—
713C22×C4—1181no—
714C22×C4—1181no—
715C22×C4—1181no—
716C22×C4—1181no—
717C22×C4—1181no—
718C22×C4—1181no—
719C22×C4—1181no—
720C22×C4—1181no—
721C22×C4—1181no—
722C22×C4—4721no—
723C22×C4—2362no—
724C22×C4—2362no—
725C22×C4C2×C4×D5911yescharacteristic
726C22×C4C2×C4×D5911yescharacteristic
727C22×C4C2×D23611yescharacteristic
728C22×C4C2×D23611yescharacteristic
729C22×C4C2×D23611yescharacteristic
730C22×C4C2×D23611yescharacteristic
731C22×C4C2×D23611yescharacteristic
732C22×C4C2×C22⋊D5911yescharacteristic
733C22×C4C2×C22⋊D5911yescharacteristic
734C22×C4C23×D5911yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—42no—
741C4⋊C4—591no—
742C4⋊C4—591no—
743C4⋊C4—591no—
744C4⋊C4—591no—
745C4⋊C4—1181no—
746C4⋊C4—1181no—
747C4⋊C4—1181no—
748C4⋊C4—1181no—
749C4⋊C4—1181no—
750C4⋊C4—1181no—
751C4⋊C4—1181no—
752C4⋊C4—1181no—
753C4⋊C4—1181no—
754C4⋊C4—1181no—
755C4⋊C4—1181no—
756C4⋊C4—4721no—
757C4⋊C4—2362no—
758C4⋊C4(C2×D59)⋊C411yescharacteristic
759C4⋊C4(C2×D59)⋊C411yescharacteristic
760C4⋊C4(C2×D59)⋊C411yescharacteristic
761C4⋊C4(C2×D59)⋊C411yescharacteristic
762C4⋊C4(C2×D59)⋊C411yescharacteristic
763C4⋊C4(C2×D59)⋊C411yescharacteristic
764C4⋊C4(C2×D59)⋊C411yescharacteristic
765C4⋊C4(C2×D59)⋊C411yescharacteristic
766C22⋊C4—1181no—
767C22⋊C4—1181no—
768C22⋊C4—1181no—
769C22⋊C4—1181no—
770C22⋊C4—1181no—
771C22⋊C4—1181no—
772C22⋊C4—1181no—
773C22⋊C4—1181no—
774C22⋊C4—1181no—
775C22⋊C4—1181no—
776C22⋊C4—1181no—
777C22⋊C4—1181no—
778C22⋊C4—1181no—
779C22⋊C4—1181no—
780C22⋊C4—1181no—
781C22⋊C4—1181no—
782C22⋊C4—1181no—
783C22⋊C4—1181no—
784C22⋊C4—1181no—
785C22⋊C4—2362no—
786C22⋊C4(C2×D59)⋊C411yescharacteristic
787C22⋊C4(C2×D59)⋊C411yescharacteristic
788C22⋊C4(C2×D59)⋊C411yescharacteristic
789C22⋊C4(C2×D59)⋊C411yescharacteristic
790C22⋊C4(C2×D59)⋊C411yescharacteristic
791C22⋊C4(C2×D59)⋊C411yescharacteristic
792C22⋊C4(C2×D59)⋊C411yescharacteristic
793C22⋊C4(C2×D59)⋊C411yescharacteristic
794C42—1181no—
795C42—1181no—
796C42—1181no—
797C42—4721no—
798C42—2362no—
799C42C2×C4×D5911yescharacteristic
800C42C2×C4×D5911yescharacteristic
801C42C2×C4×D5911yescharacteristic
802C42C2×C4×D5911yescharacteristic
803C42C2×C22⋊D5911yescharacteristic
804C42C2×C22⋊D5911yescharacteristic
805C42C2×C22⋊D5911yescharacteristic
806C42C2×C22⋊D5911yescharacteristic
807C23—21no—
808C23—21no—
809C23—22no—
810C23—41no—
811C23—1181no—
812C23—1181no—
813C23—1181no—
814C23—4721no—
815C23—4721no—
816C23—2362no—
817C23C2×(C2×D59)⋊C411yescharacteristic
818C23C2×(C2×D59)⋊C411yescharacteristic
819C23C22×D23611yescharacteristic
820Q8—4721no—
821Q8—4721no—
822Q8—2361no—
823D4—4721no—
824D4—4721no—
825D4—4721no—
826D4—4721no—
827D4—4721no—
828D4—4721no—
829D4—4721no—
830D4—2361no—
831D4—2361no—
832D4—2361no—
833D4—2362no—
834D4—2361no—
835D4—2361no—
836D4—2361no—
837D4—2361no—
838D4—2361no—
839D4—2361no—
840D4—2362no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—1182no—
854C2×C4—1181no—
855C2×C4—1181no—
856C2×C4—1181no—
857C2×C4—1181no—
858C2×C4—1181no—
859C2×C4—4721no—
860C2×C4—4721no—
861C2×C4—4721no—
862C2×C4—4721no—
863C2×C4—4721no—
864C2×C4—4721no—
865C2×C4—4724no—
866C2×C4—4721no—
867C2×C4—2362no—
868C2×C4—2361no—
869C2×C4—2361no—
870C2×C4—2361no—
871C2×C4—2361no—
872C2×C4—2361no—
873C2×C4—2361no—
874C2×C4—2361no—
875C2×C4—2361no—
876C2×C4—2361no—
877C2×C4—2361no—
878C2×C4—2361no—
879C2×C4C2×(C2×D59)⋊C411yescharacteristic
880C2×C4C2×(C2×D59)⋊C411yescharacteristic
881C2×C4C2×(C2×D59)⋊C411yescharacteristic
882C2×C4C2×(C2×D59)⋊C411yescharacteristic
883C2×C4C2×(C2×D59)⋊C411yescharacteristic
884C2×C4C2×(C2×D59)⋊C411yescharacteristic
885C2×C4C2×(C2×D59)⋊C411yescharacteristic
886C2×C4C2×(C2×D59)⋊C411yescharacteristic
887C2×C4C2×(C2×D59)⋊C411yescharacteristic
888C2×C4C2×(C2×D59)⋊C411yescharacteristic
889C2×C4C22×C4×D5911yescharacteristic
890C2×C4C22×C22⋊D5911yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—9442no—
905C22—2361no—
906C22—2361no—
907C22—2361no—
908C22—2361no—
909C22—2361no—
910C22—2361no—
911C22—2361no—
912C22—2361no—
913C22—2361no—
914C22#1683737512yes—
915C22C22×(C2×D59)⋊C411yescharacteristic
916C22#1683820711yescharacteristic
917C22#1683821411yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—4721no—
931C4—4721no—
932C4—4721no—
933C4—2362no—
934C4—2361no—
935C4—2361no—
936C4—2361no—
937C4—2361no—
938C4—2361no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—4721no—
944C2—4721no—
945C2—4721no—
946C2C2×#1683737511yescharacteristic
947C2#2143262311yescharacteristic
948C2#2143264111yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2924C2
socleC22×C59C22×C22⋊C4
prime radical#21437831C2
cosocleC22×C4×C59C24
hypercenter#2924D59
hypocenterC59#17604
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #21426956C2semidirect
3. #21422674C2semidirect
4. #21422657C2semidirect
5. #21422653C2semidirect
6. #21422644C2semidirect
7. #21422635C2semidirect
8. #21422626C2semidirect
9. #21422622C2semidirect
10. #21422605C2semidirect
11. #21422601C2semidirect
12. #21422592C2semidirect
13. #21422583C2semidirect
14. C2×#16837137C2semidirect
15. C59×#2924C2semidirect
24. #16838030C4semidirect
25. #16838023C4semidirect
26. #16838023C4semidirect
27. #16838007C4semidirect
28. #16838007C4semidirect
29. #16837971C4semidirect
36. #16837882C4semidirect
37. #16837876C4semidirect
41. #16837270C22semidirect
42. #16837268C22semidirect
44. C4×C4⋊Dic59C22semidirect
46. #16837248C22semidirect
48. #16837140C22semidirect
49. #16837140C22semidirect
50. #16837140C22semidirect
51. #16837140C22semidirect
60. #16837137C22semidirect
61. #16837137C22semidirect
62. #16837137C22semidirect
63. #16837137C22semidirect
67. C59×#432C22semidirect
68. C59×#432C22semidirect
69. C59×#431C22semidirect
70. C59×#431C22semidirect
81. #14273727C2×C4semidirect
82. #14273727C2×C4semidirect
84. #14273724C2×C4semidirect
85. #14273724C2×C4semidirect
90. #14273719C2×C4semidirect
91. #14273719C2×C4semidirect
95. #14273715C2×C4semidirect
96. #14273715C2×C4semidirect
133. C4×Dic118C2×C4semidirect
134. C4×Dic118C2×C4semidirect
137. C4×D236C2×C4semidirect
138. C4×D236C2×C4semidirect
139. C4×D236C2×C4semidirect
140. C4×D236C2×C4semidirect
141. C4×D236C2×C4semidirect
142. C4×D236C2×C4semidirect
466. #2924D59semidirect
515. #432C2×D59semidirect
516. #432C2×D59semidirect
517. #431C2×D59semidirect
518. #431C2×D59semidirect
549. C59#17604semidirect

Maximal subgroups

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

subgroupindex
#214378312
#214269562
#214226742
#214226572
#214226532
#214226442
#214226352
#214226262
#214226222
#214226052
#214226012
#214225922
#214225832
C2×#168371372
C59×#29242
#1760459