Finite Group Databasebeta

← #28556358

Subgroups — #28556358

Order 15104.

944 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437848C211yesmaximal, characteristic
2#21426956C211yesmaximal, characteristic, complemented
3#21422674C211yesmaximal, characteristic, complemented
4#21422661C211yesmaximal, characteristic, complemented
5#21422653C211yesmaximal, characteristic
6#21422648C211yesmaximal, characteristic, complemented
7#21422635C211yesmaximal, characteristic, complemented
8#21422630C211yesmaximal, characteristic, complemented
9#21422622C211yesmaximal, characteristic, complemented
10#21422609C211yesmaximal, characteristic, complemented
11#21422601C211yesmaximal, characteristic
12#21422596C211yesmaximal, characteristic, complemented
13#21422583C211yesmaximal, characteristic, complemented
14C2×#16837140C211yesmaximal, characteristic, complemented
15C59×#2924C211yesmaximal, characteristic, complemented
16#16838120—21no—
17#16838107—21no—
18#16838091—21no—
19#16838087—21no—
20#16838085—21no—
21#16838085—21no—
22#16838078—21no—
23#16838078—21no—
24#16838030C411yescharacteristic, complemented
25#16838023C411yescharacteristic, complemented
26#16838023C411yescharacteristic, complemented
27#16838014C411yescharacteristic, complemented
28#16838014C411yescharacteristic, complemented
29#16837978C411yescharacteristic, complemented
30#16837959C2211yescharacteristic
31#16837959C2211yescharacteristic
32#16837936C2211yescharacteristic
33#16837936C2211yescharacteristic
34#16837913C2211yescharacteristic
35C2×#14273706C2211yescharacteristic
36#16837882C411yescharacteristic, complemented
37#16837879C411yescharacteristic, complemented
38#16837288—21no—
39#16837288—21no—
40#16837277—21no—
41#16837270C2211yescharacteristic
42#16837268C2211yescharacteristic
43#16837265C2211yescharacteristic
44C4×C4⋊Dic59C2211yescharacteristic
45C22⋊C4×Dic59—21no—
46#16837248C2211yescharacteristic
47C2×C59⋊#95C2211yescharacteristic
48#16837140C2211yescharacteristic
49#16837140C2211yescharacteristic
50#16837140C2211yescharacteristic
51#16837140C2211yescharacteristic
52#16837140C2211yescharacteristic
53#16837140C2211yescharacteristic
54#16837140C2211yescharacteristic
55#16837140C2211yescharacteristic
56#16837140C2211yescharacteristic
57#16837140C2211yescharacteristic
58#16837140C2211yescharacteristic
59#16837140C2211yescharacteristic
60#16837137C2211yescharacteristic
61#16837137C2211yescharacteristic
62#16837137C2211yescharacteristic
63#16837137C2211yescharacteristic
64C2×#117×C59C2211yescharacteristic
65C59×#433—21no—
66C59×#433—21no—
67C59×#432C2211yescharacteristic
68C59×#432C2211yescharacteristic
69C59×#431C2211yescharacteristic
70C59×#431C2211yescharacteristic
71C59×#424—21no—
72C59×#407C2211yescharacteristic
73C2×C22⋊C8×C59C2211yescharacteristic
74C59×#405—21no—
75C2×#11745685C2×C411yescharacteristic
76C22×Dic118C2×C411yescharacteristic
77C23×Dic59—21no—
78#14273727C2×C411yescharacteristic, complemented
79#14273727C2×C411yescharacteristic, complemented
80#14273727C2×C411yescharacteristic, complemented
81#14273727C2×C411yescharacteristic, complemented
82#14273726—21no—
83#14273722—21no—
84#14273722—21no—
85#14273721—21no—
86#14273721—21no—
87#14273720—21no—
88#14273720—21no—
89#14273720—21no—
90#14273720—21no—
91#14273719—21no—
92#14273719—21no—
93#14273719C2×C411yescharacteristic, complemented
94#14273719C2×C411yescharacteristic, complemented
95#14273718—21no—
96#14273717—21no—
97#14273717—21no—
98#14273717—21no—
99#14273717—21no—
100#14273715C2×C411yescharacteristic, complemented
101#14273715C2×C411yescharacteristic, complemented
102#14273713—21no—
103#14273713—21no—
104#14273711—21no—
105#14273711—21no—
106#14273710—21no—
107#14273710—21no—
108#14273710—21no—
109#14273709—21no—
110#14273709—21no—
111#14273707—21no—
112#14273707—21no—
113#14273706—21no—
114#14273706—21no—
115#14273706—21no—
116#14273706—21no—
117#14273706C2×C411yescharacteristic
118#14273706C2×C411yescharacteristic
119#14273706C2×C411yescharacteristic
120#14273706C2311yescharacteristic
121#14273706C2311yescharacteristic
122#14273706C2311yescharacteristic
123#14273705—21no—
124#14273705—21no—
125#14273704—21no—
126#14273704—21no—
127#14273701C2×C411yescharacteristic
128#14273701C2311yescharacteristic
129#14273696—21no—
130C4×Dic118—21no—
131C4×Dic118—21no—
132C4×Dic118C2×C411yescharacteristic, complemented
133C4×Dic118C2×C411yescharacteristic, complemented
134C4×Dic118C2×C411yescharacteristic, complemented
135C4×Dic118C2×C411yescharacteristic, complemented
136C4×Dic118C2×C411yescharacteristic, complemented
137C4×Dic118C2×C411yescharacteristic, complemented
138#14273692—21no—
139#14273692—21no—
140C4×D236C2×C411yescharacteristic, complemented
141C4×D236C2×C411yescharacteristic, complemented
142C4×C22⋊D59—21no—
143C4×C22⋊D59—21no—
144C4×C22⋊D59—21no—
145C4×C22⋊D59—21no—
146(C22⋊D59)⋊C4—21no—
147(C22⋊D59)⋊C4—21no—
148#14273686—21no—
149#14273686—21no—
150#14273686C2×C411yescharacteristic
151#14273685—21no—
152#14273684—21no—
153#14273684—21no—
154#14273683—21no—
155#14273683—21no—
156C2×C4⋊Dic59—21no—
157C2×C4⋊Dic59—21no—
158C2×C4⋊Dic59C2×C411yescharacteristic
159C2×Dic59⋊C4—21no—
160C4⋊C4×D59—21no—
161C2×C22⋊Dic59—21no—
162C2×C22⋊Dic59—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
207C22×C4×C59—42no—
208C22×C4×C59C22×C411yescharacteristic
209C22×C4×C59C22×C411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
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×C59C2411yescharacteristic
218C2×C22⋊D59—21no—
219C2×C22⋊D59—21no—
220C2×C22⋊D59—21no—
221C22×Dic59—21no—
222C22×Dic59—21no—
223C22×Dic59—21no—
224C22×Dic59—21no—
225C22×Dic59—21no—
226C22×Dic59—21no—
227C22×Dic59—42no—
228C22×Dic59—42no—
229C22×Dic59—81no—
230#11745685—42no—
231C2×D236C22×C411yescharacteristic
232C2×C4×D59—21no—
233C2×C4×D59—21no—
234C2×C4×D59—21no—
235C2×Dic118—21no—
236C2×Dic118—21no—
237C2×Dic118—21no—
238C2×Dic118—42no—
239C2×Dic118C22×C411yescharacteristic
240C2×Dic118C22×C411yescharacteristic
241C2×Dic118C22×C411yescharacteristic
242M16×C59—42no—
243C2×C8×C59—21no—
244C2×C8×C59—21no—
245C2×C8×C59—21no—
246C2×C8×C59—21no—
247C2×C8×C59—42no—
248C4⋊C4×C59C22⋊C411yescharacteristic
249C4⋊C4×C59C22⋊C411yescharacteristic
250C4⋊C4×C59C22⋊C411yescharacteristic
251C4⋊C4×C59C22⋊C411yescharacteristic
252C4⋊C4×C59C22⋊C411yescharacteristic
253C4⋊C4×C59C22⋊C411yescharacteristic
254C4⋊C4×C59C22⋊C411yescharacteristic
255C4⋊C4×C59C22⋊C411yescharacteristic
256C22⋊C4×C59C22⋊C411yescharacteristic
257C22⋊C4×C59C22⋊C411yescharacteristic
258C22⋊C4×C59C22⋊C411yescharacteristic
259C22⋊C4×C59C22⋊C411yescharacteristic
260C22⋊C4×C59C22⋊C411yescharacteristic
261C22⋊C4×C59C22⋊C411yescharacteristic
262C22⋊C4×C59C22⋊C411yescharacteristic
263C22⋊C4×C59C22⋊C411yescharacteristic
264C42×C59C22×C411yescharacteristic
265C42×C59C22×C411yescharacteristic
266C42×C59C22×C411yescharacteristic
267C42×C59C22×C411yescharacteristic
268C42×C59C2×D411yescharacteristic
269C42×C59C2×D411yescharacteristic
270C42×C59C2×D411yescharacteristic
271C42×C59C2×D411yescharacteristic
272C22⋊Dic59—21no—
273C22⋊Dic59—21no—
274C22⋊Dic59—21no—
275C22⋊Dic59—21no—
276C22⋊Dic59—21no—
277C22⋊Dic59—21no—
278C22⋊Dic59—21no—
279C22⋊Dic59—42no—
280(C2×D59)⋊C4—21no—
281(C2×D59)⋊C4—21no—
282(C2×D59)⋊C4—21no—
283(C2×D59)⋊C4—21no—
284(C2×D59)⋊C4—21no—
285(C2×D59)⋊C4—21no—
286(C2×D59)⋊C4—21no—
287(C2×D59)⋊C4—21no—
288C4⋊Dic59—21no—
289C4⋊Dic59—21no—
290C4⋊Dic59—21no—
291C4⋊Dic59—21no—
292C4⋊Dic59—21no—
293C4⋊Dic59—21no—
294C4⋊Dic59—21no—
295C4⋊Dic59—42no—
296C4⋊Dic59—81no—
297C4⋊Dic59C22×C411yescharacteristic
298C4⋊Dic59C22×C411yescharacteristic
299C4⋊Dic59C22×C411yescharacteristic
300C4⋊Dic59C22×C411yescharacteristic
301Dic59⋊C4—21no—
302Dic59⋊C4—21no—
303Dic59⋊C4—21no—
304Dic59⋊C4—21no—
305Dic59⋊C4—21no—
306Dic59⋊C4—21no—
307Dic59⋊C4—21no—
308Dic59⋊C4—21no—
309Dic59⋊C4—21no—
310Dic59⋊C4—21no—
311Dic59⋊C4—21no—
312Dic59⋊C4—21no—
313Dic59⋊C4—21no—
314Dic59⋊C4—21no—
315Dic59⋊C4—21no—
316Dic59⋊C4—21no—
317C4×Dic59—21no—
318C4×Dic59—21no—
319C4×Dic59—21no—
320C4×Dic59—21no—
321C4×Dic59—21no—
322C4×Dic59—21no—
323C4×Dic59—21no—
324C4×Dic59—42no—
325C4×Dic59—81no—
326C23×C59—21no—
327C23×C59—21no—
328C23×C59—22no—
329C23×C59—41no—
330C23×C59C2×C22⋊C411yescharacteristic
331C23×C59C2×C22⋊C411yescharacteristic
332C23×C59C22×D411yescharacteristic
333C22×D59—21no—
334C2×C4×C59—21no—
335C2×C4×C59—21no—
336C2×C4×C59—21no—
337C2×C4×C59—21no—
338C2×C4×C59—22no—
339C2×C4×C59—22no—
340C2×C4×C59—41no—
341C2×C4×C59—41no—
342C2×C4×C59—41no—
343C2×C4×C59—41no—
344C2×C4×C59—41no—
345C2×C4×C59—41no—
346C2×C4×C59C2×C22⋊C411yescharacteristic
347C2×C4×C59C2×C22⋊C411yescharacteristic
348C2×C4×C59C2×C22⋊C411yescharacteristic
349C2×C4×C59C2×C22⋊C411yescharacteristic
350C2×C4×C59C2×C22⋊C411yescharacteristic
351C2×C4×C59C2×C22⋊C411yescharacteristic
352C2×C4×C59C2×C22⋊C411yescharacteristic
353C2×C4×C59C2×C22⋊C411yescharacteristic
354C2×C4×C59C2×C22⋊C411yescharacteristic
355C2×C4×C59C2×C22⋊C411yescharacteristic
356C2×C4×C59C23×C411yescharacteristic
357C2×C4×C59C22×D411yescharacteristic
358C22⋊D59—41no—
359C22⋊D59—41no—
360C22⋊D59—42no—
361C22⋊D59—81no—
362C2×Dic59—22no—
363C2×Dic59—21no—
364C2×Dic59—21no—
365C2×Dic59—21no—
366C2×Dic59—21no—
367C2×Dic59—21no—
368C2×Dic59—21no—
369C2×Dic59—21no—
370C2×Dic59—41no—
371C2×Dic59—41no—
372C2×Dic59—42no—
373C2×Dic59—41no—
374C2×Dic59—41no—
375C2×Dic59—41no—
376C2×Dic59—41no—
377C2×Dic59—41no—
378C2×Dic59—41no—
379C2×Dic59—41no—
380C2×Dic59—41no—
381C2×Dic59—41no—
382C2×Dic59—81no—
383C2×Dic59—84no—
384D236—41no—
385C4×D59—42no—
386C4×D59—81no—
387C4×D59—81no—
388Dic118—42no—
389Dic118—41no—
390Dic118—41no—
391Dic118—41no—
392Dic118—81no—
393Dic118—81no—
394C8×C59—41no—
395C8×C59—41no—
396C8×C59—41no—
397C8×C59—41no—
398#17609—591nomaximal, Sylow
399C22×C59—21no—
400C22×C59—21no—
401C22×C59—21no—
402C22×C59—21no—
403C22×C59—21no—
404C22×C59—21no—
405C22×C59—21no—
406C22×C59—42no—
407C22×C59—42no—
408C22×C59#41012yes—
409C22×C59C22×C22⋊C411yescharacteristic
410C22×C59#57711yescharacteristic
411C22×C59#57811yescharacteristic
412C2×D59—41no—
413C2×D59—41no—
414C2×D59—41no—
415C4×C59—21no—
416C4×C59—21no—
417C4×C59—21no—
418C4×C59—21no—
419C4×C59—21no—
420C4×C59—21no—
421C4×C59—21no—
422C4×C59—21no—
423C4×C59—21no—
424C4×C59—21no—
425C4×C59—21no—
426C4×C59—21no—
427Dic59—42no—
428Dic59—41no—
429Dic59—41no—
430Dic59—41no—
431Dic59—41no—
432Dic59—41no—
433Dic59—41no—
434Dic59—41no—
435Dic59—81no—
436Dic59—81no—
437Dic59—81no—
438#3495—591no—
439#2924D5911yescharacteristic, complemented
440#2343—591no—
441#1521—591no—
442#1518—591no—
443#1516—591no—
444#1515—591no—
445#1512—591no—
446#1511—591no—
447#1509—591no—
448#1506—591no—
449#1504—591no—
450#1503—591no—
451#1500—591no—
452C2×#328—591no—
453C2×C59—21no—
454C2×C59—21no—
455C2×C59—22no—
456C2×C59—41no—
457C2×C59C2×#41011yescharacteristic
458C2×C59#289811yescharacteristic
459C2×C59#290111yescharacteristic
460D59—81no—
461#556—1181no—
462#554—1181no—
463#552—1181no—
464#552—1181no—
465#552—1181no—
466#552—1181no—
467#551—1181no—
468#551—1181no—
469#544—591no—
470#542—591no—
471#542—591no—
472#541—591no—
473#541—591no—
474#536—591no—
475#533—591no—
476#533—591no—
477#529—591no—
478#529—591no—
479#525—591no—
480C2×C22⋊Q8—591no—
481#520—591no—
482#519—591no—
483C2×#117C2×D5911yescharacteristic
484#433—21no—
485#433—21no—
486#432C2×D5911yescharacteristic
487#432C2×D5911yescharacteristic
488#431C2×D5911yescharacteristic
489#431C2×D5911yescharacteristic
490#424—21no—
491#407C2×D5911yescharacteristic
492C2×C22⋊C8C2×D5911yescharacteristic
493#405—21no—
494#387—1181no—
495#387—1181no—
496#385—1181no—
497#383—591no—
498#382—591no—
499#381—591no—
500C4×C4⋊C4—591no—
501C4×C22⋊C4—1181no—
502#376—591no—
503C2×#95—591no—
504#328—591no—
505#328—591no—
506#328—591no—
507#328—591no—
508#328—591no—
509#328—591no—
510#328—591no—
511#328—591no—
512#328—591no—
513#328—591no—
514#328—591no—
515#328—591no—
516#327—591no—
517#327—591no—
518#327—591no—
519#327—591no—
520C59#1760911yescharacteristic, complemented, Sylow
521C2×#41—591no—
522C22×Q8—591no—
523C23×C4—1181no—
524C23×C4C22×D5911yescharacteristic
525C2×M16—21no—
526C22×C8—21no—
527C4⋊Q8—591no—
528C4⋊Q8—591no—
529C4⋊Q8—591no—
530C4⋊Q8—591no—
531C4⋊Q8—1181no—
532#126—1181no—
533#126—1181no—
534#126—1181no—
535#126—1181no—
536#126—1181no—
537#126—1181no—
538#126—1181no—
539#126—1181no—
540#125—591no—
541#125—591no—
542#125—1181no—
543#125—1181no—
544#125—1181no—
545#125—1181no—
546#125—1181no—
547#125—1181no—
548#125—1181no—
549#124—591no—
550#124—591no—
551#124—1181no—
552#124—1181no—
553#123—1181no—
554#123—1181no—
555#123—1181no—
556#123—1181no—
557#123—1181no—
558#123—1181no—
559#123—1181no—
560C22⋊Q8—591no—
561C22⋊Q8—591no—
562C22⋊Q8—591no—
563C22⋊Q8—591no—
564C22⋊Q8—591no—
565C22⋊Q8—591no—
566C22⋊Q8—1181no—
567C22⋊Q8—1181no—
568C22⋊Q8—1181no—
569C22⋊Q8—1181no—
570C22⋊Q8—1181no—
571C22⋊Q8—1181no—
572C22⋊Q8—1181no—
573C22⋊Q8—1181no—
574C22⋊Q8—1181no—
575C22⋊Q8—1181no—
576#121—591no—
577#121—591no—
578#120—1181no—
579C4×Q8—591no—
580C4×Q8—591no—
581C4×Q8—591no—
582C4×Q8—591no—
583C4×Q8—591no—
584C4×Q8—591no—
585C4×Q8—1181no—
586C4×Q8—1181no—
587C4×Q8—1181no—
588C4×Q8—1181no—
589C4×D4—591no—
590C4×D4—591no—
591C4×D4—1181no—
592C4×D4—1181no—
593C4×D4—1181no—
594C4×D4—1181no—
595C4×D4—1181no—
596C4×D4—1181no—
597#117—591no—
598#117—1181no—
599#117—1181no—
600#117—1181no—
601#117—1181no—
602#117—1181no—
603#117—1181no—
604#117—1181no—
605#117C4×D5911yescharacteristic
606#117C4×D5911yescharacteristic
607#117C4×D5911yescharacteristic
608#117C4×D5911yescharacteristic
609#117C22⋊D5911yescharacteristic
610#117C22⋊D5911yescharacteristic
611#117C22⋊D5911yescharacteristic
612#117C22⋊D5911yescharacteristic
613C2×C4⋊C4—591no—
614C2×C4⋊C4—1181no—
615C2×C4⋊C4—1181no—
616C2×C4⋊C4—1181no—
617C2×C4⋊C4—1181no—
618C2×C4⋊C4D23611yescharacteristic
619C2×C4⋊C4D23611yescharacteristic
620C2×C22⋊C4—1181no—
621C2×C22⋊C4—1181no—
622C2×C22⋊C4D23611yescharacteristic
623C2×C22⋊C4D23611yescharacteristic
624C2×C42—1181no—
625C2×C42—1181no—
626C2×C42C22×D5911yescharacteristic
627C2×C42C22×D5911yescharacteristic
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631C4⋊C8—21no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634C22⋊C8C22×D5911yescharacteristic
635C22⋊C8C22×D5911yescharacteristic
636C22⋊C8C22×D5911yescharacteristic
637C22⋊C8C22×D5911yescharacteristic
638#97—21no—
639#97—21no—
640C4×C8—21no—
641C4×C8—21no—
642#95—591no—
643#95—591no—
644#95—591no—
645#95—591no—
646#95—1181no—
647#95—1181no—
648#95—1181no—
649#95—1181no—
650#95—1181no—
651#95—1181no—
652C24C2×D23611yescharacteristic
653#41—2362no—
654C2×Q8—591no—
655C2×Q8—591no—
656C2×Q8—591no—
657C2×Q8—1181no—
658C2×Q8—1181no—
659C2×Q8—1181no—
660C2×Q8—2362no—
661C2×D4—591no—
662C2×D4—1181no—
663C2×D4—1181no—
664C2×D4—1181no—
665C22×C4—42no—
666C22×C4—1181no—
667C22×C4—1181no—
668C22×C4—1181no—
669C22×C4—1181no—
670C22×C4—1181no—
671C22×C4—1181no—
672C22×C4—1181no—
673C22×C4—1181no—
674C22×C4—1181no—
675C22×C4—4721no—
676C22×C4—2362no—
677C22×C4—2362no—
678C22×C4C2×C4×D5911yescharacteristic
679C22×C4C2×C4×D5911yescharacteristic
680C22×C4C2×D23611yescharacteristic
681C22×C4C2×D23611yescharacteristic
682C22×C4C2×D23611yescharacteristic
683C22×C4C2×D23611yescharacteristic
684C22×C4C2×D23611yescharacteristic
685C22×C4C2×C22⋊D5911yescharacteristic
686C22×C4C2×C22⋊D5911yescharacteristic
687C22×C4C23×D5911yescharacteristic
688M16—42no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C4⋊C4—591no—
695C4⋊C4—591no—
696C4⋊C4—591no—
697C4⋊C4—591no—
698C4⋊C4—1181no—
699C4⋊C4—1181no—
700C4⋊C4—1181no—
701C4⋊C4—1181no—
702C4⋊C4—1181no—
703C4⋊C4—1181no—
704C4⋊C4—1181no—
705C4⋊C4—1181no—
706C4⋊C4—1181no—
707C4⋊C4—1181no—
708C4⋊C4—1181no—
709C4⋊C4—1181no—
710C4⋊C4—1181no—
711C4⋊C4—1181no—
712C4⋊C4—1181no—
713C4⋊C4—1181no—
714C4⋊C4—1181no—
715C4⋊C4—1181no—
716C4⋊C4—1181no—
717C4⋊C4—1181no—
718C4⋊C4—1181no—
719C4⋊C4—1181no—
720C4⋊C4—1181no—
721C4⋊C4—4721no—
722C4⋊C4—2362no—
723C4⋊C4(C2×D59)⋊C411yescharacteristic
724C4⋊C4(C2×D59)⋊C411yescharacteristic
725C4⋊C4(C2×D59)⋊C411yescharacteristic
726C4⋊C4(C2×D59)⋊C411yescharacteristic
727C4⋊C4(C2×D59)⋊C411yescharacteristic
728C4⋊C4(C2×D59)⋊C411yescharacteristic
729C4⋊C4(C2×D59)⋊C411yescharacteristic
730C4⋊C4(C2×D59)⋊C411yescharacteristic
731C22⋊C4—1181no—
732C22⋊C4—1181no—
733C22⋊C4—1181no—
734C22⋊C4—1181no—
735C22⋊C4—1181no—
736C22⋊C4—1181no—
737C22⋊C4—1181no—
738C22⋊C4—1181no—
739C22⋊C4—1181no—
740C22⋊C4—1181no—
741C22⋊C4—1181no—
742C22⋊C4—1181no—
743C22⋊C4—1181no—
744C22⋊C4—1181no—
745C22⋊C4—1181no—
746C22⋊C4—2362no—
747C22⋊C4(C2×D59)⋊C411yescharacteristic
748C22⋊C4(C2×D59)⋊C411yescharacteristic
749C22⋊C4(C2×D59)⋊C411yescharacteristic
750C22⋊C4(C2×D59)⋊C411yescharacteristic
751C22⋊C4(C2×D59)⋊C411yescharacteristic
752C22⋊C4(C2×D59)⋊C411yescharacteristic
753C22⋊C4(C2×D59)⋊C411yescharacteristic
754C22⋊C4(C2×D59)⋊C411yescharacteristic
755C42—1181no—
756C42—1181no—
757C42—1181no—
758C42—1181no—
759C42—1181no—
760C42—1181no—
761C42—1181no—
762C42—4721no—
763C42—2362no—
764C42C2×C4×D5911yescharacteristic
765C42C2×C4×D5911yescharacteristic
766C42C2×C4×D5911yescharacteristic
767C42C2×C4×D5911yescharacteristic
768C42C2×C22⋊D5911yescharacteristic
769C42C2×C22⋊D5911yescharacteristic
770C42C2×C22⋊D5911yescharacteristic
771C42C2×C22⋊D5911yescharacteristic
772C23—21no—
773C23—21no—
774C23—22no—
775C23—41no—
776C23—1181no—
777C23C2×(C2×D59)⋊C411yescharacteristic
778C23C2×(C2×D59)⋊C411yescharacteristic
779C23C22×D23611yescharacteristic
780Q8—4721no—
781Q8—4721no—
782Q8—2361no—
783Q8—2361no—
784Q8—2361no—
785Q8—2362no—
786D4—4721no—
787D4—2361no—
788D4—2361no—
789D4—2361no—
790D4—2362no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—1182no—
804C2×C4—1181no—
805C2×C4—1181no—
806C2×C4—1181no—
807C2×C4—1181no—
808C2×C4—1181no—
809C2×C4—1181no—
810C2×C4—1181no—
811C2×C4—4721no—
812C2×C4—4721no—
813C2×C4—4724no—
814C2×C4—4721no—
815C2×C4—2362no—
816C2×C4—2361no—
817C2×C4—2361no—
818C2×C4—2361no—
819C2×C4—2361no—
820C2×C4—2361no—
821C2×C4—2361no—
822C2×C4—2361no—
823C2×C4—2361no—
824C2×C4—2361no—
825C2×C4—2361no—
826C2×C4—2361no—
827C2×C4—2362no—
828C2×C4C2×(C2×D59)⋊C411yescharacteristic
829C2×C4C2×(C2×D59)⋊C411yescharacteristic
830C2×C4C2×(C2×D59)⋊C411yescharacteristic
831C2×C4C2×(C2×D59)⋊C411yescharacteristic
832C2×C4C2×(C2×D59)⋊C411yescharacteristic
833C2×C4C2×(C2×D59)⋊C411yescharacteristic
834C2×C4C2×(C2×D59)⋊C411yescharacteristic
835C2×C4C2×(C2×D59)⋊C411yescharacteristic
836C2×C4C2×(C2×D59)⋊C411yescharacteristic
837C2×C4C2×(C2×D59)⋊C411yescharacteristic
838C2×C4C22×C4×D5911yescharacteristic
839C2×C4C22×C22⋊D5911yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C22—21no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—42no—
852C22—42no—
853C22—2361no—
854C22—2361no—
855C22—2361no—
856C22#1683737512yes—
857C22C22×(C2×D59)⋊C411yescharacteristic
858C22#1683821411yescharacteristic
859C22#1683821911yescharacteristic
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—4721no—
873C4—4721no—
874C4—4721no—
875C4—2362no—
876C4—2361no—
877C4—2361no—
878C4—2361no—
879C4—2361no—
880C4—2361no—
881C4—2361no—
882C4—2361no—
883C2—21no—
884C2—21no—
885C2—22no—
886C2—41no—
887C2—4721no—
888C2C2×#1683737511yescharacteristic
889C2#2143263011yescharacteristic
890C2#2143264111yescharacteristic
subgroupG/H
centerC22C22×(C2×D59)⋊C4
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2924C2
socleC22×C59C22×C22⋊C4
prime radical#16837913C22
cosocleC22×C4×C59C24
hypercenter#2924D59
hypocenterC59#17609
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. #21422661C2semidirect
6. #21422648C2semidirect
7. #21422635C2semidirect
8. #21422630C2semidirect
9. #21422622C2semidirect
10. #21422609C2semidirect
12. #21422596C2semidirect
13. #21422583C2semidirect
14. C2×#16837140C2semidirect
15. C59×#2924C2semidirect
24. #16838030C4semidirect
25. #16838023C4semidirect
26. #16838023C4semidirect
27. #16838014C4semidirect
28. #16838014C4semidirect
29. #16837978C4semidirect
36. #16837882C4semidirect
37. #16837879C4semidirect
78. #14273727C2×C4semidirect
79. #14273727C2×C4semidirect
80. #14273727C2×C4semidirect
81. #14273727C2×C4semidirect
93. #14273719C2×C4semidirect
94. #14273719C2×C4semidirect
100. #14273715C2×C4semidirect
101. #14273715C2×C4semidirect
132. C4×Dic118C2×C4semidirect
133. C4×Dic118C2×C4semidirect
134. C4×Dic118C2×C4semidirect
135. C4×Dic118C2×C4semidirect
136. C4×Dic118C2×C4semidirect
137. C4×Dic118C2×C4semidirect
140. C4×D236C2×C4semidirect
141. C4×D236C2×C4semidirect
439. #2924D59semidirect
520. C59#17609semidirect

Maximal subgroups

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

subgroupindex
#214378482
#214269562
#214226742
#214226612
#214226532
#214226482
#214226352
#214226302
#214226222
#214226092
#214226012
#214225962
#214225832
C2×#168371402
C59×#29242
#1760959