Finite Group Databasebeta

← #28555881

Subgroups — #28555881

Order 15104.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21438122C211yesmaximal, characteristic
2#21433127C211yesmaximal, characteristic, complemented
3#21426454C211yesmaximal, characteristic, complemented
4#21422618C211yesmaximal, characteristic, complemented
5#21422612C211yesmaximal, characteristic, complemented
6#21422610C211yesmaximal, characteristic, complemented
7#21422602C211yesmaximal, characteristic, complemented
8#21422598C211yesmaximal, characteristic, complemented
9#21422597C211yesmaximal, characteristic, complemented
10#21422589C211yesmaximal, characteristic, complemented
11#21422588C211yesmaximal, characteristic, complemented
12#21422584C211yesmaximal, characteristic, complemented
13#21422579C211yesmaximal, characteristic, complemented
14#327×D59C211yesmaximal, characteristic, complemented
15C2×C59×#327C211yesmaximal, characteristic, complemented
16#16838116C411yescharacteristic, complemented
17#16838107C411yescharacteristic, complemented
18#16838100C411yescharacteristic, complemented
19#16838099C411yescharacteristic, complemented
20#16838095—21no—
21#16838070C411yescharacteristic, complemented
22#16838049C411yescharacteristic, complemented
23#16838046—21no—
24#16838046C411yescharacteristic, complemented
25#16838041—21no—
26D4×C22⋊D59—21no—
27D4×C22⋊D59C411yescharacteristic, complemented
28#16838002—21no—
29#16837990—21no—
30#16837984—21no—
31#16837947C2211yescharacteristic
32#16837933C2211yescharacteristic
33#16837913C2211yescharacteristic
34#16837912C2211yescharacteristic
35#121×D59C2211yescharacteristic
36#16837875—21no—
37C2×C4×C22⋊D59—21no—
38C2×C4×C22⋊D59C2211yescharacteristic
39#16837477—21no—
40#16837476—21no—
41#16837473—21no—
42C8×C22⋊D59—21no—
43#16837456C2211yescharacteristic, complemented
44#16837452C2211yescharacteristic, complemented
45#16837366C2211yescharacteristic, complemented
46#16837364C2211yescharacteristic, complemented
47C22⋊C8×D59C2211yescharacteristic, complemented
48#16837253—21no—
49#16837253C2211yescharacteristic, complemented
50C4×C22⋊Dic59—21no—
51C4×C22⋊Dic59C2211yescharacteristic, complemented
52#16837249—21no—
53#16837249C2211yescharacteristic, complemented
54#16837247C2211yescharacteristic, complemented
55#95×D59C2211yescharacteristic, complemented
56#16837140C2211yescharacteristic, complemented
57#16837140C2211yescharacteristic, complemented
58#16837138C2211yescharacteristic, complemented
59#16837138C2211yescharacteristic, complemented
60#16837137C2211yescharacteristic, complemented
61#16837137C2211yescharacteristic, complemented
62#16837136C2211yescharacteristic
63#16837136C2211yescharacteristic
64#16837136C2211yescharacteristic, complemented
65#16837136C2211yescharacteristic, complemented
66#16837135C2211yescharacteristic, complemented
67#16837135C2211yescharacteristic, complemented
68C2×#121×C59C2211yescharacteristic
69C2×C22⋊C8×C59C2211yescharacteristic, complemented
70C2×#95×C59C2211yescharacteristic, complemented
71C59×#327C2211yescharacteristic
72C59×#327C2211yescharacteristic
73C59×#327C2211yescharacteristic, complemented
74C59×#327C2211yescharacteristic, complemented
75C2×#11745685C2×C411yescharacteristic, complemented
76C2×#11745687—21no—
77C2×#11745687C2×C411yescharacteristic, complemented
78C22×C22⋊D59—21no—
79C22×C22⋊D59D411yescharacteristic
80C2×D4×D59—21no—
81C2×D4×D59C2×C411yescharacteristic, complemented
82C22×C4×D59—21no—
83C22×C4×D59C2311yescharacteristic
84C2×#11745664—21no—
85C2×#11745659—21no—
86C2×C8×D59—21no—
87#14273726C2×C411yescharacteristic, complemented
88#14273723—21no—
89#14273723C2×C411yescharacteristic, complemented
90#14273722—21no—
91#14273720—21no—
92#14273720—21no—
93#14273718C2×C411yescharacteristic, complemented
94#14273717—21no—
95#14273714—21no—
96#14273714C2×C411yescharacteristic, complemented
97#14273713—21no—
98#14273713—21no—
99#14273712—21no—
100#14273710—21no—
101#14273709—21no—
102#14273709—21no—
103#14273708—21no—
104#14273708—21no—
105#14273708—21no—
106#14273707C2×C411yescharacteristic, complemented
107#14273706—21no—
108#14273706C2×C411yescharacteristic, complemented
109#14273706C2311yescharacteristic
110#14273705—21no—
111#14273702C2×C411yescharacteristic, complemented
112#14273701—21no—
113#14273701C2×C411yescharacteristic, complemented
114#14273701C2311yescharacteristic
115#14273700—21no—
116#14273700—21no—
117#14273699—21no—
118#14273699—21no—
119#14273699—21no—
120#14273699—21no—
121#14273699—21no—
122#14273699—21no—
123#14273698—21no—
124#14273698—21no—
125#14273698C2×C411yescharacteristic, complemented
126#14273698C2×C411yescharacteristic, complemented
127#14273696—21no—
128#14273696—21no—
129#14273696—21no—
130#14273695—21no—
131#14273695—21no—
132#14273695—21no—
133#14273692C2×C411yescharacteristic, complemented
134D4×Dic59—21no—
135D4×Dic59—21no—
136D4×Dic59C2×C411yescharacteristic, complemented
137D4×Dic59C2×C411yescharacteristic, complemented
138#14273689C2×C411yescharacteristic, complemented
139C4×C22⋊D59—28no—
140C4×C22⋊D59—21no—
141C4×C22⋊D59—21no—
142C4×C22⋊D59—21no—
143C4×C22⋊D59—21no—
144C4×C22⋊D59C2×C411yescharacteristic
145C4×C22⋊D59C2×C411yescharacteristic
146C4×C22⋊D59C2×C411yescharacteristic
147C4×C22⋊D59C2×C411yescharacteristic
148C4×C22⋊D59D411yescharacteristic
149C4×C22⋊D59D411yescharacteristic
150C4×C22⋊D59D411yescharacteristic
151C4×C22⋊D59D411yescharacteristic
152(C22⋊D59)⋊C4—21no—
153(C22⋊D59)⋊C4—21no—
154(C22⋊D59)⋊C4—21no—
155(C22⋊D59)⋊C4—21no—
156#14273686C2×C411yescharacteristic, complemented
157#14273685C2×C411yescharacteristic, complemented
158#14273683—21no—
159#14273683—21no—
160C2×Dic59⋊C4—21no—
161C2×Dic59⋊C4D411yescharacteristic
162C4⋊C4×D59C2×C411yescharacteristic, complemented
163C2×C22⋊Dic59—21no—
164C2×C22⋊Dic59—21no—
165C2×C22⋊Dic59D411yescharacteristic
166C2×(C2×D59)⋊C4—21no—
167C2×(C2×D59)⋊C4D411yescharacteristic
168C22⋊C4×D59—21no—
169C22⋊C4×D59—21no—
170C2×C4×Dic59—21no—
171C2×C4×Dic59—21no—
172C2×C4×Dic59—21no—
173C2×C4×Dic59—21no—
174C2×C4×Dic59C2311yescharacteristic
175Dic59⋊C8—21no—
176Dic59⋊C8—21no—
177C22⋊(C59⋊C8)—21no—
178C22⋊(C59⋊C8)C2311yescharacteristic
179C22⋊(C59⋊C8)C2311yescharacteristic
180(C2×D59)⋊C8—21no—
181(C2×D59)⋊C8—21no—
182#14273637—21no—
183C8×Dic59—21no—
184C59⋊#95—21no—
185C59⋊#95—21no—
186C59⋊#95C2311yescharacteristic
187C59⋊#95C2311yescharacteristic
188C22×D4×C59—21no—
189C22×D4×C59C2×C411yescharacteristic, complemented
190C23×C4×C59—21no—
191C23×C4×C59C2311yescharacteristic
192C22×C8×C59—21no—
193#121×C59—21no—
194#121×C59—21no—
195#121×C59C2×C411yescharacteristic, complemented
196#121×C59C2×C411yescharacteristic, complemented
197#121×C59C2311yescharacteristic
198#121×C59C2311yescharacteristic
199C2×C4⋊C4×C59C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C59—21no—
201C22⋊C8×C59—21no—
202C22⋊C8×C59C2311yescharacteristic
203C22⋊C8×C59C2311yescharacteristic
204#95×C59—21no—
205#95×C59C2311yescharacteristic
206#95×C59C2311yescharacteristic
207C24×C59—21no—
208C24×C59C2×D411yescharacteristic
209C23×D59—21no—
210C23×D59C2×D411yescharacteristic
211C2×D4×C59—21no—
212C2×D4×C59—21no—
213C2×D4×C59—21no—
214C2×D4×C59—21no—
215C2×D4×C59—21no—
216C2×D4×C59—81no—
217C2×D4×C59—81no—
218C2×D4×C59—81no—
219C2×D4×C59C22×C411yescharacteristic
220C2×D4×C59C22×C411yescharacteristic
221C22×C4×C59—21no—
222C22×C4×C59—21no—
223C22×C4×C59—24no—
224C22×C4×C59—21no—
225C22×C4×C59—81no—
226C22×C4×C59—81no—
227C22×C4×C59—81no—
228C22×C4×C59C22×C411yescharacteristic
229C22×C4×C59C22×C411yescharacteristic
230C22×C4×C59C2×D411yescharacteristic
231C22×C4×C59C2×D411yescharacteristic
232C22×C4×C59C2×D411yescharacteristic
233C22×C4×C59C2411yescharacteristic
234C2×C22⋊D59—24no—
235C2×C22⋊D59—21no—
236C2×C22⋊D59—21no—
237C2×C22⋊D59—21no—
238C2×C22⋊D59—21no—
239C2×C22⋊D59—21no—
240C2×C22⋊D59—21no—
241C2×C22⋊D59—21no—
242C2×C22⋊D59—21no—
243C2×C22⋊D59—21no—
244C2×C22⋊D59—44no—
245C2×C22⋊D59C22⋊C411yescharacteristic
246C2×C22⋊D59C22⋊C411yescharacteristic
247C2×C22⋊D59C22⋊C411yescharacteristic
248C2×C22⋊D59C22⋊C411yescharacteristic
249C22×Dic59—21no—
250C22×Dic59—21no—
251C22×Dic59—21no—
252C22×Dic59—21no—
253C22×Dic59—21no—
254C22×Dic59C2×D411yescharacteristic
255C22×Dic59C2×D411yescharacteristic
256C22×Dic59C2×D411yescharacteristic
257#11745687—81no—
258#11745687—81no—
259#11745687—81no—
260D4×D59—81no—
261D4×D59—81no—
262D4×D59—81no—
263#11745685—81no—
264C2×D236—21no—
265C2×D236C22×C411yescharacteristic
266C2×C4×D59—24no—
267C2×C4×D59—21no—
268C2×C4×D59—21no—
269C2×C4×D59—21no—
270C2×C4×D59—81no—
271C2×C4×D59—81no—
272C2×C4×D59—81no—
273C2×C4×D59C22×C411yescharacteristic
274C2×C4×D59C22×C411yescharacteristic
275C2×C4×D59C2×D411yescharacteristic
276C2×C4×D59C2×D411yescharacteristic
277C2×Dic118—21no—
278C2×Dic118C22×C411yescharacteristic
279C2×C8×C59—21no—
280C2×C8×C59—21no—
281C2×C8×C59—81no—
282C4⋊C4×C59—21no—
283C4⋊C4×C59C22×C411yescharacteristic
284C4⋊C4×C59C22×C411yescharacteristic
285C22⋊C4×C59—21no—
286C22⋊C4×C59—21no—
287C22⋊C4×C59—21no—
288C22⋊C4×C59—21no—
289C22⋊Dic59—24no—
290C22⋊Dic59—21no—
291C22⋊Dic59—21no—
292C22⋊Dic59—21no—
293C22⋊Dic59—21no—
294C22⋊Dic59—21no—
295C22⋊Dic59—21no—
296C22⋊Dic59—21no—
297C22⋊Dic59—21no—
298C22⋊Dic59—21no—
299C22⋊Dic59C22⋊C411yescharacteristic
300C22⋊Dic59C22⋊C411yescharacteristic
301C22⋊Dic59C22⋊C411yescharacteristic
302C22⋊Dic59C22⋊C411yescharacteristic
303(C2×D59)⋊C4—24no—
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—
310(C2×D59)⋊C4C22⋊C411yescharacteristic
311(C2×D59)⋊C4C22⋊C411yescharacteristic
312(C2×D59)⋊C4C22⋊C411yescharacteristic
313(C2×D59)⋊C4C22⋊C411yescharacteristic
314C4⋊Dic59—21no—
315C4⋊Dic59—21no—
316C4⋊Dic59C22×C411yescharacteristic
317C4⋊Dic59C22×C411yescharacteristic
318Dic59⋊C4—24no—
319Dic59⋊C4—21no—
320Dic59⋊C4—21no—
321Dic59⋊C4—21no—
322Dic59⋊C4—21no—
323Dic59⋊C4—21no—
324Dic59⋊C4—21no—
325Dic59⋊C4C22⋊C411yescharacteristic
326Dic59⋊C4C22⋊C411yescharacteristic
327Dic59⋊C4C22⋊C411yescharacteristic
328Dic59⋊C4C22⋊C411yescharacteristic
329C4×Dic59—24no—
330C4×Dic59—21no—
331C4×Dic59—21no—
332C4×Dic59—21no—
333C4×Dic59—81no—
334C4×Dic59—81no—
335C4×Dic59—81no—
336C4×Dic59C22×C411yescharacteristic
337C4×Dic59C22×C411yescharacteristic
338C4×Dic59C2×D411yescharacteristic
339C4×Dic59C2×D411yescharacteristic
340#11745664—81no—
341C2×C59⋊C8—21no—
342C2×C59⋊C8—21no—
343#11745659—81no—
344C8×D59—81no—
345C23×C59—21no—
346C23×C59—21no—
347C23×C59—22no—
348C23×C59—21no—
349C23×C59—21no—
350C23×C59—41no—
351C23×C59—42no—
352C23×C59—81no—
353C23×C59—81no—
354C23×C59C2×C22⋊C411yescharacteristic
355C23×C59C2×C22⋊C411yescharacteristic
356C23×C59C22×D411yescharacteristic
357C22×D59—21no—
358C22×D59—21no—
359C22×D59—22no—
360C22×D59—21no—
361C22×D59—41no—
362C22×D59—42no—
363C22×D59—81no—
364C22×D59—81no—
365C22×D59C2×C22⋊C411yescharacteristic
366C22×D59C2×C22⋊C411yescharacteristic
367D4×C59—41no—
368D4×C59—41no—
369D4×C59—41no—
370D4×C59—41no—
371D4×C59—41no—
372D4×C59—41no—
373D4×C59—81no—
374D4×C59—81no—
375D4×C59—81no—
376C2×C4×C59—22no—
377C2×C4×C59—22no—
378C2×C4×C59—21no—
379C2×C4×C59—21no—
380C2×C4×C59—41no—
381C2×C4×C59—41no—
382C2×C4×C59—41no—
383C2×C4×C59—41no—
384C2×C4×C59—41no—
385C2×C4×C59—41no—
386C2×C4×C59—41no—
387C2×C4×C59—41no—
388C2×C4×C59—41no—
389C2×C4×C59—41no—
390C2×C4×C59—81no—
391C2×C4×C59—84no—
392C2×C4×C59C2×C22⋊C411yescharacteristic
393C2×C4×C59C2×C22⋊C411yescharacteristic
394C2×C4×C59C23×C411yescharacteristic
395C2×C4×C59C22×D411yescharacteristic
396C22⋊D59—22no—
397C22⋊D59—22no—
398C22⋊D59—22no—
399C22⋊D59—41no—
400C22⋊D59—41no—
401C22⋊D59—42no—
402C22⋊D59—42no—
403C22⋊D59—42no—
404C22⋊D59—81no—
405C22⋊D59—81no—
406C22⋊D59—81no—
407C22⋊D59—81no—
408C22⋊D59—81no—
409C22⋊D59#10414yes—
410C2×Dic59—21no—
411C2×Dic59—21no—
412C2×Dic59—22no—
413C2×Dic59—22no—
414C2×Dic59—22no—
415C2×Dic59—21no—
416C2×Dic59—21no—
417C2×Dic59—21no—
418C2×Dic59—41no—
419C2×Dic59—41no—
420C2×Dic59—41no—
421C2×Dic59—41no—
422C2×Dic59—41no—
423C2×Dic59—42no—
424C2×Dic59—81no—
425C2×Dic59—81no—
426C2×Dic59C2×C22⋊C411yescharacteristic
427C2×Dic59C2×C22⋊C411yescharacteristic
428C2×Dic59C2×C22⋊C411yescharacteristic
429C2×Dic59C2×C22⋊C411yescharacteristic
430C2×Dic59C2×C22⋊C411yescharacteristic
431C2×Dic59C2×C22⋊C411yescharacteristic
432D236—41no—
433D236—81no—
434C4×D59—41no—
435C4×D59—41no—
436C4×D59—41no—
437C4×D59—41no—
438C4×D59—81no—
439C4×D59—81no—
440C4×D59—81no—
441C4×D59—84no—
442Dic118—41no—
443Dic118—81no—
444C8×C59—41no—
445C8×C59—41no—
446C59⋊C8—41no—
447C59⋊C8—41no—
448#17547—591nomaximal, Sylow
449C22×C59—21no—
450C22×C59—21no—
451C22×C59—21no—
452C22×C59—21no—
453C22×C59—21no—
454C22×C59—21no—
455C22×C59—21no—
456C22×C59—42no—
457C22×C59—42no—
458C22×C59—41no—
459C22×C59—41no—
460C22×C59—41no—
461C22×C59—41no—
462C22×C59—41no—
463C22×C59—41no—
464C22×C59—162no—
465C22×C59C2×#10412yes—
466C22×C59C22×C22⋊C411yescharacteristic
467C22×C59#57611yescharacteristic
468C22×C59#57711yescharacteristic
469C2×D59—21no—
470C2×D59—21no—
471C2×D59—21no—
472C2×D59—21no—
473C2×D59—21no—
474C2×D59—42no—
475C2×D59—42no—
476C2×D59—41no—
477C2×D59—41no—
478C2×D59—41no—
479C2×D59—162no—
480C2×D59C2×#10412yes—
481C4×C59—21no—
482C4×C59—21no—
483C4×C59—21no—
484C4×C59—21no—
485C4×C59—42no—
486C4×C59—42no—
487C4×C59—41no—
488C4×C59—41no—
489Dic59—21no—
490Dic59—21no—
491Dic59—21no—
492Dic59—21no—
493Dic59—21no—
494Dic59—42no—
495Dic59—42no—
496Dic59—41no—
497Dic59—41no—
498Dic59—41no—
499Dic59C2×#10412yes—
500#3519—591no—
501#2974—591no—
502#2275—591no—
503#1509—591no—
504#1507—591no—
505#1507—591no—
506#1505—591no—
507#1504—591no—
508#1504—591no—
509#1502—591no—
510#1501—591no—
511#1501—591no—
512#1500—591no—
513C2×#327—591no—
514C2×#327D5911yescharacteristic, complemented
515C2×C59—21no—
516C2×C59—21no—
517C2×C59—22no—
518C2×C59—41no—
519C2×C59—81no—
520C2×C59—81no—
521C2×C59#288311yescharacteristic
522C2×C59#289711yescharacteristic
523C2×C59C22×#10411yescharacteristic
524D59—22no—
525D59—41no—
526D59—81no—
527#555—591no—
528#554—591no—
529#553—591no—
530#553—591no—
531#553—1181no—
532#550—591no—
533#546—591no—
534#546—591no—
535#546—1181no—
536#546—1181no—
537D42—591no—
538D42—1181no—
539#540—1181no—
540#538—1181no—
541#538—1181no—
542#532—591no—
543#529—591no—
544#525—591no—
545#525—591no—
546C2×#121—591no—
547C2×#121C2×D5911yescharacteristic
548#518—1181no—
549C2×C4×D4—591no—
550C2×C4×D4—1181no—
551#436—1181no—
552#435—1181no—
553#435—1181no—
554C8×D4—1181no—
555#432—591no—
556#431—591no—
557#407—591no—
558#407—591no—
559C2×C22⋊C8—591no—
560C2×C22⋊C8C2×D5911yescharacteristic, complemented
561C4×C4⋊C4—591no—
562C4×C4⋊C4—1181no—
563C4×C22⋊C4—591no—
564C4×C22⋊C4—591no—
565C4×C22⋊C4—1181no—
566C4×C22⋊C4—1181no—
567#376—591no—
568C2×#95—591no—
569C2×#95C2×D5911yescharacteristic, complemented
570#328—591no—
571#328—591no—
572#328—591no—
573#328—591no—
574#327—591no—
575#327—591no—
576#327—591no—
577#327—591no—
578#327—591no—
579#327—591no—
580#327—591no—
581#327—591no—
582#327C2×D5911yescharacteristic
583#327C2×D5911yescharacteristic
584#327C2×D5911yescharacteristic, complemented
585#327C2×D5911yescharacteristic, complemented
586C59#1754711yescharacteristic, complemented, Sylow
587C2×#41—591no—
588C2×#41—591no—
589C2×#41—1181no—
590C22×D4—21no—
591C22×D4—591no—
592C22×D4—591no—
593C22×D4—1181no—
594C22×D4—1181no—
595C22×D4C4×D5911yescharacteristic, complemented
596C23×C4—21no—
597C23×C4—591no—
598C23×C4—1181no—
599C23×C4C22×D5911yescharacteristic
600C2×M16—1181no—
601C2×M16—1181no—
602C22×C8—21no—
603C22×C8—1181no—
604C4⋊Q8—591no—
605#127—591no—
606#127—1181no—
607#126—1181no—
608#126—1181no—
609#126—1181no—
610#125—591no—
611#125—1181no—
612#124—591no—
613#124—1181no—
614#124—1181no—
615#124—1181no—
616#123—1181no—
617#123—1181no—
618#123—1181no—
619#123—1181no—
620#123—1181no—
621#123—1181no—
622#123—1181no—
623C22⋊Q8—591no—
624C22⋊Q8—591no—
625C22⋊Q8—591no—
626C22⋊Q8—1181no—
627C22⋊Q8—1181no—
628#121—21no—
629#121—21no—
630#121—591no—
631#121—591no—
632#121—591no—
633#121—591no—
634#121—591no—
635#121—1181no—
636#121—1181no—
637#121—1181no—
638#121—1181no—
639#121—1181no—
640#121—1181no—
641#121—1181no—
642#121—1181no—
643#121—1181no—
644#121—1181no—
645#121—1181no—
646#121C4×D5911yescharacteristic, complemented
647#121C4×D5911yescharacteristic, complemented
648#121C22×D5911yescharacteristic
649#121C22×D5911yescharacteristic
650#120—1181no—
651#120—1181no—
652#120—1181no—
653#120—1181no—
654#120—1181no—
655#120—1181no—
656C4×Q8—591no—
657C4×D4—591no—
658C4×D4—591no—
659C4×D4—591no—
660C4×D4—591no—
661C4×D4—591no—
662C4×D4—591no—
663C4×D4—591no—
664C4×D4—591no—
665C4×D4—591no—
666C4×D4—591no—
667C4×D4—591no—
668C4×D4—1181no—
669C4×D4—1181no—
670C4×D4—1181no—
671C4×D4—1181no—
672C4×D4—1181no—
673C4×D4—1181no—
674C4×D4—1188no—
675C4×D4—1181no—
676C4×D4—1181no—
677C4×D4—1181no—
678C4×D4—1181no—
679#117—591no—
680#117—591no—
681#117—1181no—
682#117—1181no—
683C2×C4⋊C4—591no—
684C2×C4⋊C4—591no—
685C2×C4⋊C4—1181no—
686C2×C4⋊C4C4×D5911yescharacteristic, complemented
687C2×C22⋊C4—21no—
688C2×C22⋊C4—591no—
689C2×C22⋊C4—591no—
690C2×C22⋊C4—1181no—
691C2×C22⋊C4—1181no—
692C2×C22⋊C4—1181no—
693C2×C22⋊C4—1181no—
694C2×C22⋊C4—1181no—
695C2×C42—591no—
696C2×C42—1181no—
697C2×C42—1181no—
698C2×C42—1181no—
699C2×C42—1181no—
700C4⋊C8—1181no—
701C4⋊C8—1181no—
702C22⋊C8—21no—
703C22⋊C8—591no—
704C22⋊C8—591no—
705C22⋊C8—1181no—
706C22⋊C8—1181no—
707C22⋊C8—1181no—
708C22⋊C8C22×D5911yescharacteristic
709C22⋊C8C22×D5911yescharacteristic
710#97—1181no—
711C4×C8—1181no—
712#95—21no—
713#95—591no—
714#95—591no—
715#95—1181no—
716#95—1181no—
717#95C22×D5911yescharacteristic
718#95C22×D5911yescharacteristic
719C24—21no—
720C24—591no—
721C24—1181no—
722C24D4×D5911yescharacteristic
723#41—4721no—
724#41—4721no—
725#41—4721no—
726#41—4721no—
727C2×Q8—591no—
728C2×Q8—1181no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—591no—
738C2×D4—591no—
739C2×D4—591no—
740C2×D4—591no—
741C2×D4—591no—
742C2×D4—1181no—
743C2×D4—1181no—
744C2×D4—1181no—
745C2×D4—1181no—
746C2×D4—1184no—
747C2×D4—1181no—
748C2×D4—1181no—
749C2×D4—1181no—
750C2×D4—1181no—
751C2×D4—1181no—
752C2×D4—1181no—
753C2×D4—4721no—
754C2×D4—4721no—
755C2×D4—4721no—
756C2×D4—2364no—
757C2×D4C2×C4×D5911yescharacteristic
758C2×D4C2×C4×D5911yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—24no—
762C22×C4—21no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—591no—
767C22×C4—591no—
768C22×C4—591no—
769C22×C4—591no—
770C22×C4—591no—
771C22×C4—591no—
772C22×C4—591no—
773C22×C4—1181no—
774C22×C4—1181no—
775C22×C4—1184no—
776C22×C4—1181no—
777C22×C4—1181no—
778C22×C4—1181no—
779C22×C4—1181no—
780C22×C4—1181no—
781C22×C4—1181no—
782C22×C4—4721no—
783C22×C4—4721no—
784C22×C4—4721no—
785C22×C4C2×C4×D5911yescharacteristic
786C22×C4C2×C4×D5911yescharacteristic
787C22×C4D4×D5911yescharacteristic
788C22×C4D4×D5911yescharacteristic
789C22×C4D4×D5911yescharacteristic
790C22×C4C23×D5911yescharacteristic
791M16—4721no—
792M16—4721no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—81no—
796C2×C8—1181no—
797C2×C8—1181no—
798C2×C8—4721no—
799C4⋊C4—21no—
800C4⋊C4—591no—
801C4⋊C4—591no—
802C4⋊C4—591no—
803C4⋊C4—591no—
804C4⋊C4—591no—
805C4⋊C4—591no—
806C4⋊C4—1181no—
807C4⋊C4—1181no—
808C4⋊C4—1181no—
809C4⋊C4—1181no—
810C4⋊C4—1181no—
811C4⋊C4—1181no—
812C4⋊C4—1184no—
813C4⋊C4—1181no—
814C4⋊C4—1181no—
815C4⋊C4C2×C4×D5911yescharacteristic
816C4⋊C4C2×C4×D5911yescharacteristic
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—591no—
822C22⋊C4—591no—
823C22⋊C4—591no—
824C22⋊C4—591no—
825C22⋊C4—591no—
826C22⋊C4—591no—
827C22⋊C4—591no—
828C22⋊C4—591no—
829C22⋊C4—1181no—
830C22⋊C4—1181no—
831C22⋊C4—1181no—
832C22⋊C4—1181no—
833C22⋊C4—1184no—
834C22⋊C4—1181no—
835C22⋊C4—1181no—
836C22⋊C4—1181no—
837C22⋊C4—1181no—
838C22⋊C4—1181no—
839C22⋊C4—1181no—
840C22⋊C4—1184no—
841C22⋊C4—1181no—
842C22⋊C4—1181no—
843C22⋊C4—1181no—
844C22⋊C4—1181no—
845C22⋊C4—1181no—
846C42—591no—
847C42—591no—
848C42—591no—
849C42—591no—
850C42—1181no—
851C42—1181no—
852C42—1184no—
853C42—1181no—
854C42—4721no—
855C42—4721no—
856C42—4721no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—41no—
863C23—42no—
864C23—81no—
865C23—81no—
866C23—591no—
867C23—591no—
868C23—1182no—
869C23—1181no—
870C23—1181no—
871C23—1181no—
872C23—4721no—
873C23—4721no—
874C23—2361no—
875C23—2362no—
876C23C22⋊C4×D5911yescharacteristic
877C23C22⋊C4×D5911yescharacteristic
878C23C2×D4×D5911yescharacteristic
879Q8—4721no—
880Q8—2361no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—594no—
891D4—1182no—
892D4—1182no—
893D4—1182no—
894D4—4721no—
895D4—4721no—
896D4—4721no—
897D4—4721no—
898D4—4721no—
899D4—4721no—
900D4—2361no—
901D4—2362no—
902D4—2362no—
903D4—2362no—
904D4—2361no—
905D4—2361no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—81no—
921C2×C4—84no—
922C2×C4—591no—
923C2×C4—591no—
924C2×C4—591no—
925C2×C4—591no—
926C2×C4—591no—
927C2×C4—591no—
928C2×C4—1182no—
929C2×C4—1181no—
930C2×C4—1181no—
931C2×C4—1182no—
932C2×C4—1182no—
933C2×C4—1181no—
934C2×C4—1181no—
935C2×C4—1181no—
936C2×C4—4721no—
937C2×C4—4721no—
938C2×C4—4721no—
939C2×C4—4724no—
940C2×C4—4721no—
941C2×C4—4721no—
942C2×C4—2361no—
943C2×C4—2361no—
944C2×C4—2361no—
945C2×C4—2361no—
946C2×C4—2362no—
947C2×C4—2361no—
948C2×C4—2361no—
949C2×C4—2361no—
950C2×C4—2361no—
951C2×C4—2361no—
952C2×C4C22⋊C4×D5911yescharacteristic
953C2×C4C22⋊C4×D5911yescharacteristic
954C2×C4C22×C4×D5911yescharacteristic
955C2×C4C2×D4×D5911yescharacteristic
956C8—41no—
957C8—41no—
958C8—2361no—
959C8—2361no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—41no—
973C22—41no—
974C22—41no—
975C22—162no—
976C22—592no—
977C22—1181no—
978C22—1181no—
979C22—1181no—
980C22—1181no—
981C22—1181no—
982C22—9442no—
983C22—2362no—
984C22—2362no—
985C22—2361no—
986C22—2361no—
987C22—2361no—
988C22#104×D5912yes—
989C22C2×C22⋊C4×D5911yescharacteristic
990C22#1683820311yescharacteristic
991C22#1683820811yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—592no—
1001C4—1181no—
1002C4—1181no—
1003C4—1181no—
1004C4—1181no—
1005C4—1181no—
1006C4—2362no—
1007C4—2362no—
1008C4—2361no—
1009C4—2361no—
1010C4—2361no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—81no—
1017C2—1182no—
1018C2—4721no—
1019C2—2361no—
1020C2#2143255411yescharacteristic
1021C2#2143261711yescharacteristic
1022C2C2×#104×D5911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#327C2
socleC22×C59C22×C22⋊C4
prime radical#21438122C2
cosocleC22×C4×C59C24
hypercenterC2×#327D59
hypocenterC59#17547
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #21433127C2semidirect
3. #21426454C2semidirect
4. #21422618C2semidirect
5. #21422612C2semidirect
6. #21422610C2semidirect
7. #21422602C2semidirect
8. #21422598C2semidirect
9. #21422597C2semidirect
10. #21422589C2semidirect
11. #21422588C2semidirect
12. #21422584C2semidirect
13. #21422579C2semidirect
14. #327×D59C2semidirect
15. C2×C59×#327C2semidirect
16. #16838116C4semidirect
17. #16838107C4semidirect
18. #16838100C4semidirect
19. #16838099C4semidirect
21. #16838070C4semidirect
22. #16838049C4semidirect
24. #16838046C4semidirect
27. D4×C22⋊D59C4semidirect
43. #16837456C22semidirect
44. #16837452C22semidirect
45. #16837366C22semidirect
46. #16837364C22semidirect
47. C22⋊C8×D59C22semidirect
49. #16837253C22semidirect
51. C4×C22⋊Dic59C22semidirect
53. #16837249C22semidirect
54. #16837247C22semidirect
55. #95×D59C22semidirect
56. #16837140C22semidirect
57. #16837140C22semidirect
58. #16837138C22semidirect
59. #16837138C22semidirect
60. #16837137C22semidirect
61. #16837137C22semidirect
64. #16837136C22semidirect
65. #16837136C22semidirect
66. #16837135C22semidirect
67. #16837135C22semidirect
69. C2×C22⋊C8×C59C22semidirect
70. C2×#95×C59C22semidirect
73. C59×#327C22semidirect
74. C59×#327C22semidirect
75. C2×#11745685C2×C4semidirect
77. C2×#11745687C2×C4semidirect
81. C2×D4×D59C2×C4semidirect
87. #14273726C2×C4semidirect
89. #14273723C2×C4semidirect
93. #14273718C2×C4semidirect
96. #14273714C2×C4semidirect
106. #14273707C2×C4semidirect
108. #14273706C2×C4semidirect
111. #14273702C2×C4semidirect
113. #14273701C2×C4semidirect
125. #14273698C2×C4semidirect
126. #14273698C2×C4semidirect
133. #14273692C2×C4semidirect
136. D4×Dic59C2×C4semidirect
137. D4×Dic59C2×C4semidirect
138. #14273689C2×C4semidirect
156. #14273686C2×C4semidirect
157. #14273685C2×C4semidirect
162. C4⋊C4×D59C2×C4semidirect
189. C22×D4×C59C2×C4semidirect
195. #121×C59C2×C4semidirect
196. #121×C59C2×C4semidirect
199. C2×C4⋊C4×C59C2×C4semidirect
514. C2×#327D59semidirect
560. C2×C22⋊C8C2×D59semidirect
569. C2×#95C2×D59semidirect
584. #327C2×D59semidirect
585. #327C2×D59semidirect
586. C59#17547semidirect
595. C22×D4C4×D59semidirect
646. #121C4×D59semidirect
647. #121C4×D59semidirect
686. C2×C4⋊C4C4×D59semidirect

Maximal subgroups

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

subgroupindex
#214381222
#214331272
#214264542
#214226182
#214226122
#214226102
#214226022
#214225982
#214225972
#214225892
#214225882
#214225842
#214225792
#327×D592
C2×C59×#3272
#1754759