Finite Group Databasebeta

← #28749011

Subgroups — #28749011

Order 15104.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D59C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic, complemented
3C2×#117×D59C211yesmaximal, characteristic
4#21427126C212yesmaximal, complemented
5#21427120C212yesmaximal, complemented
6#21427104C212yesmaximal, complemented
7#21427098C212yesmaximal, complemented
8#21426964C212yesmaximal, complemented
9#21426962C212yesmaximal, complemented
10#21426944C212yesmaximal
11#21426940C212yesmaximal
12#21426780C211yesmaximal, characteristic, complemented
13#21426778C211yesmaximal, characteristic, complemented
14#21426774C211yesmaximal, characteristic, complemented
15#21426711C211yesmaximal, characteristic, complemented
16#21426679C211yesmaximal, characteristic, complemented
17#21426634C211yesmaximal, characteristic, complemented
18C4×#14273707C211yesmaximal, characteristic, complemented
19#21426626C211yesmaximal, characteristic, complemented
20C4×#14273703C211yesmaximal, characteristic, complemented
21#21426478C211yesmaximal, characteristic
22#21426450C211yesmaximal, characteristic, complemented
23C59×#2323C211yesmaximal, characteristic, complemented
24C22×Q8×D59C2211yescharacteristic
25C23×C4×D59C2211yescharacteristic
26C2×#14273707C2211yescharacteristic
27C2×#14273706C2211yescharacteristic
28C2×#14273705C2212yes—
29C2×#14273704C2212yes—
30C2×#14273703C2211yescharacteristic
31C22⋊Q8×D59C4116yescomplemented
32#16837878—28no—
33C2×Q8×Dic59C2211yescharacteristic, complemented
34C2×C4×Dic118C2211yescharacteristic, complemented
35C2×C4×Dic118C2212yescomplemented
36C2×#14273692C2211yescharacteristic, complemented
37C2×#14273692C2212yescomplemented
38C2×#14273686C2211yescharacteristic
39C2×#14273685C2212yes—
40C2×#14273685C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C2×#14273685C2211yescharacteristic
43C2×#14273685C2211yescharacteristic
44C2×#14273684C2212yes—
45C2×#14273684C2211yescharacteristic
46C2×#14273684C2211yescharacteristic
47C2×#14273683C2211yescharacteristic
48C2×#14273683C2211yescharacteristic
49#117×D59—28no—
50C2×C4⋊C4×D59C2211yescharacteristic
51C2×C4⋊C4×D59C2211yescharacteristic
52C2×C4⋊C4×D59C2211yescharacteristic
53C2×C4⋊C4×D59C2212yes—
54C2×C22⋊C4×D59C2211yescharacteristic
55C2×C22⋊C4×D59C2211yescharacteristic
56C2×C22⋊C4×D59C2212yes—
57C2×C42×D59C2211yescharacteristic
58C2×C42×D59C2211yescharacteristic
59#16837309C2211yescharacteristic, complemented
60#16837308C2211yescharacteristic, complemented
61#16837307C2211yescharacteristic, complemented
62#16837306C2212yescomplemented
63#16837306C2212yescomplemented
64#16837301C2212yescomplemented
65#16837301C2211yescharacteristic, complemented
66#16837300C2211yescharacteristic, complemented
67#16837299C2212yescomplemented
68#16837299C2212yescomplemented
69#16837298C2211yescharacteristic, complemented
70#16837297C2212yescomplemented
71#16837297C2212yescomplemented
72#16837296C2212yes—
73#16837296C2212yes—
74#16837295C2212yes—
75#16837295C2212yes—
76#16837290C2212yes—
77#16837290C2212yes—
78#16837289C2212yescomplemented
79#16837289C2212yescomplemented
80#16837288C2212yescomplemented
81#16837287C2212yescomplemented
82#16837285C2212yescomplemented
83#16837283C2212yescomplemented
84#16837283C2212yescomplemented
85#16837276C2212yes—
86#16837276C2212yes—
87#16837273C2212yes—
88#16837273C2212yes—
89#16837264C2212yes—
90#16837264C2212yes—
91#16837264C2212yes—
92#16837262C2211yescharacteristic
93#16837261C2212yes—
94#16837259C2212yes—
95#16837259C2211yescharacteristic
96#16837259C2211yescharacteristic
97#16837257C2212yes—
98C4⋊C4×Dic59C2211yescharacteristic, complemented
99C4⋊C4×Dic59C2211yescharacteristic, complemented
100C4⋊C4×Dic59C2212yescomplemented
101C4×Dic59⋊C4C2212yescomplemented
102C4×Dic59⋊C4C2212yescomplemented
103C4×C4⋊Dic59C2211yescharacteristic, complemented
104C4×C4⋊Dic59C2212yescomplemented
105#16837253C2212yescomplemented
106#16837253C2212yescomplemented
107C22⋊C4×Dic59C2212yes—
108C4×(C2×D59)⋊C4C2212yes—
109C4×(C2×D59)⋊C4C2212yes—
110C4×(C2×D59)⋊C4C2212yes—
111#16837249C2212yes—
112#16837249C2212yes—
113#16837249C2212yes—
114#16837249C2212yes—
115C2×C22⋊Q8×C59C2211yescharacteristic
116C2×C4×Q8×C59C2211yescharacteristic, complemented
117C2×#117×C59C2211yescharacteristic
118C59×#391C2211yescharacteristic, complemented
119C59×#389C2212yescomplemented
120C59×#389C2211yescharacteristic, complemented
121C59×#388C2212yes—
122C59×#388C2212yes—
123C59×#387C2212yescomplemented
124C59×#380C2211yescharacteristic
125C4×C4⋊C4×C59C2211yescharacteristic, complemented
126C24×D59C2311yescharacteristic
127C22×Dic118C2312yes—
128C22×Dic118C2311yescharacteristic
129C2×Q8×D59—24no—
130C2×Q8×D59—24no—
131C2×Q8×D59C2×C418yescomplemented
132C23×Dic59C2311yescharacteristic
133C22×C4×D59—24no—
134C22×C4×D59—24no—
135C22×C4×D59C2×C418yes—
136C22×C4×D59C2311yescharacteristic
137C22×C4×D59C2311yescharacteristic
138C22×C4×D59C2311yescharacteristic
139C22×C4×D59C2311yescharacteristic
140C22×C4×D59C2311yescharacteristic
141C22×C4×D59C2311yescharacteristic
142C22×C4×D59C2311yescharacteristic
143C22×C4×D59C2312yes—
144C22×C4×D59C2312yes—
145C22×C4×D59C2311yescharacteristic
146#14273707C2×C418yes—
147#14273706C2×C418yescomplemented
148#14273705C2×C4116yes—
149#14273704C2×C4116yescomplemented
150#14273703C2×C418yes—
151Q8×Dic59—24no—
152C4×Dic118—24no—
153C4×Dic118—28no—
154#14273692—28no—
155#14273692—24no—
156#14273686—24no—
157#14273685—24no—
158#14273685—24no—
159#14273685—24no—
160#14273685—24no—
161#14273685—28no—
162#14273684—24no—
163#14273684—28no—
164#14273684D418yes—
165#14273683—24no—
166#14273683—24no—
167C2×C4⋊Dic59C2311yescharacteristic
168C2×C4⋊Dic59C2311yescharacteristic
169C2×C4⋊Dic59C2312yes—
170C2×C4⋊Dic59C2311yescharacteristic
171C2×C4⋊Dic59C2311yescharacteristic
172C2×C4⋊Dic59C2312yes—
173C2×C4⋊Dic59C2311yescharacteristic
174C2×C4⋊Dic59C2312yes—
175C2×Dic59⋊C4C2312yes—
176C2×Dic59⋊C4C2312yes—
177C2×Dic59⋊C4C2311yescharacteristic
178C2×Dic59⋊C4C2311yescharacteristic
179C2×Dic59⋊C4C2312yes—
180C2×Dic59⋊C4C2312yes—
181C2×Dic59⋊C4C2312yes—
182C2×Dic59⋊C4C2312yes—
183C2×Dic59⋊C4C2312yes—
184C2×Dic59⋊C4C2311yescharacteristic
185C2×Dic59⋊C4C2311yescharacteristic
186C4⋊C4×D59—24no—
187C4⋊C4×D59—24no—
188C4⋊C4×D59C2×C4116yescomplemented
189C4⋊C4×D59C2×C418yescomplemented
190C2×C22⋊Dic59C2311yescharacteristic
191C2×C22⋊Dic59C2311yescharacteristic
192C2×C22⋊Dic59C2312yes—
193C2×C22⋊Dic59C2312yes—
194C2×(C2×D59)⋊C4C2312yes—
195C2×(C2×D59)⋊C4C2312yes—
196C2×(C2×D59)⋊C4C2312yes—
197C2×(C2×D59)⋊C4C2312yes—
198C2×(C2×D59)⋊C4C2311yescharacteristic
199C2×(C2×D59)⋊C4C2311yescharacteristic
200C2×(C2×D59)⋊C4C2312yes—
201C2×(C2×D59)⋊C4C2312yes—
202C2×(C2×D59)⋊C4C2311yescharacteristic
203C2×(C2×D59)⋊C4C2311yescharacteristic
204C22⋊C4×D59—24no—
205C22⋊C4×D59—24no—
206C22⋊C4×D59C2×C4116yes—
207C2×C4×Dic59C2312yes—
208C2×C4×Dic59C2312yes—
209C2×C4×Dic59C2312yes—
210C2×C4×Dic59C2312yes—
211C2×C4×Dic59C2312yes—
212C2×C4×Dic59C2311yescharacteristic
213C2×C4×Dic59C2311yescharacteristic
214C2×C4×Dic59C2311yescharacteristic
215C2×C4×Dic59C2311yescharacteristic
216C2×C4×Dic59C2311yescharacteristic
217C2×C4×Dic59C2312yes—
218C2×C4×Dic59C2312yes—
219C2×C4×Dic59C2312yes—
220C2×C4×Dic59C2311yescharacteristic
221C42×D59—24no—
222C42×D59—24no—
223C59⋊#95C2312yes—
224C59⋊#95C2312yes—
225C59⋊#95C2312yes—
226C59⋊#95C2312yes—
227C59⋊#95C2312yes—
228C59⋊#95C2312yes—
229C59⋊#95C2312yes—
230C59⋊#95C2312yes—
231C59⋊#95C2312yes—
232C59⋊#95C2312yes—
233C59⋊#95C2312yes—
234C59⋊#95C2312yes—
235C59⋊#95C2312yes—
236C59⋊#95C2312yes—
237C59⋊#95C2312yes—
238C22×Q8×C59C2311yescharacteristic
239C23×C4×C59C2311yescharacteristic
240C22⋊Q8×C59C2×C418yescomplemented
241C4×Q8×C59—24no—
242#117×C59—24no—
243C2×C4⋊C4×C59C2311yescharacteristic
244C2×C4⋊C4×C59C2311yescharacteristic
245C2×C4⋊C4×C59C2311yescharacteristic
246C2×C4⋊C4×C59C2312yes—
247C2×C4⋊C4×C59C2311yescharacteristic
248C2×C4⋊C4×C59C2312yes—
249C2×C4⋊C4×C59C2312yes—
250C2×C4⋊C4×C59C2311yescharacteristic
251C2×C22⋊C4×C59C2311yescharacteristic
252C2×C22⋊C4×C59C2311yescharacteristic
253C2×C22⋊C4×C59C2312yes—
254C2×C22⋊C4×C59C2312yes—
255C2×C42×C59C2312yes—
256C2×C42×C59C2311yescharacteristic
257C2×C42×C59C2312yes—
258C2×C42×C59C2311yescharacteristic
259#95×C59C2312yes—
260#95×C59C2312yes—
261#95×C59C2312yes—
262#95×C59C2312yes—
263#95×C59C2312yes—
264C24×C59C2411yescharacteristic
265C23×D59—22no—
266C23×D59—22no—
267C23×D59—22no—
268C23×D59—22no—
269C23×D59—41no—
270C23×D59—41no—
271C23×D59C22×C414yes—
272C23×D59C2411yescharacteristic
273C23×D59C2411yescharacteristic
274C2×Q8×C59—22no—
275C2×Q8×C59—22no—
276C2×Q8×C59C22×C414yes—
277C22×C4×C59—22no—
278C22×C4×C59—22no—
279C22×C4×C59C22×C414yes—
280C22×C4×C59C2412yes—
281C22×C4×C59C2411yescharacteristic
282C22×C4×C59C2411yescharacteristic
283C22×C4×C59C2412yes—
284C22×C4×C59C2412yes—
285C22×C4×C59C2412yes—
286C22×C4×C59C2411yescharacteristic
287C22×C4×C59C2411yescharacteristic
288C22×C4×C59C2411yescharacteristic
289C22×C4×C59C2411yescharacteristic
290C22×Dic59—22no—
291C22×Dic59—22no—
292C22×Dic59C22×C414yes—
293C22×Dic59C2412yes—
294C22×Dic59C2411yescharacteristic
295C22×Dic59C2411yescharacteristic
296C22×Dic59C2412yes—
297C22×Dic59C2411yescharacteristic
298C22×Dic59C2412yes—
299C22×Dic59C2412yes—
300C22×Dic59C2411yescharacteristic
301C22×Dic59C2411yescharacteristic
302C22×Dic59C2411yescharacteristic
303Q8×D59—232no—
304C2×C4×D59—24no—
305C2×C4×D59—22no—
306C2×C4×D59—22no—
307C2×C4×D59—24no—
308C2×C4×D59—22no—
309C2×C4×D59—22no—
310C2×C4×D59—22no—
311C2×C4×D59—22no—
312C2×C4×D59—232no—
313C2×C4×D59—22no—
314C2×C4×D59—22no—
315C2×C4×D59—22no—
316C2×C4×D59—22no—
317C2×C4×D59—22no—
318C2×C4×D59—22no—
319C2×C4×D59—22no—
320C2×C4×D59—22no—
321C2×C4×D59—42no—
322C2×C4×D59—42no—
323C2×C4×D59—41no—
324C2×C4×D59—41no—
325C2×C4×D59—41no—
326C2×C4×D59—41no—
327C2×C4×D59C22×C418yes—
328C2×C4×D59C22×C414yes—
329C2×C4×D59C22×C414yes—
330C2×C4×D59C22×C414yes—
331C2×C4×D59C22×C418yes—
332C2×C4×D59C22×C414yes—
333C2×C4×D59C2×D414yes—
334C2×C4×D59#4114yes—
335C2×Dic118—22no—
336C2×Dic118—22no—
337C2×Dic118—24no—
338C2×Dic118—24no—
339C2×Dic118C22×C418yes—
340C2×Dic118C22×C414yes—
341C4⋊C4×C59—22no—
342C4⋊C4×C59—22no—
343C4⋊C4×C59—24no—
344C4⋊C4×C59—22no—
345C4⋊C4×C59—22no—
346C4⋊C4×C59—42no—
347C4⋊C4×C59C22×C418yes—
348C4⋊C4×C59C22×C414yes—
349C22⋊C4×C59—22no—
350C22⋊C4×C59—22no—
351C22⋊C4×C59—42no—
352C22⋊C4×C59C22×C418yes—
353C42×C59—22no—
354C42×C59—24no—
355C42×C59—42no—
356C42×C59C2×D414yes—
357C22⋊Dic59—22no—
358C22⋊Dic59—22no—
359C22⋊Dic59—42no—
360C22⋊Dic59C22×C418yes—
361(C2×D59)⋊C4—22no—
362(C2×D59)⋊C4—22no—
363(C2×D59)⋊C4—24no—
364(C2×D59)⋊C4—24no—
365(C2×D59)⋊C4—24no—
366(C2×D59)⋊C4—24no—
367(C2×D59)⋊C4C22×C418yes—
368(C2×D59)⋊C4C22×C418yes—
369(C2×D59)⋊C4C2×D414yes—
370(C2×D59)⋊C4C2×D414yes—
371C4⋊Dic59—22no—
372C4⋊Dic59—22no—
373C4⋊Dic59—22no—
374C4⋊Dic59—22no—
375C4⋊Dic59—24no—
376C4⋊Dic59—42no—
377C4⋊Dic59C22×C414yes—
378C4⋊Dic59C22×C418yes—
379Dic59⋊C4—24no—
380Dic59⋊C4—22no—
381Dic59⋊C4—22no—
382Dic59⋊C4—24no—
383Dic59⋊C4—42no—
384Dic59⋊C4—42no—
385Dic59⋊C4C22×C418yes—
386Dic59⋊C4C22×C418yes—
387Dic59⋊C4C22×C418yes—
388Dic59⋊C4C2×D414yes—
389Dic59⋊C4C2×D414yes—
390C4×Dic59—22no—
391C4×Dic59—22no—
392C4×Dic59—22no—
393C4×Dic59—24no—
394C4×Dic59—22no—
395C4×Dic59—22no—
396C4×Dic59—24no—
397C4×Dic59—24no—
398C4×Dic59—24no—
399C4×Dic59—24no—
400C4×Dic59—42no—
401C4×Dic59—42no—
402C4×Dic59—42no—
403C4×Dic59C2×D414yes—
404C23×C59—21no—
405C23×C59—21no—
406C23×C59—21no—
407C23×C59—21no—
408C23×C59—21no—
409C23×C59—21no—
410C23×C59C23×C412yes—
411C23×C59C2511yescharacteristic
412C22×D59—21no—
413C22×D59—21no—
414C22×D59—21no—
415C22×D59—21no—
416C22×D59—21no—
417C22×D59—21no—
418C22×D59—21no—
419C22×D59—21no—
420C22×D59—28no—
421C22×D59—28no—
422C22×D59—44no—
423C22×D59—44no—
424C22×D59—44no—
425C22×D59—44no—
426C22×D59—44no—
427C22×D59C23×C412yes—
428C22×D59C23×C412yes—
429C22×D59C22×D412yes—
430C22×D59C2×#4112yes—
431C22×D592−1+412yes—
432C22×D592−1+412yes—
433Q8×C59—28no—
434C2×C4×C59—22no—
435C2×C4×C59—21no—
436C2×C4×C59—22no—
437C2×C4×C59—21no—
438C2×C4×C59—21no—
439C2×C4×C59—21no—
440C2×C4×C59—21no—
441C2×C4×C59—22no—
442C2×C4×C59—21no—
443C2×C4×C59—22no—
444C2×C4×C59—28no—
445C2×C4×C59—22no—
446C2×C4×C59—21no—
447C2×C4×C59—21no—
448C2×C4×C59—22no—
449C2×C4×C59—22no—
450C2×C4×C59—22no—
451C2×C4×C59—21no—
452C2×C4×C59—21no—
453C2×C4×C59—22no—
454C2×C4×C59—21no—
455C2×C4×C59—22no—
456C2×C4×C59—21no—
457C2×C4×C59C23×C412yes—
458C2×C4×C59C23×C414yes—
459C2×C4×C59C23×C414yes—
460C2×C4×C59C23×C412yes—
461C2×C4×C59C22×D412yes—
462C2×C4×C59C22×D412yes—
463C2×C4×C59C22×D412yes—
464C2×C4×C59C2×#4112yes—
465C2×Dic59—21no—
466C2×Dic59—22no—
467C2×Dic59—22no—
468C2×Dic59—21no—
469C2×Dic59—21no—
470C2×Dic59—21no—
471C2×Dic59—21no—
472C2×Dic59—21no—
473C2×Dic59—22no—
474C2×Dic59—22no—
475C2×Dic59—28no—
476C2×Dic59—22no—
477C2×Dic59—21no—
478C2×Dic59—21no—
479C2×Dic59—22no—
480C2×Dic59—22no—
481C2×Dic59—22no—
482C2×Dic59—21no—
483C2×Dic59—21no—
484C2×Dic59—22no—
485C2×Dic59—21no—
486C2×Dic59—22no—
487C2×Dic59—21no—
488C2×Dic59C23×C414yes—
489C2×Dic59C23×C412yes—
490C2×Dic59C23×C414yes—
491C2×Dic59C23×C412yes—
492C2×Dic59C22×D412yes—
493C2×Dic59C22×D412yes—
494C2×Dic59C22×D412yes—
495C2×Dic59C2×#4112yes—
496C4×D59—28no—
497C4×D59—216no—
498C4×D59—28no—
499C4×D59—28no—
500C4×D59—48no—
501C4×D59—44no—
502C4×D59—44no—
503C4×D59—44no—
504C4×D59—44no—
505C4×D59C4×D4116yes—
506Dic118—28no—
507Dic118—216no—
508#34203—591nomaximal, Sylow
509C22×C59—22no—
510C22×C59—22no—
511C22×C59—22no—
512C22×C59—41no—
513C22×C59—41no—
514C22×C59—41no—
515C22×C59—41no—
516C22×C59C24×C411yescharacteristic
517C22×C59C23×D411yescharacteristic
518C22×C59C22×#4111yescharacteristic
519C22×C59C2×2−1+411yescharacteristic
520C22×C59C2×2−1+411yescharacteristic
521C22×C59#58511yescharacteristic
522C22×C59#58511yescharacteristic
523C2×D59—22no—
524C2×D59—22no—
525C2×D59—22no—
526C2×D59—22no—
527C2×D59—22no—
528C2×D59—22no—
529C2×D59—22no—
530C2×D59—22no—
531C2×D59—22no—
532C2×D59—22no—
533C2×D59—22no—
534C2×D59—22no—
535C2×D59—416no—
536C2×D59C2×C4×D414yes—
537C2×D59#51914yescomplemented
538C4×C59—24no—
539C4×C59—22no—
540C4×C59—24no—
541C4×C59—22no—
542C4×C59—22no—
543C4×C59—41no—
544C4×C59—41no—
545C4×C59—42no—
546C4×C59—42no—
547C4×C59C2×C4×D414yes—
548Dic59—24no—
549Dic59—22no—
550Dic59—24no—
551Dic59—22no—
552Dic59—22no—
553Dic59—41no—
554Dic59—41no—
555Dic59—42no—
556Dic59—42no—
557Dic59C2×C4×D414yes—
558C22×C22⋊Q8—591no—
559C2×#519—591no—
560C22×#117—591no—
561#2362—592no—
562#2362—592no—
563#2360—592no—
564#2360—592no—
565#2344—592no—
566#2344—592no—
567#2342—592no—
568#2342—592no—
569#2323—591no—
570#2323—591no—
571#2323—591no—
572#2323D5911yescharacteristic, complemented
573#2316—591no—
574#2310—591no—
575C4×C22⋊Q8—591no—
576C4×C22⋊Q8—591no—
577C4×C22⋊Q8—591no—
578C4×C22⋊Q8—591no—
579#2280—591no—
580#2274—591no—
581C2×C59—42no—
582C2×C59C22×C4×D411yescharacteristic
583C2×C59C2×#51911yescharacteristic
584C2×C59#342811yescharacteristic
585C2×C59#348911yescharacteristic
586C2×C59#348911yescharacteristic
587C2×C59#349511yescharacteristic
588C2×C59#349511yescharacteristic
589D59—24no—
590D59—24no—
591C23×Q8—591no—
592C24×C4—591no—
593C2×C22⋊Q8—591no—
594C2×C22⋊Q8—591no—
595C2×C22⋊Q8—5916no—
596C2×C22⋊Q8—592no—
597C2×C22⋊Q8—591no—
598C2×C22⋊Q8—592no—
599C2×C22⋊Q8C2×D5911yescharacteristic
600#519—1188no—
601C2×C4×Q8—591no—
602C2×C4×Q8—591no—
603C2×C4×Q8—592no—
604C2×C4×Q8—591no—
605C2×C4×Q8—592no—
606C2×C4×Q8C2×D5911yescharacteristic, complemented
607C2×#117—591no—
608C2×#117—591no—
609C2×#117—591no—
610C2×#117—592no—
611C2×#117—591no—
612C2×#117—591no—
613C2×#117—591no—
614C2×#117—591no—
615C2×#117—591no—
616C2×#117—591no—
617C2×#117—592no—
618C2×#117—1188no—
619C2×#117C2×D5911yescharacteristic
620C22×C4⋊C4—591no—
621C22×C4⋊C4—592no—
622C22×C4⋊C4—591no—
623C22×C4⋊C4—591no—
624C22×C22⋊C4—592no—
625C22×C22⋊C4—591no—
626C22×C22⋊C4—591no—
627C22×C42—591no—
628C22×C42—591no—
629#391—591no—
630#391—591no—
631#391—591no—
632#391—592no—
633#391—592no—
634#391C2×D5911yescharacteristic, complemented
635#389—591no—
636#389—591no—
637#389—592no—
638#389—592no—
639#389—592no—
640#389—591no—
641#389—592no—
642#389—592no—
643#389C2×D5911yescharacteristic, complemented
644#389C2×D5912yescomplemented
645#388—592no—
646#388—592no—
647#388—592no—
648#388—592no—
649#388—592no—
650#388—592no—
651#388C2×D5912yes—
652#388C2×D5912yes—
653#387—592no—
654#387—592no—
655#387—592no—
656#387—592no—
657#387—592no—
658#387—592no—
659#387—592no—
660#387C2×D5912yescomplemented
661#385—592no—
662#385—592no—
663#385—592no—
664#385—592no—
665#381—592no—
666#381—592no—
667#381—592no—
668#380—591no—
669#380—592no—
670#380—591no—
671#380—591no—
672#380—592no—
673#380C2×D5911yescharacteristic
674#379—592no—
675C4×C4⋊C4—591no—
676C4×C4⋊C4—591no—
677C4×C4⋊C4—592no—
678C4×C4⋊C4—591no—
679C4×C4⋊C4—592no—
680C4×C4⋊C4—592no—
681C4×C4⋊C4—592no—
682C4×C4⋊C4—592no—
683C4×C4⋊C4—592no—
684C4×C4⋊C4C2×D5911yescharacteristic, complemented
685C4×C22⋊C4—592no—
686C4×C22⋊C4—592no—
687C4×C22⋊C4—592no—
688C4×C22⋊C4—592no—
689C4×C22⋊C4—592no—
690C4×C22⋊C4—592no—
691C4×C22⋊C4—592no—
692C4×C22⋊C4—592no—
693C59#3420311yescharacteristic, complemented, Sylow
694C25—591no—
695C22×Q8—598no—
696C22×Q8—592no—
697C22×Q8—591no—
698C22×Q8—1184no—
699C22×Q8—1184no—
700C22×Q8C22×D5911yescharacteristic
701C23×C4—591no—
702C23×C4—591no—
703C23×C4—598no—
704C23×C4—592no—
705C23×C4—591no—
706C23×C4—591no—
707C23×C4—591no—
708C23×C4—592no—
709C23×C4—591no—
710C23×C4—591no—
711C23×C4—591no—
712C23×C4—591no—
713C23×C4—1184no—
714C23×C4—1184no—
715C23×C4C22×D5911yescharacteristic
716C22⋊Q8—598no—
717C22⋊Q8—598no—
718C22⋊Q8—5916no—
719C22⋊Q8—598no—
720C22⋊Q8—5916no—
721C22⋊Q8C4×D5918yescomplemented
722C4×Q8—24no—
723C4×Q8—1188no—
724C4×Q8—1184no—
725C4×Q8—1184no—
726C4×Q8—1188no—
727C4×Q8—1184no—
728#117—24no—
729#117—598no—
730#117—1188no—
731#117—1184no—
732#117—1184no—
733#117—1184no—
734#117—1184no—
735#117—1184no—
736#117—1184no—
737#117—1188no—
738#117—1184no—
739#117—1184no—
740C2×C4⋊C4—591no—
741C2×C4⋊C4—591no—
742C2×C4⋊C4—592no—
743C2×C4⋊C4—592no—
744C2×C4⋊C4—592no—
745C2×C4⋊C4—591no—
746C2×C4⋊C4—592no—
747C2×C4⋊C4—598no—
748C2×C4⋊C4—5916no—
749C2×C4⋊C4—591no—
750C2×C4⋊C4—591no—
751C2×C4⋊C4—591no—
752C2×C4⋊C4—591no—
753C2×C4⋊C4—591no—
754C2×C4⋊C4—592no—
755C2×C4⋊C4—592no—
756C2×C4⋊C4—592no—
757C2×C4⋊C4—591no—
758C2×C4⋊C4—592no—
759C2×C4⋊C4—592no—
760C2×C4⋊C4—592no—
761C2×C4⋊C4—1184no—
762C2×C4⋊C4—1184no—
763C2×C4⋊C4C22×D5911yescharacteristic
764C2×C4⋊C4C22×D5911yescharacteristic
765C2×C4⋊C4C22×D5911yescharacteristic
766C2×C4⋊C4C22×D5912yes—
767C2×C4⋊C4C22×D5911yescharacteristic
768C2×C4⋊C4C22×D5912yes—
769C2×C4⋊C4C22×D5911yescharacteristic
770C2×C4⋊C4C22×D5912yes—
771C2×C22⋊C4—592no—
772C2×C22⋊C4—591no—
773C2×C22⋊C4—591no—
774C2×C22⋊C4—592no—
775C2×C22⋊C4—592no—
776C2×C22⋊C4—5916no—
777C2×C22⋊C4—591no—
778C2×C22⋊C4—591no—
779C2×C22⋊C4—591no—
780C2×C22⋊C4—591no—
781C2×C22⋊C4—592no—
782C2×C22⋊C4—592no—
783C2×C22⋊C4—592no—
784C2×C22⋊C4—592no—
785C2×C22⋊C4—592no—
786C2×C22⋊C4—1184no—
787C2×C22⋊C4—1184no—
788C2×C22⋊C4C22×D5911yescharacteristic
789C2×C22⋊C4C22×D5911yescharacteristic
790C2×C22⋊C4C22×D5912yes—
791C2×C22⋊C4C22×D5912yes—
792C2×C42—591no—
793C2×C42—591no—
794C2×C42—591no—
795C2×C42—591no—
796C2×C42—591no—
797C2×C42—591no—
798C2×C42—592no—
799C2×C42—592no—
800C2×C42—592no—
801C2×C42—592no—
802C2×C42—592no—
803C2×C42—592no—
804C2×C42—592no—
805C2×C42—592no—
806C2×C42—1184no—
807C2×C42—1184no—
808C2×C42C22×D5911yescharacteristic
809C2×C42C22×D5912yes—
810C2×C42C22×D5912yes—
811C2×C42C22×D5911yescharacteristic
812#95—592no—
813#95—592no—
814#95—592no—
815#95—592no—
816#95—592no—
817#95—592no—
818#95—592no—
819#95—592no—
820#95—592no—
821#95—592no—
822#95—592no—
823#95—592no—
824#95—592no—
825#95—592no—
826#95—592no—
827#95C22×D5912yes—
828#95C22×D5912yes—
829#95C22×D5912yes—
830#95C22×D5912yes—
831#95C22×D5912yes—
832C24—591no—
833C24—591no—
834C24—594no—
835C24—1182no—
836C24—1182no—
837C24—1182no—
838C24—1182no—
839C24—2361no—
840C24—2361no—
841C24C23×D5911yescharacteristic
842C2×Q8—22no—
843C2×Q8—22no—
844C2×Q8—598no—
845C2×Q8—594no—
846C2×Q8—1184no—
847C2×Q8—1184no—
848C2×Q8—11832no—
849C2×Q8—1182no—
850C2×Q8—1182no—
851C2×Q8C2×C4×D5914yes—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—591no—
855C22×C4—594no—
856C22×C4—594no—
857C22×C4—594no—
858C22×C4—594no—
859C22×C4—591no—
860C22×C4—592no—
861C22×C4—592no—
862C22×C4—591no—
863C22×C4—591no—
864C22×C4—598no—
865C22×C4—594no—
866C22×C4—594no—
867C22×C4—594no—
868C22×C4—598no—
869C22×C4—592no—
870C22×C4—591no—
871C22×C4—591no—
872C22×C4—592no—
873C22×C4—1182no—
874C22×C4—1182no—
875C22×C4—11832no—
876C22×C4—1182no—
877C22×C4—1182no—
878C22×C4—1182no—
879C22×C4—1184no—
880C22×C4—1182no—
881C22×C4—1184no—
882C22×C4—1182no—
883C22×C4—1182no—
884C22×C4—1182no—
885C22×C4—1182no—
886C22×C4—1182no—
887C22×C4—1182no—
888C22×C4—1182no—
889C22×C4—1182no—
890C22×C4—1182no—
891C22×C4—1182no—
892C22×C4—2361no—
893C22×C4—2362no—
894C22×C4—2361no—
895C22×C4—2362no—
896C22×C4—2361no—
897C22×C4—2361no—
898C22×C4C2×C4×D5914yes—
899C22×C4C23×D5912yes—
900C22×C4C23×D5911yescharacteristic
901C22×C4C23×D5911yescharacteristic
902C22×C4C23×D5912yes—
903C22×C4C23×D5912yes—
904C22×C4C23×D5912yes—
905C22×C4C23×D5911yescharacteristic
906C22×C4C23×D5911yescharacteristic
907C22×C4C23×D5911yescharacteristic
908C22×C4C23×D5911yescharacteristic
909C4⋊C4—22no—
910C4⋊C4—22no—
911C4⋊C4—24no—
912C4⋊C4—22no—
913C4⋊C4—22no—
914C4⋊C4—42no—
915C4⋊C4—598no—
916C4⋊C4—598no—
917C4⋊C4—598no—
918C4⋊C4—594no—
919C4⋊C4—598no—
920C4⋊C4—594no—
921C4⋊C4—594no—
922C4⋊C4—1182no—
923C4⋊C4—1182no—
924C4⋊C4—1182no—
925C4⋊C4—1182no—
926C4⋊C4—1184no—
927C4⋊C4—1184no—
928C4⋊C4—1184no—
929C4⋊C4—1182no—
930C4⋊C4—1182no—
931C4⋊C4—2362no—
932C4⋊C4—2362no—
933C4⋊C4—2362no—
934C4⋊C4C2×C4×D5914yes—
935C4⋊C4C2×C4×D5918yes—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—42no—
939C22⋊C4—598no—
940C22⋊C4—598no—
941C22⋊C4—598no—
942C22⋊C4—594no—
943C22⋊C4—594no—
944C22⋊C4—1182no—
945C22⋊C4—1182no—
946C22⋊C4—1184no—
947C22⋊C4—1184no—
948C22⋊C4—1184no—
949C22⋊C4—1184no—
950C22⋊C4—1182no—
951C22⋊C4—1182no—
952C22⋊C4—2362no—
953C22⋊C4C2×C4×D5918yes—
954C42—22no—
955C42—24no—
956C42—42no—
957C42—594no—
958C42—1182no—
959C42—1182no—
960C42—1184no—
961C42—1184no—
962C42—1184no—
963C42—1184no—
964C42—1182no—
965C42—1182no—
966C42—1182no—
967C42—1184no—
968C42—2362no—
969C42—2362no—
970C42—2362no—
971C42D4×D5914yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—592no—
979C23—592no—
980C23—592no—
981C23—592no—
982C23—592no—
983C23—592no—
984C23—1188no—
985C23—1188no—
986C23—1181no—
987C23—1181no—
988C23—1181no—
989C23—1181no—
990C23—1181no—
991C23—1181no—
992C23—1181no—
993C23—1181no—
994C23—2364no—
995C23—2364no—
996C23—2364no—
997C23—2364no—
998C23—2364no—
999C23C22×C4×D5912yes—
1000C23C24×D5911yescharacteristic
1001Q8—28no—
1002Q8—11816no—
1003Q8—1188no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—28no—
1015C2×C4—22no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—592no—
1028C2×C4—592no—
1029C2×C4—592no—
1030C2×C4—5916no—
1031C2×C4—594no—
1032C2×C4—594no—
1033C2×C4—592no—
1034C2×C4—592no—
1035C2×C4—592no—
1036C2×C4—1188no—
1037C2×C4—1188no—
1038C2×C4—11816no—
1039C2×C4—1188no—
1040C2×C4—1181no—
1041C2×C4—1182no—
1042C2×C4—1181no—
1043C2×C4—1182no—
1044C2×C4—1181no—
1045C2×C4—1181no—
1046C2×C4—1181no—
1047C2×C4—1182no—
1048C2×C4—1181no—
1049C2×C4—1182no—
1050C2×C4—1188no—
1051C2×C4—1182no—
1052C2×C4—1181no—
1053C2×C4—1181no—
1054C2×C4—1182no—
1055C2×C4—1182no—
1056C2×C4—1182no—
1057C2×C4—1181no—
1058C2×C4—1181no—
1059C2×C4—1181no—
1060C2×C4—1182no—
1061C2×C4—1182no—
1062C2×C4—1181no—
1063C2×C4—2368no—
1064C2×C4—2364no—
1065C2×C4—2364no—
1066C2×C4—2364no—
1067C2×C4—2364no—
1068C2×C4C22×C4×D5914yes—
1069C2×C4C22×C4×D5914yes—
1070C2×C4C22×C4×D5912yes—
1071C2×C4C22×C4×D5912yes—
1072C2×C4C2×D4×D5912yes—
1073C2×C4C2×D4×D5912yes—
1074C2×C4C2×D4×D5912yes—
1075C2×C4#41×D5912yes—
1076C22—22no—
1077C22—22no—
1078C22—22no—
1079C22—41no—
1080C22—41no—
1081C22—41no—
1082C22—41no—
1083C22—594no—
1084C22—594no—
1085C22—1182no—
1086C22—1182no—
1087C22—1182no—
1088C22—1182no—
1089C22—1182no—
1090C22—1182no—
1091C22—1182no—
1092C22—1182no—
1093C22—1182no—
1094C22—1182no—
1095C22—1182no—
1096C22—1182no—
1097C22—23616no—
1098C22C23×C4×D5911yescharacteristic
1099C22C22×D4×D5911yescharacteristic
1100C22C2×#41×D5911yescharacteristic
1101C222−1+4×D5911yescharacteristic
1102C222−1+4×D5911yescharacteristic
1103C22#1683823711yescharacteristic
1104C22#1683823911yescharacteristic
1105C4—22no—
1106C4—22no—
1107C4—22no—
1108C4—24no—
1109C4—24no—
1110C4—41no—
1111C4—42no—
1112C4—41no—
1113C4—42no—
1114C4—594no—
1115C4—1182no—
1116C4—1182no—
1117C4—1182no—
1118C4—1184no—
1119C4—1184no—
1120C4—2361no—
1121C4—2361no—
1122C4—2362no—
1123C4—2362no—
1124C4C4×D4×D5914yes—
1125C2—42no—
1126C2—1184no—
1127C2—1184no—
1128C2C2×C4×D4×D5911yescharacteristic
1129C2#519×D5911yescharacteristic
1130C2#2143729611yescharacteristic
1131C2#2143777111yescharacteristic
1132C2#2143777411yescharacteristic
1133C2#2143784011yescharacteristic
1134C2#2143784611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D59
commutatorC22×C59C24×C4
FittingC59×#2323C2
socle, cosocleC23×C59C25
prime radicalC24×D59C23
hypercenter#2323D59
hypocenterC59#34203
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. C2×#16837878C2semidirect
4. #21427126C2semidirect
5. #21427120C2semidirect
6. #21427104C2semidirect
7. #21427098C2semidirect
8. #21426964C2semidirect
9. #21426962C2semidirect
12. #21426780C2semidirect
13. #21426778C2semidirect
14. #21426774C2semidirect
15. #21426711C2semidirect
16. #21426679C2semidirect
17. #21426634C2semidirect
18. C4×#14273707C2semidirect
19. #21426626C2semidirect
20. C4×#14273703C2semidirect
22. #21426450C2semidirect
23. C59×#2323C2semidirect
31. C22⋊Q8×D59C4semidirect
33. C2×Q8×Dic59C22semidirect
34. C2×C4×Dic118C22semidirect
35. C2×C4×Dic118C22semidirect
36. C2×#14273692C22semidirect
37. C2×#14273692C22semidirect
59. #16837309C22semidirect
60. #16837308C22semidirect
61. #16837307C22semidirect
62. #16837306C22semidirect
63. #16837306C22semidirect
64. #16837301C22semidirect
65. #16837301C22semidirect
66. #16837300C22semidirect
67. #16837299C22semidirect
68. #16837299C22semidirect
69. #16837298C22semidirect
70. #16837297C22semidirect
71. #16837297C22semidirect
78. #16837289C22semidirect
79. #16837289C22semidirect
80. #16837288C22semidirect
81. #16837287C22semidirect
82. #16837285C22semidirect
83. #16837283C22semidirect
84. #16837283C22semidirect
98. C4⋊C4×Dic59C22semidirect
99. C4⋊C4×Dic59C22semidirect
100. C4⋊C4×Dic59C22semidirect
101. C4×Dic59⋊C4C22semidirect
102. C4×Dic59⋊C4C22semidirect
103. C4×C4⋊Dic59C22semidirect
104. C4×C4⋊Dic59C22semidirect
105. #16837253C22semidirect
106. #16837253C22semidirect
116. C2×C4×Q8×C59C22semidirect
118. C59×#391C22semidirect
119. C59×#389C22semidirect
120. C59×#389C22semidirect
123. C59×#387C22semidirect
125. C4×C4⋊C4×C59C22semidirect
131. C2×Q8×D59C2×C4semidirect
147. #14273706C2×C4semidirect
149. #14273704C2×C4semidirect
188. C4⋊C4×D59C2×C4semidirect
189. C4⋊C4×D59C2×C4semidirect
240. C22⋊Q8×C59C2×C4semidirect
537. C2×D59#519semidirect
572. #2323D59semidirect
606. C2×C4×Q8C2×D59semidirect
634. #391C2×D59semidirect
643. #389C2×D59semidirect
644. #389C2×D59semidirect
660. #387C2×D59semidirect
684. C4×C4⋊C4C2×D59semidirect
693. C59#34203semidirect
721. C22⋊Q8C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D592
C2×#168378782
C2×#117×D592
#214271262
#214271202
#214271042
#214270982
#214269642
#214269622
#214269442
#214269402
#214267802
#214267782
#214267742
#214267112
#214266792
#214266342
C4×#142737072
#214266262
C4×#142737032
#214264782
#214264502
C59×#23232
#3420359