Finite Group Databasebeta

← #27305686

Subgroups — #27305686

Order 13568.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810516C211yesmaximal, characteristic
2C2×#16810498C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic
6C2×C22⋊C4×Dic53C211yesmaximal, characteristic
7#20272952C211yesmaximal, characteristic
8#20272952C211yesmaximal, characteristic
9#20272949C211yesmaximal, characteristic, complemented
10#20272949C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272947C211yesmaximal, characteristic, complemented
13C4×#13133124C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C2×C53×#388C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810516C418yescomplemented
31#16810498C418yescomplemented
32C4⋊C4×Dic53—24no—
33C4×C4⋊Dic53—24no—
34C22⋊C4×Dic53—24no—
35C22⋊C4×Dic53—24no—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C22×C4⋊C4×C53C2211yescharacteristic
51C22×C22⋊C4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C42×C53C2211yescharacteristic
55C53×#388C418yescomplemented
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—41no—
63C23×Dic53—41no—
64C23×Dic53C2×C414yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C2×C4⋊Dic53—22no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—22no—
77C2×C4⋊Dic53—22no—
78C2×C4⋊Dic53—22no—
79C2×C4⋊Dic53C2×C414yes—
80C2×C4⋊Dic53C2×C414yes—
81C2×C4⋊Dic53C2×C414yescomplemented
82C2×C22⋊Dic53—22no—
83C2×C22⋊Dic53—22no—
84C2×C22⋊Dic53—22no—
85C2×C22⋊Dic53—22no—
86C2×C22⋊Dic53—41no—
87C2×C22⋊Dic53—41no—
88C2×C22⋊Dic53C2×C414yes—
89C2×C22⋊Dic53C2×C414yes—
90C2×C22⋊Dic53C2×C414yes—
91C2×C4×Dic53—22no—
92C2×C4×Dic53—22no—
93C2×C4×Dic53—22no—
94C2×C4×Dic53—22no—
95C2×C4×Dic53—22no—
96C2×C4×Dic53—22no—
97C2×C4×Dic53—22no—
98C2×C4×Dic53—22no—
99C2×C4×Dic53—22no—
100C2×C4×Dic53—22no—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—41no—
106C2×C4×Dic53—41no—
107C2×C4×Dic53—41no—
108C2×C4×Dic53—41no—
109C2×C4×Dic53—41no—
110C2×C4×Dic53—41no—
111C2×C4×Dic53C2×C414yescomplemented
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—22no—
118#13133124—41no—
119#13133124—41no—
120#13133124C2×C414yes—
121#13133124C2×C414yes—
122#13133124C2×C414yescomplemented
123#13133124C2×C414yescomplemented
124#13133124D414yes—
125#13133124D414yes—
126C25×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53—22no—
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53C2×C414yescomplemented
136C2×C22⋊C4×C53—22no—
137C2×C22⋊C4×C53—22no—
138C2×C22⋊C4×C53—22no—
139C2×C22⋊C4×C53—22no—
140C2×C22⋊C4×C53C2×C414yes—
141C2×C22⋊C4×C53C2×C414yes—
142C2×C22⋊C4×C53C2×C414yes—
143C2×C22⋊C4×C53C2×C414yes—
144C2×C22⋊C4×C53C2×C414yes—
145C2×C42×C53—22no—
146C2×C42×C53—22no—
147C2×C42×C53C2×C414yescomplemented
148#95×C53C2×C414yescomplemented
149#95×C53C2×C414yescomplemented
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53C22×C412yes—
163C24×C53C22×C412yes—
164C24×C53C22×C412yes—
165C24×C53C2411yescharacteristic
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53C22×C412yes—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C22×C412yes—
197C22×C4×C53C22×C412yes—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C22×C412yes—
200C22×C4×C53C22×C412yes—
201C22×C4×C53C22×C412yes—
202C22×C4×C53C22×C412yes—
203C22×C4×C53C22×C412yes—
204C22×C4×C53C2×D412yes—
205C22×C4×C53C2×D412yes—
206C22×C4×C53#4112yes—
207C22×C4×C53#4112yes—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—28no—
249C22×Dic53—28no—
250C22×Dic53—44no—
251C22×Dic53—44no—
252C22×Dic53—44no—
253C22×Dic53—44no—
254C22×Dic53—44no—
255C22×Dic53C22×C412yes—
256C22×Dic53C22×C412yes—
257C22×Dic53C22×C412yes—
258C22×Dic53C22×C412yes—
259C22×Dic53C22×C412yes—
260C22×Dic53C22×C412yes—
261C22×Dic53C22×C412yes—
262C22×Dic53C22×C412yes—
263C22×Dic53C2×D412yes—
264C22×Dic53C2×D412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×D412yes—
267C22×Dic53#4112yes—
268C22×Dic53#4112yes—
269C22×Dic53#4112yes—
270C22×Dic53#4112yes—
271C4⋊C4×C53—28no—
272C22⋊C4×C53—28no—
273C22⋊C4×C53—28no—
274C22⋊C4×C53C42116yescomplemented
275C42×C53—28no—
276C22⋊Dic53—28no—
277C22⋊Dic53—28no—
278C22⋊Dic53—44no—
279C4⋊Dic53—28no—
280C4⋊Dic53—28no—
281C4⋊Dic53—28no—
282C4×Dic53—28no—
283C4×Dic53—44no—
284C4×Dic53—44no—
285C4×Dic53—44no—
286C4×Dic53—44no—
287C4×Dic53—44no—
288C4×Dic53—44no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53C2×C4214yes—
324C23×C53C23×C411yescharacteristic
325C23×C53C23×C411yescharacteristic
326C23×C53C23×C411yescharacteristic
327C23×C53C22×D411yescharacteristic
328C23×C53C22×D411yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53C2×#4111yescharacteristic
331C23×C53C2×#4111yescharacteristic
332C23×C53C2×#4111yescharacteristic
333C23×C53C2×#4111yescharacteristic
334C23×C53C2×#4111yescharacteristic
335C23×C53H(5,𝔽2)11yescharacteristic
336C23×C53H(5,𝔽2)11yescharacteristic
337C23×C532−1+411yescharacteristic
338C23×C532−1+411yescharacteristic
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53C2×C4214yes—
378C2×C4×C53C2×C4214yes—
379C2×C4×C53C4×D414yes—
380C2×C4×C53C4×D414yes—
381C2×Dic53—22no—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—22no—
406C2×Dic53—22no—
407C2×Dic53—22no—
408C2×Dic53—22no—
409C2×Dic53—22no—
410C2×Dic53—22no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—22no—
415C2×Dic53—22no—
416C2×Dic53—22no—
417C2×Dic53—416no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53C4×D414yes—
435C2×Dic53C4×D414yes—
436C2×Dic53C4×D414yes—
437C2×Dic53C4×D414yes—
438#13823—531nomaximal, Sylow
439C22×C53—24no—
440C22×C53—24no—
441C22×C53—24no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—42no—
453C22×C53—42no—
454C22×C53C22×C4211yescharacteristic
455C22×C53C2×C4×D411yescharacteristic
456C22×C53C2×C4×D411yescharacteristic
457C22×C53C2×C4×D411yescharacteristic
458C22×C53C2×C4×D411yescharacteristic
459C22×C53C2×C4×D411yescharacteristic
460C22×C53C2×C4×D411yescharacteristic
461C22×C53C4×#4111yescharacteristic
462C22×C53C4×#4111yescharacteristic
463C22×C53C4×#4111yescharacteristic
464C22×C53C4×#4111yescharacteristic
465C22×C53C4×#4111yescharacteristic
466C22×C53C4×#4111yescharacteristic
467C22×C53#51811yescharacteristic
468C22×C53#51911yescharacteristic
469C22×C53#52011yescharacteristic
470C22×C53#52011yescharacteristic
471C22×C53#52011yescharacteristic
472C22×C53#52011yescharacteristic
473C22×C53D4211yescharacteristic
474C22×C53#54611yescharacteristic
475C22×C53#54611yescharacteristic
476C22×C53#54711yescharacteristic
477C22×C53#54711yescharacteristic
478C22×C53#54811yescharacteristic
479C22×C53#54811yescharacteristic
480C22×C53#55111yescharacteristic
481C22×C53#55111yescharacteristic
482C22×C53#55211yescharacteristic
483C22×C53#55211yescharacteristic
484C22×C53#55311yescharacteristic
485C22×C53#55311yescharacteristic
486C22×C53#55611yescharacteristic
487C22×C53#55611yescharacteristic
488C22×C53#55911yescharacteristic
489C4×C53—24no—
490C4×C53—24no—
491C4×C53—24no—
492C4×C53—24no—
493C4×C53—42no—
494C4×C53—42no—
495Dic53—24no—
496Dic53—24no—
497Dic53—24no—
498Dic53—24no—
499Dic53—42no—
500Dic53—42no—
501Dic53—42no—
502Dic53—42no—
503C2×#388—531no—
504C2×#388D5311yescharacteristic
505C2×#385—531no—
506C2×C4×C4⋊C4—531no—
507C2×C4×C4⋊C4—531no—
508C2×C4×C22⋊C4—531no—
509C2×C4×C22⋊C4—531no—
510#1437—531no—
511#1437—531no—
512#1436—531no—
513#1436—531no—
514#1436—531no—
515#1436—531no—
516C4×#95—531no—
517C4×#95—531no—
518C2×C53—44no—
519C2×C53C42×D411yescharacteristic
520C2×C53C42×D411yescharacteristic
521C2×C53#227411yescharacteristic
522C2×C53#235811yescharacteristic
523C2×C53#235911yescharacteristic
524C2×C53#235911yescharacteristic
525C2×C53#236111yescharacteristic
526C2×C53#236111yescharacteristic
527C2×C53#236211yescharacteristic
528C2×C53#236211yescharacteristic
529C2×C53#236711yescharacteristic
530C2×C53#236711yescharacteristic
531C2×C53#237311yescharacteristic
532C2×C53#237311yescharacteristic
533C2×C53#237411yescharacteristic
534C24×C4—531no—
535C22×C4⋊C4—531no—
536C22×C4⋊C4—531no—
537C22×C4⋊C4—531no—
538C22×C4⋊C4C2×D5311yescharacteristic
539C22×C22⋊C4—531no—
540C22×C22⋊C4—531no—
541C22×C22⋊C4—531no—
542C22×C22⋊C4C2×D5311yescharacteristic
543C22×C22⋊C4C2×D5311yescharacteristic
544C22×C22⋊C4C2×D5311yescharacteristic
545C22×C42—531no—
546C22×C42—531no—
547C22×C42—531no—
548C22×C42—531no—
549C22×C42—531no—
550C22×C42—531no—
551C22×C42—531no—
552C22×C42C2×D5311yescharacteristic
553#388—538no—
554#388Dic5318yescomplemented
555#385—538no—
556C4×C4⋊C4—1064no—
557C4×C4⋊C4—1064no—
558C4×C22⋊C4—1064no—
559C4×C22⋊C4—1064no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95—531no—
570C2×#95—531no—
571C2×#95—531no—
572C2×#95—531no—
573C2×#95—531no—
574C2×#95C2×D5311yescharacteristic
575C2×#95C2×D5311yescharacteristic
576C53#1382311yescharacteristic, complemented, Sylow
577C25C22×D5311yescharacteristic
578C23×C4—531no—
579C23×C4—531no—
580C23×C4—531no—
581C23×C4—531no—
582C23×C4—531no—
583C23×C4—531no—
584C23×C4—531no—
585C23×C4—531no—
586C23×C4—534no—
587C23×C4—1062no—
588C23×C4—1062no—
589C23×C4—1062no—
590C23×C4—1062no—
591C23×C4—2121no—
592C23×C4—2121no—
593C23×C4C22×D5311yescharacteristic
594C23×C4C22×D5311yescharacteristic
595C23×C4C22×D5311yescharacteristic
596C23×C4C22×D5311yescharacteristic
597C23×C4C22×D5311yescharacteristic
598C23×C4C22×D5311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—534no—
604C2×C4⋊C4—1062no—
605C2×C4⋊C4—1062no—
606C2×C4⋊C4—1062no—
607C2×C4⋊C4—1062no—
608C2×C4⋊C4—1062no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4C2×Dic5314yescomplemented
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—534no—
616C2×C22⋊C4—534no—
617C2×C22⋊C4—534no—
618C2×C22⋊C4—1062no—
619C2×C22⋊C4—1062no—
620C2×C22⋊C4—1062no—
621C2×C22⋊C4—1062no—
622C2×C22⋊C4—2121no—
623C2×C22⋊C4—2121no—
624C2×C22⋊C4C4×D5314yes—
625C2×C22⋊C4C4×D5314yes—
626C2×C22⋊C4C2×Dic5314yes—
627C2×C22⋊C4C2×Dic5314yes—
628C2×C22⋊C4C2×Dic5314yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—534no—
632C2×C42—1062no—
633C2×C42—1062no—
634C2×C42—1062no—
635C2×C42—1062no—
636C2×C42—1062no—
637C2×C42—1062no—
638C2×C42—1062no—
639C2×C42—1062no—
640C2×C42—1062no—
641C2×C42—1062no—
642C2×C42—1062no—
643C2×C42—1062no—
644C2×C42—1062no—
645C2×C42—1062no—
646C2×C42—2121no—
647C2×C42—2121no—
648C2×C42—2121no—
649C2×C42—2121no—
650C2×C42—2121no—
651C2×C42—2121no—
652C2×C42C2×Dic5314yescomplemented
653#95—534no—
654#95—534no—
655#95—534no—
656#95—534no—
657#95—534no—
658#95—534no—
659#95—1062no—
660#95—1062no—
661#95—1062no—
662#95—1062no—
663#95—1062no—
664#95—1062no—
665#95—2121no—
666#95—2121no—
667#95C2×Dic5314yescomplemented
668#95C2×Dic5314yescomplemented
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D5312yes—
682C24C2×C4×D5312yes—
683C24C22×Dic5312yes—
684C24C23×D5311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—532no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—532no—
717C22×C4—532no—
718C22×C4—532no—
719C22×C4—532no—
720C22×C4—532no—
721C22×C4—532no—
722C22×C4—532no—
723C22×C4—532no—
724C22×C4—532no—
725C22×C4—532no—
726C22×C4—532no—
727C22×C4—532no—
728C22×C4—532no—
729C22×C4—1068no—
730C22×C4—1068no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—2124no—
772C22×C4—2124no—
773C22×C4—2124no—
774C22×C4—2124no—
775C22×C4—2124no—
776C22×C4C2×C4×D5312yes—
777C22×C4C2×C4×D5312yes—
778C22×C4C2×C4×D5312yes—
779C22×C4C2×C4×D5312yes—
780C22×C4D4×D5312yes—
781C22×C4D4×D5312yes—
782C22×C4#1171994712yes—
783C22×C4#1171994712yes—
784C22×C4C22×Dic5312yes—
785C22×C4C22×Dic5312yes—
786C22×C4C22×Dic5312yes—
787C22×C4C22×Dic5312yes—
788C22×C4C22×Dic5312yes—
789C22×C4C22×Dic5312yes—
790C4⋊C4—28no—
791C4⋊C4—1068no—
792C4⋊C4—1068no—
793C4⋊C4—1068no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—1068no—
797C22⋊C4—1068no—
798C22⋊C4—2124no—
799C22⋊C4C4×Dic53116yescomplemented
800C42—28no—
801C42—1068no—
802C42—2124no—
803C42—2124no—
804C42—2124no—
805C42—2124no—
806C42—2124no—
807C42—2124no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4×Dic5314yes—
843C23C22×C4×D5311yescharacteristic
844C23C22×C4×D5311yescharacteristic
845C23C23×Dic5311yescharacteristic
846C23C2×D4×D5311yescharacteristic
847C23C2×D4×D5311yescharacteristic
848C23#41×D5311yescharacteristic
849C23#41×D5311yescharacteristic
850C23#41×D5311yescharacteristic
851C23#41×D5311yescharacteristic
852C23C2×#1171994711yescharacteristic
853C23C2×#1171994711yescharacteristic
854C23#1313326311yescharacteristic
855C23#1313326311yescharacteristic
856C23#1313326411yescharacteristic
857C23#1313326411yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—534no—
897C2×C4—534no—
898C2×C4—534no—
899C2×C4—534no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1062no—
923C2×C4—1062no—
924C2×C4—1062no—
925C2×C4—1062no—
926C2×C4—1062no—
927C2×C4—1062no—
928C2×C4—1062no—
929C2×C4—1062no—
930C2×C4—1062no—
931C2×C4—1062no—
932C2×C4—1062no—
933C2×C4—1062no—
934C2×C4—1062no—
935C2×C4—1062no—
936C2×C4—21216no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4—2121no—
953C2×C4C2×C4×Dic5314yes—
954C2×C4C2×C4×Dic5314yes—
955C2×C4D4×Dic5314yes—
956C2×C4D4×Dic5314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4×Dic5311yescharacteristic
973C22C4×D4×D5311yescharacteristic
974C22C4×D4×D5311yescharacteristic
975C22C4×D4×D5311yescharacteristic
976C22C4×D4×D5311yescharacteristic
977C22C2×D4×Dic5311yescharacteristic
978C22C2×D4×Dic5311yescharacteristic
979C22C4×#1171994711yescharacteristic
980C22C4×#1171994711yescharacteristic
981C22C4×#1171994711yescharacteristic
982C22C4×#1171994711yescharacteristic
983C22#41×Dic5311yescharacteristic
984C22#41×Dic5311yescharacteristic
985C22#1681109711yescharacteristic
986C22#1681110011yescharacteristic
987C22#1681110311yescharacteristic
988C22#1681110311yescharacteristic
989C22#1681110611yescharacteristic
990C22#1681110611yescharacteristic
991C22#1681125711yescharacteristic
992C22#1681126511yescharacteristic
993C22#1681126611yescharacteristic
994C22#1681127111yescharacteristic
995C22#1681127311yescharacteristic
996C22#1681127911yescharacteristic
997C22#1681128111yescharacteristic
998C22#1681129611yescharacteristic
999C22#1681129811yescharacteristic
1000C22#1681130911yescharacteristic
1001C22#1681131011yescharacteristic
1002C22#1681132411yescharacteristic
1003C22#1681132511yescharacteristic
1004C22#1681134011yescharacteristic
1005C22#1681134211yescharacteristic
1006C22#1681135511yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—1064no—
1014C4—1064no—
1015C4—1064no—
1016C4—1064no—
1017C4—2122no—
1018C4—2122no—
1019C4—2122no—
1020C4—2122no—
1021C2—44no—
1022C2C4×D4×Dic5311yescharacteristic
1023C2C4×D4×Dic5311yescharacteristic
1024C2#2027707111yescharacteristic
1025C2#2027769311yescharacteristic
1026C2#2027770611yescharacteristic
1027C2#2027771111yescharacteristic
1028C2#2027772811yescharacteristic
1029C2#2027773511yescharacteristic
1030C2#2027773911yescharacteristic
1031C2#2027774511yescharacteristic
1032C2#2027778911yescharacteristic
1033C2#2027779011yescharacteristic
1034C2#2027783911yescharacteristic
1035C2#2027784211yescharacteristic
1036C2#2027784511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC2×C53×#388C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#388D53
hypocenterC53#13823
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic53C2semidirect
4. C2×C4×C4⋊Dic53C2semidirect
9. #20272949C2semidirect
10. #20272949C2semidirect
11. #20272949C2semidirect
12. #20272947C2semidirect
13. C4×#13133124C2semidirect
14. #95×Dic53C2semidirect
30. #16810516C4semidirect
31. #16810498C4semidirect
55. C53×#388C4semidirect
81. C2×C4⋊Dic53C2×C4semidirect
111. C2×C4×Dic53C2×C4semidirect
122. #13133124C2×C4semidirect
123. #13133124C2×C4semidirect
135. C2×C4⋊C4×C53C2×C4semidirect
147. C2×C42×C53C2×C4semidirect
148. #95×C53C2×C4semidirect
149. #95×C53C2×C4semidirect
274. C22⋊C4×C53C42semidirect
554. #388Dic53semidirect
576. C53#13823semidirect
610. C2×C4⋊C4C2×Dic53semidirect
652. C2×C42C2×Dic53semidirect
667. #95C2×Dic53semidirect
668. #95C2×Dic53semidirect
799. C22⋊C4C4×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105162
C2×#168104982
C2×C4⋊C4×Dic532
C2×C4×C4⋊Dic532
C2×C22⋊C4×Dic532
#202729522
#202729492
#202729472
C4×#131331242
#95×Dic532
C2×C53×#3882
#1382353