Finite Group Databasebeta

← #27291010

Subgroups — #27291010

Order 13568.

1262 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133146C211yesmaximal, characteristic, complemented
2C22×#13133129C211yesmaximal, characteristic
3C22×#13133129C211yesmaximal, characteristic
4C2×C4×#11719921C211yesmaximal, characteristic
5C2×#16810378C211yesmaximal, characteristic, complemented
6C2×#16810377C211yesmaximal, characteristic, complemented
7C2×C53×#336C211yesmaximal, characteristic, complemented
8C23×C4×D53C2211yescharacteristic
9C23×#88322C2211yescharacteristic
10C23×#88322C2211yescharacteristic
11C22×#11719921C411yescharacteristic
12C22×#11719921C411yescharacteristic
13C22×C4×Dic53C2211yescharacteristic
14C2×#13133146—22no—
15C2×#13133146—22no—
16C2×#13133146—22no—
17C2×#13133129—22no—
18C2×#13133129—22no—
19C2×#13133129—22no—
20C2×#13133129—22no—
21C2×#13133129—22no—
22C2×#13133129—22no—
23C4×#11719921—22no—
24C4×#11719921—22no—
25C2×#13133124C411yescharacteristic
26C2×#13133124C411yescharacteristic
27#16810378—22no—
28#16810377—22no—
29C23×C8×C53C2211yescharacteristic
30C23×C8×C53C2211yescharacteristic
31C22×C42×C53C2211yescharacteristic
32C53×#336—22no—
33C24×D53C2×C411yescharacteristic
34C23×Dic53C2×C411yescharacteristic
35C23×Dic53C2×C411yescharacteristic
36C23×Dic53C2×C411yescharacteristic
37C22×C4×D53—21no—
38C22×C4×D53—21no—
39C22×C4×D53—21no—
40C22×C4×D53—21no—
41C22×C4×D53—21no—
42C22×C4×D53—21no—
43C22×C4×D53—21no—
44C22×C4×D53—21no—
45C22×C4×D53—21no—
46C22×C4×D53—21no—
47C22×C4×D53—21no—
48C22×C4×D53—21no—
49C22×C4×D53D412yes—
50C22×C4×D53Q812yes—
51C22×#88322—21no—
52C22×#88322—21no—
53C22×#88322—21no—
54C22×#88322—21no—
55C22×#88322—21no—
56C22×#88322—21no—
57C22×#88322—21no—
58C22×#88322—21no—
59C22×#88322—21no—
60C22×#88322—21no—
61C22×#88322—21no—
62C22×#88322—21no—
63C22×#88322D412yes—
64C22×#88322D412yes—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—22no—
68C2×#11719921—22no—
69C2×#11719921—22no—
70C2×#11719921C814yescomplemented
71C2×C4×Dic53—21no—
72C2×C4×Dic53—21no—
73C2×C4×Dic53—21no—
74C2×C4×Dic53—21no—
75C2×C4×Dic53D412yes—
76C2×C4×Dic53D412yes—
77#13133146—28no—
78#13133129—28no—
79#13133129—28no—
80#13133124—22no—
81#13133124—22no—
82C23×C4×C53C2×C411yescharacteristic
83C23×C4×C53C2×C411yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C22×C8×C53—21no—
86C22×C8×C53—21no—
87C22×C8×C53—21no—
88C22×C8×C53—21no—
89C22×C8×C53—21no—
90C22×C8×C53—21no—
91C22×C8×C53—21no—
92C22×C8×C53—21no—
93C22×C8×C53—21no—
94C22×C8×C53—21no—
95C22×C8×C53—21no—
96C22×C8×C53—21no—
97C22×C8×C53D412yes—
98C22×C8×C53D412yes—
99C2×C42×C53—21no—
100C2×C42×C53—21no—
101C2×C42×C53—21no—
102C2×C42×C53—21no—
103C2×C42×C53—21no—
104C2×C42×C53—21no—
105C24×C53C22×C411yescharacteristic
106C23×D53—21no—
107C23×D53—21no—
108C23×D53—21no—
109C23×D53—21no—
110C23×D53—21no—
111C23×D53—21no—
112C23×D53—21no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53C4⋊C412yes—
119C23×D53C2×C812yes—
120C23×D53M1612yes—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—21no—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53C2×C812yes—
134C22×C4×C53M1612yes—
135C22×C4×C53C2×D411yescharacteristic
136C22×C4×C53C2×D411yescharacteristic
137C22×C4×C53C2×D411yescharacteristic
138C22×C4×C53C2×D411yescharacteristic
139C22×C4×C53C2×D411yescharacteristic
140C22×C4×C53C2×D411yescharacteristic
141C22×C4×C53C2×D411yescharacteristic
142C22×C4×C53C2×Q811yescharacteristic
143C22×C4×C53#4111yescharacteristic
144C22×C4×C53#4111yescharacteristic
145C22×C4×C53#4111yescharacteristic
146C22×C4×C53#4111yescharacteristic
147C22×C4×C53#4111yescharacteristic
148C22×C4×C53#4111yescharacteristic
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53C22⋊C412yes—
166C22×Dic53C22⋊C412yes—
167C22×Dic53C4⋊C412yes—
168C22×Dic53C2×C812yes—
169C22×Dic53M1612yes—
170C2×C4×D53—22no—
171C2×C4×D53—22no—
172C2×C4×D53—22no—
173C2×C4×D53—22no—
174C2×C4×D53—22no—
175C2×C4×D53—22no—
176C2×C4×D53—22no—
177C2×C4×D53—22no—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—22no—
181C2×C4×D53—22no—
182C2×C4×D53—41no—
183C2×C4×D53—41no—
184C2×C4×D53—41no—
185C2×C4×D53—41no—
186C2×C4×D53—41no—
187C2×C4×D53—41no—
188C2×C4×D53—41no—
189C2×C4×D53—41no—
190C2×C4×D53—41no—
191C2×C4×D53—41no—
192C2×C4×D53—41no—
193C2×C4×D53—41no—
194C2×C4×D53—41no—
195C2×C4×D53—41no—
196C2×C4×D53—41no—
197C2×C4×D53—41no—
198C2×C8×C53—22no—
199C2×C8×C53—22no—
200C2×C8×C53—22no—
201C2×C8×C53—22no—
202C2×C8×C53—22no—
203C2×C8×C53—22no—
204C2×C8×C53—41no—
205C2×C8×C53—41no—
206C2×C8×C53—41no—
207C2×C8×C53—41no—
208C2×C8×C53—41no—
209C2×C8×C53—41no—
210C2×C8×C53—41no—
211C2×C8×C53—41no—
212C42×C53—41no—
213C42×C53—41no—
214C42×C53—41no—
215C42×C53—41no—
216#11719921—28no—
217#11719921—28no—
218C4×Dic53—22no—
219C4×Dic53—22no—
220C4×Dic53—22no—
221C4×Dic53—22no—
222C2×#88322—22no—
223C2×#88322—22no—
224C2×#88322—22no—
225C2×#88322—22no—
226C2×#88322—22no—
227C2×#88322—22no—
228C2×#88322—41no—
229C2×#88322—41no—
230C2×#88322—41no—
231C2×#88322—41no—
232C2×#88322—41no—
233C2×#88322—41no—
234C2×#88322—41no—
235C2×#88322—41no—
236C23×C53C2×C22⋊C411yescharacteristic
237C23×C53C2×C4⋊C411yescharacteristic
238C23×C53#11711yescharacteristic
239C23×C53C4×D411yescharacteristic
240C23×C53C4×D411yescharacteristic
241C23×C53C4×D411yescharacteristic
242C23×C53C4×D411yescharacteristic
243C23×C53C22×C811yescharacteristic
244C23×C53C2×M1611yescharacteristic
245C23×C53C2×M1611yescharacteristic
246C23×C53C2×M1611yescharacteristic
247C23×C53#13111yescharacteristic
248C23×C53#13111yescharacteristic
249C23×C53#13111yescharacteristic
250C23×C53#13111yescharacteristic
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—41no—
274C22×D53—41no—
275C22×D53—41no—
276C22×D53—41no—
277C22×D53—41no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53—41no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—41no—
285C22×D53C4⋊C814yescomplemented
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53#12011yescharacteristic
301C2×C4×C53#12011yescharacteristic
302C2×C4×C53#12011yescharacteristic
303C2×C4×C53#12111yescharacteristic
304C2×C4×C53#12111yescharacteristic
305C2×C4×C53#12111yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12111yescharacteristic
308C2×C4×C53#12111yescharacteristic
309C2×C4×C53#12111yescharacteristic
310C2×C4×C53#12111yescharacteristic
311C2×C4×C53C22⋊Q811yescharacteristic
312C2×C4×C53C22⋊Q811yescharacteristic
313C2×C4×C53C22⋊Q811yescharacteristic
314C2×C4×C53C22⋊Q811yescharacteristic
315C2×C4×C53C22⋊Q811yescharacteristic
316C2×C4×C53C22⋊Q811yescharacteristic
317C2×C4×C53#12311yescharacteristic
318C2×C4×C53#12311yescharacteristic
319C2×C4×C53#12311yescharacteristic
320C2×C4×C53#12311yescharacteristic
321C2×C4×C53#12311yescharacteristic
322C2×C4×C53#12411yescharacteristic
323C2×C4×C53#12411yescharacteristic
324C2×C4×C53#12411yescharacteristic
325C2×C4×C53#12611yescharacteristic
326C2×C4×C53#12611yescharacteristic
327C2×C4×C53#12711yescharacteristic
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53C22⋊C814yescomplemented
349C4×D53—42no—
350C4×D53—42no—
351C4×D53—42no—
352C4×D53—42no—
353C4×D53—42no—
354C4×D53—42no—
355C4×D53—42no—
356C4×D53—42no—
357C8×C53—42no—
358C8×C53—42no—
359#88322—42no—
360#88322—42no—
361#11042—531nomaximal, Sylow
362C22×C53#38011yescharacteristic
363C22×C53#38511yescharacteristic
364C22×C53#38511yescharacteristic
365C22×C53#38611yescharacteristic
366C22×C53#38811yescharacteristic
367C22×C53#38811yescharacteristic
368C22×C53#39011yescharacteristic
369C22×C53C2×C22⋊C811yescharacteristic
370C22×C53#40711yescharacteristic
371C22×C53#40811yescharacteristic
372C22×C53#40811yescharacteristic
373C22×C53C2×C4⋊C811yescharacteristic
374C22×C53#42311yescharacteristic
375C22×C53#42411yescharacteristic
376C22×C53#42411yescharacteristic
377C22×C53#43111yescharacteristic
378C22×C53#43211yescharacteristic
379C22×C53#43311yescharacteristic
380C22×C53#43311yescharacteristic
381C22×C53C8×D411yescharacteristic
382C22×C53C8×D411yescharacteristic
383C22×C53C8×D411yescharacteristic
384C22×C53C8×D411yescharacteristic
385C22×C53#43511yescharacteristic
386C22×C53#43511yescharacteristic
387C22×C53#43511yescharacteristic
388C22×C53#43511yescharacteristic
389C22×C53#43511yescharacteristic
390C22×C53#43511yescharacteristic
391C22×C53#43511yescharacteristic
392C22×C53#43511yescharacteristic
393C22×C53#43611yescharacteristic
394C22×C53#43611yescharacteristic
395C22×C53#43611yescharacteristic
396C22×C53#43611yescharacteristic
397C2×D53—24no—
398C2×D53—24no—
399C2×D53—24no—
400C2×D53—42no—
401C2×D53—42no—
402C2×D53—42no—
403C2×D53—42no—
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—42no—
408C2×D53—42no—
409C2×D53—42no—
410C2×D53—42no—
411C2×D53—42no—
412C4×C53—42no—
413C4×C53—42no—
414C4×C53#39211yescharacteristic
415C4×C53#39311yescharacteristic
416C4×C53#39411yescharacteristic
417C4×C53#39411yescharacteristic
418C4×C53#39611yescharacteristic
419C4×C53#39611yescharacteristic
420C4×C53#39711yescharacteristic
421C4×C53#39911yescharacteristic
422Dic53—24no—
423Dic53—42no—
424Dic53—42no—
425C22×C4⋊C8—531no—
426C22×C22⋊C8—531no—
427C22×C22⋊C8—531no—
428C2×C4×C22⋊C4—531no—
429C2×#336—531no—
430C2×#336—531no—
431C2×#336D5311yescharacteristic, complemented
432C2×C53#143911yescharacteristic
433C2×C53#179711yescharacteristic
434C2×C53#179811yescharacteristic
435C2×C53#185011yescharacteristic
436C2×C53#185011yescharacteristic
437C2×C53#185111yescharacteristic
438C2×C53#185111yescharacteristic
439C2×C53#186911yescharacteristic
440C2×C53#187011yescharacteristic
441C2×C53#192311yescharacteristic
442C2×C53#192311yescharacteristic
443C2×C53#192411yescharacteristic
444C2×C53#192411yescharacteristic
445C2×C53#195411yescharacteristic
446C2×C53#195511yescharacteristic
447D53—44no—
448C24×C4—531no—
449C23×C8—531no—
450C23×C8—531no—
451C23×C8C2×D5311yescharacteristic
452C23×C8C2×D5311yescharacteristic
453C22×C22⋊C4—531no—
454C22×C22⋊C4—531no—
455C22×C42—531no—
456C22×C42C2×D5311yescharacteristic
457C2×C4⋊C8—1062no—
458C2×C4⋊C8—1062no—
459C2×C4⋊C8—1062no—
460C2×C22⋊C8—1062no—
461C2×C22⋊C8—1062no—
462C2×C22⋊C8—1062no—
463C2×C22⋊C8—1062no—
464C2×C22⋊C8—1062no—
465C2×C22⋊C8—1062no—
466C4×C22⋊C4—1062no—
467C4×C22⋊C4—1062no—
468C2×#95—531no—
469C2×#95—531no—
470#336—22no—
471#336—1062no—
472#336—1062no—
473C53#1104211yescharacteristic, complemented, Sylow
474C25—531no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—531no—
478C23×C4—532no—
479C23×C4—532no—
480C23×C4—1061no—
481C23×C4—1061no—
482C23×C4—1061no—
483C23×C4—1061no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4—1061no—
488C23×C4—1061no—
489C23×C4—1061no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4C4×D5311yescharacteristic
493C23×C4C4×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—21no—
503C22×C8—21no—
504C22×C8—21no—
505C22×C8—21no—
506C22×C8—21no—
507C22×C8—532no—
508C22×C8—532no—
509C22×C8—1061no—
510C22×C8—1061no—
511C22×C8—1061no—
512C22×C8—1061no—
513C22×C8—1061no—
514C22×C8—1061no—
515C22×C8—1061no—
516C22×C8—1061no—
517C22×C8—1061no—
518C22×C8—1061no—
519C22×C8—1061no—
520C22×C8—1061no—
521C22×C8D21212yes—
522C22×C8C22⋊D5312yes—
523C2×C22⋊C4—534no—
524C2×C22⋊C4—1062no—
525C2×C22⋊C4—1062no—
526C2×C22⋊C4—1062no—
527C2×C22⋊C4—1062no—
528C2×C22⋊C4—1062no—
529C2×C42—21no—
530C2×C42—21no—
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42—21no—
535C2×C42—532no—
536C2×C42—532no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42—1061no—
540C2×C42—1061no—
541C4⋊C8—1068no—
542C22⋊C8—1068no—
543C22⋊C8—1068no—
544#95—1062no—
545#95—1062no—
546C24—532no—
547C24—532no—
548C24—532no—
549C24—1061no—
550C24—1061no—
551C24—1061no—
552C24—1061no—
553C24—1061no—
554C24—1061no—
555C24—1061no—
556C24—1061no—
557C24—1061no—
558C24—1061no—
559C24—1061no—
560C24—1061no—
561C24C2×C4×D5311yescharacteristic
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—532no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—2121no—
608C22×C4—2121no—
609C22×C4—2121no—
610C22×C4—2121no—
611C22×C4—2121no—
612C22×C4—2121no—
613C22×C4—2121no—
614C22×C4—2121no—
615C22×C4—2121no—
616C22×C4—2121no—
617C22×C4—2121no—
618C22×C4—2121no—
619C22×C4—2121no—
620C22×C4—2121no—
621C22×C4—2121no—
622C22×C4—2121no—
623C22×C4C8×D5312yes—
624C22×C4#1171991212yes—
625C22×C4C2×D21211yescharacteristic
626C22×C4#1171994511yescharacteristic
627C22×C4#1171994511yescharacteristic
628C22×C4#1171994511yescharacteristic
629C22×C4#1171994511yescharacteristic
630C22×C4D4×D5311yescharacteristic
631C22×C4D4×D5311yescharacteristic
632C22×C4D4×D5311yescharacteristic
633C22×C4D4×D5311yescharacteristic
634C22×C4D4×D5311yescharacteristic
635C22×C4#1171994711yescharacteristic
636C22×C4Q8×D5311yescharacteristic
637C22×C4#1171994911yescharacteristic
638C22×C4C2×C22⋊D5311yescharacteristic
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—22no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—41no—
648C2×C8—41no—
649C2×C8—41no—
650C2×C8—41no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—1062no—
654C2×C8—1062no—
655C2×C8—1062no—
656C2×C8—1062no—
657C2×C8—1062no—
658C2×C8—1062no—
659C2×C8—2121no—
660C2×C8—2121no—
661C2×C8—2121no—
662C2×C8—2121no—
663C2×C8—2121no—
664C2×C8—2121no—
665C2×C8—2121no—
666C2×C8—2121no—
667C22⋊C4—1068no—
668C22⋊C4—1068no—
669C42—41no—
670C42—41no—
671C42—41no—
672C42—41no—
673C42—1062no—
674C42—1062no—
675C42—1062no—
676C42—1062no—
677C23—534no—
678C23—1062no—
679C23—1062no—
680C23—1062no—
681C23—1062no—
682C23—1062no—
683C23—1062no—
684C23—1062no—
685C23—1062no—
686C23—1062no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—2121no—
697C23—2121no—
698C23—2121no—
699C23—2121no—
700C23—2121no—
701C23—2121no—
702C23—2121no—
703C23—2121no—
704C23—2121no—
705C23—2121no—
706C23—2121no—
707C23—2121no—
708C23—2121no—
709C23—2121no—
710C23—2121no—
711C23—2121no—
712C23C22⋊C4×D5311yescharacteristic
713C23C4⋊C4×D5311yescharacteristic
714C23#1313317411yescharacteristic
715C23#1313317711yescharacteristic
716C23C4×C22⋊D5311yescharacteristic
717C23#1313317911yescharacteristic
718C23C4×D21211yescharacteristic
719C23C2×C8×D5311yescharacteristic
720C23M16×D5311yescharacteristic
721C23M16×D5311yescharacteristic
722C23C2×#1171991211yescharacteristic
723C23#1313322311yescharacteristic
724C23#1313322311yescharacteristic
725C23#1313322511yescharacteristic
726C23#1313322511yescharacteristic
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—534no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—2121no—
755C2×C4—2121no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4—2122no—
765C2×C4—2122no—
766C2×C4—2122no—
767C2×C4—2122no—
768C2×C4—2122no—
769C2×C4—2122no—
770C2×C4#1313318511yescharacteristic
771C2×C4#1313318711yescharacteristic
772C2×C4#1313318711yescharacteristic
773C2×C4#1313318911yescharacteristic
774C2×C4#1313319011yescharacteristic
775C2×C4#1313319011yescharacteristic
776C2×C4#1313319011yescharacteristic
777C2×C4#1313319011yescharacteristic
778C2×C4#1313319011yescharacteristic
779C2×C4#1313319111yescharacteristic
780C2×C4#1313319211yescharacteristic
781C2×C4#1313319311yescharacteristic
782C2×C4#1313319511yescharacteristic
783C2×C4#1313319511yescharacteristic
784C2×C4#1313319511yescharacteristic
785C2×C4#1313319511yescharacteristic
786C2×C4#1313319711yescharacteristic
787C2×C4#1313319911yescharacteristic
788C2×C4#1313320011yescharacteristic
789C2×C4#1313320211yescharacteristic
790C2×C4#1313320211yescharacteristic
791C2×C4#1313320211yescharacteristic
792C2×C4#1313320311yescharacteristic
793C2×C4#1313320311yescharacteristic
794C2×C4#1313320511yescharacteristic
795C2×C4#1313321111yescharacteristic
796C2×C4#1313321211yescharacteristic
797C2×C4#1313321311yescharacteristic
798C8—42no—
799C8—42no—
800C8—2122no—
801C8—2122no—
802C22—1064no—
803C22—1064no—
804C22—1064no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2122no—
811C22—2122no—
812C22—2122no—
813C22—2122no—
814C22—2122no—
815C22—2122no—
816C22—2122no—
817C22#1681048211yescharacteristic
818C22#1681049411yescharacteristic
819C22#1681049711yescharacteristic
820C22#1681050111yescharacteristic
821C22#1681051211yescharacteristic
822C22#1681051411yescharacteristic
823C22#1681052311yescharacteristic
824C22C22⋊C8×D5311yescharacteristic
825C22#1681058511yescharacteristic
826C22#1681058811yescharacteristic
827C22#1681058811yescharacteristic
828C22C4⋊C8×D5311yescharacteristic
829C22#1681064511yescharacteristic
830C22#1681064811yescharacteristic
831C22#1681064811yescharacteristic
832C22#1681067411yescharacteristic
833C22#1681067811yescharacteristic
834C22#1681068211yescharacteristic
835C22#1681068511yescharacteristic
836C22#1681068611yescharacteristic
837C22C8×C22⋊D5311yescharacteristic
838C22#1681068811yescharacteristic
839C22C8×D21211yescharacteristic
840C22#1681069111yescharacteristic
841C22#1681069211yescharacteristic
842C22#1681069311yescharacteristic
843C22#1681069311yescharacteristic
844C22#1681069411yescharacteristic
845C22#1681069611yescharacteristic
846C22#1681069611yescharacteristic
847C22#1681069711yescharacteristic
848C22#1681069811yescharacteristic
849C22#1681069911yescharacteristic
850C22#1681070011yescharacteristic
851C22#1681070211yescharacteristic
852C4—42no—
853C4—42no—
854C4—1064no—
855C4—2122no—
856C4—2122no—
857C4#1681053211yescharacteristic
858C4#1681053611yescharacteristic
859C4#1681053811yescharacteristic
860C4#1681054111yescharacteristic
861C4#1681054511yescharacteristic
862C4#1681054711yescharacteristic
863C4#1681055211yescharacteristic
864C4#1681055811yescharacteristic
865C2—2124no—
866C2#2027295911yescharacteristic
867C2#2027469411yescharacteristic
868C2#2027469811yescharacteristic
869C2#2027489111yescharacteristic
870C2#2027489411yescharacteristic
871C2#2027489611yescharacteristic
872C2#2027489911yescharacteristic
873C2#2027500611yescharacteristic
874C2#2027501111yescharacteristic
875C2#2027531911yescharacteristic
876C2#2027532111yescharacteristic
877C2#2027532611yescharacteristic
878C2#2027532811yescharacteristic
879C2#2027550711yescharacteristic
880C2#2027551111yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D53
commutatorC23×C53C22×C8
FittingC2×C53×#336C2
socleC24×C53C22×C4
prime radicalC24×D53C2×C4
cosocleC23×C4×C53C23
hypercenterC2×#336D53
hypocenterC53#11042
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
1. C22×#13133146C2semidirect
5. C2×#16810378C2semidirect
6. C2×#16810377C2semidirect
7. C2×C53×#336C2semidirect
70. C2×#11719921C8semidirect
285. C22×D53C4⋊C8semidirect
348. C2×Dic53C22⋊C8semidirect
431. C2×#336D53semidirect
473. C53#11042semidirect

Maximal subgroups

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

subgroupindex
C22×#131331462
C22×#131331292
C2×C4×#117199212
C2×#168103782
C2×#168103772
C2×C53×#3362
#1104253