Finite Group Databasebeta

← #27291660

Subgroups — #27291660

Order 13568.

1206 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133129C211yesmaximal, characteristic
2C22×#13133129C211yesmaximal, characteristic
3C2×C4×#11719921C211yesmaximal, characteristic
4C2×#16810378C211yesmaximal, characteristic, complemented
5C2×#16810377C211yesmaximal, 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×#13133129—22no—
15C2×#13133129—22no—
16C2×#13133129—22no—
17C2×#13133129—22no—
18C2×#13133129—22no—
19C2×#13133129—22no—
20C4×#11719921—22no—
21C4×#11719921—22no—
22C2×#13133124C411yescharacteristic
23C2×#13133124C411yescharacteristic
24#16810378—22no—
25#16810377—22no—
26#16810377—22no—
27C23×C8×C53C2211yescharacteristic
28C23×C8×C53C2211yescharacteristic
29C22×C42×C53C2211yescharacteristic
30C53×#336—22no—
31C24×D53C2×C411yescharacteristic
32C23×Dic53C2×C411yescharacteristic
33C23×Dic53C2×C411yescharacteristic
34C23×Dic53C2×C411yescharacteristic
35C22×C4×D53—21no—
36C22×C4×D53—21no—
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×D53D412yes—
48C22×C4×D53D412yes—
49C22×#88322—21no—
50C22×#88322—21no—
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×#88322D412yes—
62C22×#88322D412yes—
63C2×#11719921—22no—
64C2×#11719921—22no—
65C2×#11719921—22no—
66C2×#11719921—22no—
67C2×#11719921—22no—
68C2×#11719921C814yescomplemented
69C2×C4×Dic53—21no—
70C2×C4×Dic53—21no—
71C2×C4×Dic53—21no—
72C2×C4×Dic53—21no—
73C2×C4×Dic53—21no—
74C2×C4×Dic53—21no—
75#13133129—28no—
76#13133129—28no—
77#13133124—22no—
78#13133124—22no—
79C23×C4×C53C2×C411yescharacteristic
80C23×C4×C53C2×C411yescharacteristic
81C23×C4×C53C2311yescharacteristic
82C22×C8×C53—21no—
83C22×C8×C53—21no—
84C22×C8×C53—21no—
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×C53D412yes—
95C22×C8×C53D412yes—
96C2×C42×C53—21no—
97C2×C42×C53—21no—
98C2×C42×C53—21no—
99C2×C42×C53—21no—
100C2×C42×C53—21no—
101C2×C42×C53—21no—
102C24×C53C22×C411yescharacteristic
103C23×D53—21no—
104C23×D53—21no—
105C23×D53—21no—
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×D53C22⋊C412yes—
116C23×D53C2×C812yes—
117C23×D53M1612yes—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—21no—
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×C53C2×C812yes—
131C22×C4×C53M1612yes—
132C22×C4×C53C2×D411yescharacteristic
133C22×C4×C53C2×D411yescharacteristic
134C22×C4×C53C2×D411yescharacteristic
135C22×C4×C53C2×D411yescharacteristic
136C22×C4×C53C2×D411yescharacteristic
137C22×C4×C53C2×D411yescharacteristic
138C22×C4×C53#4111yescharacteristic
139C22×C4×C53#4111yescharacteristic
140C22×C4×C53#4111yescharacteristic
141C22×C4×C53#4111yescharacteristic
142C22×C4×C53#4111yescharacteristic
143C22×C4×C53#4111yescharacteristic
144C22×C4×C53#4111yescharacteristic
145C22×C4×C53#4111yescharacteristic
146C22×Dic53—21no—
147C22×Dic53—21no—
148C22×Dic53—21no—
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×Dic53C22⋊C412yes—
165C22×Dic53C2×C812yes—
166C22×Dic53M1612yes—
167C2×C4×D53—22no—
168C2×C4×D53—22no—
169C2×C4×D53—22no—
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—41no—
180C2×C4×D53—41no—
181C2×C4×D53—41no—
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×C8×C53—22no—
196C2×C8×C53—22no—
197C2×C8×C53—22no—
198C2×C8×C53—22no—
199C2×C8×C53—22no—
200C2×C8×C53—22no—
201C2×C8×C53—41no—
202C2×C8×C53—41no—
203C2×C8×C53—41no—
204C2×C8×C53—41no—
205C2×C8×C53—41no—
206C2×C8×C53—41no—
207C2×C8×C53—41no—
208C2×C8×C53—41no—
209C42×C53—41no—
210C42×C53—41no—
211C42×C53—41no—
212C42×C53—41no—
213#11719921—28no—
214#11719921—28no—
215C4×Dic53—41no—
216C4×Dic53—41no—
217C4×Dic53—41no—
218C4×Dic53—41no—
219C2×#88322—22no—
220C2×#88322—22no—
221C2×#88322—22no—
222C2×#88322—22no—
223C2×#88322—22no—
224C2×#88322—22no—
225C2×#88322—41no—
226C2×#88322—41no—
227C2×#88322—41no—
228C2×#88322—41no—
229C2×#88322—41no—
230C2×#88322—41no—
231C2×#88322—41no—
232C2×#88322—41no—
233C23×C53C2×C22⋊C411yescharacteristic
234C23×C53#11711yescharacteristic
235C23×C53#11711yescharacteristic
236C23×C53C4×D411yescharacteristic
237C23×C53C4×D411yescharacteristic
238C23×C53C4×D411yescharacteristic
239C23×C53C4×D411yescharacteristic
240C23×C53C22×C811yescharacteristic
241C23×C53C2×M1611yescharacteristic
242C23×C53C2×M1611yescharacteristic
243C23×C53C2×M1611yescharacteristic
244C23×C53#13111yescharacteristic
245C23×C53#13111yescharacteristic
246C23×C53#13111yescharacteristic
247C23×C53#13111yescharacteristic
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
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—41no—
267C22×D53—41no—
268C22×D53—41no—
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×D53C22⋊C814yes—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53#12011yescharacteristic
298C2×C4×C53#12011yescharacteristic
299C2×C4×C53#12111yescharacteristic
300C2×C4×C53#12111yescharacteristic
301C2×C4×C53#12111yescharacteristic
302C2×C4×C53#12111yescharacteristic
303C2×C4×C53#12111yescharacteristic
304C2×C4×C53#12111yescharacteristic
305C2×C4×C53#12111yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12311yescharacteristic
308C2×C4×C53#12311yescharacteristic
309C2×C4×C53#12311yescharacteristic
310C2×C4×C53#12311yescharacteristic
311C2×C4×C53#12311yescharacteristic
312C2×C4×C53#12311yescharacteristic
313C2×C4×C53#12311yescharacteristic
314C2×C4×C53#12311yescharacteristic
315C2×C4×C53#12311yescharacteristic
316C2×C4×C53#12311yescharacteristic
317C2×C4×C53#12411yescharacteristic
318C2×C4×C53#12411yescharacteristic
319C2×C4×C53#12411yescharacteristic
320C2×C4×C53#12411yescharacteristic
321C2×C4×C53#12611yescharacteristic
322C2×C4×C53#12611yescharacteristic
323C2×C4×C53#12611yescharacteristic
324C2×C4×C53#12611yescharacteristic
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C4×D53—42no—
347C4×D53—42no—
348C4×D53—42no—
349C4×D53—42no—
350C4×D53—42no—
351C4×D53—42no—
352C4×D53—42no—
353C4×D53—42no—
354C8×C53—42no—
355C8×C53—42no—
356#88322—42no—
357#88322—42no—
358#11147—531nomaximal, Sylow
359C22×C53#38111yescharacteristic
360C22×C53#38611yescharacteristic
361C22×C53#38611yescharacteristic
362C22×C53#38811yescharacteristic
363C22×C53#38811yescharacteristic
364C22×C53#38811yescharacteristic
365C22×C53#38811yescharacteristic
366C22×C53C2×C22⋊C811yescharacteristic
367C22×C53#40711yescharacteristic
368C22×C53#40811yescharacteristic
369C22×C53#40811yescharacteristic
370C22×C53#43111yescharacteristic
371C22×C53#43111yescharacteristic
372C22×C53#43211yescharacteristic
373C22×C53#43211yescharacteristic
374C22×C53#43311yescharacteristic
375C22×C53#43311yescharacteristic
376C22×C53#43311yescharacteristic
377C22×C53#43311yescharacteristic
378C22×C53C8×D411yescharacteristic
379C22×C53C8×D411yescharacteristic
380C22×C53C8×D411yescharacteristic
381C22×C53C8×D411yescharacteristic
382C22×C53#43511yescharacteristic
383C22×C53#43511yescharacteristic
384C22×C53#43511yescharacteristic
385C22×C53#43511yescharacteristic
386C22×C53#43511yescharacteristic
387C22×C53#43511yescharacteristic
388C22×C53#43511yescharacteristic
389C22×C53#43511yescharacteristic
390C22×C53#43611yescharacteristic
391C22×C53#43611yescharacteristic
392C22×C53#43611yescharacteristic
393C22×C53#43611yescharacteristic
394C2×D53—24no—
395C2×D53—24no—
396C2×D53—24no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
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—
409C4×C53—42no—
410C4×C53—42no—
411C4×C53#39411yescharacteristic
412C4×C53#39411yescharacteristic
413C4×C53#39411yescharacteristic
414C4×C53#39411yescharacteristic
415C4×C53#39711yescharacteristic
416C4×C53#39711yescharacteristic
417C4×C53#39711yescharacteristic
418C4×C53#39711yescharacteristic
419Dic53—42no—
420Dic53—42no—
421Dic53—42no—
422C22×C22⋊C8—531no—
423C22×C22⋊C8—531no—
424C2×C4×C22⋊C4—531no—
425C2×#336—531no—
426C2×#336—531no—
427C2×#336—531no—
428C2×#336D5311yescharacteristic, complemented
429C2×C53#144011yescharacteristic
430C2×C53#181711yescharacteristic
431C2×C53#181811yescharacteristic
432C2×C53#186911yescharacteristic
433C2×C53#186911yescharacteristic
434C2×C53#187011yescharacteristic
435C2×C53#187011yescharacteristic
436C2×C53#192311yescharacteristic
437C2×C53#192311yescharacteristic
438C2×C53#192311yescharacteristic
439C2×C53#192311yescharacteristic
440C2×C53#192411yescharacteristic
441C2×C53#192411yescharacteristic
442C2×C53#192411yescharacteristic
443C2×C53#192411yescharacteristic
444D53—44no—
445C24×C4—531no—
446C23×C8—531no—
447C23×C8—531no—
448C23×C8C2×D5311yescharacteristic
449C23×C8C2×D5311yescharacteristic
450C22×C22⋊C4—531no—
451C22×C22⋊C4—531no—
452C22×C42—531no—
453C22×C42C2×D5311yescharacteristic
454C2×C22⋊C8—1062no—
455C2×C22⋊C8—1062no—
456C2×C22⋊C8—1062no—
457C2×C22⋊C8—1062no—
458C2×C22⋊C8—1062no—
459C2×C22⋊C8—1062no—
460C4×C22⋊C4—1062no—
461C4×C22⋊C4—1062no—
462C2×#95—531no—
463C2×#95—531no—
464#336—22no—
465#336—1062no—
466#336—1062no—
467#336—1062no—
468C53#1114711yescharacteristic, complemented, Sylow
469C25—531no—
470C23×C4—531no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—532no—
474C23×C4—532no—
475C23×C4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4—1061no—
482C23×C4—1061no—
483C23×C4—1061no—
484C23×C4—1061no—
485C23×C4—1061no—
486C23×C4—1061no—
487C23×C4C4×D5311yescharacteristic
488C23×C4C4×D5311yescharacteristic
489C23×C4C22×D5311yescharacteristic
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—21no—
500C22×C8—21no—
501C22×C8—21no—
502C22×C8—532no—
503C22×C8—532no—
504C22×C8—1061no—
505C22×C8—1061no—
506C22×C8—1061no—
507C22×C8—1061no—
508C22×C8—1061no—
509C22×C8—1061no—
510C22×C8—1061no—
511C22×C8—1061no—
512C22×C8—1061no—
513C22×C8—1061no—
514C22×C8—1061no—
515C22×C8—1061no—
516C22×C8D21212yes—
517C22×C8C22⋊D5312yes—
518C2×C22⋊C4—534no—
519C2×C22⋊C4—1062no—
520C2×C22⋊C4—1062no—
521C2×C22⋊C4—1062no—
522C2×C22⋊C4—1062no—
523C2×C22⋊C4—1062no—
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—1061no—
531C2×C42—1061no—
532C2×C42—1061no—
533C2×C42—1061no—
534C2×C42—1061no—
535C2×C42—1061no—
536C22⋊C8—1068no—
537C22⋊C8—1068no—
538#95—1062no—
539#95—1062no—
540C24—532no—
541C24—532no—
542C24—532no—
543C24—1061no—
544C24—1061no—
545C24—1061no—
546C24—1061no—
547C24—1061no—
548C24—1061no—
549C24—1061no—
550C24—1061no—
551C24—1061no—
552C24—1061no—
553C24—1061no—
554C24—1061no—
555C24C2×C4×D5311yescharacteristic
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
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—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—2121no—
602C22×C4—2121no—
603C22×C4—2121no—
604C22×C4—2121no—
605C22×C4—2121no—
606C22×C4—2121no—
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×C4C8×D5312yes—
618C22×C4#1171991212yes—
619C22×C4C2×D21211yescharacteristic
620C22×C4#1171994511yescharacteristic
621C22×C4#1171994511yescharacteristic
622C22×C4#1171994511yescharacteristic
623C22×C4#1171994511yescharacteristic
624C22×C4D4×D5311yescharacteristic
625C22×C4D4×D5311yescharacteristic
626C22×C4D4×D5311yescharacteristic
627C22×C4D4×D5311yescharacteristic
628C22×C4#1171994711yescharacteristic
629C22×C4#1171994711yescharacteristic
630C22×C4#1171994911yescharacteristic
631C22×C4#1171994911yescharacteristic
632C22×C4C2×C22⋊D5311yescharacteristic
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—41no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—41no—
646C2×C8—41no—
647C2×C8—1062no—
648C2×C8—1062no—
649C2×C8—1062no—
650C2×C8—1062no—
651C2×C8—1062no—
652C2×C8—1062no—
653C2×C8—2121no—
654C2×C8—2121no—
655C2×C8—2121no—
656C2×C8—2121no—
657C2×C8—2121no—
658C2×C8—2121no—
659C2×C8—2121no—
660C2×C8—2121no—
661C22⋊C4—1068no—
662C22⋊C4—1068no—
663C42—41no—
664C42—41no—
665C42—41no—
666C42—41no—
667C42—2121no—
668C42—2121no—
669C42—2121no—
670C42—2121no—
671C23—534no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—1062no—
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—2121no—
691C23—2121no—
692C23—2121no—
693C23—2121no—
694C23—2121no—
695C23—2121no—
696C23—2121no—
697C23—2121no—
698C23—2121no—
699C23—2121no—
700C23—2121no—
701C23—2121no—
702C23—2121no—
703C23—2121no—
704C23—2121no—
705C23—2121no—
706C23C22⋊C4×D5311yescharacteristic
707C23#1313317411yescharacteristic
708C23#1313317511yescharacteristic
709C23#1313317711yescharacteristic
710C23C4×C22⋊D5311yescharacteristic
711C23#1313317911yescharacteristic
712C23C4×D21211yescharacteristic
713C23C2×C8×D5311yescharacteristic
714C23M16×D5311yescharacteristic
715C23M16×D5311yescharacteristic
716C23C2×#1171991211yescharacteristic
717C23#1313322311yescharacteristic
718C23#1313322311yescharacteristic
719C23#1313322511yescharacteristic
720C23#1313322511yescharacteristic
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2121no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4—2122no—
764C2×C4#1313318511yescharacteristic
765C2×C4#1313318711yescharacteristic
766C2×C4#1313318811yescharacteristic
767C2×C4#1313318911yescharacteristic
768C2×C4#1313319011yescharacteristic
769C2×C4#1313319011yescharacteristic
770C2×C4#1313319011yescharacteristic
771C2×C4#1313319111yescharacteristic
772C2×C4#1313319211yescharacteristic
773C2×C4#1313319211yescharacteristic
774C2×C4#1313319911yescharacteristic
775C2×C4#1313319911yescharacteristic
776C2×C4#1313319911yescharacteristic
777C2×C4#1313320011yescharacteristic
778C2×C4#1313320111yescharacteristic
779C2×C4#1313320211yescharacteristic
780C2×C4#1313320211yescharacteristic
781C2×C4#1313320211yescharacteristic
782C2×C4#1313320211yescharacteristic
783C2×C4#1313320211yescharacteristic
784C2×C4#1313320311yescharacteristic
785C2×C4#1313320311yescharacteristic
786C2×C4#1313320511yescharacteristic
787C2×C4#1313320611yescharacteristic
788C2×C4#1313321111yescharacteristic
789C2×C4#1313321211yescharacteristic
790C2×C4#1313321211yescharacteristic
791C2×C4#1313321211yescharacteristic
792C8—42no—
793C8—42no—
794C8—2122no—
795C8—2122no—
796C22—1064no—
797C22—1064no—
798C22—1064no—
799C22—2122no—
800C22—2122no—
801C22—2122no—
802C22—2122no—
803C22—2122no—
804C22—2122no—
805C22—2122no—
806C22—2122no—
807C22—2122no—
808C22—2122no—
809C22—2122no—
810C22—2122no—
811C22#1681048511yescharacteristic
812C22#1681049911yescharacteristic
813C22#1681050111yescharacteristic
814C22#1681051211yescharacteristic
815C22#1681051311yescharacteristic
816C22#1681051411yescharacteristic
817C22#1681051511yescharacteristic
818C22C22⋊C8×D5311yescharacteristic
819C22#1681058511yescharacteristic
820C22#1681058811yescharacteristic
821C22#1681058811yescharacteristic
822C22#1681067411yescharacteristic
823C22#1681067511yescharacteristic
824C22#1681067811yescharacteristic
825C22#1681067911yescharacteristic
826C22#1681068211yescharacteristic
827C22#1681068311yescharacteristic
828C22#1681068311yescharacteristic
829C22#1681068511yescharacteristic
830C22#1681068611yescharacteristic
831C22C8×C22⋊D5311yescharacteristic
832C22#1681068811yescharacteristic
833C22C8×D21211yescharacteristic
834C22#1681069111yescharacteristic
835C22#1681069211yescharacteristic
836C22#1681069311yescharacteristic
837C22#1681069311yescharacteristic
838C22#1681069411yescharacteristic
839C22#1681069611yescharacteristic
840C22#1681069611yescharacteristic
841C22#1681069711yescharacteristic
842C22#1681069811yescharacteristic
843C22#1681069911yescharacteristic
844C22#1681070011yescharacteristic
845C22#1681070211yescharacteristic
846C4—42no—
847C4—42no—
848C4—2122no—
849C4—2122no—
850C4—2122no—
851C4#1681053811yescharacteristic
852C4#1681053911yescharacteristic
853C4#1681054011yescharacteristic
854C4#1681054111yescharacteristic
855C4#1681054911yescharacteristic
856C4#1681055011yescharacteristic
857C4#1681055211yescharacteristic
858C4#1681055211yescharacteristic
859C2—2124no—
860C2#2027296311yescharacteristic
861C2#2027478211yescharacteristic
862C2#2027478511yescharacteristic
863C2#2027500411yescharacteristic
864C2#2027500611yescharacteristic
865C2#2027500911yescharacteristic
866C2#2027501111yescharacteristic
867C2#2027531911yescharacteristic
868C2#2027532011yescharacteristic
869C2#2027532111yescharacteristic
870C2#2027532211yescharacteristic
871C2#2027532611yescharacteristic
872C2#2027532711yescharacteristic
873C2#2027532811yescharacteristic
874C2#2027532911yescharacteristic
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#11147
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. C2×#16810378C2semidirect
5. C2×#16810377C2semidirect
6. C2×#16810377C2semidirect
7. C2×C53×#336C2semidirect
68. C2×#11719921C8semidirect
428. C2×#336D53semidirect
468. C53#11147semidirect

Maximal subgroups

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

subgroupindex
C22×#131331292
C2×C4×#117199212
C2×#168103782
C2×#168103772
C2×C53×#3362
#1114753