Finite Group Databasebeta

← #27395212

Subgroups — #27395212

Order 13568.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810699C211yesmaximal, characteristic, complemented
2C2×#16810591C211yesmaximal, characteristic, complemented
3#20277931C211yesmaximal, characteristic
4#20275513C211yesmaximal, characteristic, complemented
5#20275509C211yesmaximal, characteristic, complemented
6#20275328C211yesmaximal, characteristic, complemented
7#20275322C211yesmaximal, characteristic, complemented
8#20275322C211yesmaximal, characteristic, complemented
9#20275321C211yesmaximal, characteristic, complemented
10#20275011C211yesmaximal, characteristic, complemented
11#20275011C211yesmaximal, characteristic, complemented
12#20275005C211yesmaximal, characteristic, complemented
13#20274895C211yesmaximal, characteristic, complemented
14#20274626C211yesmaximal, characteristic, complemented
15C53×#1753C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C2×C4×D212C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic
21C2×C4×C22⋊D53C2211yescharacteristic
22#16810699—24no—
23C2×C4⋊#88322C2211yescharacteristic
24C2×C4⋊#88322C2211yescharacteristic
25C2×#13133146C2211yescharacteristic
26#16810591—24no—
27C2×C22⋊#88322C2211yescharacteristic
28C2×#13133129C2211yescharacteristic
29C2×#13133129C2211yescharacteristic
30C2×#13133129C2211yescharacteristic
31C2×#13133129C2211yescharacteristic
32C2×#13133129C2211yescharacteristic
33C2×#13133129C2211yescharacteristic
34C2×#13133129C2211yescharacteristic
35C2×#13133129C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40#16810544C411yescharacteristic
41#16810541C411yescharacteristic
42#16810539C411yescharacteristic
43#16810539C411yescharacteristic
44#16810536C411yescharacteristic
45#16810533C411yescharacteristic
46#16810532C411yescharacteristic
47#16810532C411yescharacteristic
48C4×#11719921C2211yescharacteristic
49C4×#11719921C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54C22×M16×C53C2211yescharacteristic
55C2×C22⋊C8×C53C2211yescharacteristic
56C2×#97×C53C2211yescharacteristic
57C2×C4×C8×C53C2211yescharacteristic
58C4×C22⋊C4×C53C2211yescharacteristic
59C53×#336C2211yescharacteristic
60C53×#336C2211yescharacteristic
61C2×#11719945—22no—
62C2×#11719945—22no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C22×Dic106C2×C411yescharacteristic
68C22×D212C2×C411yescharacteristic
69C22×D212C2×C411yescharacteristic
70C22×D212C2×C411yescharacteristic
71C22×C22⋊D53C2×C411yescharacteristic
72C22×C22⋊D53C2×C411yescharacteristic
73C22×C22⋊D53C2×C411yescharacteristic
74C22×C4×D53C2311yescharacteristic
75C22×C4×D53C2311yescharacteristic
76C22×C4×D53C2311yescharacteristic
77C2×#11719912—22no—
78C2×#11719912—41no—
79C2×#11719912—41no—
80C22×#88322—22no—
81C22×#88322—41no—
82C22×#88322—41no—
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C4×D212—41no—
88C4×D212—41no—
89C4×D212—41no—
90C4×D212—41no—
91C4×C22⋊D53—22no—
92C4×C22⋊D53—22no—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×#11719919C2×C411yescharacteristic
96C2×C22⋊Dic53C2×C411yescharacteristic
97C2×#11719921C2×C411yescharacteristic
98C2×#11719921C2×C411yescharacteristic
99C2×#11719921C2×C411yescharacteristic
100C2×#11719921C2×C411yescharacteristic
101C2×#11719921C2×C411yescharacteristic
102C2×#11719921C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×C4×Dic53C2311yescharacteristic
107C4⋊#88322—41no—
108C4⋊#88322—41no—
109#13133146—22no—
110C22⋊#88322—22no—
111#13133129—22no—
112#13133129—22no—
113#13133129—22no—
114#13133129—22no—
115#13133129—22no—
116#13133129—41no—
117#13133129—41no—
118#13133129—41no—
119#13133129—41no—
120#13133129—41no—
121#13133129—41no—
122C8×Dic53—22no—
123#13133124C2×C411yescharacteristic
124#13133124C2×C411yescharacteristic
125#13133124C2×C411yescharacteristic
126#13133124C2×C411yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C2×M16×C53—41no—
129C2×M16×C53—41no—
130C2×M16×C53D414yescomplemented
131C22×C8×C53C2311yescharacteristic
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C2×C22⋊C4×C53C2×C411yescharacteristic
136C2×C22⋊C4×C53C2×C411yescharacteristic
137C2×C42×C53C2311yescharacteristic
138C2×C42×C53C2311yescharacteristic
139C22⋊C8×C53—22no—
140#97×C53—41no—
141C4×C8×C53—41no—
142#95×C53C2×C411yescharacteristic
143#95×C53C2×C411yescharacteristic
144C24×C53C22×C411yescharacteristic
145C23×D53C22×C411yescharacteristic
146C23×D53C22×C411yescharacteristic
147C23×D53C22×C411yescharacteristic
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53C22×C411yescharacteristic
153C22×C4×C53C22×C411yescharacteristic
154C22×C4×C53C22×C411yescharacteristic
155C22×C4×C53C22×C411yescharacteristic
156C22×C4×C53C22×C411yescharacteristic
157C22×C4×C53C2×D412yes—
158C22×C4×C53#4112yes—
159C22×C4×C53C2411yescharacteristic
160C2×C22⋊D53—22no—
161C2×C22⋊D53—22no—
162C2×C22⋊D53—22no—
163C2×C22⋊D53—22no—
164C2×C22⋊D53—41no—
165C2×C22⋊D53—41no—
166C2×C22⋊D53—41no—
167C2×C22⋊D53—41no—
168C2×C22⋊D53—41no—
169C22×Dic53C22×C411yescharacteristic
170C22×Dic53C22×C411yescharacteristic
171C22×Dic53C22×C411yescharacteristic
172C22×Dic53C22×C411yescharacteristic
173C22×Dic53C22×C411yescharacteristic
174#11719945—44no—
175#11719945—44no—
176#11719945—44no—
177#11719945—44no—
178C2×D212—22no—
179C2×D212—22no—
180C2×D212—41no—
181C2×D212—41no—
182C2×D212—41no—
183C2×D212—41no—
184C2×D212—41no—
185C2×D212—41no—
186C2×D212—41no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—21no—
196C2×C4×D53—21no—
197C2×C4×D53—21no—
198C2×C4×D53—21no—
199C2×C4×D53—21no—
200C2×C4×D53—21no—
201C2×C4×D53—21no—
202C2×C4×D53—21no—
203C2×C4×D53—21no—
204C2×C4×D53—21no—
205C2×Dic106—22no—
206C2×Dic106—41no—
207C2×Dic106—41no—
208M16×C53—44no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—21no—
214C2×C8×C53—21no—
215C2×C8×C53—21no—
216C2×C8×C53—21no—
217C2×C8×C53—21no—
218C2×C8×C53—21no—
219C2×C8×C53C2×D412yes—
220C2×C8×C53C2×D412yes—
221C22⋊C4×C53—22no—
222C22⋊C4×C53—41no—
223C42×C53—21no—
224C42×C53—21no—
225C42×C53—21no—
226C42×C53—21no—
227C22⋊Dic53—22no—
228#11719921—22no—
229#11719921—22no—
230#11719921—22no—
231#11719921—22no—
232#11719921—41no—
233#11719921—41no—
234#11719921—41no—
235#11719921—41no—
236#11719921—41no—
237C4⋊Dic53—41no—
238C4⋊Dic53—41no—
239#11719919—22no—
240C4×Dic53—21no—
241C4×Dic53—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—44no—
255#11719912—44no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53C4×D412yes—
263C23×C53C23×C411yescharacteristic
264C22×D53—21no—
265C22×D53—21no—
266C22×D53—21no—
267C22×D53—21no—
268C22×D53—21no—
269C22×D53—21no—
270C22×D53—21no—
271C22×D53—21no—
272C22×D53—21no—
273C22×D53—21no—
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53—21no—
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—21no—
282C22×D53—21no—
283C22×D53—21no—
284C22×D53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53C4×D412yes—
303C2×C4×C53#13112yes—
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C2×C4×C53H(5,𝔽2)11yescharacteristic
309C2×C4×C53H(5,𝔽2)11yescharacteristic
310C22⋊D53—44no—
311C22⋊D53—44no—
312C22⋊D53—44no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323C2×Dic53—21no—
324C2×Dic53—21no—
325C2×Dic53—21no—
326C2×Dic53—21no—
327C2×Dic53#13112yes—
328D212—44no—
329D212—44no—
330D212—44no—
331C4×D53—41no—
332C4×D53—41no—
333C4×D53—41no—
334C4×D53—41no—
335C4×D53—41no—
336C4×D53—41no—
337C4×D53—41no—
338C4×D53—41no—
339C4×D53—41no—
340C4×D53—41no—
341C4×D53—41no—
342C4×D53—41no—
343Dic106—44no—
344C8×C53—22no—
345C8×C53—22no—
346C8×C53—41no—
347C8×C53—41no—
348#88322—41no—
349#88322—41no—
350#88322—41no—
351#88322—41no—
352#22039—531nomaximal, Sylow
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53C2×C4×D411yescharacteristic
361C22×C53#51811yescharacteristic
362C22×C53#51811yescharacteristic
363C22×C53C2×#13111yescharacteristic
364C22×C53C2×#13111yescharacteristic
365C22×C53#56811yescharacteristic
366C22×C53#56811yescharacteristic
367C2×D53—41no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—41no—
372C2×D53—41no—
373C2×D53—41no—
374C2×D53—41no—
375C2×D53—41no—
376C2×D53—41no—
377C2×D53—41no—
378C2×D53—41no—
379C2×D53—41no—
380C2×D53—41no—
381C2×D53—41no—
382C2×D53—41no—
383C2×D53—41no—
384C2×D53—41no—
385C2×D53—41no—
386C2×D53—41no—
387C2×D53—41no—
388C4×C53—22no—
389C4×C53—22no—
390C4×C53—41no—
391C4×C53—41no—
392C4×C53—41no—
393C4×C53#53411yescharacteristic
394C4×C53#53511yescharacteristic
395C4×C53#53811yescharacteristic
396C4×C53#53811yescharacteristic
397Dic53—22no—
398Dic53—41no—
399Dic53—41no—
400Dic53—41no—
401Dic53—41no—
402C2×#436—531no—
403C2×#408—531no—
404#2388—531no—
405#1955—531no—
406#1954—531no—
407#1924—531no—
408#1923—531no—
409#1923—531no—
410#1923—531no—
411#1870—531no—
412#1870—531no—
413#1869—531no—
414#1850—531no—
415#1780—531no—
416#1753D5311yescharacteristic, complemented
417C2×C53—42no—
418C2×C53#232111yescharacteristic
419C2×C53#293311yescharacteristic
420C2×C53#293511yescharacteristic
421C2×C53#297611yescharacteristic
422C2×C53#297811yescharacteristic
423C2×C53#297911yescharacteristic
424C2×C53#298111yescharacteristic
425D53—81no—
426D53—81no—
427D53—81no—
428C22×#41—531no—
429C22×M16—531no—
430C22×M16C2×D5311yescharacteristic
431C23×C8—531no—
432C2×C4×D4—531no—
433C2×C4×D4—531no—
434C2×C4×D4—531no—
435#436—1064no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8—531no—
438C2×C4⋊C8—531no—
439#408—1064no—
440C2×C22⋊C8—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C22⋊C8—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×C22⋊C8—531no—
450C2×C22⋊C8—531no—
451C2×C22⋊C8—531no—
452C2×C22⋊C8C2×D5311yescharacteristic
453C2×#97C2×D5311yescharacteristic
454C2×C4×C8—531no—
455C2×C4×C8C2×D5311yescharacteristic
456#395—531no—
457#394—531no—
458#394—531no—
459#394—531no—
460#393—531no—
461#392—531no—
462#392—531no—
463#392—531no—
464C4×C22⋊C4—531no—
465C4×C22⋊C4—531no—
466C4×C22⋊C4C2×D5311yescharacteristic
467#336—531no—
468#336—531no—
469#336—531no—
470#336—531no—
471#336C2×D5311yescharacteristic
472#336C2×D5311yescharacteristic
473C53#2203911yescharacteristic, complemented, Sylow
474C2×#41—1062no—
475C2×#41—1062no—
476C2×#41—2121no—
477C2×#41—2121no—
478C2×#41—2121no—
479C2×#41—2121no—
480C22×Q8—531no—
481C22×D4—531no—
482C22×D4—531no—
483C22×D4—531no—
484C22×D4—531no—
485C22×D4—531no—
486C22×D4—531no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4C22×D5311yescharacteristic
491C2×M16—41no—
492C2×M16—41no—
493C2×M16—1062no—
494C2×M16—2121no—
495C2×M16—2121no—
496C2×M16D21214yescomplemented
497C22×C8—531no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C22×C8—1062no—
502C22×C8—2121no—
503C22×C8—2121no—
504C22×C8C22×D5311yescharacteristic
505C22×C8C22×D5311yescharacteristic
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C4×D4—1062no—
509C4×D4—1062no—
510C4×D4—2121no—
511C4×D4—2121no—
512C4×D4—2121no—
513C4×D4—2121no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—531no—
519C2×C22⋊C4—531no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—531no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4C4×D5311yescharacteristic
528C2×C22⋊C4C4×D5311yescharacteristic
529C2×C42—531no—
530C2×C42C22×D5311yescharacteristic
531C2×C42C22×D5311yescharacteristic
532C4⋊C8—1062no—
533C4⋊C8—2121no—
534C4⋊C8—2121no—
535C22⋊C8—22no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—1062no—
539C22⋊C8—1062no—
540C22⋊C8—1062no—
541C22⋊C8—1062no—
542C22⋊C8—2121no—
543C22⋊C8—2121no—
544C22⋊C8—2121no—
545C22⋊C8—2121no—
546C22⋊C8—2121no—
547C22⋊C8—2121no—
548#97—41no—
549C4×C8—41no—
550C4×C8—1062no—
551#95—531no—
552#95—531no—
553#95—531no—
554#95—531no—
555#95C4×D5311yescharacteristic
556#95C4×D5311yescharacteristic
557C24—531no—
558C24—531no—
559C24—531no—
560C24C2×C4×D5311yescharacteristic
561#41—2124no—
562#41—2124no—
563#41—2124no—
564#41—2124no—
565C2×Q8—1062no—
566C2×Q8—2121no—
567C2×Q8—2121no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—2121no—
575C2×D4—2121no—
576C2×D4—2121no—
577C2×D4—2121no—
578C2×D4—2121no—
579C2×D4—2121no—
580C2×D4—2121no—
581C2×D4—2121no—
582C2×D4—2121no—
583C2×D4—2121no—
584C2×D4—2121no—
585C2×D4—2121no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—531no—
591C22×C4—531no—
592C22×C4—531no—
593C22×C4—531no—
594C22×C4—531no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4C2×C4×D5311yescharacteristic
614C22×C4C2×C4×D5311yescharacteristic
615C22×C4C2×C4×D5311yescharacteristic
616C22×C4C2×C4×D5311yescharacteristic
617C22×C4C2×C4×D5311yescharacteristic
618C22×C4C2×D21212yes—
619C22×C4#1171994512yes—
620C22×C4C23×D5311yescharacteristic
621M16—44no—
622M16—2124no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—1061no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—2124no—
646C2×C8C2×D21212yes—
647C2×C8C2×D21212yes—
648C4⋊C4—1062no—
649C4⋊C4—2121no—
650C4⋊C4—2121no—
651C22⋊C4—22no—
652C22⋊C4—41no—
653C22⋊C4—1062no—
654C22⋊C4—1062no—
655C22⋊C4—1062no—
656C22⋊C4—1062no—
657C22⋊C4—1062no—
658C22⋊C4—2121no—
659C22⋊C4—2121no—
660C22⋊C4—2121no—
661C22⋊C4—2121no—
662C22⋊C4—2121no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—1061no—
668C42—1061no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—1061no—
676C23—1061no—
677C23—1061no—
678C23—1061no—
679C23—1061no—
680C23—1061no—
681C23—1061no—
682C23—1061no—
683C23—1061no—
684C23—1061no—
685C23—1061no—
686C23—1061no—
687C23—1061no—
688C23—1061no—
689C23—1061no—
690C23—1061no—
691C23—1061no—
692C23—1061no—
693C23—1061no—
694C23—1061no—
695C23—1061no—
696C23C4×D21212yes—
697C23C22×C4×D5311yescharacteristic
698Q8—2124no—
699D4—2124no—
700D4—2124no—
701D4—2124no—
702D4—2124no—
703D4—2124no—
704D4—2124no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—532no—
723C2×C4—1061no—
724C2×C4—1061no—
725C2×C4—1061no—
726C2×C4—1061no—
727C2×C4—1061no—
728C2×C4—1061no—
729C2×C4—1061no—
730C2×C4—1061no—
731C2×C4—1061no—
732C2×C4—1061no—
733C2×C4—1061no—
734C2×C4—1061no—
735C2×C4—1061no—
736C2×C4—1061no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2121no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4C4×D21212yes—
750C2×C4#1313322512yes—
751C2×C4C22×D21211yescharacteristic
752C2×C4C2×#1171994511yescharacteristic
753C2×C4#1313326211yescharacteristic
754C2×C4#1313326211yescharacteristic
755C2×C4#1313326311yescharacteristic
756C2×C4#1313326311yescharacteristic
757C8—22no—
758C8—22no—
759C8—41no—
760C8—41no—
761C8—2121no—
762C8—2121no—
763C8—2121no—
764C8—2121no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—2121no—
773C22—2121no—
774C22—2121no—
775C22—2121no—
776C22—2121no—
777C22—2121no—
778C22—2121no—
779C22—2121no—
780C22—2121no—
781C22—2121no—
782C22—2121no—
783C22—2121no—
784C22—2121no—
785C22—2121no—
786C22—2121no—
787C22—2121no—
788C22—2121no—
789C22—2121no—
790C22—2121no—
791C22—2121no—
792C22—2121no—
793C22C2×C4×D21211yescharacteristic
794C22#1681109511yescharacteristic
795C22#1681109511yescharacteristic
796C22#131×D5311yescharacteristic
797C22C2×#1313322511yescharacteristic
798C22#1681138811yescharacteristic
799C22#1681138911yescharacteristic
800C4—22no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—41no—
805C4—1062no—
806C4—2121no—
807C4—2121no—
808C4—2121no—
809C4—2121no—
810C4#1681118511yescharacteristic
811C4#1681119211yescharacteristic
812C4#1681120611yescharacteristic
813C4#1681120611yescharacteristic
814C2—42no—
815C2—4241no—
816C2—4241no—
817C2—4241no—
818C2#2027737511yescharacteristic
819C2#2028344311yescharacteristic
820C2#2028346111yescharacteristic
821C2#2028376411yescharacteristic
822C2#2028377211yescharacteristic
823C2#2028378011yescharacteristic
824C2#2028378711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1753C2
prime radical#20277931C2
cosocleC22×C4×C53C24
hypercenter#1753D53
hypocenterC53#22039
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. C2×#16810699C2semidirect
2. C2×#16810591C2semidirect
4. #20275513C2semidirect
5. #20275509C2semidirect
6. #20275328C2semidirect
7. #20275322C2semidirect
8. #20275322C2semidirect
9. #20275321C2semidirect
10. #20275011C2semidirect
11. #20275011C2semidirect
12. #20275005C2semidirect
13. #20274895C2semidirect
14. #20274626C2semidirect
15. C53×#1753C2semidirect
130. C2×M16×C53D4semidirect
416. #1753D53semidirect
473. C53#22039semidirect
496. C2×M16D212semidirect

Maximal subgroups

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

subgroupindex
C2×#168106992
C2×#168105912
#202779312
#202755132
#202755092
#202753282
#202753222
#202753212
#202750112
#202750052
#202748952
#202746262
C53×#17532
#2203953