Finite Group Databasebeta

← #28320751

Subgroups — #28320751

Order 13568.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811647C211yesmaximal, characteristic, complemented
2C2×#16811587C211yesmaximal, characteristic, complemented
3#20290888C211yesmaximal, characteristic, complemented
4#20290886C211yesmaximal, characteristic, complemented
5#20290839C211yesmaximal, characteristic, complemented
6#20290836C211yesmaximal, characteristic, complemented
7#20290692C211yesmaximal, characteristic, complemented
8#20290692C211yesmaximal, characteristic, complemented
9#20290688C211yesmaximal, characteristic, complemented
10#20290688C211yesmaximal, characteristic, complemented
11#20290445C211yesmaximal, characteristic, complemented
12#20290445C211yesmaximal, characteristic, complemented
13#20290441C211yesmaximal, characteristic, complemented
14C4×C22⋊#88324C211yesmaximal, characteristic, complemented
15C2×#16811154C211yesmaximal, characteristic
16C22×#11719940C2211yescharacteristic
17C23×#88324C2211yescharacteristic
18#16811647—24no—
19C2×#13133284C2211yescharacteristic
20C2×C4⋊#88324C2211yescharacteristic
21C2×C22⋊#88324C2211yescharacteristic
22C2×C22⋊#88324C2211yescharacteristic
23C2×C22⋊#88324C2211yescharacteristic
24C2×C22⋊#88324C2211yescharacteristic
25C2×C22⋊#88324C2211yescharacteristic
26C2×C22⋊#88324C2211yescharacteristic
27C2×C22⋊#88324C2211yescharacteristic
28C2×C22⋊#88324C2211yescharacteristic
29C2×C22⋊#88324C2211yescharacteristic
30C2×C22⋊#88324C2211yescharacteristic
31#16811587—24no—
32C2×#13133272C2211yescharacteristic
33C2×#13133272C2211yescharacteristic
34C2×#13133272C2211yescharacteristic
35C2×C4×#88324C2211yescharacteristic
36C2×C4×#88324C2211yescharacteristic
37C2×C4×#88324C2211yescharacteristic
38#16811489C2211yescharacteristic
39#16811489C2211yescharacteristic
40#16811489C2211yescharacteristic
41#16811489C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44#16811489C2211yescharacteristic
45#16811489C2211yescharacteristic
46#16811154—24no—
47#16811154—24no—
48C2×#13133210C411yescharacteristic
49C2×#13133210C411yescharacteristic
50C2×#13133208C411yescharacteristic
51C2×#13133204C411yescharacteristic
52C2×#13133198C411yescharacteristic
53C2×#13133198C411yescharacteristic
54C2×#13133196C411yescharacteristic
55C2×#13133182C2211yescharacteristic
56C2×D4×Dic53C2211yescharacteristic
57C2×D4×Dic53C2211yescharacteristic
58C2×D4×Dic53C2211yescharacteristic
59C2×#13133173C2211yescharacteristic
60C2×#13133173C2211yescharacteristic
61C22×C4×Dic53C2211yescharacteristic
62C2×#121×C53C411yescharacteristic
63C2×#11719940—22no—
64C2×#11719940—22no—
65C2×#11719940—22no—
66C22×#88324—22no—
67C22×#88324—22no—
68C22×#88324—22no—
69C22×#88324C2311yescharacteristic
70C22×#88324C2311yescharacteristic
71C22×#88324C2311yescharacteristic
72C22×#88324C2311yescharacteristic
73C22×#88324C2311yescharacteristic
74C22×#88324C2311yescharacteristic
75C22×#88324C2311yescharacteristic
76C22×#88324C2311yescharacteristic
77#13133284—22no—
78C4⋊#88324—22no—
79C22⋊#88324—22no—
80C22⋊#88324—22no—
81C22⋊#88324—22no—
82C22⋊#88324—22no—
83C22⋊#88324—22no—
84C22⋊#88324—22no—
85C22⋊#88324—22no—
86C22⋊#88324—22no—
87C22⋊#88324—22no—
88C22⋊#88324—22no—
89#13133272—22no—
90#13133272—22no—
91#13133272—22no—
92C4×#88324—22no—
93C4×#88324—22no—
94C4×#88324—22no—
95C22×Dic106C2×C411yescharacteristic
96C23×Dic53C2×C411yescharacteristic
97C23×Dic53C2311yescharacteristic
98C23×Dic53C2311yescharacteristic
99C23×Dic53C2311yescharacteristic
100#13133210—24no—
101#13133210—24no—
102#13133208—24no—
103#13133204—24no—
104#13133198—24no—
105#13133198—24no—
106#13133196—24no—
107#13133182—22no—
108#13133182—22no—
109D4×Dic53—22no—
110D4×Dic53—22no—
111D4×Dic53—22no—
112D4×Dic53—22no—
113D4×Dic53—22no—
114D4×Dic53—22no—
115#13133173—22no—
116#13133173—22no—
117#13133173D414yes—
118#13133173D414yes—
119C2×C4⋊Dic53C2×C411yescharacteristic
120C2×C4⋊Dic53C2×C411yescharacteristic
121C2×C4⋊Dic53C2×C411yescharacteristic
122C2×#11719919C2×C411yescharacteristic
123C2×#11719919C2×C411yescharacteristic
124C2×#11719919C2×C411yescharacteristic
125C2×#11719919C2×C411yescharacteristic
126C2×#11719919C2×C411yescharacteristic
127C2×#11719919C2×C411yescharacteristic
128C2×C22⋊Dic53C2×C411yescharacteristic
129C2×C22⋊Dic53C2×C411yescharacteristic
130C2×C22⋊Dic53C2×C411yescharacteristic
131C2×C22⋊Dic53C2×C411yescharacteristic
132C2×C22⋊Dic53C2×C411yescharacteristic
133C2×C22⋊Dic53C2×C411yescharacteristic
134C2×C22⋊Dic53C2×C411yescharacteristic
135C2×C22⋊Dic53C2×C411yescharacteristic
136C2×C4×Dic53—22no—
137C2×C4×Dic53—22no—
138C2×C4×Dic53C2×C411yescharacteristic
139C2×C4×Dic53C2×C411yescharacteristic
140C2×C4×Dic53C2311yescharacteristic
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143C2×C4×Dic53C2311yescharacteristic
144C22×D4×C53C2×C411yescharacteristic
145C22×D4×C53C2×C411yescharacteristic
146C22×D4×C53C2×C411yescharacteristic
147C23×C4×C53C2×C411yescharacteristic
148#121×C53—24no—
149C2×C4⋊C4×C53C2×C411yescharacteristic
150C2×C22⋊C4×C53C2×C411yescharacteristic
151C2×C22⋊C4×C53C2×C411yescharacteristic
152C24×C53C22×C411yescharacteristic
153C24×C53C22×C411yescharacteristic
154C24×C53C22×C411yescharacteristic
155C2×D4×C53—22no—
156C2×D4×C53—22no—
157C2×D4×C53—22no—
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53—22no—
161C2×D4×C53—41no—
162C2×D4×C53—41no—
163C2×D4×C53—41no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—41no—
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C22×Dic53—41no—
190C22×Dic53C22×C411yescharacteristic
191C22×Dic53C22×C411yescharacteristic
192C22×Dic53C22×C411yescharacteristic
193C22×Dic53C22×C411yescharacteristic
194C22×Dic53C22×C411yescharacteristic
195C22×Dic53C22×C411yescharacteristic
196C22×Dic53C22×C411yescharacteristic
197C22×Dic53C2×D412yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2411yescharacteristic
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—41no—
203#11719940—28no—
204C2×#88324—28no—
205C2×#88324—21no—
206C2×#88324—21no—
207C2×#88324—21no—
208C2×#88324—21no—
209C2×#88324—21no—
210C2×#88324—21no—
211C2×#88324—21no—
212C2×#88324—21no—
213C2×#88324—21no—
214C2×#88324—21no—
215C2×#88324—21no—
216C2×#88324—21no—
217C2×#88324—21no—
218C2×#88324—21no—
219C2×#88324—21no—
220C2×#88324—21no—
221C2×#88324—21no—
222C2×#88324—21no—
223C2×#88324—21no—
224C2×#88324—21no—
225C2×#88324#4112yes—
226C2×#88324#4112yes—
227C2×#88324#4112yes—
228C2×#88324#4112yes—
229C4⋊C4×C53—22no—
230C22⋊C4×C53—22no—
231C22⋊C4×C53C22⋊C414yes—
232C22⋊Dic53—22no—
233C22⋊Dic53—22no—
234C22⋊Dic53—22no—
235C22⋊Dic53—22no—
236C22⋊Dic53—22no—
237C22⋊Dic53—22no—
238C22⋊Dic53—22no—
239C22⋊Dic53C22⋊C414yes—
240C4⋊Dic53—22no—
241C4⋊Dic53—22no—
242C4⋊Dic53—22no—
243#11719919—22no—
244#11719919—22no—
245#11719919—22no—
246#11719919—22no—
247#11719919C22⋊C414yes—
248#11719919C22⋊C414yes—
249C4×Dic53—22no—
250C4×Dic53—22no—
251C4×Dic53—21no—
252C4×Dic53—21no—
253C4×Dic53—21no—
254C4×Dic53—21no—
255C4×Dic53C2×D412yes—
256C4×Dic53C2×D412yes—
257C4×Dic53C2×D412yes—
258C4×Dic53C2×D412yes—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53C2×C22⋊C412yes—
279C23×C53#13112yes—
280C23×C53C23×C411yescharacteristic
281D4×C53—44no—
282D4×C53—44no—
283D4×C53—44no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—44no—
294C2×C4×C53C2×C22⋊C412yes—
295C2×C4×C53C2×C22⋊C412yes—
296C2×C4×C53#13112yes—
297C2×Dic53—21no—
298C2×Dic53—21no—
299C2×Dic53—21no—
300C2×Dic53—21no—
301C2×Dic53—21no—
302C2×Dic53—21no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—44no—
320C2×Dic53—41no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53C2×C22⋊C412yes—
329C2×Dic53C2×C22⋊C412yes—
330C2×Dic53C2×C22⋊C412yes—
331C2×Dic53C22×D411yescharacteristic
332C2×Dic53C22×D411yescharacteristic
333C2×Dic53C2×#4111yescharacteristic
334C2×Dic53C2×#4111yescharacteristic
335C2×Dic53C2×#4111yescharacteristic
336C2×Dic53C2×#4111yescharacteristic
337Dic106—44no—
338#88324—22no—
339#88324—22no—
340#88324—22no—
341#88324—22no—
342#88324—41no—
343#88324—41no—
344#88324—41no—
345#88324—41no—
346#21381—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53—41no—
366C22×C53—41no—
367C22×C53—41no—
368C22×C53C22×C22⋊C411yescharacteristic
369C22×C53C4×#4111yescharacteristic
370C22×C53C4×#4111yescharacteristic
371C22×C53C2×#13111yescharacteristic
372C22×C53C2×#13111yescharacteristic
373C22×C53#56811yescharacteristic
374C22×C53#56811yescharacteristic
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—41no—
379Dic53—22no—
380Dic53—22no—
381Dic53—22no—
382Dic53—41no—
383Dic53—41no—
384Dic53—41no—
385Dic53—41no—
386Dic53#52511yescharacteristic
387Dic53#52511yescharacteristic
388Dic53#53211yescharacteristic
389Dic53#53211yescharacteristic
390C2×#529—531no—
391C2×#433—531no—
392C2×#405—531no—
393#1985—531no—
394#1984—531no—
395#1955—531no—
396#1954—531no—
397#1870—531no—
398#1870—531no—
399#1869—531no—
400#1869—531no—
401#1750—531no—
402#1750—531no—
403#1749—531no—
404C4×C22⋊C8—531no—
405C2×C53—42no—
406C2×C53—42no—
407C2×C53—81no—
408C2×C53#229711yescharacteristic
409C2×C53#288011yescharacteristic
410C2×C53#288011yescharacteristic
411C2×C53#296611yescharacteristic
412C2×C53#296711yescharacteristic
413C2×C53#296811yescharacteristic
414C2×C53#296911yescharacteristic
415C22×M16—531no—
416C23×C8—531no—
417#529—1064no—
418#529—1064no—
419C2×#126—531no—
420C2×#126—531no—
421C2×#125—531no—
422C2×#124—531no—
423C2×#123—531no—
424C2×#123—531no—
425C2×C22⋊Q8—531no—
426C2×#121#615711yescharacteristic
427C2×C4×Q8—531no—
428C2×C4×D4—531no—
429C2×C4×D4—531no—
430C2×C4×D4—531no—
431C2×#117—531no—
432C2×#117—531no—
433C22×C42—531no—
434#433—1064no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C22⋊C8—531no—
438C2×C22⋊C8—531no—
439C2×C22⋊C8—531no—
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—
447#405—1064no—
448C2×#97—531no—
449C2×#97—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C2×C4×C8—531no—
453C2×C4×C8—531no—
454#336—531no—
455#336—531no—
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460#336—531no—
461#336—531no—
462C53#2138111yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×D4C2×#615711yescharacteristic
465C22×D4C2×#615711yescharacteristic
466C22×D4C2×#615711yescharacteristic
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4C2×#615711yescharacteristic
472C2×M16—1062no—
473C2×M16—1062no—
474C2×M16—1062no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8—531no—
483C22×C8—1062no—
484C22×C8—1062no—
485C22×C8—1062no—
486#126—1064no—
487#126—1064no—
488#125—1064no—
489#124—1064no—
490#123—1064no—
491#123—1064no—
492C22⋊Q8—1064no—
493#121—24no—
494C4×Q8—1062no—
495C4×Q8—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1062no—
502#117—534no—
503#117—534no—
504#117—1062no—
505#117—1062no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4C2×#615711yescharacteristic
516C2×C22⋊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⋊C4C2×#615711yescharacteristic
525C2×C22⋊C4C2×#615711yescharacteristic
526C2×C42—531no—
527C2×C42—531no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—531no—
531C2×C42—531no—
532C2×C42—1062no—
533C2×C42—1062no—
534C4⋊C8—1062no—
535C4⋊C8—1062no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—1062no—
539C22⋊C8—1062no—
540C22⋊C8—1062no—
541C22⋊C8—1062no—
542C22⋊C8—1062no—
543C22⋊C8—1062no—
544C22⋊C8—1062no—
545C22⋊C8—1062no—
546#97—1062no—
547#97—1062no—
548#97—1062no—
549C4×C8—1062no—
550C4×C8—1062no—
551C4×C8—1062no—
552C24C22×#615711yescharacteristic
553C24C22×#615711yescharacteristic
554C24C22×#615711yescharacteristic
555C2×Q8—1062no—
556C2×Q8—1062no—
557C2×Q8—2121no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—41no—
570C22×C4—531no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—531no—
578C22×C4—531no—
579C22×C4—531no—
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—1062no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1062no—
598C22×C4—2121no—
599C22×C4C22×#615711yescharacteristic
600C22×C4C22×#615711yescharacteristic
601C22×C4C22×#615711yescharacteristic
602C22×C4C22×#615711yescharacteristic
603M16—1068no—
604C2×C8—532no—
605C2×C8—532no—
606C2×C8—532no—
607C2×C8—532no—
608C2×C8—1061no—
609C2×C8—1061no—
610C2×C8—1061no—
611C2×C8—1061no—
612C2×C8—1061no—
613C2×C8—1061no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1068no—
617C2×C8—1061no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C4⋊C4—22no—
630C4⋊C4—534no—
631C4⋊C4—534no—
632C4⋊C4—1062no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C4⋊C4—1062no—
636C4⋊C4—1062no—
637C4⋊C4—1062no—
638C4⋊C4—1062no—
639C22⋊C4—22no—
640C22⋊C4—534no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—1062no—
646C22⋊C4—1062no—
647C22⋊C4—1062no—
648C22⋊C4C22⋊#615714yes—
649C42—532no—
650C42—532no—
651C42—532no—
652C42—532no—
653C42—1061no—
654C42—1061no—
655C42—1062no—
656C42—1061no—
657C42—1061no—
658C42—1062no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊#615712yes—
679C23#1313330412yes—
680C23C23×#615711yescharacteristic
681Q8—2124no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—531no—
696C2×C4—531no—
697C2×C4—531no—
698C2×C4—531no—
699C2×C4—531no—
700C2×C4—531no—
701C2×C4—532no—
702C2×C4—532no—
703C2×C4—532no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1061no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—1061no—
723C2×C4—1061no—
724C2×C4—1061no—
725C2×C4—1061no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4—2121no—
732C2×C4—2121no—
733C2×C4—2121no—
734C2×C4—2124no—
735C2×C4C2×C22⋊#615712yes—
736C2×C4C2×C22⋊#615712yes—
737C2×C4#1313330412yes—
738C8—1062no—
739C8—1062no—
740C8—1062no—
741C8—1062no—
742C8—2121no—
743C8—2121no—
744C8—2121no—
745C8—2121no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊#615711yescharacteristic
768C22#41×#615711yescharacteristic
769C22#41×#615711yescharacteristic
770C22C2×#1313330411yescharacteristic
771C22C2×#1313330411yescharacteristic
772C22#1681170111yescharacteristic
773C22#1681170111yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—531no—
779C4—531no—
780C4—531no—
781C4—531no—
782C4—1062no—
783C4—1062no—
784C4—1062no—
785C4—2121no—
786C4—2121no—
787C4—2121no—
788C4—2121no—
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2029117611yescharacteristic
793C2#2029130311yescharacteristic
794C2#2029130311yescharacteristic
795C2#2029152811yescharacteristic
796C2#2029153411yescharacteristic
797C2#2029154011yescharacteristic
798C2#2029154611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
Fitting, prime radicalC2×#121×C53C4
cosocleC22×Dic53C24
hypercenterC2×#121#6157
hypocenterC53#21381
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16811647C2semidirect
2. C2×#16811587C2semidirect
3. #20290888C2semidirect
4. #20290886C2semidirect
5. #20290839C2semidirect
6. #20290836C2semidirect
7. #20290692C2semidirect
8. #20290692C2semidirect
9. #20290688C2semidirect
10. #20290688C2semidirect
11. #20290445C2semidirect
12. #20290445C2semidirect
13. #20290441C2semidirect
14. C4×C22⋊#88324C2semidirect
462. C53#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168116472
C2×#168115872
#202908882
#202908862
#202908392
#202908362
#202906922
#202906882
#202904452
#202904412
C4×C22⋊#883242
C2×#168111542
#2138153