Finite Group Databasebeta

← #27400472

Subgroups — #27400472

Order 13568.

1174 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811330C211yesmaximal, characteristic
2#20277644C211yesmaximal, characteristic
3#20275688C211yesmaximal, characteristic, complemented
4#20275666C211yesmaximal, characteristic, complemented
5#20275148C211yesmaximal, characteristic, complemented
6#20275138C211yesmaximal, characteristic, complemented
7#20275025C211yesmaximal, characteristic, complemented
8#20275020C211yesmaximal, characteristic, complemented
9#20274806C211yesmaximal, characteristic, complemented
10#20274802C211yesmaximal, characteristic, complemented
11#20274731C211yesmaximal, characteristic, complemented
12#20274546C211yesmaximal, characteristic, complemented
13#20274435C211yesmaximal, characteristic, complemented
14C2×#16810386C211yesmaximal, characteristic, complemented
15C2×C53×#435C211yesmaximal, characteristic
16#16811330—24no—
17#16811330C418yescomplemented
18C2×#13133217C2211yescharacteristic
19C2×#13133208—21no—
20C2×#13133196C2211yescharacteristic
21C2×#13133196C2211yescharacteristic
22C2×#13133194—21no—
23C2×#13133194—21no—
24C2×C4×Dic106C2211yescharacteristic
25C2×D4×Dic53—21no—
26C2×#13133176C2211yescharacteristic
27C22×C4⋊Dic53C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C2×#13133142C2211yescharacteristic
31C2×#13133142C2211yescharacteristic
32C2×#13133142C2211yescharacteristic
33C2×#13133142C2211yescharacteristic
34#16810516—21no—
35#16810509—21no—
36#16810503—21no—
37#16810489C2211yescharacteristic
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40C4×C4⋊Dic53C2211yescharacteristic
41C22⋊C4×Dic53—21no—
42#16810386C2211yescharacteristic
43#16810386C2211yescharacteristic
44#16810386C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54C22×M16×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C53×#435—24no—
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C22×Dic106—21no—
63C22×Dic106C2311yescharacteristic
64C23×Dic53—21no—
65C23×Dic53—21no—
66C23×Dic53—21no—
67#13133217—22no—
68#13133217C2×C414yescomplemented
69#13133208—28no—
70#13133196—22no—
71#13133196—22no—
72#13133196C2×C414yes—
73#13133196C2×C414yescomplemented
74#13133194—28no—
75#13133194—28no—
76C4×Dic106—22no—
77C4×Dic106C2×C414yescomplemented
78D4×Dic53—28no—
79#13133176—22no—
80#13133176—41no—
81C2×C4⋊Dic53—22no—
82C2×C4⋊Dic53—22no—
83C2×C4⋊Dic53—21no—
84C2×C4⋊Dic53—21no—
85C2×C4⋊Dic53—21no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—22no—
88C2×C4⋊Dic53—41no—
89C2×C4⋊Dic53C2×C414yes—
90C2×C4⋊Dic53C2×C414yescomplemented
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×#11719919—21no—
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×C22⋊Dic53—21no—
102C2×C22⋊Dic53—21no—
103C2×C22⋊Dic53—21no—
104C2×C22⋊Dic53—21no—
105C2×C22⋊Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109#13133142—22no—
110#13133142—22no—
111#13133142—41no—
112#13133142—41no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118C22×D4×C53D411yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C2×M16×C53—22no—
122C2×M16×C53—22no—
123C2×M16×C53—41no—
124C22×C8×C53—22no—
125C22×C8×C53—22no—
126C22×C8×C53—41no—
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C4×D4×C53C2×C414yes—
132C4×D4×C53D414yes—
133C2×C4⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C4⋊C8×C53—22no—
138C22⋊C8×C53—22no—
139C22⋊C8×C53—22no—
140#97×C53—22no—
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C2×D4×C53—22no—
144C2×D4×C53—22no—
145C2×D4×C53C22⋊C414yes—
146C22×C4×C53—21no—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53C22×C412yes—
155C22×C4×C53C22×C412yes—
156C22×C4×C53C2×D411yescharacteristic
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D412yes—
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2411yescharacteristic
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—24no—
169C22×Dic53—24no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—42no—
174C22×Dic53—42no—
175C22×Dic53—81no—
176C22×Dic53—81no—
177C22×Dic53—81no—
178C22×Dic53—81no—
179C22×Dic53—81no—
180C2×Dic106—21no—
181C2×Dic106—21no—
182C2×Dic106—21no—
183C2×Dic106—21no—
184C2×Dic106—21no—
185C2×Dic106—24no—
186C2×Dic106—81no—
187C2×Dic106—81no—
188C2×Dic106C22×C412yes—
189M16×C53—44no—
190C2×C8×C53—21no—
191C2×C8×C53—21no—
192C2×C8×C53—21no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—44no—
202C2×C8×C53#4112yes—
203C4⋊C4×C53C22⋊C414yes—
204C22⋊C4×C53C22⋊C414yes—
205C22⋊C4×C53C22⋊C414yes—
206C42×C53C22×C412yes—
207C42×C53C2×D412yes—
208C22⋊Dic53—24no—
209C22⋊Dic53—24no—
210C22⋊Dic53—42no—
211C22⋊Dic53—42no—
212C22⋊Dic53—81no—
213C4⋊Dic53—24no—
214C4⋊Dic53—24no—
215C4⋊Dic53—24no—
216C4⋊Dic53—21no—
217C4⋊Dic53—21no—
218C4⋊Dic53—21no—
219C4⋊Dic53—21no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—42no—
227C4⋊Dic53C22×C412yes—
228C4⋊Dic53C22×C412yes—
229C4⋊Dic53C22×C412yes—
230C4⋊Dic53#4112yes—
231#11719919—24no—
232#11719919—24no—
233#11719919—24no—
234C4×Dic53—24no—
235C4×Dic53—42no—
236C4×Dic53—81no—
237C23×C53—21no—
238C23×C53—21no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53C2×C22⋊C412yes—
248C23×C53C2×C22⋊C412yes—
249C23×C53#13712yes—
250C23×C53#13712yes—
251C23×C53C22×D411yescharacteristic
252D4×C53—28no—
253C2×C4×C53—21no—
254C2×C4×C53—21no—
255C2×C4×C53—21no—
256C2×C4×C53—21no—
257C2×C4×C53—21no—
258C2×C4×C53—21no—
259C2×C4×C53—21no—
260C2×C4×C53—21no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53C2×C22⋊C412yes—
270C2×C4×C53C2×C22⋊C412yes—
271C2×C4×C53C2×C22⋊C412yes—
272C2×C4×C53C2×C22⋊C412yes—
273C2×C4×C53C23×C411yescharacteristic
274C2×C4×C53C22×D411yescharacteristic
275C2×C4×C53C2×#4111yescharacteristic
276C2×C4×C53C2×#4111yescharacteristic
277C2×C4×C53H(5,𝔽2)11yescharacteristic
278C2×C4×C532−1+411yescharacteristic
279C2×Dic53—22no—
280C2×Dic53—22no—
281C2×Dic53—22no—
282C2×Dic53—22no—
283C2×Dic53—22no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—41no—
289C2×Dic53—41no—
290C2×Dic53—41no—
291C2×Dic53—41no—
292C2×Dic53—41no—
293C2×Dic53—41no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—84no—
304C2×Dic53—84no—
305C2×Dic53—84no—
306Dic106—22no—
307Dic106—22no—
308Dic106—41no—
309Dic106—41no—
310Dic106—84no—
311C8×C53—22no—
312C8×C53—41no—
313C8×C53—41no—
314C8×C53—41no—
315#22497—531nomaximal, Sylow
316C22×C53—22no—
317C22×C53—22no—
318C22×C53—22no—
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—22no—
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53#41914yes—
330C22×C53C22×C22⋊C411yescharacteristic
331C22×C53#54611yescharacteristic
332C22×C53#54711yescharacteristic
333C22×C53C2×#13711yescharacteristic
334C22×C53C2×#13711yescharacteristic
335C22×C53#57611yescharacteristic
336C22×C53#57711yescharacteristic
337C4×C53—22no—
338C4×C53—22no—
339C4×C53—22no—
340C4×C53—22no—
341C4×C53C4×#4111yescharacteristic
342C4×C53#52011yescharacteristic
343C4×C53#54611yescharacteristic
344C4×C53#54711yescharacteristic
345Dic53—42no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—81no—
351Dic53—81no—
352Dic53—81no—
353C2×#554—531no—
354C2×#435D5311yescharacteristic
355#2352—531no—
356#1993—531no—
357#1988—531no—
358#1894—531no—
359#1892—531no—
360#1873—531no—
361#1872—531no—
362#1824—531no—
363#1823—531no—
364#1805—531no—
365#1763—531no—
366#1736—531no—
367C2×#340—531no—
368C2×C53—24no—
369C2×C53—42no—
370C2×C53#233911yescharacteristic
371C2×C53C2×#41911yescharacteristic
372C2×C53#289711yescharacteristic
373C2×C53#331411yescharacteristic
374C2×C53#331611yescharacteristic
375C2×C53#334411yescharacteristic
376C2×C53#334611yescharacteristic
377C22×M16C2×D5311yescharacteristic
378C23×C8C2×D5311yescharacteristic
379#554—538no—
380#554—1064no—
381C2×C4⋊Q8—531no—
382C2×#125—1061no—
383C2×C22⋊Q8—531no—
384C2×C22⋊Q8—531no—
385C2×C22⋊Q8—1061no—
386C2×C22⋊Q8—1061no—
387C2×C4×Q8—531no—
388C2×C4×D4—1061no—
389C2×C4×D4C2×D5311yescharacteristic
390C2×#117—531no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394#435—24no—
395C2×C4⋊C8C2×D5311yescharacteristic
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#103—531no—
400C2×C22⋊C8C2×D5311yescharacteristic
401C2×C22⋊C8C2×D5311yescharacteristic
402C2×#97C2×D5311yescharacteristic
403#388—1061no—
404#387—1061no—
405#386—1061no—
406#382—531no—
407#380—531no—
408#380—531no—
409C4×C4⋊C4—531no—
410C4×C22⋊C4—1061no—
411#340—531no—
412#340—531no—
413#340—531no—
414#340—531no—
415#340—531no—
416#340—531no—
417#340—531no—
418#340—531no—
419#340—531no—
420#340—531no—
421#340—531no—
422#340—531no—
423C53#2249711yescharacteristic, complemented, Sylow
424C22×Q8—531no—
425C22×Q8—1061no—
426C22×D4D21211yescharacteristic
427C23×C4—1061no—
428C23×C4—1061no—
429C23×C4—1061no—
430C23×C4C22×D5311yescharacteristic
431C23×C4C22×D5311yescharacteristic
432C2×M16—22no—
433C2×M16—22no—
434C2×M16—41no—
435C22×C8—22no—
436C22×C8—22no—
437C22×C8—41no—
438C22×C8C22×D5311yescharacteristic
439C22×C8C22×D5311yescharacteristic
440C22×C8C22×D5311yescharacteristic
441C22×C8C22×D5311yescharacteristic
442C4⋊Q8—534no—
443C4⋊Q8—1062no—
444#125—1068no—
445C22⋊Q8—534no—
446C22⋊Q8—534no—
447C22⋊Q8—1062no—
448C22⋊Q8—1062no—
449C22⋊Q8—1068no—
450C22⋊Q8—1068no—
451C4×Q8—534no—
452C4×Q8—1062no—
453C4×D4—1068no—
454C4×D4C4×D5314yes—
455C4×D4C22⋊D5314yes—
456#117—1062no—
457#117—2121no—
458C2×C4⋊C4—534no—
459C2×C4⋊C4—534no—
460C2×C4⋊C4—531no—
461C2×C4⋊C4—531no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—531no—
467C2×C4⋊C4—1062no—
468C2×C4⋊C4—1061no—
469C2×C4⋊C4—1061no—
470C2×C4⋊C4—1061no—
471C2×C4⋊C4—1061no—
472C2×C4⋊C4—1061no—
473C2×C4⋊C4—1061no—
474C2×C4⋊C4—1062no—
475C2×C4⋊C4—1062no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—2121no—
478C2×C4⋊C4D21211yescharacteristic
479C2×C22⋊C4—1061no—
480C2×C22⋊C4—1061no—
481C2×C22⋊C4—1061no—
482C2×C22⋊C4—1061no—
483C2×C22⋊C4—1061no—
484C2×C22⋊C4D21211yescharacteristic
485C2×C22⋊C4D21211yescharacteristic
486C2×C42—1061no—
487C2×C42—1061no—
488C2×C42—1061no—
489C2×C42C22×D5311yescharacteristic
490C4⋊C8—22no—
491#103—1062no—
492#103—1062no—
493#103—2121no—
494#103—2121no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497#97—22no—
498#95—1061no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503C24C2×D21211yescharacteristic
504C24C2×D21211yescharacteristic
505C2×Q8—532no—
506C2×Q8—1064no—
507C2×Q8—1061no—
508C2×Q8—1061no—
509C2×Q8—1061no—
510C2×Q8—1061no—
511C2×Q8—1061no—
512C2×Q8—4241no—
513C2×Q8—4241no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4#1171992114yes—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—1064no—
526C22×C4—1064no—
527C22×C4—1061no—
528C22×C4—1061no—
529C22×C4—1061no—
530C22×C4—1061no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1061no—
534C22×C4—1061no—
535C22×C4—4241no—
536C22×C4—4241no—
537C22×C4—4241no—
538C22×C4—4241no—
539C22×C4—4241no—
540C22×C4—2122no—
541C22×C4—2122no—
542C22×C4C2×C4×D5312yes—
543C22×C4C2×C4×D5312yes—
544C22×C4C2×D21211yescharacteristic
545C22×C4C2×D21211yescharacteristic
546C22×C4C2×D21211yescharacteristic
547C22×C4C2×D21211yescharacteristic
548C22×C4C2×C22⋊D5312yes—
549C22×C4C2×C22⋊D5312yes—
550C22×C4C23×D5311yescharacteristic
551M16—44no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—44no—
564C2×C8#1171994712yes—
565C4⋊C4—532no—
566C4⋊C4—532no—
567C4⋊C4—532no—
568C4⋊C4—532no—
569C4⋊C4—1064no—
570C4⋊C4—1064no—
571C4⋊C4—1064no—
572C4⋊C4—1064no—
573C4⋊C4—1064no—
574C4⋊C4—1064no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—1061no—
578C4⋊C4—1061no—
579C4⋊C4—1061no—
580C4⋊C4—1061no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—2122no—
586C4⋊C4#1171992114yes—
587C22⋊C4—1064no—
588C22⋊C4—1064no—
589C22⋊C4—4241no—
590C22⋊C4—2122no—
591C22⋊C4—2122no—
592C22⋊C4#1171992114yes—
593C22⋊C4#1171992114yes—
594C42—1064no—
595C42—4241no—
596C42—2122no—
597C42C2×C4×D5312yes—
598C42C2×C22⋊D5312yes—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23C2×#1171992112yes—
610C23C2×#1171992112yes—
611C23#1313325012yes—
612C23#1313325012yes—
613C23C22×D21211yescharacteristic
614Q8—1062no—
615Q8—1062no—
616Q8—4244no—
617Q8—2121no—
618Q8—2121no—
619D4—28no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—1062no—
637C2×C4—1062no—
638C2×C4—1062no—
639C2×C4—1062no—
640C2×C4—1062no—
641C2×C4—4244no—
642C2×C4—4244no—
643C2×C4—4244no—
644C2×C4—2121no—
645C2×C4—2121no—
646C2×C4—2121no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2121no—
652C2×C4—2121no—
653C2×C4—2121no—
654C2×C4—2121no—
655C2×C4—2121no—
656C2×C4—2121no—
657C2×C4—2121no—
658C2×C4—2121no—
659C2×C4—2121no—
660C2×C4—2121no—
661C2×C4—2121no—
662C2×C4—2121no—
663C2×C4C2×#1171992112yes—
664C2×C4C2×#1171992112yes—
665C2×C4C2×#1171992112yes—
666C2×C4C2×#1171992112yes—
667C2×C4C22×C4×D5311yescharacteristic
668C2×C4C22×C22⋊D5311yescharacteristic
669C2×C4#41×D5311yescharacteristic
670C2×C4C2×#1171994711yescharacteristic
671C2×C4#1313326211yescharacteristic
672C2×C4#1313326411yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22#1681063314yes—
691C22C22×#1171992111yescharacteristic
692C22#1681126811yescharacteristic
693C22#1681127711yescharacteristic
694C22C2×#1313325011yescharacteristic
695C22C2×#1313325011yescharacteristic
696C22#1681142811yescharacteristic
697C22#1681143511yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—4241no—
703C4—4241no—
704C4—4241no—
705C4—2122no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C4C4×#1171994711yescharacteristic
711C4#1681110211yescharacteristic
712C4#1681126711yescharacteristic
713C4#1681127211yescharacteristic
714C2—24no—
715C2—42no—
716C2#2027754011yescharacteristic
717C2C2×#1681063311yescharacteristic
718C2#2028324211yescharacteristic
719C2#2028679811yescharacteristic
720C2#2028682811yescharacteristic
721C2#2028717211yescharacteristic
722C2#2028720211yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
cosocleC22×C4×C53C24
hypercenterC2×#435D53
hypocenterC53#22497
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20275688C2semidirect
4. #20275666C2semidirect
5. #20275148C2semidirect
6. #20275138C2semidirect
7. #20275025C2semidirect
8. #20275020C2semidirect
9. #20274806C2semidirect
10. #20274802C2semidirect
11. #20274731C2semidirect
12. #20274546C2semidirect
13. #20274435C2semidirect
14. C2×#16810386C2semidirect
17. #16811330C4semidirect
68. #13133217C2×C4semidirect
73. #13133196C2×C4semidirect
77. C4×Dic106C2×C4semidirect
90. C2×C4⋊Dic53C2×C4semidirect
423. C53#22497semidirect

Maximal subgroups

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

subgroupindex
C2×#168113302
#202776442
#202756882
#202756662
#202751482
#202751382
#202750252
#202750202
#202748062
#202748022
#202747312
#202745462
#202744352
C2×#168103862
C2×C53×#4352
#2249753