Finite Group Databasebeta

← #27393211

Subgroups — #27393211

Order 13568.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic
2#20277307C211yesmaximal, characteristic, complemented
3#20275153C211yesmaximal, characteristic, complemented
4#20275148C211yesmaximal, characteristic, complemented
5#20275143C211yesmaximal, characteristic, complemented
6#20275138C211yesmaximal, characteristic, complemented
7#20275035C211yesmaximal, characteristic, complemented
8#20275030C211yesmaximal, characteristic, complemented
9#20275025C211yesmaximal, characteristic, complemented
10#20275020C211yesmaximal, characteristic, complemented
11#20274806C211yesmaximal, characteristic, complemented
12#20274802C211yesmaximal, characteristic, complemented
13#20274656C211yesmaximal, characteristic, complemented
14#20274656C211yesmaximal, characteristic, complemented
15C2×C53×#408C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17#16811201—24no—
18#16811201C418yescomplemented
19C2×#13133196C2211yescharacteristic
20C2×#13133196C2211yescharacteristic
21C2×#13133193—21no—
22C2×#13133191C2211yescharacteristic
23C2×#13133191C2211yescharacteristic
24C2×#13133189—21no—
25C2×#13133189—21no—
26C2×#13133188—21no—
27C2×#13133176C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29C22×C4⋊Dic53C2211yescharacteristic
30C2×#13133142C2211yescharacteristic
31C2×#13133142C2211yescharacteristic
32C2×#13133142C2211yescharacteristic
33C2×#13133142C2211yescharacteristic
34C2×#13133139C2211yescharacteristic
35C2×#13133139C2211yescharacteristic
36C2×#13133139C2211yescharacteristic
37C2×#13133139C2211yescharacteristic
38#16810530—21no—
39#16810526—21no—
40#16810503—21no—
41#16810503—21no—
42#16810483C2211yescharacteristic
43#16810483C2211yescharacteristic
44#16810483C2211yescharacteristic
45#16810483C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54C22×#41×C53C2211yescharacteristic
55C22×M16×C53C2211yescharacteristic
56C23×C8×C53C2211yescharacteristic
57C53×#408—24no—
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×#11719945—22no—
63C2×#11719945—41no—
64C2×#11719945—41no—
65C2×#11719945—41no—
66C2×#11719945—41no—
67C2×#11719945C2×C414yescomplemented
68C22×Dic106C2311yescharacteristic
69C22×D212C2311yescharacteristic
70C22×C22⋊D53—21no—
71C22×C22⋊D53—21no—
72C22×C22⋊D53—21no—
73C23×Dic53—21no—
74C23×Dic53—21no—
75C22×C4×D53—21no—
76#13133196—22no—
77#13133196—22no—
78#13133196C2×C414yes—
79#13133196C2×C414yescomplemented
80#13133193—28no—
81#13133191—22no—
82#13133191—22no—
83#13133191C2×C414yes—
84#13133191C2×C414yescomplemented
85#13133189—28no—
86#13133189—28no—
87#13133188—28no—
88#13133176—41no—
89#13133176—41no—
90C2×C4⋊Dic53—21no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—21no—
93C2×C4⋊Dic53—41no—
94C2×C4⋊Dic53—41no—
95C2×C4⋊Dic53C2×C414yescomplemented
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C4⋊Dic53C2311yescharacteristic
98C2×C4⋊Dic53C2311yescharacteristic
99C2×C4⋊Dic53C2311yescharacteristic
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×#11719919—21no—
103C2×#11719919—21no—
104C2×C22⋊Dic53—21no—
105C2×C22⋊Dic53—21no—
106C2×C22⋊Dic53—21no—
107C2×C22⋊Dic53—21no—
108C2×C22⋊Dic53—21no—
109C2×C22⋊Dic53—21no—
110C2×C22⋊Dic53—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C2×C4×Dic53—21no—
114#13133142—41no—
115#13133142—41no—
116#13133142—41no—
117#13133142—41no—
118#13133139—41no—
119#13133139—41no—
120#13133139—41no—
121#13133139—41no—
122#13133124—21no—
123#13133124—21no—
124#13133124—21no—
125#13133124—21no—
126C2×#41×C53—41no—
127C2×#41×C53—41no—
128C2×#41×C53—41no—
129C2×#41×C53—41no—
130C2×#41×C53C2×C414yes—
131C2×#41×C53D414yes—
132C22×Q8×C53D411yescharacteristic
133C22×D4×C53D411yescharacteristic
134C22×D4×C53D411yescharacteristic
135C22×D4×C53D411yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C2×M16×C53—22no—
140C2×M16×C53—41no—
141C2×M16×C53—41no—
142C22×C8×C53—22no—
143C22×C8×C53—41no—
144C22×C8×C53—41no—
145C22×C8×C53C2311yescharacteristic
146C22×C8×C53C2311yescharacteristic
147C22×C8×C53C2311yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C22⋊C8×C53—22no—
150C22⋊C8×C53—22no—
151C22⋊C8×C53—22no—
152C22⋊C8×C53—22no—
153C24×C53C2×D411yescharacteristic
154C24×C53C2×D411yescharacteristic
155C24×C53C2×D411yescharacteristic
156C23×D53—21no—
157#41×C53—44no—
158#41×C53—44no—
159#41×C53—44no—
160#41×C53—44no—
161C2×Q8×C53—41no—
162C2×Q8×C53—41no—
163C2×Q8×C53C22⋊C414yes—
164C2×D4×C53—41no—
165C2×D4×C53—41no—
166C2×D4×C53—41no—
167C2×D4×C53—41no—
168C2×D4×C53—41no—
169C2×D4×C53—41no—
170C2×D4×C53C22⋊C414yes—
171C2×D4×C53C22⋊C414yes—
172C2×D4×C53C22⋊C414yes—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53C22×C412yes—
186C22×C4×C53C22×C412yes—
187C22×C4×C53C22×C412yes—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2411yescharacteristic
195C2×C22⋊D53—24no—
196C2×C22⋊D53—24no—
197C2×C22⋊D53—24no—
198C2×C22⋊D53—42no—
199C2×C22⋊D53—42no—
200C2×C22⋊D53—81no—
201C2×C22⋊D53—81no—
202C2×C22⋊D53—81no—
203C2×C22⋊D53—81no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—42no—
213C22×Dic53—81no—
214C22×Dic53—81no—
215C22×Dic53—81no—
216C22×Dic53—81no—
217#11719945—44no—
218#11719945—44no—
219#11719945—44no—
220#11719945—44no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—21no—
226C2×D212C22×C412yes—
227C2×C4×D53—24no—
228C2×C4×D53—42no—
229C2×C4×D53—42no—
230C2×Dic106—21no—
231C2×Dic106—21no—
232C2×Dic106—21no—
233C2×Dic106—21no—
234C2×Dic106—21no—
235C2×Dic106C22×C412yes—
236M16×C53—44no—
237C2×C8×C53—21no—
238C2×C8×C53—21no—
239C2×C8×C53—21no—
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—44no—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252C22⋊Dic53—42no—
253C22⋊Dic53—81no—
254C22⋊Dic53—81no—
255C22⋊Dic53—81no—
256C22⋊Dic53—81no—
257#11719921—24no—
258#11719921—24no—
259C4⋊Dic53—24no—
260C4⋊Dic53—21no—
261C4⋊Dic53—21no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—42no—
271C4⋊Dic53C22×C412yes—
272C4⋊Dic53C22×C412yes—
273#11719919—24no—
274#11719919—24no—
275C4×Dic53—42no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53C2×C22⋊C412yes—
295C23×C53C2×C22⋊C412yes—
296C23×C53C2×C22⋊C412yes—
297C23×C53C22×D411yescharacteristic
298C22×D53—22no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305Q8×C53—44no—
306D4×C53—44no—
307D4×C53—44no—
308D4×C53—44no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53C2×C22⋊C412yes—
328C2×C4×C53C2×C22⋊C412yes—
329C2×C4×C53C2×C22⋊C412yes—
330C2×C4×C53C23×C411yescharacteristic
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53H(5,𝔽2)11yescharacteristic
333C2×C4×C53H(5,𝔽2)11yescharacteristic
334C2×C4×C53H(5,𝔽2)11yescharacteristic
335C2×C4×C53H(5,𝔽2)11yescharacteristic
336C22⋊D53—48no—
337C22⋊D53—84no—
338C22⋊D53—84no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—41no—
358C2×Dic53—41no—
359C2×Dic53—41no—
360C2×Dic53—84no—
361C2×Dic53—84no—
362D212—22no—
363D212—22no—
364D212—41no—
365D212—41no—
366C4×D53—48no—
367Dic106—22no—
368Dic106—22no—
369Dic106—41no—
370Dic106—41no—
371C8×C53—41no—
372C8×C53—41no—
373C8×C53—41no—
374C8×C53—41no—
375#21772—531nomaximal, Sylow
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—22no—
384C22×C53—22no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—41no—
393C22×C53—41no—
394C22×C53—41no—
395C22×C53—41no—
396C22×C53—41no—
397C22×C53C22×C22⋊C411yescharacteristic
398C22×C53#53411yescharacteristic
399C22×C53#53411yescharacteristic
400C22×C53#57611yescharacteristic
401C22×C53#57711yescharacteristic
402C22×C53#57711yescharacteristic
403C22×C53#57811yescharacteristic
404C2×D53—42no—
405C2×D53—42no—
406C2×D53—42no—
407C2×D53—81no—
408C2×D53—81no—
409C2×D53—81no—
410C2×D53—81no—
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53#51811yescharacteristic
415C4×C53#51811yescharacteristic
416C4×C53#53411yescharacteristic
417C4×C53#53411yescharacteristic
418Dic53—42no—
419Dic53—42no—
420Dic53—42no—
421Dic53—81no—
422Dic53—81no—
423Dic53—81no—
424Dic53—81no—
425C2×#537—531no—
426C2×#408D5311yescharacteristic, complemented
427#2311—531no—
428#1895—531no—
429#1894—531no—
430#1893—531no—
431#1892—531no—
432#1875—531no—
433#1874—531no—
434#1873—531no—
435#1872—531no—
436#1824—531no—
437#1823—531no—
438#1788—531no—
439#1788—531no—
440C2×C53—42no—
441C2×C53—42no—
442C2×C53—42no—
443C2×C53#230811yescharacteristic
444C2×C53#289711yescharacteristic
445C2×C53#289811yescharacteristic
446C2×C53#319811yescharacteristic
447C2×C53#320111yescharacteristic
448C2×C53#320311yescharacteristic
449C2×C53#320411yescharacteristic
450D53—82no—
451C22×#41—531no—
452C22×#41C2×D5311yescharacteristic
453C22×M16C2×D5311yescharacteristic
454C23×C8C2×D5311yescharacteristic
455#537—538no—
456#537—1064no—
457C2×C22⋊Q8—531no—
458C2×C22⋊Q8—531no—
459C2×C22⋊Q8—1061no—
460C2×#121—531no—
461C2×#121—531no—
462C2×#121—1061no—
463C2×#121—1061no—
464C2×#121—1061no—
465C2×#117—531no—
466C22×C4⋊C4—531no—
467C22×C4⋊C4—531no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476#408—24no—
477C2×C22⋊C8C2×D5311yescharacteristic
478C2×C22⋊C8C2×D5311yescharacteristic
479C2×C22⋊C8C2×D5311yescharacteristic
480C2×C22⋊C8C2×D5311yescharacteristic
481#391—1061no—
482#390—1061no—
483#386—1061no—
484#386—1061no—
485#380—531no—
486#380—531no—
487#380—531no—
488#380—531no—
489#340—531no—
490#340—531no—
491#340—531no—
492#340—531no—
493#340—531no—
494#340—531no—
495#340—531no—
496#340—531no—
497C53#2177211yescharacteristic, complemented, Sylow
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—534no—
503C2×#41—1062no—
504C2×#41—2121no—
505C2×#41—2121no—
506C2×#41—2121no—
507C2×#41—2121no—
508C2×#41C4×D5314yes—
509C2×#41C22⋊D5314yes—
510C22×Q8—531no—
511C22×Q8D21211yescharacteristic
512C22×D4—531no—
513C22×D4—1061no—
514C22×D4—1061no—
515C22×D4—1061no—
516C22×D4D21211yescharacteristic
517C22×D4D21211yescharacteristic
518C22×D4D21211yescharacteristic
519C23×C4—1061no—
520C23×C4—1061no—
521C23×C4—1061no—
522C23×C4C22×D5311yescharacteristic
523C23×C4C22×D5311yescharacteristic
524C23×C4C22×D5311yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C22×D5311yescharacteristic
532C22×C8C22×D5311yescharacteristic
533C22×C8C22×D5311yescharacteristic
534C22×C8C22×D5311yescharacteristic
535C22⋊Q8—534no—
536C22⋊Q8—534no—
537C22⋊Q8—1068no—
538C22⋊Q8—1062no—
539C22⋊Q8—1062no—
540#121—534no—
541#121—534no—
542#121—1068no—
543#121—1068no—
544#121—1068no—
545#121—1062no—
546#121—1062no—
547#117—2121no—
548#117—2121no—
549C2×C4⋊C4—534no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1062no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—2121no—
562C2×C4⋊C4—2121no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C42—1061no—
573#103—2121no—
574#103—2121no—
575#103—2121no—
576#103—2121no—
577#102—2121no—
578#102—2121no—
579#102—2121no—
580#102—2121no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—1061no—
586#95—1061no—
587#95—1061no—
588#95—1061no—
589C24—1061no—
590C24C2×D21211yescharacteristic
591C24C2×D21211yescharacteristic
592C24C2×D21211yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—2124no—
598#41—2124no—
599#41—2124no—
600#41—2124no—
601C2×Q8—41no—
602C2×Q8—41no—
603C2×Q8—532no—
604C2×Q8—1061no—
605C2×Q8—1061no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—1061no—
609C2×Q8#1171992114yes—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—532no—
617C2×D4—1064no—
618C2×D4—1064no—
619C2×D4—1064no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1061no—
623C2×D4—1061no—
624C2×D4—1061no—
625C2×D4—4241no—
626C2×D4—4241no—
627C2×D4—4241no—
628C2×D4—4241no—
629C2×D4—2122no—
630C2×D4—2122no—
631C2×D4#1171992114yes—
632C2×D4#1171992114yes—
633C2×D4#1171992114yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—1064no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—1064no—
651C22×C4—1061no—
652C22×C4—1061no—
653C22×C4—1061no—
654C22×C4—1061no—
655C22×C4—4241no—
656C22×C4—4241no—
657C22×C4—4241no—
658C22×C4—4241no—
659C22×C4—2122no—
660C22×C4—2122no—
661C22×C4—2122no—
662C22×C4C2×C4×D5312yes—
663C22×C4C2×C4×D5312yes—
664C22×C4C2×C4×D5312yes—
665C22×C4C2×D21211yescharacteristic
666C22×C4C2×D21211yescharacteristic
667C22×C4C2×D21211yescharacteristic
668C22×C4C2×C22⋊D5312yes—
669C22×C4C2×C22⋊D5312yes—
670C22×C4C2×C22⋊D5312yes—
671C22×C4C23×D5311yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—532no—
687C4⋊C4—532no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4—1061no—
694C4⋊C4—1061no—
695C4⋊C4—1061no—
696C4⋊C4—1061no—
697C4⋊C4—1061no—
698C4⋊C4—1061no—
699C4⋊C4—1061no—
700C4⋊C4—1061no—
701C4⋊C4—2122no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C22⋊C4—1064no—
705C22⋊C4—1064no—
706C22⋊C4—4241no—
707C22⋊C4—4241no—
708C22⋊C4—4241no—
709C22⋊C4—4241no—
710C22⋊C4—2122no—
711C42—2122no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—1062no—
731C23—2121no—
732C23—2121no—
733C23—2121no—
734C23—2121no—
735C23—2121no—
736C23—2121no—
737C23C2×#1171992112yes—
738C23C2×#1171992112yes—
739C23C2×#1171992112yes—
740C23C22×D21211yescharacteristic
741Q8—44no—
742Q8—1062no—
743Q8—1062no—
744Q8—2121no—
745Q8—2121no—
746D4—44no—
747D4—44no—
748D4—44no—
749D4—1062no—
750D4—1062no—
751D4—4244no—
752D4—4244no—
753D4—2128no—
754D4—2121no—
755D4—2121no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—1062no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—4244no—
778C2×C4—4244no—
779C2×C4—2128no—
780C2×C4—2121no—
781C2×C4—2121no—
782C2×C4—2121no—
783C2×C4—2121no—
784C2×C4—2121no—
785C2×C4—2121no—
786C2×C4—2121no—
787C2×C4—2121no—
788C2×C4—2121no—
789C2×C4—2121no—
790C2×C4—2121no—
791C2×C4—2121no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4C2×#1171992112yes—
799C2×C4C2×#1171992112yes—
800C2×C4C2×#1171992112yes—
801C2×C4C22×C4×D5311yescharacteristic
802C2×C4C22×C22⋊D5311yescharacteristic
803C2×C4#1313326211yescharacteristic
804C2×C4#1313326211yescharacteristic
805C2×C4#1313326211yescharacteristic
806C2×C4#1313326211yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—4241no—
833C22—4241no—
834C22—4241no—
835C22—4241no—
836C22—2122no—
837C22—2122no—
838C22—2122no—
839C22C22×#1171992111yescharacteristic
840C22#1681118511yescharacteristic
841C22#1681118511yescharacteristic
842C22#1681142811yescharacteristic
843C22#1681143511yescharacteristic
844C22#1681143511yescharacteristic
845C22#1681144011yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—4241no—
850C4—4241no—
851C4—4241no—
852C4—4241no—
853C4—2122no—
854C4—2122no—
855C4—2122no—
856C4#1681109611yescharacteristic
857C4#1681109611yescharacteristic
858C4#1681118211yescharacteristic
859C4#1681118211yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—4242no—
864C2#2027729011yescharacteristic
865C2#2028324211yescharacteristic
866C2#2028324911yescharacteristic
867C2#2028556911yescharacteristic
868C2#2028559911yescharacteristic
869C2#2028561711yescharacteristic
870C2#2028562711yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#408C2
socleC23×C53C22×D4
prime radicalC2×#16811201C2
cosocleC22×C4×C53C24
hypercenterC2×#408D53
hypocenterC53#21772
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #20277307C2semidirect
3. #20275153C2semidirect
4. #20275148C2semidirect
5. #20275143C2semidirect
6. #20275138C2semidirect
7. #20275035C2semidirect
8. #20275030C2semidirect
9. #20275025C2semidirect
10. #20275020C2semidirect
11. #20274806C2semidirect
12. #20274802C2semidirect
13. #20274656C2semidirect
14. #20274656C2semidirect
15. C2×C53×#408C2semidirect
18. #16811201C4semidirect
67. C2×#11719945C2×C4semidirect
79. #13133196C2×C4semidirect
84. #13133191C2×C4semidirect
95. C2×C4⋊Dic53C2×C4semidirect
426. C2×#408D53semidirect
497. C53#21772semidirect

Maximal subgroups

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

subgroupindex
C2×#168112012
#202773072
#202751532
#202751482
#202751432
#202751382
#202750352
#202750302
#202750252
#202750202
#202748062
#202748022
#202746562
C2×C53×#4082
#2177253