Finite Group Databasebeta

← #103×C22⋊D53 #27399520

Subgroups — #103×C22⋊D53 #27399520

Order 13568.

1530 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×Q8×C22⋊D53C211yesmaximal, characteristic
2C2×C8×C22⋊D53C211yesmaximal, characteristic
3C2×#103×D53C211yesmaximal, characteristic, complemented
4C4⋊C4×C22⋊D53C211yesmaximal, characteristic
5#20275636C211yesmaximal, characteristic, complemented
6#20275515C211yesmaximal, characteristic, complemented
7#20275138C211yesmaximal, characteristic, complemented
8#20275135C211yesmaximal, characteristic, complemented
9#20275022C211yesmaximal, characteristic, complemented
10#20275019C211yesmaximal, characteristic, complemented
11#20274718C211yesmaximal, characteristic, complemented
12#20274650C211yesmaximal, characteristic, complemented
13#20274648C211yesmaximal, characteristic, complemented
14#103×Dic53C211yesmaximal, characteristic, complemented
15C22×#103×C53C211yesmaximal, characteristic, complemented
16C22×Q8×D53C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18Q8×C22⋊D53—24no—
19Q8×C22⋊D53C418yescomplemented
20C2×#13133215—21no—
21C2×#13133215C2211yescharacteristic
22C2×#13133196—21no—
23C2×#13133196C2211yescharacteristic
24C2×#13133193—21no—
25C2×#13133193C2211yescharacteristic
26C2×Q8×Dic53C2211yescharacteristic
27C2×C4×C22⋊D53—21no—
28C2×C4×C22⋊D53—21no—
29C2×C4×C22⋊D53C2211yescharacteristic
30C2×C4⋊C4×D53C2211yescharacteristic
31C8×C22⋊D53—24no—
32C2×#13133146C2211yescharacteristic
33C2×#13133142C2211yescharacteristic
34C2×#13133142C2211yescharacteristic
35C2×#13133141C2211yescharacteristic
36C2×#13133141C2211yescharacteristic
37C2×#13133141C2211yescharacteristic
38C2×#13133141C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41#103×D53—24no—
42C2×C22⋊#88322C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×C8×Dic53C2211yescharacteristic
45#16810518—21no—
46#16810496—21no—
47#16810494—21no—
48#16810492C2211yescharacteristic
49#16810483C2211yescharacteristic
50#16810480C2211yescharacteristic
51C4⋊C4×Dic53C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54#16810385C2211yescharacteristic
55#16810385C2211yescharacteristic
56C23×Q8×C53C2211yescharacteristic
57C23×C8×C53C2211yescharacteristic
58C22×C4⋊C4×C53C2211yescharacteristic
59C2×#103×C53—24no—
60C2×#103×C53C2211yescharacteristic
61C2×#103×C53C2211yescharacteristic
62C2×#103×C53C2211yescharacteristic
63C2×#103×C53C2211yescharacteristic
64C22×Dic106—21no—
65C22×Dic106C2311yescharacteristic
66C2×Q8×D53—22no—
67C2×Q8×D53—22no—
68C2×Q8×D53—22no—
69C2×Q8×D53—41no—
70C2×Q8×D53—41no—
71C2×Q8×D53C2×C414yescomplemented
72C22×C22⋊D53D411yescharacteristic
73C22×C4×D53—21no—
74C22×C4×D53—21no—
75C22×C4×D53C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C2×C8×D53—22no—
79C2×C8×D53—22no—
80C2×C8×D53—41no—
81#13133215—28no—
82#13133215—22no—
83#13133215C2×C414yescomplemented
84#13133196—28no—
85#13133196—22no—
86#13133196C2×C414yescomplemented
87#13133193—28no—
88#13133193—22no—
89#13133193C2×C414yescomplemented
90Q8×Dic53—22no—
91Q8×Dic53C2×C414yescomplemented
92C4×C22⋊D53—28no—
93C4×C22⋊D53—44no—
94C4×C22⋊D53C2×C414yes—
95C4×C22⋊D53D414yes—
96C2×C4⋊Dic53—21no—
97C2×C4⋊Dic53C2311yescharacteristic
98C2×C4⋊Dic53C2311yescharacteristic
99C2×C4⋊Dic53C2311yescharacteristic
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C2×#11719919—21no—
104C2×#11719919—21no—
105C2×#11719919—21no—
106C2×#11719919—21no—
107C2×#11719919D411yescharacteristic
108C4⋊C4×D53—22no—
109C4⋊C4×D53—41no—
110C2×C22⋊Dic53—21no—
111C2×C22⋊Dic53—21no—
112C2×C22⋊Dic53D411yescharacteristic
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921D411yescharacteristic
116C2×C4×Dic53—21no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53C2311yescharacteristic
119#13133146—22no—
120#13133142—22no—
121#13133142—41no—
122#13133141—22no—
123#13133141—22no—
124#13133141—41no—
125#13133141—41no—
126#13133140—22no—
127#13133140—41no—
128C22⋊#88322—22no—
129#13133129—22no—
130C8×Dic53—22no—
131#13133124—21no—
132#13133124—21no—
133#13133124—21no—
134C22×Q8×C53—22no—
135C22×Q8×C53—21no—
136C22×Q8×C53—22no—
137C22×Q8×C53—22no—
138C22×Q8×C53—41no—
139C22×Q8×C53—41no—
140C22×Q8×C53C2×C414yescomplemented
141C22×Q8×C53C2311yescharacteristic
142C22×Q8×C53C2311yescharacteristic
143C23×C4×C53—21no—
144C23×C4×C53—21no—
145C23×C4×C53C2311yescharacteristic
146C22×C8×C53—22no—
147C22×C8×C53—22no—
148C22×C8×C53—41no—
149C22×C8×C53C2311yescharacteristic
150C22×C8×C53C2311yescharacteristic
151C2×C4⋊C4×C53—21no—
152C2×C4⋊C4×C53—22no—
153C2×C4⋊C4×C53—41no—
154C2×C4⋊C4×C53C2311yescharacteristic
155C2×C4⋊C4×C53C2311yescharacteristic
156#103×C53—22no—
157#103×C53—22no—
158#103×C53—22no—
159#103×C53D414yescomplemented
160C24×C53C2×D411yescharacteristic
161C23×D53C2×D411yescharacteristic
162C2×Q8×C53—24no—
163C2×Q8×C53—21no—
164C2×Q8×C53—21no—
165C2×Q8×C53—21no—
166C2×Q8×C53—21no—
167C2×Q8×C53—28no—
168C2×Q8×C53—21no—
169C2×Q8×C53—21no—
170C2×Q8×C53—21no—
171C2×Q8×C53—21no—
172C2×Q8×C53—42no—
173C2×Q8×C53—42no—
174C2×Q8×C53—44no—
175C2×Q8×C53—44no—
176C2×Q8×C53—44no—
177C2×Q8×C53C22×C412yes—
178C2×Q8×C53C22×C412yes—
179C2×Q8×C53C2×D412yes—
180C2×Q8×C53#4112yes—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—24no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—42no—
191C22×C4×C53—42no—
192C22×C4×C53—42no—
193C22×C4×C53—42no—
194C22×C4×C53—81no—
195C22×C4×C53C22×C412yes—
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2411yescharacteristic
199C2×C22⋊D53C22⋊C414yes—
200C2×C22⋊D53SD1614yes—
201C2×C22⋊D53Q1614yes—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209Q8×D53—28no—
210Q8×D53—44no—
211Q8×D53—44no—
212Q8×D53—44no—
213C2×C4×D53—21no—
214C2×C4×D53—21no—
215C2×C4×D53—21no—
216C2×C4×D53—21no—
217C2×C4×D53—24no—
218C2×C4×D53—42no—
219C2×C4×D53—42no—
220C2×C4×D53—42no—
221C2×C4×D53—42no—
222C2×C4×D53—81no—
223C2×C4×D53C22×C412yes—
224C2×C4×D53C2×D412yes—
225C2×Dic106—21no—
226C2×Dic106—21no—
227C2×Dic106—21no—
228C2×Dic106—21no—
229C2×Dic106—21no—
230C2×Dic106—24no—
231C2×Dic106—42no—
232C2×Dic106—42no—
233C2×Dic106C22×C412yes—
234C2×C8×C53—21no—
235C2×C8×C53—21no—
236C2×C8×C53—21no—
237C2×C8×C53—21no—
238C2×C8×C53—21no—
239C2×C8×C53—44no—
240C2×C8×C53C2×D412yes—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—42no—
245C4⋊C4×C53C2×D412yes—
246C22⋊Dic53—24no—
247C22⋊Dic53—42no—
248C22⋊Dic53C22⋊C414yes—
249#11719921—24no—
250#11719921—42no—
251#11719921C22⋊C414yes—
252C4⋊Dic53—21no—
253C4⋊Dic53—24no—
254C4⋊Dic53—21no—
255C4⋊Dic53—21no—
256C4⋊Dic53—21no—
257C4⋊Dic53—21no—
258C4⋊Dic53C22×C412yes—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—42no—
264#11719919—42no—
265#11719919—81no—
266#11719919C22⋊C414yes—
267C4×Dic53—24no—
268C4×Dic53—42no—
269C4×Dic53C22×C412yes—
270C4×Dic53C2×D412yes—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C8×D53—44no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53C2×C22⋊C412yes—
283C23×C53C2×SD1612yes—
284C23×C53C2×Q1612yes—
285C23×C53C22×D411yescharacteristic
286C22×D53—21no—
287C22×D53—21no—
288C22×D53—21no—
289C22×D53—21no—
290C22×D53C2×C22⋊C412yes—
291C22×D53C2×SD1612yes—
292C22×D53C2×Q1612yes—
293Q8×C53—22no—
294Q8×C53—22no—
295Q8×C53—22no—
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53—48no—
299Q8×C53—41no—
300Q8×C53—41no—
301Q8×C53C4×D414yescomplemented
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—21no—
305C2×C4×C53—22no—
306C2×C4×C53—21no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—48no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—41no—
319C2×C4×C53—41no—
320C2×C4×C53—41no—
321C2×C4×C53—84no—
322C2×C4×C53C2×C22⋊C412yes—
323C2×C4×C53C23×C411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4111yescharacteristic
327C2×C4×C53H(5,𝔽2)11yescharacteristic
328C2×C4×C53H(5,𝔽2)11yescharacteristic
329C22⋊D53#103116yesdirect product factor
330C2×Dic53—21no—
331C2×Dic53—21no—
332C2×Dic53—21no—
333C2×Dic53—21no—
334C2×Dic53—22no—
335C2×Dic53—22no—
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—
346C2×Dic53C2×C22⋊C412yes—
347C2×Dic53C2×C22⋊C412yes—
348C2×Dic53C2×C22⋊C412yes—
349C2×Dic53C2×SD1612yes—
350C2×Dic53C2×Q1612yes—
351C4×D53—22no—
352C4×D53—22no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—48no—
356C4×D53—84no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—41no—
361Dic106—41no—
362C8×C53—22no—
363C8×C53—41no—
364#88322—41no—
365#88322—41no—
366D4×#103—531nomaximal, Sylow
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53C2×#10314yescomplemented
374C22×C53C22×C22⋊C411yescharacteristic
375C22×C53D4211yescharacteristic
376C22×C53#54611yescharacteristic
377C22×C53C22×SD1611yescharacteristic
378C22×C53C22×Q1611yescharacteristic
379C22×C53#57711yescharacteristic
380C22×C53#57811yescharacteristic
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—22no—
386C2×D53—22no—
387C2×D53C2×#10314yescomplemented
388C4×C53—24no—
389C4×C53—22no—
390C4×C53—42no—
391C4×C53—42no—
392C4×C53—81no—
393C4×C53C2×C4×D411yescharacteristic
394C4×C53#51811yescharacteristic
395C4×C53D4211yescharacteristic
396C4×C53#54611yescharacteristic
397Dic53—22no—
398Dic53—22no—
399Dic53—42no—
400Dic53—42no—
401Dic53—81no—
402Dic53—81no—
403Dic53C2×#10314yescomplemented
404C2×D4×Q8—531no—
405C2×C8×D4—531no—
406C22×#103—531no—
407C22×#103D5311yescharacteristic, complemented
408D4×C4⋊C4—531no—
409#1981—531no—
410#1956—531no—
411#1892—531no—
412#1892—531no—
413#1872—531no—
414#1872—531no—
415#1803—531no—
416#1787—531no—
417#1787—531no—
418C4×#103—531no—
419C2×C53—24no—
420C2×C53D4×C22⋊C411yescharacteristic
421C2×C53C22×#10311yescharacteristic
422C2×C53#289811yescharacteristic
423C2×C53D4×SD1611yescharacteristic
424C2×C53D4×Q1611yescharacteristic
425C2×C53#329811yescharacteristic
426C2×C53#329911yescharacteristic
427D53—24no—
428C23×Q8—531no—
429C23×Q8C2×D5311yescharacteristic
430C23×C8—531no—
431C23×C8C2×D5311yescharacteristic
432D4×Q8—538no—
433D4×Q8—1064no—
434C2×C4⋊Q8—531no—
435C2×C4⋊Q8—1061no—
436C2×C22⋊Q8—531no—
437C2×C22⋊Q8—531no—
438C2×C22⋊Q8—1061no—
439C2×C22⋊Q8—1061no—
440C2×C4×Q8—531no—
441C2×C4×D4—531no—
442C2×C4×D4—1061no—
443C2×C4×D4—1061no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4C2×D5311yescharacteristic
446C8×D4—1064no—
447C2×C4⋊C8—531no—
448C2×#103—24no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103—1064no—
458C2×#103C2×D5311yescharacteristic
459C2×#103C2×D5311yescharacteristic
460C2×#103C2×D5311yescharacteristic
461C2×#103C2×D5311yescharacteristic
462C2×C22⋊C8—531no—
463C2×C22⋊C8—531no—
464C2×C4×C8—531no—
465#389—1061no—
466#385—1061no—
467#385—1061no—
468#384—531no—
469#380—531no—
470#380—531no—
471C4×C4⋊C4—531no—
472#340—531no—
473#340—531no—
474#340—531no—
475#340—531no—
476C53D4×#10311yescharacteristic, complemented, Sylow
477C22×Q8—21no—
478C22×Q8—22no—
479C22×Q8—22no—
480C22×Q8—22no—
481C22×Q8—41no—
482C22×Q8—41no—
483C22×Q8—534no—
484C22×Q8—531no—
485C22×Q8—1061no—
486C22×Q8—1062no—
487C22×Q8—1062no—
488C22×Q8—1062no—
489C22×Q8—2121no—
490C22×Q8—2121no—
491C22×Q8C4×D5314yescomplemented
492C22×Q8C22×D5311yescharacteristic
493C22×Q8C22×D5311yescharacteristic
494C22×D4—531no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—531no—
498C23×C4—1061no—
499C23×C4—1061no—
500C23×C4C22×D5311yescharacteristic
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8—1062no—
507C22×C8—1062no—
508C22×C8—2121no—
509C22×C8C22×D5311yescharacteristic
510C22×C8C22×D5311yescharacteristic
511C4⋊Q8—534no—
512C4⋊Q8—1062no—
513C4⋊Q8—1068no—
514C22⋊Q8—534no—
515C22⋊Q8—534no—
516C22⋊Q8—1068no—
517C22⋊Q8—1068no—
518C22⋊Q8—1062no—
519C22⋊Q8—1062no—
520C4×Q8—534no—
521C4×Q8—1062no—
522C4×D4—534no—
523C4×D4—534no—
524C4×D4—1068no—
525C4×D4—2124no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—41no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—531no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4—531no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1062no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—2121no—
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C22⋊C4—531no—
546C2×C22⋊C4—531no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C42—531no—
552C2×C42—1061no—
553C2×C42—1061no—
554C4⋊C8—1062no—
555#103—22no—
556#103—22no—
557#103—22no—
558#103—1062no—
559#103—1062no—
560#103—1062no—
561#103—1062no—
562#103—2121no—
563#103—2121no—
564#103—2121no—
565#103—2121no—
566#103C22⋊D5314yesdirect product factor
567C22⋊C8—1062no—
568C22⋊C8—1062no—
569C4×C8—1062no—
570#95—1061no—
571#95—1061no—
572#95—1061no—
573C24—531no—
574C24D4×D5311yescharacteristic
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—28no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—42no—
586C2×Q8—42no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C2×Q8—532no—
591C2×Q8—1064no—
592C2×Q8—1061no—
593C2×Q8—1068no—
594C2×Q8—1061no—
595C2×Q8—1061no—
596C2×Q8—1061no—
597C2×Q8—1061no—
598C2×Q8—2122no—
599C2×Q8—2122no—
600C2×Q8—2124no—
601C2×Q8—2124no—
602C2×Q8—2124no—
603C2×Q8C2×C4×D5312yes—
604C2×Q8C2×C4×D5312yes—
605C2×Q8#1171994512yes—
606C2×Q8C2×C22⋊D5312yes—
607C2×D4—534no—
608C2×D4—534no—
609C2×D4—534no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—42no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—81no—
624C22×C4—531no—
625C22×C4—531no—
626C22×C4—531no—
627C22×C4—532no—
628C22×C4—532no—
629C22×C4—1064no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1061no—
634C22×C4—1061no—
635C22×C4—1061no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—4241no—
639C22×C4—2122no—
640C22×C4—2122no—
641C22×C4—2122no—
642C22×C4—2122no—
643C22×C4C2×C4×D5312yes—
644C22×C4D4×D5311yescharacteristic
645C22×C4D4×D5312yes—
646C22×C4C23×D5311yescharacteristic
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—44no—
653C2×C8—1061no—
654C2×C8—1061no—
655C2×C8—1061no—
656C2×C8—1061no—
657C2×C8—1061no—
658C2×C8—1061no—
659C2×C8—2124no—
660C2×C8C2×C22⋊D5312yes—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—42no—
665C4⋊C4—534no—
666C4⋊C4—532no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1064no—
671C4⋊C4—1064no—
672C4⋊C4—1061no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—4241no—
678C4⋊C4—2122no—
679C4⋊C4—2122no—
680C4⋊C4C2×C22⋊D5312yes—
681C22⋊C4—534no—
682C22⋊C4—534no—
683C22⋊C4—1064no—
684C22⋊C4—1064no—
685C22⋊C4—2122no—
686C22⋊C4—2122no—
687C42—532no—
688C42—532no—
689C42—1064no—
690C42—2122no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—532no—
696C23—532no—
697C23—532no—
698C23—1061no—
699C23—1061no—
700C23—1061no—
701C23—1061no—
702C23C22⋊C4×D5312yes—
703C23SD16×D5312yes—
704C23Q16×D5312yes—
705C23C2×D4×D5311yescharacteristic
706Q8—22no—
707Q8—22no—
708Q8—22no—
709Q8—22no—
710Q8—22no—
711Q8—48no—
712Q8—41no—
713Q8—41no—
714Q8—1062no—
715Q8—1062no—
716Q8—2128no—
717Q8—2121no—
718Q8—2121no—
719Q8C4×C22⋊D5314yescomplemented
720D4—5316no—
721C2×C4—22no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—48no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—84no—
741C2×C4—532no—
742C2×C4—532no—
743C2×C4—532no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—1061no—
747C2×C4—1061no—
748C2×C4—1061no—
749C2×C4—1061no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—4244no—
757C2×C4—2128no—
758C2×C4—2121no—
759C2×C4—2121no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2121no—
766C2×C4—2121no—
767C2×C4—2121no—
768C2×C4C22⋊C4×D5312yes—
769C2×C4C22×C4×D5311yescharacteristic
770C2×C4C2×D4×D5311yescharacteristic
771C2×C4C22×C22⋊D5311yescharacteristic
772C2×C4C2×#1171994511yescharacteristic
773C2×C4#1313326211yescharacteristic
774C2×C4#1313326211yescharacteristic
775C8—22no—
776C8—41no—
777C8—2121no—
778C8—2121no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—534no—
786C22—1062no—
787C22—1062no—
788C22—1062no—
789C22—1062no—
790C22—1062no—
791C22—1062no—
792C22#103×D5314yescomplemented
793C22C2×C22⋊C4×D5311yescharacteristic
794C22D4×C22⋊D5311yescharacteristic
795C22#1681126311yescharacteristic
796C22C2×SD16×D5311yescharacteristic
797C22C2×Q16×D5311yescharacteristic
798C22#1681142911yescharacteristic
799C22#1681143611yescharacteristic
800C4—22no—
801C4—24no—
802C4—42no—
803C4—42no—
804C4—81no—
805C4—534no—
806C4—1062no—
807C4—1062no—
808C4—4241no—
809C4—4241no—
810C4—2122no—
811C4—2122no—
812C4C2×C4×C22⋊D5311yescharacteristic
813C4#1681109611yescharacteristic
814C4D4×C22⋊D5311yescharacteristic
815C4#1681126311yescharacteristic
816C2—24no—
817C2—1064no—
818C2C22⋊C4×C22⋊D5311yescharacteristic
819C2C2×#103×D5311yescharacteristic
820C2#2028324311yescharacteristic
821C2SD16×C22⋊D5311yescharacteristic
822C2Q16×C22⋊D5311yescharacteristic
823C2#2028657611yescharacteristic
824C2#2028658711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#103×C53C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
cosocleC22×C4×C53C24
hypercenterC22×#103D53
hypocenterC53D4×#103
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#103×D53C2semidirect
5. #20275636C2semidirect
6. #20275515C2semidirect
7. #20275138C2semidirect
8. #20275135C2semidirect
9. #20275022C2semidirect
10. #20275019C2semidirect
11. #20274718C2semidirect
12. #20274650C2semidirect
13. #20274648C2semidirect
14. #103×Dic53C2semidirect
15. C22×#103×C53C2semidirect
19. Q8×C22⋊D53C4semidirect
71. C2×Q8×D53C2×C4semidirect
83. #13133215C2×C4semidirect
86. #13133196C2×C4semidirect
89. #13133193C2×C4semidirect
91. Q8×Dic53C2×C4semidirect
140. C22×Q8×C53C2×C4semidirect
159. #103×C53D4semidirect
301. Q8×C53C4×D4semidirect
329. C22⋊D53#103direct (N × H)
373. C22×C53C2×#103semidirect
387. C2×D53C2×#103semidirect
403. Dic53C2×#103semidirect
407. C22×#103D53semidirect
476. C53D4×#103semidirect
491. C22×Q8C4×D53semidirect
566. #103C22⋊D53direct (N × H)
719. Q8C4×C22⋊D53semidirect
792. C22#103×D53semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D532
C2×C8×C22⋊D532
C2×#103×D532
C4⋊C4×C22⋊D532
#202756362
#202755152
#202751382
#202751352
#202750222
#202750192
#202747182
#202746502
#202746482
#103×Dic532
C22×#103×C532
D4×#10353