Finite Group Databasebeta

← #27306504

Subgroups — #27306504

Order 13568.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic106C211yesmaximal, characteristic
2C2×#16810527C212yesmaximal
3C2×#16810492C211yesmaximal, characteristic
4C2×C4⋊C4×Dic53C211yesmaximal, characteristic
5#20272967C212yesmaximal
6#20272966C212yesmaximal
7#20272945C211yesmaximal, characteristic
8#20272944C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10#20272943C212yesmaximal
11C53×C4⋊#95C211yesmaximal, characteristic
12C23×Dic106C2211yescharacteristic
13C2×C4×Dic106—24no—
14C2×C4×Dic106—24no—
15C2×C4×Dic106C418yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2212yes—
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810527—28no—
27#16810492—24no—
28C4⋊C4×Dic53—24no—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C42×C53C2211yescharacteristic
39C2×#95×C53C2212yes—
40C2×#95×C53C2212yes—
41C22×Dic106—22no—
42C22×Dic106—22no—
43C22×Dic106—22no—
44C22×Dic106—22no—
45C22×Dic106C2×C414yes—
46C22×Dic106D414yes—
47C22×Dic106Q814yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2312yes—
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C4×Dic106—232no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53—22no—
61C2×C4⋊Dic53—22no—
62C2×C4⋊Dic53C2×C414yes—
63C2×C4⋊Dic53Q814yescomplemented
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—22no—
67C2×#11719919—22no—
68C2×#11719919—24no—
69C2×#11719919—24no—
70C2×#11719919—24no—
71C2×#11719919—24no—
72C2×#11719919—42no—
73C2×#11719919—42no—
74C2×#11719919C2×C414yes—
75C2×#11719919C2×C414yes—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53C2×C414yes—
82C2×C4×Dic53C2×C414yes—
83C2×C4×Dic53D414yes—
84C2×C4×Dic53D414yes—
85#13133124—24no—
86#13133124—24no—
87#13133124—24no—
88#13133124—24no—
89#13133124—42no—
90#13133124—42no—
91#13133124—42no—
92C23×C4×C53C2312yes—
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53Q814yescomplemented
103C2×C42×C53—22no—
104C2×C42×C53—22no—
105C2×C42×C53C2×C414yes—
106#95×C53—24no—
107#95×C53—42no—
108C24×C53C2411yescharacteristic
109C22×C4×C53—21no—
110C22×C4×C53—21no—
111C22×C4×C53—21no—
112C22×C4×C53—21no—
113C22×C4×C53—22no—
114C22×C4×C53—21no—
115C22×C4×C53—21no—
116C22×C4×C53—22no—
117C22×C4×C53—22no—
118C22×C4×C53—22no—
119C22×C4×C53—21no—
120C22×C4×C53—22no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53C22×C412yes—
133C22×C4×C53C22×C412yes—
134C22×C4×C53C22×C412yes—
135C22×C4×C53C2×D412yes—
136C22×C4×C53C2×D412yes—
137C22×C4×C53C2×D412yes—
138C22×C4×C53C2×Q814yes—
139C22×C4×C53C2×Q812yes—
140C22×C4×C53C2×Q812yes—
141C22×C4×C53C2×Q812yes—
142C22×C4×C53#4112yes—
143C22×C4×C53#4112yes—
144C22×Dic53—21no—
145C22×Dic53—21no—
146C22×Dic53—21no—
147C22×Dic53—21no—
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—22no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53C22×C412yes—
172C22×Dic53C22×C412yes—
173C22×Dic53C22×C412yes—
174C22×Dic53C22×C412yes—
175C22×Dic53C2×D412yes—
176C22×Dic53C2×D412yes—
177C22×Dic53C2×D412yes—
178C22×Dic53C2×D412yes—
179C22×Dic53C2×D412yes—
180C22×Dic53C2×D412yes—
181C22×Dic53C2×Q814yes—
182C22×Dic53C2×Q812yes—
183C22×Dic53C2×Q812yes—
184C22×Dic53#4112yes—
185C22×Dic53#4112yes—
186C2×Dic106—28no—
187C2×Dic106—28no—
188C2×Dic106—28no—
189C2×Dic106—28no—
190C2×Dic106—28no—
191C2×Dic106—28no—
192C2×Dic106C4⋊C4116yescomplemented
193C4⋊C4×C53—28no—
194C4⋊C4×C53—44no—
195C42×C53—28no—
196C4⋊Dic53—28no—
197C4⋊Dic53—28no—
198C4⋊Dic53—44no—
199#11719919—28no—
200#11719919—28no—
201#11719919—48no—
202#11719919—48no—
203C4×Dic53—28no—
204C4×Dic53—48no—
205C4×Dic53C22⋊C4116yes—
206C23×C53C23×C411yescharacteristic
207C23×C53C22×D411yescharacteristic
208C23×C53C22×D411yescharacteristic
209C23×C53C22×D411yescharacteristic
210C23×C53C22×Q811yescharacteristic
211C23×C53C22×Q811yescharacteristic
212C23×C53C22×Q811yescharacteristic
213C23×C53C2×#4111yescharacteristic
214C23×C53C2×#4111yescharacteristic
215C23×C53C2×#4111yescharacteristic
216C23×C53C2×#4111yescharacteristic
217C23×C53H(5,𝔽2)11yescharacteristic
218C23×C53H(5,𝔽2)11yescharacteristic
219C23×C532−1+411yescharacteristic
220C23×C532−1+411yescharacteristic
221C2×C4×C53—22no—
222C2×C4×C53—22no—
223C2×C4×C53—22no—
224C2×C4×C53—22no—
225C2×C4×C53—22no—
226C2×C4×C53—22no—
227C2×C4×C53—22no—
228C2×C4×C53—22no—
229C2×C4×C53—22no—
230C2×C4×C53—24no—
231C2×C4×C53—24no—
232C2×C4×C53—24no—
233C2×C4×C53—42no—
234C2×C4×C53—41no—
235C2×C4×C53—41no—
236C2×C4×C53—41no—
237C2×C4×C53—42no—
238C2×C4×C53—41no—
239C2×C4×C53—42no—
240C2×C4×C53—42no—
241C2×C4×C53—42no—
242C2×C4×C53—42no—
243C2×C4×C53—42no—
244C2×C4×C53—42no—
245C2×C4×C53—42no—
246C2×C4×C53—42no—
247C2×C4×C53—42no—
248C2×C4×C53C2×C22⋊C414yes—
249C2×C4×C53C2×C4⋊C414yes—
250C2×C4×C53C4×Q814yes—
251C2×C4×C53C4×Q814yes—
252C2×C4×C53C22⋊Q814yes—
253C2×C4×C53C22⋊Q814yes—
254C2×C4×C53#12414yes—
255C2×C4×C53C4⋊Q814yes—
256C2×Dic53—22no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—22no—
262C2×Dic53—22no—
263C2×Dic53—22no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—22no—
271C2×Dic53—24no—
272C2×Dic53—24no—
273C2×Dic53—24no—
274C2×Dic53—42no—
275C2×Dic53—41no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53C2×C22⋊C414yes—
290C2×Dic53C2×C22⋊C414yes—
291C2×Dic53C2×C4⋊C414yes—
292C2×Dic53C2×C4⋊C414yes—
293C2×Dic53#11714yes—
294C2×Dic53#12114yes—
295C2×Dic53#12114yes—
296C2×Dic53C22⋊Q814yes—
297C2×Dic53C22⋊Q814yes—
298Dic106—232no—
299#13926—531nomaximal, Sylow
300C22×C53C22×C22⋊C411yescharacteristic
301C22×C53C22×C4⋊C411yescharacteristic
302C22×C53C2×#11711yescharacteristic
303C22×C53C2×C4×Q811yescharacteristic
304C22×C53C2×C4×Q811yescharacteristic
305C22×C53#52011yescharacteristic
306C22×C53#52011yescharacteristic
307C22×C53C2×#12111yescharacteristic
308C22×C53C2×#12111yescharacteristic
309C22×C53C2×C22⋊Q811yescharacteristic
310C22×C53C2×C22⋊Q811yescharacteristic
311C22×C53C2×C22⋊Q811yescharacteristic
312C22×C53C2×C22⋊Q811yescharacteristic
313C22×C53C2×#12411yescharacteristic
314C22×C53C2×C4⋊Q811yescharacteristic
315C22×C53#53511yescharacteristic
316C22×C53#53611yescharacteristic
317C22×C53#53711yescharacteristic
318C22×C53#53711yescharacteristic
319C22×C53D4×Q811yescharacteristic
320C22×C53D4×Q811yescharacteristic
321C22×C53#55011yescharacteristic
322C22×C53#55011yescharacteristic
323C22×C53#55411yescharacteristic
324C22×C53#55411yescharacteristic
325C22×C53#55611yescharacteristic
326C22×C53#55611yescharacteristic
327C22×C53#55711yescharacteristic
328C22×C53#55711yescharacteristic
329C22×C53#55711yescharacteristic
330C22×C53#55711yescharacteristic
331C22×C53Q8211yescharacteristic
332C22×C53Q8211yescharacteristic
333C22×C53#55911yescharacteristic
334C22×C53#55911yescharacteristic
335C4×C53—24no—
336C4×C53—42no—
337C4×C53—44no—
338C4×C53—82no—
339C4×C53#39118yescomplemented
340Dic53—24no—
341Dic53—24no—
342Dic53—42no—
343Dic53—44no—
344Dic53—82no—
345Dic53#38018yes—
346C22×C4×Q8—531no—
347C2×#391—532no—
348C2×#384—531no—
349C2×C4×C4⋊C4—531no—
350#1441—532no—
351#1441—532no—
352C4⋊#95—531no—
353C4⋊#95—532no—
354C4⋊#95—531no—
355C4⋊#95—531no—
356C4⋊#95D5311yescharacteristic
357C2×C53C2×#38011yescharacteristic
358C2×C53C2×#39111yescharacteristic
359C2×C53#231111yescharacteristic
360C2×C53Q8×C4⋊C411yescharacteristic
361C2×C53Q8×C4⋊C411yescharacteristic
362C2×C53#235511yescharacteristic
363C2×C53#235511yescharacteristic
364C2×C53#253811yescharacteristic
365C2×C53#253811yescharacteristic
366C2×C53#254611yescharacteristic
367C2×C53#254811yescharacteristic
368C2×C53#256711yescharacteristic
369C2×C53#256811yescharacteristic
370C2×C53#258211yescharacteristic
371C2×C53#258211yescharacteristic
372C23×Q8—531no—
373C2×C4×Q8—538no—
374C2×C4×Q8—1064no—
375C2×C4×Q8—1064no—
376C22×C4⋊C4—531no—
377C22×C4⋊C4—531no—
378C22×C4⋊C4—531no—
379C22×C4⋊C4—531no—
380C22×C4⋊C4—532no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—532no—
383C22×C4⋊C4C2×D5311yescharacteristic
384C22×C4⋊C4C2×D5311yescharacteristic
385C22×C42—531no—
386C22×C42—531no—
387C22×C42—532no—
388C22×C42C2×D5311yescharacteristic
389#391—1068no—
390#384—1064no—
391C4×C4⋊C4—1064no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—532no—
395C2×#95—532no—
396C2×#95—532no—
397C2×#95—532no—
398C2×#95—532no—
399C2×#95C2×D5312yes—
400C2×#95C2×D5312yes—
401C53#1392611yescharacteristic, complemented, Sylow
402C22×Q8—534no—
403C22×Q8—534no—
404C22×Q8—534no—
405C22×Q8—1062no—
406C22×Q8—1062no—
407C22×Q8—1062no—
408C22×Q8—1062no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—531no—
412C23×C4—531no—
413C23×C4—532no—
414C23×C4—532no—
415C23×C4C22×D5312yes—
416C23×C4C22×D5312yes—
417C23×C4C22×D5311yescharacteristic
418C23×C4C22×D5311yescharacteristic
419C23×C4C22×D5311yescharacteristic
420C4×Q8—10632no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—534no—
427C2×C4⋊C4—534no—
428C2×C4⋊C4—534no—
429C2×C4⋊C4—534no—
430C2×C4⋊C4—1062no—
431C2×C4⋊C4—1062no—
432C2×C4⋊C4—1062no—
433C2×C4⋊C4—1062no—
434C2×C4⋊C4—1062no—
435C2×C4⋊C4—1062no—
436C2×C4⋊C4—1062no—
437C2×C4⋊C4—1062no—
438C2×C4⋊C4—1064no—
439C2×C4⋊C4—1064no—
440C2×C4⋊C4—1064no—
441C2×C4⋊C4—1064no—
442C2×C4⋊C4—1062no—
443C2×C4⋊C4—1062no—
444C2×C4⋊C4—1062no—
445C2×C4⋊C4—2122no—
446C2×C4⋊C4—2122no—
447C2×C4⋊C4Dic10614yescomplemented
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—534no—
451C2×C42—534no—
452C2×C42—534no—
453C2×C42—534no—
454C2×C42—1062no—
455C2×C42—1062no—
456C2×C42—1064no—
457C2×C42—1064no—
458C2×C42—1064no—
459C2×C42C4×D5314yes—
460#95—24no—
461#95—42no—
462#95—1064no—
463#95—1064no—
464#95—1064no—
465#95—1064no—
466#95—2122no—
467#95—2122no—
468#95—2122no—
469C24C23×D5311yescharacteristic
470C2×Q8—5316no—
471C2×Q8—1068no—
472C2×Q8—1068no—
473C2×Q8—1068no—
474C2×Q8—1068no—
475C2×Q8—1068no—
476C2×Q8—1068no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—532no—
501C22×C4—532no—
502C22×C4—532no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—532no—
506C22×C4—532no—
507C22×C4—532no—
508C22×C4—532no—
509C22×C4—532no—
510C22×C4—532no—
511C22×C4—532no—
512C22×C4—532no—
513C22×C4—532no—
514C22×C4—534no—
515C22×C4—1061no—
516C22×C4—1061no—
517C22×C4—1061no—
518C22×C4—1061no—
519C22×C4—1061no—
520C22×C4—1061no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1061no—
526C22×C4—1061no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1061no—
530C22×C4—1062no—
531C22×C4—1061no—
532C22×C4—1061no—
533C22×C4—1062no—
534C22×C4—1061no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4C2×Dic10614yes—
543C22×C4C2×Dic10612yes—
544C22×C4C2×C4×D5312yes—
545C22×C4C2×C4×D5312yes—
546C22×C4C2×C4×D5312yes—
547C22×C4#1171994512yes—
548C22×C4D4×D5312yes—
549C22×C4D4×D5312yes—
550C22×C4D4×D5312yes—
551C22×C4#1171994712yes—
552C22×C4Q8×D5312yes—
553C22×C4Q8×D5312yes—
554C4⋊C4—28no—
555C4⋊C4—44no—
556C4⋊C4—1068no—
557C4⋊C4—1068no—
558C4⋊C4—1068no—
559C4⋊C4—1068no—
560C4⋊C4—2128no—
561C4⋊C4—2128no—
562C4⋊C4—2124no—
563C42—28no—
564C42—5316no—
565C42—1068no—
566C42—2128no—
567C23C22×C4×D5311yescharacteristic
568C23C2×D4×D5311yescharacteristic
569C23C2×D4×D5311yescharacteristic
570C23C2×D4×D5311yescharacteristic
571C23C2×Q8×D5311yescharacteristic
572C23C2×Q8×D5311yescharacteristic
573C23C22×Dic10611yescharacteristic
574C23#41×D5311yescharacteristic
575C23#41×D5311yescharacteristic
576C23C2×#1171994711yescharacteristic
577C23C2×#1171994511yescharacteristic
578C23#1313326211yescharacteristic
579C23#1313326311yescharacteristic
580C23#1313326411yescharacteristic
581C23#1313326511yescharacteristic
582Q8—10632no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—534no—
611C2×C4—534no—
612C2×C4—534no—
613C2×C4—534no—
614C2×C4—534no—
615C2×C4—534no—
616C2×C4—534no—
617C2×C4—534no—
618C2×C4—534no—
619C2×C4—1062no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1062no—
623C2×C4—1062no—
624C2×C4—1062no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1064no—
632C2×C4—1062no—
633C2×C4—1064no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1064no—
637C2×C4—2122no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4—2122no—
641C2×C4—2122no—
642C2×C4—2122no—
643C2×C4—2122no—
644C2×C4—2122no—
645C2×C4—2122no—
646C2×C4—2122no—
647C2×C4—2121no—
648C2×C4—2121no—
649C2×C4—2121no—
650C2×C4—2121no—
651C2×C4—2122no—
652C2×C4C22⋊C4×D5314yes—
653C2×C4C4⋊C4×D5314yes—
654C2×C4#1313318214yes—
655C2×C4C4×Dic10614yes—
656C2×C4#1313319414yes—
657C2×C4#1313319514yes—
658C2×C4#1313320314yes—
659C2×C4#1313321614yes—
660C22C2×C22⋊C4×D5311yescharacteristic
661C22C2×C4⋊C4×D5311yescharacteristic
662C22#117×D5311yescharacteristic
663C22C2×#1313318211yescharacteristic
664C22C2×C4×Dic10611yescharacteristic
665C22#1681110311yescharacteristic
666C22#1681110411yescharacteristic
667C22#121×D5311yescharacteristic
668C22#121×D5311yescharacteristic
669C22C22⋊Q8×D5311yescharacteristic
670C22C22⋊Q8×D5311yescharacteristic
671C22C2×#1313319411yescharacteristic
672C22C2×#1313319511yescharacteristic
673C22C2×#1313320311yescharacteristic
674C22C2×#1313321611yescharacteristic
675C22#1681118911yescharacteristic
676C22#1681119611yescharacteristic
677C22#1681120211yescharacteristic
678C22#1681120311yescharacteristic
679C22#1681128811yescharacteristic
680C22D4×Dic10611yescharacteristic
681C22#1681129311yescharacteristic
682C22#1681129411yescharacteristic
683C22#1681132911yescharacteristic
684C22#1681133211yescharacteristic
685C22#1681134211yescharacteristic
686C22#1681134511yescharacteristic
687C22#1681134811yescharacteristic
688C22#1681134911yescharacteristic
689C22#1681135011yescharacteristic
690C22#1681135111yescharacteristic
691C22#1681135311yescharacteristic
692C22Q8×Dic10611yescharacteristic
693C22#1681135511yescharacteristic
694C22#1681135611yescharacteristic
695C4—24no—
696C4—42no—
697C4—44no—
698C4—82no—
699C4—538no—
700C4—1064no—
701C4—1064no—
702C4—4242no—
703C4—2122no—
704C4—2124no—
705C4#1681052718yescomplemented
706C2#380×D5311yescharacteristic
707C2C2×#1681052711yescharacteristic
708C2#2027730411yescharacteristic
709C2#2027762711yescharacteristic
710C2C4⋊C4×Dic10611yescharacteristic
711C2#2027766711yescharacteristic
712C2#2027767311yescharacteristic
713C2#2027963511yescharacteristic
714C2#2027963611yescharacteristic
715C2#2027970211yescharacteristic
716C2#2027971611yescharacteristic
717C2#2027992211yescharacteristic
718C2#2027992911yescharacteristic
719C2#2028008611yescharacteristic
720C2#2028008711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, prime radical, cosocleC24×C53C24
hypercenterC4⋊#95D53
hypocenterC53#13926
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic106C4semidirect
63. C2×C4⋊Dic53Q8semidirect
102. C2×C4⋊C4×C53Q8semidirect
192. C2×Dic106C4⋊C4semidirect
339. C4×C53#391semidirect
401. C53#13926semidirect
447. C2×C4⋊C4Dic106semidirect
705. C4#16810527semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1062
C2×#168105272
C2×#168104922
C2×C4⋊C4×Dic532
#202729672
#202729662
#202729452
#202729442
#202729432
C53×C4⋊#952
#1392653