Finite Group Databasebeta

← #27307908

Subgroups — #27307908

Order 13568.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810530C212yesmaximal
2C2×#16810522C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic
4#20272986C212yesmaximal
5#20272968C212yesmaximal
6#20272947C212yesmaximal
7#20272945C211yesmaximal, characteristic
8#20272944C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10C4×#13133124C211yesmaximal, characteristic
11C22×C4⋊Q8×C53C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×C4×Dic53C2211yescharacteristic
16C22×C4×Dic53C2212yes—
17C22×C4×Dic53C2211yescharacteristic
18#16810530—28no—
19#16810522—24no—
20C4⋊C4×Dic53—24no—
21C2×#13133124C2211yescharacteristic
22C2×#13133124C2211yescharacteristic
23C2×#13133124C2212yes—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C23×Q8×C53C2212yes—
34C2×C4⋊Q8×C53—24no—
35C2×C4⋊Q8×C53—24no—
36C2×C4⋊Q8×C53C418yescomplemented
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C23×Dic53C2312yes—
42C23×Dic53C2311yescharacteristic
43C23×Dic53C2312yes—
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C2×C4⋊Dic53—22no—
48C2×C4⋊Dic53—24no—
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—22no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—22no—
53C2×C4⋊Dic53—24no—
54C2×C4⋊Dic53—42no—
55C2×C4⋊Dic53Q814yescomplemented
56C2×C4×Dic53—22no—
57C2×C4×Dic53—22no—
58C2×C4×Dic53—24no—
59C2×C4×Dic53—22no—
60C2×C4×Dic53—22no—
61C2×C4×Dic53—22no—
62C2×C4×Dic53—24no—
63C2×C4×Dic53—42no—
64C2×C4×Dic53Q814yescomplemented
65#13133124—24no—
66#13133124—24no—
67#13133124—24no—
68#13133124—22no—
69#13133124—22no—
70#13133124—24no—
71#13133124—24no—
72#13133124—24no—
73#13133124—42no—
74#13133124—42no—
75#13133124D414yes—
76#13133124Q814yescomplemented
77C22×Q8×C53—24no—
78C22×Q8×C53—24no—
79C22×Q8×C53—24no—
80C22×Q8×C53—24no—
81C22×Q8×C53—42no—
82C22×Q8×C53—42no—
83C22×Q8×C53C2×C418yes—
84C23×C4×C53C2312yes—
85C23×C4×C53C2312yes—
86C23×C4×C53C2311yescharacteristic
87C23×C4×C53C2311yescharacteristic
88C23×C4×C53C2311yescharacteristic
89C4⋊Q8×C53—232no—
90C2×C4⋊C4×C53—24no—
91C2×C4⋊C4×C53—24no—
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53C2×C414yes—
95C2×C4⋊C4×C53C2×C418yes—
96C2×C4⋊C4×C53C2×C414yes—
97C2×C4⋊C4×C53D414yes—
98C2×C4⋊C4×C53D414yes—
99C2×C42×C53—22no—
100C2×C42×C53—22no—
101C2×C42×C53C2×C414yes—
102C24×C53C2411yescharacteristic
103C2×Q8×C53—216no—
104C2×Q8×C53—216no—
105C2×Q8×C53—48no—
106C2×Q8×C53—48no—
107C2×Q8×C53—48no—
108C2×Q8×C53—48no—
109C2×Q8×C53—48no—
110C22×C4×C53—21no—
111C22×C4×C53—21no—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—22no—
115C22×C4×C53—22no—
116C22×C4×C53—21no—
117C22×C4×C53—21no—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—22no—
123C22×C4×C53—22no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53C22×C414yes—
129C22×C4×C53C22×C414yes—
130C22×C4×C53C22×C412yes—
131C22×C4×C53C22×C412yes—
132C22×C4×C53C22×C412yes—
133C22×C4×C53C2×D414yes—
134C22×C4×C53C2×D414yes—
135C22×C4×C53C2×D412yes—
136C22×C4×C53C2×D412yes—
137C22×C4×C53C2×D412yes—
138C22×C4×C53C2×Q812yes—
139C22×C4×C53C2×Q812yes—
140C22×C4×C53C2×Q812yes—
141C22×C4×C53#4112yes—
142C22×C4×C53#4112yes—
143C22×C4×C53#4112yes—
144C22×C4×C53#4112yes—
145C22×Dic53—21no—
146C22×Dic53—21no—
147C22×Dic53—21no—
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—22no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—22no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—21no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53C2×D412yes—
181C22×Dic53C2×D412yes—
182C22×Dic53C2×Q812yes—
183C22×Dic53C2×Q812yes—
184C22×Dic53C2×Q814yes—
185C22×Dic53C2×Q812yes—
186C22×Dic53C2×Q812yes—
187C4⋊C4×C53—216no—
188C4⋊C4×C53—28no—
189C4⋊C4×C53C22⋊C4116yes—
190C42×C53—28no—
191C4⋊Dic53—28no—
192C4⋊Dic53—48no—
193C4⋊Dic53—44no—
194C4×Dic53—28no—
195C4×Dic53—48no—
196C4×Dic53—44no—
197C23×C53C23×C411yescharacteristic
198C23×C53C22×D411yescharacteristic
199C23×C53C22×D411yescharacteristic
200C23×C53C22×D411yescharacteristic
201C23×C53C22×Q811yescharacteristic
202C23×C53C22×Q811yescharacteristic
203C23×C53C22×Q811yescharacteristic
204C23×C53C2×#4111yescharacteristic
205C23×C53C2×#4111yescharacteristic
206C23×C53C2×#4111yescharacteristic
207C23×C53C2×#4111yescharacteristic
208C23×C53H(5,𝔽2)11yescharacteristic
209C23×C53H(5,𝔽2)11yescharacteristic
210C23×C532−1+411yescharacteristic
211C23×C532−1+411yescharacteristic
212Q8×C53—432no—
213C2×C4×C53—22no—
214C2×C4×C53—22no—
215C2×C4×C53—24no—
216C2×C4×C53—24no—
217C2×C4×C53—22no—
218C2×C4×C53—22no—
219C2×C4×C53—22no—
220C2×C4×C53—22no—
221C2×C4×C53—24no—
222C2×C4×C53—24no—
223C2×C4×C53—24no—
224C2×C4×C53—24no—
225C2×C4×C53—22no—
226C2×C4×C53—22no—
227C2×C4×C53—22no—
228C2×C4×C53—22no—
229C2×C4×C53—22no—
230C2×C4×C53—22no—
231C2×C4×C53—24no—
232C2×C4×C53—24no—
233C2×C4×C53—24no—
234C2×C4×C53—42no—
235C2×C4×C53—42no—
236C2×C4×C53—42no—
237C2×C4×C53—42no—
238C2×C4×C53C2×C22⋊C418yes—
239C2×C4×C53C2×C22⋊C414yes—
240C2×C4×C53C4×D414yes—
241C2×C4×C53C4×Q814yes—
242C2×C4×C53C4×Q814yes—
243C2×C4×C53C4×Q814yes—
244C2×C4×C53C22⋊Q814yes—
245C2×C4×C53C22⋊Q814yes—
246C2×C4×C53#12414yes—
247C2×C4×C53C4⋊Q814yes—
248C2×Dic53—22no—
249C2×Dic53—22no—
250C2×Dic53—22no—
251C2×Dic53—22no—
252C2×Dic53—22no—
253C2×Dic53—22no—
254C2×Dic53—22no—
255C2×Dic53—24no—
256C2×Dic53—22no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—22no—
262C2×Dic53—22no—
263C2×Dic53—24no—
264C2×Dic53—24no—
265C2×Dic53—22no—
266C2×Dic53—41no—
267C2×Dic53—41no—
268C2×Dic53—42no—
269C2×Dic53—42no—
270C2×Dic53—41no—
271C2×Dic53—41no—
272C2×Dic53—42no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—41no—
276C2×Dic53—42no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—41no—
280C2×Dic53—41no—
281C2×Dic53—41no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53C4⋊Q814yescomplemented
290#14053—531nomaximal, Sylow
291C22×C53C22×C22⋊C411yescharacteristic
292C22×C53C2×C4×D411yescharacteristic
293C22×C53C2×C4×Q811yescharacteristic
294C22×C53C2×C4×Q811yescharacteristic
295C22×C53C2×C4×Q811yescharacteristic
296C22×C53#51811yescharacteristic
297C22×C53#51911yescharacteristic
298C22×C53C2×C22⋊Q811yescharacteristic
299C22×C53C2×C22⋊Q811yescharacteristic
300C22×C53C2×#12411yescharacteristic
301C22×C53C2×C4⋊Q811yescharacteristic
302C22×C53C2×C4⋊Q811yescharacteristic
303C22×C53#53211yescharacteristic
304C22×C53#53311yescharacteristic
305C22×C53#53311yescharacteristic
306C22×C53#54211yescharacteristic
307C22×C53#54211yescharacteristic
308C22×C53#54411yescharacteristic
309C22×C53#54411yescharacteristic
310C22×C53D4211yescharacteristic
311C22×C53D4211yescharacteristic
312C22×C53#54611yescharacteristic
313C22×C53#54611yescharacteristic
314C22×C53#54711yescharacteristic
315C22×C53#54811yescharacteristic
316C22×C53#54811yescharacteristic
317C22×C53D4×Q811yescharacteristic
318C22×C53D4×Q811yescharacteristic
319C22×C53D4×Q811yescharacteristic
320C22×C53#55411yescharacteristic
321C22×C53#55411yescharacteristic
322C22×C53#55511yescharacteristic
323C22×C53#55611yescharacteristic
324C22×C53#55711yescharacteristic
325C22×C53Q8211yescharacteristic
326C4×C53—28no—
327C4×C53—24no—
328C4×C53—24no—
329C4×C53—44no—
330C4×C53#39118yescomplemented
331Dic53—24no—
332Dic53—42no—
333Dic53—44no—
334Dic53—42no—
335Dic53—42no—
336Dic53—82no—
337C22×C4⋊Q8D5311yescharacteristic
338C2×#391—532no—
339C2×#389—531no—
340C2×C4×C4⋊C4—531no—
341#1446—532no—
342#1441—532no—
343#1436—532no—
344C4⋊#95—531no—
345C4⋊#95—531no—
346C4⋊#95—531no—
347C4×#95—531no—
348C2×C53C2×#39111yescharacteristic
349C2×C53C4×C4⋊Q811yescharacteristic
350C2×C53#233111yescharacteristic
351C2×C53D4×C22⋊C411yescharacteristic
352C2×C53Q8×C22⋊C411yescharacteristic
353C2×C53#236511yescharacteristic
354C2×C53#236911yescharacteristic
355C2×C53#243911yescharacteristic
356C2×C53#244011yescharacteristic
357C2×C53#245111yescharacteristic
358C2×C53#245211yescharacteristic
359C2×C53#249111yescharacteristic
360C2×C53#249211yescharacteristic
361C2×C53#255011yescharacteristic
362C2×C53#255111yescharacteristic
363C23×Q8C2×D5312yes—
364C2×C4⋊Q8—24no—
365C2×C4⋊Q8—24no—
366C2×C4⋊Q8Dic5318yescomplemented
367C22×C4⋊C4—531no—
368C22×C4⋊C4—531no—
369C22×C4⋊C4—532no—
370C22×C4⋊C4C2×D5311yescharacteristic
371C22×C4⋊C4C2×D5312yes—
372C22×C4⋊C4C2×D5311yescharacteristic
373C22×C42—531no—
374C22×C42—531no—
375C22×C42—532no—
376C22×C42C2×D5311yescharacteristic
377#391—1068no—
378#389—1064no—
379C4×C4⋊C4—1064no—
380C2×#95—531no—
381C2×#95—531no—
382C2×#95—531no—
383C2×#95—531no—
384C2×#95—532no—
385C2×#95—532no—
386C2×#95—532no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95—532no—
392C53#1405311yescharacteristic, complemented, Sylow
393C22×Q8—24no—
394C22×Q8—24no—
395C22×Q8—24no—
396C22×Q8—24no—
397C22×Q8—42no—
398C22×Q8—42no—
399C22×Q8C2×Dic5318yes—
400C23×C4—531no—
401C23×C4—531no—
402C23×C4—532no—
403C23×C4—531no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4C22×D5312yes—
407C23×C4C22×D5311yescharacteristic
408C23×C4C22×D5311yescharacteristic
409C23×C4C22×D5312yes—
410C23×C4C22×D5311yescharacteristic
411C4⋊Q8—232no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—534no—
417C2×C4⋊C4—1062no—
418C2×C4⋊C4—1062no—
419C2×C4⋊C4—1064no—
420C2×C4⋊C4—1062no—
421C2×C4⋊C4—1062no—
422C2×C4⋊C4—1064no—
423C2×C4⋊C4—1062no—
424C2×C4⋊C4—2122no—
425C2×C4⋊C4C2×Dic5314yes—
426C2×C4⋊C4C2×Dic5318yes—
427C2×C4⋊C4C2×Dic5314yes—
428C2×C4⋊C4C22⋊D5314yes—
429C2×C4⋊C4C22⋊D5314yes—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—534no—
433C2×C42—1062no—
434C2×C42—1062no—
435C2×C42—1064no—
436C2×C42—1062no—
437C2×C42—1062no—
438C2×C42—1064no—
439C2×C42—1062no—
440C2×C42—2122no—
441C2×C42C2×Dic5314yes—
442#95—534no—
443#95—534no—
444#95—1064no—
445#95—1064no—
446#95—1064no—
447#95—1062no—
448#95—1062no—
449#95—1064no—
450#95—1064no—
451#95—1064no—
452#95—2122no—
453#95—2122no—
454C24C23×D5311yescharacteristic
455C2×Q8—216no—
456C2×Q8—216no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—532no—
481C22×C4—532no—
482C22×C4—532no—
483C22×C4—532no—
484C22×C4—532no—
485C22×C4—532no—
486C22×C4—534no—
487C22×C4—1061no—
488C22×C4—1061no—
489C22×C4—1061no—
490C22×C4—1061no—
491C22×C4—1062no—
492C22×C4—1061no—
493C22×C4—1061no—
494C22×C4—1062no—
495C22×C4—1061no—
496C22×C4—1061no—
497C22×C4—1061no—
498C22×C4—1062no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1061no—
503C22×C4—1061no—
504C22×C4—1061no—
505C22×C4—1061no—
506C22×C4—1062no—
507C22×C4—1061no—
508C22×C4—1061no—
509C22×C4—1062no—
510C22×C4—1061no—
511C22×C4—1061no—
512C22×C4—1061no—
513C22×C4—1062no—
514C22×C4—1061no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4D4×D5312yes—
523C22×C4#1171994712yes—
524C22×C4Q8×D5312yes—
525C22×C4Q8×D5312yes—
526C22×C4Q8×D5312yes—
527C22×C4#1171994912yes—
528C22×C4#1171994912yes—
529C22×C4#1171994912yes—
530C22×C4C22×Dic5314yes—
531C22×C4C22×Dic5314yes—
532C22×C4C22×Dic5312yes—
533C22×C4C22×Dic5312yes—
534C22×C4C22×Dic5312yes—
535C22×C4C2×C22⋊D5314yes—
536C22×C4C2×C22⋊D5314yes—
537C22×C4C2×C22⋊D5312yes—
538C22×C4C2×C22⋊D5312yes—
539C4⋊C4—216no—
540C4⋊C4—28no—
541C4⋊C4—1068no—
542C4⋊C4—2128no—
543C4⋊C4—2124no—
544C4⋊C4C22⋊Dic53116yes—
545C42—28no—
546C42—1068no—
547C42—2128no—
548C42—2124no—
549C23C23×Dic5311yescharacteristic
550C23C2×D4×D5311yescharacteristic
551C23C22×C22⋊D5311yescharacteristic
552C23C22×C22⋊D5311yescharacteristic
553C23C2×Q8×D5311yescharacteristic
554C23C2×Q8×D5311yescharacteristic
555C23C2×Q8×D5311yescharacteristic
556C23C2×#1171994711yescharacteristic
557C23C2×#1171994911yescharacteristic
558C23C2×#1171994911yescharacteristic
559C23C2×#1171994911yescharacteristic
560C23#1313326211yescharacteristic
561C23#1313326211yescharacteristic
562C23#1313326511yescharacteristic
563C23#1313326511yescharacteristic
564Q8—432no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—534no—
591C2×C4—1062no—
592C2×C4—1062no—
593C2×C4—1062no—
594C2×C4—1062no—
595C2×C4—1062no—
596C2×C4—1062no—
597C2×C4—1062no—
598C2×C4—1062no—
599C2×C4—1064no—
600C2×C4—1064no—
601C2×C4—1062no—
602C2×C4—1062no—
603C2×C4—1064no—
604C2×C4—1062no—
605C2×C4—1062no—
606C2×C4—1062no—
607C2×C4—1062no—
608C2×C4—1062no—
609C2×C4—2122no—
610C2×C4—2122no—
611C2×C4—2122no—
612C2×C4—2122no—
613C2×C4—2122no—
614C2×C4—2122no—
615C2×C4—2122no—
616C2×C4—2121no—
617C2×C4—2121no—
618C2×C4—2122no—
619C2×C4—2121no—
620C2×C4—2121no—
621C2×C4—2121no—
622C2×C4—2121no—
623C2×C4—2121no—
624C2×C4—2121no—
625C2×C4—2121no—
626C2×C4—2121no—
627C2×C4—2122no—
628C2×C4—2122no—
629C2×C4—2121no—
630C2×C4—2121no—
631C2×C4—2122no—
632C2×C4C2×C22⋊Dic5318yes—
633C2×C4C2×C22⋊Dic5314yes—
634C2×C4D4×Dic5314yes—
635C2×C4Q8×Dic5314yes—
636C2×C4Q8×Dic5314yes—
637C2×C4Q8×Dic5314yes—
638C2×C4#1313319314yes—
639C2×C4#1313319314yes—
640C2×C4#1313320614yes—
641C2×C4#1313321514yes—
642C22C22×C22⋊Dic5311yescharacteristic
643C22C2×D4×Dic5311yescharacteristic
644C22C2×Q8×Dic5311yescharacteristic
645C22C2×Q8×Dic5311yescharacteristic
646C22C2×Q8×Dic5311yescharacteristic
647C22#1681109811yescharacteristic
648C22#1681110111yescharacteristic
649C22C2×#1313319311yescharacteristic
650C22C2×#1313319311yescharacteristic
651C22C2×#1313320611yescharacteristic
652C22C4⋊Q8×D5311yescharacteristic
653C22C2×#1313321511yescharacteristic
654C22#1681117411yescharacteristic
655C22#1681117811yescharacteristic
656C22#1681117811yescharacteristic
657C22#1681124711yescharacteristic
658C22#1681124711yescharacteristic
659C22#1681125011yescharacteristic
660C22#1681125011yescharacteristic
661C22D4×C22⋊D5311yescharacteristic
662C22D4×C22⋊D5311yescharacteristic
663C22#1681126711yescharacteristic
664C22#1681126711yescharacteristic
665C22#1681127611yescharacteristic
666C22#1681128411yescharacteristic
667C22#1681128411yescharacteristic
668C22Q8×C22⋊D5311yescharacteristic
669C22Q8×C22⋊D5311yescharacteristic
670C22#1681128811yescharacteristic
671C22#1681133411yescharacteristic
672C22#1681133411yescharacteristic
673C22#1681133911yescharacteristic
674C22#1681134711yescharacteristic
675C22#1681134811yescharacteristic
676C22#1681135311yescharacteristic
677C4—28no—
678C4—24no—
679C4—24no—
680C4—44no—
681C4—1064no—
682C4—4242no—
683C4—2124no—
684C4—2122no—
685C4—2122no—
686C4—2122no—
687C4#1681053018yescomplemented
688C2C2×#1681053011yescharacteristic
689C2C4⋊Q8×Dic5311yescharacteristic
690C2#2027746411yescharacteristic
691C2D4×C22⋊Dic5311yescharacteristic
692C2Q8×C22⋊Dic5311yescharacteristic
693C2#2027777511yescharacteristic
694C2#2027780511yescharacteristic
695C2#2027840211yescharacteristic
696C2#2027841311yescharacteristic
697C2#2027855011yescharacteristic
698C2#2027856111yescharacteristic
699C2#2027908111yescharacteristic
700C2#2027909211yescharacteristic
701C2#2027973211yescharacteristic
702C2#2027974211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×C4⋊Q8×C53C2
socle, prime radical, cosocleC24×C53C24
hypercenterC22×C4⋊Q8D53
hypocenterC53#14053
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
36. C2×C4⋊Q8×C53C4semidirect
55. C2×C4⋊Dic53Q8semidirect
64. C2×C4×Dic53Q8semidirect
76. #13133124Q8semidirect
289. C2×Dic53C4⋊Q8semidirect
330. C4×C53#391semidirect
366. C2×C4⋊Q8Dic53semidirect
392. C53#14053semidirect
687. C4#16810530semidirect

Maximal subgroups

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

subgroupindex
C2×#168105302
C2×#168105222
C2×C4⋊C4×Dic532
#202729862
#202729682
#202729472
#202729452
#202729442
C4×#131331242
C22×C4⋊Q8×C532
#1405353