Finite Group Databasebeta

← C2×#20286886 #28260714

Subgroups — C2×#20286886 #28260714

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic
2#20286886C2116yesmaximal, direct product factor
3C2×#16810991C211yesmaximal, characteristic, complemented
4C2×#16810956C211yesmaximal, characteristic, complemented
5C2×#16810961C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810854C211yesmaximal, characteristic, complemented
9C2×#16810825C211yesmaximal, characteristic, complemented
10C2×#16810762C211yesmaximal, characteristic, complemented
11C2×#16810762C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810632C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C53C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21C23×#88322C2211yescharacteristic
22#16811319—24no—
23#16811319C2218yes—
24C2×#13133212—21no—
25C2×#13133209C2211yescharacteristic
26C2×#13133199—21no—
27C2×#13133191C2211yescharacteristic
28C2×#13133191C2211yescharacteristic
29C2×#13133189—21no—
30C2×C4×D212C2211yescharacteristic
31C2×#13133177—21no—
32C2×#13133176C2211yescharacteristic
33C22×C4⋊Dic53C2211yescharacteristic
34#16810991C2218yescomplemented
35#16810961C2218yescomplemented
36#16810956C2218yescomplemented
37#16810930C2218yescomplemented
38#16810871C2218yescomplemented
39#16810854C2218yescomplemented
40#16810825C2218yescomplemented
41#16810762C2218yescomplemented
42#16810762C2218yescomplemented
43#16810721C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49#16810632C2218yescomplemented
50C2×#13133141C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133141C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133141C2211yescharacteristic
58C2×#13133141C2211yescharacteristic
59C2×#13133141C2218yescomplemented
60C2×#13133137C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic
63C2×#13133128C2211yescharacteristic
64C23×Q8×C53C2211yescharacteristic
65C23×Q8×C53C2211yescharacteristic
66D4×Q8×C53—24no—
67D4×Q8×C53C2218yescomplemented
68C2×C4⋊Q8×C53—21no—
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×C22⋊Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53—21no—
76C2×C4×D4×C53C2211yescharacteristic
77C22×D212C2311yescharacteristic
78C22×C22⋊D53—21no—
79C22×C22⋊D53—21no—
80C23×Dic53—21no—
81C22×C4×D53—21no—
82C2×#11719924—24no—
83C2×#11719924—42no—
84C2×#11719924—42no—
85C2×#11719924C2314yes—
86C2×#11719924C2314yes—
87C2×#11719924C2314yes—
88C2×#11719917—42no—
89C2×#11719917C2314yes—
90C22×#88322—42no—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2311yescharacteristic
95C22×#88322C2314yes—
96#13133212—28no—
97#13133209—22no—
98#13133209C2314yes—
99#13133199—28no—
100#13133191—22no—
101#13133191—22no—
102#13133191C2314yes—
103#13133191C2314yes—
104#13133189—28no—
105C4×D212—22no—
106C4×D212C2314yes—
107#13133177—28no—
108#13133176—22no—
109#13133176C2314yes—
110C2×C4⋊Dic53—22no—
111C2×C4⋊Dic53—21no—
112C2×C4⋊Dic53C2314yes—
113C2×C4⋊Dic53C2311yescharacteristic
114C2×C4⋊Dic53C2311yescharacteristic
115C2×C4⋊Dic53C2311yescharacteristic
116C2×#11719919—21no—
117C2×#11719919—21no—
118C2×C22⋊Dic53—21no—
119C2×#11719921—21no—
120C2×#11719921—21no—
121C2×#11719921—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yes—
124#13133150C2314yes—
125#13133148C2314yes—
126C4⋊#88322C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133141C2314yes—
132#13133141C2314yes—
133#13133141C2314yes—
134#13133141C2314yes—
135#13133141C2314yes—
136#13133137C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yes—
139#13133128C2314yes—
140C22×Q8×C53—21no—
141C22×Q8×C53—21no—
142C22×Q8×C53—22no—
143C22×Q8×C53—22no—
144C22×Q8×C53—24no—
145C22×Q8×C53—24no—
146C22×Q8×C53—42no—
147C22×Q8×C53—42no—
148C22×Q8×C53C2311yescharacteristic
149C22×Q8×C53C2311yescharacteristic
150C22×Q8×C53C2314yes—
151C22×Q8×C53C2314yes—
152C22×Q8×C53C2311yescharacteristic
153C22×D4×C53D411yescharacteristic
154C23×C4×C53—21no—
155C23×C4×C53—21no—
156C23×C4×C53C2311yescharacteristic
157C23×C4×C53C2311yescharacteristic
158C4⋊Q8×C53—28no—
159C4⋊Q8×C53—22no—
160C4⋊Q8×C53C2314yes—
161C22⋊Q8×C53—28no—
162C22⋊Q8×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53C2314yes—
166C22⋊Q8×C53C2314yes—
167C4×Q8×C53—22no—
168C4×Q8×C53C2314yes—
169C4×D4×C53—28no—
170C4×D4×C53D414yes—
171C4×D4×C53C2314yes—
172C2×C4⋊C4×C53—21no—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53D411yescharacteristic
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C42×C53—21no—
184C2×C42×C53C2311yescharacteristic
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—24no—
191C2×Q8×C53—21no—
192C2×Q8×C53—21no—
193C2×Q8×C53—22no—
194C2×Q8×C53—28no—
195C2×Q8×C53—28no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—44no—
201C2×Q8×C53—44no—
202C2×Q8×C53—44no—
203C2×Q8×C53—44no—
204C2×Q8×C53—48no—
205C2×Q8×C53—48no—
206C2×Q8×C53#4114yes—
207C2×Q8×C53C2412yes—
208C2×Q8×C53C2412yes—
209C2×Q8×C53C2412yes—
210C2×D4×C53—24no—
211C2×D4×C53C2×D414yes—
212C22×C4×C53—21no—
213C22×C4×C53—22no—
214C22×C4×C53—22no—
215C22×C4×C53—22no—
216C22×C4×C53—22no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—24no—
221C22×C4×C53—24no—
222C22×C4×C53—44no—
223C22×C4×C53—44no—
224C22×C4×C53C2×D411yescharacteristic
225C22×C4×C53C2×D411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53C2×D412yes—
229C22×C4×C53C2×D412yes—
230C22×C4×C53C2412yes—
231C22×C4×C53C2412yes—
232C22×C4×C53C2411yescharacteristic
233C2×C22⋊D53—24no—
234C2×C22⋊D53—24no—
235C2×C22⋊D53—44no—
236C2×C22⋊D53—82no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—24no—
241C22×Dic53—82no—
242C2×D212—22no—
243C2×D212—22no—
244C2×D212—21no—
245C2×D212C2412yes—
246C2×C4×D53—24no—
247C2×C4×D53—82no—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—24no—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53C2×D414yes—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊C4×C53—24no—
258C22⋊C4×C53C2×D414yes—
259C22⋊C4×C53C2×D414yes—
260C42×C53—24no—
261C42×C53C2×D412yes—
262C42×C53C2412yes—
263C22⋊Dic53—24no—
264#11719924—28no—
265#11719924—44no—
266#11719924—44no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53—21no—
274C4⋊Dic53C2412yes—
275C4⋊Dic53C2412yes—
276C4⋊Dic53C2412yes—
277#11719919—24no—
278#11719919—24no—
279C4×Dic53—24no—
280#11719917—44no—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—44no—
286C2×#88322C2412yes—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53#13714yes—
296C23×C53C22×D412yes—
297C23×C53C22×D412yes—
298C23×C53C22×D411yescharacteristic
299C22×D53—22no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53—42no—
303Q8×C53—24no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—22no—
307Q8×C53—22no—
308Q8×C53—22no—
309Q8×C53—48no—
310Q8×C53—48no—
311Q8×C53—42no—
312Q8×C53—42no—
313Q8×C53C2×#4114yes—
314D4×C53—28no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—24no—
322C2×C4×C53—24no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—48no—
331C2×C4×C53—48no—
332C2×C4×C53—42no—
333C2×C4×C53—42no—
334C2×C4×C53—42no—
335C2×C4×C53C22×D412yes—
336C2×C4×C53C22×D412yes—
337C2×C4×C53C22×D412yes—
338C2×C4×C53C22×D412yes—
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C2×#4112yes—
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53C2511yescharacteristic
343C22⋊D53—48no—
344C22⋊D53—84no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—84no—
352D212—22no—
353D212—22no—
354D212—42no—
355C4×D53—84no—
356#88322—22no—
357#88322—22no—
358#88322—22no—
359#88322—22no—
360C2×#3320—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—28no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—44no—
368C22×C53#54612yes—
369C22×C53C2×#13714yes—
370C22×C53C2×#13712yes—
371C22×C53#57712yes—
372C22×C53C23×D411yescharacteristic
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—84no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—24no—
380C4×C53—22no—
381C4×C53—22no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53#54612yes—
386C4×C53C22×#4111yescharacteristic
387C4×C53C2×H(5,𝔽2)11yescharacteristic
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391C2×#553—531no—
392C2×D4×Q8D5311yescharacteristic, complemented
393#3320—5316no—
394C2×#491—531no—
395C2×#484—531no—
396C2×#485—531no—
397C2×#479—531no—
398C2×#468—531no—
399C2×#465—531no—
400C2×#461—531no—
401C2×#448—531no—
402C2×#448—531no—
403C2×#440—531no—
404C2×#435—531no—
405C2×#419—531no—
406C22×#103—531no—
407C2×C53—24no—
408C2×C53—42no—
409C2×C53#332014yescomplemented
410C2×C53C2×#54611yescharacteristic
411C2×C53C22×#13711yescharacteristic
412C2×C53C2×#57711yescharacteristic
413D53—82no—
414C23×Q8C2×D5311yescharacteristic
415C23×Q8C2×D5311yescharacteristic
416C22×SD16—531no—
417C22×SD16—531no—
418C22×SD16—531no—
419C22×M16—531no—
420C23×C8—531no—
421#553—538no—
422#553—1064no—
423D4×Q8—24no—
424D4×Q8C2×D5318yescomplemented
425C2×C4⋊Q8—21no—
426C2×C4⋊Q8C2×D5311yescharacteristic
427C2×#126—1061no—
428C2×#125—531no—
429C2×#123—1061no—
430C2×C22⋊Q8—21no—
431C2×C22⋊Q8—21no—
432C2×C22⋊Q8C2×D5311yescharacteristic
433C2×C22⋊Q8C2×D5311yescharacteristic
434C2×#121—531no—
435C2×#121—531no—
436C2×#121—1061no—
437C2×C4×Q8C2×D5311yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×#117—531no—
443C22×C4⋊C4—531no—
444#491—538no—
445#485—538no—
446#484—538no—
447#479—538no—
448#468—538no—
449#465—538no—
450#461—538no—
451#448—538no—
452#448—538no—
453#440—538no—
454#435—538no—
455C2×#107—531no—
456C2×#107—531no—
457C2×#106—531no—
458C2×C4⋊C8—531no—
459#419—538no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—531no—
469C2×#103—538no—
470C2×#102—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8—531no—
473C2×#97—531no—
474C53C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—21no—
476C22×Q8—21no—
477C22×Q8—22no—
478C22×Q8—22no—
479C22×Q8—24no—
480C22×Q8—24no—
481C22×Q8—42no—
482C22×Q8—42no—
483C22×Q8C22×D5311yescharacteristic
484C22×Q8C22×D5311yescharacteristic
485C22×Q8C22×D5314yes—
486C22×Q8C22×D5314yes—
487C22×Q8C22×D5311yescharacteristic
488C22×D4—531no—
489C22×D4—1061no—
490C22×D4—1061no—
491C22×D4C22⋊D5311yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—534no—
501C2×SD16—1064no—
502C2×SD16—2122no—
503C2×SD16—2122no—
504C2×M16—534no—
505C2×M16—2122no—
506C22×C8—531no—
507C22×C8—531no—
508C22×C8—531no—
509C22×C8—531no—
510C22×C8—534no—
511C22×C8—2122no—
512C4⋊Q8—28no—
513C4⋊Q8—22no—
514C4⋊Q8C22×D5314yes—
515#126—1068no—
516#125—534no—
517#125—1062no—
518#123—1068no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521C22⋊Q8—28no—
522C22⋊Q8—28no—
523C22⋊Q8C22×D5314yes—
524C22⋊Q8C22×D5314yes—
525#121—534no—
526#121—534no—
527#121—1068no—
528#121—1062no—
529#121—1062no—
530C4×Q8—22no—
531C4×Q8C22×D5314yes—
532C4×D4—28no—
533C4×D4—534no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4C22⋊D5314yes—
537C4×D4C22×D5314yes—
538#117—534no—
539#117—1062no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—531no—
547C2×C4⋊C4—534no—
548C2×C4⋊C4—531no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1062no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4C22⋊D5311yescharacteristic
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4C22⋊D5311yescharacteristic
562C2×C22⋊C4C22⋊D5311yescharacteristic
563C2×C42—21no—
564C2×C42—1061no—
565C2×C42C22×D5311yescharacteristic
566#107—534no—
567#107—534no—
568#106—534no—
569C4⋊C8—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#103—534no—
576#103—534no—
577#103—534no—
578#103—534no—
579#102—534no—
580C22⋊C8—534no—
581C22⋊C8—534no—
582#97—534no—
583C24—1061no—
584C24C2×C22⋊D5311yescharacteristic
585C24C2×C22⋊D5311yescharacteristic
586C2×Q8—21no—
587C2×Q8—24no—
588C2×Q8—24no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—28no—
593C2×Q8—28no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8—22no—
598C2×Q8—44no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8—48no—
603C2×Q8—48no—
604C2×Q8#1171994714yes—
605C2×Q8C23×D5312yes—
606C2×Q8C23×D5312yes—
607C2×Q8C23×D5312yes—
608C2×D4—24no—
609C2×D4—532no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1061no—
613C2×D4—1062no—
614C2×D4—1062no—
615C2×D4—4242no—
616C2×D4—2124no—
617C2×D4C2×C22⋊D5314yes—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—1064no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—1061no—
634C22×C4—1064no—
635C22×C4—4242no—
636C22×C4—4242no—
637C22×C4C2×C22⋊D5312yes—
638C22×C4C2×C22⋊D5312yes—
639C22×C4C2×C22⋊D5311yescharacteristic
640C22×C4C2×C22⋊D5311yescharacteristic
641C22×C4C2×C22⋊D5311yescharacteristic
642C22×C4C2×C22⋊D5311yescharacteristic
643C22×C4C23×D5312yes—
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646SD16—1068no—
647SD16—2124no—
648SD16—2124no—
649M16—2124no—
650C2×C8—532no—
651C2×C8—532no—
652C2×C8—532no—
653C2×C8—532no—
654C2×C8—1062no—
655C2×C8—1062no—
656C2×C8—1062no—
657C2×C8—1062no—
658C2×C8—2124no—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—21no—
665C4⋊C4—532no—
666C4⋊C4—532no—
667C4⋊C4—532no—
668C4⋊C4—1061no—
669C4⋊C4—1061no—
670C4⋊C4—1064no—
671C4⋊C4—1061no—
672C4⋊C4—1064no—
673C4⋊C4—1064no—
674C4⋊C4C2×C22⋊D5314yes—
675C4⋊C4C23×D5312yes—
676C22⋊C4—24no—
677C22⋊C4—24no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4C2×C22⋊D5314yes—
683C22⋊C4C2×C22⋊D5314yes—
684C42—24no—
685C42—1064no—
686C42C2×C22⋊D5312yes—
687C42C23×D5312yes—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—1062no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23#1313324814yes—
698C23C22×C22⋊D5312yes—
699C23C22×C22⋊D5312yes—
700C23C22×C22⋊D5311yescharacteristic
701Q8—24no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—22no—
706Q8—22no—
707Q8—48no—
708Q8—48no—
709Q8—42no—
710Q8—42no—
711Q8C2×#1171994714yes—
712D4—28no—
713D4—1062no—
714D4—1062no—
715D4—4244no—
716D4—2128no—
717D4—2122no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—48no—
734C2×C4—48no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—4244no—
742C2×C4—4244no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4C22×C22⋊D5312yes—
747C2×C4C22×C22⋊D5312yes—
748C2×C4C22×C22⋊D5312yes—
749C2×C4C22×C22⋊D5312yes—
750C2×C4C22×C22⋊D5311yescharacteristic
751C2×C4C2×#1171994712yes—
752C2×C4#1313326212yes—
753C2×C4C24×D5311yescharacteristic
754C8—1062no—
755C8—1062no—
756C8—1062no—
757C8—1062no—
758C22—22no—
759C22—28no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—44no—
765C22—4244no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22#1681126712yes—
770C22C2×#1313324814yes—
771C22C2×#1313324812yes—
772C22#1681143112yes—
773C22C23×C22⋊D5311yescharacteristic
774C4—22no—
775C4—22no—
776C4—24no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C4#1681126712yes—
786C4C22×#1171994711yescharacteristic
787C4C2×#1313326211yescharacteristic
788C2—24no—
789C2—42no—
790C2—4242no—
791C2#2028688614yesdirect product factor
792C2C2×#1681126711yescharacteristic
793C2C22×#1313324811yescharacteristic
794C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811319C2
hypercenterC2×D4×Q8D53
hypocenterC53C2×#3320
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #20286886C2direct (N × H)
3. C2×#16810991C2semidirect
4. C2×#16810956C2semidirect
5. C2×#16810961C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810854C2semidirect
9. C2×#16810825C2semidirect
10. C2×#16810762C2semidirect
11. C2×#16810762C2semidirect
12. C2×#16810721C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810632C2semidirect
15. C22×#13133141C2semidirect
16. C2×D4×Q8×C53C2semidirect
34. #16810991C22semidirect
35. #16810961C22semidirect
36. #16810956C22semidirect
37. #16810930C22semidirect
38. #16810871C22semidirect
39. #16810854C22semidirect
40. #16810825C22semidirect
41. #16810762C22semidirect
42. #16810762C22semidirect
43. #16810721C22semidirect
44. #16810695C22semidirect
49. #16810632C22semidirect
59. C2×#13133141C22semidirect
67. D4×Q8×C53C22semidirect
392. C2×D4×Q8D53semidirect
409. C2×C53#3320semidirect
424. D4×Q8C2×D53semidirect
474. C53C2×#3320semidirect
791. C2#20286886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
#202868862
C2×#168109912
C2×#168109562
C2×#168109612
C2×#168109302
C2×#168108712
C2×#168108542
C2×#168108252
C2×#168107622
C2×#168107212
C2×#168106952
C2×#168106322
C22×#131331412
C2×D4×Q8×C532
C2×#332053