Finite Group Databasebeta

← C2×#20288332 #28291184

Subgroups — C2×#20288332 #28291184

Order 13568.

7706 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288332C2132yesmaximal, direct product factor
2C2×#16811349C211yesmaximal, characteristic, complemented
3C2×#16811345C213yesmaximal, complemented
4C2×#16811314C213yesmaximal, complemented
5C2×#16811308C213yesmaximal, complemented
6C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
7C2×#16811285C211yesmaximal, characteristic, complemented
8C2×#16811284C211yesmaximal, characteristic, complemented
9C2×#16811274C213yesmaximal, complemented
10C2×#16811177C213yesmaximal, complemented
11C2×#16811160C213yesmaximal, complemented
12C2×#16811157C213yesmaximal, complemented
13C2×C4×#11719949C211yesmaximal, characteristic, complemented
14C2×C4×#11719945C213yesmaximal, complemented
15C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2213yes—
19C22×Q8×D53C2211yescharacteristic
20#16811349C22116yescomplemented
21#16811345C22148yescomplemented
22#16811314C22148yescomplemented
23#16811308C22148yescomplemented
24Q8×C22⋊D53C22116yescomplemented
25#16811285C22116yescomplemented
26#16811284C22116yescomplemented
27#16811274C22148yescomplemented
28#16811177C22148yescomplemented
29C2×#13133216C2213yes—
30C2×#13133215C2213yes—
31#16811160C22148yescomplemented
32#16811157C22148yescomplemented
33C2×#13133212C2216yes—
34C2×#13133211C2216yes—
35C2×#13133209C2213yes—
36C2×#13133208C2213yes—
37C2×#13133207C2216yes—
38C2×#13133206C2213yes—
39C2×#13133205C2213yes—
40C2×#13133202C2216yes—
41C2×#13133200C2216yes—
42C2×#13133197C2213yes—
43C2×#13133196C2213yes—
44C2×#13133195C2216yes—
45C2×#13133193C2213yes—
46C2×#13133193C2213yes—
47C2×#13133192C2213yes—
48C2×#13133191C2213yes—
49C4×#11719949C22116yescomplemented
50C4×#11719945C22148yescomplemented
51C2×Q8×Dic53C2211yescharacteristic
52C2×Q8×Dic53C2211yescharacteristic
53C2×C4×Dic106C2213yes—
54C2×C4×Dic106C2213yes—
55C2×C4×Dic106C2213yes—
56C2×#13133182C2213yes—
57C4×Q8×D53C22116yescomplemented
58C2×C4×D212C2213yes—
59C2×C4×D212C2213yes—
60C2×C4×D212C2213yes—
61C2×#13133179C2213yes—
62C2×C4×C22⋊D53C2211yescharacteristic
63C2×C4×C22⋊D53C2213yes—
64C2×C4×C22⋊D53C2213yes—
65C2×C4×C22⋊D53C2213yes—
66C2×#13133176C2213yes—
67C2×#13133175C2213yes—
68C2×#13133174C2216yes—
69C2×#13133174C2213yes—
70C2×#13133174C2213yes—
71C2×C4⋊C4×D53C2213yes—
72C2×C42×D53C2213yes—
73C2×C42×D53C2213yes—
74C23×Q8×C53C2211yescharacteristic
75C2×C4×Q8×C53C2213yes—
76C2×C4×Q8×C53C2213yes—
77C2×C4×Q8×C53C2211yescharacteristic
78C2×C4×Q8×C53C2211yescharacteristic
79C2×C4×Q8×C53C22116yescomplemented
80C22×C4⋊C4×C53C2213yes—
81C22×C42×C53C2213yes—
82C2×#11719949—28no—
83C2×#11719949C2318yes—
84C2×#11719945—224no—
85C2×#11719945C23124yes—
86C22×Dic106C2313yes—
87C22×Dic106C2313yes—
88C2×Q8×D53—28no—
89C2×Q8×D53C2318yes—
90C22×D212C2313yes—
91C22×D212C2313yes—
92C22×C22⋊D53C2313yes—
93C22×C22⋊D53C2311yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2313yes—
96C22×C4×D53C2313yes—
97C22×C4×D53C2313yes—
98C22×C4×D53C2313yes—
99C22×C4×D53C2313yes—
100#13133216C23124yes—
101#13133215C23124yes—
102#13133212C23148yes—
103#13133211C23148yes—
104#13133209C23124yes—
105#13133208C23124yes—
106#13133207C23148yes—
107#13133206C23124yes—
108#13133205C23124yes—
109#13133202C23148yes—
110#13133200C23148yes—
111#13133197C23124yes—
112#13133196C23124yes—
113#13133195C23148yes—
114#13133193C23124yes—
115#13133193C23124yes—
116#13133192C23124yes—
117#13133191C23124yes—
118Q8×Dic53C2318yes—
119Q8×Dic53C2318yes—
120C4×Dic106C23124yes—
121C4×Dic106C23124yes—
122C4×Dic106C23124yes—
123#13133182C23124yes—
124C4×D212C23124yes—
125C4×D212C23124yes—
126C4×D212C23124yes—
127#13133179C23124yes—
128C4×C22⋊D53C23124yes—
129C4×C22⋊D53C23124yes—
130C4×C22⋊D53C2318yes—
131C4×C22⋊D53C23124yes—
132#13133176C23124yes—
133#13133175C23124yes—
134#13133174C23124yes—
135#13133174C23124yes—
136#13133174C23148yes—
137C2×C4⋊Dic53C2313yes—
138C2×C4⋊Dic53C2313yes—
139C2×C4⋊Dic53C2313yes—
140C2×C4⋊Dic53C2313yes—
141C2×#11719919C2316yes—
142C2×#11719919C2311yescharacteristic
143C2×#11719919C2313yes—
144C2×#11719919C2313yes—
145C2×#11719919C2313yes—
146C2×#11719919C2316yes—
147C2×#11719919C2316yes—
148C4⋊C4×D53C23124yes—
149C2×C22⋊Dic53C2311yescharacteristic
150C2×C22⋊Dic53C2313yes—
151C2×#11719921C2311yescharacteristic
152C2×#11719921C2313yes—
153C2×#11719921C2313yes—
154C2×#11719921C2313yes—
155C2×#11719921C2316yes—
156C2×#11719921C2316yes—
157C2×#11719921C2316yes—
158C2×C4×Dic53C2311yescharacteristic
159C2×C4×Dic53C2313yes—
160C2×C4×Dic53C2313yes—
161C2×C4×Dic53C2313yes—
162C2×C4×Dic53C2313yes—
163C2×C4×Dic53C2313yes—
164C42×D53C23124yes—
165C42×D53C23124yes—
166C22×Q8×C53—28no—
167C22×Q8×C53C2318yes—
168C22×Q8×C53C2313yes—
169C22×Q8×C53C2311yescharacteristic
170C23×C4×C53C2311yescharacteristic
171C23×C4×C53C2313yes—
172C23×C4×C53C2313yes—
173C4×Q8×C53C2318yes—
174C4×Q8×C53C23124yes—
175C4×Q8×C53C2318yes—
176C4×Q8×C53C23124yes—
177C2×C4⋊C4×C53C23124yes—
178C2×C4⋊C4×C53C2313yes—
179C2×C4⋊C4×C53C2313yes—
180C2×C4⋊C4×C53C2316yes—
181C2×C42×C53C2313yes—
182C2×C42×C53C2313yes—
183C2×C42×C53C2313yes—
184C2×C42×C53C2313yes—
185C2×C42×C53C23124yes—
186C24×C53C2411yescharacteristic
187C23×D53C2413yes—
188C23×D53C2411yescharacteristic
189C2×Q8×C53—232no—
190C2×Q8×C53—212no—
191C2×Q8×C53#4118yescomplemented
192C2×Q8×C53C24112yes—
193C2×Q8×C53C2414yes—
194C22×C4×C53—212no—
195C22×C4×C53—212no—
196C22×C4×C53—24no—
197C22×C4×C53C2411yescharacteristic
198C22×C4×C53C2414yes—
199C22×C4×C53C2413yes—
200C22×C4×C53C2413yes—
201C22×C4×C53C24112yes—
202C22×C4×C53C2413yes—
203C22×C4×C53C24112yes—
204C22×C4×C53C2413yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—212no—
207C2×C22⋊D53#4118yescomplemented
208C2×C22⋊D53C24112yes—
209C2×C22⋊D53C2414yes—
210C22×Dic53C2411yescharacteristic
211C22×Dic53C2411yescharacteristic
212C22×Dic53C2413yes—
213C22×Dic53C2413yes—
214C22×Dic53C2413yes—
215C22×Dic53C2411yescharacteristic
216#11719949—232no—
217Q8×D53—232no—
218#11719945—296no—
219C2×D212—212no—
220C2×D212—212no—
221C2×D212C24112yes—
222C2×D212C24112yes—
223C2×C4×D53—212no—
224C2×C4×D53—212no—
225C2×C4×D53—212no—
226C2×C4×D53—24no—
227C2×C4×D53—212no—
228C2×C4×D53—212no—
229C2×C4×D53C2414yes—
230C2×C4×D53C24112yes—
231C2×C4×D53C24112yes—
232C2×C4×D53C24112yes—
233C2×C4×D53C24112yes—
234C2×C4×D53C24112yes—
235C2×Dic106—212no—
236C2×Dic106—212no—
237C2×Dic106C24112yes—
238C2×Dic106C24112yes—
239C4⋊C4×C53C24112yes—
240C4⋊C4×C53C24112yes—
241C4⋊C4×C53C24124yes—
242C42×C53C24112yes—
243C42×C53C24112yes—
244C42×C53C24112yes—
245C42×C53C24112yes—
246C22⋊Dic53C2414yes—
247C22⋊Dic53C24112yes—
248#11719921C2414yes—
249#11719921C24112yes—
250#11719921C24112yes—
251#11719921C24112yes—
252#11719921C24124yes—
253#11719921C24124yes—
254#11719921C24124yes—
255C4⋊Dic53C24112yes—
256C4⋊Dic53C24112yes—
257C4⋊Dic53C24112yes—
258C4⋊Dic53C24112yes—
259#11719919C24124yes—
260#11719919C2414yes—
261#11719919C24112yes—
262#11719919C24112yes—
263#11719919C24112yes—
264#11719919C24124yes—
265#11719919C24124yes—
266C4×Dic53C2414yes—
267C4×Dic53C24112yes—
268C4×Dic53C24112yes—
269C4×Dic53C24112yes—
270C4×Dic53C24112yes—
271C4×Dic53C24112yes—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53C2×#4114yes—
275C23×C53C2512yes—
276C23×C53C2511yescharacteristic
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—26no—
280C22×D53—26no—
281C22×D53—26no—
282C22×D53C2×#4114yes—
283C22×D53C2516yes—
284C22×D53C2512yes—
285Q8×C53—224no—
286Q8×C53C2×#41116yescomplemented
287C2×C4×C53—26no—
288C2×C4×C53—26no—
289C2×C4×C53—224no—
290C2×C4×C53—26no—
291C2×C4×C53—22no—
292C2×C4×C53—224no—
293C2×C4×C53—28no—
294C2×C4×C53C2×#41112yes—
295C2×C4×C532−1+414yes—
296C2×C4×C53C2516yes—
297C2×C4×C53C2516yes—
298C2×C4×C53C2516yes—
299C2×C4×C53C2512yes—
300C2×C4×C53C2516yes—
301C2×C4×C53C2512yes—
302C22⋊D53—224no—
303C22⋊D53C2×#41116yescomplemented
304C2×Dic53—26no—
305C2×Dic53—26no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—26no—
309C2×Dic53C2×#4114yes—
310C2×Dic53C2516yes—
311C2×Dic53C2516yes—
312C2×Dic53C2512yes—
313C2×Dic53C2512yes—
314C2×Dic53C2516yes—
315C2×Dic53C2512yes—
316D212—224no—
317D212—224no—
318C4×D53—224no—
319C4×D53—224no—
320C4×D53—224no—
321C4×D53—28no—
322C4×D53—224no—
323C4×D53—224no—
324Dic106—224no—
325Dic106—224no—
326C2×#3482—531nomaximal, Sylow
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—28no—
330C22×C53C22×#4114yes—
331C22×C53C22×#4112yes—
332C22×C53C22×#4112yes—
333C22×C53C2×2−1+412yes—
334C22×C53C2611yescharacteristic
335C2×D53—22no—
336C2×D53—22no—
337C2×D53—28no—
338C2×D53—26no—
339C2×D53—26no—
340C2×D53—26no—
341C2×D53—412no—
342C2×D53C22×#4114yes—
343C4×C53—26no—
344C4×C53—26no—
345C4×C53—26no—
346C4×C53—22no—
347C4×C53C22×#41112yes—
348C4×C53C2×2−1+414yes—
349Dic53—26no—
350Dic53—26no—
351Dic53—22no—
352Dic53—22no—
353Dic53—26no—
354Dic53C22×#4114yes—
355#3482—5332no—
356C2×#557—531no—
357C2×#556—533no—
358C2×#552—533no—
359C2×#552—533no—
360C2×D4×Q8—531no—
361C2×#548—531no—
362C2×#548—531no—
363C2×#547—533no—
364C2×#533—533no—
365C2×#529—533no—
366C2×#529—533no—
367C2×C4×#41—533no—
368C2×C4×#41—531no—
369C22×C4×Q8—531no—
370C22×C4×Q8D5311yescharacteristic, complemented
371C2×C53—24no—
372C2×C53#348214yescomplemented
373C2×C53C23×#4111yescharacteristic
374C2×C53C23×#4111yescharacteristic
375C2×C53C22×2−1+411yescharacteristic
376D53—24no—
377D53—46no—
378C22×#41—531no—
379C22×#41—533no—
380C23×Q8—531no—
381C23×Q8C2×D5311yescharacteristic
382#557—5316no—
383#556—5348no—
384#552—5348no—
385#552—5348no—
386D4×Q8—5316no—
387#548—5316no—
388#548—5316no—
389#547—5348no—
390#533—5348no—
391C2×C4⋊Q8—533no—
392C2×C4⋊Q8—533no—
393#529—5348no—
394#529—5348no—
395C2×#126—536no—
396C2×#126—536no—
397C2×#125—533no—
398C2×#125—536no—
399C2×#125—533no—
400C2×#124—533no—
401C2×#124—533no—
402C2×#123—536no—
403C2×#123—536no—
404C2×C22⋊Q8—533no—
405C2×C22⋊Q8—533no—
406C2×C22⋊Q8—533no—
407C2×C22⋊Q8—536no—
408C2×C22⋊Q8—533no—
409C2×#121—533no—
410C2×#121—533no—
411C4×#41—5316no—
412C4×#41—5348no—
413C2×C4×Q8—531no—
414C2×C4×Q8—531no—
415C2×C4×Q8—5316no—
416C2×C4×Q8—533no—
417C2×C4×Q8—533no—
418C2×C4×Q8—533no—
419C2×C4×Q8—533no—
420C2×C4×Q8C2×D5311yescharacteristic
421C2×C4×Q8C2×D5313yes—
422C2×C4×Q8C2×D5311yescharacteristic
423C2×C4×Q8C2×D5313yes—
424C2×C4×Q8C2×D53116yescomplemented
425C2×C4×D4—531no—
426C2×C4×D4—533no—
427C2×C4×D4—533no—
428C2×C4×D4—533no—
429C2×C4×D4—533no—
430C2×C4×D4—533no—
431C2×C4×D4—533no—
432C2×C4×D4—533no—
433C2×#117—533no—
434C2×#117—533no—
435C2×#117—533no—
436C2×#117—533no—
437C2×#117—536no—
438C22×C4⋊C4—533no—
439C22×C4⋊C4C2×D5313yes—
440C22×C42—533no—
441C22×C42—533no—
442C22×C42C2×D5313yes—
443C53C2×#348211yescharacteristic, complemented, Sylow
444C2×#41—538no—
445C2×#41—5324no—
446C2×#41—10624no—
447C2×#41—1068no—
448C22×Q8—28no—
449C22×Q8—538no—
450C22×Q8—533no—
451C22×Q8—533no—
452C22×Q8—1068no—
453C22×Q8C22×D5313yes—
454C22×Q8C22×D5318yes—
455C22×Q8C22×D5311yescharacteristic
456C22×D4—531no—
457C22×D4—533no—
458C22×D4—533no—
459C22×D4—533no—
460C23×C4—533no—
461C23×C4—533no—
462C23×C4—533no—
463C23×C4—533no—
464C23×C4—533no—
465C23×C4—531no—
466C23×C4C22×D5313yes—
467C23×C4C22×D5313yes—
468C23×C4C22×D5311yescharacteristic
469C4⋊Q8—5324no—
470C4⋊Q8—5324no—
471#126—5348no—
472#126—5348no—
473#125—5324no—
474#125—5348no—
475#125—5324no—
476#124—5324no—
477#124—5324no—
478#123—5348no—
479#123—5348no—
480C22⋊Q8—5324no—
481C22⋊Q8—5324no—
482C22⋊Q8—5324no—
483C22⋊Q8—5348no—
484C22⋊Q8—5324no—
485#121—5324no—
486#121—5324no—
487C4×Q8—538no—
488C4×Q8—538no—
489C4×Q8—5324no—
490C4×Q8—5324no—
491C4×Q8—5324no—
492C4×Q8—5324no—
493C4×Q8C22×D5318yes—
494C4×Q8C22×D53124yes—
495C4×Q8C22×D5318yes—
496C4×Q8C22×D53124yes—
497C4×D4—538no—
498C4×D4—5324no—
499C4×D4—5324no—
500C4×D4—5324no—
501C4×D4—5324no—
502C4×D4—5324no—
503C4×D4—5324no—
504C4×D4—5324no—
505#117—5324no—
506#117—5324no—
507#117—5324no—
508#117—5324no—
509#117—5348no—
510C2×C4⋊C4—533no—
511C2×C4⋊C4—536no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—533no—
514C2×C4⋊C4—533no—
515C2×C4⋊C4—533no—
516C2×C4⋊C4—533no—
517C2×C4⋊C4—533no—
518C2×C4⋊C4—533no—
519C2×C4⋊C4—536no—
520C2×C4⋊C4—536no—
521C2×C4⋊C4—5324no—
522C2×C4⋊C4C22×D5313yes—
523C2×C4⋊C4C22×D5313yes—
524C2×C4⋊C4C22×D5316yes—
525C2×C4⋊C4C22×D53124yes—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—533no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4—533no—
530C2×C22⋊C4—536no—
531C2×C22⋊C4—533no—
532C2×C22⋊C4—533no—
533C2×C22⋊C4—536no—
534C2×C22⋊C4—536no—
535C2×C42—533no—
536C2×C42—533no—
537C2×C42—533no—
538C2×C42—533no—
539C2×C42—533no—
540C2×C42—531no—
541C2×C42—5324no—
542C2×C42—5324no—
543C2×C42C22×D5313yes—
544C2×C42C22×D5313yes—
545C2×C42C22×D53124yes—
546C2×C42C22×D5313yes—
547C2×C42C22×D5313yes—
548C24—531no—
549C24—533no—
550C24C23×D5311yescharacteristic
551#41—10696no—
552#41—10632no—
553C2×Q8—232no—
554C2×Q8—212no—
555C2×Q8—5312no—
556C2×Q8—5312no—
557C2×Q8—10612no—
558C2×Q8—10632no—
559C2×Q8—10612no—
560C2×Q8#1171994518yescomplemented
561C2×Q8C23×D53112yes—
562C2×Q8C23×D5314yes—
563C2×D4—538no—
564C2×D4—534no—
565C2×D4—5312no—
566C2×D4—5312no—
567C2×D4—5312no—
568C2×D4—10612no—
569C2×D4—10612no—
570C2×D4—10612no—
571C22×C4—212no—
572C22×C4—212no—
573C22×C4—24no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—533no—
578C22×C4—533no—
579C22×C4—533no—
580C22×C4—534no—
581C22×C4—5312no—
582C22×C4—5312no—
583C22×C4—5312no—
584C22×C4—5312no—
585C22×C4—5312no—
586C22×C4—10612no—
587C22×C4—10612no—
588C22×C4—10612no—
589C22×C4—10612no—
590C22×C4—1064no—
591C22×C4—10612no—
592C22×C4C23×D5313yes—
593C22×C4C23×D5311yescharacteristic
594C22×C4C23×D5314yes—
595C22×C4C23×D5313yes—
596C22×C4C23×D5313yes—
597C22×C4C23×D53112yes—
598C22×C4C23×D53112yes—
599C22×C4C23×D5313yes—
600C22×C4C23×D5311yescharacteristic
601C4⋊C4—5312no—
602C4⋊C4—5324no—
603C4⋊C4—534no—
604C4⋊C4—5312no—
605C4⋊C4—5312no—
606C4⋊C4—5312no—
607C4⋊C4—5312no—
608C4⋊C4—5312no—
609C4⋊C4—5312no—
610C4⋊C4—5324no—
611C4⋊C4—5324no—
612C4⋊C4C23×D53112yes—
613C4⋊C4C23×D53112yes—
614C4⋊C4C23×D53124yes—
615C22⋊C4—534no—
616C22⋊C4—5312no—
617C22⋊C4—534no—
618C22⋊C4—5312no—
619C22⋊C4—5324no—
620C22⋊C4—5312no—
621C22⋊C4—5312no—
622C22⋊C4—5324no—
623C22⋊C4—5324no—
624C42—534no—
625C42—5312no—
626C42—5312no—
627C42—5312no—
628C42—5312no—
629C42—5312no—
630C42C23×D53112yes—
631C42C23×D53112yes—
632C42C23×D53112yes—
633C42C23×D53112yes—
634C23—22no—
635C23—22no—
636C23—534no—
637C23—532no—
638C23—536no—
639C23—1062no—
640C23—1062no—
641C23—1066no—
642C23—1066no—
643C23—1066no—
644C23#41×D5314yes—
645C23C24×D5312yes—
646C23C24×D5311yescharacteristic
647Q8—224no—
648Q8—10624no—
649Q8—10624no—
650Q8C2×#11719945116yescomplemented
651D4—5316no—
652D4—10624no—
653D4—10624no—
654D4—10624no—
655C2×C4—26no—
656C2×C4—26no—
657C2×C4—224no—
658C2×C4—26no—
659C2×C4—22no—
660C2×C4—224no—
661C2×C4—28no—
662C2×C4—534no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—532no—
666C2×C4—536no—
667C2×C4—536no—
668C2×C4—536no—
669C2×C4—10624no—
670C2×C4—10624no—
671C2×C4—1066no—
672C2×C4—1062no—
673C2×C4—1066no—
674C2×C4—1062no—
675C2×C4—1066no—
676C2×C4—10624no—
677C2×C4—10624no—
678C2×C4—1068no—
679C2×C4—10624no—
680C2×C4C2×#11719945112yes—
681C2×C4#1313326514yes—
682C2×C4C24×D5316yes—
683C2×C4C24×D5312yes—
684C2×C4C24×D5316yes—
685C2×C4C24×D5316yes—
686C2×C4C24×D5316yes—
687C2×C4C24×D5312yes—
688C22—28no—
689C22—22no—
690C22—22no—
691C22—534no—
692C22—1068no—
693C22—1062no—
694C22—1062no—
695C22—1066no—
696C22—1066no—
697C22—1066no—
698C22—21212no—
699C22C2×#41×D5314yes—
700C22C2×#41×D5312yes—
701C22C22×#1171994512yes—
702C22C2×#1313326512yes—
703C22C25×D5311yescharacteristic
704C4—26no—
705C4—26no—
706C4—26no—
707C4—22no—
708C4—534no—
709C4—1066no—
710C4—1062no—
711C4—1066no—
712C4—1062no—
713C4—1066no—
714C4C22×#11719945112yes—
715C4C2×#1313326514yes—
716C2—24no—
717C2—1064no—
718C2—2126no—
719C2#2028833214yesdirect product factor
720C2C22×#41×D5311yescharacteristic
721C2C23×#1171994511yescharacteristic
722C2C22×#1313326511yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC22×C4×Q8×C53C2
socleC23×C53C25
hypercenterC22×C4×Q8D53
hypocenterC53C2×#3482
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #20288332C2direct (N × H)
2. C2×#16811349C2semidirect
3. C2×#16811345C2semidirect
4. C2×#16811314C2semidirect
5. C2×#16811308C2semidirect
6. C2×Q8×C22⋊D53C2semidirect
7. C2×#16811285C2semidirect
8. C2×#16811284C2semidirect
9. C2×#16811274C2semidirect
10. C2×#16811177C2semidirect
11. C2×#16811160C2semidirect
12. C2×#16811157C2semidirect
13. C2×C4×#11719949C2semidirect
14. C2×C4×#11719945C2semidirect
15. C2×C4×Q8×D53C2semidirect
16. C22×C4×Q8×C53C2semidirect
20. #16811349C22semidirect
21. #16811345C22semidirect
22. #16811314C22semidirect
23. #16811308C22semidirect
24. Q8×C22⋊D53C22semidirect
25. #16811285C22semidirect
26. #16811284C22semidirect
27. #16811274C22semidirect
28. #16811177C22semidirect
31. #16811160C22semidirect
32. #16811157C22semidirect
49. C4×#11719949C22semidirect
50. C4×#11719945C22semidirect
57. C4×Q8×D53C22semidirect
79. C2×C4×Q8×C53C22semidirect
191. C2×Q8×C53#41semidirect
207. C2×C22⋊D53#41semidirect
286. Q8×C53C2×#41semidirect
303. C22⋊D53C2×#41semidirect
370. C22×C4×Q8D53semidirect
372. C2×C53#3482semidirect
424. C2×C4×Q8C2×D53semidirect
443. C53C2×#3482semidirect
560. C2×Q8#11719945semidirect
650. Q8C2×#11719945semidirect
719. C2#20288332direct (N × H)

Maximal subgroups

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

subgroupindex
#202883322
C2×#168113492
C2×#168113452
C2×#168113142
C2×#168113082
C2×Q8×C22⋊D532
C2×#168112852
C2×#168112842
C2×#168112742
C2×#168111772
C2×#168111602
C2×#168111572
C2×C4×#117199492
C2×C4×#117199452
C2×C4×Q8×D532
C22×C4×Q8×C532
C2×#348253