Finite Group Databasebeta

← C2×#20288313 #28291150

Subgroups — C2×#20288313 #28291150

Order 13568.

7802 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288313C2132yesmaximal, direct product factor
2C2×#16811356C213yesmaximal, complemented
3C2×#16811349C211yesmaximal, characteristic, complemented
4C2×#16811341C213yesmaximal, complemented
5C2×#16811323C213yesmaximal, complemented
6C2×#16811317C213yesmaximal, complemented
7C2×#16811292C211yesmaximal, characteristic, complemented
8C2×#16811285C211yesmaximal, characteristic, complemented
9C2×#16811280C211yesmaximal, characteristic, complemented
10C2×#16811170C213yesmaximal, complemented
11C2×#16811157C213yesmaximal, complemented
12C2×#16811155C213yesmaximal, complemented
13C2×C4×#11719949C211yesmaximal, characteristic, complemented
14C2×C4×#11719945C213yesmaximal, complemented
15C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
16C2×C4×#41×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945C2213yes—
19C22×Q8×D53C2211yescharacteristic
20#16811356C22148yescomplemented
21#16811349C22116yescomplemented
22#16811341C22148yescomplemented
23#16811323C22148yescomplemented
24#16811317C22148yescomplemented
25#16811292C22116yescomplemented
26#16811285C22116yescomplemented
27#16811280C22116yescomplemented
28#16811170C22148yescomplemented
29C2×#13133216C2213yes—
30C2×#13133213C2213yes—
31#16811157C22148yescomplemented
32#16811155C22148yescomplemented
33C2×#13133211C2216yes—
34C2×#13133210C2216yes—
35C2×#13133209C2213yes—
36C2×#13133208C2213yes—
37C2×#13133205C2213yes—
38C2×#13133204C2213yes—
39C2×#13133203C2216yes—
40C2×#13133200C2216yes—
41C2×#13133199C2216yes—
42C2×#13133197C2213yes—
43C2×#13133196C2213yes—
44C2×#13133192C2213yes—
45C2×#13133191C2213yes—
46C2×#13133190C2216yes—
47C2×#13133188C2213yes—
48C2×#13133188C2213yes—
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⋊D53C2213yes—
63C2×C4×C22⋊D53C2213yes—
64C2×C4×C22⋊D53C2213yes—
65C2×C4×C22⋊D53C2213yes—
66C2×C4×C22⋊D53C2216yes—
67C2×#13133176C2213yes—
68C2×#13133175C2213yes—
69C2×#13133174C2211yescharacteristic
70C2×#13133174C2213yes—
71C2×C4⋊C4×D53C2213yes—
72C2×C42×D53C2213yes—
73C2×C42×D53C2213yes—
74C22×#41×C53C2211yescharacteristic
75C4×#41×C53C22116yescomplemented
76C2×C4×Q8×C53C2211yescharacteristic
77C2×C4×Q8×C53C2211yescharacteristic
78C2×C4×D4×C53C2213yes—
79C2×C4×D4×C53C2213yes—
80C2×#117×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⋊D53C2313yes—
94C22×C22⋊D53C2316yes—
95C22×C4×D53C2313yes—
96C22×C4×D53C2313yes—
97C22×C4×D53C2313yes—
98C22×C4×D53C2313yes—
99C22×C4×D53C2313yes—
100C22×C4×D53C2311yescharacteristic
101#13133216C23124yes—
102#13133213C23124yes—
103#13133211C23148yes—
104#13133210C23148yes—
105#13133209C23124yes—
106#13133208C23124yes—
107#13133205C23124yes—
108#13133204C23124yes—
109#13133203C23148yes—
110#13133200C23148yes—
111#13133199C23148yes—
112#13133197C23124yes—
113#13133196C23124yes—
114#13133192C23124yes—
115#13133191C23124yes—
116#13133190C23148yes—
117#13133188C23124yes—
118#13133188C23124yes—
119Q8×Dic53C2318yes—
120Q8×Dic53C2318yes—
121C4×Dic106C23124yes—
122C4×Dic106C23124yes—
123C4×Dic106C23124yes—
124#13133182C23124yes—
125C4×D212C23124yes—
126C4×D212C23124yes—
127C4×D212C23124yes—
128#13133179C23124yes—
129C4×C22⋊D53C23124yes—
130C4×C22⋊D53C23124yes—
131C4×C22⋊D53C23124yes—
132C4×C22⋊D53C23124yes—
133C4×C22⋊D53C23148yes—
134#13133176C23124yes—
135#13133175C23124yes—
136#13133174C2318yes—
137#13133174C23124yes—
138C2×C4⋊Dic53C2313yes—
139C2×C4⋊Dic53C2313yes—
140C2×C4⋊Dic53C2313yes—
141C2×C4⋊Dic53C2313yes—
142C2×#11719919C2316yes—
143C2×#11719919C2311yescharacteristic
144C2×#11719919C2311yescharacteristic
145C2×#11719919C2313yes—
146C2×#11719919C2313yes—
147C2×#11719919C2316yes—
148C4⋊C4×D53C23124yes—
149C2×C22⋊Dic53C2313yes—
150C2×C22⋊Dic53C2313yes—
151C2×C22⋊Dic53C2316yes—
152C2×#11719921C2311yescharacteristic
153C2×#11719921C2311yescharacteristic
154C2×#11719921C2313yes—
155C2×#11719921C2313yes—
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—
166C2×#41×C53—28no—
167C2×#41×C53C2318yes—
168C22×Q8×C53C2311yescharacteristic
169C22×D4×C53C2313yes—
170C23×C4×C53C2313yes—
171C23×C4×C53C2313yes—
172C23×C4×C53C2313yes—
173C4×Q8×C53C2318yes—
174C4×Q8×C53C2318yes—
175C4×D4×C53C23124yes—
176C4×D4×C53C23124yes—
177#117×C53C23124yes—
178C2×C4⋊C4×C53C2313yes—
179C2×C4⋊C4×C53C2313yes—
180C2×C22⋊C4×C53C2316yes—
181C2×C42×C53C2311yescharacteristic
182C2×C42×C53C2313yes—
183C2×C42×C53C2313yes—
184C2×C42×C53C2313yes—
185C2×C42×C53C23124yes—
186C24×C53C2413yes—
187C23×D53C2413yes—
188C23×D53C2411yescharacteristic
189#41×C53—232no—
190C2×Q8×C53#4118yescomplemented
191C2×Q8×C53C2414yes—
192C2×D4×C53—212no—
193C2×D4×C53C24112yes—
194C22×C4×C53—212no—
195C22×C4×C53—212no—
196C22×C4×C53—46no—
197C22×C4×C53C2411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×C4×C53C2413yes—
200C22×C4×C53C2413yes—
201C22×C4×C53C24112yes—
202C22×C4×C53C24112yes—
203C22×C4×C53C24112yes—
204C22×C4×C53C2413yes—
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—212no—
207C2×C22⋊D53—212no—
208C2×C22⋊D53—412no—
209C2×C22⋊D53C24112yes—
210C2×C22⋊D53C24112yes—
211C2×C22⋊D53C24124yes—
212C22×Dic53C2411yescharacteristic
213C22×Dic53C2411yescharacteristic
214C22×Dic53C2413yes—
215C22×Dic53C2413yes—
216C22×Dic53C2413yes—
217C22×Dic53C2411yescharacteristic
218#11719949—232no—
219Q8×D53—232no—
220#11719945—296no—
221C2×D212—212no—
222C2×D212—212no—
223C2×D212C24112yes—
224C2×D212C24112yes—
225C2×C4×D53—212no—
226C2×C4×D53—212no—
227C2×C4×D53—212no—
228C2×C4×D53—46no—
229C2×C4×D53—46no—
230C2×C4×D53#4118yescomplemented
231C2×C4×D53C24112yes—
232C2×C4×D53C24112yes—
233C2×C4×D53C24112yes—
234C2×C4×D53C24112yes—
235C2×C4×D53C24112yes—
236C2×C4×D53C2414yes—
237C2×Dic106—212no—
238C2×Dic106—212no—
239C2×Dic106C24112yes—
240C2×Dic106C24112yes—
241C4⋊C4×C53C24112yes—
242C4⋊C4×C53C24112yes—
243C22⋊C4×C53C24124yes—
244C42×C53C2414yes—
245C42×C53C24112yes—
246C42×C53C24112yes—
247C42×C53C24112yes—
248C22⋊Dic53C24112yes—
249C22⋊Dic53C24112yes—
250C22⋊Dic53C24124yes—
251#11719921C2414yes—
252#11719921C2414yes—
253#11719921C24112yes—
254#11719921C24112yes—
255#11719921C24124yes—
256#11719921C24124yes—
257C4⋊Dic53C24112yes—
258C4⋊Dic53C24112yes—
259C4⋊Dic53C24112yes—
260C4⋊Dic53C24112yes—
261#11719919C24124yes—
262#11719919C2414yes—
263#11719919C2414yes—
264#11719919C24112yes—
265#11719919C24112yes—
266#11719919C24124yes—
267C4×Dic53C2414yes—
268C4×Dic53C24112yes—
269C4×Dic53C24112yes—
270C4×Dic53C24112yes—
271C4×Dic53C24112yes—
272C4×Dic53C24112yes—
273C23×C53—26no—
274C23×C53—26no—
275C23×C53—26no—
276C23×C53C2516yes—
277C23×C53C2511yescharacteristic
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—26no—
281C22×D53—26no—
282C22×D53—26no—
283C22×D53C2×#4114yes—
284C22×D53C2516yes—
285C22×D53C2512yes—
286Q8×C53C2×#41116yescomplemented
287D4×C53—224no—
288C2×C4×C53—26no—
289C2×C4×C53—22no—
290C2×C4×C53—26no—
291C2×C4×C53—22no—
292C2×C4×C53—224no—
293C2×C4×C53—224no—
294C2×C4×C53—412no—
295C2×C4×C53C2×#4114yes—
296C2×C4×C53C2×#41112yes—
297C2×C4×C53C2516yes—
298C2×C4×C53C2516yes—
299C2×C4×C53C2512yes—
300C2×C4×C53C2512yes—
301C2×C4×C53C2516yes—
302C2×C4×C53C2512yes—
303C22⋊D53—224no—
304C22⋊D53—224no—
305C22⋊D53—424no—
306C2×Dic53—26no—
307C2×Dic53—26no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—26no—
311C2×Dic53C2×#4114yes—
312C2×Dic53C2516yes—
313C2×Dic53C2516yes—
314C2×Dic53C2512yes—
315C2×Dic53C2512yes—
316C2×Dic53C2516yes—
317C2×Dic53C2512yes—
318D212—224no—
319D212—224no—
320C4×D53—224no—
321C4×D53—224no—
322C4×D53—224no—
323C4×D53—412no—
324C4×D53—412no—
325C4×D53C2×#41116yescomplemented
326Dic106—224no—
327Dic106—224no—
328C2×#3480—531nomaximal, Sylow
329C22×C53—26no—
330C22×C53—26no—
331C22×C53—26no—
332C22×C53—412no—
333C22×C53C22×#4112yes—
334C22×C53C22×#4112yes—
335C22×C53#58512yes—
336C22×C53C2611yescharacteristic
337C2×D53—22no—
338C2×D53—22no—
339C2×D53—28no—
340C2×D53—26no—
341C2×D53—26no—
342C2×D53—26no—
343C2×D53—412no—
344C2×D53C22×#4114yes—
345C4×C53—26no—
346C4×C53—22no—
347C4×C53—26no—
348C4×C53—22no—
349C4×C53C22×#4114yes—
350C4×C53C22×#41112yes—
351Dic53—26no—
352Dic53—26no—
353Dic53—22no—
354Dic53—22no—
355Dic53—26no—
356Dic53C22×#4114yes—
357#3480—5332no—
358C2×#559—533no—
359C2×#557—531no—
360C2×#556—533no—
361C2×#553—533no—
362C2×#553—533no—
363C2×#550—531no—
364C2×#548—531no—
365C2×#548—531no—
366C2×#532—533no—
367C2×#529—533no—
368C2×#529—533no—
369C2×C4×#41—533no—
370C2×C4×#41—531no—
371C2×C4×#41D5311yescharacteristic, complemented
372C22×C4×Q8—531no—
373C2×C53—46no—
374C2×C53#348014yescomplemented
375C2×C53C23×#4111yescharacteristic
376C2×C53C23×#4111yescharacteristic
377C2×C53C2×#58511yescharacteristic
378D53—24no—
379D53—46no—
380C22×#41—531no—
381C22×#41—533no—
382C22×#41C2×D5311yescharacteristic
383C23×Q8—531no—
384#559—5348no—
385#557—5316no—
386#556—5348no—
387#553—5348no—
388#553—5348no—
389#550—5316no—
390#548—5316no—
391#548—5316no—
392#532—5348no—
393C2×C4⋊Q8—533no—
394C2×#127—533no—
395#529—5348no—
396#529—5348no—
397C2×#126—536no—
398C2×#126—536no—
399C2×#125—533no—
400C2×#125—533no—
401C2×#124—533no—
402C2×#124—536no—
403C2×#124—533no—
404C2×#123—536no—
405C2×#123—536no—
406C2×C22⋊Q8—533no—
407C2×C22⋊Q8—533no—
408C2×#121—533no—
409C2×#121—533no—
410C2×#121—533no—
411C2×#121—533no—
412C2×#121—536no—
413C4×#41—5316no—
414C4×#41—5348no—
415C4×#41C2×D53116yescomplemented
416C2×C4×Q8—531no—
417C2×C4×Q8—531no—
418C2×C4×Q8—5316no—
419C2×C4×Q8—533no—
420C2×C4×Q8—533no—
421C2×C4×Q8—533no—
422C2×C4×Q8—533no—
423C2×C4×Q8C2×D5311yescharacteristic
424C2×C4×Q8C2×D5311yescharacteristic
425C2×C4×D4—533no—
426C2×C4×D4—533no—
427C2×C4×D4—533no—
428C2×C4×D4—533no—
429C2×C4×D4—536no—
430C2×C4×D4—533no—
431C2×C4×D4—533no—
432C2×C4×D4—533no—
433C2×C4×D4—533no—
434C2×C4×D4C2×D5313yes—
435C2×C4×D4C2×D5313yes—
436C2×#117—533no—
437C2×#117—533no—
438C2×#117—531no—
439C2×#117—533no—
440C2×#117C2×D5313yes—
441C22×C4⋊C4—533no—
442C22×C42—533no—
443C22×C42—533no—
444C22×C42C2×D5313yes—
445C53C2×#348011yescharacteristic, complemented, Sylow
446C2×#41—28no—
447C2×#41—538no—
448C2×#41—5324no—
449C2×#41—10624no—
450C2×#41—1068no—
451C2×#41C22×D5318yes—
452C22×Q8—538no—
453C22×Q8—533no—
454C22×Q8—533no—
455C22×Q8—1068no—
456C22×Q8C22×D5311yescharacteristic
457C22×D4—533no—
458C22×D4—533no—
459C22×D4—536no—
460C22×D4—533no—
461C22×D4—533no—
462C22×D4C22×D5313yes—
463C23×C4—531no—
464C23×C4—533no—
465C23×C4—533no—
466C23×C4—533no—
467C23×C4—533no—
468C23×C4—533no—
469C23×C4C22×D5313yes—
470C23×C4C22×D5313yes—
471C23×C4C22×D5313yes—
472C4⋊Q8—5324no—
473#127—5324no—
474#126—5348no—
475#126—5348no—
476#125—5324no—
477#125—5324no—
478#124—5324no—
479#124—5348no—
480#124—5324no—
481#123—5348no—
482#123—5348no—
483C22⋊Q8—5324no—
484C22⋊Q8—5324no—
485#121—5324no—
486#121—5324no—
487#121—5324no—
488#121—5324no—
489#121—5348no—
490C4×Q8—538no—
491C4×Q8—538no—
492C4×Q8—5324no—
493C4×Q8—5324no—
494C4×Q8—5324no—
495C4×Q8—5324no—
496C4×Q8C22×D5318yes—
497C4×Q8C22×D5318yes—
498C4×D4—5324no—
499C4×D4—5324no—
500C4×D4—5324no—
501C4×D4—5324no—
502C4×D4—5348no—
503C4×D4—5324no—
504C4×D4—5324no—
505C4×D4—5324no—
506C4×D4—5324no—
507C4×D4C22×D53124yes—
508C4×D4C22×D53124yes—
509#117—5324no—
510#117—5324no—
511#117—538no—
512#117—5324no—
513#117C22×D53124yes—
514C2×C4⋊C4—533no—
515C2×C4⋊C4—536no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—531no—
518C2×C4⋊C4—533no—
519C2×C4⋊C4—533no—
520C2×C4⋊C4—533no—
521C2×C4⋊C4—533no—
522C2×C4⋊C4—533no—
523C2×C4⋊C4—536no—
524C2×C4⋊C4—5324no—
525C2×C4⋊C4C22×D5313yes—
526C2×C4⋊C4C22×D5313yes—
527C2×C22⋊C4—533no—
528C2×C22⋊C4—533no—
529C2×C22⋊C4—536no—
530C2×C22⋊C4—531no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4—533no—
533C2×C22⋊C4—536no—
534C2×C22⋊C4—533no—
535C2×C22⋊C4—536no—
536C2×C22⋊C4C22×D5316yes—
537C2×C42—533no—
538C2×C42—533no—
539C2×C42—533no—
540C2×C42—533no—
541C2×C42—531no—
542C2×C42—533no—
543C2×C42—5324no—
544C2×C42—5324no—
545C2×C42C22×D5313yes—
546C2×C42C22×D5313yes—
547C2×C42C22×D53124yes—
548C2×C42C22×D5311yescharacteristic
549C2×C42C22×D5313yes—
550C24—531no—
551C24—533no—
552C24C23×D5313yes—
553#41—232no—
554#41—10696no—
555#41—10632no—
556C2×Q8—5312no—
557C2×Q8—5312no—
558C2×Q8—10612no—
559C2×Q8—10632no—
560C2×Q8—10612no—
561C2×Q8#1171994518yescomplemented
562C2×Q8C23×D5314yes—
563C2×D4—212no—
564C2×D4—5312no—
565C2×D4—5312no—
566C2×D4—5324no—
567C2×D4—5312no—
568C2×D4—5312no—
569C2×D4—10612no—
570C2×D4—10612no—
571C2×D4—10612no—
572C2×D4—10612no—
573C2×D4—21212no—
574C2×D4C23×D53112yes—
575C22×C4—212no—
576C22×C4—212no—
577C22×C4—46no—
578C22×C4—531no—
579C22×C4—538no—
580C22×C4—534no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—533no—
584C22×C4—533no—
585C22×C4—533no—
586C22×C4—5312no—
587C22×C4—5312no—
588C22×C4—5312no—
589C22×C4—5312no—
590C22×C4—5312no—
591C22×C4—10612no—
592C22×C4—10612no—
593C22×C4—10612no—
594C22×C4—2126no—
595C22×C4—2126no—
596C22×C4C23×D5313yes—
597C22×C4C23×D5311yescharacteristic
598C22×C4C23×D5311yescharacteristic
599C22×C4C23×D5313yes—
600C22×C4C23×D53112yes—
601C22×C4C23×D53112yes—
602C22×C4C23×D53112yes—
603C22×C4C23×D5313yes—
604C22×C4C23×D5311yescharacteristic
605C4⋊C4—5312no—
606C4⋊C4—5324no—
607C4⋊C4—534no—
608C4⋊C4—534no—
609C4⋊C4—5312no—
610C4⋊C4—5312no—
611C4⋊C4—5312no—
612C4⋊C4—5312no—
613C4⋊C4—5312no—
614C4⋊C4—5324no—
615C4⋊C4C23×D53112yes—
616C4⋊C4C23×D53112yes—
617C22⋊C4—5312no—
618C22⋊C4—5312no—
619C22⋊C4—5324no—
620C22⋊C4—534no—
621C22⋊C4—534no—
622C22⋊C4—5312no—
623C22⋊C4—5324no—
624C22⋊C4—5312no—
625C22⋊C4—5324no—
626C22⋊C4C23×D53124yes—
627C42—534no—
628C42—5312no—
629C42—5312no—
630C42—5312no—
631C42—5312no—
632C42—5312no—
633C42C23×D53112yes—
634C42C23×D5314yes—
635C42C23×D53112yes—
636C42C23×D53112yes—
637C23—26no—
638C23—26no—
639C23—26no—
640C23—534no—
641C23—532no—
642C23—536no—
643C23—1062no—
644C23—1062no—
645C23—1066no—
646C23—1066no—
647C23—1066no—
648C23C24×D5316yes—
649C23C24×D5311yescharacteristic
650Q8—10624no—
651Q8—10624no—
652Q8C2×#11719945116yescomplemented
653D4—224no—
654D4—10624no—
655D4—10624no—
656D4—10624no—
657D4—10624no—
658D4—21224no—
659C2×C4—26no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—26no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—412no—
666C2×C4—534no—
667C2×C4—532no—
668C2×C4—5316no—
669C2×C4—532no—
670C2×C4—532no—
671C2×C4—536no—
672C2×C4—536no—
673C2×C4—536no—
674C2×C4—1066no—
675C2×C4—1062no—
676C2×C4—1066no—
677C2×C4—1062no—
678C2×C4—1066no—
679C2×C4—10624no—
680C2×C4—10624no—
681C2×C4—10624no—
682C2×C4—21212no—
683C2×C4—21212no—
684C2×C4#41×D5314yes—
685C2×C4C2×#11719945112yes—
686C2×C4C24×D5316yes—
687C2×C4C24×D5312yes—
688C2×C4C24×D5312yes—
689C2×C4C24×D5316yes—
690C2×C4C24×D5312yes—
691C2×C4C24×D5316yes—
692C22—26no—
693C22—26no—
694C22—26no—
695C22—412no—
696C22—534no—
697C22—1068no—
698C22—1062no—
699C22—1062no—
700C22—1066no—
701C22—1066no—
702C22—1066no—
703C22—21212no—
704C22C2×#41×D5312yes—
705C22C22×#1171994512yes—
706C22#1681145912yes—
707C22C25×D5311yescharacteristic
708C4—26no—
709C4—22no—
710C4—22no—
711C4—26no—
712C4—534no—
713C4—1066no—
714C4—1062no—
715C4—1066no—
716C4—1062no—
717C4—1066no—
718C4C2×#41×D5314yes—
719C4C22×#11719945112yes—
720C2—46no—
721C2—1064no—
722C2—2126no—
723C2#2028831314yesdirect product factor
724C2C22×#41×D5311yescharacteristic
725C2C23×#1171994511yescharacteristic
726C2C2×#1681145911yescharacteristic
subgroupG/H
centerC22×C4C23×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C4×#41×C53C2
socleC23×C53C25
hypercenterC2×C4×#41D53
hypocenterC53C2×#3480
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20288313C2direct (N × H)
2. C2×#16811356C2semidirect
3. C2×#16811349C2semidirect
4. C2×#16811341C2semidirect
5. C2×#16811323C2semidirect
6. C2×#16811317C2semidirect
7. C2×#16811292C2semidirect
8. C2×#16811285C2semidirect
9. C2×#16811280C2semidirect
10. C2×#16811170C2semidirect
11. C2×#16811157C2semidirect
12. C2×#16811155C2semidirect
13. C2×C4×#11719949C2semidirect
14. C2×C4×#11719945C2semidirect
15. C2×C4×Q8×D53C2semidirect
16. C2×C4×#41×C53C2semidirect
20. #16811356C22semidirect
21. #16811349C22semidirect
22. #16811341C22semidirect
23. #16811323C22semidirect
24. #16811317C22semidirect
25. #16811292C22semidirect
26. #16811285C22semidirect
27. #16811280C22semidirect
28. #16811170C22semidirect
31. #16811157C22semidirect
32. #16811155C22semidirect
49. C4×#11719949C22semidirect
50. C4×#11719945C22semidirect
57. C4×Q8×D53C22semidirect
75. C4×#41×C53C22semidirect
190. C2×Q8×C53#41semidirect
230. C2×C4×D53#41semidirect
286. Q8×C53C2×#41semidirect
325. C4×D53C2×#41semidirect
371. C2×C4×#41D53semidirect
374. C2×C53#3480semidirect
415. C4×#41C2×D53semidirect
445. C53C2×#3480semidirect
561. C2×Q8#11719945semidirect
652. Q8C2×#11719945semidirect
723. C2#20288313direct (N × H)

Maximal subgroups

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

subgroupindex
#202883132
C2×#168113562
C2×#168113492
C2×#168113412
C2×#168113232
C2×#168113172
C2×#168112922
C2×#168112852
C2×#168112802
C2×#168111702
C2×#168111572
C2×#168111552
C2×C4×#117199492
C2×C4×#117199452
C2×C4×Q8×D532
C2×C4×#41×C532
C2×#348053