Finite Group Databasebeta

← C2×#20287557 #28263889

Subgroups — C2×#20287557 #28263889

Order 13568.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811346C211yesmaximal, characteristic
2#20287557C2116yesmaximal, direct product factor
3C2×#16810993C211yesmaximal, characteristic, complemented
4C2×#16810985C211yesmaximal, characteristic
5C2×#16810980C211yesmaximal, characteristic
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810915C211yesmaximal, characteristic, complemented
8C2×#16810920C211yesmaximal, characteristic
9C2×#16810845C211yesmaximal, characteristic
10C2×#16810845C211yesmaximal, characteristic
11C2×#16810833C211yesmaximal, characteristic, complemented
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810728C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic
15C2×C4×#11719925C211yesmaximal, characteristic, complemented
16C2×C53×#557C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20#16811346—24no—
21#16811346C2218yes—
22C2×#13133217C2211yescharacteristic
23C2×#13133212—21no—
24C2×#13133212—21no—
25C2×#13133205C2211yescharacteristic
26C2×#13133205C2211yescharacteristic
27C2×#13133193—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×Dic106C2211yescharacteristic
30C2×C4×D212C2211yescharacteristic
31C2×#13133175—21no—
32#16810993C2218yescomplemented
33#16810985C2218yes—
34#16810980C2218yes—
35#16810927C2218yescomplemented
36#16810920C2218yes—
37#16810915C2218yescomplemented
38#16810845C2218yes—
39#16810845C2218yes—
40#16810833C2218yescomplemented
41#16810754C2218yescomplemented
42#16810728C2218yescomplemented
43#16810721C2218yes—
44C4×#11719925C2218yescomplemented
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×C4⋊#88322C2211yescharacteristic
49C2×C4⋊#88322C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133140C2211yescharacteristic
53C2×#13133140C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#557—24no—
65C53×#557C2218yescomplemented
66C2×C4⋊Q8×C53—21no—
67C2×C4⋊Q8×C53C2211yescharacteristic
68C2×#125×C53—21no—
69C2×#125×C53—21no—
70C2×#125×C53C2211yescharacteristic
71C2×#125×C53C2211yescharacteristic
72C2×C4×Q8×C53—21no—
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×Q8×C53C2211yescharacteristic
76C2×C4×Q8×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C4×D53—21no—
81C2×#11719925—24no—
82C2×#11719925—24no—
83C2×#11719925C2314yes—
84C2×#11719925C2314yes—
85C2×#11719924—24no—
86C2×#11719924C2314yes—
87C22×#88322C2311yescharacteristic
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91#13133217—22no—
92#13133217C2314yes—
93#13133212—28no—
94#13133212—28no—
95#13133205—22no—
96#13133205—22no—
97#13133205C2314yes—
98#13133205C2314yes—
99#13133193—28no—
100C4×Dic106—22no—
101C4×Dic106—22no—
102C4×Dic106C2314yes—
103C4×Dic106C2314yes—
104C4×D212—22no—
105C4×D212C2314yes—
106#13133175—28no—
107C2×C4⋊Dic53—21no—
108C2×C4⋊Dic53—21no—
109C2×C4⋊Dic53C2311yescharacteristic
110C2×#11719919—21no—
111C2×#11719919—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921—21no—
115C2×#11719921—21no—
116C2×#11719921—21no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53—21no—
119#13133150C2314yes—
120#13133150C2314yes—
121#13133148C2314yes—
122C4⋊#88322C2314yes—
123C4⋊#88322C2314yes—
124C4⋊#88322C2314yes—
125#13133141C2314yes—
126#13133140C2314yes—
127#13133140C2314yes—
128#13133140C2314yes—
129#13133140C2314yes—
130#13133140C2314yes—
131#13133140C2314yes—
132#13133137C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133128C2314yes—
136#13133128C2314yes—
137C4×#88322C2314yes—
138C22×Q8×C53—21no—
139C22×Q8×C53D411yescharacteristic
140C22×Q8×C53C2311yescharacteristic
141C4⋊Q8×C53—22no—
142C4⋊Q8×C53—28no—
143C4⋊Q8×C53C2314yes—
144#125×C53—28no—
145#125×C53—28no—
146#125×C53—22no—
147#125×C53—22no—
148#125×C53C2314yes—
149#125×C53C2314yes—
150C4×Q8×C53—28no—
151C4×Q8×C53—22no—
152C4×Q8×C53—22no—
153C4×Q8×C53—22no—
154C4×Q8×C53D414yes—
155C4×Q8×C53C2314yes—
156C4×Q8×C53C2314yes—
157C4×Q8×C53C2314yes—
158C4×Q8×C53C2314yes—
159C2×C4⋊C4×C53—21no—
160C2×C4⋊C4×C53—21no—
161C2×C4⋊C4×C53—21no—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53—21no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C42×C53—21no—
174C2×C42×C53—21no—
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C23×D53—21no—
180C2×Q8×C53—21no—
181C2×Q8×C53—24no—
182C2×Q8×C53—22no—
183C2×Q8×C53—42no—
184C2×Q8×C53—44no—
185C2×Q8×C53C2×D414yes—
186C2×Q8×C53#4114yes—
187C2×Q8×C53C2412yes—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—21no—
205C2×D212C2412yes—
206C2×C4×D53—24no—
207C2×C4×D53—44no—
208C2×Dic106—22no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—22no—
212C2×Dic106—21no—
213C2×Dic106—21no—
214C2×Dic106C2412yes—
215C2×Dic106C2412yes—
216C4⋊C4×C53—24no—
217C4⋊C4×C53—24no—
218C4⋊C4×C53—24no—
219C4⋊C4×C53—24no—
220C4⋊C4×C53—24no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53C2×D414yes—
228C4⋊C4×C53C2×D414yes—
229C4⋊C4×C53C2×D414yes—
230C4⋊C4×C53C2412yes—
231C4⋊C4×C53C2412yes—
232C4⋊C4×C53C2412yes—
233C42×C53—24no—
234C42×C53—24no—
235C42×C53—24no—
236C42×C53C2×D412yes—
237C42×C53C2×D412yes—
238C42×C53C2×D412yes—
239C42×C53C2412yes—
240C42×C53C2412yes—
241C42×C53C2412yes—
242#11719925—28no—
243#11719925—28no—
244#11719924—28no—
245#11719921—24no—
246#11719921—24no—
247#11719921—24no—
248#11719921—24no—
249#11719921—24no—
250C4⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—21no—
253C4⋊Dic53C2412yes—
254#11719919—24no—
255#11719919—24no—
256C4×Dic53—24no—
257C4×Dic53—24no—
258C2×#88322—22no—
259C2×#88322—22no—
260C2×#88322—22no—
261C2×#88322—22no—
262C2×#88322C2412yes—
263C2×#88322C2412yes—
264C2×#88322C2412yes—
265C2×#88322C2412yes—
266C23×C53C22×D411yescharacteristic
267C22×D53—22no—
268C22×D53—42no—
269C22×D53—42no—
270C22×D53—42no—
271Q8×C53—24no—
272Q8×C53—22no—
273Q8×C53—44no—
274Q8×C53—48no—
275Q8×C53C2×#4114yes—
276C2×C4×C53—24no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D412yes—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4112yes—
298C2×C4×C532−1+412yes—
299C2×C4×C53C2511yescharacteristic
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306D212—22no—
307D212—22no—
308D212—42no—
309C4×D53—48no—
310Dic106—22no—
311Dic106—22no—
312Dic106—22no—
313Dic106—22no—
314Dic106—42no—
315Dic106—42no—
316#88322—22no—
317#88322—22no—
318#88322—22no—
319#88322—22no—
320C2×#3377—531nomaximal, Sylow
321C22×C53#54812yes—
322C22×C53#57512yes—
323C22×C53#57812yes—
324C22×C53C23×D411yescharacteristic
325C2×D53—42no—
326C2×D53—42no—
327C2×D53—42no—
328C2×D53—84no—
329C4×C53—24no—
330C4×C53—22no—
331C4×C53—22no—
332C4×C53—22no—
333C4×C53—22no—
334C4×C53—22no—
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53#54812yes—
340C4×C53C22×#4111yescharacteristic
341C4×C53C2×2−1+411yescharacteristic
342Dic53—42no—
343Dic53—42no—
344Dic53—42no—
345C2×#557D5311yescharacteristic, complemented
346C2×#556—531no—
347#3377—5316no—
348C2×#491—531no—
349C2×#489—531no—
350C2×#488—531no—
351C2×#479—531no—
352C2×#477—531no—
353C2×#478—531no—
354C2×#464—531no—
355C2×#464—531no—
356C2×#462—531no—
357C2×#446—531no—
358C2×#441—531no—
359C2×#440—531no—
360C2×C4×Q16—531no—
361C2×C53#337714yescomplemented
362C2×C53C2×#54811yescharacteristic
363C2×C53C2×#57511yescharacteristic
364C2×C53C2×#57811yescharacteristic
365D53—82no—
366C22×Q16—531no—
367C22×Q16—531no—
368C22×SD16—531no—
369#557—24no—
370#557C2×D5318yescomplemented
371#556—538no—
372#556—1064no—
373C2×C4⋊Q8—21no—
374C2×C4⋊Q8—531no—
375C2×C4⋊Q8C2×D5311yescharacteristic
376C2×#126—1061no—
377C2×#126—1061no—
378C2×#125—21no—
379C2×#125—21no—
380C2×#125C2×D5311yescharacteristic
381C2×#125C2×D5311yescharacteristic
382C2×#124—531no—
383C2×#124—531no—
384C2×C22⋊Q8—1061no—
385C2×C4×Q8—21no—
386C2×C4×Q8—531no—
387C2×C4×Q8—531no—
388C2×C4×Q8C2×D5311yescharacteristic
389C2×C4×Q8C2×D5311yescharacteristic
390C2×C4×Q8C2×D5311yescharacteristic
391C2×C4×Q8C2×D5311yescharacteristic
392C2×C4×D4—531no—
393C2×#117—1061no—
394#491—538no—
395#489—538no—
396#488—538no—
397#479—538no—
398#478—538no—
399#477—538no—
400#464—538no—
401#464—538no—
402#462—538no—
403#446—538no—
404#441—538no—
405#440—538no—
406C4×Q16—538no—
407C2×#107—531no—
408C2×#107—531no—
409C2×#106—531no—
410C2×C4⋊C8—531no—
411C2×C4⋊C8—531no—
412C2×C4⋊C8—531no—
413C2×#103—531no—
414C2×#103—531no—
415C2×#103—531no—
416C2×#103—531no—
417C2×#103—531no—
418C2×#103—531no—
419C2×#103—531no—
420C2×#102—531no—
421C2×#102—531no—
422C2×#102—531no—
423C2×#97—531no—
424C2×#97—531no—
425C2×C4×C8—531no—
426C53C2×#337711yescharacteristic, complemented, Sylow
427C22×Q8—21no—
428C22×Q8—531no—
429C22×Q8—531no—
430C22×Q8C22⋊D5311yescharacteristic
431C22×Q8C22×D5311yescharacteristic
432C22×D4—531no—
433C23×C4—1061no—
434C2×Q16—534no—
435C2×Q16—534no—
436C2×Q16—1064no—
437C2×Q16—1064no—
438C2×SD16—534no—
439C2×SD16—1064no—
440C22×C8—531no—
441C22×C8—531no—
442C22×C8—531no—
443C22×C8—531no—
444C4⋊Q8—28no—
445C4⋊Q8—22no—
446C4⋊Q8—534no—
447C4⋊Q8—1062no—
448C4⋊Q8C22×D5314yes—
449#126—1068no—
450#126—1068no—
451#125—28no—
452#125—28no—
453#125—22no—
454#125—22no—
455#125C22×D5314yes—
456#125C22×D5314yes—
457#124—534no—
458#124—534no—
459#124—1062no—
460#124—1062no—
461C22⋊Q8—1068no—
462C4×Q8—28no—
463C4×Q8—22no—
464C4×Q8—22no—
465C4×Q8—22no—
466C4×Q8—534no—
467C4×Q8—534no—
468C4×Q8—1062no—
469C4×Q8—1062no—
470C4×Q8C22⋊D5314yes—
471C4×Q8C22×D5314yes—
472C4×Q8C22×D5314yes—
473C4×Q8C22×D5314yes—
474C4×Q8C22×D5314yes—
475C4×D4—534no—
476C4×D4—1062no—
477#117—1068no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—531no—
487C2×C4⋊C4—1061no—
488C2×C4⋊C4—1061no—
489C2×C4⋊C4—1061no—
490C2×C4⋊C4—1061no—
491C2×C4⋊C4C22⋊D5311yescharacteristic
492C2×C4⋊C4C22⋊D5311yescharacteristic
493C2×C4⋊C4C22⋊D5311yescharacteristic
494C2×C4⋊C4C22×D5311yescharacteristic
495C2×C4⋊C4C22×D5311yescharacteristic
496C2×C4⋊C4C22×D5311yescharacteristic
497C2×C22⋊C4—1061no—
498C2×C22⋊C4—1061no—
499C2×C22⋊C4—1061no—
500C2×C22⋊C4—1061no—
501C2×C22⋊C4—1061no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42—21no—
505C2×C42—1061no—
506C2×C42—1061no—
507C2×C42C22×D5311yescharacteristic
508C2×C42C22×D5311yescharacteristic
509C2×C42C22×D5311yescharacteristic
510#107—534no—
511#107—534no—
512#106—534no—
513C4⋊C8—534no—
514C4⋊C8—534no—
515C4⋊C8—534no—
516#103—534no—
517#103—534no—
518#103—534no—
519#103—534no—
520#103—534no—
521#103—534no—
522#103—534no—
523#102—534no—
524#102—534no—
525#102—534no—
526#97—534no—
527#97—534no—
528C4×C8—534no—
529C24—1061no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—22no—
533C2×Q8—42no—
534C2×Q8—44no—
535C2×Q8—532no—
536C2×Q8—532no—
537C2×Q8—1061no—
538C2×Q8—1061no—
539C2×Q8—1062no—
540C2×Q8—1062no—
541C2×Q8—1062no—
542C2×Q8—1062no—
543C2×Q8#1171994914yes—
544C2×Q8C2×C22⋊D5314yes—
545C2×Q8C23×D5312yes—
546C2×D4—532no—
547C2×D4—1061no—
548C2×D4—1062no—
549C2×D4—1062no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4—1064no—
558C22×C4—2124no—
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C2×C22⋊D5311yescharacteristic
562C22×C4C2×C22⋊D5311yescharacteristic
563C22×C4C2×C22⋊D5311yescharacteristic
564C22×C4C2×C22⋊D5311yescharacteristic
565C22×C4C23×D5311yescharacteristic
566Q16—1068no—
567Q16—1068no—
568SD16—1068no—
569C2×C8—532no—
570C2×C8—532no—
571C2×C8—532no—
572C2×C8—532no—
573C2×C8—1062no—
574C2×C8—1062no—
575C2×C8—1062no—
576C2×C8—1062no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—532no—
589C4⋊C4—1061no—
590C4⋊C4—1064no—
591C4⋊C4—1064no—
592C4⋊C4—1064no—
593C4⋊C4—1064no—
594C4⋊C4C2×C22⋊D5314yes—
595C4⋊C4C2×C22⋊D5314yes—
596C4⋊C4C2×C22⋊D5314yes—
597C4⋊C4C23×D5312yes—
598C4⋊C4C23×D5312yes—
599C4⋊C4C23×D5312yes—
600C22⋊C4—1064no—
601C22⋊C4—1064no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—1064no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—1064no—
609C42—1064no—
610C42C2×C22⋊D5312yes—
611C42C2×C22⋊D5312yes—
612C42C2×C22⋊D5312yes—
613C42C23×D5312yes—
614C42C23×D5312yes—
615C42C23×D5312yes—
616C23—1062no—
617C23—2122no—
618C23—2122no—
619C23—2122no—
620C23C22×C22⋊D5311yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—44no—
624Q8—48no—
625Q8—1062no—
626Q8—1062no—
627Q8—1062no—
628Q8—1062no—
629Q8—2122no—
630Q8—2122no—
631Q8C2×#1171994914yes—
632D4—1062no—
633D4—1062no—
634D4—2122no—
635C2×C4—24no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—2128no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4—2122no—
656C2×C4C22×C22⋊D5312yes—
657C2×C4C22×C22⋊D5312yes—
658C2×C4C22×C22⋊D5312yes—
659C2×C4C22×C22⋊D5312yes—
660C2×C4C22×C22⋊D5312yes—
661C2×C4C22×C22⋊D5312yes—
662C2×C4C22×C22⋊D5311yescharacteristic
663C2×C4C2×#1171994912yes—
664C2×C4#1313326512yes—
665C2×C4C24×D5311yescharacteristic
666C8—1062no—
667C8—1062no—
668C8—1062no—
669C8—1062no—
670C22—4244no—
671C22—2122no—
672C22—2122no—
673C22—2122no—
674C22#1681128412yes—
675C22#1681142112yes—
676C22#1681143812yes—
677C22C23×C22⋊D5311yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—2122no—
689C4—2122no—
690C4—2122no—
691C4#1681128412yes—
692C4C22×#1171994911yescharacteristic
693C4C2×#1313326511yescharacteristic
694C2—4242no—
695C2#2028755714yesdirect product factor
696C2C2×#1681128411yescharacteristic
697C2C2×#1681142111yescharacteristic
698C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#557C2
socleC23×C53C22×D4
prime radicalC22×D212C23
hypercenterC2×#557D53
hypocenterC53C2×#3377
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #20287557C2direct (N × H)
3. C2×#16810993C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810915C2semidirect
11. C2×#16810833C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810728C2semidirect
15. C2×C4×#11719925C2semidirect
16. C2×C53×#557C2semidirect
32. #16810993C22semidirect
35. #16810927C22semidirect
37. #16810915C22semidirect
40. #16810833C22semidirect
41. #16810754C22semidirect
42. #16810728C22semidirect
44. C4×#11719925C22semidirect
65. C53×#557C22semidirect
345. C2×#557D53semidirect
361. C2×C53#3377semidirect
370. #557C2×D53semidirect
426. C53C2×#3377semidirect
695. C2#20287557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113462
#202875572
C2×#168109932
C2×#168109852
C2×#168109802
C2×#168109272
C2×#168109152
C2×#168109202
C2×#168108452
C2×#168108332
C2×#168107542
C2×#168107282
C2×#168107212
C2×C4×#117199252
C2×C53×#5572
C2×#337753