Finite Group Databasebeta

← C2×#20287660 #28264619

Subgroups — C2×#20287660 #28264619

Order 13568.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811351C211yesmaximal, characteristic, complemented
2#20287660C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16811029C211yesmaximal, characteristic, complemented
5C2×#16811022C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810927C211yesmaximal, characteristic, complemented
8C2×#16810905C211yesmaximal, characteristic, complemented
9C2×#16810923C211yesmaximal, characteristic
10C2×#16810923C211yesmaximal, characteristic
11C2×#16810913C211yesmaximal, characteristic
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810723C211yesmaximal, characteristic
14C2×#16810723C211yesmaximal, characteristic
15C2×C4×#11719923C211yesmaximal, characteristic
16C2×C53×#554C211yesmaximal, characteristic
17C22×#11719923C2211yescharacteristic
18#16811351—24no—
19#16811351C2218yescomplemented
20C2×#13133217C2211yescharacteristic
21C2×#13133215—21no—
22C2×#13133209C2211yescharacteristic
23C2×#13133209C2211yescharacteristic
24C2×#13133207—21no—
25C2×#13133207—21no—
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×Dic106C2211yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×#13133182—21no—
30#16811033C2218yescomplemented
31#16811029C2218yescomplemented
32#16811022C2218yescomplemented
33#16810927C2218yescomplemented
34#16810927C2218yescomplemented
35#16810923C2218yes—
36#16810923C2218yes—
37#16810913C2218yes—
38#16810905C2218yescomplemented
39#16810754C2218yescomplemented
40#16810723C2218yes—
41#16810723C2218yes—
42C4×#11719923C2218yes—
43C2×#13133150C2211yescharacteristic
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133150C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133148C2211yescharacteristic
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133140C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#554—24no—
65C53×#554C2218yes—
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#125×C53C2211yescharacteristic
68C2×#125×C53C2211yescharacteristic
69C2×C22⋊Q8×C53—21no—
70C2×C22⋊Q8×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×D4×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C4⋊C4×C53—21no—
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×#11719923Q818yescomplemented
80C2×#11719923C2314yes—
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C22×#88322C2311yescharacteristic
85#13133217—22no—
86#13133217C2314yes—
87#13133215—28no—
88#13133209—22no—
89#13133209—22no—
90#13133209C2314yes—
91#13133209C2314yes—
92#13133207—28no—
93#13133207—28no—
94C4×Dic106—22no—
95C4×Dic106—22no—
96C4×Dic106—22no—
97C4×Dic106C2314yes—
98C4×Dic106C2314yes—
99C4×Dic106C2314yes—
100#13133182—28no—
101C2×C4⋊Dic53—21no—
102C2×C4⋊Dic53C2311yescharacteristic
103C2×C4⋊Dic53C2311yescharacteristic
104C2×C4⋊Dic53C2311yescharacteristic
105C2×#11719919—21no—
106C2×#11719919—21no—
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×#11719919—21no—
110C2×#11719919—21no—
111C2×#11719919—21no—
112C2×C4×Dic53—21no—
113C2×C4×Dic53—21no—
114C2×C4×Dic53—21no—
115#13133150C2314yes—
116#13133150C2314yes—
117#13133150C2314yes—
118#13133150C2314yes—
119#13133148C2314yes—
120#13133148C2314yes—
121#13133148C2314yes—
122#13133148C2314yes—
123#13133148C2314yes—
124C4⋊#88322C2314yes—
125C4⋊#88322C2314yes—
126C4⋊#88322C2314yes—
127#13133140C2314yes—
128#13133140C2314yes—
129#13133140C2314yes—
130#13133138C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133128C2314yes—
134#13133128C2314yes—
135C4×#88322C2314yes—
136C22×Q8×C53—21no—
137C22×Q8×C53D411yescharacteristic
138C22×D4×C53C2311yescharacteristic
139C23×C4×C53—21no—
140C23×C4×C53—21no—
141C23×C4×C53—21no—
142C4⋊Q8×C53—22no—
143C4⋊Q8×C53C2314yes—
144#125×C53—22no—
145#125×C53—22no—
146#125×C53C2314yes—
147#125×C53C2314yes—
148C22⋊Q8×C53—28no—
149C22⋊Q8×C53—28no—
150C22⋊Q8×C53—28no—
151C4×Q8×C53D414yes—
152C4×Q8×C53C2314yes—
153C4×D4×C53—22no—
154C4×D4×C53—22no—
155C4×D4×C53—22no—
156C4×D4×C53C2314yes—
157C4×D4×C53C2314yes—
158C4×D4×C53C2314yes—
159C2×C4⋊C4×C53—28no—
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×C53D411yescharacteristic
166C2×C4⋊C4×C53D411yescharacteristic
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53C2311yescharacteristic
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C42×C53C2311yescharacteristic
175C2×C42×C53C2311yescharacteristic
176C2×C42×C53C2311yescharacteristic
177C24×C53—21no—
178C2×Q8×C53—24no—
179C2×Q8×C53—42no—
180C2×Q8×C53—82no—
181C2×Q8×C53C2×D414yes—
182C2×D4×C53—21no—
183C2×D4×C53—22no—
184C2×D4×C53C2×Q814yes—
185C2×D4×C53C2412yes—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—24no—
190C22×C4×C53—24no—
191C22×C4×C53—24no—
192C22×C4×C53—44no—
193C22×C4×C53—82no—
194C22×C4×C53—82no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C2×Dic106—21no—
207C2×Dic106—22no—
208C2×Dic106—24no—
209C2×Dic106—44no—
210C2×Dic106C2×Q814yes—
211C2×Dic106C2412yes—
212C4⋊C4×C53—24no—
213C4⋊C4×C53—24no—
214C4⋊C4×C53—24no—
215C4⋊C4×C53—24no—
216C4⋊C4×C53—24no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—21no—
219C4⋊C4×C53—21no—
220C4⋊C4×C53C2×D414yes—
221C4⋊C4×C53C2×D414yes—
222C4⋊C4×C53C2×D414yes—
223C4⋊C4×C53C2412yes—
224C4⋊C4×C53C2412yes—
225C4⋊C4×C53C2412yes—
226C22⋊C4×C53—24no—
227C22⋊C4×C53—24no—
228C22⋊C4×C53—24no—
229C42×C53C2×D412yes—
230C42×C53C2×D412yes—
231C42×C53C2×D412yes—
232C42×C53C2412yes—
233C42×C53C2412yes—
234C42×C53C2412yes—
235#11719923C2×Q8116yescomplemented
236C4⋊Dic53—24no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—21no—
240C4⋊Dic53C2412yes—
241C4⋊Dic53C2412yes—
242C4⋊Dic53C2412yes—
243#11719919—24no—
244#11719919—24no—
245#11719919—24no—
246#11719919—24no—
247#11719919—24no—
248#11719919—24no—
249#11719919—24no—
250C4×Dic53—24no—
251C4×Dic53—24no—
252C4×Dic53—24no—
253C2×#88322—22no—
254C2×#88322—22no—
255C2×#88322—22no—
256C2×#88322C2×Q814yes—
257C2×#88322C2412yes—
258C2×#88322C2412yes—
259C2×#88322C2412yes—
260C2×#88322C2412yes—
261C23×C53—24no—
262C23×C53—22no—
263C23×C53—42no—
264C23×C53—42no—
265C23×C53C22×D411yescharacteristic
266Q8×C53—44no—
267Q8×C53—84no—
268D4×C53—24no—
269D4×C53—22no—
270D4×C53C22×Q814yes—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—48no—
281C2×C4×C53—42no—
282C2×C4×C53—42no—
283C2×C4×C53—42no—
284C2×C4×C53—84no—
285C2×C4×C53—84no—
286C2×C4×C53C22×D412yes—
287C2×C4×C53C22×D412yes—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D412yes—
292C2×C4×C53C22×D411yescharacteristic
293C2×C4×C53C22×Q812yes—
294C2×C4×C532−1+412yes—
295C2×C4×C53C2511yescharacteristic
296C2×Dic53—24no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304Dic106—24no—
305Dic106—22no—
306Dic106—48no—
307Dic106C22×Q814yes—
308#88322—22no—
309#88322—22no—
310#88322—22no—
311#88322C22×Q814yes—
312C2×#3388—531nomaximal, Sylow
313C22×C53—24no—
314C22×C53—48no—
315C22×C53—42no—
316C22×C53—42no—
317C22×C53D4×Q812yes—
318C22×C53#57512yes—
319C22×C53#57712yes—
320C22×C53C23×D411yescharacteristic
321C4×C53—22no—
322C4×C53—22no—
323C4×C53—22no—
324C4×C53—22no—
325C4×C53—22no—
326C4×C53—22no—
327C4×C53—42no—
328C4×C53—42no—
329C4×C53—42no—
330C4×C53D4×Q812yes—
331C4×C53C23×Q811yescharacteristic
332C4×C53C2×2−1+411yescharacteristic
333Dic53—24no—
334Dic53—42no—
335Dic53—42no—
336Dic53—42no—
337C2×#557—531no—
338C2×#554D5311yescharacteristic
339#3388—5316no—
340C2×#501—531no—
341C2×#501—531no—
342C2×#499—531no—
343C2×#479—531no—
344C2×#479—531no—
345C2×#475—531no—
346C2×#478—531no—
347C2×#478—531no—
348C2×#476—531no—
349C2×#446—531no—
350C2×#440—531no—
351C2×#440—531no—
352C2×C4×SD16—531no—
353C2×C53—44no—
354C2×C53#338814yescomplemented
355C2×C53C2×D4×Q811yescharacteristic
356C2×C53C2×#57511yescharacteristic
357C2×C53C2×#57711yescharacteristic
358C22×SD16—531no—
359#557—538no—
360#557—1064no—
361#554—24no—
362#554C2×D5318yes—
363C2×C4⋊Q8—531no—
364C2×C4⋊Q8—1061no—
365C2×C4⋊Q8C2×D5311yescharacteristic
366C2×#125—531no—
367C2×#125—531no—
368C2×#125—1061no—
369C2×#125—1061no—
370C2×#125C2×D5311yescharacteristic
371C2×#125C2×D5311yescharacteristic
372C2×C22⋊Q8—21no—
373C2×C22⋊Q8—21no—
374C2×C22⋊Q8—21no—
375C2×C4×Q8—531no—
376C2×C4×Q8—531no—
377C2×C4×Q8—531no—
378C2×C4×Q8—1061no—
379C2×C4×Q8C2×D5311yescharacteristic
380C2×C4×D4C2×D5311yescharacteristic
381C2×C4×D4C2×D5311yescharacteristic
382C2×C4×D4C2×D5311yescharacteristic
383C22×C4⋊C4—21no—
384#501—538no—
385#501—538no—
386#499—538no—
387#479—538no—
388#479—538no—
389#478—538no—
390#478—538no—
391#476—538no—
392#475—538no—
393#446—538no—
394#440—538no—
395#440—538no—
396C4×SD16—538no—
397C2×#107—531no—
398C2×#107—531no—
399C2×#107—531no—
400C2×#107—531no—
401C2×#106—531no—
402C2×#106—531no—
403C2×#106—531no—
404C2×#106—531no—
405C2×#106—531no—
406C2×C4⋊C8—531no—
407C2×C4⋊C8—531no—
408C2×C4⋊C8—531no—
409C2×#103—531no—
410C2×#103—531no—
411C2×#103—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×#102—531no—
415C2×#97—531no—
416C2×#97—531no—
417C2×C4×C8—531no—
418C53C2×#338811yescharacteristic, complemented, Sylow
419C22×Q8—21no—
420C22×Q8—531no—
421C22×Q8—1061no—
422C22×Q8C22⋊D5311yescharacteristic
423C22×D4C22×D5311yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C2×SD16—538no—
428C2×SD16—534no—
429C22×C8—531no—
430C22×C8—531no—
431C22×C8—531no—
432C22×C8—531no—
433C4⋊Q8—22no—
434C4⋊Q8—534no—
435C4⋊Q8—1068no—
436C4⋊Q8—1062no—
437C4⋊Q8C22×D5314yes—
438#125—22no—
439#125—22no—
440#125—534no—
441#125—534no—
442#125—1068no—
443#125—1068no—
444#125—1062no—
445#125—1062no—
446#125C22×D5314yes—
447#125C22×D5314yes—
448C22⋊Q8—28no—
449C22⋊Q8—28no—
450C22⋊Q8—28no—
451C4×Q8—534no—
452C4×Q8—534no—
453C4×Q8—534no—
454C4×Q8—1068no—
455C4×Q8—1062no—
456C4×Q8—1062no—
457C4×Q8—1062no—
458C4×Q8C22⋊D5314yes—
459C4×Q8C22×D5314yes—
460C4×D4—22no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4C22×D5314yes—
464C4×D4C22×D5314yes—
465C4×D4C22×D5314yes—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—28no—
472C2×C4⋊C4—531no—
473C2×C4⋊C4—531no—
474C2×C4⋊C4—531no—
475C2×C4⋊C4—1061no—
476C2×C4⋊C4—1061no—
477C2×C4⋊C4—1061no—
478C2×C4⋊C4—1061no—
479C2×C4⋊C4—1061no—
480C2×C4⋊C4—1061no—
481C2×C4⋊C4—1061no—
482C2×C4⋊C4—1061no—
483C2×C4⋊C4C22⋊D5311yescharacteristic
484C2×C4⋊C4C22⋊D5311yescharacteristic
485C2×C4⋊C4C22⋊D5311yescharacteristic
486C2×C4⋊C4C22×D5311yescharacteristic
487C2×C4⋊C4C22×D5311yescharacteristic
488C2×C4⋊C4C22×D5311yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C42—1061no—
493C2×C42—1061no—
494C2×C42—1061no—
495C2×C42C22×D5311yescharacteristic
496C2×C42C22×D5311yescharacteristic
497C2×C42C22×D5311yescharacteristic
498#107—534no—
499#107—534no—
500#107—534no—
501#107—534no—
502#106—534no—
503#106—534no—
504#106—534no—
505#106—534no—
506#106—534no—
507C4⋊C8—534no—
508C4⋊C8—534no—
509C4⋊C8—534no—
510#103—534no—
511#103—534no—
512#103—534no—
513#102—534no—
514#102—534no—
515#102—534no—
516#97—534no—
517#97—534no—
518C4×C8—534no—
519C24—21no—
520C2×Q8—24no—
521C2×Q8—42no—
522C2×Q8—82no—
523C2×Q8—534no—
524C2×Q8—532no—
525C2×Q8—1061no—
526C2×Q8—1064no—
527C2×Q8—1062no—
528C2×Q8—2124no—
529C2×Q8C2×C22⋊D5314yes—
530C2×D4—21no—
531C2×D4—22no—
532C2×D4Q8×D5314yes—
533C2×D4C23×D5312yes—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—44no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—1061no—
544C22×C4—1061no—
545C22×C4—1061no—
546C22×C4—1061no—
547C22×C4C2×C22⋊D5311yescharacteristic
548C22×C4C2×C22⋊D5311yescharacteristic
549C22×C4C2×C22⋊D5311yescharacteristic
550C22×C4C2×C22⋊D5311yescharacteristic
551C22×C4C2×C22⋊D5311yescharacteristic
552C22×C4C2×C22⋊D5311yescharacteristic
553C22×C4C23×D5311yescharacteristic
554SD16—5316no—
555C2×C8—534no—
556C2×C8—532no—
557C2×C8—532no—
558C2×C8—532no—
559C2×C8—532no—
560C2×C8—1062no—
561C2×C8—1062no—
562C2×C8—1062no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—532no—
572C4⋊C4—532no—
573C4⋊C4—532no—
574C4⋊C4—1061no—
575C4⋊C4—1061no—
576C4⋊C4—1061no—
577C4⋊C4—1064no—
578C4⋊C4—1064no—
579C4⋊C4—1064no—
580C4⋊C4—1064no—
581C4⋊C4—1064no—
582C4⋊C4—1064no—
583C4⋊C4—1064no—
584C4⋊C4—1064no—
585C4⋊C4C2×C22⋊D5314yes—
586C4⋊C4C2×C22⋊D5314yes—
587C4⋊C4C2×C22⋊D5314yes—
588C4⋊C4C23×D5312yes—
589C4⋊C4C23×D5312yes—
590C4⋊C4C23×D5312yes—
591C22⋊C4—24no—
592C22⋊C4—24no—
593C22⋊C4—24no—
594C42—1064no—
595C42—1064no—
596C42—1064no—
597C42C2×C22⋊D5312yes—
598C42C2×C22⋊D5312yes—
599C42C2×C22⋊D5312yes—
600C42C23×D5312yes—
601C42C23×D5312yes—
602C42C23×D5312yes—
603C23—24no—
604C23—22no—
605C23—42no—
606C23—42no—
607C23C22×C22⋊D5311yescharacteristic
608Q8—44no—
609Q8—84no—
610Q8—534no—
611Q8—1064no—
612Q8—1062no—
613Q8—2128no—
614D4—24no—
615D4—22no—
616D4C2×Q8×D5314yes—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—48no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—84no—
631C2×C4—84no—
632C2×C4—1064no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1062no—
637C2×C4—2122no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4C22×C22⋊D5312yes—
641C2×C4C22×C22⋊D5312yes—
642C2×C4C22×C22⋊D5312yes—
643C2×C4C22×C22⋊D5312yes—
644C2×C4C22×C22⋊D5312yes—
645C2×C4C22×C22⋊D5312yes—
646C2×C4C22×C22⋊D5311yescharacteristic
647C2×C4C2×Q8×D5312yes—
648C2×C4#1313326512yes—
649C2×C4C24×D5311yescharacteristic
650C8—534no—
651C8—1062no—
652C8—1062no—
653C8—1062no—
654C22—24no—
655C22—48no—
656C22—42no—
657C22—42no—
658C22Q8×C22⋊D5312yes—
659C22#1681142112yes—
660C22#1681143412yes—
661C22C23×C22⋊D5311yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—22no—
666C4—22no—
667C4—22no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—1064no—
672C4—2122no—
673C4—2122no—
674C4—2122no—
675C4Q8×C22⋊D5312yes—
676C4C22×Q8×D5311yescharacteristic
677C4C2×#1313326511yescharacteristic
678C2—44no—
679C2#2028766014yesdirect product factor
680C2C2×Q8×C22⋊D5311yescharacteristic
681C2C2×#1681142111yescharacteristic
682C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#554C2
socleC23×C53C22×D4
prime radicalC22×D4×C53C23
hypercenterC2×#554D53
hypocenterC53C2×#3388
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16811351C2semidirect
2. #20287660C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16811029C2semidirect
5. C2×#16811022C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810927C2semidirect
8. C2×#16810905C2semidirect
12. C2×#16810754C2semidirect
19. #16811351C22semidirect
30. #16811033C22semidirect
31. #16811029C22semidirect
32. #16811022C22semidirect
33. #16810927C22semidirect
34. #16810927C22semidirect
38. #16810905C22semidirect
39. #16810754C22semidirect
79. C2×#11719923Q8semidirect
235. #11719923C2×Q8semidirect
354. C2×C53#3388semidirect
418. C53C2×#3388semidirect
679. C2#20287660direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113512
#202876602
C2×#168110332
C2×#168110292
C2×#168110222
C2×#168109272
C2×#168109052
C2×#168109232
C2×#168109132
C2×#168107542
C2×#168107232
C2×C4×#117199232
C2×C53×#5542
C2×#338853