Finite Group Databasebeta

← C2×#20275994 #27411929

Subgroups — C2×#20275994 #27411929

Order 13568.

1322 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133248C211yesmaximal, characteristic
2C2×#16810672C211yesmaximal, characteristic, complemented
3C2×#16810639C211yesmaximal, characteristic
4C2×#16810632C211yesmaximal, characteristic, complemented
5C2×#16810605C211yesmaximal, characteristic
6#20275994C218yesmaximal, direct product factor
7C2×#16810394C211yesmaximal, characteristic, complemented
8C22×#101×C53C211yesmaximal, characteristic, complemented
9C22×#11719945C2211yescharacteristic
10C2×#13133248—22no—
11C2×#13133248—22no—
12C2×#13133248—22no—
13C2×#13133248—22no—
14C2×#13133248—22no—
15C2×#13133248C2214yes—
16C22×#11719925—21no—
17C22×#11719924—21no—
18C22×#11719917C2211yescharacteristic
19C22×#11719917C2211yescharacteristic
20C2×#13133176C2211yescharacteristic
21#16810672—22no—
22#16810672C2214yescomplemented
23C2×#13133153—22no—
24#16810639—22no—
25#16810639C2214yes—
26C2×#13133143—22no—
27#16810632—22no—
28#16810632C2214yescomplemented
29C2×#13133141—22no—
30#16810605—22no—
31#16810605C2214yes—
32C2×#13133135—21no—
33C2×#13133133—21no—
34#16810394C2214yescomplemented
35C23×Q8×C53C2211yescharacteristic
36C22×M16×C53C2211yescharacteristic
37C22×M16×C53C2211yescharacteristic
38C2×#101×C53—22no—
39C2×#101×C53—22no—
40C2×#101×C53C2214yescomplemented
41C2×#11719945—21no—
42C2×#11719945—21no—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—21no—
48C2×#11719945—21no—
49C2×#11719945—21no—
50C2×#11719945—21no—
51C2×#11719945D412yes—
52C2×#11719945C2312yes—
53C22×Dic106D411yescharacteristic
54C22×D212D411yescharacteristic
55C22×C22⋊D53—21no—
56C22×C4×D53—21no—
57#13133248—28no—
58#13133248—28no—
59#13133248—28no—
60#13133248—28no—
61C2×#11719925—24no—
62C2×#11719925—24no—
63C2×#11719925—24no—
64C2×#11719924—24no—
65C2×#11719924—24no—
66C2×#11719924—24no—
67C2×#11719917—21no—
68C2×#11719917—21no—
69C2×#11719917—21no—
70C2×#11719917—21no—
71C2×#11719917—21no—
72C2×#11719917—21no—
73C2×#11719917—21no—
74C2×#11719917—21no—
75C2×#11719917D412yes—
76C2×#11719917D412yes—
77C2×#11719917C2312yes—
78C2×#11719917C2312yes—
79C22×#88322—21no—
80C22×#88322—21no—
81#13133176—21no—
82#13133176—21no—
83#13133176—21no—
84#13133176C2312yes—
85C2×C4⋊Dic53—21no—
86C2×C22⋊Dic53—21no—
87C2×C4×Dic53—21no—
88#13133153—28no—
89#13133143—28no—
90#13133141—28no—
91#13133135—24no—
92#13133133—24no—
93C22×Q8×C53—21no—
94C22×Q8×C53—21no—
95C22×Q8×C53—21no—
96C22×Q8×C53—21no—
97C22×Q8×C53—21no—
98C22×Q8×C53—21no—
99C22×Q8×C53—21no—
100C22×Q8×C53—21no—
101C22×Q8×C53—21no—
102C22×Q8×C53—21no—
103C22×Q8×C53—21no—
104C22×Q8×C53D412yes—
105C22×Q8×C53D412yes—
106C22×Q8×C53C2312yes—
107C23×C4×C53—21no—
108C23×C4×C53C2311yescharacteristic
109C2×M16×C53—21no—
110C2×M16×C53—21no—
111C2×M16×C53—21no—
112C2×M16×C53—21no—
113C2×M16×C53—21no—
114C2×M16×C53—21no—
115C2×M16×C53—21no—
116C2×M16×C53—21no—
117C2×M16×C53D412yes—
118C2×M16×C53D412yes—
119C2×M16×C53C2312yes—
120C2×M16×C53C2312yes—
121C22×C8×C53—21no—
122C22×C8×C53—21no—
123#101×C53—28no—
124C24×C53#4111yescharacteristic
125C23×D53—21no—
126C2×Q8×C53—22no—
127C2×Q8×C53—22no—
128C2×Q8×C53—22no—
129C2×Q8×C53—22no—
130C2×Q8×C53—22no—
131C2×Q8×C53—22no—
132C2×Q8×C53—22no—
133C2×Q8×C53—22no—
134C2×Q8×C53—22no—
135C2×Q8×C53—22no—
136C2×Q8×C53—22no—
137C2×Q8×C53—22no—
138C2×Q8×C53—22no—
139C2×Q8×C53—22no—
140C2×Q8×C53—22no—
141C2×Q8×C53—41no—
142C2×Q8×C53—41no—
143C2×Q8×C53—41no—
144C2×Q8×C53—41no—
145C2×Q8×C53—41no—
146C2×Q8×C53—41no—
147C2×Q8×C53—41no—
148C2×Q8×C53—41no—
149C2×Q8×C53—41no—
150C2×Q8×C53—41no—
151C2×Q8×C53—41no—
152C2×Q8×C53—41no—
153C2×Q8×C53C2×D414yes—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—41no—
158C22×C4×C53—41no—
159C22×C4×C53—41no—
160C22×C4×C53—41no—
161C22×C4×C53C2×D411yescharacteristic
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D411yescharacteristic
164C22×C4×C53C2×D411yescharacteristic
165C22×C4×C53C2×D411yescharacteristic
166C22×C4×C53C2×D411yescharacteristic
167C22×C4×C53C2×D411yescharacteristic
168C22×C4×C53C2×D411yescharacteristic
169C22×C4×C53#4111yescharacteristic
170C22×C4×C53#4111yescharacteristic
171C22×C4×C53#4111yescharacteristic
172C22×C4×C53#4111yescharacteristic
173C22×C4×C53#4111yescharacteristic
174C22×C4×C53C2411yescharacteristic
175C2×C22⋊D53—22no—
176C2×C22⋊D53—22no—
177C2×C22⋊D53—41no—
178C2×C22⋊D53—41no—
179C2×C22⋊D53—41no—
180C2×C22⋊D53—41no—
181C22×Dic53—21no—
182C22×Dic53—41no—
183#11719945—22no—
184#11719945—22no—
185#11719945—22no—
186#11719945—22no—
187#11719945—22no—
188#11719945—22no—
189#11719945—22no—
190#11719945—22no—
191#11719945—41no—
192#11719945—41no—
193#11719945—41no—
194#11719945—41no—
195#11719945—41no—
196#11719945—41no—
197#11719945—41no—
198#11719945—41no—
199C2×D212—21no—
200C2×D212—21no—
201C2×D212—21no—
202C2×D212—21no—
203C2×D212—21no—
204C2×D212C2×D412yes—
205C2×C4×D53—22no—
206C2×C4×D53—22no—
207C2×C4×D53—41no—
208C2×C4×D53—41no—
209C2×C4×D53—41no—
210C2×C4×D53—41no—
211C2×Dic106—21no—
212C2×Dic106—21no—
213C2×Dic106—21no—
214C2×Dic106—21no—
215C2×Dic106—21no—
216C2×Dic106C2×D412yes—
217M16×C53—22no—
218M16×C53—22no—
219M16×C53—22no—
220M16×C53—22no—
221M16×C53—22no—
222M16×C53—41no—
223M16×C53—41no—
224M16×C53C2×D414yes—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53—22no—
228C2×C8×C53—22no—
229C2×C8×C53—41no—
230C2×C8×C53—41no—
231C22⋊Dic53—22no—
232C22⋊Dic53—41no—
233#11719925—216no—
234#11719924—216no—
235C4⋊Dic53—22no—
236C4⋊Dic53—41no—
237C4×Dic53—22no—
238C4×Dic53—41no—
239#11719917—22no—
240#11719917—22no—
241#11719917—22no—
242#11719917—22no—
243#11719917—22no—
244#11719917—41no—
245#11719917—41no—
246#11719917C2×D414yes—
247C2×#88322—22no—
248C2×#88322—22no—
249C2×#88322—22no—
250C2×#88322—22no—
251C2×#88322—41no—
252C2×#88322—41no—
253C23×C53—42no—
254C23×C53#12111yescharacteristic
255C23×C53#12111yescharacteristic
256C23×C53#12311yescharacteristic
257C23×C53#12311yescharacteristic
258C23×C53#12411yescharacteristic
259C23×C53#12411yescharacteristic
260C23×C53C2×#4111yescharacteristic
261C22×D53—22no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—82no—
265Q8×C53—24no—
266Q8×C53—24no—
267Q8×C53—42no—
268Q8×C53—42no—
269Q8×C53—42no—
270Q8×C53—42no—
271Q8×C53—42no—
272Q8×C53—42no—
273C2×C4×C53—24no—
274C2×C4×C53—42no—
275C2×C4×C53—42no—
276C2×C4×C53—42no—
277C2×C4×C53—42no—
278C2×C4×C53—42no—
279C2×C4×C53—42no—
280C2×C4×C53#12011yescharacteristic
281C2×C4×C53#12011yescharacteristic
282C2×C4×C53#12011yescharacteristic
283C2×C4×C53#12011yescharacteristic
284C2×C4×C53#12111yescharacteristic
285C2×C4×C53#12111yescharacteristic
286C2×C4×C53#12111yescharacteristic
287C2×C4×C53#12111yescharacteristic
288C2×C4×C53#12111yescharacteristic
289C2×C4×C53#12111yescharacteristic
290C2×C4×C53#12111yescharacteristic
291C2×C4×C53#12111yescharacteristic
292C2×C4×C53#12111yescharacteristic
293C2×C4×C53#12111yescharacteristic
294C2×C4×C53#12311yescharacteristic
295C2×C4×C53#12311yescharacteristic
296C2×C4×C53#12311yescharacteristic
297C2×C4×C53#12311yescharacteristic
298C2×C4×C53#12311yescharacteristic
299C2×C4×C53#12311yescharacteristic
300C2×C4×C53#12411yescharacteristic
301C2×C4×C53#12411yescharacteristic
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C22×D411yescharacteristic
305C2×C4×C53C22×D411yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53C2×#4111yescharacteristic
308C22⋊D53—42no—
309C22⋊D53—42no—
310C22⋊D53—42no—
311C22⋊D53—42no—
312C2×Dic53—22no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53—42no—
316C2×Dic53—82no—
317D212—22no—
318D212—22no—
319D212—41no—
320D212—41no—
321C4×D53—42no—
322C4×D53—42no—
323C4×D53—42no—
324C4×D53—42no—
325Dic106—22no—
326Dic106—22no—
327Dic106—41no—
328Dic106—41no—
329C8×C53—24no—
330C8×C53—42no—
331#88322—24no—
332#88322—42no—
333C2×#2049—531nomaximal, Sylow
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—41no—
338C22×C53—41no—
339C22×C53—41no—
340C22×C53—41no—
341C22×C53#39411yescharacteristic
342C22×C53#39411yescharacteristic
343C22×C53#39411yescharacteristic
344C22×C53#39411yescharacteristic
345C22×C53C2×#12111yescharacteristic
346C22×C53C2×#12311yescharacteristic
347C22×C53C2×#12411yescharacteristic
348C2×D53—42no—
349C2×D53—82no—
350C2×D53—82no—
351C2×D53—82no—
352C4×C53—44no—
353C4×C53#39411yescharacteristic
354C4×C53#39411yescharacteristic
355C4×C53#39411yescharacteristic
356C4×C53#39411yescharacteristic
357C4×C53C2×#12011yescharacteristic
358C4×C53C2×#12111yescharacteristic
359C4×C53C2×#12111yescharacteristic
360C4×C53C2×#12311yescharacteristic
361Dic53—42no—
362Dic53—82no—
363C22×#137—531no—
364C2×#430—531no—
365C2×#421—531no—
366C2×#419—531no—
367C2×#413—531no—
368C22×#101D5311yescharacteristic, complemented
369#2049—538no—
370C2×#344—531no—
371C2×C53—21no—
372C2×C53—21no—
373C2×C53—21no—
374C2×C53—21no—
375C2×C53—21no—
376C2×C53—21no—
377C2×C53#204912yescomplemented
378C2×C53C2×#39411yescharacteristic
379D53—82no—
380C22×#41—531no—
381C23×Q8C2×D5311yescharacteristic
382C2×#137—534no—
383C2×#137—1062no—
384C2×#137—1062no—
385C2×#137—1062no—
386C2×#137—1062no—
387C2×#137—1062no—
388C22×Q16—1061no—
389C22×SD16—1061no—
390C22×M16—531no—
391C22×M16—531no—
392C22×M16C2×D5311yescharacteristic
393C22×M16C2×D5311yescharacteristic
394C2×#117—531no—
395#430—534no—
396#430—1062no—
397C2×#108—1062no—
398#421—534no—
399#421—1062no—
400C2×#104—1062no—
401#419—534no—
402#419—1062no—
403C2×#103—1062no—
404#413—534no—
405#413—1062no—
406C2×#101—22no—
407C2×#101—22no—
408C2×#101—1061no—
409C2×#101C2×D5314yescomplemented
410C2×#100—1061no—
411#344—534no—
412C53C2×#204911yescharacteristic, complemented, Sylow
413C2×#41—532no—
414C2×#41—532no—
415C2×#41—1061no—
416C2×#41—1061no—
417C2×#41—1061no—
418C2×#41—1061no—
419C2×#41—1061no—
420C2×#41—1061no—
421C2×#41—1061no—
422C2×#41—1061no—
423C2×#41—1061no—
424C2×#41—1061no—
425C22×Q8—21no—
426C22×Q8—21no—
427C22×Q8—21no—
428C22×Q8—21no—
429C22×Q8—21no—
430C22×Q8—21no—
431C22×Q8—21no—
432C22×Q8—21no—
433C22×Q8—21no—
434C22×Q8—21no—
435C22×Q8—21no—
436C22×Q8—531no—
437C22×Q8D21212yes—
438C22×Q8D21212yes—
439C22×Q8C22×D5312yes—
440C22×D4—531no—
441C22×D4—1061no—
442C23×C4—21no—
443C23×C4—1061no—
444C23×C4C22×D5311yescharacteristic
445#137—1068no—
446#137—1068no—
447#137—1068no—
448#137—1068no—
449C2×Q16—1064no—
450C2×Q16—1064no—
451C2×Q16—1064no—
452C2×SD16—1064no—
453C2×SD16—1064no—
454C2×SD16—1064no—
455C2×M16—21no—
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—532no—
464C2×M16—532no—
465C2×M16—532no—
466C2×M16—532no—
467C2×M16—1061no—
468C2×M16—1061no—
469C2×M16—1061no—
470C2×M16—1061no—
471C2×M16—1061no—
472C2×M16—1061no—
473C2×M16—1061no—
474C2×M16—1061no—
475C2×M16C22⋊D5312yes—
476C2×M16C22⋊D5312yes—
477C2×M16C22×D5312yes—
478C2×M16C22×D5312yes—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—1061no—
482C22×C8—1061no—
483#117—532no—
484#117—1061no—
485#117—1061no—
486#117—1061no—
487C2×C4⋊C4—1061no—
488C2×C22⋊C4—1061no—
489C2×C42—1061no—
490#108—1068no—
491#104—1068no—
492#103—1068no—
493#101—28no—
494#101—1064no—
495#100—1064no—
496C24—1061no—
497C24#1171994511yescharacteristic
498#41—1062no—
499#41—1062no—
500#41—1062no—
501#41—1062no—
502#41—1062no—
503#41—1062no—
504#41—1062no—
505#41—1062no—
506#41—2121no—
507#41—2121no—
508#41—2121no—
509#41—2121no—
510#41—2121no—
511#41—2121no—
512#41—2121no—
513#41—2121no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—22no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—22no—
523C2×Q8—22no—
524C2×Q8—22no—
525C2×Q8—22no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—22no—
529C2×Q8—41no—
530C2×Q8—41no—
531C2×Q8—41no—
532C2×Q8—41no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×Q8—41no—
536C2×Q8—41no—
537C2×Q8—41no—
538C2×Q8—41no—
539C2×Q8—41no—
540C2×Q8—41no—
541C2×Q8—532no—
542C2×Q8—1061no—
543C2×Q8—1061no—
544C2×Q8—1061no—
545C2×Q8—1061no—
546C2×Q8—1061no—
547C2×Q8C2×D21214yes—
548C2×D4—532no—
549C2×D4—1062no—
550C2×D4—1062no—
551C2×D4—1061no—
552C2×D4—1061no—
553C2×D4—1061no—
554C2×D4—1061no—
555C2×D4—1061no—
556C2×D4—2121no—
557C2×D4—2121no—
558C2×D4—2121no—
559C2×D4—2121no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—41no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—1061no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—2121no—
571C22×C4—2121no—
572C22×C4—2121no—
573C22×C4—2121no—
574C22×C4—2121no—
575C22×C4C2×D21211yescharacteristic
576C22×C4C2×D21211yescharacteristic
577C22×C4#1171994511yescharacteristic
578C22×C4D4×D5311yescharacteristic
579C22×C4D4×D5311yescharacteristic
580C22×C4D4×D5311yescharacteristic
581C22×C4D4×D5311yescharacteristic
582C22×C4#1171994711yescharacteristic
583C22×C4#1171994711yescharacteristic
584C22×C4#1171994711yescharacteristic
585C22×C4#1171994711yescharacteristic
586C22×C4C2×C22⋊D5311yescharacteristic
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C23×D5311yescharacteristic
589Q16—10616no—
590SD16—10616no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—22no—
595M16—22no—
596M16—41no—
597M16—41no—
598M16—534no—
599M16—1062no—
600M16—1062no—
601M16—1062no—
602M16—1062no—
603M16—1062no—
604M16—2121no—
605M16—2121no—
606M16C2×C22⋊D5314yes—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—41no—
612C2×C8—41no—
613C2×C8—1062no—
614C2×C8—1062no—
615C2×C8—1062no—
616C2×C8—1062no—
617C2×C8—2121no—
618C2×C8—2121no—
619C4⋊C4—1062no—
620C4⋊C4—2121no—
621C22⋊C4—1062no—
622C22⋊C4—2121no—
623C42—1062no—
624C42—2121no—
625C23—42no—
626C23—1062no—
627C23—4242no—
628C23—2121no—
629C23—2121no—
630C23#1313319111yescharacteristic
631C23#1313319111yescharacteristic
632C23#1313319911yescharacteristic
633C23#1313319911yescharacteristic
634C23#1313320311yescharacteristic
635C23#1313320311yescharacteristic
636C23C2×#1171994511yescharacteristic
637Q8—24no—
638Q8—24no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—1062no—
646Q8—1062no—
647Q8—2121no—
648Q8—2121no—
649D4—1062no—
650D4—1062no—
651D4—2122no—
652D4—2122no—
653D4—2122no—
654D4—2122no—
655D4—2121no—
656D4—2121no—
657C2×C4—24no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—1062no—
665C2×C4—4242no—
666C2×C4—2122no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2122no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4#1313318711yescharacteristic
674C2×C4#1313318711yescharacteristic
675C2×C4#1313318711yescharacteristic
676C2×C4#1313318711yescharacteristic
677C2×C4#1313318811yescharacteristic
678C2×C4#1313318811yescharacteristic
679C2×C4#1313318811yescharacteristic
680C2×C4#1313318811yescharacteristic
681C2×C4#1313318911yescharacteristic
682C2×C4#1313318911yescharacteristic
683C2×C4#1313318911yescharacteristic
684C2×C4#1313318911yescharacteristic
685C2×C4#1313319111yescharacteristic
686C2×C4#1313319111yescharacteristic
687C2×C4#1313319911yescharacteristic
688C2×C4#1313319911yescharacteristic
689C2×C4#1313320111yescharacteristic
690C2×C4#1313320111yescharacteristic
691C2×C4#1313320111yescharacteristic
692C2×C4#1313320111yescharacteristic
693C2×C4#1313320311yescharacteristic
694C2×C4#1313320311yescharacteristic
695C2×C4C2×D4×D5311yescharacteristic
696C2×C4C2×D4×D5311yescharacteristic
697C2×C4C22×C22⋊D5311yescharacteristic
698C2×C4C22×D21211yescharacteristic
699C2×C4C2×#1171994711yescharacteristic
700C2×C4C2×#1171994711yescharacteristic
701C8—24no—
702C8—42no—
703C8—1064no—
704C8—2122no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—4242no—
713C22—4242no—
714C22—4242no—
715C22—2122no—
716C22#1681053911yescharacteristic
717C22#1681053911yescharacteristic
718C22#1681053911yescharacteristic
719C22#1681053911yescharacteristic
720C22C2×#1313319111yescharacteristic
721C22C2×#1313319911yescharacteristic
722C22C2×#1313320311yescharacteristic
723C4—44no—
724C4—4242no—
725C4—2122no—
726C4#1681053911yescharacteristic
727C4#1681053911yescharacteristic
728C4#1681053911yescharacteristic
729C4#1681053911yescharacteristic
730C4C2×#1313318711yescharacteristic
731C4C2×#1313318811yescharacteristic
732C4C2×#1313318911yescharacteristic
733C4C2×#1313320111yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2—21no—
739C2—21no—
740C2—4242no—
741C2#2027599412yesdirect product factor
742C2C2×#1681053911yescharacteristic
subgroupG/H
centerC22#16810539
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingC22×#101×C53C2
socleC22×C53#394
prime radicalC22×#11719945C22
hypercenterC22×#101D53
hypocenterC53C2×#2049
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#101

Complements

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

NH ≅ G/Ntype
2. C2×#16810672C2semidirect
4. C2×#16810632C2semidirect
6. #20275994C2direct (N × H)
7. C2×#16810394C2semidirect
8. C22×#101×C53C2semidirect
22. #16810672C22semidirect
28. #16810632C22semidirect
34. #16810394C22semidirect
40. C2×#101×C53C22semidirect
368. C22×#101D53semidirect
377. C2×C53#2049semidirect
409. C2×#101C2×D53semidirect
412. C53C2×#2049semidirect
741. C2#20275994direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332482
C2×#168106722
C2×#168106392
C2×#168106322
C2×#168106052
#202759942
C2×#168103942
C22×#101×C532
C2×#204953