Finite Group Databasebeta

← C2×#20287544 #28263859

Subgroups — C2×#20287544 #28263859

Order 13568.

1886 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
1C2×#16811346C211yesmaximal, characteristic, complemented
2C2×#16811333C211yesmaximal, characteristic, complemented
3#20287544C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810983C211yesmaximal, characteristic, complemented
6C2×#16810978C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810909C211yesmaximal, characteristic, complemented
9C2×#16810924C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic
11C2×#16810839C211yesmaximal, characteristic
12C2×#16810829C211yesmaximal, characteristic, complemented
13C2×#16810736C211yesmaximal, characteristic
14C2×#16810725C211yesmaximal, characteristic, complemented
15C2×C4×#11719913C211yesmaximal, characteristic, complemented
16C2×C53×#446C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18C22×#11719913C2211yescharacteristic
19C22×D424C2211yescharacteristic
20#16811346—24no—
21#16811346C2218yescomplemented
22#16811333—24no—
23#16811333C2218yescomplemented
24C2×#13133217C2211yescharacteristic
25C2×#13133217C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133212—21no—
28C2×#13133209C2211yescharacteristic
29C2×#13133209C2211yescharacteristic
30C2×#13133205C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133195—21no—
34C2×#13133193—21no—
35C2×#13133193—21no—
36C2×C4×Dic106C2211yescharacteristic
37C2×C4×Dic106C2211yescharacteristic
38C2×C4×D212C2211yescharacteristic
39C2×C4×D212C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×C4×D212C2211yescharacteristic
42C2×#13133175—21no—
43C2×C4⋊C4×D53—21no—
44#16810992C2218yescomplemented
45#16810983C2218yescomplemented
46#16810978C2218yescomplemented
47#16810931C2218yescomplemented
48#16810924C2218yescomplemented
49#16810909C2218yescomplemented
50#16810839C2218yes—
51#16810839C2218yes—
52#16810829C2218yescomplemented
53#16810736C2218yes—
54#16810725C2218yescomplemented
55C4×#11719913C2218yescomplemented
56C2×#13133151C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C2×C4×Q8×C53C2211yescharacteristic
70C53×#446C2218yescomplemented
71C2×C4⋊C8×C53C2211yescharacteristic
72C2×C4⋊C8×C53C2211yescharacteristic
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×#97×C53C2211yescharacteristic
75C2×#97×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C22×C4×D53—21no—
86C2×#11719913—24no—
87C2×#11719913—24no—
88C2×#11719913C2314yes—
89C2×#11719913C2314yes—
90C2×D424—24no—
91C2×D424C2314yes—
92#13133217—22no—
93#13133217—22no—
94#13133217C2314yes—
95#13133217C2314yes—
96#13133212—28no—
97#13133212—28no—
98#13133209—22no—
99#13133209—22no—
100#13133209C2314yes—
101#13133209C2314yes—
102#13133205—22no—
103#13133205—22no—
104#13133205C2314yes—
105#13133205C2314yes—
106#13133195—28no—
107#13133195—28no—
108#13133193—28no—
109#13133193—28no—
110C4×Dic106—22no—
111C4×Dic106—22no—
112C4×Dic106C2314yes—
113C4×Dic106C2314yes—
114C4×D212—22no—
115C4×D212—22no—
116C4×D212—22no—
117C4×D212—22no—
118C4×D212C2314yes—
119C4×D212C2314yes—
120C4×D212C2314yes—
121C4×D212C2314yes—
122#13133175—28no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2311yescharacteristic
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C4⋊C4×D53—28no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53—21no—
147#13133151C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133142C2314yes—
151#13133142C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133139C2314yes—
159#13133139C2314yes—
160C22×Q8×C53D411yescharacteristic
161C22×C8×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165C4×Q8×C53D414yes—
166C4×Q8×C53C2314yes—
167C2×C4⋊C4×C53D411yescharacteristic
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C42×C53C2311yescharacteristic
171C2×C42×C53C2311yescharacteristic
172C2×C42×C53C2311yescharacteristic
173C4⋊C8×C53C2314yes—
174C4⋊C8×C53C2314yes—
175C4⋊C8×C53C2314yes—
176#97×C53C2314yes—
177#97×C53C2314yes—
178C4×C8×C53C2314yes—
179C23×D53—21no—
180C23×D53—21no—
181C2×Q8×C53—42no—
182C2×Q8×C53C2×D414yes—
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2411yescharacteristic
190C22×Dic53—21no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C2×D212—21no—
197C2×D212—22no—
198C2×D212—22no—
199C2×D212—22no—
200C2×D212—21no—
201C2×D212#4114yes—
202C2×D212C2412yes—
203C2×D212C2412yes—
204C2×C4×D53—24no—
205C2×C4×D53—24no—
206C2×C4×D53—24no—
207C2×C4×D53—24no—
208C2×C4×D53—44no—
209C2×C4×D53—44no—
210C2×C4×D53—82no—
211C2×C4×D53—82no—
212C2×Dic106—22no—
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—22no—
216C2×Dic106—21no—
217C2×Dic106—21no—
218C2×Dic106—24no—
219C2×Dic106—82no—
220C2×Dic106C2412yes—
221C2×Dic106C2412yes—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C4⋊C4×C53C2×D414yes—
231C4⋊C4×C53C2×D414yes—
232C4⋊C4×C53C2×D414yes—
233C42×C53C2×D412yes—
234C42×C53C2×D412yes—
235C42×C53C2×D412yes—
236C42×C53C2412yes—
237C42×C53C2412yes—
238C42×C53C2412yes—
239#11719921—24no—
240#11719921—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244#11719921—24no—
245#11719921—24no—
246#11719921—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53—21no—
253C4⋊Dic53—21no—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264C4×Dic53—24no—
265C4×Dic53—24no—
266D424—28no—
267#11719913—28no—
268#11719913—28no—
269C23×C53C22×D411yescharacteristic
270C22×D53—24no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—42no—
274C22×D53—42no—
275C22×D53—42no—
276C22×D53—42no—
277C22×D53—42no—
278Q8×C53—44no—
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×C53C22×D412yes—
286C2×C4×C53C22×D412yes—
287C2×C4×C53C22×D412yes—
288C2×C4×C53C22×D412yes—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D411yescharacteristic
292C2×C4×C53C2×#4112yes—
293C2×C4×C532−1+412yes—
294C2×C4×C53C2511yescharacteristic
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53—42no—
307D212—24no—
308D212—22no—
309D212—22no—
310D212—22no—
311D212—42no—
312D212C2×#4114yes—
313C4×D53—48no—
314C4×D53—48no—
315C4×D53—84no—
316C4×D53—84no—
317Dic106—22no—
318Dic106—22no—
319Dic106—22no—
320Dic106—22no—
321Dic106—42no—
322Dic106—42no—
323Dic106—84no—
324C8×C53—22no—
325C8×C53—22no—
326C8×C53—22no—
327C8×C53—22no—
328C2×#3376—531nomaximal, Sylow
329C22×C53#54812yes—
330C22×C53#57512yes—
331C22×C53#57712yes—
332C22×C53C23×D411yescharacteristic
333C2×D53—24no—
334C2×D53—48no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—42no—
339C2×D53—42no—
340C2×D53—84no—
341C4×C53—22no—
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53#54812yes—
348C4×C53C22×#4111yescharacteristic
349C4×C53C2×2−1+411yescharacteristic
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#556—531no—
357C2×#554—531no—
358#3376—5316no—
359C2×#491—531no—
360C2×#489—531no—
361C2×#488—531no—
362C2×#479—531no—
363C2×#475—531no—
364C2×#478—531no—
365C2×#463—531no—
366C2×#463—531no—
367C2×#461—531no—
368C2×#446D5311yescharacteristic, complemented
369C2×#442—531no—
370C2×#440—531no—
371C2×C4×SD16—531no—
372C2×C53#337614yescomplemented
373C2×C53C2×#54811yescharacteristic
374C2×C53C2×#57511yescharacteristic
375C2×C53C2×#57711yescharacteristic
376D53—44no—
377D53—82no—
378C22×SD16—531no—
379C22×SD16—531no—
380C22×D8—531no—
381#556—538no—
382#556—1064no—
383#554—538no—
384#554—1064no—
385C2×C4⋊Q8—531no—
386C2×C4⋊Q8—531no—
387C2×#126—1061no—
388C2×#126—1061no—
389C2×#125—531no—
390C2×#125—531no—
391C2×#124—531no—
392C2×#124—531no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×C22⋊Q8—1061no—
396C2×C22⋊Q8—1061no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8C2×D5311yescharacteristic
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×C4×D4—531no—
403C2×C4×D4—531no—
404C2×#117—1061no—
405C22×C4⋊C4—1061no—
406#491—538no—
407#489—538no—
408#488—538no—
409#479—538no—
410#478—538no—
411#475—538no—
412#463—538no—
413#463—538no—
414#461—538no—
415#446C2×D5318yescomplemented
416#442—538no—
417#440—538no—
418C4×SD16—538no—
419C2×#107—531no—
420C2×#106—531no—
421C2×#106—531no—
422C2×C4⋊C8C2×D5311yescharacteristic
423C2×C4⋊C8C2×D5311yescharacteristic
424C2×C4⋊C8C2×D5311yescharacteristic
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103—531no—
430C2×#103—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×#97C2×D5311yescharacteristic
436C2×#97C2×D5311yescharacteristic
437C2×C4×C8C2×D5311yescharacteristic
438C53C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—531no—
440C22×Q8—531no—
441C22×Q8—1061no—
442C22×Q8D21211yescharacteristic
443C22×D4—531no—
444C22×D4—531no—
445C23×C4—1061no—
446C23×C4—1061no—
447C23×C4—1061no—
448C23×C4—1061no—
449C2×SD16—534no—
450C2×SD16—534no—
451C2×SD16—1064no—
452C2×SD16—1064no—
453C2×D8—534no—
454C2×D8—1064no—
455C22×C8C22×D5311yescharacteristic
456C22×C8C22×D5311yescharacteristic
457C22×C8C22×D5311yescharacteristic
458C22×C8C22×D5311yescharacteristic
459C4⋊Q8—534no—
460C4⋊Q8—534no—
461C4⋊Q8—1062no—
462C4⋊Q8—1062no—
463#126—1068no—
464#126—1068no—
465#125—534no—
466#125—534no—
467#125—1062no—
468#125—1062no—
469#124—534no—
470#124—534no—
471#124—1062no—
472#124—1062no—
473C22⋊Q8—1068no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C22⋊Q8—1068no—
477C4×Q8—534no—
478C4×Q8—534no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8D21214yes—
482C4×Q8C22×D5314yes—
483C4×D4—534no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491#117—1068no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1068no—
506C2×C4⋊C4D21211yescharacteristic
507C2×C4⋊C4D21211yescharacteristic
508C2×C4⋊C4D21211yescharacteristic
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42C22×D5311yescharacteristic
520C2×C42C22×D5311yescharacteristic
521C2×C42C22×D5311yescharacteristic
522#107—534no—
523#106—534no—
524#106—534no—
525C4⋊C8C22×D5314yes—
526C4⋊C8C22×D5314yes—
527C4⋊C8C22×D5314yes—
528#103—534no—
529#103—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#102—534no—
535#102—534no—
536#102—534no—
537#102—534no—
538#97C22×D5314yes—
539#97C22×D5314yes—
540C4×C8C22×D5314yes—
541C24—1061no—
542C24—1061no—
543C2×Q8—42no—
544C2×Q8—532no—
545C2×Q8—532no—
546C2×Q8—1064no—
547C2×Q8—1061no—
548C2×Q8—1061no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8—4242no—
554C2×Q8C2×D21214yes—
555C2×D4—534no—
556C2×D4—532no—
557C2×D4—532no—
558C2×D4—1061no—
559C2×D4—1061no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C22×C4—1061no—
564C22×C4—1061no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1064no—
570C22×C4—1064no—
571C22×C4—1064no—
572C22×C4—1064no—
573C22×C4—4242no—
574C22×C4—4242no—
575C22×C4—2124no—
576C22×C4—2124no—
577C22×C4C2×D21211yescharacteristic
578C22×C4C2×D21211yescharacteristic
579C22×C4C2×D21211yescharacteristic
580C22×C4C2×D21211yescharacteristic
581C22×C4C2×D21211yescharacteristic
582C22×C4C2×D21211yescharacteristic
583C22×C4C23×D5311yescharacteristic
584SD16—1068no—
585SD16—1068no—
586D8—1068no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8C23×D5312yes—
592C2×C8C23×D5312yes—
593C2×C8C23×D5312yes—
594C2×C8C23×D5312yes—
595C4⋊C4—532no—
596C4⋊C4—532no—
597C4⋊C4—532no—
598C4⋊C4—532no—
599C4⋊C4—1061no—
600C4⋊C4—1061no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4C2×D21214yes—
613C4⋊C4C2×D21214yes—
614C4⋊C4C2×D21214yes—
615C22⋊C4—1064no—
616C22⋊C4—1064no—
617C22⋊C4—1064no—
618C22⋊C4—1064no—
619C22⋊C4—1064no—
620C22⋊C4—1064no—
621C22⋊C4—1064no—
622C22⋊C4—1064no—
623C42—1064no—
624C42—1064no—
625C42C2×D21212yes—
626C42C2×D21212yes—
627C42C2×D21212yes—
628C42C23×D5312yes—
629C42C23×D5312yes—
630C42C23×D5312yes—
631C23—1064no—
632C23—1062no—
633C23—1062no—
634C23—2122no—
635C23—2122no—
636C23—2122no—
637C23—2122no—
638C23—2122no—
639C23C22×D21211yescharacteristic
640Q8—44no—
641Q8—1062no—
642Q8—1062no—
643Q8—1062no—
644Q8—1062no—
645Q8—4244no—
646Q8—2122no—
647Q8—2122no—
648D4—534no—
649D4—1064no—
650D4—1062no—
651D4—1062no—
652D4—1062no—
653D4—2122no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—4244no—
667C2×C4—4244no—
668C2×C4—2128no—
669C2×C4—2128no—
670C2×C4—2122no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4C22×D21212yes—
677C2×C4C22×D21212yes—
678C2×C4C22×D21212yes—
679C2×C4C22×D21212yes—
680C2×C4C22×D21212yes—
681C2×C4C22×D21212yes—
682C2×C4C22×D21211yescharacteristic
683C2×C4#41×D5312yes—
684C2×C4#1313326512yes—
685C2×C4C24×D5311yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C22—1064no—
691C22—4244no—
692C22—2122no—
693C22—2122no—
694C22—2122no—
695C22—2128no—
696C22—2122no—
697C22—2122no—
698C22#1681128512yes—
699C22#1681142312yes—
700C22#1681143512yes—
701C22C23×D21211yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4#1681128512yes—
715C4C2×#41×D5311yescharacteristic
716C4C2×#1313326511yescharacteristic
717C2—4242no—
718C2—2124no—
719C2#2028754414yesdirect product factor
720C2C2×#1681128511yescharacteristic
721C2C2×#1681142311yescharacteristic
722C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#446C2
socleC23×C53C22×D4
prime radicalC22×D424C22
hypercenterC2×#446D53
hypocenterC53C2×#3376
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#16811346C2semidirect
2. C2×#16811333C2semidirect
3. #20287544C2direct (N × H)
4. C2×#16810992C2semidirect
5. C2×#16810983C2semidirect
6. C2×#16810978C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810909C2semidirect
9. C2×#16810924C2semidirect
12. C2×#16810829C2semidirect
14. C2×#16810725C2semidirect
15. C2×C4×#11719913C2semidirect
16. C2×C53×#446C2semidirect
21. #16811346C22semidirect
23. #16811333C22semidirect
44. #16810992C22semidirect
45. #16810983C22semidirect
46. #16810978C22semidirect
47. #16810931C22semidirect
48. #16810924C22semidirect
49. #16810909C22semidirect
52. #16810829C22semidirect
54. #16810725C22semidirect
55. C4×#11719913C22semidirect
70. C53×#446C22semidirect
368. C2×#446D53semidirect
372. C2×C53#3376semidirect
415. #446C2×D53semidirect
438. C53C2×#3376semidirect
719. C2#20287544direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113462
C2×#168113332
#202875442
C2×#168109922
C2×#168109832
C2×#168109782
C2×#168109312
C2×#168109092
C2×#168109242
C2×#168108392
C2×#168108292
C2×#168107362
C2×#168107252
C2×C4×#117199132
C2×C53×#4462
C2×#337653