Finite Group Databasebeta

← C2×#20287783 #28265100

Subgroups — C2×#20287783 #28265100

Order 13568.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811358C211yesmaximal, characteristic, complemented
2C2×#16811346C211yesmaximal, characteristic, complemented
3#20287783C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic, complemented
5C2×#16811012C211yesmaximal, characteristic
6C2×#16811007C211yesmaximal, characteristic, complemented
7C2×#16810846C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810824C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810839C211yesmaximal, characteristic, complemented
12C2×#16810829C211yesmaximal, characteristic, complemented
13C2×#16810736C211yesmaximal, characteristic, complemented
14C2×#16810731C211yesmaximal, characteristic, complemented
15C2×C4×#11719913C211yesmaximal, characteristic, complemented
16C2×C53×#446C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719913C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×D424C2211yescharacteristic
25C22×D424C2211yescharacteristic
26#16811358—24no—
27#16811358C2218yescomplemented
28#16811346—24no—
29#16811346C2218yescomplemented
30C2×#13133217C2211yescharacteristic
31C2×#13133214C2211yescharacteristic
32C2×#13133212—21no—
33C2×#13133212—21no—
34C2×#13133206—21no—
35C2×#13133205C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133205C2211yescharacteristic
38C2×#13133205C2211yescharacteristic
39C2×#13133202—21no—
40C2×#13133202—21no—
41C2×#13133193—21no—
42C2×C4×Dic106C2211yescharacteristic
43C2×C4×Dic106C2211yescharacteristic
44C2×C4×Dic106C2211yescharacteristic
45C2×C4×D212C2211yescharacteristic
46C2×C4×D212C2211yescharacteristic
47C2×C4×D212C2211yescharacteristic
48C2×#13133179—21no—
49C2×#13133175—21no—
50#16811017C2218yescomplemented
51#16811012C2218yes—
52#16811007C2218yescomplemented
53#16810846C2218yescomplemented
54#16810846C2218yescomplemented
55#16810839C2218yescomplemented
56#16810839C2218yescomplemented
57#16810829C2218yescomplemented
58#16810824C2218yescomplemented
59#16810736C2218yescomplemented
60#16810731C2218yescomplemented
61C4×#11719913C2218yescomplemented
62C2×#13133149C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
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×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×D212—21no—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×D212C2311yescharacteristic
85C22×C4×D53—21no—
86C22×C4×D53—21no—
87C22×C4×D53—21no—
88C2×Dic212—24no—
89C2×Dic212—42no—
90C2×Dic212C2314yes—
91C2×Dic212C2314yes—
92C2×#11719913—24no—
93C2×#11719913—42no—
94C2×#11719913—42no—
95C2×#11719913—42no—
96C2×#11719913—42no—
97C2×#11719913C2314yes—
98C2×#11719913C2314yes—
99C2×#11719913C2314yes—
100C2×#11719913C2314yes—
101C2×#11719913C2314yes—
102C2×D424—24no—
103C2×D424—42no—
104C2×D424C2314yes—
105C2×D424C2314yes—
106#13133217—22no—
107#13133217C2314yes—
108#13133214—22no—
109#13133214C2314yes—
110#13133212—28no—
111#13133212—28no—
112#13133206—28no—
113#13133205—22no—
114#13133205—22no—
115#13133205—22no—
116#13133205—22no—
117#13133205C2314yes—
118#13133205C2314yes—
119#13133205C2314yes—
120#13133205C2314yes—
121#13133202—28no—
122#13133202—28no—
123#13133193—28no—
124C4×Dic106—22no—
125C4×Dic106—22no—
126C4×Dic106—22no—
127C4×Dic106C2314yes—
128C4×Dic106C2314yes—
129C4×Dic106C2314yes—
130C4×D212—22no—
131C4×D212—22no—
132C4×D212—22no—
133C4×D212C2314yes—
134C4×D212C2314yes—
135C4×D212C2314yes—
136#13133179—28no—
137#13133175—28no—
138C2×C4⋊Dic53—21no—
139C2×C4⋊Dic53—21no—
140C2×C4⋊Dic53C2311yescharacteristic
141C2×C4⋊Dic53C2311yescharacteristic
142C2×#11719919—21no—
143C2×#11719919—21no—
144C2×#11719919—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921—21no—
151C2×#11719921—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×C4×Dic53—21no—
157C2×C4×Dic53—21no—
158C2×C4×Dic53—21no—
159#13133149C2314yes—
160#13133142C2314yes—
161#13133142C2314yes—
162#13133142C2314yes—
163#13133139C2314yes—
164#13133139C2314yes—
165#13133139C2314yes—
166C22×Q8×C53D411yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C4×Q8×C53D414yes—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53D411yescharacteristic
176C2×C42×C53C2311yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180C4⋊C8×C53C2314yes—
181C4⋊C8×C53C2314yes—
182#97×C53C2314yes—
183#97×C53C2314yes—
184C4×C8×C53C2314yes—
185C23×D53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C2×Q8×C53—42no—
189C2×Q8×C53C2×D414yes—
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C2×D212—22no—
203C2×D212—22no—
204C2×D212—22no—
205C2×D212—22no—
206C2×D212—22no—
207C2×D212—22no—
208C2×D212—24no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—24no—
213C2×D212—44no—
214C2×D212—82no—
215C2×D212C2412yes—
216C2×D212C2412yes—
217C2×D212C2412yes—
218C2×C4×D53—24no—
219C2×C4×D53—24no—
220C2×C4×D53—24no—
221C2×C4×D53—44no—
222C2×C4×D53—82no—
223C2×C4×D53—82no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—21no—
231C2×Dic106—21no—
232C2×Dic106—21no—
233C2×Dic106C2412yes—
234C2×Dic106C2412yes—
235C2×Dic106C2412yes—
236C2×C8×C53—22no—
237C2×C8×C53—22no—
238C2×C8×C53—22no—
239C2×C8×C53#4114yes—
240C2×C8×C53C2412yes—
241C2×C8×C53C2412yes—
242C2×C8×C53C2412yes—
243C2×C8×C53C2412yes—
244C4⋊C4×C53C2×D414yes—
245C4⋊C4×C53C2×D414yes—
246C4⋊C4×C53C2×D414yes—
247C42×C53C2×D412yes—
248C42×C53C2×D412yes—
249C42×C53C2×D412yes—
250C42×C53C2412yes—
251C42×C53C2412yes—
252C42×C53C2412yes—
253#11719921—24no—
254#11719921—24no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264C4⋊Dic53—24no—
265C4⋊Dic53—24no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273C4×Dic53—24no—
274C4×Dic53—24no—
275C4×Dic53—24no—
276Dic212—28no—
277Dic212—44no—
278D424—28no—
279D424—44no—
280#11719913—28no—
281#11719913—44no—
282#11719913—44no—
283#11719913—44no—
284#11719913—44no—
285C23×C53C22×D411yescharacteristic
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—42no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298Q8×C53—44no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D412yes—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53C2×#4112yes—
313C2×C4×C53H(5,𝔽2)12yes—
314C2×C4×C53C2511yescharacteristic
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325D212—22no—
326D212—22no—
327D212—22no—
328D212—22no—
329D212—22no—
330D212—22no—
331D212—48no—
332D212—42no—
333D212—42no—
334D212—42no—
335D212—84no—
336C4×D53—48no—
337C4×D53—84no—
338C4×D53—84no—
339Dic106—22no—
340Dic106—22no—
341Dic106—22no—
342Dic106—22no—
343Dic106—22no—
344Dic106—22no—
345Dic106—42no—
346Dic106—42no—
347Dic106—42no—
348C8×C53—22no—
349C8×C53—22no—
350C8×C53—22no—
351C8×C53C2×#4114yes—
352C2×#3401—531nomaximal, Sylow
353C22×C53#55012yes—
354C22×C53#57512yes—
355C22×C53#57712yes—
356C22×C53C23×D411yescharacteristic
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—84no—
367C2×D53—84no—
368C2×D53—84no—
369C4×C53—22no—
370C4×C53—22no—
371C4×C53—22no—
372C4×C53—22no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53#55012yes—
376C4×C53C22×#4111yescharacteristic
377C4×C53C2×H(5,𝔽2)11yescharacteristic
378Dic53—42no—
379Dic53—42no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383C2×#559—531no—
384C2×#556—531no—
385#3401—5316no—
386C2×#497—531no—
387C2×#496—531no—
388C2×#495—531no—
389C2×#464—531no—
390C2×#464—531no—
391C2×#460—531no—
392C2×#463—531no—
393C2×#463—531no—
394C2×#461—531no—
395C2×#446D5311yescharacteristic, complemented
396C2×#442—531no—
397C2×#441—531no—
398C2×C4×SD16—531no—
399C2×C53#340114yescomplemented
400C2×C53C2×#55011yescharacteristic
401C2×C53C2×#57511yescharacteristic
402C2×C53C2×#57711yescharacteristic
403D53—82no—
404D53—82no—
405D53—82no—
406C22×Q16—531no—
407C22×Q16—531no—
408C22×SD16—531no—
409C22×SD16—531no—
410C22×SD16—531no—
411C22×SD16—531no—
412C22×SD16—531no—
413C22×D8—531no—
414C22×D8—531no—
415#559—538no—
416#559—1064no—
417#556—538no—
418#556—1064no—
419C2×C4⋊Q8—531no—
420C2×#127—531no—
421C2×#126—1061no—
422C2×#126—1061no—
423C2×#124—531no—
424C2×#124—531no—
425C2×#124—531no—
426C2×#124—531no—
427C2×#124—1061no—
428C2×#123—1061no—
429C2×#123—1061no—
430C2×C22⋊Q8—1061no—
431C2×C4×Q8—531no—
432C2×C4×Q8—531no—
433C2×C4×Q8—531no—
434C2×C4×Q8C2×D5311yescharacteristic
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×C4×D4—531no—
438C2×C4×D4—1061no—
439C2×#117—1061no—
440#497—538no—
441#496—538no—
442#495—538no—
443#464—538no—
444#464—538no—
445#463—538no—
446#463—538no—
447#461—538no—
448#460—538no—
449#446C2×D5318yescomplemented
450#442—538no—
451#441—538no—
452C4×SD16—538no—
453C2×#106—531no—
454C2×C4⋊C8C2×D5311yescharacteristic
455C2×C4⋊C8C2×D5311yescharacteristic
456C2×C4⋊C8C2×D5311yescharacteristic
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#102—531no—
461C2×#102—531no—
462C2×#102—531no—
463C2×#97C2×D5311yescharacteristic
464C2×#97C2×D5311yescharacteristic
465C2×C4×C8C2×D5311yescharacteristic
466C53C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—531no—
468C22×Q8—531no—
469C22×Q8—531no—
470C22×Q8D21211yescharacteristic
471C22×D4—531no—
472C22×D4—531no—
473C22×D4—531no—
474C22×D4—1061no—
475C22×D4—1061no—
476C23×C4—1061no—
477C23×C4—1061no—
478C23×C4—1061no—
479C2×Q16—534no—
480C2×Q16—534no—
481C2×Q16—1064no—
482C2×Q16—2122no—
483C2×SD16—534no—
484C2×SD16—534no—
485C2×SD16—534no—
486C2×SD16—534no—
487C2×SD16—534no—
488C2×SD16—1064no—
489C2×SD16—2122no—
490C2×SD16—2122no—
491C2×SD16—2122no—
492C2×SD16—2122no—
493C2×D8—534no—
494C2×D8—534no—
495C2×D8—1064no—
496C2×D8—2122no—
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499C22×C8C22×D5311yescharacteristic
500C22×C8C22×D5311yescharacteristic
501C4⋊Q8—534no—
502C4⋊Q8—1062no—
503#127—534no—
504#127—1062no—
505#126—1068no—
506#126—1068no—
507#124—534no—
508#124—534no—
509#124—534no—
510#124—534no—
511#124—1068no—
512#124—1062no—
513#124—1062no—
514#124—1062no—
515#124—1062no—
516#123—1068no—
517#123—1068no—
518C22⋊Q8—1068no—
519C4×Q8—534no—
520C4×Q8—534no—
521C4×Q8—534no—
522C4×Q8—1062no—
523C4×Q8—1062no—
524C4×Q8—1062no—
525C4×Q8D21214yes—
526C4×Q8C22×D5314yes—
527C4×D4—534no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—1068no—
531C4×D4—1062no—
532C4×D4—1062no—
533C4×D4—1062no—
534#117—1068no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4D21211yescharacteristic
543C2×C4⋊C4D21211yescharacteristic
544C2×C4⋊C4D21211yescharacteristic
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C42—1061no—
557C2×C42—1061no—
558C2×C42—1061no—
559C2×C42C22×D5311yescharacteristic
560C2×C42C22×D5311yescharacteristic
561C2×C42C22×D5311yescharacteristic
562#106—534no—
563C4⋊C8C22×D5314yes—
564C4⋊C8C22×D5314yes—
565C4⋊C8C22×D5314yes—
566#103—534no—
567#103—534no—
568#103—534no—
569#102—534no—
570#102—534no—
571#102—534no—
572#97C22×D5314yes—
573#97C22×D5314yes—
574C4×C8C22×D5314yes—
575C24—1061no—
576C24—1061no—
577C24—1061no—
578C2×Q8—42no—
579C2×Q8—532no—
580C2×Q8—532no—
581C2×Q8—532no—
582C2×Q8—1061no—
583C2×Q8—1061no—
584C2×Q8—1061no—
585C2×Q8—1062no—
586C2×Q8—1062no—
587C2×Q8—1062no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8C2×D21214yes—
592C2×D4—532no—
593C2×D4—532no—
594C2×D4—532no—
595C2×D4—1064no—
596C2×D4—1061no—
597C2×D4—1064no—
598C2×D4—1061no—
599C2×D4—1061no—
600C2×D4—1062no—
601C2×D4—1062no—
602C2×D4—1062no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—4242no—
607C2×D4—2124no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1064no—
614C22×C4—1064no—
615C22×C4—1064no—
616C22×C4—4242no—
617C22×C4—4242no—
618C22×C4—2124no—
619C22×C4C2×D21211yescharacteristic
620C22×C4C2×D21211yescharacteristic
621C22×C4C2×D21211yescharacteristic
622C22×C4C2×D21211yescharacteristic
623C22×C4C2×D21211yescharacteristic
624C22×C4C2×D21211yescharacteristic
625C22×C4C23×D5311yescharacteristic
626Q16—1068no—
627Q16—2124no—
628SD16—1068no—
629SD16—2124no—
630SD16—2124no—
631SD16—2124no—
632SD16—2124no—
633D8—1068no—
634D8—2124no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8#1171994914yes—
639C2×C8C23×D5312yes—
640C2×C8C23×D5312yes—
641C2×C8C23×D5312yes—
642C2×C8C23×D5312yes—
643C4⋊C4—532no—
644C4⋊C4—532no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4C2×D21214yes—
653C4⋊C4C2×D21214yes—
654C4⋊C4C2×D21214yes—
655C22⋊C4—1064no—
656C22⋊C4—1064no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C42—1064no—
667C42—1064no—
668C42—1064no—
669C42C2×D21212yes—
670C42C2×D21212yes—
671C42C2×D21212yes—
672C42C23×D5312yes—
673C42C23×D5312yes—
674C42C23×D5312yes—
675C23—1062no—
676C23—1062no—
677C23—1062no—
678C23—2122no—
679C23—2122no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23C22×D21211yescharacteristic
688Q8—44no—
689Q8—1062no—
690Q8—1062no—
691Q8—1062no—
692Q8—1062no—
693Q8—1062no—
694Q8—1062no—
695Q8—2122no—
696Q8—2122no—
697Q8—2122no—
698D4—1062no—
699D4—1062no—
700D4—1062no—
701D4—1062no—
702D4—1062no—
703D4—1062no—
704D4—4244no—
705D4—2128no—
706D4—2122no—
707D4—2122no—
708D4—2122no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—4244no—
721C2×C4—4244no—
722C2×C4—2128no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4C22×D21212yes—
729C2×C4C22×D21212yes—
730C2×C4C22×D21212yes—
731C2×C4C22×D21212yes—
732C2×C4C22×D21212yes—
733C2×C4C22×D21212yes—
734C2×C4C22×D21211yescharacteristic
735C2×C4C2×#1171994912yes—
736C2×C4#1313326312yes—
737C2×C4C24×D5311yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8C2×#1171994914yes—
742C22—4244no—
743C22—4244no—
744C22—4244no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22#1681129512yes—
755C22#1681142312yes—
756C22#1681143512yes—
757C22C23×D21211yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—2122no—
765C4—2122no—
766C4—2122no—
767C4—2122no—
768C4—2122no—
769C4#1681129512yes—
770C4C22×#1171994911yescharacteristic
771C4C2×#1313326311yescharacteristic
772C2—4242no—
773C2—4242no—
774C2—4242no—
775C2#2028778314yesdirect product factor
776C2C2×#1681129511yescharacteristic
777C2C2×#1681142311yescharacteristic
778C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#446C2
socleC23×C53C22×D4
prime radicalC2×#16811012C2
hypercenterC2×#446D53
hypocenterC53C2×#3401
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×#16811358C2semidirect
2. C2×#16811346C2semidirect
3. #20287783C2direct (N × H)
4. C2×#16811017C2semidirect
6. C2×#16811007C2semidirect
7. C2×#16810846C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810824C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810839C2semidirect
12. C2×#16810829C2semidirect
13. C2×#16810736C2semidirect
14. C2×#16810731C2semidirect
15. C2×C4×#11719913C2semidirect
16. C2×C53×#446C2semidirect
27. #16811358C22semidirect
29. #16811346C22semidirect
50. #16811017C22semidirect
52. #16811007C22semidirect
53. #16810846C22semidirect
54. #16810846C22semidirect
55. #16810839C22semidirect
56. #16810839C22semidirect
57. #16810829C22semidirect
58. #16810824C22semidirect
59. #16810736C22semidirect
60. #16810731C22semidirect
61. C4×#11719913C22semidirect
70. C53×#446C22semidirect
395. C2×#446D53semidirect
399. C2×C53#3401semidirect
449. #446C2×D53semidirect
466. C53C2×#3401semidirect
775. C2#20287783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113582
C2×#168113462
#202877832
C2×#168110172
C2×#168110122
C2×#168110072
C2×#168108462
C2×#168108242
C2×#168108392
C2×#168108292
C2×#168107362
C2×#168107312
C2×C4×#117199132
C2×C53×#4462
C2×#340153