Finite Group Databasebeta

← C2×#20285826 #28255489

Subgroups — C2×#20285826 #28255489

Order 13568.

2086 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic, complemented
2C2×#16811199C211yesmaximal, characteristic, complemented
3#20285826C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic, complemented
5C2×#16811007C211yesmaximal, characteristic, complemented
6C2×#16810983C211yesmaximal, characteristic, complemented
7C2×#16810974C211yesmaximal, characteristic, complemented
8C2×#16810846C211yesmaximal, characteristic, complemented
9C2×#16810834C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810829C211yesmaximal, characteristic, complemented
12C2×#16810787C211yesmaximal, characteristic, complemented
13C2×#16810770C211yesmaximal, characteristic
14C2×#16810781C211yesmaximal, characteristic, complemented
15C2×#16810764C211yesmaximal, characteristic, complemented
16C2×C53×#433C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×Dic212C2211yescharacteristic
22C22×#11719913C2211yescharacteristic
23C22×#11719913C2211yescharacteristic
24C22×#11719913C2211yescharacteristic
25C22×#11719913C2211yescharacteristic
26C22×D424C2211yescharacteristic
27#16811244—24no—
28#16811244C2218yescomplemented
29#16811199—24no—
30#16811199C2218yescomplemented
31C2×#13133217C2211yescharacteristic
32C2×#13133217C2211yescharacteristic
33C2×#13133217C2211yescharacteristic
34C2×#13133212—21no—
35C2×#13133205C2211yescharacteristic
36C2×#13133205C2211yescharacteristic
37C2×#13133205C2211yescharacteristic
38C2×#13133203—21no—
39C2×#13133201—21no—
40C2×#13133201—21no—
41C2×#13133199—21no—
42C2×#13133197—21no—
43C2×#13133197—21no—
44C2×#13133196C2211yescharacteristic
45C2×#13133195—21no—
46C2×#13133191C2211yescharacteristic
47C2×C4×Dic106C2211yescharacteristic
48C2×C4×D212C2211yescharacteristic
49#16811017C2218yescomplemented
50#16811007C2218yescomplemented
51#16810983C2218yescomplemented
52#16810974C2218yescomplemented
53#16810846C2218yescomplemented
54#16810839C2218yescomplemented
55#16810834C2218yescomplemented
56#16810829C2218yescomplemented
57#16810787C2218yescomplemented
58#16810781C2218yescomplemented
59#16810770C2218yes—
60#16810764C2218yescomplemented
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C2×#117×C53C2211yescharacteristic
70C53×#433C2218yescomplemented
71C2×C4⋊C8×C53C2211yescharacteristic
72C2×C4⋊C8×C53C2211yescharacteristic
73C2×C22⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×#97×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—42no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106—42no—
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2311yescharacteristic
89C22×Dic106C2311yescharacteristic
90C22×Dic106C2314yes—
91C22×D212C2311yescharacteristic
92C22×D212C2311yescharacteristic
93C22×C22⋊D53—21no—
94C22×C22⋊D53—21no—
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C2×Dic212—42no—
99C2×Dic212—42no—
100C2×Dic212—42no—
101C2×Dic212C2314yes—
102C2×Dic212C2314yes—
103C2×Dic212C2314yes—
104C2×#11719913—42no—
105C2×#11719913—42no—
106C2×#11719913—42no—
107C2×#11719913—42no—
108C2×#11719913C2314yes—
109C2×#11719913C2314yes—
110C2×#11719913C2314yes—
111C2×#11719913C2314yes—
112C2×D424—42no—
113C2×D424C2314yes—
114#13133217—22no—
115#13133217—22no—
116#13133217—22no—
117#13133217C2314yes—
118#13133217C2314yes—
119#13133217C2314yes—
120#13133212—28no—
121#13133205—22no—
122#13133205—22no—
123#13133205—22no—
124#13133205C2314yes—
125#13133205C2314yes—
126#13133205C2314yes—
127#13133203—28no—
128#13133201—28no—
129#13133201—28no—
130#13133199—28no—
131#13133197—28no—
132#13133197—28no—
133#13133196—22no—
134#13133196C2314yes—
135#13133195—28no—
136#13133191—22no—
137#13133191C2314yes—
138C4×Dic106—22no—
139C4×Dic106C2314yes—
140C4×D212—22no—
141C4×D212C2314yes—
142C2×C4⋊Dic53—21no—
143C2×C4⋊Dic53—21no—
144C2×C4⋊Dic53—21no—
145C2×C4⋊Dic53—21no—
146C2×C4⋊Dic53—21no—
147C2×C4⋊Dic53C2311yescharacteristic
148C2×C4⋊Dic53C2311yescharacteristic
149C2×#11719919—21no—
150C2×#11719919—21no—
151C2×C22⋊Dic53—21no—
152C2×#11719921—21no—
153C2×#11719921—21no—
154C2×#11719921—21no—
155C2×#11719921—21no—
156C2×#11719921—21no—
157C2×#11719921—21no—
158C2×#11719921—21no—
159C2×#11719921—21no—
160C2×C4×Dic53—21no—
161#13133142C2314yes—
162#13133142C2314yes—
163#13133142C2314yes—
164#13133142C2314yes—
165#13133142C2314yes—
166#13133142C2314yes—
167#13133139C2314yes—
168#13133139C2314yes—
169C23×C4×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174#117×C53D414yes—
175#117×C53C2314yes—
176C2×C4⋊C4×C53D411yescharacteristic
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C4⋊C8×C53C2314yes—
183C4⋊C8×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C22⋊C8×C53C2314yes—
186#97×C53C2314yes—
187C4×C8×C53C2314yes—
188C24×C53C2×D411yescharacteristic
189C23×D53—21no—
190C23×D53—21no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53—24no—
203C2×C22⋊D53—44no—
204C2×C22⋊D53—82no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—24no—
212C22×Dic53—44no—
213#11719945—44no—
214#11719945—44no—
215#11719945—48no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—21no—
221C2×D212—21no—
222C2×D212C2412yes—
223C2×D212C2412yes—
224C2×C4×D53—24no—
225C2×C4×D53—24no—
226C2×C4×D53—44no—
227C2×C4×D53—82no—
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—22no—
235C2×Dic106—22no—
236C2×Dic106—21no—
237C2×Dic106—24no—
238C2×Dic106—21no—
239C2×Dic106—21no—
240C2×Dic106—21no—
241C2×Dic106—24no—
242C2×Dic106—44no—
243C2×Dic106—44no—
244C2×Dic106—44no—
245C2×Dic106—48no—
246C2×Dic106—82no—
247C2×Dic106C2412yes—
248C2×Dic106C2412yes—
249C2×Dic106C2412yes—
250C2×Dic106C2412yes—
251C2×C8×C53—22no—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53—22no—
255C2×C8×C53C2412yes—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C4⋊C4×C53C2×D414yes—
260C4⋊C4×C53C2×D414yes—
261C22⋊C4×C53C2×D414yes—
262C22⋊C4×C53C2×D414yes—
263C42×C53C2×D412yes—
264C42×C53C2×D412yes—
265C42×C53C2412yes—
266C42×C53C2412yes—
267C22⋊Dic53—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276C4⋊Dic53—24no—
277C4⋊Dic53—24no—
278C4⋊Dic53—24no—
279C4⋊Dic53—24no—
280C4⋊Dic53—24no—
281C4⋊Dic53—21no—
282C4⋊Dic53—21no—
283C4⋊Dic53C2412yes—
284C4⋊Dic53C2412yes—
285#11719919—24no—
286#11719919—24no—
287C4×Dic53—24no—
288Dic212—44no—
289Dic212—44no—
290Dic212—44no—
291D424—44no—
292#11719913—44no—
293#11719913—44no—
294#11719913—44no—
295#11719913—44no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53C22×D412yes—
300C23×C53C22×D411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—24no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53H(5,𝔽2)12yes—
324C2×C4×C53H(5,𝔽2)12yes—
325C2×C4×C53C2511yescharacteristic
326C22⋊D53—48no—
327C22⋊D53—84no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—48no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341D212—22no—
342D212—22no—
343D212—22no—
344D212—22no—
345D212—42no—
346D212—42no—
347C4×D53—48no—
348C4×D53—84no—
349Dic106—22no—
350Dic106—22no—
351Dic106—22no—
352Dic106—22no—
353Dic106—22no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—48no—
358Dic106—42no—
359Dic106—42no—
360Dic106—42no—
361Dic106—42no—
362Dic106—84no—
363C8×C53—22no—
364C8×C53—22no—
365C8×C53—22no—
366C8×C53—22no—
367C2×#3225—531nomaximal, Sylow
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53#53512yes—
373C22×C53#57712yes—
374C22×C53#57812yes—
375C22×C53C23×D411yescharacteristic
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—84no—
383C2×D53—84no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53#53512yes—
390C4×C53C2×H(5,𝔽2)11yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—42no—
393Dic53—42no—
394Dic53—42no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#542—531no—
399C2×#536—531no—
400#3225—5316no—
401C2×#497—531no—
402C2×#495—531no—
403C2×#489—531no—
404C2×#487—531no—
405C2×#464—531no—
406C2×#462—531no—
407C2×#463—531no—
408C2×#461—531no—
409C2×#452—531no—
410C2×#449—531no—
411C2×#451—531no—
412C2×#448—531no—
413C2×#433D5311yescharacteristic, complemented
414C2×C53—42no—
415C2×C53#322514yescomplemented
416C2×C53C2×#53511yescharacteristic
417C2×C53C2×#57711yescharacteristic
418C2×C53C2×#57811yescharacteristic
419D53—82no—
420D53—82no—
421C22×#41—531no—
422C23×Q8—531no—
423C22×Q16—531no—
424C22×Q16—531no—
425C22×Q16—531no—
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×SD16—531no—
430C22×D8—531no—
431#542—538no—
432#542—1064no—
433#536—538no—
434#536—1064no—
435C2×C4⋊Q8—531no—
436C2×C4⋊Q8—531no—
437C2×C4⋊Q8—531no—
438C2×#126—1061no—
439C2×#124—531no—
440C2×#124—531no—
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×#123—1061no—
446C2×C22⋊Q8—531no—
447C2×C22⋊Q8—1061no—
448C2×C22⋊Q8—1061no—
449C2×C22⋊Q8—1061no—
450C2×#121—531no—
451C2×C4×Q8—531no—
452C2×C4×D4—531no—
453C2×#117C2×D5311yescharacteristic
454#497—538no—
455#495—538no—
456#489—538no—
457#487—538no—
458#464—538no—
459#463—538no—
460#462—538no—
461#461—538no—
462#452—538no—
463#451—538no—
464#449—538no—
465#448—538no—
466#433C2×D5318yescomplemented
467C2×C4⋊C8C2×D5311yescharacteristic
468C2×C4⋊C8C2×D5311yescharacteristic
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×C22⋊C8C2×D5311yescharacteristic
478C2×C22⋊C8C2×D5311yescharacteristic
479C2×#97C2×D5311yescharacteristic
480C2×C4×C8C2×D5311yescharacteristic
481C53C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—534no—
483C2×#41—1062no—
484C2×#41—2122no—
485C2×#41—2122no—
486C22×Q8—531no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8—531no—
490C22×Q8—534no—
491C22×Q8—1061no—
492C22×Q8—1061no—
493C22×Q8—1062no—
494C22×Q8—2122no—
495C22×Q8—2122no—
496C22×D4—531no—
497C22×D4—531no—
498C22×D4—1061no—
499C22×D4—1061no—
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4C22×D5311yescharacteristic
504C2×Q16—534no—
505C2×Q16—534no—
506C2×Q16—534no—
507C2×Q16—2122no—
508C2×Q16—2122no—
509C2×Q16—2122no—
510C2×SD16—534no—
511C2×SD16—534no—
512C2×SD16—534no—
513C2×SD16—534no—
514C2×SD16—2122no—
515C2×SD16—2122no—
516C2×SD16—2122no—
517C2×SD16—2122no—
518C2×D8—534no—
519C2×D8—2122no—
520C22×C8C22×D5311yescharacteristic
521C22×C8C22×D5311yescharacteristic
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524C4⋊Q8—534no—
525C4⋊Q8—534no—
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528C4⋊Q8—1062no—
529C4⋊Q8—1062no—
530#126—1068no—
531#124—534no—
532#124—534no—
533#124—534no—
534#124—1068no—
535#124—1062no—
536#124—1062no—
537#124—1062no—
538#123—1068no—
539#123—1068no—
540#123—1068no—
541C22⋊Q8—534no—
542C22⋊Q8—1062no—
543C22⋊Q8—1068no—
544C22⋊Q8—1068no—
545C22⋊Q8—1068no—
546#121—534no—
547#121—1062no—
548C4×Q8—534no—
549C4×Q8—1062no—
550C4×D4—534no—
551C4×D4—1062no—
552#117D21214yes—
553#117C22×D5314yes—
554C2×C4⋊C4—531no—
555C2×C4⋊C4—531no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4D21211yescharacteristic
564C2×C4⋊C4D21211yescharacteristic
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4D21211yescharacteristic
575C2×C22⋊C4D21211yescharacteristic
576C2×C42—1061no—
577C2×C42C22×D5311yescharacteristic
578C2×C42C22×D5311yescharacteristic
579C4⋊C8C22×D5314yes—
580C4⋊C8C22×D5314yes—
581#103—534no—
582#103—534no—
583#103—534no—
584#103—534no—
585#103—534no—
586#103—534no—
587#102—534no—
588#102—534no—
589C22⋊C8C22×D5314yes—
590C22⋊C8C22×D5314yes—
591#97C22×D5314yes—
592C4×C8C22×D5314yes—
593C24—1061no—
594C24—1061no—
595C24C2×D21211yescharacteristic
596#41—2124no—
597#41—2124no—
598#41—2128no—
599C2×Q8—532no—
600C2×Q8—532no—
601C2×Q8—532no—
602C2×Q8—532no—
603C2×Q8—1064no—
604C2×Q8—1061no—
605C2×Q8—1064no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—1061no—
609C2×Q8—1062no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×Q8—1062no—
613C2×Q8—1062no—
614C2×Q8—1062no—
615C2×Q8—1062no—
616C2×Q8—1062no—
617C2×Q8—4242no—
618C2×Q8—2124no—
619C2×Q8—2124no—
620C2×Q8—2124no—
621C2×Q8—2128no—
622C2×D4—532no—
623C2×D4—532no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1061no—
627C2×D4—1061no—
628C2×D4—1062no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—1062no—
632C2×D4—4242no—
633C2×D4—2124no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—1064no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1061no—
642C22×C4—1061no—
643C22×C4—1064no—
644C22×C4—1064no—
645C22×C4—4242no—
646C22×C4—2124no—
647C22×C4—2124no—
648C22×C4C2×D21212yes—
649C22×C4C2×D21211yescharacteristic
650C22×C4C2×D21211yescharacteristic
651C22×C4C2×D21211yescharacteristic
652C22×C4C2×D21211yescharacteristic
653C22×C4C2×D21211yescharacteristic
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657Q16—2124no—
658Q16—2124no—
659SD16—2124no—
660SD16—2124no—
661SD16—2124no—
662SD16—2124no—
663D8—2124no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8C23×D5312yes—
669C2×C8C23×D5312yes—
670C2×C8C23×D5312yes—
671C2×C8C23×D5312yes—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1064no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1064no—
683C4⋊C4C2×D21214yes—
684C4⋊C4C2×D21214yes—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4C2×D21214yes—
695C22⋊C4C2×D21214yes—
696C42—1064no—
697C42C2×D21212yes—
698C42C2×D21212yes—
699C42C23×D5312yes—
700C42C23×D5312yes—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—1062no—
705C23—1062no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23—2122no—
711C23—2122no—
712C23C22×D21212yes—
713C23C22×D21211yescharacteristic
714Q8—1062no—
715Q8—1062no—
716Q8—1062no—
717Q8—1062no—
718Q8—1062no—
719Q8—1062no—
720Q8—1062no—
721Q8—1062no—
722Q8—4244no—
723Q8—2128no—
724Q8—2122no—
725Q8—2122no—
726Q8—2122no—
727Q8—2122no—
728D4—1062no—
729D4—1062no—
730D4—1062no—
731D4—1062no—
732D4—4244no—
733D4—2128no—
734D4—2122no—
735D4—2122no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—4244no—
751C2×C4—2128no—
752C2×C4—2128no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4C22×D21212yes—
760C2×C4C22×D21212yes—
761C2×C4C22×D21212yes—
762C2×C4C22×D21212yes—
763C2×C4C22×D21212yes—
764C2×C4C22×D21211yescharacteristic
765C2×C4#1313326312yes—
766C2×C4#1313326312yes—
767C2×C4C24×D5311yescharacteristic
768C8—22no—
769C8—22no—
770C8—22no—
771C8—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—44no—
776C22—4244no—
777C22—4244no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22#1681119212yes—
785C22#1681143512yes—
786C22#1681144012yes—
787C22C23×D21211yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—22no—
793C4—2122no—
794C4—2122no—
795C4—2122no—
796C4—2122no—
797C4—2122no—
798C4—2122no—
799C4#1681119212yes—
800C4C2×#1313326311yescharacteristic
801C4C2×#1313326311yescharacteristic
802C2—42no—
803C2—4242no—
804C2—4242no—
805C2#2028582614yesdirect product factor
806C2C2×#1681119211yescharacteristic
807C2C2×#1681143511yescharacteristic
808C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#433C2
socleC23×C53C22×D4
prime radicalC2×#16810770C2
hypercenterC2×#433D53
hypocenterC53C2×#3225
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#16811244C2semidirect
2. C2×#16811199C2semidirect
3. #20285826C2direct (N × H)
4. C2×#16811017C2semidirect
5. C2×#16811007C2semidirect
6. C2×#16810983C2semidirect
7. C2×#16810974C2semidirect
8. C2×#16810846C2semidirect
9. C2×#16810834C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810829C2semidirect
12. C2×#16810787C2semidirect
14. C2×#16810781C2semidirect
15. C2×#16810764C2semidirect
16. C2×C53×#433C2semidirect
28. #16811244C22semidirect
30. #16811199C22semidirect
49. #16811017C22semidirect
50. #16811007C22semidirect
51. #16810983C22semidirect
52. #16810974C22semidirect
53. #16810846C22semidirect
54. #16810839C22semidirect
55. #16810834C22semidirect
56. #16810829C22semidirect
57. #16810787C22semidirect
58. #16810781C22semidirect
60. #16810764C22semidirect
70. C53×#433C22semidirect
413. C2×#433D53semidirect
415. C2×C53#3225semidirect
466. #433C2×D53semidirect
481. C53C2×#3225semidirect
805. C2#20285826direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
C2×#168111992
#202858262
C2×#168110172
C2×#168110072
C2×#168109832
C2×#168109742
C2×#168108462
C2×#168108342
C2×#168108392
C2×#168108292
C2×#168107872
C2×#168107702
C2×#168107812
C2×#168107642
C2×C53×#4332
C2×#322553