Finite Group Databasebeta

← C2×#20285819 #28255482

Subgroups — C2×#20285819 #28255482

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×#16811242C211yesmaximal, characteristic, complemented
2C2×#16811198C211yesmaximal, characteristic, complemented
3#20285819C2116yesmaximal, direct product factor
4C2×#16811005C211yesmaximal, characteristic, complemented
5C2×#16810983C211yesmaximal, characteristic, complemented
6C2×#16810973C211yesmaximal, characteristic, complemented
7C2×#16810847C211yesmaximal, characteristic, complemented
8C2×#16810831C211yesmaximal, characteristic, complemented
9C2×#16810840C211yesmaximal, characteristic, complemented
10C2×#16810826C211yesmaximal, characteristic, complemented
11C2×#16810784C211yesmaximal, characteristic, complemented
12C2×#16810767C211yesmaximal, characteristic
13C2×#16810777C211yesmaximal, characteristic, complemented
14C2×#16810760C211yesmaximal, characteristic, complemented
15C2×#16810685C211yesmaximal, characteristic, complemented
16C2×C53×#497C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719922C2211yescharacteristic
23#16811242—24no—
24#16811242C2218yescomplemented
25#16811198—24no—
26#16811198C2218yescomplemented
27C2×#13133217C2211yescharacteristic
28C2×#13133215C2211yescharacteristic
29C2×#13133210—21no—
30C2×#13133206C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133202—21no—
34C2×#13133202—21no—
35C2×#13133201—21no—
36C2×#13133195—21no—
37C2×#13133195—21no—
38C2×#13133194—21no—
39C2×#13133193C2211yescharacteristic
40C2×#13133188C2211yescharacteristic
41C2×Q8×Dic53C2211yescharacteristic
42C2×D4×Dic53C2211yescharacteristic
43C2×#13133174C2211yescharacteristic
44#16811005C2218yescomplemented
45#16810983C2218yescomplemented
46#16810973C2218yescomplemented
47#16810847C2218yescomplemented
48#16810840C2218yescomplemented
49#16810831C2218yescomplemented
50#16810826C2218yescomplemented
51#16810784C2218yescomplemented
52#16810777C2218yescomplemented
53#16810767C2218yes—
54#16810760C2218yescomplemented
55#16810685C2218yescomplemented
56C2×#13133146C2211yescharacteristic
57C2×#13133146C2211yescharacteristic
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C22×SD16×C53C2211yescharacteristic
73C2×C4⋊Q8×C53C2211yescharacteristic
74C2×#124×C53C2211yescharacteristic
75C53×#497C2218yescomplemented
76C2×#97×C53C2211yescharacteristic
77C2×#11719949—22no—
78C2×#11719949—42no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—42no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C22×D212—21no—
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C23×Dic53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×#11719925—42no—
96C2×#11719925C2314yes—
97C2×#11719923—42no—
98C2×#11719923C2314yes—
99C2×#11719924—42no—
100C2×#11719924C2314yes—
101C2×#11719922—42no—
102C2×#11719922C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133217—22no—
106#13133217C2314yes—
107#13133215—22no—
108#13133215C2314yes—
109#13133210—28no—
110#13133206—22no—
111#13133206C2314yes—
112#13133205—22no—
113#13133205C2314yes—
114#13133203—28no—
115#13133202—28no—
116#13133202—28no—
117#13133201—28no—
118#13133195—28no—
119#13133195—28no—
120#13133194—28no—
121#13133193—22no—
122#13133193C2314yes—
123#13133188—22no—
124#13133188C2314yes—
125Q8×Dic53—22no—
126Q8×Dic53C2314yes—
127D4×Dic53—22no—
128D4×Dic53C2314yes—
129#13133174D414yes—
130#13133174C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919D411yescharacteristic
139C2×#11719919D411yescharacteristic
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921D411yescharacteristic
148C2×#11719921D411yescharacteristic
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133146C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133139C2314yes—
160#13133139C2314yes—
161#13133129C2314yes—
162#13133129C2314yes—
163C4×#88322C2314yes—
164C22×Q8×C53C2311yescharacteristic
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C2×Q16×C53—42no—
169C2×Q16×C53—42no—
170C2×Q16×C53C2314yes—
171C2×Q16×C53C2314yes—
172C2×SD16×C53—42no—
173C2×SD16×C53—42no—
174C2×SD16×C53C2314yes—
175C2×SD16×C53C2314yes—
176C22×C8×C53C2311yescharacteristic
177C22×C8×C53C2311yescharacteristic
178C4⋊Q8×C53—22no—
179C4⋊Q8×C53C2314yes—
180#124×C53—22no—
181#124×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53—21no—
184C2×C22⋊C4×C53—21no—
185C2×C22⋊C4×C53—21no—
186C2×C42×C53C2311yescharacteristic
187#97×C53C2314yes—
188C24×C53—21no—
189C23×D53—21no—
190C23×D53C2×D411yescharacteristic
191C2×Q8×C53—21no—
192C2×Q8×C53—21no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53C2412yes—
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C2×D4×C53—21no—
204C2×D4×C53—22no—
205C2×D4×C53—22no—
206C2×D4×C53C2412yes—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—82no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—82no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223#11719949—44no—
224#11719949—44no—
225#11719949—48no—
226Q8×D53—44no—
227Q8×D53—44no—
228Q8×D53—48no—
229C2×D212—22no—
230C2×D212—22no—
231C2×D212—24no—
232C2×D212—21no—
233C2×D212—44no—
234C2×D212C2412yes—
235C2×C4×D53—22no—
236C2×C4×D53—22no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—44no—
240C2×C4×D53—44no—
241C2×C4×D53C2×D412yes—
242C2×C4×D53C2412yes—
243C2×Dic106—22no—
244C2×Dic106—22no—
245C2×Dic106—21no—
246C2×Dic106—24no—
247C2×Dic106—24no—
248C2×Dic106—44no—
249C2×Dic106—82no—
250C2×Dic106C2412yes—
251Q16×C53—44no—
252Q16×C53—44no—
253SD16×C53—44no—
254SD16×C53—44no—
255C2×C8×C53—22no—
256C2×C8×C53—22no—
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C4⋊C4×C53—24no—
260C4⋊C4×C53—24no—
261C22⋊C4×C53—24no—
262C22⋊C4×C53—24no—
263C42×C53C2×D412yes—
264C42×C53C2412yes—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267#11719925—44no—
268#11719924—44no—
269#11719923—44no—
270#11719922—44no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277#11719921C2×D414yes—
278C4⋊Dic53—24no—
279C4⋊Dic53—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53—24no—
282C4⋊Dic53C2412yes—
283C4⋊Dic53C2412yes—
284#11719919—24no—
285#11719919—24no—
286#11719919—24no—
287#11719919C2×D414yes—
288#11719919C2×D414yes—
289C4×Dic53—24no—
290C4×Dic53C2×D412yes—
291C4×Dic53C2412yes—
292C2×#88322—22no—
293C2×#88322—22no—
294C2×#88322C2412yes—
295C2×#88322C2412yes—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53C22×D411yescharacteristic
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53C22×D412yes—
309Q8×C53—22no—
310Q8×C53—22no—
311Q8×C53—22no—
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—22no—
315Q8×C53—42no—
316Q8×C53—42no—
317Q8×C53—42no—
318D4×C53—22no—
319D4×C53—22no—
320D4×C53—42no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—42no—
327C2×C4×C53—42no—
328C2×C4×C53—42no—
329C2×C4×C53C22×D412yes—
330C2×C4×C53C22×D412yes—
331C2×C4×C53C22×D411yescharacteristic
332C2×C4×C53H(5,𝔽2)12yes—
333C2×C4×C53H(5,𝔽2)12yes—
334C2×C4×C53C2511yescharacteristic
335C22⋊D53—84no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—84no—
346C2×Dic53C22×D412yes—
347C2×Dic53C22×D412yes—
348C2×Dic53C22×D412yes—
349D212—22no—
350D212—22no—
351D212—48no—
352D212—42no—
353C4×D53—24no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—48no—
357C4×D53—48no—
358Dic106—22no—
359Dic106—22no—
360Dic106—48no—
361Dic106—42no—
362Dic106—84no—
363C8×C53—22no—
364C8×C53—22no—
365#88322—22no—
366#88322—22no—
367C2×#3225—531nomaximal, Sylow
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—84no—
372C22×C53#53512yes—
373C22×C53#57712yes—
374C22×C53#57812yes—
375C22×C53C23×D411yescharacteristic
376C2×D53—22no—
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—44no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—42no—
387C4×C53—42no—
388C4×C53—42no—
389C4×C53#53512yes—
390C4×C53C2×H(5,𝔽2)11yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—22no—
393Dic53—22no—
394Dic53—22no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#542—531no—
399C2×#536—531no—
400#3225—5316no—
401C2×#497D5311yescharacteristic, complemented
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×#433—531no—
414C2×C53—82no—
415C2×C53#322514yescomplemented
416C2×C53C2×#53511yescharacteristic
417C2×C53C2×#57711yescharacteristic
418C2×C53C2×#57811yescharacteristic
419D53—42no—
420D53—82no—
421C22×#41—531no—
422C23×Q8—531no—
423C22×Q16—531no—
424C22×Q16C2×D5311yescharacteristic
425C22×Q16C2×D5311yescharacteristic
426C22×SD16—531no—
427C22×SD16—531no—
428C22×SD16C2×D5311yescharacteristic
429C22×SD16C2×D5311yescharacteristic
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⋊Q8C2×D5311yescharacteristic
438C2×#126—1061no—
439C2×#124—531no—
440C2×#124—531no—
441C2×#124—1061no—
442C2×#124C2×D5311yescharacteristic
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×#117—531no—
454#497C2×D5318yescomplemented
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#433—538no—
467C2×C4⋊C8—531no—
468C2×C4⋊C8—531no—
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⋊C8—531no—
478C2×C22⋊C8—531no—
479C2×#97C2×D5311yescharacteristic
480C2×C4×C8—531no—
481C53C2×#322511yescharacteristic, complemented, Sylow
482C2×#41—534no—
483C2×#41—1062no—
484C2×#41—2122no—
485C2×#41—2122no—
486C22×Q8—534no—
487C22×Q8—531no—
488C22×Q8—1061no—
489C22×Q8—1062no—
490C22×Q8—1061no—
491C22×Q8—2122no—
492C22×Q8—2122no—
493C22×Q8C22×D5311yescharacteristic
494C22×Q8C22×D5311yescharacteristic
495C22×Q8C22×D5311yescharacteristic
496C22×D4—531no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C23×C4—531no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4—1061no—
504C2×Q16—42no—
505C2×Q16—42no—
506C2×Q16—534no—
507C2×Q16—2122no—
508C2×Q16C22×D5314yes—
509C2×Q16C22×D5314yes—
510C2×SD16—42no—
511C2×SD16—42no—
512C2×SD16—534no—
513C2×SD16—534no—
514C2×SD16—2122no—
515C2×SD16—2122no—
516C2×SD16C22×D5314yes—
517C2×SD16C22×D5314yes—
518C2×D8—534no—
519C2×D8—2122no—
520C22×C8—531no—
521C22×C8—531no—
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524C4⋊Q8—22no—
525C4⋊Q8—534no—
526C4⋊Q8—534no—
527C4⋊Q8—1062no—
528C4⋊Q8—1062no—
529C4⋊Q8C22×D5314yes—
530#126—1068no—
531#124—22no—
532#124—534no—
533#124—534no—
534#124—1062no—
535#124—1068no—
536#124—1062no—
537#124C22×D5314yes—
538#123—1068no—
539#123—1068no—
540#123—1068no—
541C22⋊Q8—534no—
542C22⋊Q8—1068no—
543C22⋊Q8—1068no—
544C22⋊Q8—1068no—
545C22⋊Q8—1062no—
546#121—534no—
547#121—1062no—
548C4×Q8—534no—
549C4×Q8—1062no—
550C4×D4—534no—
551C4×D4—1062no—
552#117—534no—
553#117—534no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—1061no—
561C2×C4⋊C4—1061no—
562C2×C4⋊C4—1061no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—531no—
568C2×C22⋊C4—531no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C22⋊C4—1061no—
572C2×C22⋊C4—1061no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C42—531no—
577C2×C42—1061no—
578C2×C42C22×D5311yescharacteristic
579C4⋊C8—534no—
580C4⋊C8—534no—
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⋊C8—534no—
590C22⋊C8—534no—
591#97C22×D5314yes—
592C4×C8—534no—
593C24—21no—
594C24—531no—
595C24—1061no—
596#41—2124no—
597#41—2124no—
598#41—2128no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—22no—
608C2×Q8—532no—
609C2×Q8—1064no—
610C2×Q8—1064no—
611C2×Q8—1061no—
612C2×Q8—1062no—
613C2×Q8—1062no—
614C2×Q8—4242no—
615C2×Q8—2124no—
616C2×Q8—2124no—
617C2×Q8—2124no—
618C2×Q8—2128no—
619C2×Q8C23×D5312yes—
620C2×Q8C23×D5312yes—
621C2×Q8C23×D5312yes—
622C2×D4—21no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—532no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1061no—
629C2×D4—1062no—
630C2×D4—1062no—
631C2×D4—4242no—
632C2×D4—2124no—
633C2×D4C23×D5312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—531no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—532no—
641C22×C4—532no—
642C22×C4—1064no—
643C22×C4—1064no—
644C22×C4—1064no—
645C22×C4—1062no—
646C22×C4—1062no—
647C22×C4—1061no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—4242no—
651C22×C4—2124no—
652C22×C4—2124no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656Q16—44no—
657Q16—44no—
658Q16—2124no—
659SD16—44no—
660SD16—44no—
661SD16—2124no—
662SD16—2124no—
663D8—2124no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—532no—
667C2×C8—532no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8C23×D5312yes—
671C2×C8C23×D5312yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—534no—
675C4⋊C4—534no—
676C4⋊C4—532no—
677C4⋊C4—532no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1061no—
683C4⋊C4—1061no—
684C4⋊C4—1064no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—534no—
688C22⋊C4—534no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4—1064no—
693C22⋊C4—1064no—
694C22⋊C4—1064no—
695C22⋊C4—1064no—
696C42—532no—
697C42—532no—
698C42—1064no—
699C42D4×D5312yes—
700C42C23×D5312yes—
701C23—22no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—532no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—1062no—
710C23—2122no—
711C23—2122no—
712C23—2122no—
713C23C2×D4×D5311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—42no—
721Q8—42no—
722Q8—42no—
723Q8—1062no—
724Q8—1062no—
725Q8—4244no—
726Q8—2128no—
727Q8—2122no—
728D4—22no—
729D4—22no—
730D4—42no—
731D4—1062no—
732D4—1062no—
733D4—4244no—
734D4—2128no—
735D4—2122no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—532no—
745C2×C4—532no—
746C2×C4—532no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1064no—
751C2×C4—1062no—
752C2×C4—1062no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—4244no—
757C2×C4—2128no—
758C2×C4—2128no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4C2×D4×D5312yes—
763C2×C4C2×D4×D5312yes—
764C2×C4C2×D4×D5311yescharacteristic
765C2×C4#1313326212yes—
766C2×C4#1313326212yes—
767C2×C4C24×D5311yescharacteristic
768C8—22no—
769C8—22no—
770C8—1062no—
771C8—1062no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—84no—
776C22—1062no—
777C22—1062no—
778C22—1062no—
779C22—4244no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2124no—
784C22#1681118612yes—
785C22#1681143212yes—
786C22#1681143912yes—
787C22C22×D4×D5311yescharacteristic
788C4—22no—
789C4—22no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—1062no—
794C4—1062no—
795C4—1062no—
796C4—2122no—
797C4—2122no—
798C4—2122no—
799C4#1681118612yes—
800C4C2×#1313326211yescharacteristic
801C4C2×#1313326211yescharacteristic
802C2—82no—
803C2—4242no—
804C2—2122no—
805C2#2028581914yesdirect product factor
806C2C2×#1681118611yescharacteristic
807C2C2×#1681143211yescharacteristic
808C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#497C2
socleC23×C53C22×D4
prime radicalC2×#16810767C2
hypercenterC2×#497D53
hypocenterC53C2×#3225
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#16811242C2semidirect
2. C2×#16811198C2semidirect
3. #20285819C2direct (N × H)
4. C2×#16811005C2semidirect
5. C2×#16810983C2semidirect
6. C2×#16810973C2semidirect
7. C2×#16810847C2semidirect
8. C2×#16810831C2semidirect
9. C2×#16810840C2semidirect
10. C2×#16810826C2semidirect
11. C2×#16810784C2semidirect
13. C2×#16810777C2semidirect
14. C2×#16810760C2semidirect
15. C2×#16810685C2semidirect
16. C2×C53×#497C2semidirect
24. #16811242C22semidirect
26. #16811198C22semidirect
44. #16811005C22semidirect
45. #16810983C22semidirect
46. #16810973C22semidirect
47. #16810847C22semidirect
48. #16810840C22semidirect
49. #16810831C22semidirect
50. #16810826C22semidirect
51. #16810784C22semidirect
52. #16810777C22semidirect
54. #16810760C22semidirect
55. #16810685C22semidirect
75. C53×#497C22semidirect
401. C2×#497D53semidirect
415. C2×C53#3225semidirect
454. #497C2×D53semidirect
481. C53C2×#3225semidirect
805. C2#20285819direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112422
C2×#168111982
#202858192
C2×#168110052
C2×#168109832
C2×#168109732
C2×#168108472
C2×#168108312
C2×#168108402
C2×#168108262
C2×#168107842
C2×#168107672
C2×#168107772
C2×#168107602
C2×#168106852
C2×C53×#4972
C2×#322553