Finite Group Databasebeta

← C2×#20285596 #28254777

Subgroups — C2×#20285596 #28254777

Order 13568.

2186 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811201C211yesmaximal, characteristic
2C2×#16811196C211yesmaximal, characteristic, complemented
3#20285596C2116yesmaximal, direct product factor
4C2×#16810959C211yesmaximal, characteristic, complemented
5C2×#16810963C211yesmaximal, characteristic, complemented
6C2×#16810945C211yesmaximal, characteristic, complemented
7C2×#16810951C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic, complemented
9C2×#16810866C211yesmaximal, characteristic, complemented
10C2×#16810861C211yesmaximal, characteristic, complemented
11C2×#16810851C211yesmaximal, characteristic, complemented
12C2×#16810785C211yesmaximal, characteristic, complemented
13C2×#16810777C211yesmaximal, characteristic, complemented
14C2×#16810760C211yesmaximal, characteristic, complemented
15C2×#16810588C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811201—24no—
24#16811201C2218yes—
25#16811196—24no—
26#16811196C2218yescomplemented
27C2×#13133216—21no—
28C2×#13133203—21no—
29C2×#13133202—21no—
30C2×#13133199—21no—
31C2×#13133197C2211yescharacteristic
32C2×#13133196—21no—
33C2×#13133196C2211yescharacteristic
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×#13133193C2211yescharacteristic
37C2×#13133191—21no—
38C2×#13133189—21no—
39C2×#13133189—21no—
40C2×#13133188C2211yescharacteristic
41C2×#13133188C2211yescharacteristic
42C2×#13133175C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic
44#16810963C2218yescomplemented
45#16810959C2218yescomplemented
46#16810951C2218yescomplemented
47#16810945C2218yescomplemented
48#16810880C2218yescomplemented
49#16810866C2218yescomplemented
50#16810861C2218yescomplemented
51#16810851C2218yescomplemented
52#16810785C2218yescomplemented
53#16810777C2218yescomplemented
54#16810760C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65#16810588C2218yescomplemented
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719945—42no—
78C2×#11719945—42no—
79C2×#11719945D414yes—
80C2×#11719945C2314yes—
81C22×Dic106—21no—
82C22×Dic106D411yescharacteristic
83C22×Dic106C2311yescharacteristic
84C2×Q8×D53—22no—
85C2×Q8×D53—42no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C22×D212D411yescharacteristic
89C22×C22⋊D53—21no—
90C22×C22⋊D53—21no—
91C22×C22⋊D53D411yescharacteristic
92C22×C22⋊D53D411yescharacteristic
93C23×Dic53—21no—
94C22×C4×D53—21no—
95C22×C4×D53C2311yescharacteristic
96C22×C4×D53C2311yescharacteristic
97C2×#11719925—42no—
98C2×#11719925C2314yes—
99C2×#11719923—42no—
100C2×#11719923C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C2×C8×D53—42no—
106C2×C8×D53C2314yes—
107#13133216—28no—
108#13133203—28no—
109#13133202—28no—
110#13133199—28no—
111#13133197—22no—
112#13133197C2314yes—
113#13133196—22no—
114#13133196—28no—
115#13133196C2314yes—
116#13133193—22no—
117#13133193—22no—
118#13133193—22no—
119#13133193C2314yes—
120#13133193C2314yes—
121#13133193C2314yes—
122#13133191—28no—
123#13133189—28no—
124#13133189—28no—
125#13133188—22no—
126#13133188—22no—
127#13133188C2314yes—
128#13133188C2314yes—
129#13133175—22no—
130#13133175C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—22no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2314yes—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133151C2314yes—
153#13133148C2314yes—
154#13133148C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133141C2314yes—
160#13133138C2314yes—
161C22⋊#88322C2314yes—
162#13133129C2314yes—
163#13133129C2314yes—
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×Q8×C53C2311yescharacteristic
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C23×C4×C53—21no—
173C23×C4×C53C2311yescharacteristic
174C2×Q16×C53—42no—
175C2×Q16×C53C2314yes—
176C2×SD16×C53—42no—
177C2×SD16×C53C2314yes—
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yes—
186#102×C53C2314yes—
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190C23×D53C2×D411yescharacteristic
191C23×D53C2×D411yescharacteristic
192#41×C53—44no—
193#41×C53—44no—
194#41×C53—48no—
195C2×Q8×C53—21no—
196C2×Q8×C53—21no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53—22no—
200C2×Q8×C53—22no—
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C2×D4×C53—24no—
204C2×D4×C53—21no—
205C2×D4×C53—22no—
206C2×D4×C53—22no—
207C2×D4×C53—44no—
208C2×D4×C53C2412yes—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—24no—
215C22×C4×C53—44no—
216C22×C4×C53C2×D411yescharacteristic
217C22×C4×C53C2×D412yes—
218C22×C4×C53C2412yes—
219C22×C4×C53C2411yescharacteristic
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—42no—
223C2×C22⋊D53—42no—
224C2×C22⋊D53—82no—
225C2×C22⋊D53—82no—
226C2×C22⋊D53C2×D414yes—
227C2×C22⋊D53C2×D414yes—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—24no—
233C22×Dic53—82no—
234C22×Dic53C2×D411yescharacteristic
235C22×Dic53C2×D411yescharacteristic
236Q8×D53—44no—
237Q8×D53—44no—
238Q8×D53—48no—
239#11719945—48no—
240#11719945—44no—
241#11719945—44no—
242C2×D212—42no—
243C2×D212C2×D414yes—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—22no—
247C2×C4×D53—22no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53C2×D412yes—
251C2×C4×D53C2×D412yes—
252C2×C4×D53C2412yes—
253C2×C4×D53C2412yes—
254C2×Dic106—22no—
255C2×Dic106—22no—
256C2×Dic106—21no—
257C2×Dic106—24no—
258C2×Dic106—42no—
259C2×Dic106—44no—
260C2×Dic106C2×D414yes—
261C2×Dic106C2412yes—
262Q16×C53—44no—
263SD16×C53—44no—
264C2×C8×C53—22no—
265C2×C8×C53—22no—
266C2×C8×C53C2412yes—
267C2×C8×C53C2412yes—
268C4⋊C4×C53—24no—
269C4⋊C4×C53—21no—
270C4⋊C4×C53C2412yes—
271C22⋊C4×C53—24no—
272C22⋊Dic53—24no—
273C22⋊Dic53—24no—
274C22⋊Dic53—24no—
275#11719925—44no—
276#11719923—44no—
277#11719921—24no—
278#11719921—24no—
279#11719921—24no—
280#11719921—24no—
281#11719921—24no—
282C4⋊Dic53—21no—
283C4⋊Dic53—21no—
284C4⋊Dic53—24no—
285C4⋊Dic53—21no—
286C4⋊Dic53—24no—
287C4⋊Dic53C2412yes—
288C4⋊Dic53C2412yes—
289C4⋊Dic53C2412yes—
290#11719919—24no—
291#11719919—24no—
292#11719919—24no—
293#11719919—24no—
294C4×Dic53—24no—
295C2×#88322—22no—
296C2×#88322—22no—
297C2×#88322C2412yes—
298C2×#88322C2412yes—
299#11719912—44no—
300C8×D53—44no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—42no—
308C23×C53C22×D412yes—
309C23×C53C22×D411yescharacteristic
310C22×D53—22no—
311C22×D53—22no—
312C22×D53—22no—
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—22no—
316C22×D53C22×D412yes—
317C22×D53C22×D412yes—
318Q8×C53—22no—
319Q8×C53—22no—
320Q8×C53—22no—
321Q8×C53—22no—
322Q8×C53—42no—
323Q8×C53—42no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—48no—
327D4×C53—42no—
328C2×C4×C53—22no—
329C2×C4×C53—24no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—48no—
336C2×C4×C53—42no—
337C2×C4×C53—42no—
338C2×C4×C53—42no—
339C2×C4×C53C22×D412yes—
340C2×C4×C53C22×D411yescharacteristic
341C2×C4×C53H(5,𝔽2)12yes—
342C2×C4×C53H(5,𝔽2)12yes—
343C2×C4×C53C2511yescharacteristic
344C22⋊D53—44no—
345C22⋊D53—44no—
346C22⋊D53—84no—
347C22⋊D53—84no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—22no—
354C2×Dic53—42no—
355C2×Dic53—42no—
356C2×Dic53—42no—
357C2×Dic53—42no—
358C2×Dic53—84no—
359C2×Dic53C22×D412yes—
360C2×Dic53C22×D412yes—
361D212—44no—
362C4×D53—24no—
363C4×D53—24no—
364C4×D53—22no—
365C4×D53—22no—
366C4×D53—22no—
367C4×D53—22no—
368C4×D53—48no—
369Dic106—22no—
370Dic106—22no—
371Dic106—44no—
372Dic106—48no—
373Dic106—42no—
374C8×C53—22no—
375C8×C53—22no—
376#88322—22no—
377#88322—22no—
378C2×#3201—531nomaximal, Sylow
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—44no—
383C22×C53—42no—
384C22×C53—42no—
385C22×C53—42no—
386C22×C53—84no—
387C22×C53#53412yes—
388C22×C53#57712yes—
389C22×C53#57812yes—
390C22×C53C23×D411yescharacteristic
391C2×D53—22no—
392C2×D53—22no—
393C2×D53—22no—
394C2×D53—22no—
395C2×D53—22no—
396C2×D53—22no—
397C2×D53—44no—
398C2×D53—44no—
399C4×C53—22no—
400C4×C53—42no—
401C4×C53—42no—
402C4×C53—42no—
403C4×C53#53412yes—
404C4×C53C2×H(5,𝔽2)11yescharacteristic
405C4×C53C2×H(5,𝔽2)11yescharacteristic
406Dic53—22no—
407Dic53—22no—
408Dic53—42no—
409Dic53—42no—
410Dic53—42no—
411Dic53—42no—
412C2×#537—531no—
413C2×#536—531no—
414#3201—5316no—
415C2×#484—531no—
416C2×#485—531no—
417C2×#482—531no—
418C2×#483—531no—
419C2×#470—531no—
420C2×#468—531no—
421C2×#467—531no—
422C2×#465—531no—
423C2×#452—531no—
424C2×#452D5311yescharacteristic, complemented
425C2×#451—531no—
426C2×#448—531no—
427C2×#408—531no—
428C2×C53—42no—
429C2×C53—82no—
430C2×C53#320114yescomplemented
431C2×C53C2×#53411yescharacteristic
432C2×C53C2×#57711yescharacteristic
433C2×C53C2×#57811yescharacteristic
434D53—42no—
435D53—42no—
436C22×#41—531no—
437C22×#41C2×D5311yescharacteristic
438C23×Q8—531no—
439C22×Q16—531no—
440C22×Q16C2×D5311yescharacteristic
441C22×SD16—531no—
442C22×SD16C2×D5311yescharacteristic
443C22×M16—531no—
444C23×C8—531no—
445#537—538no—
446#537—1064no—
447#536—538no—
448#536—1064no—
449C2×C4⋊Q8—1061no—
450C2×#124—1061no—
451C2×#123—1061no—
452C2×#123—1061no—
453C2×C22⋊Q8—531no—
454C2×C22⋊Q8—531no—
455C2×C22⋊Q8—531no—
456C2×C22⋊Q8—531no—
457C2×C22⋊Q8—531no—
458C2×C22⋊Q8—1061no—
459C2×C22⋊Q8C2×D5311yescharacteristic
460C2×#121—531no—
461C2×#121—531no—
462C2×#121—1061no—
463C2×#121—1061no—
464C2×#121—1061no—
465C2×#117—531no—
466C22×C4⋊C4—531no—
467#485—538no—
468#484—538no—
469#483—538no—
470#482—538no—
471#470—538no—
472#468—538no—
473#467—538no—
474#465—538no—
475#452—538no—
476#452C2×D5318yescomplemented
477#451—538no—
478#448—538no—
479C2×#107—531no—
480C2×#107—531no—
481C2×#106—531no—
482C2×#106—531no—
483C2×#103—531no—
484C2×#103—531no—
485C2×#103—531no—
486C2×#103—531no—
487C2×#103—531no—
488C2×#103C2×D5311yescharacteristic
489C2×#102—531no—
490C2×#102C2×D5311yescharacteristic
491#408—538no—
492C2×C22⋊C8—531no—
493C2×C22⋊C8—531no—
494C2×C22⋊C8—531no—
495C2×C22⋊C8C2×D5311yescharacteristic
496C53C2×#320111yescharacteristic, complemented, Sylow
497C2×#41—22no—
498C2×#41—42no—
499C2×#41—42no—
500C2×#41—534no—
501C2×#41—534no—
502C2×#41—2122no—
503C2×#41—2122no—
504C2×#41C22×D5314yes—
505C22×Q8—531no—
506C22×Q8—534no—
507C22×Q8—531no—
508C22×Q8—1061no—
509C22×Q8—1062no—
510C22×Q8—2122no—
511C22×Q8—2122no—
512C22×Q8C22×D5311yescharacteristic
513C22×Q8C22×D5311yescharacteristic
514C22×D4—21no—
515C22×D4—531no—
516C22×D4—531no—
517C22×D4—531no—
518C22×D4—1061no—
519C22×D4—1061no—
520C22×D4C22×D5311yescharacteristic
521C23×C4—21no—
522C23×C4—531no—
523C23×C4—531no—
524C23×C4—1061no—
525C23×C4—1061no—
526C23×C4C22×D5311yescharacteristic
527C2×Q16—42no—
528C2×Q16—534no—
529C2×Q16—2122no—
530C2×Q16C22×D5314yes—
531C2×SD16—42no—
532C2×SD16—534no—
533C2×SD16—2122no—
534C2×SD16C22×D5314yes—
535C2×M16—534no—
536C2×M16—2122no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—534no—
540C22×C8—2122no—
541C22×C8C22×D5311yescharacteristic
542C22×C8C22×D5311yescharacteristic
543C4⋊Q8—1068no—
544#124—1068no—
545#123—1068no—
546#123—1068no—
547C22⋊Q8—22no—
548C22⋊Q8—534no—
549C22⋊Q8—534no—
550C22⋊Q8—534no—
551C22⋊Q8—534no—
552C22⋊Q8—534no—
553C22⋊Q8—1062no—
554C22⋊Q8—1068no—
555C22⋊Q8—1062no—
556C22⋊Q8—1062no—
557C22⋊Q8—1062no—
558C22⋊Q8—1062no—
559C22⋊Q8C22×D5314yes—
560#121—534no—
561#121—534no—
562#121—1068no—
563#121—1062no—
564#121—1062no—
565#121—1068no—
566#121—1068no—
567#117—534no—
568#117—1062no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—531no—
571C2×C4⋊C4—531no—
572C2×C4⋊C4—534no—
573C2×C4⋊C4—531no—
574C2×C4⋊C4—1061no—
575C2×C4⋊C4—1061no—
576C2×C4⋊C4—1061no—
577C2×C4⋊C4—1061no—
578C2×C4⋊C4—1061no—
579C2×C4⋊C4—1062no—
580C2×C4⋊C4—1061no—
581C2×C4⋊C4C22×D5311yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—1061no—
584C2×C22⋊C4—1061no—
585C2×C22⋊C4—1061no—
586C2×C22⋊C4—1061no—
587C2×C22⋊C4—1061no—
588C2×C22⋊C4—1061no—
589C2×C22⋊C4—1061no—
590C2×C22⋊C4—1061no—
591C2×C42—1061no—
592#107—534no—
593#107—534no—
594#106—534no—
595#106—534no—
596#103—534no—
597#103—534no—
598#103—534no—
599#103—534no—
600#103—534no—
601#103C22×D5314yes—
602#102—534no—
603#102C22×D5314yes—
604C22⋊C8—534no—
605C22⋊C8—534no—
606C22⋊C8—534no—
607C22⋊C8C22×D5314yes—
608C24—21no—
609C24—531no—
610C24—531no—
611C24D4×D5311yescharacteristic
612#41—44no—
613#41—44no—
614#41—48no—
615#41—2128no—
616#41—2124no—
617#41—2124no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—534no—
625C2×Q8—532no—
626C2×Q8—1064no—
627C2×Q8—1061no—
628C2×Q8—1062no—
629C2×Q8—1062no—
630C2×Q8—2122no—
631C2×Q8—2124no—
632C2×Q8—2124no—
633C2×Q8—2124no—
634C2×Q8—2128no—
635C2×Q8C23×D5312yes—
636C2×Q8C23×D5312yes—
637C2×D4—24no—
638C2×D4—21no—
639C2×D4—22no—
640C2×D4—22no—
641C2×D4—44no—
642C2×D4—534no—
643C2×D4—534no—
644C2×D4—534no—
645C2×D4—1064no—
646C2×D4—1064no—
647C2×D4—4242no—
648C2×D4—4242no—
649C2×D4—2122no—
650C2×D4—2122no—
651C2×D4—2122no—
652C2×D4C23×D5312yes—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—44no—
660C22×C4—531no—
661C22×C4—531no—
662C22×C4—532no—
663C22×C4—532no—
664C22×C4—532no—
665C22×C4—532no—
666C22×C4—1064no—
667C22×C4—1062no—
668C22×C4—1062no—
669C22×C4—1062no—
670C22×C4—1062no—
671C22×C4—1064no—
672C22×C4—1061no—
673C22×C4—1061no—
674C22×C4—1061no—
675C22×C4—1061no—
676C22×C4—4242no—
677C22×C4—2124no—
678C22×C4D4×D5312yes—
679C22×C4D4×D5311yescharacteristic
680C22×C4C23×D5312yes—
681C22×C4C23×D5311yescharacteristic
682Q16—44no—
683Q16—2124no—
684SD16—44no—
685SD16—2124no—
686M16—2124no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—532no—
690C2×C8—532no—
691C2×C8—1062no—
692C2×C8—1062no—
693C2×C8—2124no—
694C2×C8C23×D5312yes—
695C2×C8C23×D5312yes—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—532no—
699C4⋊C4—532no—
700C4⋊C4—532no—
701C4⋊C4—1064no—
702C4⋊C4—1064no—
703C4⋊C4—1064no—
704C4⋊C4—1064no—
705C4⋊C4—1064no—
706C4⋊C4—1061no—
707C4⋊C4—1061no—
708C4⋊C4—1061no—
709C4⋊C4—1064no—
710C4⋊C4C23×D5312yes—
711C22⋊C4—24no—
712C22⋊C4—1064no—
713C22⋊C4—1064no—
714C22⋊C4—1064no—
715C22⋊C4—1064no—
716C22⋊C4—1064no—
717C22⋊C4—1064no—
718C22⋊C4—1064no—
719C22⋊C4—1064no—
720C42—1064no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—532no—
729C23—532no—
730C23—1062no—
731C23—1062no—
732C23—1062no—
733C23—1062no—
734C23—1062no—
735C23—1062no—
736C23C2×D4×D5312yes—
737C23C2×D4×D5311yescharacteristic
738Q8—22no—
739Q8—22no—
740Q8—22no—
741Q8—22no—
742Q8—42no—
743Q8—42no—
744Q8—1062no—
745Q8—1062no—
746Q8—2124no—
747Q8—2128no—
748Q8—2122no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—42no—
753D4—4244no—
754D4—4244no—
755D4—2124no—
756D4—2124no—
757D4—2124no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—48no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—532no—
770C2×C4—532no—
771C2×C4—1062no—
772C2×C4—1062no—
773C2×C4—1064no—
774C2×C4—1064no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—1062no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—4244no—
784C2×C4—2128no—
785C2×C4—2122no—
786C2×C4—2122no—
787C2×C4—2122no—
788C2×C4—2122no—
789C2×C4C2×D4×D5312yes—
790C2×C4C2×D4×D5311yescharacteristic
791C2×C4#1313326212yes—
792C2×C4#1313326212yes—
793C2×C4C24×D5311yescharacteristic
794C8—22no—
795C8—22no—
796C8—1062no—
797C8—1062no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—84no—
806C22—1062no—
807C22—1062no—
808C22—1062no—
809C22—1062no—
810C22—1062no—
811C22—1062no—
812C22—2124no—
813C22—2124no—
814C22#1681118312yes—
815C22#1681143212yes—
816C22#1681143712yes—
817C22C22×D4×D5311yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—1062no—
823C4—1062no—
824C4—2122no—
825C4—2122no—
826C4—2122no—
827C4—2122no—
828C4#1681118312yes—
829C4C2×#1313326211yescharacteristic
830C4C2×#1313326211yescharacteristic
831C2—42no—
832C2—82no—
833C2—2122no—
834C2—2122no—
835C2#2028559614yesdirect product factor
836C2C2×#1681118311yescharacteristic
837C2C2×#1681143211yescharacteristic
838C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC2×#16811201C2
hypercenterC2×#452D53
hypocenterC53C2×#3201
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#16811196C2semidirect
3. #20285596C2direct (N × H)
4. C2×#16810959C2semidirect
5. C2×#16810963C2semidirect
6. C2×#16810945C2semidirect
7. C2×#16810951C2semidirect
8. C2×#16810880C2semidirect
9. C2×#16810866C2semidirect
10. C2×#16810861C2semidirect
11. C2×#16810851C2semidirect
12. C2×#16810785C2semidirect
13. C2×#16810777C2semidirect
14. C2×#16810760C2semidirect
15. C2×#16810588C2semidirect
16. C2×C53×#452C2semidirect
26. #16811196C22semidirect
44. #16810963C22semidirect
45. #16810959C22semidirect
46. #16810951C22semidirect
47. #16810945C22semidirect
48. #16810880C22semidirect
49. #16810866C22semidirect
50. #16810861C22semidirect
51. #16810851C22semidirect
52. #16810785C22semidirect
53. #16810777C22semidirect
54. #16810760C22semidirect
65. #16810588C22semidirect
73. C53×#452C22semidirect
424. C2×#452D53semidirect
430. C2×C53#3201semidirect
476. #452C2×D53semidirect
496. C53C2×#3201semidirect
835. C2#20285596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112012
C2×#168111962
#202855962
C2×#168109592
C2×#168109632
C2×#168109452
C2×#168109512
C2×#168108802
C2×#168108662
C2×#168108612
C2×#168108512
C2×#168107852
C2×#168107772
C2×#168107602
C2×#168105882
C2×C53×#4522
C2×#320153