Finite Group Databasebeta

← C2×#20286751 #28260762

Subgroups — C2×#20286751 #28260762

Order 13568.

2254 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811343C211yesmaximal, characteristic, complemented
2#20286751C2116yesmaximal, direct product factor
3C2×#16810982C211yesmaximal, characteristic, complemented
4C2×#16810961C211yesmaximal, characteristic, complemented
5C2×#16810944C211yesmaximal, characteristic, complemented
6C2×#16810913C211yesmaximal, characteristic, complemented
7C2×#16810879C211yesmaximal, characteristic, complemented
8C2×#16810850C211yesmaximal, characteristic, complemented
9C2×#16810842C211yesmaximal, characteristic, complemented
10C2×#16810785C211yesmaximal, characteristic, complemented
11C2×#16810774C211yesmaximal, characteristic, complemented
12C2×#16810723C211yesmaximal, characteristic, complemented
13C2×#16810695C211yesmaximal, characteristic, complemented
14C2×#16810628C211yesmaximal, characteristic, complemented
15C2×#16810619C211yesmaximal, characteristic, complemented
16C2×C53×#546C211yesmaximal, characteristic
17C22×#11719925C2211yescharacteristic, complemented
18C22×#11719923C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21C23×#88322C2211yescharacteristic, complemented
22#16811343—24no—
23#16811343C2218yescomplemented
24C2×#13133217C2211yescharacteristic, complemented
25C2×#13133210—21no—
26C2×#13133210—21no—
27C2×#13133204—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133196C2211yescharacteristic, complemented
30C2×C4×Dic106C2211yescharacteristic, complemented
31C2×#13133182—21no—
32C2×#13133176C2211yescharacteristic
33C2×#13133176C2211yescharacteristic, complemented
34#16810982C2218yescomplemented
35#16810961C2218yescomplemented
36#16810944C2218yescomplemented
37#16810913C2218yescomplemented
38#16810879C2218yescomplemented
39#16810850C2218yescomplemented
40#16810842C2218yescomplemented
41#16810785C2218yescomplemented
42#16810774C2218yescomplemented
43#16810723C2218yescomplemented
44#16810695C2218yescomplemented
45C2×#13133150C2211yescharacteristic, complemented
46C2×#13133148C2211yescharacteristic, complemented
47C2×#13133148C2211yescharacteristic, complemented
48C2×C4⋊#88322C2211yescharacteristic, complemented
49#16810628C2218yescomplemented
50#16810619C2218yescomplemented
51C2×#13133141C2211yescharacteristic, complemented
52C2×#13133141C2211yescharacteristic, complemented
53C2×#13133141C2211yescharacteristic, complemented
54C2×#13133140C2211yescharacteristic, complemented
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×#13133138C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×C22⋊#88322C2211yescharacteristic, complemented
63C2×#13133128C2211yescharacteristic, complemented
64C22×#41×C53C2211yescharacteristic
65C23×D4×C53C2211yescharacteristic
66C53×#546—24no—
67C53×#546C2218yes—
68C2×#124×C53C2211yescharacteristic
69C2×#123×C53—21no—
70C2×C22⋊Q8×C53C2211yescharacteristic
71C2×#121×C53—21no—
72C2×#121×C53C2211yescharacteristic
73C2×#120×C53—21no—
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C22×C22⋊C4×C53—21no—
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×#11719925—42no—
80C2×#11719925C2314yescomplemented
81C2×#11719923—24no—
82C2×#11719923—42no—
83C2×#11719923C2314yes—
84C2×#11719923C2314yes—
85C2×#11719917—42no—
86C2×#11719917C2314yes—
87C22×#88322—42no—
88C22×#88322C2311yescharacteristic
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2314yescomplemented
93#13133217—22no—
94#13133217C2314yescomplemented
95#13133210—28no—
96#13133210—28no—
97#13133204—28no—
98#13133196—22no—
99#13133196—22no—
100#13133196C2314yes—
101#13133196C2314yescomplemented
102C4×Dic106—22no—
103C4×Dic106C2314yescomplemented
104#13133182—28no—
105#13133176—22no—
106#13133176—22no—
107#13133176C2314yes—
108#13133176C2314yescomplemented
109C2×C4⋊Dic53—21no—
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×#11719919—21no—
116C2×C22⋊Dic53—21no—
117C2×C22⋊Dic53—21no—
118C2×C22⋊Dic53—21no—
119C2×C22⋊Dic53—21no—
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53—21no—
123#13133150C2314yescomplemented
124#13133148C2314yescomplemented
125#13133148C2314yescomplemented
126C4⋊#88322C2314yescomplemented
127#13133141C2314yescomplemented
128#13133141C2314yescomplemented
129#13133141C2314yescomplemented
130#13133140C2314yescomplemented
131#13133138C2314yes—
132#13133138C2314yes—
133#13133138C2314yes—
134#13133138C2314yes—
135#13133138C2314yes—
136#13133138C2314yes—
137C22⋊#88322C2314yes—
138C22⋊#88322C2314yescomplemented
139#13133128C2314yescomplemented
140C25×C53—21no—
141C2×#41×C53—22no—
142C2×#41×C53—24no—
143C2×#41×C53—42no—
144C2×#41×C53C2314yes—
145C22×Q8×C53C2311yescharacteristic
146C22×D4×C53—24no—
147C22×D4×C53—21no—
148C22×D4×C53—21no—
149C22×D4×C53—21no—
150C22×D4×C53—22no—
151C22×D4×C53—42no—
152C22×D4×C53D411yescharacteristic
153C22×D4×C53C2311yescharacteristic
154C22×D4×C53C2314yes—
155C22×D4×C53C2311yescharacteristic
156C23×C4×C53—21no—
157C23×C4×C53—21no—
158C23×C4×C53C2311yescharacteristic
159C23×C4×C53C2311yescharacteristic
160#124×C53—22no—
161#124×C53C2314yes—
162#123×C53—28no—
163C22⋊Q8×C53—22no—
164C22⋊Q8×C53C2314yes—
165#121×C53—28no—
166#121×C53—22no—
167#121×C53C2314yes—
168#120×C53—28no—
169C4×D4×C53—22no—
170C4×D4×C53D414yes—
171C4×D4×C53C2314yes—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53D411yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—28no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C22⋊C4×C53—21no—
181C2×C22⋊C4×C53—21no—
182C2×C22⋊C4×C53D411yescharacteristic
183C2×C22⋊C4×C53D411yescharacteristic
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C24×C53—21no—
187C24×C53—24no—
188C24×C53—44no—
189C24×C53—44no—
190C24×C53—82no—
191C24×C53C2×D411yescharacteristic
192C24×C53C2×D411yescharacteristic
193#41×C53—28no—
194#41×C53—44no—
195#41×C53—48no—
196C2×Q8×C53—21no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53C2412yes—
200C2×D4×C53—28no—
201C2×D4×C53—24no—
202C2×D4×C53—24no—
203C2×D4×C53—21no—
204C2×D4×C53—24no—
205C2×D4×C53—21no—
206C2×D4×C53—22no—
207C2×D4×C53—22no—
208C2×D4×C53—22no—
209C2×D4×C53—44no—
210C2×D4×C53—48no—
211C2×D4×C53—42no—
212C2×D4×C53—44no—
213C2×D4×C53—44no—
214C2×D4×C53—82no—
215C2×D4×C53C2×D414yes—
216C2×D4×C53#4114yes—
217C2×D4×C53C2412yes—
218C2×D4×C53C2412yes—
219C22×C4×C53—22no—
220C22×C4×C53—22no—
221C22×C4×C53—22no—
222C22×C4×C53—22no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—24no—
226C22×C4×C53—24no—
227C22×C4×C53—44no—
228C22×C4×C53—82no—
229C22×C4×C53C2×D411yescharacteristic
230C22×C4×C53C2×D411yescharacteristic
231C22×C4×C53C2×D411yescharacteristic
232C22×C4×C53C2×D411yescharacteristic
233C22×C4×C53C2×D412yes—
234C22×C4×C53C2×D412yes—
235C22×C4×C53C2412yes—
236C22×C4×C53C2412yes—
237C22×C4×C53C2411yescharacteristic
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C2×Dic106—22no—
243C2×Dic106—22no—
244C2×Dic106—24no—
245C2×Dic106—21no—
246C2×Dic106—44no—
247C2×Dic106C2412yes—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2×D414yes—
251C4⋊C4×C53C2412yes—
252C22⋊C4×C53—24no—
253C22⋊C4×C53—24no—
254C22⋊C4×C53—24no—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—24no—
257C22⋊C4×C53C2×D414yes—
258C22⋊C4×C53C2×D414yes—
259C42×C53C2×D412yes—
260C42×C53C2412yes—
261C22⋊Dic53—24no—
262C22⋊Dic53—24no—
263C22⋊Dic53—24no—
264C22⋊Dic53—24no—
265#11719925—44no—
266#11719923—28no—
267#11719923—44no—
268C4⋊Dic53—24no—
269C4⋊Dic53—21no—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53C2412yes—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53—24no—
281#11719917—44no—
282C2×#88322—22no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322—22no—
286C2×#88322—44no—
287C2×#88322C2412yes—
288C2×#88322C2412yes—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—24no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—48no—
301C23×C53—48no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—84no—
308C23×C53—816no—
309C23×C53C22×D412yes—
310C23×C53C22×D412yes—
311C23×C53C22×D411yescharacteristic
312Q8×C53—22no—
313Q8×C53—22no—
314Q8×C53—42no—
315D4×C53—24no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—44no—
320D4×C53—48no—
321D4×C53—48no—
322D4×C53—42no—
323D4×C53—84no—
324D4×C53C2×#4114yes—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—24no—
330C2×C4×C53—24no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—48no—
338C2×C4×C53—42no—
339C2×C4×C53—42no—
340C2×C4×C53—84no—
341C2×C4×C53C22×D412yes—
342C2×C4×C53C22×D412yes—
343C2×C4×C53C22×D412yes—
344C2×C4×C53C22×D412yes—
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C2×#4112yes—
347C2×C4×C53H(5,𝔽2)12yes—
348C2×C4×C53C2511yescharacteristic
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53—22no—
352C2×Dic53—22no—
353C2×Dic53—42no—
354C2×Dic53—42no—
355C2×Dic53—42no—
356C2×Dic53—42no—
357Dic106—22no—
358Dic106—22no—
359Dic106—48no—
360Dic106—42no—
361#88322—22no—
362#88322—22no—
363#88322—22no—
364#88322—22no—
365C2×#3311—531nomaximal, Sylow
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—24no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—22no—
372C22×C53—22no—
373C22×C53—44no—
374C22×C53—44no—
375C22×C53—48no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—816no—
382C22×C53—84no—
383C22×C53#54612yes—
384C22×C53#57512yes—
385C22×C53#57712yes—
386C22×C53C23×D411yescharacteristic
387C4×C53—22no—
388C4×C53—22no—
389C4×C53—22no—
390C4×C53—22no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53#54612yes—
394C4×C53C22×#4111yescharacteristic
395C4×C53C2×H(5,𝔽2)11yescharacteristic
396Dic53—42no—
397Dic53—42no—
398Dic53—42no—
399Dic53—42no—
400C2×#556—531no—
401C2×#546D5311yescharacteristic
402#3311—5316no—
403C2×#489—531no—
404C2×#485—531no—
405C2×#482—531no—
406C2×#476—531no—
407C2×#470—531no—
408C2×#465—531no—
409C2×#464—531no—
410C2×#452—531no—
411C2×#450—531no—
412C2×#440—531no—
413C2×#435—531no—
414C2×#418—531no—
415C2×#416—531no—
416C2×C53—42no—
417C2×C53—42no—
418C2×C53—44no—
419C2×C53—82no—
420C2×C53#331114yescomplemented
421C2×C53C2×#54611yescharacteristic
422C2×C53C2×#57511yescharacteristic
423C2×C53C2×#57711yescharacteristic
424C22×#41C2×D5311yescharacteristic
425C23×D4C2×D5311yescharacteristic
426C22×Q16—531no—
427C22×SD16—531no—
428C22×SD16—531no—
429C22×M16—531no—
430C23×C8—531no—
431#556—538no—
432#556—1064no—
433#546—24no—
434#546C2×D5318yes—
435C2×C4⋊Q8—531no—
436C2×#126—1061no—
437C2×#126—1061no—
438C2×#124—1061no—
439C2×#124C2×D5311yescharacteristic
440C2×#123—21no—
441C2×C22⋊Q8—531no—
442C2×C22⋊Q8—531no—
443C2×C22⋊Q8C2×D5311yescharacteristic
444C2×#121—21no—
445C2×#121C2×D5311yescharacteristic
446C2×#120—21no—
447C2×C4×Q8—531no—
448C2×C4×Q8—1061no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×C4×D4C2×D5311yescharacteristic
451C2×#117—531no—
452C2×#117—531no—
453C22×C22⋊C4—21no—
454#489—538no—
455#485—538no—
456#482—538no—
457#476—538no—
458#470—538no—
459#465—538no—
460#464—538no—
461#452—538no—
462#450—538no—
463#440—538no—
464#435—538no—
465C2×#107—531no—
466C2×#106—531no—
467C2×#106—531no—
468C2×C4⋊C8—531no—
469#418—538no—
470#416—538no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102—531no—
481C2×C22⋊C8—531no—
482C2×C22⋊C8—531no—
483C2×#97—531no—
484C53C2×#331111yescharacteristic, complemented, Sylow
485C25—21no—
486C2×#41—22no—
487C2×#41—24no—
488C2×#41—42no—
489C2×#41C22×D5314yes—
490C22×Q8—531no—
491C22×Q8—1061no—
492C22×Q8C22×D5311yescharacteristic
493C22×D4—24no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—42no—
499C22×D4C22⋊D5311yescharacteristic
500C22×D4C22×D5311yescharacteristic
501C22×D4C22×D5314yes—
502C22×D4C22×D5311yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×Q16—534no—
508C2×Q16—2122no—
509C2×SD16—534no—
510C2×SD16—534no—
511C2×SD16—1064no—
512C2×SD16—2122no—
513C2×M16—534no—
514C2×M16—2122no—
515C22×C8—531no—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8—531no—
519C22×C8—534no—
520C22×C8—2122no—
521C4⋊Q8—534no—
522C4⋊Q8—1062no—
523#126—1068no—
524#126—1068no—
525#124—22no—
526#124—1068no—
527#124C22×D5314yes—
528#123—28no—
529C22⋊Q8—22no—
530C22⋊Q8—534no—
531C22⋊Q8—534no—
532C22⋊Q8—1062no—
533C22⋊Q8—1062no—
534C22⋊Q8C22×D5314yes—
535#121—22no—
536#121—28no—
537#121C22×D5314yes—
538#120—28no—
539C4×Q8—534no—
540C4×Q8—1068no—
541C4×Q8—1062no—
542C4×D4—22no—
543C4×D4C22⋊D5314yes—
544C4×D4C22×D5314yes—
545C4×D4C22×D5314yes—
546#117—534no—
547#117—534no—
548#117—1062no—
549#117—1062no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4C22⋊D5311yescharacteristic
559C2×C4⋊C4C22×D5311yescharacteristic
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4C22⋊D5311yescharacteristic
571C2×C22⋊C4C22⋊D5311yescharacteristic
572C2×C42—1061no—
573C2×C42—1061no—
574C2×C42—1061no—
575C2×C42C22×D5311yescharacteristic
576#107—534no—
577#106—534no—
578#106—534no—
579C4⋊C8—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588#102—534no—
589#102—534no—
590C22⋊C8—534no—
591C22⋊C8—534no—
592#97—534no—
593C24—21no—
594C24—21no—
595C24—24no—
596C24—44no—
597C24—44no—
598C24—82no—
599C24C2×C22⋊D5311yescharacteristic
600C24C2×C22⋊D5311yescharacteristic
601#41—28no—
602#41—44no—
603#41—48no—
604C2×Q8—21no—
605C2×Q8—22no—
606C2×Q8—22no—
607C2×Q8—532no—
608C2×Q8—1061no—
609C2×Q8—1064no—
610C2×Q8—1062no—
611C2×Q8—1062no—
612C2×Q8—2124no—
613C2×Q8C23×D5312yes—
614C2×D4—28no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—44no—
624C2×D4—48no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—82no—
629C2×D4#1171994714yes—
630C2×D4C2×C22⋊D5314yes—
631C2×D4C23×D5312yes—
632C2×D4C23×D5312yes—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—24no—
641C22×C4—44no—
642C22×C4—82no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4C2×C22⋊D5312yes—
648C22×C4C2×C22⋊D5312yes—
649C22×C4C2×C22⋊D5311yescharacteristic
650C22×C4C2×C22⋊D5311yescharacteristic
651C22×C4C2×C22⋊D5311yescharacteristic
652C22×C4C2×C22⋊D5311yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656Q16—2124no—
657SD16—1068no—
658SD16—2124no—
659M16—2124no—
660C2×C8—532no—
661C2×C8—532no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8—1062no—
667C2×C8—1062no—
668C2×C8—2124no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—532no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—1061no—
675C4⋊C4—1061no—
676C4⋊C4—1061no—
677C4⋊C4—1064no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4C2×C22⋊D5314yes—
682C4⋊C4C23×D5312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4—1064no—
692C22⋊C4C2×C22⋊D5314yes—
693C22⋊C4C2×C22⋊D5314yes—
694C42—1064no—
695C42—1064no—
696C42—1064no—
697C42C2×C22⋊D5312yes—
698C42C23×D5312yes—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—48no—
709C23—48no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—84no—
716C23—816no—
717C23C22×C22⋊D5312yes—
718C23C22×C22⋊D5312yes—
719C23C22×C22⋊D5311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—42no—
723Q8—1062no—
724Q8—1062no—
725Q8—2128no—
726Q8—2122no—
727D4—24no—
728D4—22no—
729D4—22no—
730D4—22no—
731D4—44no—
732D4—48no—
733D4—48no—
734D4—42no—
735D4—84no—
736D4C2×#1171994714yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—84no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—2122no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4C22×C22⋊D5312yes—
762C2×C4C22×C22⋊D5312yes—
763C2×C4C22×C22⋊D5312yes—
764C2×C4C22×C22⋊D5312yes—
765C2×C4C22×C22⋊D5311yescharacteristic
766C2×C4C2×#1171994712yes—
767C2×C4#1313326212yes—
768C2×C4C24×D5311yescharacteristic
769C8—1062no—
770C8—1062no—
771C8—1062no—
772C8—1062no—
773C22—22no—
774C22—22no—
775C22—24no—
776C22—22no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—44no—
781C22—44no—
782C22—48no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—816no—
789C22—84no—
790C22#1681126712yes—
791C22#1681142112yes—
792C22#1681143412yes—
793C22C23×C22⋊D5311yescharacteristic
794C4—22no—
795C4—22no—
796C4—22no—
797C4—22no—
798C4—42no—
799C4—42no—
800C4—2122no—
801C4—2122no—
802C4—2122no—
803C4—2122no—
804C4#1681126712yes—
805C4C22×#1171994711yescharacteristic
806C4C2×#1313326211yescharacteristic
807C2—42no—
808C2—42no—
809C2—44no—
810C2—82no—
811C2#2028675114yesdirect product factor
812C2C2×#1681126711yescharacteristic
813C2C2×#1681142111yescharacteristic
814C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#546C2
socleC23×C53C22×D4
hypercenterC2×#546D53
hypocenterC53C2×#3311
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16811343C2semidirect
2. #20286751C2direct (N × H)
3. C2×#16810982C2semidirect
4. C2×#16810961C2semidirect
5. C2×#16810944C2semidirect
6. C2×#16810913C2semidirect
7. C2×#16810879C2semidirect
8. C2×#16810850C2semidirect
9. C2×#16810842C2semidirect
10. C2×#16810785C2semidirect
11. C2×#16810774C2semidirect
12. C2×#16810723C2semidirect
13. C2×#16810695C2semidirect
14. C2×#16810628C2semidirect
15. C2×#16810619C2semidirect
17. C22×#11719925C22semidirect
21. C23×#88322C22semidirect
23. #16811343C22semidirect
24. C2×#13133217C22semidirect
29. C2×#13133196C22semidirect
30. C2×C4×Dic106C22semidirect
33. C2×#13133176C22semidirect
34. #16810982C22semidirect
35. #16810961C22semidirect
36. #16810944C22semidirect
37. #16810913C22semidirect
38. #16810879C22semidirect
39. #16810850C22semidirect
40. #16810842C22semidirect
41. #16810785C22semidirect
42. #16810774C22semidirect
43. #16810723C22semidirect
44. #16810695C22semidirect
45. C2×#13133150C22semidirect
46. C2×#13133148C22semidirect
47. C2×#13133148C22semidirect
48. C2×C4⋊#88322C22semidirect
49. #16810628C22semidirect
50. #16810619C22semidirect
51. C2×#13133141C22semidirect
52. C2×#13133141C22semidirect
53. C2×#13133141C22semidirect
54. C2×#13133140C22semidirect
62. C2×C22⋊#88322C22semidirect
63. C2×#13133128C22semidirect
80. C2×#11719925C23semidirect
92. C22×#88322C23semidirect
94. #13133217C23semidirect
101. #13133196C23semidirect
103. C4×Dic106C23semidirect
108. #13133176C23semidirect
123. #13133150C23semidirect
124. #13133148C23semidirect
125. #13133148C23semidirect
126. C4⋊#88322C23semidirect
127. #13133141C23semidirect
128. #13133141C23semidirect
129. #13133141C23semidirect
130. #13133140C23semidirect
138. C22⋊#88322C23semidirect
139. #13133128C23semidirect
420. C2×C53#3311semidirect
484. C53C2×#3311semidirect
811. C2#20286751direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113432
#202867512
C2×#168109822
C2×#168109612
C2×#168109442
C2×#168109132
C2×#168108792
C2×#168108502
C2×#168108422
C2×#168107852
C2×#168107742
C2×#168107232
C2×#168106952
C2×#168106282
C2×#168106192
C2×C53×#5462
C2×#331153