Finite Group Databasebeta

← #28254849

Subgroups — #28254849

Order 13568.

2342 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2#20285545C214yesmaximal, complemented
3#20285536C212yesmaximal, complemented
4#20285517C212yesmaximal, complemented
5#20285496C214yesmaximal, complemented
6#20285487C212yesmaximal, complemented
7#20285468C212yesmaximal, complemented
8#20284659C212yesmaximal, complemented
9#20284638C212yesmaximal, complemented
10#20284341C214yesmaximal, complemented
11#20283973C212yesmaximal, complemented
12#20283949C212yesmaximal, complemented
13C2×#16810587C211yesmaximal, characteristic, complemented
14C22×C22⋊Q8×C53C211yesmaximal, characteristic, complemented
15C22×#11719945C2211yescharacteristic
16C2×#13133248C2214yescomplemented
17C22×#11719917C2212yescomplemented
18#16811134—21no—
19#16811134—21no—
20#16811134—21no—
21#16811134—21no—
22#16811134C2212yes—
23#16811134C2212yes—
24#16811134C2212yes—
25#16811134C2212yes—
26C2×#13133200—21no—
27C2×#13133196C2211yescharacteristic
28C2×#13133196C2211yescharacteristic
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133186—21no—
32C2×C4×C22⋊D53—21no—
33C2×C4×C22⋊D53—21no—
34C2×#13133176C2211yescharacteristic
35#16810961C2218yescomplemented
36#16810958C2214yescomplemented
37#16810956C2214yescomplemented
38#16810953C2214yescomplemented
39#16810951C2214yescomplemented
40#16810941C2214yescomplemented
41#16810936C2214yescomplemented
42#16810879C2218yescomplemented
43#16810871C2218yescomplemented
44#16810862C2218yescomplemented
45#16810854C2218yescomplemented
46#16810783C2218yescomplemented
47#16810779C2214yescomplemented
48#16810779C2214yescomplemented
49#16810778C2214yescomplemented
50#16810773C2214yescomplemented
51#16810762C2214yescomplemented
52#16810762C2214yescomplemented
53#16810663C2214yescomplemented
54#16810632C2214yescomplemented
55#16810622C2214yescomplemented
56#16810587C2212yes—
57#16810587C2212yes—
58#16810587C2212yescomplemented
59#16810587C2212yescomplemented
60C2×C22⋊#88322C2212yes—
61C2×C22⋊#88322C2212yescomplemented
62C23×Q8×C53C2211yescharacteristic, complemented
63C24×C4×C53C2211yescharacteristic
64C2×C22⋊Q8×C53—21no—
65C2×C22⋊Q8×C53—21no—
66C2×C22⋊Q8×C53—21no—
67C2×C22⋊Q8×C53—21no—
68C2×C22⋊Q8×C53—21no—
69C2×C22⋊Q8×C53—21no—
70C2×C22⋊Q8×C53C2212yes—
71C2×C22⋊Q8×C53C2212yes—
72C2×C22⋊Q8×C53C2212yes—
73C2×C22⋊Q8×C53C2212yescomplemented
74C2×C22⋊Q8×C53C2212yescomplemented
75C2×C22⋊Q8×C53C2212yescomplemented
76C22×C4⋊C4×C53—21no—
77C22×C4⋊C4×C53C2211yescharacteristic, complemented
78C22×C22⋊C4×C53—21no—
79C2×#11719945—21no—
80C2×#11719945—21no—
81C2×#11719945—44no—
82C2×#11719945C2312yes—
83C2×#11719945C2312yes—
84C22×Dic106C2311yescharacteristic
85C22×D212C2311yescharacteristic
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53—21no—
89C22×C4×D53—21no—
90#13133248—48no—
91C2×#11719925C2318yescomplemented
92C2×#11719924C2318yescomplemented
93C2×#11719917—44no—
94C2×#11719917C2314yes—
95C2×#11719917C2314yes—
96C22×#88322C2314yes—
97#13133200—22no—
98#13133200—22no—
99#13133200—22no—
100#13133200—22no—
101#13133196—21no—
102#13133196—21no—
103#13133196—21no—
104#13133196—21no—
105#13133196C2312yes—
106#13133196C2312yes—
107#13133196C2312yes—
108#13133196C2312yes—
109#13133191—21no—
110#13133191—21no—
111#13133191—21no—
112#13133191—21no—
113#13133191C2312yes—
114#13133191C2312yes—
115#13133191C2312yes—
116#13133191C2312yes—
117#13133186—22no—
118#13133186—22no—
119#13133186—22no—
120#13133186—22no—
121C4×C22⋊D53—22no—
122C4×C22⋊D53—22no—
123C4×C22⋊D53—22no—
124C4×C22⋊D53—22no—
125C4×C22⋊D53—22no—
126C4×C22⋊D53—22no—
127C4×C22⋊D53—22no—
128C4×C22⋊D53—22no—
129#13133176—21no—
130#13133176—21no—
131#13133176C2312yes—
132#13133176C2312yes—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×C4×Dic53—21no—
143#13133150C2318yescomplemented
144#13133148C2318yescomplemented
145#13133141C2318yescomplemented
146#13133141C2318yescomplemented
147#13133140C2318yescomplemented
148#13133137C2318yescomplemented
149C22⋊#88322C2314yes—
150C22⋊#88322C2314yes—
151C22⋊#88322C2314yes—
152C22⋊#88322C2314yes—
153C25×C53D411yescharacteristic
154C22×Q8×C53—21no—
155C22×Q8×C53—21no—
156C22×Q8×C53—21no—
157C22×Q8×C53—44no—
158C22×Q8×C53C2312yes—
159C22×Q8×C53C2312yes—
160C22×Q8×C53C2312yes—
161C23×C4×C53—21no—
162C23×C4×C53—21no—
163C23×C4×C53—44no—
164C23×C4×C53D411yescharacteristic
165C23×C4×C53D411yescharacteristic
166C23×C4×C53D411yescharacteristic
167C23×C4×C53D411yescharacteristic
168C23×C4×C53D411yescharacteristic
169C23×C4×C53D411yescharacteristic
170C23×C4×C53D411yescharacteristic
171C23×C4×C53C2311yescharacteristic
172C23×C4×C53C2311yescharacteristic
173C23×C4×C53C2311yescharacteristic
174C23×C4×C53C2311yescharacteristic
175C23×C4×C53C2311yescharacteristic
176C23×C4×C53C2311yescharacteristic
177C23×C4×C53C2311yescharacteristic
178C22⋊Q8×C53—22no—
179C22⋊Q8×C53—22no—
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53—22no—
182C22⋊Q8×C53—22no—
183C22⋊Q8×C53—22no—
184C22⋊Q8×C53—22no—
185C22⋊Q8×C53—22no—
186C22⋊Q8×C53—22no—
187C22⋊Q8×C53—22no—
188C22⋊Q8×C53—22no—
189C22⋊Q8×C53—22no—
190C22⋊Q8×C53C2314yes—
191C22⋊Q8×C53C2314yes—
192C22⋊Q8×C53C2314yes—
193C22⋊Q8×C53C2314yes—
194C2×C4⋊C4×C53—22no—
195C2×C4⋊C4×C53—22no—
196C2×C4⋊C4×C53—22no—
197C2×C4⋊C4×C53—22no—
198C2×C4⋊C4×C53—22no—
199C2×C4⋊C4×C53—22no—
200C2×C4⋊C4×C53—21no—
201C2×C4⋊C4×C53—21no—
202C2×C4⋊C4×C53—21no—
203C2×C4⋊C4×C53C2312yes—
204C2×C4⋊C4×C53C2312yes—
205C2×C4⋊C4×C53C2312yes—
206C2×C22⋊C4×C53—22no—
207C2×C22⋊C4×C53—22no—
208C2×C22⋊C4×C53—22no—
209C2×C22⋊C4×C53—22no—
210C2×C22⋊C4×C53—22no—
211C2×C22⋊C4×C53—22no—
212C24×C53—24no—
213C24×C53—42no—
214C24×C53—42no—
215C24×C53C2×D411yescharacteristic
216C24×C53C2×D411yescharacteristic
217C24×C53C2×D411yescharacteristic
218C24×C53C2×D411yescharacteristic
219C24×C53C2×D411yescharacteristic
220C24×C53C2×D411yescharacteristic
221C24×C53C2×D411yescharacteristic
222C23×D53—21no—
223C2×Q8×C53—22no—
224C2×Q8×C53—22no—
225C2×Q8×C53—22no—
226C2×Q8×C53—28no—
227C2×Q8×C53—44no—
228C2×Q8×C53—44no—
229C2×Q8×C53—44no—
230C2×Q8×C53—44no—
231C2×Q8×C53—44no—
232C2×Q8×C53C2414yes—
233C22×C4×C53—24no—
234C22×C4×C53—24no—
235C22×C4×C53—24no—
236C22×C4×C53—22no—
237C22×C4×C53—22no—
238C22×C4×C53—22no—
239C22×C4×C53—22no—
240C22×C4×C53—22no—
241C22×C4×C53—22no—
242C22×C4×C53—42no—
243C22×C4×C53—42no—
244C22×C4×C53—42no—
245C22×C4×C53—42no—
246C22×C4×C53—42no—
247C22×C4×C53—42no—
248C22×C4×C53—42no—
249C22×C4×C53—42no—
250C22×C4×C53—42no—
251C22×C4×C53—42no—
252C22×C4×C53—42no—
253C22×C4×C53—44no—
254C22×C4×C53—44no—
255C22×C4×C53C2×D411yescharacteristic
256C22×C4×C53C2×D411yescharacteristic
257C22×C4×C53C2×D411yescharacteristic
258C22×C4×C53C2×D411yescharacteristic
259C22×C4×C53C2×D411yescharacteristic
260C22×C4×C53C2×D411yescharacteristic
261C22×C4×C53C2×D411yescharacteristic
262C22×C4×C53C2×D411yescharacteristic
263C22×C4×C53C2×D411yescharacteristic
264C22×C4×C53C2×D411yescharacteristic
265C22×C4×C53C2×D411yescharacteristic
266C22×C4×C53C2×D411yescharacteristic
267C22×C4×C53C2×D411yescharacteristic
268C22×C4×C53C2×D411yescharacteristic
269C22×C4×C53C2×D411yescharacteristic
270C22×C4×C53C2×D411yescharacteristic
271C22×C4×C53C2×D411yescharacteristic
272C22×C4×C53C2×D411yescharacteristic
273C22×C4×C53C2×D411yescharacteristic
274C22×C4×C53C2×D411yescharacteristic
275C22×C4×C53C2×D411yescharacteristic
276C22×C4×C53C2411yescharacteristic
277C22×C4×C53C2411yescharacteristic
278C22×C4×C53C2411yescharacteristic
279C22×C4×C53C2411yescharacteristic
280C22×C4×C53C2411yescharacteristic
281C22×C4×C53C2411yescharacteristic
282C22×C4×C53C2411yescharacteristic
283C2×C22⋊D53—22no—
284C2×C22⋊D53—22no—
285C2×C22⋊D53—22no—
286C2×C22⋊D53—22no—
287C2×C22⋊D53—22no—
288C2×C22⋊D53—22no—
289C2×C22⋊D53—44no—
290C2×C22⋊D53—44no—
291C2×C22⋊D53—44no—
292C22×Dic53—21no—
293C22×Dic53—21no—
294C22×Dic53—21no—
295#11719945—28no—
296#11719945—44no—
297#11719945—44no—
298#11719945—44no—
299C2×D212—21no—
300C2×D212—42no—
301C2×D212C2412yes—
302C2×C4×D53—22no—
303C2×C4×D53—22no—
304C2×C4×D53—44no—
305C2×Dic106—21no—
306C2×Dic106—42no—
307C2×Dic106C2412yes—
308C4⋊C4×C53—24no—
309C4⋊C4×C53—24no—
310C4⋊C4×C53—24no—
311C4⋊C4×C53—24no—
312C4⋊C4×C53—22no—
313C4⋊C4×C53—22no—
314C4⋊C4×C53—22no—
315C4⋊C4×C53C2414yes—
316C22⋊C4×C53—24no—
317C22⋊C4×C53—24no—
318C22⋊C4×C53—24no—
319C22⋊C4×C53—24no—
320C22⋊Dic53—22no—
321C22⋊Dic53—22no—
322C22⋊Dic53—22no—
323C22⋊Dic53—22no—
324C22⋊Dic53—22no—
325C22⋊Dic53—22no—
326#11719925—48no—
327#11719924—48no—
328#11719921—22no—
329#11719921—22no—
330#11719921—22no—
331#11719921—22no—
332C4⋊Dic53—21no—
333C4⋊Dic53—21no—
334C4⋊Dic53C2412yes—
335C4⋊Dic53C2412yes—
336#11719919—22no—
337#11719919—22no—
338#11719919—22no—
339#11719919—22no—
340C4×Dic53—22no—
341C4×Dic53—22no—
342#11719917—28no—
343#11719917—44no—
344C2×#88322—44no—
345C2×#88322C2418yes—
346C23×C53—22no—
347C23×C53—22no—
348C23×C53—22no—
349C23×C53—22no—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—22no—
353C23×C53—22no—
354C23×C53—22no—
355C23×C53—22no—
356C23×C53—22no—
357C23×C53—22no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—416no—
367C23×C53#13714yescomplemented
368C23×C53C22×D411yescharacteristic
369C23×C53C22×D411yescharacteristic
370C23×C53C22×D411yescharacteristic
371C23×C53C22×D411yescharacteristic
372C23×C53C22×D411yescharacteristic
373C23×C53C22×D411yescharacteristic
374C23×C53C22×D411yescharacteristic
375C22×D53—22no—
376C22×D53—42no—
377C22×D53—42no—
378C22×D53—42no—
379Q8×C53—28no—
380Q8×C53—44no—
381Q8×C53—44no—
382Q8×C53—44no—
383C2×C4×C53—22no—
384C2×C4×C53—22no—
385C2×C4×C53—22no—
386C2×C4×C53—22no—
387C2×C4×C53—22no—
388C2×C4×C53—22no—
389C2×C4×C53—22no—
390C2×C4×C53—22no—
391C2×C4×C53—22no—
392C2×C4×C53—22no—
393C2×C4×C53—22no—
394C2×C4×C53—22no—
395C2×C4×C53—22no—
396C2×C4×C53—22no—
397C2×C4×C53—22no—
398C2×C4×C53—24no—
399C2×C4×C53—24no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53—41no—
406C2×C4×C53—41no—
407C2×C4×C53—41no—
408C2×C4×C53—41no—
409C2×C4×C53—41no—
410C2×C4×C53—41no—
411C2×C4×C53—41no—
412C2×C4×C53—44no—
413C2×C4×C53—44no—
414C2×C4×C53—44no—
415C2×C4×C53—44no—
416C2×C4×C53—44no—
417C2×C4×C53—44no—
418C2×C4×C53C22×D411yescharacteristic
419C2×C4×C53C22×D411yescharacteristic
420C2×C4×C53C22×D411yescharacteristic
421C2×C4×C53C22×D411yescharacteristic
422C2×C4×C53C22×D411yescharacteristic
423C2×C4×C53C22×D411yescharacteristic
424C2×C4×C53C22×D411yescharacteristic
425C2×C4×C53H(5,𝔽2)14yes—
426C2×C4×C53C2511yescharacteristic
427C22⋊D53—44no—
428C22⋊D53—44no—
429C22⋊D53—44no—
430C22⋊D53—44no—
431C22⋊D53—44no—
432C22⋊D53—44no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—22no—
436C2×Dic53—42no—
437C2×Dic53—42no—
438C2×Dic53—42no—
439D212—24no—
440D212—42no—
441C4×D53—44no—
442C4×D53—44no—
443Dic106—24no—
444Dic106—42no—
445#88322—28no—
446#60751—531nomaximal, Sylow
447C22×C53—28no—
448C22×C53—21no—
449C22×C53—21no—
450C22×C53—21no—
451C22×C53—21no—
452C22×C53—21no—
453C22×C53—21no—
454C22×C53—21no—
455C22×C53—21no—
456C22×C53—21no—
457C22×C53—21no—
458C22×C53—21no—
459C22×C53—21no—
460C22×C53—21no—
461C22×C53—21no—
462C22×C53—21no—
463C22×C53—21no—
464C22×C53—44no—
465C22×C53—44no—
466C22×C53—44no—
467C22×C53—44no—
468C22×C53—44no—
469C22×C53—44no—
470C22×C53#53412yes—
471C22×C53C2×#13712yes—
472C22×C53C2×#13712yes—
473C22×C53C2×#13712yes—
474C22×C53#57512yes—
475C22×C53C23×D411yescharacteristic
476C2×D53—42no—
477C2×D53—42no—
478C2×D53—42no—
479C2×D53—84no—
480C4×C53—21no—
481C4×C53—21no—
482C4×C53—21no—
483C4×C53—21no—
484C4×C53—21no—
485C4×C53—21no—
486C4×C53—44no—
487C4×C53—44no—
488C4×C53#53412yes—
489C4×C53C2×H(5,𝔽2)12yes—
490Dic53—42no—
491Dic53—42no—
492Dic53—42no—
493C2×#525—531no—
494C22×C22⋊Q8D5311yescharacteristic, complemented
495#3196—534no—
496#3195—532no—
497#3193—532no—
498#3190—534no—
499#3189—532no—
500#3187—532no—
501#3095—532no—
502#3092—532no—
503#3056—534no—
504#3007—532no—
505#3004—532no—
506C2×#407—531no—
507C2×C53—22no—
508C2×C53—22no—
509C2×C53—22no—
510C2×C53—22no—
511C2×C53—22no—
512C2×C53—41no—
513C2×C53—41no—
514C2×C53C2×#53411yescharacteristic
515C2×C53C22×#13711yescharacteristic
516C2×C53C2×#57511yescharacteristic
517D53—82no—
518C22×#41—531no—
519C23×Q8C2×D5311yescharacteristic, complemented
520C24×C4C2×D5311yescharacteristic
521C2×#137—534no—
522C22×M16—532no—
523#525—532no—
524#525—532no—
525#525—532no—
526#525—532no—
527#525—1061no—
528#525—1061no—
529#525—1061no—
530#525—1061no—
531C2×#123—1061no—
532C2×C22⋊Q8—21no—
533C2×C22⋊Q8—21no—
534C2×C22⋊Q8—21no—
535C2×C22⋊Q8—21no—
536C2×C22⋊Q8—21no—
537C2×C22⋊Q8—21no—
538C2×C22⋊Q8—531no—
539C2×C22⋊Q8—531no—
540C2×C22⋊Q8C2×D5312yes—
541C2×C22⋊Q8C2×D5312yes—
542C2×C22⋊Q8C2×D5312yes—
543C2×C22⋊Q8C2×D5312yescomplemented
544C2×C22⋊Q8C2×D5312yescomplemented
545C2×C22⋊Q8C2×D5312yescomplemented
546C2×#121—531no—
547C2×#121—531no—
548C2×#120—1061no—
549C2×C4×D4—1061no—
550C2×C4×D4—1061no—
551C2×#117—531no—
552C22×C4⋊C4—21no—
553C22×C4⋊C4C2×D5311yescharacteristic, complemented
554C22×C22⋊C4—21no—
555#485—538no—
556#484—534no—
557#484—534no—
558#483—534no—
559#483—534no—
560#481—534no—
561#480—534no—
562#470—538no—
563#468—538no—
564#467—538no—
565#465—538no—
566#452—538no—
567#451—534no—
568#451—534no—
569#451—534no—
570#450—534no—
571#448—534no—
572#448—534no—
573#428—534no—
574#419—534no—
575#417—534no—
576#407—532no—
577#407—532no—
578#407—532no—
579#407—532no—
580C2×C22⋊C8—532no—
581C2×C22⋊C8—532no—
582C53#6075111yescharacteristic, complemented, Sylow
583C25C22⋊D5311yescharacteristic
584C2×#41—532no—
585C2×#41—532no—
586C2×#41—1061no—
587C2×#41—1061no—
588C2×#41—2124no—
589C22×Q8—21no—
590C22×Q8—21no—
591C22×Q8—21no—
592C22×Q8—44no—
593C22×Q8—531no—
594C22×Q8C22×D5312yes—
595C22×Q8C22×D5312yes—
596C22×Q8C22×D5312yes—
597C22×D4—531no—
598C22×D4—1061no—
599C22×D4—1061no—
600C22×D4—1061no—
601C23×C4—21no—
602C23×C4—21no—
603C23×C4—44no—
604C23×C4—1061no—
605C23×C4C22⋊D5311yescharacteristic
606C23×C4C22⋊D5311yescharacteristic
607C23×C4C22⋊D5311yescharacteristic
608C23×C4C22⋊D5311yescharacteristic
609C23×C4C22⋊D5311yescharacteristic
610C23×C4C22⋊D5311yescharacteristic
611C23×C4C22⋊D5311yescharacteristic
612C23×C4C22×D5311yescharacteristic
613C23×C4C22×D5311yescharacteristic
614C23×C4C22×D5311yescharacteristic
615C23×C4C22×D5311yescharacteristic
616C23×C4C22×D5311yescharacteristic
617C23×C4C22×D5311yescharacteristic
618C23×C4C22×D5311yescharacteristic
619#137—2128no—
620C2×Q16—538no—
621C2×SD16—538no—
622C2×M16—534no—
623C2×M16—534no—
624C2×M16—2124no—
625C22×C8—534no—
626#123—1062no—
627#123—1062no—
628#123—1062no—
629#123—1062no—
630C22⋊Q8—22no—
631C22⋊Q8—22no—
632C22⋊Q8—22no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—532no—
643C22⋊Q8—532no—
644C22⋊Q8—532no—
645C22⋊Q8—532no—
646C22⋊Q8—1061no—
647C22⋊Q8—1061no—
648C22⋊Q8—1061no—
649C22⋊Q8—1061no—
650C22⋊Q8C22×D5314yes—
651C22⋊Q8C22×D5314yes—
652C22⋊Q8C22×D5314yes—
653C22⋊Q8C22×D5314yes—
654#121—532no—
655#121—532no—
656#121—532no—
657#121—532no—
658#121—1061no—
659#121—1061no—
660#121—1061no—
661#121—1061no—
662#120—1062no—
663#120—1062no—
664#120—1062no—
665#120—1062no—
666C4×D4—1062no—
667C4×D4—1062no—
668C4×D4—1062no—
669C4×D4—1062no—
670C4×D4—1062no—
671C4×D4—1062no—
672C4×D4—1062no—
673C4×D4—1062no—
674#117—532no—
675#117—532no—
676#117—1061no—
677#117—1061no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—531no—
688C2×C4⋊C4—531no—
689C2×C4⋊C4—1061no—
690C2×C4⋊C4—1061no—
691C2×C4⋊C4C22×D5312yes—
692C2×C4⋊C4C22×D5312yes—
693C2×C4⋊C4C22×D5312yes—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—1061no—
701C2×C22⋊C4—1061no—
702C2×C22⋊C4—1061no—
703C2×C22⋊C4—1061no—
704C2×C22⋊C4—1061no—
705C2×C42—1061no—
706#107—538no—
707#106—538no—
708#103—538no—
709#103—538no—
710#103—538no—
711#102—538no—
712C22⋊C8—534no—
713C22⋊C8—534no—
714C22⋊C8—534no—
715C22⋊C8—534no—
716C24—24no—
717C24—42no—
718C24—42no—
719C24—1061no—
720C24C2×C22⋊D5311yescharacteristic
721C24C2×C22⋊D5311yescharacteristic
722C24C2×C22⋊D5311yescharacteristic
723C24C2×C22⋊D5311yescharacteristic
724C24C2×C22⋊D5311yescharacteristic
725C24C2×C22⋊D5311yescharacteristic
726C24C2×C22⋊D5311yescharacteristic
727#41—1068no—
728#41—2124no—
729#41—2124no—
730#41—2124no—
731C2×Q8—22no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—28no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—44no—
738C2×Q8—44no—
739C2×Q8—44no—
740C2×Q8—532no—
741C2×Q8—1061no—
742C2×Q8—2122no—
743C2×Q8C23×D5314yes—
744C2×D4—532no—
745C2×D4—1062no—
746C2×D4—1062no—
747C2×D4—1062no—
748C2×D4—1062no—
749C2×D4—1062no—
750C2×D4—1062no—
751C2×D4—1061no—
752C2×D4—2122no—
753C2×D4—2124no—
754C2×D4—2124no—
755C2×D4—2124no—
756C22×C4—24no—
757C22×C4—24no—
758C22×C4—24no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—42no—
766C22×C4—42no—
767C22×C4—42no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—42no—
771C22×C4—42no—
772C22×C4—42no—
773C22×C4—42no—
774C22×C4—42no—
775C22×C4—42no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1062no—
782C22×C4—1062no—
783C22×C4—2124no—
784C22×C4C2×C22⋊D5311yescharacteristic
785C22×C4C2×C22⋊D5311yescharacteristic
786C22×C4C2×C22⋊D5311yescharacteristic
787C22×C4C2×C22⋊D5311yescharacteristic
788C22×C4C2×C22⋊D5311yescharacteristic
789C22×C4C2×C22⋊D5311yescharacteristic
790C22×C4C2×C22⋊D5311yescharacteristic
791C22×C4C2×C22⋊D5311yescharacteristic
792C22×C4C2×C22⋊D5311yescharacteristic
793C22×C4C2×C22⋊D5311yescharacteristic
794C22×C4C2×C22⋊D5311yescharacteristic
795C22×C4C2×C22⋊D5311yescharacteristic
796C22×C4C2×C22⋊D5311yescharacteristic
797C22×C4C2×C22⋊D5311yescharacteristic
798C22×C4C2×C22⋊D5311yescharacteristic
799C22×C4C2×C22⋊D5311yescharacteristic
800C22×C4C2×C22⋊D5311yescharacteristic
801C22×C4C2×C22⋊D5311yescharacteristic
802C22×C4C2×C22⋊D5311yescharacteristic
803C22×C4C2×C22⋊D5311yescharacteristic
804C22×C4C2×C22⋊D5311yescharacteristic
805C22×C4C23×D5311yescharacteristic
806C22×C4C23×D5311yescharacteristic
807C22×C4C23×D5311yescharacteristic
808C22×C4C23×D5311yescharacteristic
809C22×C4C23×D5311yescharacteristic
810C22×C4C23×D5311yescharacteristic
811C22×C4C23×D5311yescharacteristic
812Q16—2128no—
813SD16—2128no—
814M16—1068no—
815M16—2124no—
816C2×C8—538no—
817C2×C8—2124no—
818C4⋊C4—24no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—532no—
826C4⋊C4—532no—
827C4⋊C4—1061no—
828C4⋊C4—1061no—
829C4⋊C4—1062no—
830C4⋊C4—1062no—
831C4⋊C4—1062no—
832C4⋊C4—1062no—
833C4⋊C4C23×D5314yes—
834C22⋊C4—24no—
835C22⋊C4—24no—
836C22⋊C4—24no—
837C22⋊C4—24no—
838C22⋊C4—1062no—
839C22⋊C4—1062no—
840C22⋊C4—1062no—
841C22⋊C4—1062no—
842C22⋊C4—1062no—
843C22⋊C4—1062no—
844C22⋊C4—1062no—
845C22⋊C4—1062no—
846C22⋊C4—1062no—
847C22⋊C4—1062no—
848C42—1062no—
849C42—1062no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—416no—
871C23—1062no—
872C23—2122no—
873C23—2122no—
874C23—2122no—
875C23#1313324814yescomplemented
876C23C22×C22⋊D5311yescharacteristic
877C23C22×C22⋊D5311yescharacteristic
878C23C22×C22⋊D5311yescharacteristic
879C23C22×C22⋊D5311yescharacteristic
880C23C22×C22⋊D5311yescharacteristic
881C23C22×C22⋊D5311yescharacteristic
882C23C22×C22⋊D5311yescharacteristic
883Q8—28no—
884Q8—44no—
885Q8—44no—
886Q8—44no—
887Q8—1064no—
888Q8—2122no—
889D4—1064no—
890D4—2122no—
891D4—2124no—
892D4—2124no—
893D4—2124no—
894D4—2124no—
895D4—2124no—
896D4—2124no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—1062no—
933C2×C4—1062no—
934C2×C4—1062no—
935C2×C4—2124no—
936C2×C4—2122no—
937C2×C4—2122no—
938C2×C4—2122no—
939C2×C4—2124no—
940C2×C4C22×C22⋊D5311yescharacteristic
941C2×C4C22×C22⋊D5311yescharacteristic
942C2×C4C22×C22⋊D5311yescharacteristic
943C2×C4C22×C22⋊D5311yescharacteristic
944C2×C4C22×C22⋊D5311yescharacteristic
945C2×C4C22×C22⋊D5311yescharacteristic
946C2×C4C22×C22⋊D5311yescharacteristic
947C2×C4#1313326214yes—
948C2×C4C24×D5311yescharacteristic
949C8—1068no—
950C22—28no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—44no—
968C22—44no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—4244no—
974C22—2122no—
975C22—2122no—
976C22—2122no—
977C22#1681118212yes—
978C22C2×#1313324812yes—
979C22C2×#1313324812yes—
980C22C2×#1313324812yes—
981C22#1681142112yes—
982C22C23×C22⋊D5311yescharacteristic
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—44no—
990C4—44no—
991C4—2122no—
992C4—2122no—
993C4—2122no—
994C4#1681118212yes—
995C4C2×#1313326212yes—
996C2—22no—
997C2—22no—
998C2—22no—
999C2—22no—
1000C2—22no—
1001C2—41no—
1002C2—41no—
1003C2—4242no—
1004C2C2×#1681118211yescharacteristic
1005C2C22×#1313324811yescharacteristic
1006C2C2×#1681142111yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×C22⋊Q8×C53C2
socleC22×C53C23×D4
prime radicalC2×#16811134C2
hypercenterC22×C22⋊Q8D53
hypocenterC53#60751
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #20285545C2semidirect
3. #20285536C2semidirect
4. #20285517C2semidirect
5. #20285496C2semidirect
6. #20285487C2semidirect
7. #20285468C2semidirect
8. #20284659C2semidirect
9. #20284638C2semidirect
10. #20284341C2semidirect
11. #20283973C2semidirect
12. #20283949C2semidirect
13. C2×#16810587C2semidirect
14. C22×C22⋊Q8×C53C2semidirect
16. C2×#13133248C22semidirect
17. C22×#11719917C22semidirect
35. #16810961C22semidirect
36. #16810958C22semidirect
37. #16810956C22semidirect
38. #16810953C22semidirect
39. #16810951C22semidirect
40. #16810941C22semidirect
41. #16810936C22semidirect
42. #16810879C22semidirect
43. #16810871C22semidirect
44. #16810862C22semidirect
45. #16810854C22semidirect
46. #16810783C22semidirect
47. #16810779C22semidirect
48. #16810779C22semidirect
49. #16810778C22semidirect
50. #16810773C22semidirect
51. #16810762C22semidirect
52. #16810762C22semidirect
53. #16810663C22semidirect
54. #16810632C22semidirect
55. #16810622C22semidirect
58. #16810587C22semidirect
59. #16810587C22semidirect
61. C2×C22⋊#88322C22semidirect
62. C23×Q8×C53C22semidirect
73. C2×C22⋊Q8×C53C22semidirect
74. C2×C22⋊Q8×C53C22semidirect
75. C2×C22⋊Q8×C53C22semidirect
77. C22×C4⋊C4×C53C22semidirect
91. C2×#11719925C23semidirect
92. C2×#11719924C23semidirect
143. #13133150C23semidirect
144. #13133148C23semidirect
145. #13133141C23semidirect
146. #13133141C23semidirect
147. #13133140C23semidirect
148. #13133137C23semidirect
367. C23×C53#137semidirect
494. C22×C22⋊Q8D53semidirect
519. C23×Q8C2×D53semidirect
543. C2×C22⋊Q8C2×D53semidirect
544. C2×C22⋊Q8C2×D53semidirect
545. C2×C22⋊Q8C2×D53semidirect
553. C22×C4⋊C4C2×D53semidirect
582. C53#60751semidirect
875. C23#13133248semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
#202855452
#202855362
#202855172
#202854962
#202854872
#202854682
#202846592
#202846382
#202843412
#202839732
#202839492
C2×#168105872
C22×C22⋊Q8×C532
#6075153