Finite Group Databasebeta

← D53×#1806 #27383625

Subgroups — D53×#1806 #27383625

Order 13568.

1618 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#41×D53C211yesmaximal, characteristic
2#423×D53C211yesmaximal, characteristic, complemented
3C2×#104×D53C212yesmaximal
4C4×C4⋊C4×D53C211yesmaximal, characteristic, complemented
5#20274736C211yesmaximal, characteristic, complemented
6#20274735C211yesmaximal, characteristic, complemented
7#20274734C212yesmaximal, complemented
8#20274733C212yesmaximal, complemented
9#20274732C211yesmaximal, characteristic, complemented
10#339×D53C212yesmaximal, complemented
11C53×#1806C211yesmaximal, characteristic, complemented
12C2×#41×D53C2211yescharacteristic
13C2×M16×D53C2212yes—
14#41×Dic53C2211yescharacteristic
15C4×#11719949C411yescharacteristic, complemented
16C4×#11719949C411yescharacteristic, complemented
17C4×#11719945—21no—
18C4×#11719945C2211yescharacteristic
19#16811091—21no—
20#16811091C2211yescharacteristic
21C4×#11719947—21no—
22C4×#11719947—21no—
23C4×#11719947C411yescharacteristic, complemented
24C4×#11719947C411yescharacteristic, complemented
25C4×Q8×D53C411yescharacteristic, complemented
26C4×Q8×D53C411yescharacteristic, complemented
27C4×D4×D53—21no—
28C4×D4×D53—21no—
29C4×D4×D53C411yescharacteristic, complemented
30C4×D4×D53C411yescharacteristic, complemented
31#117×D53—21no—
32#117×D53C2211yescharacteristic
33C2×C4⋊C4×D53—21no—
34C2×C42×D53—21no—
35C2×C42×D53C2212yes—
36C2×C42×D53C2211yescharacteristic
37#16810647C2211yescharacteristic, complemented
38#16810646C2212yescomplemented
39#16810645—21no—
40#16810645—21no—
41C4⋊C8×D53—21no—
42C4⋊C8×D53—21no—
43C2×#13133145C2212yes—
44C2×#13133144C2212yes—
45C2×#13133143C2212yes—
46#104×D53—28no—
47C4⋊C4×Dic53—21no—
48C4×#11719919C2212yescomplemented
49C4×C4⋊Dic53C2211yescharacteristic, complemented
50#16810474—21no—
51#95×D53—21no—
52#16810384C2212yescomplemented
53#16810383C2212yescomplemented
54#16810382C2212yescomplemented
55C4×#41×C53C2211yescharacteristic
56C53×#423C2211yescharacteristic, complemented
57C2×#104×C53C2212yes—
58C4×C4⋊C4×C53C2211yescharacteristic, complemented
59C53×#339C2212yescomplemented
60C2×#11719949C2×C411yescharacteristic
61C2×#11719945—21no—
62C2×#11719945C2311yescharacteristic
63C2×#11719947—21no—
64C2×#11719947C2×C411yescharacteristic
65#41×D53—22no—
66#41×D53—22no—
67#41×D53D414yes—
68#41×D53Q814yes—
69C2×Q8×D53C2×C411yescharacteristic
70C2×D4×D53—21no—
71C2×D4×D53C2×C411yescharacteristic
72C22×C4×D53—21no—
73C22×C4×D53—22no—
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76C22×C4×D53D411yescharacteristic
77C22×C4×D53D411yescharacteristic
78C22×C4×D53C2311yescharacteristic
79C2×#11719917C2312yes—
80C2×#11719912—22no—
81M16×D53—24no—
82M16×D53—24no—
83C2×C8×D53—22no—
84Q8×Dic53C2×C411yescharacteristic, complemented
85Q8×Dic53C2×C411yescharacteristic, complemented
86C4×Dic106—21no—
87C4×Dic106—21no—
88C4×Dic106C2×C411yescharacteristic, complemented
89C4×Dic106C2×C411yescharacteristic, complemented
90#13133182—21no—
91#13133182—21no—
92#13133182C2×C411yescharacteristic, complemented
93#13133182C2×C411yescharacteristic, complemented
94C4×D212—21no—
95C4×D212—21no—
96C4×D212C2×C411yescharacteristic, complemented
97C4×D212C2×C411yescharacteristic, complemented
98D4×Dic53—21no—
99D4×Dic53—21no—
100D4×Dic53C2×C411yescharacteristic, complemented
101D4×Dic53C2×C411yescharacteristic, complemented
102#13133179—21no—
103#13133179—21no—
104#13133179C2×C411yescharacteristic, complemented
105#13133179C2×C411yescharacteristic, complemented
106C4×C22⋊D53—21no—
107C4×C22⋊D53—21no—
108C4×C22⋊D53—21no—
109C4×C22⋊D53—21no—
110C4×C22⋊D53—21no—
111C4×C22⋊D53—21no—
112#13133177—21no—
113#13133177—21no—
114#13133177—21no—
115#13133177—21no—
116#13133177—21no—
117#13133177—21no—
118#13133176—21no—
119#13133176C2311yescharacteristic
120#13133175—21no—
121#13133175—21no—
122#13133175C2×C411yescharacteristic
123#13133175C2×C411yescharacteristic
124#13133174—21no—
125#13133174—21no—
126#13133174—21no—
127#13133173—21no—
128#13133173—21no—
129#13133173—21no—
130C2×C4⋊Dic53—21no—
131C2×#11719919—22no—
132C4⋊C4×D53—28no—
133C4⋊C4×D53—21no—
134C4⋊C4×D53—21no—
135C4⋊C4×D53C2×C411yescharacteristic
136C4⋊C4×D53C2×C411yescharacteristic
137C22⋊C4×D53—21no—
138C22⋊C4×D53—21no—
139C22⋊C4×D53—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143C2×C4×Dic53—22no—
144C2×C4×Dic53D411yescharacteristic
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53C2312yes—
147C2×C4×Dic53C2311yescharacteristic
148C42×D53—21no—
149C42×D53—21no—
150C42×D53—21no—
151C42×D53—21no—
152C42×D53—21no—
153C42×D53—21no—
154C42×D53—21no—
155C42×D53—24no—
156C42×D53—24no—
157C42×D53C2×C411yescharacteristic
158C42×D53C2×C411yescharacteristic
159C42×D53C2×C411yescharacteristic
160C42×D53C2×C411yescharacteristic
161C42×D53D411yescharacteristic
162C42×D53D411yescharacteristic
163C42×D53D411yescharacteristic
164C42×D53D411yescharacteristic
165C4⋊#88322—21no—
166C4⋊#88322—21no—
167#13133146—22no—
168#13133146—22no—
169#13133145—24no—
170#13133144—24no—
171#13133143—24no—
172#13133124—21no—
173#13133124—22no—
174C2×#41×C53C2311yescharacteristic
175C2×M16×C53C2312yes—
176C4×Q8×C53C2×C411yescharacteristic, complemented
177C4×Q8×C53C2×C411yescharacteristic, complemented
178C4×D4×C53—21no—
179C4×D4×C53—21no—
180C4×D4×C53C2×C411yescharacteristic, complemented
181C4×D4×C53C2×C411yescharacteristic, complemented
182#117×C53—21no—
183#117×C53C2311yescharacteristic
184C2×C4⋊C4×C53—21no—
185C2×C42×C53—21no—
186C2×C42×C53C2312yes—
187C2×C42×C53C2311yescharacteristic
188C4⋊C8×C53—21no—
189C4⋊C8×C53—21no—
190#104×C53—24no—
191#95×C53—21no—
192C23×D53—21no—
193C23×D53C2×D411yescharacteristic
194#41×C53—21no—
195#41×C53—21no—
196#41×C53C2×D412yes—
197#41×C53C2×Q812yes—
198C2×Q8×C53C22×C411yescharacteristic
199C2×D4×C53—21no—
200C2×D4×C53C22×C411yescharacteristic
201C22×C4×C53—21no—
202C22×C4×C53—22no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—21no—
209C2×C22⋊D53—21no—
210C2×C22⋊D53—21no—
211C22×Dic53—21no—
212C22×Dic53—22no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218#11719949—22no—
219#11719949C4⋊C414yescomplemented
220Q8×D53—22no—
221Q8×D53C4⋊C414yescomplemented
222#11719947—24no—
223#11719947—24no—
224#11719947—22no—
225#11719947C4⋊C414yescomplemented
226D4×D53—24no—
227D4×D53—24no—
228D4×D53—22no—
229D4×D53C4⋊C414yescomplemented
230#11719945—21no—
231#11719945—21no—
232#11719945—24no—
233#11719945—24no—
234#11719945C2×D412yes—
235#11719945C2×Q812yes—
236C2×D212—21no—
237C2×D212C22×C411yescharacteristic
238C2×C4×D53—21no—
239C2×C4×D53—21no—
240C2×C4×D53—21no—
241C2×C4×D53—24no—
242C2×C4×D53—24no—
243C2×C4×D53—24no—
244C2×C4×D53—28no—
245C2×C4×D53—21no—
246C2×C4×D53—21no—
247C2×C4×D53—21no—
248C2×C4×D53—21no—
249C2×C4×D53—21no—
250C2×C4×D53—21no—
251C2×C4×D53—42no—
252C2×C4×D53—44no—
253C2×C4×D53—44no—
254C2×C4×D53—44no—
255C2×C4×D53—44no—
256C2×C4×D53C22⋊C411yescharacteristic
257C2×C4×D53C22⋊C411yescharacteristic
258C2×C4×D53C22⋊C411yescharacteristic
259C2×C4×D53C22⋊C411yescharacteristic
260C2×C4×D53C22⋊C411yescharacteristic
261C2×C4×D53C22⋊C411yescharacteristic
262C2×C4×D53C22⋊C411yescharacteristic
263C2×C4×D53C22⋊C411yescharacteristic
264C2×C4×D53C22×C411yescharacteristic
265C2×C4×D53C22×C411yescharacteristic
266C2×C4×D53C2×D412yes—
267C2×C4×D53C2×D411yescharacteristic
268C2×C4×D53C2×D411yescharacteristic
269C2×C4×D53C2×Q812yes—
270C2×C4×D53#4112yes—
271C2×C4×D53#4112yes—
272C2×Dic106—21no—
273C2×Dic106C22×C411yescharacteristic
274M16×C53—22no—
275M16×C53—22no—
276C2×C8×C53—22no—
277C4⋊C4×C53—24no—
278C4⋊C4×C53—21no—
279C4⋊C4×C53—21no—
280C4⋊C4×C53C22×C411yescharacteristic
281C4⋊C4×C53C22×C411yescharacteristic
282C22⋊C4×C53—21no—
283C22⋊C4×C53—21no—
284C22⋊C4×C53—21no—
285C42×C53—21no—
286C42×C53—21no—
287C42×C53—21no—
288C42×C53—22no—
289C42×C53—22no—
290C42×C53C22×C411yescharacteristic
291C42×C53C22×C411yescharacteristic
292C42×C53C2×D411yescharacteristic
293C42×C53C2×D411yescharacteristic
294C22⋊Dic53—21no—
295C22⋊Dic53—21no—
296C22⋊Dic53—21no—
297#11719921—21no—
298#11719921—21no—
299#11719921—21no—
300#11719921—21no—
301#11719921—21no—
302#11719921—21no—
303C4⋊Dic53—24no—
304C4⋊Dic53—21no—
305C4⋊Dic53—21no—
306C4⋊Dic53C22×C411yescharacteristic
307C4⋊Dic53C22×C411yescharacteristic
308#11719919—28no—
309#11719919—21no—
310#11719919—21no—
311#11719919—21no—
312#11719919—21no—
313#11719919—21no—
314#11719919—21no—
315C4×Dic53—21no—
316C4×Dic53—21no—
317C4×Dic53—21no—
318C4×Dic53—21no—
319C4×Dic53—21no—
320C4×Dic53—21no—
321C4×Dic53—21no—
322C4×Dic53—21no—
323C4×Dic53—21no—
324C4×Dic53—22no—
325C4×Dic53—22no—
326C4×Dic53—44no—
327C4×Dic53C22⋊C411yescharacteristic
328C4×Dic53C22⋊C411yescharacteristic
329C4×Dic53C22⋊C411yescharacteristic
330C4×Dic53C22⋊C411yescharacteristic
331C4×Dic53C22⋊C411yescharacteristic
332C4×Dic53C22⋊C411yescharacteristic
333C4×Dic53C22⋊C411yescharacteristic
334C4×Dic53C22⋊C411yescharacteristic
335C4×Dic53C22×C411yescharacteristic
336C4×Dic53C22×C411yescharacteristic
337C4×Dic53C2×D411yescharacteristic
338C4×Dic53C2×D411yescharacteristic
339#11719917—22no—
340#11719917—22no—
341C2×#88322—22no—
342#11719912—44no—
343C8×D53—44no—
344C23×C53—21no—
345C23×C53C22×D411yescharacteristic
346C22×D53—22no—
347C22×D53—22no—
348C22×D53—21no—
349C22×D53—24no—
350C22×D53—42no—
351C22×D53—42no—
352C22×D53C2×C22⋊C411yescharacteristic
353C22×D53C2×C22⋊C411yescharacteristic
354C22×D53#12112yes—
355C22×D53C22⋊Q812yes—
356Q8×C53—21no—
357Q8×C53C2×C4⋊C412yescomplemented
358D4×C53—22no—
359D4×C53—22no—
360D4×C53—21no—
361D4×C53C2×C4⋊C412yescomplemented
362C2×C4×C53—21no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—24no—
367C2×C4×C53—21no—
368C2×C4×C53—21no—
369C2×C4×C53—41no—
370C2×C4×C53—42no—
371C2×C4×C53—42no—
372C2×C4×C53—42no—
373C2×C4×C53—42no—
374C2×C4×C53C2×C22⋊C411yescharacteristic
375C2×C4×C53C2×C22⋊C411yescharacteristic
376C2×C4×C53C2×C22⋊C411yescharacteristic
377C2×C4×C53C2×C22⋊C411yescharacteristic
378C2×C4×C53C23×C411yescharacteristic
379C2×C4×C53C22×D411yescharacteristic
380C2×C4×C53C22×D411yescharacteristic
381C2×C4×C53C22×Q811yescharacteristic
382C2×C4×C53C2×#4111yescharacteristic
383C2×C4×C53C2×#4111yescharacteristic
384C22⋊D53—22no—
385C22⋊D53—22no—
386C22⋊D53—24no—
387C22⋊D53—24no—
388C2×Dic53—21no—
389C2×Dic53—24no—
390C2×Dic53—22no—
391C2×Dic53—24no—
392C2×Dic53—21no—
393C2×Dic53—21no—
394C2×Dic53—41no—
395C2×Dic53—42no—
396C2×Dic53—42no—
397C2×Dic53—42no—
398C2×Dic53—42no—
399C2×Dic53C2×C22⋊C411yescharacteristic
400C2×Dic53C2×C22⋊C411yescharacteristic
401C2×Dic53C2×C22⋊C411yescharacteristic
402C2×Dic53C2×C22⋊C411yescharacteristic
403C2×Dic53C2×C22⋊C411yescharacteristic
404C2×Dic53C2×C22⋊C411yescharacteristic
405C2×Dic53#12112yes—
406C2×Dic53C22⋊Q812yes—
407D212—24no—
408D212—21no—
409D212C2×C4⋊C412yescomplemented
410C4×D53—24no—
411C4×D53—22no—
412C4×D53—22no—
413C4×D53—22no—
414C4×D53—22no—
415C4×D53—22no—
416C4×D53—22no—
417C4×D53—24no—
418C4×D53—22no—
419C4×D53—41no—
420C4×D53—41no—
421C4×D53—42no—
422C4×D53—42no—
423C4×D53—416no—
424C4×D53—42no—
425C4×D53—42no—
426C4×D53—42no—
427C4×D53—42no—
428C4×D53#10414yescomplemented
429C4×D53C2×C4⋊C412yes—
430C4×D53C2×C4⋊C412yes—
431C4×D53#11712yes—
432C4×D53#11712yes—
433C4×D53#12112yes—
434C4×D53#12112yes—
435C4×D53C22⋊Q812yes—
436C4×D53C22⋊Q812yes—
437Dic106—21no—
438Dic106—24no—
439Dic106C2×C4⋊C412yescomplemented
440C8×C53—42no—
441#88322—42no—
442C2×#1806—531nomaximal, Sylow
443C22×C53—21no—
444C22×C53—21no—
445C22×C53—22no—
446C22×C53—41no—
447C22×C53—41no—
448C22×C53C22×C22⋊C411yescharacteristic
449C22×C53C2×#12111yescharacteristic
450C22×C53C2×C22⋊Q811yescharacteristic
451C2×D53—21no—
452C2×D53—21no—
453C2×D53—24no—
454C2×D53—24no—
455C2×D53—22no—
456C2×D53—41no—
457C2×D53—41no—
458C2×D53—48no—
459C2×D53#38012yes—
460C2×D53#38012yes—
461C2×D53C2×#10412yes—
462C2×D53#42112yes—
463C4×C53—21no—
464C4×C53—21no—
465C4×C53—21no—
466C4×C53—22no—
467C4×C53—44no—
468C4×C53—41no—
469C4×C53—41no—
470C4×C53C2×#10412yescomplemented
471C4×C53C22×C4⋊C411yescharacteristic
472C4×C53C2×#11711yescharacteristic
473C4×C53C2×#12111yescharacteristic
474C4×C53C2×C22⋊Q811yescharacteristic
475Dic53—21no—
476Dic53—21no—
477Dic53—21no—
478Dic53—22no—
479Dic53—44no—
480Dic53—41no—
481Dic53—41no—
482Dic53#38012yes—
483Dic53#38012yes—
484Dic53C2×#10412yescomplemented
485C2×C4×#41—531no—
486C2×#423—531no—
487C22×#104—532no—
488C2×C4×C4⋊C4—531no—
489#1806—531no—
490#1806—532no—
491#1806—531no—
492#1806—532no—
493#1806—531no—
494#1806D5311yescharacteristic, direct product factor
495C2×#339—532no—
496C2×C53—21no—
497C2×C53—21no—
498C2×C53—42no—
499C2×C53C2×#38011yescharacteristic
500C2×C53C22×#10411yescharacteristic
501C2×C53C2×#42111yescharacteristic
502D53—22no—
503D53—42no—
504D53#180614yesdirect product factor
505C22×#41—531no—
506C22×M16—532no—
507C4×#41—531no—
508C4×#41—531no—
509C4×#41—531no—
510C4×#41—531no—
511C4×#41—531no—
512C4×#41—531no—
513C4×#41—531no—
514C4×#41—1061no—
515C4×#41—1061no—
516C4×#41—1061no—
517C4×#41—1061no—
518C4×#41C2×D5311yescharacteristic
519C2×C4×Q8—531no—
520C2×C4×Q8—531no—
521C2×C4×D4—531no—
522C2×C4×D4—531no—
523C2×C4×D4—1061no—
524C2×C4×D4—1061no—
525C2×#117—531no—
526C2×#117—1061no—
527C22×C4⋊C4—1061no—
528C22×C42—531no—
529C22×C42—532no—
530C22×C42—1061no—
531#423—532no—
532#423—531no—
533#423—1061no—
534#423—1061no—
535#423C2×D5311yescharacteristic, complemented
536C2×C4⋊C8—1061no—
537C2×C4⋊C8—1061no—
538C2×#104—532no—
539C2×#104—532no—
540C2×#104—532no—
541C2×#104—1068no—
542C2×#104C2×D5312yes—
543C4×C4⋊C4—532no—
544C4×C4⋊C4—531no—
545C4×C4⋊C4—1061no—
546C4×C4⋊C4—1061no—
547C4×C4⋊C4C2×D5311yescharacteristic, complemented
548C2×#95—1061no—
549#339—532no—
550#339—532no—
551#339—532no—
552#339C2×D5312yescomplemented
553C53C2×#180611yescharacteristic, complemented, Sylow
554C2×#41—534no—
555C2×#41—534no—
556C2×#41—531no—
557C2×#41—531no—
558C2×#41—531no—
559C2×#41—1061no—
560C2×#41—1061no—
561C2×#41—1062no—
562C2×#41—1062no—
563C2×#41C22×D5311yescharacteristic
564C22×Q8—531no—
565C22×D4—531no—
566C22×D4—1061no—
567C23×C4—531no—
568C23×C4—531no—
569C23×C4—531no—
570C23×C4—1061no—
571C23×C4—1061no—
572C23×C4—1061no—
573C23×C4—1062no—
574C2×M16—532no—
575C2×M16—1062no—
576C2×M16—1064no—
577C2×M16—1064no—
578C2×M16C22×D5312yes—
579C22×C8—1062no—
580C4×Q8—531no—
581C4×Q8—531no—
582C4×Q8—531no—
583C4×Q8—531no—
584C4×Q8—531no—
585C4×Q8—531no—
586C4×Q8—1061no—
587C4×Q8—1061no—
588C4×Q8—1061no—
589C4×Q8—1061no—
590C4×Q8C4×D5311yescharacteristic, complemented
591C4×Q8C4×D5311yescharacteristic, complemented
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—531no—
595C4×D4—531no—
596C4×D4—531no—
597C4×D4—531no—
598C4×D4—531no—
599C4×D4—531no—
600C4×D4—1061no—
601C4×D4—1061no—
602C4×D4—1061no—
603C4×D4—1061no—
604C4×D4—1061no—
605C4×D4—1061no—
606C4×D4—1061no—
607C4×D4—1061no—
608C4×D4—1061no—
609C4×D4—1061no—
610C4×D4—1061no—
611C4×D4—1061no—
612C4×D4—1061no—
613C4×D4—1061no—
614C4×D4—1061no—
615C4×D4—1061no—
616C4×D4—1061no—
617C4×D4—1061no—
618C4×D4C4×D5311yescharacteristic, complemented
619C4×D4C4×D5311yescharacteristic, complemented
620#117—21no—
621#117—531no—
622#117—531no—
623#117—531no—
624#117—1061no—
625#117—1061no—
626#117—1061no—
627#117—1061no—
628#117—1061no—
629#117—1061no—
630#117—1061no—
631#117—1061no—
632#117—1061no—
633#117C22×D5311yescharacteristic
634C2×C4⋊C4—21no—
635C2×C4⋊C4—531no—
636C2×C4⋊C4—531no—
637C2×C4⋊C4—1061no—
638C2×C4⋊C4—1061no—
639C2×C4⋊C4—1068no—
640C2×C4⋊C4—1062no—
641C2×C4⋊C4—1061no—
642C2×C22⋊C4—1061no—
643C2×C22⋊C4—1061no—
644C2×C22⋊C4—1061no—
645C2×C42—21no—
646C2×C42—531no—
647C2×C42—531no—
648C2×C42—531no—
649C2×C42—531no—
650C2×C42—531no—
651C2×C42—531no—
652C2×C42—531no—
653C2×C42—531no—
654C2×C42—531no—
655C2×C42—531no—
656C2×C42—531no—
657C2×C42—532no—
658C2×C42—1061no—
659C2×C42—1061no—
660C2×C42—1061no—
661C2×C42—1061no—
662C2×C42—1061no—
663C2×C42—1061no—
664C2×C42—1064no—
665C2×C42—1064no—
666C2×C42—1061no—
667C2×C42—1061no—
668C2×C42—1061no—
669C2×C42—1061no—
670C2×C42—1062no—
671C2×C42C22×D5312yes—
672C2×C42C22×D5311yescharacteristic
673C4⋊C8—21no—
674C4⋊C8—21no—
675C4⋊C8—1062no—
676C4⋊C8—1062no—
677C4⋊C8—1061no—
678C4⋊C8—1061no—
679#104—24no—
680#104—1064no—
681#104—1064no—
682#104—1064no—
683#95—21no—
684#95—1062no—
685#95—1061no—
686C24—531no—
687C24—1061no—
688#41—21no—
689#41—21no—
690#41—534no—
691#41—534no—
692#41—532no—
693#41—532no—
694#41—1064no—
695#41—1064no—
696#41—1064no—
697#41—1064no—
698#41—1062no—
699#41—1062no—
700#41—1061no—
701#41—1061no—
702#41D4×D5312yes—
703#41Q8×D5312yes—
704C2×Q8—534no—
705C2×Q8—531no—
706C2×Q8—1061no—
707C2×Q8—1062no—
708C2×Q8C2×C4×D5311yescharacteristic
709C2×D4—21no—
710C2×D4—534no—
711C2×D4—531no—
712C2×D4—1061no—
713C2×D4—1062no—
714C2×D4—1061no—
715C2×D4—1064no—
716C2×D4—1064no—
717C2×D4—1061no—
718C2×D4—1061no—
719C2×D4C2×C4×D5311yescharacteristic
720C22×C4—21no—
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—531no—
725C22×C4—531no—
726C22×C4—531no—
727C22×C4—531no—
728C22×C4—532no—
729C22×C4—531no—
730C22×C4—531no—
731C22×C4—532no—
732C22×C4—532no—
733C22×C4—532no—
734C22×C4—531no—
735C22×C4—531no—
736C22×C4—531no—
737C22×C4—531no—
738C22×C4—531no—
739C22×C4—531no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—531no—
743C22×C4—1061no—
744C22×C4—1064no—
745C22×C4—1064no—
746C22×C4—1064no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1068no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1062no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—2124no—
761C22×C4—2122no—
762C22×C4—2124no—
763C22×C4—2124no—
764C22×C4—2124no—
765C22×C4D4×D5311yescharacteristic
766C22×C4D4×D5311yescharacteristic
767C22×C4C23×D5311yescharacteristic
768M16—22no—
769M16—22no—
770M16—1062no—
771M16—1062no—
772M16—2124no—
773C2×C8—22no—
774C2×C8—1062no—
775C2×C8—2124no—
776C4⋊C4—24no—
777C4⋊C4—21no—
778C4⋊C4—21no—
779C4⋊C4—531no—
780C4⋊C4—531no—
781C4⋊C4—1061no—
782C4⋊C4—1061no—
783C4⋊C4—1061no—
784C4⋊C4—1061no—
785C4⋊C4—1061no—
786C4⋊C4—1061no—
787C4⋊C4—1068no—
788C4⋊C4—1064no—
789C4⋊C4—1061no—
790C4⋊C4—1061no—
791C4⋊C4C2×C4×D5311yescharacteristic
792C4⋊C4C2×C4×D5311yescharacteristic
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—1061no—
797C22⋊C4—1061no—
798C22⋊C4—1061no—
799C22⋊C4—1061no—
800C22⋊C4—1061no—
801C22⋊C4—1061no—
802C22⋊C4—1061no—
803C22⋊C4—1061no—
804C22⋊C4—1061no—
805C42—21no—
806C42—21no—
807C42—21no—
808C42—22no—
809C42—22no—
810C42—531no—
811C42—531no—
812C42—531no—
813C42—531no—
814C42—531no—
815C42—531no—
816C42—531no—
817C42—531no—
818C42—531no—
819C42—531no—
820C42—531no—
821C42—531no—
822C42—1061no—
823C42—1061no—
824C42—1061no—
825C42—1061no—
826C42—1061no—
827C42—1061no—
828C42—1061no—
829C42—1061no—
830C42—1061no—
831C42—1062no—
832C42—1062no—
833C42—2124no—
834C42C2×C4×D5311yescharacteristic
835C42C2×C4×D5311yescharacteristic
836C42D4×D5311yescharacteristic
837C42D4×D5311yescharacteristic
838C23—21no—
839C23—531no—
840C23—531no—
841C23—532no—
842C23—532no—
843C23—1062no—
844C23—1062no—
845C23—1064no—
846C23—1061no—
847C23—2122no—
848C23—2122no—
849C23C2×D4×D5311yescharacteristic
850Q8—21no—
851Q8—532no—
852Q8—1064no—
853Q8—1061no—
854Q8C4⋊C4×D5312yescomplemented
855D4—22no—
856D4—22no—
857D4—21no—
858D4—532no—
859D4—1064no—
860D4—1064no—
861D4—1064no—
862D4—1062no—
863D4—1062no—
864D4—1061no—
865D4C4⋊C4×D5312yescomplemented
866C2×C4—21no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—531no—
879C2×C4—531no—
880C2×C4—531no—
881C2×C4—532no—
882C2×C4—532no—
883C2×C4—532no—
884C2×C4—532no—
885C2×C4—532no—
886C2×C4—532no—
887C2×C4—532no—
888C2×C4—532no—
889C2×C4—532no—
890C2×C4—532no—
891C2×C4—534no—
892C2×C4—531no—
893C2×C4—531no—
894C2×C4—531no—
895C2×C4—1062no—
896C2×C4—1064no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1064no—
901C2×C4—1062no—
902C2×C4—1064no—
903C2×C4—1061no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1064no—
908C2×C4—1061no—
909C2×C4—1061no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—2122no—
913C2×C4—2122no—
914C2×C4—2122no—
915C2×C4—2122no—
916C2×C4—2122no—
917C2×C4—21216no—
918C2×C4—2122no—
919C2×C4—2121no—
920C2×C4—2122no—
921C2×C4—2122no—
922C2×C4—2122no—
923C2×C4—2122no—
924C2×C4C22⋊C4×D5311yescharacteristic
925C2×C4C22⋊C4×D5311yescharacteristic
926C2×C4C22⋊C4×D5311yescharacteristic
927C2×C4C22⋊C4×D5311yescharacteristic
928C2×C4C22×C4×D5311yescharacteristic
929C2×C4C2×D4×D5311yescharacteristic
930C2×C4C2×D4×D5311yescharacteristic
931C2×C4C2×Q8×D5311yescharacteristic
932C2×C4#41×D5311yescharacteristic
933C2×C4#41×D5311yescharacteristic
934C8—42no—
935C8—2122no—
936C22—21no—
937C22—21no—
938C22—22no—
939C22—41no—
940C22—41no—
941C22—532no—
942C22—532no—
943C22—532no—
944C22—532no—
945C22—1064no—
946C22—1064no—
947C22—1061no—
948C22—1061no—
949C22—1062no—
950C22—2128no—
951C22—2121no—
952C22—2121no—
953C22C2×C22⋊C4×D5311yescharacteristic
954C22#121×D5311yescharacteristic
955C22C22⋊Q8×D5311yescharacteristic
956C4—22no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—44no—
961C4—41no—
962C4—41no—
963C4—532no—
964C4—532no—
965C4—532no—
966C4—1062no—
967C4—1061no—
968C4—1061no—
969C4—1061no—
970C4—2124no—
971C4—2121no—
972C4—2121no—
973C4#104×D5312yescomplemented
974C4C2×C4⋊C4×D5311yescharacteristic
975C4#117×D5311yescharacteristic
976C4#121×D5311yescharacteristic
977C4C22⋊Q8×D5311yescharacteristic
978C2—21no—
979C2—21no—
980C2—42no—
981C2—534no—
982C2—1062no—
983C2—2122no—
984C2#380×D5311yescharacteristic
985C2C2×#104×D5311yescharacteristic
986C2#421×D5311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1806C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#41×D53C22
cosocleC22×C4×C53C24
hypercenter#1806D53
hypocenterC53C2×#1806
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #423×D53C2semidirect
4. C4×C4⋊C4×D53C2semidirect
5. #20274736C2semidirect
6. #20274735C2semidirect
7. #20274734C2semidirect
8. #20274733C2semidirect
9. #20274732C2semidirect
10. #339×D53C2semidirect
11. C53×#1806C2semidirect
15. C4×#11719949C4semidirect
16. C4×#11719949C4semidirect
23. C4×#11719947C4semidirect
24. C4×#11719947C4semidirect
25. C4×Q8×D53C4semidirect
26. C4×Q8×D53C4semidirect
29. C4×D4×D53C4semidirect
30. C4×D4×D53C4semidirect
37. #16810647C22semidirect
38. #16810646C22semidirect
48. C4×#11719919C22semidirect
49. C4×C4⋊Dic53C22semidirect
52. #16810384C22semidirect
53. #16810383C22semidirect
54. #16810382C22semidirect
56. C53×#423C22semidirect
58. C4×C4⋊C4×C53C22semidirect
59. C53×#339C22semidirect
84. Q8×Dic53C2×C4semidirect
85. Q8×Dic53C2×C4semidirect
88. C4×Dic106C2×C4semidirect
89. C4×Dic106C2×C4semidirect
92. #13133182C2×C4semidirect
93. #13133182C2×C4semidirect
96. C4×D212C2×C4semidirect
97. C4×D212C2×C4semidirect
100. D4×Dic53C2×C4semidirect
101. D4×Dic53C2×C4semidirect
104. #13133179C2×C4semidirect
105. #13133179C2×C4semidirect
176. C4×Q8×C53C2×C4semidirect
177. C4×Q8×C53C2×C4semidirect
180. C4×D4×C53C2×C4semidirect
181. C4×D4×C53C2×C4semidirect
219. #11719949C4⋊C4semidirect
221. Q8×D53C4⋊C4semidirect
225. #11719947C4⋊C4semidirect
229. D4×D53C4⋊C4semidirect
357. Q8×C53C2×C4⋊C4semidirect
361. D4×C53C2×C4⋊C4semidirect
409. D212C2×C4⋊C4semidirect
428. C4×D53#104semidirect
439. Dic106C2×C4⋊C4semidirect
470. C4×C53C2×#104semidirect
484. Dic53C2×#104semidirect
494. #1806D53direct (N × H)
504. D53#1806direct (N × H)
535. #423C2×D53semidirect
547. C4×C4⋊C4C2×D53semidirect
552. #339C2×D53semidirect
553. C53C2×#1806semidirect
590. C4×Q8C4×D53semidirect
591. C4×Q8C4×D53semidirect
618. C4×D4C4×D53semidirect
619. C4×D4C4×D53semidirect
854. Q8C4⋊C4×D53semidirect
865. D4C4⋊C4×D53semidirect
973. C4#104×D53semidirect

Maximal subgroups

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

subgroupindex
C4×#41×D532
#423×D532
C2×#104×D532
C4×C4⋊C4×D532
#202747362
#202747352
#202747342
#202747332
#202747322
#339×D532
C53×#18062
C2×#180653