Finite Group Databasebeta

← #261×#548 #16807620

Subgroups — #261×#548 #16807620

Order 3328.

3232 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×#261C211yesmaximal, characteristic, complemented
2C22×Q8×#261C211yesmaximal, characteristic, complemented
3#13131367C213yesmaximal, complemented
4#13131362C213yesmaximal, complemented
5#13131361C213yesmaximal, complemented
6#13131352C213yesmaximal, complemented
7#13131351C211yesmaximal, characteristic, complemented
8#13131341C211yesmaximal, characteristic, complemented
9Q8×C22⋊#261C211yesmaximal, characteristic, complemented
10#124×#261C213yesmaximal, complemented
11C22⋊Q8×#261C213yesmaximal, complemented
12#121×#261C213yesmaximal, complemented
13C4×Q8×#261C211yesmaximal, characteristic, complemented
14C4×D4×#261C213yesmaximal, complemented
15D13×#548C211yesmaximal, characteristic
16C2×#41×D13C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18#41×#261—28no—
19C2×Q8×#261—28no—
20C2×Q8×#261C2211yescharacteristic
21C2×Q8×#261C2213yes—
22C2×Q8×#261C2211yescharacteristic
23C2×Q8×#261C2213yes—
24C2×Q8×#261C2211yescharacteristic
25C2×Q8×#261C2211yescharacteristic
26C2×D4×#261C2213yes—
27C2×D4×#261C2213yes—
28C2×D4×#261C2213yes—
29C2×D4×#261C2213yes—
30C2×#88237C2213yes—
31C22×C4⋊#261C2213yes—
32C22×C4×#261C2213yes—
33C22×C4×#261C2213yes—
34C13×#548C411yescharacteristic, complemented
35#11719536C411yescharacteristic, complemented
36#11719522C411yescharacteristic, complemented
37#11719382C413yescomplemented
38D13×#124C2213yes—
39#11719338C413yescomplemented
40D13×C22⋊Q8C2213yes—
41D13×#121C2213yes—
42#11719303C413yescomplemented
43#11719281C411yescharacteristic, complemented
44C4×Q8×D13C2211yescharacteristic
45#11719257C413yescomplemented
46C4×D4×D13C2213yes—
47(C2×#261)⋊Q8C2213yes—
48(C2×#261)⋊Q8C2213yes—
49#11719151C2213yes—
50#11719151C2213yes—
51#11719150C2216yes—
52#11719136C2213yes—
53#11719136C2213yes—
54C4×C22⋊#261C2213yes—
55C4×C22⋊#261C2213yes—
56#11719083C2213yes—
57#11719083C2213yes—
58#11719082C2216yes—
59C4⋊C4×#261C2213yes—
60C4⋊C4×#261C2213yes—
61C4⋊C4×#261C2213yes—
62C4⋊C4×#261C2213yes—
63#11719071C2216yes—
64#11719071C2216yes—
65#11719071C2216yes—
66#11719070C2216yes—
67C22⋊C4×#261C2211yescharacteristic
68C22⋊C4×#261C2213yes—
69C22⋊C4×#261C2213yes—
70C22⋊C4×#261C2213yes—
71C22⋊C4×#261C2216yes—
72#11719060C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75C42×#261C2213yes—
76C23×#261C2313yes—
77C23×#261C2313yes—
78C23×#261C2313yes—
79C23×#261C2311yescharacteristic
80C2×C13×#41C2×C411yescharacteristic, complemented
81C22×Q8×C13C2×C411yescharacteristic, complemented
82#41×D13—24no—
83#41×D13—24no—
84C2×#6131C2×C411yescharacteristic, complemented
85C2×Q8×D13—24no—
86C2×Q8×D13—24no—
87C2×Q8×D13C2×C411yescharacteristic, complemented
88C2×Q8×D13C2×C413yescomplemented
89C2×Q8×D13C2313yes—
90C2×Q8×D13C2311yescharacteristic
91C2×#6129C2×C413yescomplemented
92C2×D4×D13C2313yes—
93C2×D4×D13C2313yes—
94C2×#6127C2×C413yescomplemented
95C22×C4×D13C2313yes—
96C22×C4×D13C2313yes—
97C22×Dic26C2×C413yescomplemented
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2313yes—
100C2×C22⋊#261C2313yes—
101C2×C22⋊#261C2316yes—
102C2×C22⋊#261C2316yes—
103C2×C22⋊#261C2311yescharacteristic
104Q8×#261—24no—
105Q8×#261—24no—
106Q8×#261—24no—
107Q8×#261—212no—
108Q8×#261—212no—
109Q8×#261D418yescomplemented
110D4×#261—212no—
111D4×#261—212no—
112D4×#261—212no—
113D4×#261—212no—
114#88237—212no—
115C2×C4⋊#261—212no—
116C2×C4⋊#261C2313yes—
117C2×C4⋊#261C2313yes—
118C2×C4⋊#261C2313yes—
119C2×C4⋊#261C2313yes—
120C2×C4⋊#261C2313yes—
121C2×C4⋊#261C2316yes—
122C2×C4⋊#261C2313yes—
123C2×C4×#261—212no—
124C2×C4×#261—212no—
125C2×C4×#261C2311yescharacteristic
126C2×C4×#261C2313yes—
127C2×C4×#261C2313yes—
128C2×C4×#261C2313yes—
129C2×C4×#261C2313yes—
130C2×C4×#261C2313yes—
131C2×C4×#261C2313yes—
132C2×C4×#261C2313yes—
133C2×C4×#261C2311yescharacteristic
134C2×C4×#261C2313yes—
135C2×C4×#261C2313yes—
136C2×C4×#261C2313yes—
137C13×#124C2×C413yescomplemented
138C13×C22⋊Q8C2×C413yescomplemented
139C13×#121C2×C413yescomplemented
140C4×Q8×C13C2×C411yescharacteristic, complemented
141C4×D4×C13C2×C413yescomplemented
142#88201C2×C413yescomplemented
143#88200C2×C413yescomplemented
144Q8×Dic13C2×C411yescharacteristic, complemented
145#88193C2×C416yescomplemented
146#88192C2×C413yescomplemented
147#88190C2×C413yescomplemented
148D4×Dic13C2×C413yescomplemented
149#88184C2×C413yescomplemented
150C4×C22⋊D13C2×C413yescomplemented
151C4×C22⋊D13C2×C413yescomplemented
152#88178C2×C413yescomplemented
153#88151C2×C413yescomplemented
154#88150C2×C416yescomplemented
155#88149C2×C413yescomplemented
156#88147C2×C413yescomplemented
157C4⋊C4×D13C2313yes—
158C4⋊C4×D13C2313yes—
159#88141C2×C413yescomplemented
160#88139C2×C416yescomplemented
161#88139C2×C416yescomplemented
162#88138C2×C416yescomplemented
163#88135C2×C413yescomplemented
164#88135C2×C413yescomplemented
165C22⋊C4×D13C2311yescharacteristic
166C22⋊C4×D13C2313yes—
167C22⋊C4×D13C2316yes—
168#88132C2×C416yescomplemented
169#88129C2×C413yescomplemented
170C4×D52C2×C413yescomplemented
171C42×D13C2313yes—
172C4×Dic26C2×C413yescomplemented
173(C2×#261)⋊C4C2311yescharacteristic
174(C2×#261)⋊C4C2313yes—
175(C2×#261)⋊C4C2316yes—
176(C2×#261)⋊C4C2316yes—
177(C2×#261)⋊C4C2313yes—
178(C2×#261)⋊C4C2313yes—
179(C2×#261)⋊C4C2316yes—
180(C2×#261)⋊C4C2311yescharacteristic
181(C2×#261)⋊C4C2313yes—
182C4×#548—131nomaximal, Sylow
183C23×D13C2413yes—
184C23×D13C2411yescharacteristic
185C22×#261—22no—
186C22×#261—22no—
187C22×#261—26no—
188C22×#261—26no—
189C22×#261—26no—
190C22×#261—26no—
191C22×#261—26no—
192C22×#261—26no—
193C22×#261—26no—
194C22×#261—43no—
195C22×#261—43no—
196C22×#261#4114yescomplemented
197C22×#261C2413yes—
198C22×#261C2413yes—
199C22×#261C2413yes—
200C22×#261C2413yes—
201C22×#261C2411yescharacteristic
202C22×#261C2411yescharacteristic
203C22×#261C2411yescharacteristic
204C22×#261C2411yescharacteristic
205C13×#41—24no—
206C2×Q8×C13—24no—
207C2×Q8×C13C22×C413yes—
208C2×Q8×C13C22×C411yescharacteristic
209C2×D4×C13C22×C413yes—
210C2×D4×C13C22×C413yes—
211C22×C4×C13C22×C413yes—
212C22×C4×C13C22×C413yes—
213C2×C22⋊D13C22×C413yes—
214C2×C22⋊D13C22×C413yes—
215C2×C22⋊D13C22×C416yes—
216C22×Dic13C22×C413yes—
217C22×Dic13C22×C413yes—
218#6131—24no—
219Q8×D13—24no—
220Q8×D13—26no—
221Q8×D13—26no—
222Q8×D13—212no—
223Q8×D13C2×D414yes—
224Q8×D13#4114yes—
225#6129—212no—
226D4×D13—26no—
227D4×D13—26no—
228D4×D13—26no—
229D4×D13—26no—
230#6127—212no—
231C2×D52C22×C413yes—
232C2×D52C22×C413yes—
233C2×C4×D13—26no—
234C2×C4×D13—26no—
235C2×C4×D13—26no—
236C2×C4×D13—26no—
237C2×C4×D13C22×C413yes—
238C2×C4×D13C22×C413yes—
239C2×C4×D13C22×C413yes—
240C2×C4×D13C22×C413yes—
241C2×C4×D13C2411yescharacteristic
242C2×C4×D13C2413yes—
243C2×C4×D13C2413yes—
244C2×C4×D13C2411yescharacteristic
245C2×C4×D13C2413yes—
246C2×Dic26—212no—
247C2×Dic26C22×C413yes—
248C2×Dic26C22×C416yes—
249C2×Dic26C22×C413yes—
250C22⋊#261—26no—
251C22⋊#261—212no—
252C22⋊#261—26no—
253C22⋊#261—26no—
254C22⋊#261—46no—
255C22⋊#261#4114yescomplemented
256C4⋊#261—212no—
257C4⋊#261—26no—
258C4⋊#261—26no—
259C4⋊#261—26no—
260C4⋊#261—26no—
261C4⋊#261—26no—
262C4⋊#261C2×D4112yes—
263C4×#261—22no—
264C4×#261—26no—
265C4×#261—26no—
266C4×#261—26no—
267C4×#261—26no—
268C4×#261—26no—
269C4×#261—22no—
270C4×#261—26no—
271C4×#261—26no—
272C4×#261—26no—
273C4×#261—43no—
274C4×#261C2×D4112yes—
275C13×C4⋊C4C22×C413yes—
276C13×C4⋊C4C22×C413yes—
277C13×C22⋊C4C22×C416yes—
278C13×C22⋊C4C22×C411yescharacteristic
279C13×C22⋊C4C22×C413yes—
280C42×C13C22×C413yes—
281C22⋊Dic13C22×C416yes—
282C22⋊Dic13C22×C413yes—
283C22⋊Dic13C22×C411yescharacteristic
284#6103C22×C411yescharacteristic
285#6103C22×C413yes—
286#6103C22×C416yes—
287#6103C22×C416yes—
288#6103C22×C413yes—
289#6103C22×C411yescharacteristic
290C4⋊Dic13C22×C413yes—
291C4⋊Dic13C22×C413yes—
292#6101C22×C416yes—
293#6101C22×C413yes—
294#6101C22×C413yes—
295C4×Dic13C22×C413yes—
296C4×Dic13C22×C413yes—
297C4×Dic13C22×C413yes—
298C2×#548—131no—
299C2×C4×#41—131no—
300C22×C4×Q8—131no—
301#2367—133no—
302#2362—133no—
303#2361—133no—
304#2352—133no—
305#2351—131no—
306#2341—131no—
307Q8×C22⋊C4—131no—
308C4×#124—133no—
309C4×C22⋊Q8—133no—
310C4×#121—133no—
311C42×Q8—131no—
312C42×D4—133no—
313C23×C13C23×C413yes—
314C23×C13C23×C411yescharacteristic
315C22×D13—21no—
316C22×D13—21no—
317C22×D13—21no—
318C22×D13—21no—
319C22×D13—23no—
320C22×D13—23no—
321C22×D13—23no—
322C22×D13—23no—
323C22×D13—23no—
324C22×D13—23no—
325C22×D13C23×C413yes—
326C22×D13C23×C411yescharacteristic
327C22×D13C2×#4112yes—
328C22×D13C2×#4112yes—
329C22×D13C2511yescharacteristic
330C2×#261—21no—
331C2×#261—21no—
332C2×#261—21no—
333C2×#261—23no—
334C2×#261—21no—
335C2×#261—21no—
336C2×#261—23no—
337C2×#261—21no—
338C2×#261—28no—
339C2×#261—23no—
340C2×#261—23no—
341C2×#261—23no—
342C2×#261—23no—
343C2×#261—23no—
344C2×#261—23no—
345C2×#261—23no—
346C2×#261—23no—
347C2×#261—23no—
348C2×#261—412no—
349C2×#261—412no—
350C2×#261—412no—
351C2×#261C22×D416yes—
352C2×#261C22×D412yes—
353C2×#261C2×#4112yes—
354C2×#261C2×#4112yes—
355C2×#261C2×#4112yes—
356C2×#261C2×#4112yes—
357C2×#2612−1+412yes—
358Q8×C13—26no—
359Q8×C13C4×D414yescomplemented
360D4×C13—26no—
361D4×C13—26no—
362C2×C4×C13—26no—
363C2×C4×C13—26no—
364C2×C4×C13C23×C411yescharacteristic
365C2×C4×C13C23×C413yes—
366C2×C4×C13C23×C411yescharacteristic
367C2×C4×C13C23×C413yes—
368C2×C4×C13C23×C413yes—
369C22⋊D13—26no—
370C22⋊D13—26no—
371C22⋊D13—212no—
372C2×Dic13—26no—
373C2×Dic13—26no—
374C2×Dic13C23×C411yescharacteristic
375C2×Dic13C23×C413yes—
376C2×Dic13C23×C411yescharacteristic
377C2×Dic13C23×C413yes—
378C2×Dic13C23×C413yes—
379D52—26no—
380D52—26no—
381C4×D13—21no—
382C4×D13—23no—
383C4×D13—23no—
384C4×D13—23no—
385C4×D13—21no—
386C4×D13—23no—
387C4×D13—21no—
388C4×D13—21no—
389C4×D13—26no—
390C4×D13—26no—
391C4×D13—26no—
392C4×D13—26no—
393C4×D13C22×D416yes—
394C4×D13C2×#4116yes—
395Dic26—26no—
396Dic26—212no—
397Dic26C4×D4112yescomplemented
398C22×#41—131no—
399C23×Q8—131no—
400#548—131no—
401#548—131no—
402#548—133no—
403#548—133no—
404#548—133no—
405#548—131no—
406#548—133no—
407#548#26111yescharacteristic, direct product factor
408C2×#124—133no—
409C2×C22⋊Q8—133no—
410C2×#121—133no—
411C4×#41—268no—
412C2×C4×Q8—131no—
413C2×C4×Q8—131no—
414C2×C4×Q8—131no—
415C2×C4×Q8—131no—
416C2×C4×Q8—131no—
417C2×C4×Q8—133no—
418C2×C4×Q8—133no—
419C2×C4×Q8—268no—
420C2×C4×D4—133no—
421C2×C4×D4—133no—
422C2×C4×D4—133no—
423C2×C4×D4—133no—
424C2×C4×D4—133no—
425C2×#117—133no—
426C22×C4⋊C4—133no—
427C22×C42—133no—
428C22×C42—133no—
429#391—133no—
430#391—133no—
431#390—133no—
432#390—133no—
433#389—133no—
434#389—133no—
435#388—136no—
436#388—136no—
437#388—136no—
438#387—136no—
439#386—136no—
440#385—136no—
441#382—133no—
442#380—133no—
443#380—133no—
444C4×C4⋊C4—133no—
445C4×C4⋊C4—133no—
446C4×C4⋊C4—133no—
447C4×C4⋊C4—133no—
448C4×C4⋊C4—133no—
449C4×C4⋊C4—133no—
450C4×C22⋊C4—133no—
451C4×C22⋊C4—133no—
452C4×C22⋊C4—133no—
453C4×C22⋊C4—133no—
454C4×C22⋊C4—131no—
455C4×C22⋊C4—133no—
456C4×C22⋊C4—136no—
457C43—133no—
458C22×C13—21no—
459C22×C13—21no—
460C22×C13—23no—
461C22×C13—23no—
462C22×C13—23no—
463C22×C13C4×#4112yescomplemented
464C22×C13C24×C411yescharacteristic
465C2×D13—21no—
466C2×D13—21no—
467C2×D13—22no—
468C2×D13—22no—
469C2×D13—22no—
470C2×D13—22no—
471C2×D13—23no—
472C2×D13—23no—
473C2×D13—23no—
474C2×D13—43no—
475C2×D13—43no—
476C2×D13—43no—
477C2×D13—43no—
478C2×D13C4×#4112yescomplemented
479C2×D13C23×D411yescharacteristic
480C2×D13C22×#4111yescharacteristic
481C2×D13C22×#4111yescharacteristic
482C2×D13C22×#4111yescharacteristic
483C2×D13C2×2−1+411yescharacteristic
484C2×D13#58511yescharacteristic
485#261—22no—
486#261—22no—
487#261—26no—
488#261—22no—
489#261—43no—
490#261—43no—
491#261—43no—
492#261#54814yesdirect product factor
493C4×C13—23no—
494C4×C13—21no—
495C4×C13—23no—
496C4×C13—21no—
497C4×C13C2×C4×D416yes—
498Dic13—23no—
499Dic13—21no—
500Dic13—23no—
501Dic13—21no—
502Dic13C2×C4×D416yes—
503C2×#41—131no—
504C2×#41—133no—
505C2×#41—133no—
506C2×#41—264no—
507C2×#41—264no—
508C2×#41C2×#26111yescharacteristic, complemented
509C22×Q8—131no—
510C22×Q8—133no—
511C22×Q8—133no—
512C22×Q8—131no—
513C22×Q8—133no—
514C22×Q8—264no—
515C22×Q8—264no—
516C22×Q8C2×#26111yescharacteristic, complemented
517C22×D4—133no—
518C22×D4—133no—
519C23×C4—131no—
520C23×C4—133no—
521C23×C4—133no—
522C23×C4—133no—
523C23×C4—133no—
524C23×C4—133no—
525#124—133no—
526#124—133no—
527#124—136no—
528#124—136no—
529#124—133no—
530#124C2×#26113yescomplemented
531C22⋊Q8—133no—
532C22⋊Q8—133no—
533C22⋊Q8—136no—
534C22⋊Q8—133no—
535C22⋊Q8—136no—
536C22⋊Q8C2×#26113yescomplemented
537#121—133no—
538#121—136no—
539#121—133no—
540#121—133no—
541#121—136no—
542#121C2×#26113yescomplemented
543C4×Q8—138no—
544C4×Q8—131no—
545C4×Q8—133no—
546C4×Q8—133no—
547C4×Q8—2612no—
548C4×Q8—2612no—
549C4×Q8—264no—
550C4×Q8—264no—
551C4×Q8—264no—
552C4×Q8C2×#26111yescharacteristic, complemented
553C4×D4—133no—
554C4×D4—133no—
555C4×D4—133no—
556C4×D4—133no—
557C4×D4—133no—
558C4×D4—133no—
559C4×D4—133no—
560C4×D4—2612no—
561C4×D4—2612no—
562C4×D4—2612no—
563C4×D4—2612no—
564C4×D4C2×#26113yescomplemented
565#117—2612no—
566C2×C4⋊C4—133no—
567C2×C4⋊C4—133no—
568C2×C4⋊C4—133no—
569C2×C4⋊C4—133no—
570C2×C4⋊C4—136no—
571C2×C4⋊C4—133no—
572C2×C4⋊C4—133no—
573C2×C4⋊C4—133no—
574C2×C4⋊C4—133no—
575C2×C4⋊C4—2612no—
576C2×C22⋊C4—131no—
577C2×C22⋊C4—131no—
578C2×C22⋊C4—133no—
579C2×C22⋊C4—136no—
580C2×C22⋊C4—136no—
581C2×C22⋊C4—133no—
582C2×C22⋊C4—133no—
583C2×C22⋊C4—133no—
584C2×C22⋊C4—136no—
585C2×C42—133no—
586C2×C42—133no—
587C2×C42—133no—
588C2×C42—133no—
589C2×C42—133no—
590C2×C42—133no—
591C2×C42—133no—
592C2×C42—133no—
593C2×C42—133no—
594C2×C42—133no—
595C2×C42—131no—
596C2×C42—131no—
597C2×C42—133no—
598C2×C42—2612no—
599C2×C42—2612no—
600#95—131no—
601#95—131no—
602#95—133no—
603#95—133no—
604#95—133no—
605#95—133no—
606#95—136no—
607#95—136no—
608#95—136no—
609C2×C13—22no—
610C2×C13—43no—
611C2×C13C22×C4×D411yescharacteristic
612C2×C13C2×C4×#4111yescharacteristic
613C2×C13C4×2−1+411yescharacteristic
614D13—22no—
615D13—43no—
616D13C2×#54811yescharacteristic
617D13D4×#4111yescharacteristic
618D13#348011yescharacteristic
619D13#348211yescharacteristic
620C24—131no—
621C24—133no—
622#41—24no—
623#41—2612no—
624#41—2612no—
625#41—264no—
626C2×Q8—24no—
627C2×Q8—134no—
628C2×Q8—134no—
629C2×Q8—133no—
630C2×Q8—136no—
631C2×Q8—133no—
632C2×Q8—2612no—
633C2×Q8—266no—
634C2×Q8—266no—
635C2×Q8—2612no—
636C2×Q8—264no—
637C2×Q8C22×#26113yes—
638C2×Q8C22×#26111yescharacteristic
639C2×D4—133no—
640C2×D4—133no—
641C2×D4—136no—
642C2×D4—133no—
643C2×D4—133no—
644C2×D4—266no—
645C2×D4—266no—
646C2×D4—266no—
647C2×D4—266no—
648C2×D4C22×#26113yes—
649C2×D4C22×#26113yes—
650C22×C4—131no—
651C22×C4—133no—
652C22×C4—131no—
653C22×C4—131no—
654C22×C4—131no—
655C22×C4—133no—
656C22×C4—134no—
657C22×C4—133no—
658C22×C4—133no—
659C22×C4—131no—
660C22×C4—131no—
661C22×C4—133no—
662C22×C4—133no—
663C22×C4—133no—
664C22×C4—133no—
665C22×C4—133no—
666C22×C4—133no—
667C22×C4—133no—
668C22×C4—133no—
669C22×C4—133no—
670C22×C4—266no—
671C22×C4—266no—
672C22×C4—266no—
673C22×C4—266no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—266no—
677C22×C4—266no—
678C22×C4—266no—
679C22×C4—266no—
680C22×C4—266no—
681C22×C4—266no—
682C22×C4—266no—
683C22×C4—523no—
684C22×C4—523no—
685C22×C4C22×#26113yes—
686C22×C4C22×#26113yes—
687C4⋊C4—1312no—
688C4⋊C4—133no—
689C4⋊C4—133no—
690C4⋊C4—133no—
691C4⋊C4—136no—
692C4⋊C4—133no—
693C4⋊C4—266no—
694C4⋊C4—2612no—
695C4⋊C4—266no—
696C4⋊C4—266no—
697C4⋊C4—266no—
698C4⋊C4—266no—
699C4⋊C4C22×#26113yes—
700C4⋊C4C22×#26113yes—
701C22⋊C4—134no—
702C22⋊C4—131no—
703C22⋊C4—133no—
704C22⋊C4—136no—
705C22⋊C4—131no—
706C22⋊C4—131no—
707C22⋊C4—133no—
708C22⋊C4—133no—
709C22⋊C4—136no—
710C22⋊C4—136no—
711C22⋊C4—2612no—
712C22⋊C4—266no—
713C22⋊C4—266no—
714C22⋊C4—266no—
715C22⋊C4—526no—
716C22⋊C4C22×#26111yescharacteristic
717C22⋊C4C22×#26113yes—
718C22⋊C4C22×#26116yes—
719C42—1312no—
720C42—133no—
721C42—133no—
722C42—133no—
723C42—262no—
724C42—266no—
725C42—266no—
726C42—266no—
727C42—266no—
728C42—266no—
729C42—266no—
730C42—266no—
731C42—266no—
732C42—262no—
733C42—523no—
734C42C22×#26113yes—
735C13C4×#54811yescharacteristic, complemented, Sylow
736C23—131no—
737C23—132no—
738C23—132no—
739C23—131no—
740C23—133no—
741C23—261no—
742C23—261no—
743C23—261no—
744C23—261no—
745C23—263no—
746C23—263no—
747C23—263no—
748C23—263no—
749C23—263no—
750C23—263no—
751C23C23×#26113yes—
752C23C23×#26111yescharacteristic
753Q8—26no—
754Q8—1312no—
755Q8—2612no—
756Q8—266no—
757Q8D4×#26114yescomplemented
758D4—26no—
759D4—26no—
760D4—266no—
761D4—2612no—
762D4—266no—
763D4—266no—
764D4—266no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—132no—
768C2×C4—132no—
769C2×C4—132no—
770C2×C4—133no—
771C2×C4—136no—
772C2×C4—136no—
773C2×C4—136no—
774C2×C4—132no—
775C2×C4—132no—
776C2×C4—132no—
777C2×C4—131no—
778C2×C4—133no—
779C2×C4—133no—
780C2×C4—131no—
781C2×C4—266no—
782C2×C4—266no—
783C2×C4—261no—
784C2×C4—263no—
785C2×C4—263no—
786C2×C4—263no—
787C2×C4—261no—
788C2×C4—261no—
789C2×C4—261no—
790C2×C4—263no—
791C2×C4—266no—
792C2×C4—266no—
793C2×C4—268no—
794C2×C4—261no—
795C2×C4—261no—
796C2×C4—261no—
797C2×C4—263no—
798C2×C4—261no—
799C2×C4—263no—
800C2×C4—261no—
801C2×C4—261no—
802C2×C4—266no—
803C2×C4—266no—
804C2×C4—263no—
805C2×C4—263no—
806C2×C4—263no—
807C2×C4—263no—
808C2×C4—263no—
809C2×C4—263no—
810C2×C4—263no—
811C2×C4—263no—
812C2×C4—263no—
813C2×C4—5212no—
814C2×C4—5212no—
815C2×C4—5212no—
816C2×C4C23×#26111yescharacteristic
817C2×C4C23×#26113yes—
818C2×C4C23×#26113yes—
819C2×C4C23×#26111yescharacteristic
820C2×C4C23×#26113yes—
821C22—21no—
822C22—21no—
823C22—23no—
824C22—23no—
825C22—23no—
826C22—131no—
827C22—131no—
828C22—131no—
829C22—131no—
830C22—131no—
831C22—131no—
832C22—132no—
833C22—262no—
834C22—262no—
835C22—262no—
836C22—262no—
837C22—261no—
838C22—261no—
839C22—263no—
840C22—263no—
841C22—263no—
842C22—523no—
843C22—523no—
844C22—523no—
845C22—523no—
846C22#41×#26112yescomplemented
847C22C24×#26111yescharacteristic
848C4—21no—
849C4—23no—
850C4—23no—
851C4—21no—
852C4—134no—
853C4—136no—
854C4—262no—
855C4—262no—
856C4—266no—
857C4—262no—
858C4—261no—
859C4—263no—
860C4—263no—
861C4—261no—
862C4—523no—
863C4—523no—
864C4—523no—
865C4C2×D4×#26116yes—
866C2—22no—
867C2—43no—
868C2—131no—
869C2—131no—
870C2—131no—
871C2—131no—
872C2—262no—
873C2—523no—
874C2C22×D4×#26111yescharacteristic
875C2C2×#41×#26111yescharacteristic
876C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#548C4
prime radicalD13×#548C2
cosocleC22×D13C25
hypercenter#548#261
hypocenterC13C4×#548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×#261C2semidirect
2. C22×Q8×#261C2semidirect
3. #13131367C2semidirect
4. #13131362C2semidirect
5. #13131361C2semidirect
6. #13131352C2semidirect
7. #13131351C2semidirect
8. #13131341C2semidirect
9. Q8×C22⋊#261C2semidirect
10. #124×#261C2semidirect
11. C22⋊Q8×#261C2semidirect
12. #121×#261C2semidirect
13. C4×Q8×#261C2semidirect
14. C4×D4×#261C2semidirect
34. C13×#548C4semidirect
35. #11719536C4semidirect
36. #11719522C4semidirect
37. #11719382C4semidirect
39. #11719338C4semidirect
42. #11719303C4semidirect
43. #11719281C4semidirect
45. #11719257C4semidirect
80. C2×C13×#41C2×C4semidirect
81. C22×Q8×C13C2×C4semidirect
84. C2×#6131C2×C4semidirect
87. C2×Q8×D13C2×C4semidirect
88. C2×Q8×D13C2×C4semidirect
91. C2×#6129C2×C4semidirect
94. C2×#6127C2×C4semidirect
97. C22×Dic26C2×C4semidirect
109. Q8×#261D4semidirect
137. C13×#124C2×C4semidirect
138. C13×C22⋊Q8C2×C4semidirect
139. C13×#121C2×C4semidirect
140. C4×Q8×C13C2×C4semidirect
141. C4×D4×C13C2×C4semidirect
142. #88201C2×C4semidirect
143. #88200C2×C4semidirect
144. Q8×Dic13C2×C4semidirect
145. #88193C2×C4semidirect
146. #88192C2×C4semidirect
147. #88190C2×C4semidirect
148. D4×Dic13C2×C4semidirect
149. #88184C2×C4semidirect
150. C4×C22⋊D13C2×C4semidirect
151. C4×C22⋊D13C2×C4semidirect
152. #88178C2×C4semidirect
153. #88151C2×C4semidirect
154. #88150C2×C4semidirect
155. #88149C2×C4semidirect
156. #88147C2×C4semidirect
159. #88141C2×C4semidirect
160. #88139C2×C4semidirect
161. #88139C2×C4semidirect
162. #88138C2×C4semidirect
163. #88135C2×C4semidirect
164. #88135C2×C4semidirect
168. #88132C2×C4semidirect
169. #88129C2×C4semidirect
170. C4×D52C2×C4semidirect
172. C4×Dic26C2×C4semidirect
196. C22×#261#41semidirect
255. C22⋊#261#41semidirect
359. Q8×C13C4×D4semidirect
397. Dic26C4×D4semidirect
407. #548#261direct (N × H)
463. C22×C13C4×#41semidirect
478. C2×D13C4×#41semidirect
492. #261#548direct (N × H)
508. C2×#41C2×#261semidirect
516. C22×Q8C2×#261semidirect
530. #124C2×#261semidirect
536. C22⋊Q8C2×#261semidirect
542. #121C2×#261semidirect
552. C4×Q8C2×#261semidirect
564. C4×D4C2×#261semidirect
735. C13C4×#548semidirect
757. Q8D4×#261semidirect
846. C22#41×#261semidirect

Maximal subgroups

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

subgroupindex
C2×#41×#2612
C22×Q8×#2612
#131313672
#131313622
#131313612
#131313522
#131313512
#131313412
Q8×C22⋊#2612
#124×#2612
C22⋊Q8×#2612
#121×#2612
C4×Q8×#2612
C4×D4×#2612
D13×#5482
C4×#54813