Finite Group Databasebeta

← #16807755

Subgroups — #16807755

Order 3328.

2984 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719627C211yesmaximal, characteristic, complemented
2C2×#41×#261C211yesmaximal, characteristic, complemented
3#13131367C213yesmaximal, complemented
4#13131363C213yesmaximal, complemented
5#13131362C213yesmaximal, complemented
6#13131354C213yesmaximal, complemented
7Q8×C4⋊#261C211yesmaximal, characteristic, complemented
8#13131341C211yesmaximal, characteristic, complemented
9Q8×C22⋊#261C211yesmaximal, characteristic, complemented
10#13131326C213yesmaximal, complemented
11#13131324C213yesmaximal, complemented
12C22⋊Q8×#261C213yesmaximal, complemented
13#13131290C213yesmaximal, complemented
14#13131276C211yesmaximal, characteristic, complemented
15D13×#548C211yesmaximal, characteristic
16C2×#41×D13C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18#41×#261—28no—
19#11719627—28no—
20C2×Q8×#261C2211yescharacteristic
21C2×Q8×#261C2211yescharacteristic
22C2×Q8×#261C2213yes—
23C2×Q8×#261C2211yescharacteristic
24C2×Q8×#261C2213yes—
25C2×Q8×#261C2211yescharacteristic
26C2×D4×#261C2213yes—
27C2×D4×#261C2213yes—
28C2×#88237C2213yes—
29C2×#88237C2213yes—
30C2×#88237C2213yes—
31C22×C4×#261C2213yes—
32C13×#548C411yescharacteristic, complemented
33#11719536C411yescharacteristic, complemented
34#11719522C411yescharacteristic, complemented
35#11719382C413yescomplemented
36D13×#124C2213yes—
37#11719338C413yescomplemented
38D13×C22⋊Q8C2213yes—
39D13×#121C2213yes—
40#11719303C413yescomplemented
41#11719281C411yescharacteristic, complemented
42C4×Q8×D13C2211yescharacteristic
43#11719257C413yescomplemented
44C4×D4×D13C2213yes—
45(C2×#261)⋊Q8C2213yes—
46(C2×#261)⋊Q8C2213yes—
47#11719151C2213yes—
48#11719151C2216yes—
49#11719151C2213yes—
50#11719150C2213yes—
51#11719150C2213yes—
52#11719136C2213yes—
53#11719136C2213yes—
54C4×C22⋊#261C2213yes—
55C4×C22⋊#261C2213yes—
56#11719083C2213yes—
57#11719083C2213yes—
58#11719082C2213yes—
59#11719082C2213yes—
60C4⋊C4×#261C2213yes—
61C4⋊C4×#261C2213yes—
62C4⋊C4×#261C2216yes—
63#11719071C2211yescharacteristic
64#11719071C2213yes—
65#11719071C2216yes—
66#11719071C2216yes—
67#11719071C2216yes—
68#11719070C2213yes—
69#11719070C2213yes—
70#11719070C2216yes—
71C22⋊C4×#261C2216yes—
72#11719059C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75#11719057C2213yes—
76C23×#261C2313yes—
77C23×#261C2313yes—
78C2×C13×#41C2×C411yescharacteristic
79C22×Q8×C13C2×C411yescharacteristic, complemented
80#41×D13—24no—
81#41×D13—24no—
82C2×#6131C2×C411yescharacteristic
83C2×Q8×D13—24no—
84C2×Q8×D13—24no—
85C2×Q8×D13C2×C411yescharacteristic, complemented
86C2×Q8×D13C2×C413yescomplemented
87C2×Q8×D13C2313yes—
88C2×Q8×D13C2311yescharacteristic
89C2×#6129C2×C413yes—
90C2×D4×D13C2313yes—
91C2×D4×D13C2313yes—
92C2×#6127C2×C413yes—
93C22×C4×D13C2313yes—
94C22×C4×D13C2313yes—
95C22×Dic26C2×C413yescomplemented
96C2×C22⋊#261C2316yes—
97C2×C22⋊#261C2311yescharacteristic
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2311yescharacteristic
100C2×C22⋊#261C2316yes—
101C2×C22⋊#261C2313yes—
102C2×C22⋊#261C2313yes—
103C2×C22⋊#261C2313yes—
104Q8×#261—24no—
105Q8×#261—24no—
106Q8×#261—24no—
107Q8×#261—212no—
108Q8×#261—212no—
109Q8×#261D418yescomplemented
110D4×#261—212no—
111D4×#261—212no—
112#88237—212no—
113#88237—212no—
114#88237—212no—
115C2×C4⋊#261C2311yescharacteristic
116C2×C4⋊#261C2313yes—
117C2×C4⋊#261C2313yes—
118C2×C4⋊#261C2313yes—
119C2×C4⋊#261C2313yes—
120C2×C4⋊#261C2313yes—
121C2×C4⋊#261C2313yes—
122C2×C4⋊#261C2316yes—
123C2×C4⋊#261C2313yes—
124C2×C4×#261—212no—
125C2×C4×#261C2313yes—
126C2×C4×#261C2313yes—
127C2×C4×#261C2313yes—
128C2×C4×#261C2316yes—
129C2×C4×#261C2313yes—
130C2×C4×#261C2311yescharacteristic
131C2×C4×#261C2316yes—
132C2×C4×#261C2313yes—
133C13×#124C2×C413yescomplemented
134C13×C22⋊Q8C2×C413yescomplemented
135C13×#121C2×C413yescomplemented
136C4×Q8×C13C2×C411yescharacteristic, complemented
137C4×D4×C13C2×C413yescomplemented
138#88201C2×C413yescomplemented
139#88200C2×C413yescomplemented
140Q8×Dic13C2×C411yescharacteristic, complemented
141#88193C2×C416yescomplemented
142#88192C2×C413yescomplemented
143#88190C2×C413yescomplemented
144D4×Dic13C2×C413yescomplemented
145#88184C2×C413yescomplemented
146C4×C22⋊D13C2×C413yescomplemented
147C4×C22⋊D13C2×C413yescomplemented
148#88178C2×C413yescomplemented
149#88151C2×C413yescomplemented
150#88150C2×C416yescomplemented
151#88149C2×C413yescomplemented
152#88147C2×C413yescomplemented
153C4⋊C4×D13C2313yes—
154C4⋊C4×D13C2313yes—
155#88141C2×C413yescomplemented
156#88139C2×C416yescomplemented
157#88139C2×C416yescomplemented
158#88138C2×C416yescomplemented
159#88135C2×C413yescomplemented
160#88135C2×C413yescomplemented
161C22⋊C4×D13C2311yescharacteristic
162C22⋊C4×D13C2313yes—
163C22⋊C4×D13C2316yes—
164#88132C2×C416yescomplemented
165#88129C2×C413yescomplemented
166C4×D52C2×C413yescomplemented
167C42×D13C2313yes—
168C4×Dic26C2×C413yescomplemented
169(C2×#261)⋊C4C2311yescharacteristic
170(C2×#261)⋊C4C2313yes—
171(C2×#261)⋊C4C2313yes—
172(C2×#261)⋊C4C2313yes—
173(C2×#261)⋊C4C2313yes—
174(C2×#261)⋊C4C2313yes—
175(C2×#261)⋊C4C2313yes—
176(C2×#261)⋊C4C2316yes—
177(C2×#261)⋊C4C2313yes—
178(C2×#261)⋊C4C2313yes—
179(C2×#261)⋊C4C2311yescharacteristic
180#34293—131nomaximal, Sylow
181C23×D13C2413yes—
182C23×D13C2411yescharacteristic
183C22×#261—26no—
184C22×#261—26no—
185C22×#261—26no—
186C22×#261—43no—
187C22×#261—43no—
188C22×#261—43no—
189C22×#261C2411yescharacteristic
190C22×#261C2413yes—
191C22×#261C2411yescharacteristic
192C22×#261C2413yes—
193C22×#261C2413yes—
194C22×#261C2411yescharacteristic
195C22×#261C2413yes—
196C22×#261C2411yescharacteristic
197C13×#41—24no—
198C2×Q8×C13—24no—
199C2×Q8×C13C22×C413yes—
200C2×Q8×C13C22×C411yescharacteristic
201C2×D4×C13C22×C413yes—
202C2×D4×C13C22×C413yes—
203C22×C4×C13C22×C413yes—
204C22×C4×C13C22×C413yes—
205C2×C22⋊D13C22×C416yes—
206C2×C22⋊D13C22×C413yes—
207C2×C22⋊D13C22×C413yes—
208C22×Dic13C22×C413yes—
209C22×Dic13C22×C413yes—
210#6131—24no—
211Q8×D13—24no—
212Q8×D13—26no—
213Q8×D13—26no—
214Q8×D13—212no—
215Q8×D13C2×D414yes—
216Q8×D13#4114yes—
217#6129—212no—
218D4×D13—26no—
219D4×D13—26no—
220D4×D13—43no—
221D4×D13—43no—
222#6127—212no—
223C2×D52C22×C413yes—
224C2×D52C22×C413yes—
225C2×C4×D13—26no—
226C2×C4×D13—26no—
227C2×C4×D13—26no—
228C2×C4×D13—26no—
229C2×C4×D13C22×C413yes—
230C2×C4×D13C22×C413yes—
231C2×C4×D13C22×C413yes—
232C2×C4×D13C22×C413yes—
233C2×C4×D13C2411yescharacteristic
234C2×C4×D13C2413yes—
235C2×C4×D13C2413yes—
236C2×C4×D13C2411yescharacteristic
237C2×C4×D13C2413yes—
238C2×Dic26—212no—
239C2×Dic26C22×C413yes—
240C2×Dic26C22×C416yes—
241C2×Dic26C22×C413yes—
242C22⋊#261—26no—
243C22⋊#261—22no—
244C22⋊#261—212no—
245C22⋊#261—22no—
246C22⋊#261—43no—
247C22⋊#261—43no—
248C22⋊#261—46no—
249C22⋊#261—43no—
250C4⋊#261—26no—
251C4⋊#261—26no—
252C4⋊#261—22no—
253C4⋊#261—26no—
254C4⋊#261—26no—
255C4⋊#261—26no—
256C4⋊#261—43no—
257C4⋊#261—46no—
258C4⋊#261C2×D4112yes—
259C4×#261—22no—
260C4×#261—26no—
261C4×#261—212no—
262C4×#261—26no—
263C4×#261—26no—
264C4×#261—26no—
265C4×#261—46no—
266C4×#261C2×D4112yes—
267C13×C4⋊C4C22×C413yes—
268C13×C4⋊C4C22×C413yes—
269C13×C22⋊C4C22×C416yes—
270C13×C22⋊C4C22×C411yescharacteristic
271C13×C22⋊C4C22×C413yes—
272C42×C13C22×C413yes—
273C22⋊Dic13C22×C416yes—
274C22⋊Dic13C22×C413yes—
275C22⋊Dic13C22×C411yescharacteristic
276#6103C22×C411yescharacteristic
277#6103C22×C413yes—
278#6103C22×C416yes—
279#6103C22×C416yes—
280#6103C22×C413yes—
281#6103C22×C411yescharacteristic
282C4⋊Dic13C22×C413yes—
283C4⋊Dic13C22×C413yes—
284#6101C22×C416yes—
285#6101C22×C413yes—
286#6101C22×C413yes—
287C4×Dic13C22×C413yes—
288C4×Dic13C22×C413yes—
289C4×Dic13C22×C413yes—
290C2×#548—131no—
291C2×#519—131no—
292C2×C4×#41—131no—
293#2367—133no—
294#2363—133no—
295#2362—133no—
296#2354—133no—
297Q8×C4⋊C4—131no—
298#2341—131no—
299Q8×C22⋊C4—131no—
300#2326—133no—
301#2324—133no—
302C4×C22⋊Q8—133no—
303#2290—133no—
304#2276—131no—
305C23×C13C23×C413yes—
306C23×C13C23×C411yescharacteristic
307C22×D13—21no—
308C22×D13—23no—
309C22×D13—21no—
310C22×D13—23no—
311C22×D13—21no—
312C22×D13—23no—
313C22×D13—21no—
314C22×D13—23no—
315C22×D13—23no—
316C22×D13—23no—
317C22×D13—21no—
318C22×D13—21no—
319C22×D13C23×C413yes—
320C22×D13C23×C411yescharacteristic
321C22×D13C2511yescharacteristic
322C2×#261—21no—
323C2×#261—23no—
324C2×#261—23no—
325C2×#261—21no—
326C2×#261—21no—
327C2×#261—21no—
328C2×#261—23no—
329C2×#261—21no—
330C2×#261—23no—
331C2×#261—21no—
332C2×#261—23no—
333C2×#261—21no—
334C2×#261—21no—
335C2×#261—23no—
336C2×#261—23no—
337C2×#261—23no—
338C2×#261—23no—
339C2×#261—23no—
340C2×#261—21no—
341C2×#261—21no—
342C2×#261—23no—
343C2×#261—412no—
344C2×#261—412no—
345C2×#261C22×D416yes—
346C2×#261C22×D412yes—
347C2×#2612−1+412yes—
348Q8×C13—26no—
349Q8×C13C4×D414yes—
350D4×C13—26no—
351D4×C13—43no—
352C2×C4×C13—26no—
353C2×C4×C13—26no—
354C2×C4×C13C23×C411yescharacteristic
355C2×C4×C13C23×C413yes—
356C2×C4×C13C23×C411yescharacteristic
357C2×C4×C13C23×C413yes—
358C2×C4×C13C23×C413yes—
359C22⋊D13—212no—
360C22⋊D13—43no—
361C22⋊D13—43no—
362C2×Dic13—26no—
363C2×Dic13—26no—
364C2×Dic13C23×C411yescharacteristic
365C2×Dic13C23×C413yes—
366C2×Dic13C23×C411yescharacteristic
367C2×Dic13C23×C413yes—
368C2×Dic13C23×C413yes—
369D52—26no—
370D52—43no—
371C4×D13—21no—
372C4×D13—23no—
373C4×D13—21no—
374C4×D13—23no—
375C4×D13—21no—
376C4×D13—23no—
377C4×D13—21no—
378C4×D13—23no—
379C4×D13—26no—
380C4×D13—26no—
381C4×D13—26no—
382C4×D13—26no—
383C4×D13C22×D416yes—
384C4×D13C2×#4116yes—
385Dic26—26no—
386Dic26—212no—
387Dic26C4×D4112yes—
388C22×#41—131no—
389C23×Q8—131no—
390#548—131no—
391#548—131no—
392#548—133no—
393#548—133no—
394#548—133no—
395#548—131no—
396#548—133no—
397#548#26111yescharacteristic, complemented
398C2×#124—133no—
399C2×C22⋊Q8—133no—
400C2×#121—133no—
401#519—268no—
402C4×#41—268no—
403C2×C4×Q8—131no—
404C2×C4×Q8—131no—
405C2×C4×Q8—133no—
406C2×C4×Q8—131no—
407C2×C4×Q8—131no—
408C2×C4×Q8—131no—
409C2×C4×Q8—133no—
410C2×C4×D4—133no—
411C2×C4×D4—133no—
412C2×C4×D4—133no—
413C2×#117—133no—
414C2×#117—133no—
415C2×#117—133no—
416C22×C42—133no—
417#391—133no—
418#391—133no—
419#390—133no—
420#390—136no—
421#390—133no—
422#389—133no—
423#389—133no—
424#388—136no—
425#388—136no—
426#388—136no—
427#388—133no—
428#388—131no—
429#387—133no—
430#387—133no—
431#386—133no—
432#386—133no—
433#385—136no—
434#385—133no—
435#385—133no—
436#384—133no—
437#380—133no—
438#380—133no—
439C4×C4⋊C4—133no—
440C4×C4⋊C4—133no—
441C4×C4⋊C4—136no—
442C4×C4⋊C4—133no—
443C4×C4⋊C4—133no—
444C4×C22⋊C4—133no—
445C4×C22⋊C4—133no—
446C4×C22⋊C4—136no—
447#376—133no—
448C22×C13—21no—
449C22×C13—23no—
450C22×C13—21no—
451C22×C13—23no—
452C22×C13—21no—
453C22×C13—23no—
454C22×C13C24×C411yescharacteristic
455C2×D13—21no—
456C2×D13—23no—
457C2×D13—21no—
458C2×D13—23no—
459C2×D13—21no—
460C2×D13—23no—
461C2×D13—43no—
462C2×D13—41no—
463C2×D13—43no—
464C2×D13—41no—
465C2×D13—41no—
466C2×D13—43no—
467C2×D13—41no—
468C2×D13—43no—
469C2×D13C23×D411yescharacteristic
470C2×D13C22×#4111yescharacteristic
471C2×D13C2×2−1+411yescharacteristic
472C2×D13#58511yescharacteristic
473C2×D13#58511yescharacteristic
474C2×D13#58511yescharacteristic
475#261—22no—
476#261—22no—
477#261—26no—
478#261—43no—
479#261—43no—
480#261—41no—
481#261—41no—
482#261—43no—
483C4×C13—23no—
484C4×C13—21no—
485C4×C13—23no—
486C4×C13—21no—
487C4×C13C2×C4×D416yes—
488Dic13—23no—
489Dic13—21no—
490Dic13—23no—
491Dic13—21no—
492Dic13C2×C4×D416yes—
493C2×#41—131no—
494C2×#41—133no—
495C2×#41—133no—
496C2×#41—264no—
497C2×#41—264no—
498C2×#41C2×#26111yescharacteristic
499C22×Q8—131no—
500C22×Q8—133no—
501C22×Q8—133no—
502C22×Q8—131no—
503C22×Q8—133no—
504C22×Q8—264no—
505C22×Q8—264no—
506C22×Q8C2×#26111yescharacteristic, complemented
507C22×D4—133no—
508C22×D4—133no—
509C23×C4—133no—
510C23×C4—133no—
511C23×C4—133no—
512C23×C4—133no—
513#124—133no—
514#124—133no—
515#124—136no—
516#124—136no—
517#124—133no—
518#124C2×#26113yescomplemented
519C22⋊Q8—133no—
520C22⋊Q8—133no—
521C22⋊Q8—136no—
522C22⋊Q8—133no—
523C22⋊Q8—136no—
524C22⋊Q8C2×#26113yescomplemented
525#121—133no—
526#121—136no—
527#121—133no—
528#121—133no—
529#121—136no—
530#121C2×#26113yescomplemented
531C4×Q8—138no—
532C4×Q8—131no—
533C4×Q8—133no—
534C4×Q8—133no—
535C4×Q8—2612no—
536C4×Q8—2612no—
537C4×Q8—264no—
538C4×Q8—264no—
539C4×Q8—264no—
540C4×Q8C2×#26111yescharacteristic, complemented
541C4×D4—133no—
542C4×D4—133no—
543C4×D4—133no—
544C4×D4—133no—
545C4×D4—133no—
546C4×D4—133no—
547C4×D4—133no—
548C4×D4—2612no—
549C4×D4—2612no—
550C4×D4C2×#26113yescomplemented
551#117—2612no—
552#117—2612no—
553#117—2612no—
554C2×C4⋊C4—133no—
555C2×C4⋊C4—133no—
556C2×C4⋊C4—133no—
557C2×C4⋊C4—133no—
558C2×C4⋊C4—133no—
559C2×C4⋊C4—133no—
560C2×C4⋊C4—133no—
561C2×C4⋊C4—133no—
562C2×C4⋊C4—131no—
563C2×C4⋊C4—133no—
564C2×C4⋊C4—136no—
565C2×C22⋊C4—131no—
566C2×C22⋊C4—133no—
567C2×C22⋊C4—136no—
568C2×C22⋊C4—131no—
569C2×C22⋊C4—133no—
570C2×C22⋊C4—136no—
571C2×C22⋊C4—131no—
572C2×C22⋊C4—133no—
573C2×C22⋊C4—136no—
574C2×C22⋊C4—133no—
575C2×C22⋊C4—133no—
576C2×C42—133no—
577C2×C42—133no—
578C2×C42—133no—
579C2×C42—136no—
580C2×C42—133no—
581C2×C42—133no—
582C2×C42—133no—
583C2×C42—131no—
584C2×C42—136no—
585C2×C42—2612no—
586#95—131no—
587#95—133no—
588#95—133no—
589#95—133no—
590#95—133no—
591#95—131no—
592#95—133no—
593#95—133no—
594#95—133no—
595#95—136no—
596#95—133no—
597C2×C13—43no—
598C2×C13—41no—
599C2×C13C22×C4×D411yescharacteristic
600C2×C13#342811yescharacteristic
601C2×C13C4×2−1+411yescharacteristic
602D13—41no—
603D13—43no—
604D13#348711yescharacteristic
605D13#348911yescharacteristic
606D13#351811yescharacteristic
607D13#352411yescharacteristic
608C24—133no—
609C24—131no—
610#41—24no—
611#41—2612no—
612#41—2612no—
613#41—264no—
614C2×Q8—24no—
615C2×Q8—134no—
616C2×Q8—134no—
617C2×Q8—133no—
618C2×Q8—136no—
619C2×Q8—133no—
620C2×Q8—2612no—
621C2×Q8—266no—
622C2×Q8—266no—
623C2×Q8—2612no—
624C2×Q8—264no—
625C2×Q8C22×#26113yes—
626C2×Q8C22×#26111yescharacteristic
627C2×D4—136no—
628C2×D4—133no—
629C2×D4—133no—
630C2×D4—133no—
631C2×D4—133no—
632C2×D4—266no—
633C2×D4—266no—
634C2×D4—523no—
635C2×D4—523no—
636C2×D4C22×#26113yes—
637C2×D4C22×#26113yes—
638C22×C4—133no—
639C22×C4—131no—
640C22×C4—131no—
641C22×C4—133no—
642C22×C4—133no—
643C22×C4—133no—
644C22×C4—131no—
645C22×C4—131no—
646C22×C4—133no—
647C22×C4—133no—
648C22×C4—133no—
649C22×C4—133no—
650C22×C4—133no—
651C22×C4—133no—
652C22×C4—131no—
653C22×C4—133no—
654C22×C4—131no—
655C22×C4—133no—
656C22×C4—133no—
657C22×C4—266no—
658C22×C4—266no—
659C22×C4—266no—
660C22×C4—266no—
661C22×C4—266no—
662C22×C4—266no—
663C22×C4—266no—
664C22×C4—523no—
665C22×C4—523no—
666C22×C4—523no—
667C22×C4C22×#26113yes—
668C22×C4C22×#26113yes—
669C4⋊C4—1312no—
670C4⋊C4—133no—
671C4⋊C4—133no—
672C4⋊C4—133no—
673C4⋊C4—136no—
674C4⋊C4—133no—
675C4⋊C4—266no—
676C4⋊C4—266no—
677C4⋊C4—266no—
678C4⋊C4—266no—
679C4⋊C4—266no—
680C4⋊C4—262no—
681C4⋊C4—523no—
682C4⋊C4—526no—
683C4⋊C4C22×#26113yes—
684C4⋊C4C22×#26113yes—
685C22⋊C4—131no—
686C22⋊C4—133no—
687C22⋊C4—136no—
688C22⋊C4—131no—
689C22⋊C4—131no—
690C22⋊C4—133no—
691C22⋊C4—133no—
692C22⋊C4—136no—
693C22⋊C4—136no—
694C22⋊C4—262no—
695C22⋊C4—266no—
696C22⋊C4—2612no—
697C22⋊C4—262no—
698C22⋊C4—523no—
699C22⋊C4—526no—
700C22⋊C4—523no—
701C22⋊C4—523no—
702C22⋊C4C22×#26111yescharacteristic
703C22⋊C4C22×#26113yes—
704C22⋊C4C22×#26116yes—
705C42—1312no—
706C42—133no—
707C42—133no—
708C42—133no—
709C42—262no—
710C42—266no—
711C42—266no—
712C42—266no—
713C42—2612no—
714C42—266no—
715C42—526no—
716C42C22×#26113yes—
717C13#3429311yescharacteristic, complemented, Sylow
718C23—131no—
719C23—133no—
720C23—131no—
721C23—261no—
722C23—263no—
723C23—261no—
724C23—261no—
725C23—263no—
726C23—263no—
727C23—263no—
728C23—261no—
729C23—263no—
730C23—263no—
731C23—261no—
732C23—261no—
733C23C23×#26113yes—
734C23C23×#26111yescharacteristic
735Q8—26no—
736Q8—1312no—
737Q8—2612no—
738Q8—266no—
739Q8D4×#26114yes—
740D4—26no—
741D4—43no—
742D4—2612no—
743D4—266no—
744D4—523no—
745D4—523no—
746D4—523no—
747C2×C4—26no—
748C2×C4—26no—
749C2×C4—133no—
750C2×C4—136no—
751C2×C4—136no—
752C2×C4—132no—
753C2×C4—136no—
754C2×C4—132no—
755C2×C4—131no—
756C2×C4—133no—
757C2×C4—133no—
758C2×C4—131no—
759C2×C4—266no—
760C2×C4—266no—
761C2×C4—261no—
762C2×C4—263no—
763C2×C4—263no—
764C2×C4—261no—
765C2×C4—261no—
766C2×C4—263no—
767C2×C4—261no—
768C2×C4—263no—
769C2×C4—266no—
770C2×C4—266no—
771C2×C4—261no—
772C2×C4—263no—
773C2×C4—263no—
774C2×C4—261no—
775C2×C4—261no—
776C2×C4—261no—
777C2×C4—266no—
778C2×C4—266no—
779C2×C4—261no—
780C2×C4—263no—
781C2×C4—261no—
782C2×C4—263no—
783C2×C4—263no—
784C2×C4—263no—
785C2×C4—261no—
786C2×C4—261no—
787C2×C4—261no—
788C2×C4—263no—
789C2×C4—263no—
790C2×C4—263no—
791C2×C4—263no—
792C2×C4—261no—
793C2×C4—263no—
794C2×C4—5212no—
795C2×C4—5212no—
796C2×C4C23×#26111yescharacteristic
797C2×C4C23×#26113yes—
798C2×C4C23×#26113yes—
799C2×C4C23×#26111yescharacteristic
800C2×C4C23×#26113yes—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—21no—
806C22—23no—
807C22—131no—
808C22—131no—
809C22—131no—
810C22—131no—
811C22—131no—
812C22—131no—
813C22—261no—
814C22—263no—
815C22—261no—
816C22—263no—
817C22—263no—
818C22—261no—
819C22—523no—
820C22—523no—
821C22—521no—
822C22—521no—
823C22—521no—
824C22—523no—
825C22—521no—
826C22—523no—
827C22C24×#26111yescharacteristic
828C4—21no—
829C4—23no—
830C4—23no—
831C4—21no—
832C4—136no—
833C4—266no—
834C4—262no—
835C4—262no—
836C4—261no—
837C4—263no—
838C4—263no—
839C4—261no—
840C4—521no—
841C4—523no—
842C4—523no—
843C4—521no—
844C4—523no—
845C4C2×D4×#26116yes—
846C2—41no—
847C2—43no—
848C2—131no—
849C2—131no—
850C2—131no—
851C2—131no—
852C2—521no—
853C2—523no—
854C2C22×D4×#26111yescharacteristic
855C2#1313181611yescharacteristic
856C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#548C4
prime radicalD13×#548C2
cosocleC22×D13C25
hypercenter#548#261
hypocenterC13#34293
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11719627C2semidirect
2. C2×#41×#261C2semidirect
3. #13131367C2semidirect
4. #13131363C2semidirect
5. #13131362C2semidirect
6. #13131354C2semidirect
7. Q8×C4⋊#261C2semidirect
8. #13131341C2semidirect
9. Q8×C22⋊#261C2semidirect
10. #13131326C2semidirect
11. #13131324C2semidirect
12. C22⋊Q8×#261C2semidirect
13. #13131290C2semidirect
14. #13131276C2semidirect
32. C13×#548C4semidirect
33. #11719536C4semidirect
34. #11719522C4semidirect
35. #11719382C4semidirect
37. #11719338C4semidirect
40. #11719303C4semidirect
41. #11719281C4semidirect
43. #11719257C4semidirect
79. C22×Q8×C13C2×C4semidirect
85. C2×Q8×D13C2×C4semidirect
86. C2×Q8×D13C2×C4semidirect
95. C22×Dic26C2×C4semidirect
109. Q8×#261D4semidirect
133. C13×#124C2×C4semidirect
134. C13×C22⋊Q8C2×C4semidirect
135. C13×#121C2×C4semidirect
136. C4×Q8×C13C2×C4semidirect
137. C4×D4×C13C2×C4semidirect
138. #88201C2×C4semidirect
139. #88200C2×C4semidirect
140. Q8×Dic13C2×C4semidirect
141. #88193C2×C4semidirect
142. #88192C2×C4semidirect
143. #88190C2×C4semidirect
144. D4×Dic13C2×C4semidirect
145. #88184C2×C4semidirect
146. C4×C22⋊D13C2×C4semidirect
147. C4×C22⋊D13C2×C4semidirect
148. #88178C2×C4semidirect
149. #88151C2×C4semidirect
150. #88150C2×C4semidirect
151. #88149C2×C4semidirect
152. #88147C2×C4semidirect
155. #88141C2×C4semidirect
156. #88139C2×C4semidirect
157. #88139C2×C4semidirect
158. #88138C2×C4semidirect
159. #88135C2×C4semidirect
160. #88135C2×C4semidirect
164. #88132C2×C4semidirect
165. #88129C2×C4semidirect
166. C4×D52C2×C4semidirect
168. C4×Dic26C2×C4semidirect
397. #548#261semidirect
506. C22×Q8C2×#261semidirect
518. #124C2×#261semidirect
524. C22⋊Q8C2×#261semidirect
530. #121C2×#261semidirect
540. C4×Q8C2×#261semidirect
550. C4×D4C2×#261semidirect
717. C13#34293semidirect

Maximal subgroups

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

subgroupindex
C2×#117196272
C2×#41×#2612
#131313672
#131313632
#131313622
#131313542
Q8×C4⋊#2612
#131313412
Q8×C22⋊#2612
#131313262
#131313242
C22⋊Q8×#2612
#131312902
#131312762
D13×#5482
#3429313