Finite Group Databasebeta

← #16807774

Subgroups — #16807774

Order 3328.

2960 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719631C211yesmaximal, characteristic, complemented
2C2×#11719627C211yesmaximal, characteristic, complemented
3#13131367C213yesmaximal, complemented
4#13131363C213yesmaximal, complemented
5#13131360C213yesmaximal, complemented
6#13131352C213yesmaximal, complemented
7#13131351C211yesmaximal, characteristic, complemented
8#13131341C211yesmaximal, characteristic, complemented
9Q8×C22⋊#261C211yesmaximal, characteristic, complemented
10#13131324C213yesmaximal, complemented
11#13131323C213yesmaximal, complemented
12#124×#261C213yesmaximal, complemented
13#13131293C213yesmaximal, complemented
14C4×Q8×#261C211yesmaximal, characteristic, complemented
15D13×#548C211yesmaximal, characteristic
16C2×#41×D13C2211yescharacteristic
17C22×Q8×D13C2211yescharacteristic
18#11719631—28no—
19#11719627—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×#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#11719151C2213yes—
49#11719151C2213yes—
50#11719151C2213yes—
51#11719150C2216yes—
52#11719136C2213yes—
53#11719136C2213yes—
54C4×C22⋊#261C2213yes—
55C4×C22⋊#261C2213yes—
56#11719083C2213yes—
57#11719083C2213yes—
58#11719083C2213yes—
59#11719083C2213yes—
60#11719082C2216yes—
61C4⋊C4×#261C2213yes—
62C4⋊C4×#261C2213yes—
63#11719071C2211yescharacteristic
64#11719071C2213yes—
65#11719071C2213yes—
66#11719071C2213yes—
67#11719071C2216yes—
68#11719071C2216yes—
69#11719070C2216yes—
70C22⋊C4×#261C2216yes—
71C22⋊C4×#261C2216yes—
72#11719060C2213yes—
73C4×C4⋊#261C2213yes—
74C4×C4⋊#261C2213yes—
75C42×#261C2213yes—
76C23×#261C2316yes—
77C2×C13×#41C2×C411yescharacteristic
78C22×Q8×C13C2×C411yescharacteristic, complemented
79#41×D13—24no—
80#41×D13—24no—
81C2×#6131C2×C411yescharacteristic
82C2×Q8×D13—24no—
83C2×Q8×D13—24no—
84C2×Q8×D13C2×C411yescharacteristic, complemented
85C2×Q8×D13C2×C413yescomplemented
86C2×Q8×D13C2313yes—
87C2×Q8×D13C2311yescharacteristic
88C2×#6129C2×C413yes—
89C2×D4×D13C2313yes—
90C2×D4×D13C2313yes—
91C2×#6127C2×C413yes—
92C22×C4×D13C2313yes—
93C22×C4×D13C2313yes—
94C22×Dic26C2×C413yescomplemented
95C2×C22⋊#261C2313yes—
96C2×C22⋊#261C2313yes—
97C2×C22⋊#261C2313yes—
98C2×C22⋊#261C2313yes—
99C2×C22⋊#261C2311yescharacteristic
100C2×C22⋊#261C2311yescharacteristic
101C2×C22⋊#261C2316yes—
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⋊#261—212no—
116C2×C4⋊#261C2313yes—
117C2×C4⋊#261C2313yes—
118C2×C4⋊#261C2313yes—
119C2×C4⋊#261C2313yes—
120C2×C4⋊#261C2313yes—
121C2×C4⋊#261C2313yes—
122C2×C4⋊#261C2311yescharacteristic
123C2×C4⋊#261C2313yes—
124C2×C4⋊#261C2313yes—
125C2×C4⋊#261C2313yes—
126C2×C4×#261C2311yescharacteristic
127C2×C4×#261C2313yes—
128C2×C4×#261C2313yes—
129C2×C4×#261C2313yes—
130C2×C4×#261C2316yes—
131C2×C4×#261C2313yes—
132C2×C4×#261C2313yes—
133C2×C4×#261C2313yes—
134C2×C4×#261C2313yes—
135C13×#124C2×C413yescomplemented
136C13×C22⋊Q8C2×C413yescomplemented
137C13×#121C2×C413yescomplemented
138C4×Q8×C13C2×C411yescharacteristic, complemented
139C4×D4×C13C2×C413yescomplemented
140#88201C2×C413yescomplemented
141#88200C2×C413yescomplemented
142Q8×Dic13C2×C411yescharacteristic, complemented
143#88193C2×C416yescomplemented
144#88192C2×C413yescomplemented
145#88190C2×C413yescomplemented
146D4×Dic13C2×C413yescomplemented
147#88184C2×C413yescomplemented
148C4×C22⋊D13C2×C413yescomplemented
149C4×C22⋊D13C2×C413yescomplemented
150#88178C2×C413yescomplemented
151#88151C2×C413yescomplemented
152#88150C2×C416yescomplemented
153#88149C2×C413yescomplemented
154#88147C2×C413yescomplemented
155C4⋊C4×D13C2313yes—
156C4⋊C4×D13C2313yes—
157#88141C2×C413yescomplemented
158#88139C2×C416yescomplemented
159#88139C2×C416yescomplemented
160#88138C2×C416yescomplemented
161#88135C2×C413yescomplemented
162#88135C2×C413yescomplemented
163C22⋊C4×D13C2311yescharacteristic
164C22⋊C4×D13C2313yes—
165C22⋊C4×D13C2316yes—
166#88132C2×C416yescomplemented
167#88129C2×C413yescomplemented
168C4×D52C2×C413yescomplemented
169C42×D13C2313yes—
170C4×Dic26C2×C413yescomplemented
171(C2×#261)⋊C4C2311yescharacteristic
172(C2×#261)⋊C4C2313yes—
173(C2×#261)⋊C4C2316yes—
174(C2×#261)⋊C4C2316yes—
175(C2×#261)⋊C4C2313yes—
176(C2×#261)⋊C4C2316yes—
177(C2×#261)⋊C4C2313yes—
178(C2×#261)⋊C4C2313yes—
179(C2×#261)⋊C4C2311yescharacteristic
180#34312—131nomaximal, Sylow
181C23×D13C2413yes—
182C23×D13C2411yescharacteristic
183C22×#261—212no—
184C22×#261—46no—
185C22×#261—46no—
186C22×#261C2413yes—
187C22×#261C2413yes—
188C22×#261C2413yes—
189C22×#261C2411yescharacteristic
190C22×#261C2411yescharacteristic
191C22×#261C2413yes—
192C22×#261C2411yescharacteristic
193C22×#261C2411yescharacteristic
194C13×#41—24no—
195C2×Q8×C13—24no—
196C2×Q8×C13C22×C413yes—
197C2×Q8×C13C22×C411yescharacteristic
198C2×D4×C13C22×C413yes—
199C2×D4×C13C22×C413yes—
200C22×C4×C13C22×C413yes—
201C22×C4×C13C22×C413yes—
202C2×C22⋊D13C22×C416yes—
203C2×C22⋊D13C22×C413yes—
204C2×C22⋊D13C22×C413yes—
205C22×Dic13C22×C413yes—
206C22×Dic13C22×C413yes—
207#6131—24no—
208Q8×D13—24no—
209Q8×D13—26no—
210Q8×D13—26no—
211Q8×D13—212no—
212Q8×D13C2×D414yes—
213Q8×D13#4114yes—
214#6129—212no—
215D4×D13—26no—
216D4×D13—26no—
217D4×D13—43no—
218D4×D13—43no—
219#6127—212no—
220C2×D52C22×C413yes—
221C2×D52C22×C413yes—
222C2×C4×D13—26no—
223C2×C4×D13—26no—
224C2×C4×D13—26no—
225C2×C4×D13—26no—
226C2×C4×D13C22×C413yes—
227C2×C4×D13C22×C413yes—
228C2×C4×D13C22×C413yes—
229C2×C4×D13C22×C413yes—
230C2×C4×D13C2411yescharacteristic
231C2×C4×D13C2413yes—
232C2×C4×D13C2413yes—
233C2×C4×D13C2411yescharacteristic
234C2×C4×D13C2413yes—
235C2×Dic26—212no—
236C2×Dic26C22×C413yes—
237C2×Dic26C22×C416yes—
238C2×Dic26C22×C413yes—
239C22⋊#261—26no—
240C22⋊#261—22no—
241C22⋊#261—26no—
242C22⋊#261—26no—
243C22⋊#261—26no—
244C22⋊#261—22no—
245C22⋊#261—46no—
246C22⋊#261—43no—
247C22⋊#261—43no—
248C4⋊#261—26no—
249C4⋊#261—22no—
250C4⋊#261—26no—
251C4⋊#261—26no—
252C4⋊#261—26no—
253C4⋊#261—26no—
254C4⋊#261—26no—
255C4⋊#261—43no—
256C4⋊#261—43no—
257C4⋊#261C2×D4112yes—
258C4×#261—212no—
259C4×#261—22no—
260C4×#261—26no—
261C4×#261—26no—
262C4×#261—26no—
263C4×#261—43no—
264C4×#261—43no—
265C4×#261—43no—
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×#520—131no—
292C2×#519—131no—
293#2367—133no—
294#2363—133no—
295#2360—133no—
296#2352—133no—
297#2351—131no—
298#2341—131no—
299Q8×C22⋊C4—131no—
300#2324—133no—
301#2323—133no—
302C4×#124—133no—
303#2293—133no—
304C42×Q8—131no—
305C23×C13C23×C413yes—
306C23×C13C23×C411yescharacteristic
307C22×D13—21no—
308C22×D13—23no—
309C22×D13—21no—
310C22×D13—23no—
311C22×D13—23no—
312C22×D13—21no—
313C22×D13—21no—
314C22×D13—23no—
315C22×D13—23no—
316C22×D13—21no—
317C22×D13—21no—
318C22×D13—23no—
319C22×D13C23×C413yes—
320C22×D13C23×C411yescharacteristic
321C22×D13C2511yescharacteristic
322C2×#261—21no—
323C2×#261—21no—
324C2×#261—21no—
325C2×#261—21no—
326C2×#261—23no—
327C2×#261—23no—
328C2×#261—23no—
329C2×#261—21no—
330C2×#261—21no—
331C2×#261—23no—
332C2×#261—23no—
333C2×#261—23no—
334C2×#261—21no—
335C2×#261—23no—
336C2×#261—23no—
337C2×#261—21no—
338C2×#261—21no—
339C2×#261—23no—
340C2×#261—23no—
341C2×#261—21no—
342C2×#261—23no—
343C2×#261—812no—
344C2×#261C22×D416yes—
345C2×#261C22×D412yes—
346C2×#2612−1+412yes—
347Q8×C13—26no—
348Q8×C13C4×D414yes—
349D4×C13—26no—
350D4×C13—43no—
351C2×C4×C13—26no—
352C2×C4×C13—26no—
353C2×C4×C13C23×C411yescharacteristic
354C2×C4×C13C23×C413yes—
355C2×C4×C13C23×C411yescharacteristic
356C2×C4×C13C23×C413yes—
357C2×C4×C13C23×C413yes—
358C22⋊D13—212no—
359C22⋊D13—43no—
360C22⋊D13—43no—
361C2×Dic13—26no—
362C2×Dic13—26no—
363C2×Dic13C23×C411yescharacteristic
364C2×Dic13C23×C413yes—
365C2×Dic13C23×C411yescharacteristic
366C2×Dic13C23×C413yes—
367C2×Dic13C23×C413yes—
368D52—26no—
369D52—43no—
370C4×D13—23no—
371C4×D13—21no—
372C4×D13—21no—
373C4×D13—23no—
374C4×D13—21no—
375C4×D13—21no—
376C4×D13—23no—
377C4×D13—23no—
378C4×D13—26no—
379C4×D13—26no—
380C4×D13—26no—
381C4×D13—26no—
382C4×D13C22×D416yes—
383C4×D13C2×#4116yes—
384Dic26—26no—
385Dic26—212no—
386Dic26C4×D4112yes—
387C22×#41—131no—
388C23×Q8—131no—
389#548—131no—
390#548—131no—
391#548—133no—
392#548—133no—
393#548—133no—
394#548—131no—
395#548—133no—
396#548#26111yescharacteristic, complemented
397C2×#124—133no—
398C2×C22⋊Q8—133no—
399C2×#121—133no—
400#520—268no—
401#519—268no—
402C2×C4×Q8—131no—
403C2×C4×Q8—131no—
404C2×C4×Q8—133no—
405C2×C4×Q8—131no—
406C2×C4×Q8—131no—
407C2×C4×Q8—131no—
408C2×C4×Q8—133no—
409C2×C4×D4—133no—
410C2×C4×D4—133no—
411C2×C4×D4—133no—
412C2×#117—133no—
413C2×#117—133no—
414C2×#117—133no—
415C22×C4⋊C4—133no—
416#391—133no—
417#391—133no—
418#390—133no—
419#390—133no—
420#390—133no—
421#390—133no—
422#389—133no—
423#389—133no—
424#389—133no—
425#389—133no—
426#388—136no—
427#388—136no—
428#388—133no—
429#388—133no—
430#388—131no—
431#388—133no—
432#387—136no—
433#386—136no—
434#385—136no—
435#382—133no—
436#380—133no—
437#380—133no—
438C4×C4⋊C4—133no—
439C4×C4⋊C4—133no—
440C4×C4⋊C4—133no—
441C4×C4⋊C4—133no—
442C4×C22⋊C4—133no—
443C4×C22⋊C4—133no—
444C4×C22⋊C4—136no—
445C4×C22⋊C4—136no—
446C43—133no—
447C22×C13—21no—
448C22×C13—23no—
449C22×C13—21no—
450C22×C13—23no—
451C22×C13—21no—
452C22×C13—23no—
453C22×C13C24×C411yescharacteristic
454C2×D13—21no—
455C2×D13—23no—
456C2×D13—21no—
457C2×D13—23no—
458C2×D13—21no—
459C2×D13—23no—
460C2×D13—41no—
461C2×D13—43no—
462C2×D13—43no—
463C2×D13—41no—
464C2×D13—41no—
465C2×D13—43no—
466C2×D13—41no—
467C2×D13—43no—
468C2×D13C23×D411yescharacteristic
469C2×D13C22×#4111yescharacteristic
470C2×D13C2×2−1+411yescharacteristic
471C2×D13#58511yescharacteristic
472C2×D13#58511yescharacteristic
473C2×D13#58511yescharacteristic
474#261—22no—
475#261—26no—
476#261—22no—
477#261—43no—
478#261—41no—
479#261—41no—
480#261—43no—
481#261—43no—
482C4×C13—23no—
483C4×C13—21no—
484C4×C13—23no—
485C4×C13—21no—
486C4×C13C2×C4×D416yes—
487Dic13—23no—
488Dic13—21no—
489Dic13—23no—
490Dic13—21no—
491Dic13C2×C4×D416yes—
492C2×#41—131no—
493C2×#41—133no—
494C2×#41—133no—
495C2×#41—264no—
496C2×#41—264no—
497C2×#41C2×#26111yescharacteristic
498C22×Q8—131no—
499C22×Q8—133no—
500C22×Q8—133no—
501C22×Q8—131no—
502C22×Q8—133no—
503C22×Q8—264no—
504C22×Q8—264no—
505C22×Q8C2×#26111yescharacteristic, complemented
506C22×D4—133no—
507C22×D4—133no—
508C23×C4—133no—
509C23×C4—133no—
510C23×C4—136no—
511#124—133no—
512#124—133no—
513#124—136no—
514#124—136no—
515#124—133no—
516#124C2×#26113yescomplemented
517C22⋊Q8—133no—
518C22⋊Q8—133no—
519C22⋊Q8—136no—
520C22⋊Q8—133no—
521C22⋊Q8—136no—
522C22⋊Q8C2×#26113yescomplemented
523#121—133no—
524#121—136no—
525#121—133no—
526#121—133no—
527#121—136no—
528#121C2×#26113yescomplemented
529C4×Q8—138no—
530C4×Q8—131no—
531C4×Q8—133no—
532C4×Q8—133no—
533C4×Q8—2612no—
534C4×Q8—2612no—
535C4×Q8—264no—
536C4×Q8—264no—
537C4×Q8—264no—
538C4×Q8C2×#26111yescharacteristic, complemented
539C4×D4—133no—
540C4×D4—133no—
541C4×D4—133no—
542C4×D4—133no—
543C4×D4—133no—
544C4×D4—133no—
545C4×D4—133no—
546C4×D4—2612no—
547C4×D4—2612no—
548C4×D4C2×#26113yescomplemented
549#117—2612no—
550#117—2612no—
551#117—2612no—
552C2×C4⋊C4—133no—
553C2×C4⋊C4—133no—
554C2×C4⋊C4—133no—
555C2×C4⋊C4—133no—
556C2×C4⋊C4—133no—
557C2×C4⋊C4—131no—
558C2×C4⋊C4—133no—
559C2×C4⋊C4—133no—
560C2×C4⋊C4—133no—
561C2×C4⋊C4—133no—
562C2×C4⋊C4—133no—
563C2×C4⋊C4—133no—
564C2×C4⋊C4—2612no—
565C2×C22⋊C4—131no—
566C2×C22⋊C4—133no—
567C2×C22⋊C4—136no—
568C2×C22⋊C4—133no—
569C2×C22⋊C4—131no—
570C2×C22⋊C4—133no—
571C2×C22⋊C4—133no—
572C2×C22⋊C4—131no—
573C2×C22⋊C4—133no—
574C2×C22⋊C4—133no—
575C2×C22⋊C4—136no—
576C2×C22⋊C4—133no—
577C2×C42—133no—
578C2×C42—133no—
579C2×C42—133no—
580C2×C42—136no—
581C2×C42—133no—
582C2×C42—133no—
583C2×C42—131no—
584C2×C42—133no—
585C2×C42—133no—
586C2×C42—133no—
587#95—131no—
588#95—133no—
589#95—133no—
590#95—133no—
591#95—136no—
592#95—136no—
593#95—133no—
594#95—136no—
595#95—131no—
596C2×C13—43no—
597C2×C13—41no—
598C2×C13C22×C4×D411yescharacteristic
599C2×C13#342811yescharacteristic
600C2×C13C4×2−1+411yescharacteristic
601D13—41no—
602D13—43no—
603D13#349711yescharacteristic
604D13#350011yescharacteristic
605D13#351611yescharacteristic
606D13#352411yescharacteristic
607C24—133no—
608C24—131no—
609#41—24no—
610#41—2612no—
611#41—2612no—
612#41—264no—
613C2×Q8—24no—
614C2×Q8—134no—
615C2×Q8—134no—
616C2×Q8—133no—
617C2×Q8—136no—
618C2×Q8—133no—
619C2×Q8—2612no—
620C2×Q8—266no—
621C2×Q8—266no—
622C2×Q8—2612no—
623C2×Q8—264no—
624C2×Q8C22×#26113yes—
625C2×Q8C22×#26111yescharacteristic
626C2×D4—136no—
627C2×D4—133no—
628C2×D4—133no—
629C2×D4—133no—
630C2×D4—133no—
631C2×D4—266no—
632C2×D4—266no—
633C2×D4—523no—
634C2×D4—523no—
635C2×D4C22×#26113yes—
636C2×D4C22×#26113yes—
637C22×C4—133no—
638C22×C4—131no—
639C22×C4—133no—
640C22×C4—131no—
641C22×C4—133no—
642C22×C4—133no—
643C22×C4—131no—
644C22×C4—133no—
645C22×C4—133no—
646C22×C4—131no—
647C22×C4—133no—
648C22×C4—133no—
649C22×C4—133no—
650C22×C4—133no—
651C22×C4—133no—
652C22×C4—133no—
653C22×C4—131no—
654C22×C4—133no—
655C22×C4—131no—
656C22×C4—266no—
657C22×C4—266no—
658C22×C4—266no—
659C22×C4—266no—
660C22×C4—2612no—
661C22×C4—526no—
662C22×C4—526no—
663C22×C4C22×#26113yes—
664C22×C4C22×#26113yes—
665C4⋊C4—1312no—
666C4⋊C4—133no—
667C4⋊C4—133no—
668C4⋊C4—133no—
669C4⋊C4—136no—
670C4⋊C4—133no—
671C4⋊C4—266no—
672C4⋊C4—266no—
673C4⋊C4—262no—
674C4⋊C4—266no—
675C4⋊C4—266no—
676C4⋊C4—266no—
677C4⋊C4—266no—
678C4⋊C4—523no—
679C4⋊C4—523no—
680C4⋊C4C22×#26113yes—
681C4⋊C4C22×#26113yes—
682C22⋊C4—131no—
683C22⋊C4—133no—
684C22⋊C4—136no—
685C22⋊C4—131no—
686C22⋊C4—131no—
687C22⋊C4—133no—
688C22⋊C4—133no—
689C22⋊C4—136no—
690C22⋊C4—136no—
691C22⋊C4—262no—
692C22⋊C4—266no—
693C22⋊C4—266no—
694C22⋊C4—266no—
695C22⋊C4—262no—
696C22⋊C4—266no—
697C22⋊C4—523no—
698C22⋊C4—526no—
699C22⋊C4—523no—
700C22⋊C4C22×#26111yescharacteristic
701C22⋊C4C22×#26113yes—
702C22⋊C4C22×#26116yes—
703C42—1312no—
704C42—133no—
705C42—133no—
706C42—133no—
707C42—266no—
708C42—266no—
709C42—2612no—
710C42—266no—
711C42—262no—
712C42—523no—
713C42—523no—
714C42—523no—
715C42C22×#26113yes—
716C13#3431211yescharacteristic, complemented, Sylow
717C23—131no—
718C23—133no—
719C23—131no—
720C23—261no—
721C23—263no—
722C23—261no—
723C23—263no—
724C23—261no—
725C23—263no—
726C23—263no—
727C23—261no—
728C23—263no—
729C23—263no—
730C23—261no—
731C23—261no—
732C23C23×#26113yes—
733C23C23×#26111yescharacteristic
734Q8—26no—
735Q8—1312no—
736Q8—2612no—
737Q8—266no—
738Q8D4×#26114yes—
739D4—26no—
740D4—43no—
741D4—2612no—
742D4—266no—
743D4—523no—
744D4—523no—
745D4—523no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—133no—
749C2×C4—136no—
750C2×C4—136no—
751C2×C4—132no—
752C2×C4—136no—
753C2×C4—132no—
754C2×C4—131no—
755C2×C4—133no—
756C2×C4—133no—
757C2×C4—131no—
758C2×C4—266no—
759C2×C4—266no—
760C2×C4—263no—
761C2×C4—261no—
762C2×C4—261no—
763C2×C4—263no—
764C2×C4—263no—
765C2×C4—261no—
766C2×C4—261no—
767C2×C4—263no—
768C2×C4—266no—
769C2×C4—266no—
770C2×C4—261no—
771C2×C4—261no—
772C2×C4—261no—
773C2×C4—261no—
774C2×C4—263no—
775C2×C4—263no—
776C2×C4—266no—
777C2×C4—266no—
778C2×C4—261no—
779C2×C4—263no—
780C2×C4—261no—
781C2×C4—263no—
782C2×C4—263no—
783C2×C4—263no—
784C2×C4—263no—
785C2×C4—261no—
786C2×C4—263no—
787C2×C4—261no—
788C2×C4—263no—
789C2×C4—263no—
790C2×C4—261no—
791C2×C4—261no—
792C2×C4—263no—
793C2×C4—10412no—
794C2×C4C23×#26111yescharacteristic
795C2×C4C23×#26113yes—
796C2×C4C23×#26113yes—
797C2×C4C23×#26111yescharacteristic
798C2×C4C23×#26113yes—
799C22—21no—
800C22—23no—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—131no—
806C22—131no—
807C22—131no—
808C22—131no—
809C22—131no—
810C22—131no—
811C22—261no—
812C22—263no—
813C22—261no—
814C22—263no—
815C22—263no—
816C22—261no—
817C22—523no—
818C22—521no—
819C22—521no—
820C22—523no—
821C22—521no—
822C22—523no—
823C22—521no—
824C22—523no—
825C22C24×#26111yescharacteristic
826C4—21no—
827C4—23no—
828C4—23no—
829C4—21no—
830C4—136no—
831C4—262no—
832C4—262no—
833C4—266no—
834C4—261no—
835C4—263no—
836C4—263no—
837C4—261no—
838C4—521no—
839C4—521no—
840C4—523no—
841C4—523no—
842C4—523no—
843C4C2×D4×#26116yes—
844C2—41no—
845C2—43no—
846C2—131no—
847C2—131no—
848C2—131no—
849C2—131no—
850C2—521no—
851C2—523no—
852C2C22×D4×#26111yescharacteristic
853C2#1313181611yescharacteristic
854C22−1+4×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#548C4
prime radicalD13×#548C2
cosocleC22×D13C25
hypercenter#548#261
hypocenterC13#34312
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#11719631C2semidirect
2. C2×#11719627C2semidirect
3. #13131367C2semidirect
4. #13131363C2semidirect
5. #13131360C2semidirect
6. #13131352C2semidirect
7. #13131351C2semidirect
8. #13131341C2semidirect
9. Q8×C22⋊#261C2semidirect
10. #13131324C2semidirect
11. #13131323C2semidirect
12. #124×#261C2semidirect
13. #13131293C2semidirect
14. C4×Q8×#261C2semidirect
32. C13×#548C4semidirect
33. #11719536C4semidirect
34. #11719522C4semidirect
35. #11719382C4semidirect
37. #11719338C4semidirect
40. #11719303C4semidirect
41. #11719281C4semidirect
43. #11719257C4semidirect
78. C22×Q8×C13C2×C4semidirect
84. C2×Q8×D13C2×C4semidirect
85. C2×Q8×D13C2×C4semidirect
94. C22×Dic26C2×C4semidirect
109. Q8×#261D4semidirect
135. C13×#124C2×C4semidirect
136. C13×C22⋊Q8C2×C4semidirect
137. C13×#121C2×C4semidirect
138. C4×Q8×C13C2×C4semidirect
139. C4×D4×C13C2×C4semidirect
140. #88201C2×C4semidirect
141. #88200C2×C4semidirect
142. Q8×Dic13C2×C4semidirect
143. #88193C2×C4semidirect
144. #88192C2×C4semidirect
145. #88190C2×C4semidirect
146. D4×Dic13C2×C4semidirect
147. #88184C2×C4semidirect
148. C4×C22⋊D13C2×C4semidirect
149. C4×C22⋊D13C2×C4semidirect
150. #88178C2×C4semidirect
151. #88151C2×C4semidirect
152. #88150C2×C4semidirect
153. #88149C2×C4semidirect
154. #88147C2×C4semidirect
157. #88141C2×C4semidirect
158. #88139C2×C4semidirect
159. #88139C2×C4semidirect
160. #88138C2×C4semidirect
161. #88135C2×C4semidirect
162. #88135C2×C4semidirect
166. #88132C2×C4semidirect
167. #88129C2×C4semidirect
168. C4×D52C2×C4semidirect
170. C4×Dic26C2×C4semidirect
396. #548#261semidirect
505. C22×Q8C2×#261semidirect
516. #124C2×#261semidirect
522. C22⋊Q8C2×#261semidirect
528. #121C2×#261semidirect
538. C4×Q8C2×#261semidirect
548. C4×D4C2×#261semidirect
716. C13#34312semidirect

Maximal subgroups

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

subgroupindex
C2×#117196312
C2×#117196272
#131313672
#131313632
#131313602
#131313522
#131313512
#131313412
Q8×C22⋊#2612
#131313242
#131313232
#124×#2612
#131312932
C4×Q8×#2612
D13×#5482
#3431213