Finite Group Databasebeta

← C2×#13128627 #16771387

Subgroups — C2×#13128627 #16771387

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88254C211yesmaximal, characteristic, complemented
2C22×#88256C211yesmaximal, characteristic, complemented
3#13128627C2132yesmaximal, direct product factor
4C2×#11719281C211yesmaximal, characteristic, complemented
5C2×#11719522C211yesmaximal, characteristic, complemented
6C2×#11719536C211yesmaximal, characteristic, complemented
7C2×#11719317C213yesmaximal, complemented
8C2×#11719255C213yesmaximal, complemented
9C2×#11719381C213yesmaximal, complemented
10C2×#11719335C213yesmaximal, complemented
11C2×#11719333C213yesmaximal, complemented
12C2×#11719312C213yesmaximal, complemented
13C2×#11719253C213yesmaximal, complemented
14C2×D13×#124C213yesmaximal, complemented
15C2×C4×#6131C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#88256—216no—
20C2×#88256C22116yescomplemented
21C2×#88254—216no—
22C2×#88254C22116yescomplemented
23C22×#6131C2211yescharacteristic
24C22×#6131C2211yescharacteristic
25C22×#6131C2213yescomplemented
26C22×Q8×D13C2211yescharacteristic, complemented
27C22×Q8×D13C2213yescomplemented
28C22×D4×D13C2213yes—
29C22×D4×D13C2213yes—
30C22×#6127C2213yes—
31C22×#6127C2213yescomplemented
32C22×#6127C2213yescomplemented
33C23×D52C2213yes—
34C13×#548C22116yescomplemented
35C2×C13×#124C2213yescomplemented
36C2×C13×C22⋊Q8C2213yescomplemented
37C2×C13×#121C2213yescomplemented
38C2×C4×Q8×C13C2211yescharacteristic, complemented
39C2×C4×D4×C13C2213yescomplemented
40#11719536C22116yescomplemented
41#11719522C22116yescomplemented
42C2×#88201C2213yescomplemented
43C2×#88200C2213yescomplemented
44C2×Q8×Dic13C2211yescharacteristic, complemented
45C2×#88194C2213yescomplemented
46C2×#88192C2213yescomplemented
47C2×#88192C2213yescomplemented
48C2×#88191C2216yescomplemented
49C2×#88190C2213yescomplemented
50C2×#88184C2213yescomplemented
51C2×C4×C22⋊D13C2213yescomplemented
52C2×C4×C22⋊D13C2213yescomplemented
53C2×#88178C2213yescomplemented
54#11719381C22148yescomplemented
55D13×#124C22148yescomplemented
56#11719335C22148yescomplemented
57#11719333C22148yescomplemented
58#11719317C22148yescomplemented
59#11719312C22148yescomplemented
60#11719281C22116yescomplemented
61C4×#6131C22116yescomplemented
62#11719255C22148yescomplemented
63#11719253C22148yescomplemented
64C2×#88151C2213yescomplemented
65C2×#88149C2213yescomplemented
66C2×#88149C2213yescomplemented
67C2×#88148C2216yescomplemented
68C2×#88147C2213yescomplemented
69C2×#88146C2213yescomplemented
70C2×#88142C2213yescomplemented
71C2×#88139C2213yescomplemented
72C2×#88139C2216yescomplemented
73C2×#88139C2211yescharacteristic, complemented
74C2×#88138C2213yescomplemented
75C2×#88138C2213yescomplemented
76C2×#88137C2216yescomplemented
77C2×#88136C2216yescomplemented
78C2×C22⋊C4×D13C2216yescomplemented
79C2×C22⋊C4×D13C2216yescomplemented
80C2×#88129C2213yescomplemented
81C2×C4×D52C2213yescomplemented
82C2×C4×D52C2213yescomplemented
83C2×C42×D13C2213yescomplemented
84C24×D13C2316yes—
85C2×C13×#41—28no—
86C2×C13×#41C2318yes—
87C22×Q8×C13—28no—
88C22×Q8×C13C2313yes—
89C22×Q8×C13C2311yescharacteristic
90C22×Q8×C13C2318yescomplemented
91C22×D4×C13C2313yes—
92C22×D4×C13C2313yes—
93C23×C4×C13C2313yes—
94C23×C4×C13C2313yes—
95C22×C22⋊D13C2313yes—
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2313yes—
98C22×C22⋊D13C2311yescharacteristic
99C22×C22⋊D13C2313yes—
100C22×C22⋊D13C2313yes—
101#88256—2128no—
102#88254—2128no—
103C2×#6131—28no—
104C2×#6131—224no—
105C2×#6131D4116yescomplemented
106C2×#6131C2318yes—
107C2×#6131C2318yes—
108C2×#6131C23124yescomplemented
109C2×Q8×D13—28no—
110C2×Q8×D13—224no—
111C2×Q8×D13C2318yescomplemented
112C2×Q8×D13C23124yescomplemented
113C2×D4×D13—224no—
114C2×D4×D13—224no—
115C2×D4×D13C23124yes—
116C2×D4×D13C23124yes—
117C2×#6127—224no—
118C2×#6127—224no—
119C2×#6127—224no—
120C2×#6127C23124yes—
121C2×#6127C23124yescomplemented
122C2×#6127C23124yescomplemented
123C22×D52—224no—
124C22×D52C2313yes—
125C22×D52C2313yes—
126C22×D52C2313yes—
127C22×D52C23124yes—
128C22×D52C2313yes—
129C22×D52C2313yes—
130C22×C4×D13C2313yes—
131C22×C4×D13C2313yes—
132C22×C4×D13C2316yes—
133C22×C4×D13C2313yes—
134C22×C4×D13C2313yes—
135C22×C4×D13C2313yes—
136C22×Dic26C2313yes—
137C22×Dic26C2313yes—
138C22×Dic26C2311yescharacteristic
139C13×#124C23124yescomplemented
140C13×C22⋊Q8C23124yescomplemented
141C13×#121C23124yescomplemented
142C4×Q8×C13C2318yescomplemented
143C4×D4×C13C23124yescomplemented
144C2×C13×C4⋊C4C2313yes—
145C2×C13×C4⋊C4C2313yes—
146C2×C13×C22⋊C4C2313yes—
147C2×C13×C22⋊C4C2316yes—
148C2×C13×C22⋊C4C2311yescharacteristic
149C2×C42×C13C2313yes—
150C2×C22⋊Dic13C2313yes—
151C2×C22⋊Dic13C2316yes—
152C2×C22⋊Dic13C2311yescharacteristic
153#88201C23124yescomplemented
154#88200C23124yescomplemented
155Q8×Dic13C2318yescomplemented
156#88194C23124yescomplemented
157#88192C23124yescomplemented
158#88192C23124yescomplemented
159#88191C23148yescomplemented
160#88190C23124yescomplemented
161#88184C23124yescomplemented
162C4×C22⋊D13C23124yescomplemented
163C4×C22⋊D13C23124yescomplemented
164C2×#6103C2311yescharacteristic
165C2×#6103C2313yes—
166C2×#6103C2316yes—
167C2×#6103C2316yes—
168C2×#6103C2313yes—
169C2×#6103C2316yes—
170C2×#6103C2311yescharacteristic
171C2×C4⋊Dic13C2313yes—
172C2×C4⋊Dic13C2313yes—
173#88178C23124yescomplemented
174C2×#6101C2313yes—
175C2×#6101C2313yes—
176C2×C4×Dic13C2311yescharacteristic
177C2×C4×Dic13C2313yes—
178C2×C4×Dic13C2313yes—
179#88151C23124yescomplemented
180#88149C23124yescomplemented
181#88149C23124yescomplemented
182#88148C23148yescomplemented
183#88147C23124yescomplemented
184#88146C23124yescomplemented
185#88142C23124yescomplemented
186#88139C2318yescomplemented
187#88139C23124yescomplemented
188#88139C23148yescomplemented
189#88138C23124yescomplemented
190#88138C23124yescomplemented
191#88137C23148yescomplemented
192#88136C23148yescomplemented
193C22⋊C4×D13C23148yescomplemented
194C22⋊C4×D13C23148yescomplemented
195#88129C23124yescomplemented
196C4×D52C23124yescomplemented
197C4×D52C23124yescomplemented
198C42×D13C23124yescomplemented
199C2×#3500—131nomaximal, Sylow
200C24×C13C2413yes—
201C24×C13C2411yescharacteristic
202C23×D13—224no—
203C23×D13—412no—
204C23×D13—412no—
205C23×D13C2413yes—
206C23×D13C2411yescharacteristic
207C23×D13C2413yes—
208C23×D13C24124yes—
209C13×#41—232no—
210C2×Q8×C13—232no—
211C2×Q8×C13—212no—
212C2×Q8×C13C2×D418yes—
213C2×Q8×C13C24112yes—
214C2×Q8×C13C2414yes—
215C2×D4×C13—212no—
216C2×D4×C13—46no—
217C2×D4×C13C24112yes—
218C2×D4×C13C24112yes—
219C22×C4×C13—212no—
220C22×C4×C13—212no—
221C22×C4×C13C2413yes—
222C22×C4×C13C2411yescharacteristic
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2413yes—
225C22×C4×C13C24112yes—
226C22×C4×C13C24112yes—
227C22×C4×C13C2413yes—
228C2×C22⋊D13—212no—
229C2×C22⋊D13—212no—
230C2×C22⋊D13—24no—
231C2×C22⋊D13—212no—
232C2×C22⋊D13—46no—
233C2×C22⋊D13—46no—
234C2×C22⋊D13C24112yes—
235C2×C22⋊D13C24112yes—
236C2×C22⋊D13C24112yes—
237C2×C22⋊D13C2414yes—
238C2×C22⋊D13C24112yes—
239C2×C22⋊D13C24112yes—
240C22×Dic13C2411yescharacteristic
241C22×Dic13C2413yes—
242C22×Dic13C2411yescharacteristic
243C22×Dic13C2413yes—
244C22×Dic13C2411yescharacteristic
245#6131—232no—
246#6131—296no—
247#6131C2×D4164yescomplemented
248Q8×D13—232no—
249Q8×D13—296no—
250D4×D13—296no—
251D4×D13—296no—
252#6127—296no—
253#6127—296no—
254#6127—296no—
255C2×D52—212no—
256C2×D52—212no—
257C2×D52—212no—
258C2×D52—296no—
259C2×D52—46no—
260C2×D52C2×D4124yes—
261C2×D52C24112yes—
262C2×D52C24112yes—
263C2×D52C24112yes—
264C2×D52C24112yes—
265C2×D52C24112yes—
266C2×C4×D13—224no—
267C2×C4×D13—212no—
268C2×C4×D13—212no—
269C2×C4×D13—46no—
270C2×C4×D13—46no—
271C2×C4×D13C2×D4124yes—
272C2×C4×D13C24112yes—
273C2×C4×D13C24112yes—
274C2×C4×D13C24124yes—
275C2×C4×D13C24112yes—
276C2×C4×D13C24112yes—
277C2×C4×D13C24112yes—
278C2×Dic26—212no—
279C2×Dic26—24no—
280C2×Dic26—212no—
281C2×Dic26C24112yes—
282C2×Dic26C24112yes—
283C2×Dic26C2414yes—
284C13×C4⋊C4C24112yes—
285C13×C4⋊C4C24112yes—
286C13×C22⋊C4C24112yes—
287C13×C22⋊C4C24124yes—
288C13×C22⋊C4C2414yes—
289C42×C13C24112yes—
290C22⋊Dic13C24112yes—
291C22⋊Dic13C24124yes—
292C22⋊Dic13C2414yes—
293#6103C2414yes—
294#6103C24112yes—
295#6103C24124yes—
296#6103C24124yes—
297#6103C24112yes—
298#6103C24124yes—
299#6103C2414yes—
300C4⋊Dic13C24112yes—
301C4⋊Dic13C24112yes—
302#6101C24112yes—
303#6101C24112yes—
304C4×Dic13C2414yes—
305C4×Dic13C24112yes—
306C4×Dic13C24112yes—
307C22×2−1+4—131no—
308C22×H(5,𝔽2)—131no—
309#3500—1332no—
310C2×#548—131no—
311C2×#548—131no—
312C2×#548—131no—
313C2×#548D1311yescharacteristic, complemented
314C2×#546—133no—
315C2×#546—133no—
316C2×#546—133no—
317C2×#546—133no—
318C2×#536—133no—
319C2×#535—133no—
320C2×#532—133no—
321C22×#124—133no—
322C2×C4×#41—131no—
323C23×C13—22no—
324C23×C13—26no—
325C23×C13—22no—
326C23×C13—26no—
327C23×C13—22no—
328C23×C13—26no—
329C23×C13C2516yes—
330C23×C13C2512yes—
331C23×C13C2511yescharacteristic
332C22×D13—26no—
333C22×D13—26no—
334C22×D13—22no—
335C22×D13—26no—
336C22×D13—22no—
337C22×D13—26no—
338C22×D13—22no—
339C22×D13—26no—
340C22×D13—248no—
341C22×D13—424no—
342C22×D13—424no—
343C22×D13—848no—
344C22×D13C22×D4112yes—
345C22×D13C2516yes—
346C22×D13C2512yes—
347C22×D13C2516yes—
348Q8×C13—224no—
349Q8×C13C22×D4116yes—
350D4×C13—224no—
351D4×C13—412no—
352C2×C4×C13—26no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—26no—
356C2×C4×C13—224no—
357C2×C4×C13—224no—
358C2×C4×C13C22×D4112yes—
359C2×C4×C13C2516yes—
360C2×C4×C13C2512yes—
361C2×C4×C13C2512yes—
362C2×C4×C13C2516yes—
363C2×C4×C13C2516yes—
364C22⋊D13—224no—
365C22⋊D13—224no—
366C22⋊D13—28no—
367C22⋊D13—224no—
368C22⋊D13—412no—
369C22⋊D13—412no—
370C2×Dic13—26no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—26no—
374C2×Dic13C22×D414yes—
375C2×Dic13C2512yes—
376C2×Dic13C2516yes—
377C2×Dic13C2512yes—
378C2×Dic13C2516yes—
379C2×Dic13C2512yes—
380D52—224no—
381D52—224no—
382D52—224no—
383D52—412no—
384D52C22×D4148yes—
385C4×D13—248no—
386C4×D13—224no—
387C4×D13—224no—
388C4×D13—412no—
389C4×D13—412no—
390C4×D13C22×D4148yes—
391Dic26—224no—
392Dic26—28no—
393Dic26—224no—
394C2×2−1+4—1316no—
395C2×2−1+4—2616no—
396C2×H(5,𝔽2)—1316no—
397C2×H(5,𝔽2)—2616no—
398C22×#41—131no—
399C22×#41—131no—
400C22×#41—133no—
401C22×#41—133no—
402C22×#41—133no—
403C22×#41—133no—
404C22×#41C2×D1311yescharacteristic
405C23×Q8—133no—
406C23×Q8—131no—
407C23×Q8C2×D1311yescharacteristic, complemented
408C23×D4—133no—
409C23×D4—133no—
410C23×D4—133no—
411#548—1316no—
412#548—1316no—
413#548—1316no—
414#548C2×D13116yescomplemented
415#546—1348no—
416#546—1348no—
417#546—1348no—
418#546—1348no—
419#536—1348no—
420#535—1348no—
421#532—1348no—
422C2×C4⋊Q8—133no—
423C2×#127—133no—
424C2×#124—133no—
425C2×#124—133no—
426C2×#124—1348no—
427C2×#124—133no—
428C2×#124—136no—
429C2×#124—131no—
430C2×#124—133no—
431C2×#124C2×D1313yescomplemented
432C2×#123—136no—
433C2×#123—136no—
434C2×C22⋊Q8—133no—
435C2×C22⋊Q8—133no—
436C2×C22⋊Q8—133no—
437C2×C22⋊Q8C2×D1313yescomplemented
438C2×#121—133no—
439C2×#121—133no—
440C2×#121—133no—
441C2×#121—133no—
442C2×#121—133no—
443C2×#121—133no—
444C2×#121—133no—
445C2×#121C2×D1313yescomplemented
446C2×#120—136no—
447C2×#120—136no—
448C4×#41—1316no—
449C2×C4×Q8—131no—
450C2×C4×Q8C2×D1311yescharacteristic, complemented
451C2×C4×D4—133no—
452C2×C4×D4—133no—
453C2×C4×D4—133no—
454C2×C4×D4—133no—
455C2×C4×D4—133no—
456C2×C4×D4C2×D1313yescomplemented
457C2×#117—133no—
458C22×C22⋊C4—136no—
459C22×C22⋊C4—136no—
460C22×C42—133no—
461C22×C13—22no—
462C22×C13—26no—
463C22×C13—22no—
464C22×C13—26no—
465C22×C13—22no—
466C22×C13—26no—
467C22×C13—412no—
468C22×C13—44no—
469C22×C13C23×D412yes—
470C22×C13#58512yes—
471C22×C13#58512yes—
472C22×C13C2611yescharacteristic
473C2×D13—26no—
474C2×D13—26no—
475C2×D13—224no—
476C2×D13—22no—
477C2×D13—26no—
478C2×D13—22no—
479C2×D13—26no—
480C2×D13—22no—
481C2×D13—26no—
482C2×D13—44no—
483C2×D13—412no—
484C2×D13—848no—
485C2×D13C23×D4112yes—
486C4×C13—26no—
487C4×C13—22no—
488C4×C13—22no—
489C4×C13—26no—
490C4×C13C23×D4112yes—
491Dic13—26no—
492Dic13—22no—
493Dic13—22no—
494Dic13—26no—
495Dic13C23×D414yes—
496C25—136no—
4972−1+4—26128no—
498H(5,𝔽2)—26128no—
499C2×#41—28no—
500C2×#41—1316no—
501C2×#41—138no—
502C2×#41—1324no—
503C2×#41—138no—
504C2×#41—1324no—
505C2×#41—1324no—
506C2×#41—1324no—
507C2×#41—2624no—
508C2×#41—2624no—
509C2×#41—2624no—
510C2×#41—2624no—
511C2×#41—268no—
512C2×#41C22×D1318yes—
513C22×Q8—28no—
514C22×Q8—1324no—
515C22×Q8—138no—
516C22×Q8—133no—
517C22×Q8—133no—
518C22×Q8—131no—
519C22×Q8—2624no—
520C22×Q8—268no—
521C22×Q8C22×D1313yes—
522C22×Q8C22×D1311yescharacteristic
523C22×Q8C22×D1318yescomplemented
524C22×D4—133no—
525C22×D4—133no—
526C22×D4—133no—
527C22×D4—131no—
528C22×D4—133no—
529C22×D4—133no—
530C22×D4—1324no—
531C22×D4—1324no—
532C22×D4—133no—
533C22×D4—133no—
534C22×D4—133no—
535C22×D4—133no—
536C22×D4—1324no—
537C22×D4—133no—
538C22×D4—2624no—
539C22×D4—2624no—
540C22×D4—2624no—
541C22×D4C22×D1313yes—
542C22×D4C22×D1313yes—
543C23×C4—133no—
544C23×C4—136no—
545C23×C4—133no—
546C23×C4—133no—
547C23×C4—133no—
548C23×C4—133no—
549C23×C4C22×D1313yes—
550C23×C4C22×D1313yes—
551C4⋊Q8—1324no—
552#127—1324no—
553#124—1324no—
554#124—1324no—
555#124—1324no—
556#124—1348no—
557#124—138no—
558#124—1324no—
559#124C22×D13124yescomplemented
560#123—1348no—
561#123—1348no—
562C22⋊Q8—1324no—
563C22⋊Q8—1324no—
564C22⋊Q8—1324no—
565C22⋊Q8C22×D13124yescomplemented
566#121—1324no—
567#121—1324no—
568#121—1324no—
569#121—1324no—
570#121—1324no—
571#121—1324no—
572#121—1324no—
573#121C22×D13124yescomplemented
574#120—1348no—
575#120—1348no—
576C4×Q8—138no—
577C4×Q8C22×D1318yescomplemented
578C4×D4—1324no—
579C4×D4—1324no—
580C4×D4—1324no—
581C4×D4—1324no—
582C4×D4—1324no—
583C4×D4C22×D13124yescomplemented
584#117—1324no—
585C2×C4⋊C4—133no—
586C2×C4⋊C4—133no—
587C2×C4⋊C4—133no—
588C2×C4⋊C4—133no—
589C2×C4⋊C4C22×D1313yes—
590C2×C4⋊C4C22×D1313yes—
591C2×C22⋊C4—133no—
592C2×C22⋊C4—136no—
593C2×C22⋊C4—131no—
594C2×C22⋊C4—133no—
595C2×C22⋊C4—133no—
596C2×C22⋊C4—136no—
597C2×C22⋊C4—136no—
598C2×C22⋊C4—136no—
599C2×C22⋊C4—131no—
600C2×C22⋊C4—131no—
601C2×C22⋊C4—1348no—
602C2×C22⋊C4—1348no—
603C2×C22⋊C4C22×D1313yes—
604C2×C22⋊C4C22×D1316yes—
605C2×C22⋊C4C22×D1311yescharacteristic
606C2×C42—133no—
607C2×C42—133no—
608C2×C42—131no—
609C2×C42—1324no—
610C2×C42C22×D1313yes—
611C2×C13—46no—
612C2×C13—42no—
613C2×C13#350014yescomplemented
614C2×C13C24×D411yescharacteristic
615C2×C13C2×#58511yescharacteristic
616C2×C13C2×#58511yescharacteristic
617D13—212no—
618D13—42no—
619D13—46no—
620C24—133no—
621C24—133no—
622C24—131no—
623C24—1324no—
624C24—2624no—
625C24—5212no—
626C24—5212no—
627C24C23×D1313yes—
628C24C23×D1311yescharacteristic
629#41—232no—
630#41—1364no—
631#41—2696no—
632#41—2696no—
633#41—2696no—
634#41—2696no—
635#41—2632no—
636C2×Q8—232no—
637C2×Q8—212no—
638C2×Q8—1312no—
639C2×Q8—1312no—
640C2×Q8—134no—
641C2×Q8—2612no—
642C2×Q8—264no—
643C2×Q8—2696no—
644C2×Q8—2632no—
645C2×Q8—2612no—
646C2×Q8D4×D1318yes—
647C2×Q8C23×D13112yes—
648C2×Q8C23×D1314yes—
649C2×D4—212no—
650C2×D4—46no—
651C2×D4—1312no—
652C2×D4—1312no—
653C2×D4—1312no—
654C2×D4—134no—
655C2×D4—1312no—
656C2×D4—1312no—
657C2×D4—1324no—
658C2×D4—1312no—
659C2×D4—1312no—
660C2×D4—1312no—
661C2×D4—1312no—
662C2×D4—1312no—
663C2×D4—2696no—
664C2×D4—2612no—
665C2×D4—2612no—
666C2×D4—2696no—
667C2×D4—2612no—
668C2×D4—264no—
669C2×D4—2696no—
670C2×D4—2612no—
671C2×D4—2612no—
672C2×D4—2612no—
673C2×D4—526no—
674C2×D4—526no—
675C2×D4—526no—
676C2×D4C23×D13112yes—
677C2×D4C23×D13112yes—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—131no—
681C22×C4—1324no—
682C22×C4—1312no—
683C22×C4—131no—
684C22×C4—133no—
685C22×C4—133no—
686C22×C4—131no—
687C22×C4—1324no—
688C22×C4—1312no—
689C22×C4—1312no—
690C22×C4—1312no—
691C22×C4—1312no—
692C22×C4—2624no—
693C22×C4—2612no—
694C22×C4—2612no—
695C22×C4—526no—
696C22×C4—526no—
697C22×C4C23×D13112yes—
698C22×C4C23×D13112yes—
699C22×C4C23×D1311yescharacteristic
700C22×C4C23×D1313yes—
701C22×C4C23×D1313yes—
702C22×C4C23×D1311yescharacteristic
703C22×C4C23×D1313yes—
704C4⋊C4—1312no—
705C4⋊C4—1312no—
706C4⋊C4—1312no—
707C4⋊C4—1312no—
708C4⋊C4C23×D13112yes—
709C4⋊C4C23×D13112yes—
710C22⋊C4—1312no—
711C22⋊C4—1324no—
712C22⋊C4—134no—
713C22⋊C4—1312no—
714C22⋊C4—1312no—
715C22⋊C4—1324no—
716C22⋊C4—1324no—
717C22⋊C4—1324no—
718C22⋊C4—134no—
719C22⋊C4—134no—
720C22⋊C4C23×D13112yes—
721C22⋊C4C23×D13124yes—
722C22⋊C4C23×D1314yes—
723C42—134no—
724C42—1312no—
725C42—1312no—
726C42C23×D13112yes—
727C13C2×#350011yescharacteristic, complemented, Sylow
728C23—22no—
729C23—26no—
730C23—22no—
731C23—26no—
732C23—22no—
733C23—26no—
734C23—1312no—
735C23—136no—
736C23—136no—
737C23—132no—
738C23—2648no—
739C23—266no—
740C23—266no—
741C23—262no—
742C23—266no—
743C23—262no—
744C23—266no—
745C23—262no—
746C23—266no—
747C23—5224no—
748C23—5224no—
749C23—10448no—
750C23C24×D1316yes—
751C23C24×D1312yes—
752C23C24×D1311yescharacteristic
753Q8—224no—
754Q8—2624no—
755Q8—268no—
756Q8—2624no—
757Q8C2×D4×D13116yes—
758D4—224no—
759D4—412no—
760D4—1348no—
761D4—2624no—
762D4—2624no—
763D4—2624no—
764D4—268no—
765D4—2624no—
766D4—2624no—
767D4—2624no—
768D4—5212no—
769D4—5212no—
770D4—5212no—
771C2×C4—22no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—22no—
775C2×C4—224no—
776C2×C4—224no—
777C2×C4—134no—
778C2×C4—132no—
779C2×C4—1348no—
780C2×C4—132no—
781C2×C4—136no—
782C2×C4—136no—
783C2×C4—132no—
784C2×C4—2648no—
785C2×C4—262no—
786C2×C4—266no—
787C2×C4—262no—
788C2×C4—266no—
789C2×C4—2624no—
790C2×C4—2624no—
791C2×C4—5212no—
792C2×C4—5212no—
793C2×C4C2×D4×D13112yes—
794C2×C4C24×D1312yes—
795C2×C4C24×D1316yes—
796C2×C4C24×D1316yes—
797C2×C4C24×D1312yes—
798C2×C4C24×D1316yes—
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—44no—
806C22—412no—
807C22—1312no—
808C22—266no—
809C22—266no—
810C22—2624no—
811C22—262no—
812C22—266no—
813C22—262no—
814C22—266no—
815C22—262no—
816C22—266no—
817C22—524no—
818C22—5212no—
819C22—10448no—
820C22C22×D4×D1312yes—
821C22#1171964812yes—
822C22#1171965212yes—
823C22C25×D1311yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—134no—
829C4—262no—
830C4—266no—
831C4—262no—
832C4—266no—
833C4C22×D4×D13112yes—
834C2—46no—
835C2—42no—
836C2—2612no—
837C2—526no—
838C2—522no—
839C2#1312862714yesdirect product factor
840C2C23×D4×D1311yescharacteristic
841C2C2×#1171964811yescharacteristic
842C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#548C2
socleC23×C13C25
hypercenterC2×#548D13
hypocenterC13C2×#3500
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#88254C2semidirect
2. C22×#88256C2semidirect
3. #13128627C2direct (N × H)
4. C2×#11719281C2semidirect
5. C2×#11719522C2semidirect
6. C2×#11719536C2semidirect
7. C2×#11719317C2semidirect
8. C2×#11719255C2semidirect
9. C2×#11719381C2semidirect
10. C2×#11719335C2semidirect
11. C2×#11719333C2semidirect
12. C2×#11719312C2semidirect
13. C2×#11719253C2semidirect
14. C2×D13×#124C2semidirect
15. C2×C4×#6131C2semidirect
16. C2×C13×#548C2semidirect
18. C23×Q8×C13C22semidirect
20. C2×#88256C22semidirect
22. C2×#88254C22semidirect
25. C22×#6131C22semidirect
26. C22×Q8×D13C22semidirect
27. C22×Q8×D13C22semidirect
31. C22×#6127C22semidirect
32. C22×#6127C22semidirect
34. C13×#548C22semidirect
35. C2×C13×#124C22semidirect
36. C2×C13×C22⋊Q8C22semidirect
37. C2×C13×#121C22semidirect
38. C2×C4×Q8×C13C22semidirect
39. C2×C4×D4×C13C22semidirect
40. #11719536C22semidirect
41. #11719522C22semidirect
42. C2×#88201C22semidirect
43. C2×#88200C22semidirect
44. C2×Q8×Dic13C22semidirect
45. C2×#88194C22semidirect
46. C2×#88192C22semidirect
47. C2×#88192C22semidirect
48. C2×#88191C22semidirect
49. C2×#88190C22semidirect
50. C2×#88184C22semidirect
51. C2×C4×C22⋊D13C22semidirect
52. C2×C4×C22⋊D13C22semidirect
53. C2×#88178C22semidirect
54. #11719381C22semidirect
55. D13×#124C22semidirect
56. #11719335C22semidirect
57. #11719333C22semidirect
58. #11719317C22semidirect
59. #11719312C22semidirect
60. #11719281C22semidirect
61. C4×#6131C22semidirect
62. #11719255C22semidirect
63. #11719253C22semidirect
64. C2×#88151C22semidirect
65. C2×#88149C22semidirect
66. C2×#88149C22semidirect
67. C2×#88148C22semidirect
68. C2×#88147C22semidirect
69. C2×#88146C22semidirect
70. C2×#88142C22semidirect
71. C2×#88139C22semidirect
72. C2×#88139C22semidirect
73. C2×#88139C22semidirect
74. C2×#88138C22semidirect
75. C2×#88138C22semidirect
76. C2×#88137C22semidirect
77. C2×#88136C22semidirect
78. C2×C22⋊C4×D13C22semidirect
79. C2×C22⋊C4×D13C22semidirect
80. C2×#88129C22semidirect
81. C2×C4×D52C22semidirect
82. C2×C4×D52C22semidirect
83. C2×C42×D13C22semidirect
90. C22×Q8×C13C23semidirect
105. C2×#6131D4semidirect
108. C2×#6131C23semidirect
111. C2×Q8×D13C23semidirect
112. C2×Q8×D13C23semidirect
121. C2×#6127C23semidirect
122. C2×#6127C23semidirect
139. C13×#124C23semidirect
140. C13×C22⋊Q8C23semidirect
141. C13×#121C23semidirect
142. C4×Q8×C13C23semidirect
143. C4×D4×C13C23semidirect
153. #88201C23semidirect
154. #88200C23semidirect
155. Q8×Dic13C23semidirect
156. #88194C23semidirect
157. #88192C23semidirect
158. #88192C23semidirect
159. #88191C23semidirect
160. #88190C23semidirect
161. #88184C23semidirect
162. C4×C22⋊D13C23semidirect
163. C4×C22⋊D13C23semidirect
173. #88178C23semidirect
179. #88151C23semidirect
180. #88149C23semidirect
181. #88149C23semidirect
182. #88148C23semidirect
183. #88147C23semidirect
184. #88146C23semidirect
185. #88142C23semidirect
186. #88139C23semidirect
187. #88139C23semidirect
188. #88139C23semidirect
189. #88138C23semidirect
190. #88138C23semidirect
191. #88137C23semidirect
192. #88136C23semidirect
193. C22⋊C4×D13C23semidirect
194. C22⋊C4×D13C23semidirect
195. #88129C23semidirect
196. C4×D52C23semidirect
197. C4×D52C23semidirect
198. C42×D13C23semidirect
247. #6131C2×D4semidirect
313. C2×#548D13semidirect
407. C23×Q8C2×D13semidirect
414. #548C2×D13semidirect
431. C2×#124C2×D13semidirect
437. C2×C22⋊Q8C2×D13semidirect
445. C2×#121C2×D13semidirect
450. C2×C4×Q8C2×D13semidirect
456. C2×C4×D4C2×D13semidirect
523. C22×Q8C22×D13semidirect
559. #124C22×D13semidirect
565. C22⋊Q8C22×D13semidirect
573. #121C22×D13semidirect
577. C4×Q8C22×D13semidirect
583. C4×D4C22×D13semidirect
613. C2×C13#3500semidirect
727. C13C2×#3500semidirect
839. C2#13128627direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882542
C22×#882562
#131286272
C2×#117192812
C2×#117195222
C2×#117195362
C2×#117193172
C2×#117192552
C2×#117193812
C2×#117193352
C2×#117193332
C2×#117193122
C2×#117192532
C2×D13×#1242
C2×C4×#61312
C2×C13×#5482
C2×#350013