Finite Group Databasebeta

← C2×#13128513 #16771319

Subgroups — C2×#13128513 #16771319

Order 3328.

11438 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88254C211yesmaximal, characteristic, complemented
2C23×#6131C211yesmaximal, characteristic, complemented
3#13128513C2132yesmaximal, direct product factor
4C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
5C2×#11719281C211yesmaximal, characteristic, complemented
6C2×#11719522C211yesmaximal, characteristic, complemented
7C2×#11719431C213yesmaximal, complemented
8C2×#11719336C213yesmaximal, complemented
9C2×#11719255C213yesmaximal, complemented
10C2×#11719335C213yesmaximal, complemented
11C2×#11719334C213yesmaximal, complemented
12C2×#11719429C213yesmaximal, complemented
13C2×#11719252C213yesmaximal, complemented
14C2×D13×C22⋊Q8C213yesmaximal, complemented
15C2×#11719279C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#88254—216no—
20C2×#88254C22116yescomplemented
21C22×#6131—216no—
22C22×#6131C2213yes—
23C22×#6131C2211yescharacteristic
24C22×#6131C2213yes—
25C22×#6131C2211yescharacteristic
26C22×#6131C22116yescomplemented
27C22×#6131C2213yescomplemented
28C22×Q8×D13C2211yescharacteristic, complemented
29C22×Q8×D13C2213yescomplemented
30C22×#6127C2213yescomplemented
31C22×#6127C2213yescomplemented
32C23×D52C2213yes—
33C23×C4×D13C2213yes—
34D4×Q8×C13C22116yescomplemented
35C2×C13×C4⋊Q8C2213yescomplemented
36C2×C13×C22⋊Q8C2213yes—
37C2×C13×C22⋊Q8C2213yescomplemented
38C2×C4×Q8×C13C2211yescharacteristic, complemented
39C2×C4×D4×C13C2213yes—
40#11719522C22116yescomplemented
41Q8×C22⋊D13C22116yescomplemented
42C2×#88201C2213yescomplemented
43C2×#88200C2213yescomplemented
44C2×#88200C2213yescomplemented
45C2×Q8×Dic13C2211yescharacteristic, complemented
46C2×#88198C2213yescomplemented
47C2×#88193C2211yescharacteristic
48C2×#88191C2213yes—
49C2×#88184C2213yescomplemented
50C2×C4×C22⋊D13C2213yes—
51C2×C4×C22⋊D13C2213yescomplemented
52C2×#88178C2213yes—
53#11719431C22148yescomplemented
54#11719429C22148yescomplemented
55#11719336C22148yescomplemented
56#11719335C22148yescomplemented
57#11719334C22148yescomplemented
58D13×C22⋊Q8C22148yescomplemented
59#11719281C22116yescomplemented
60#11719279C22116yescomplemented
61#11719255C22148yescomplemented
62#11719252C22148yescomplemented
63C2×#88151C2213yescomplemented
64C2×#88150C2216yescomplemented
65C2×#88150C2213yescomplemented
66C2×#88149C2216yescomplemented
67C2×#88149C2213yescomplemented
68C2×#88148C2216yescomplemented
69C2×#88148C2216yescomplemented
70C2×#88148C2213yescomplemented
71C2×#88147C2213yescomplemented
72C2×C4⋊C4×D13C2213yescomplemented
73C2×C4⋊C4×D13C2216yescomplemented
74C2×#88138C2216yescomplemented
75C2×#88138C2213yescomplemented
76C2×#88137C2213yescomplemented
77C2×#88136C2213yes—
78C2×C22⋊C4×D13C2216yes—
79C2×#88132C2213yes—
80C2×#88129C2213yescomplemented
81C2×C4×D52C2213yescomplemented
82C2×C4×D52C2213yescomplemented
83C2×#88126C2213yescomplemented
84C24×D13C2313yes—
85C22×Q8×C13—28no—
86C22×Q8×C13—28no—
87C22×Q8×C13C2313yes—
88C22×Q8×C13C2313yes—
89C22×Q8×C13C2318yes—
90C22×Q8×C13C2311yescharacteristic
91C22×Q8×C13C2318yescomplemented
92C22×D4×C13C2311yescharacteristic
93C23×C4×C13C2313yes—
94C23×C4×C13C2313yes—
95C22×C22⋊D13C2311yescharacteristic
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2311yescharacteristic
98C22×C22⋊D13C2313yes—
99C23×Dic13C2311yescharacteristic
100#88254—2128no—
101C2×#6131—28no—
102C2×#6131—2128no—
103C2×#6131—224no—
104C2×#6131—224no—
105C2×#6131—224no—
106C2×#6131D4116yescomplemented
107C2×#6131C23124yes—
108C2×#6131C23124yes—
109C2×#6131C2318yes—
110C2×#6131C2318yes—
111C2×#6131C23124yescomplemented
112C2×Q8×D13—28no—
113C2×Q8×D13—224no—
114C2×Q8×D13C23124yescomplemented
115C2×Q8×D13C2318yescomplemented
116C2×#6127—224no—
117C2×#6127—224no—
118C2×#6127C23124yescomplemented
119C2×#6127C23124yescomplemented
120C22×D52—224no—
121C22×D52C2313yes—
122C22×D52C2313yes—
123C22×D52C2316yes—
124C22×D52C23124yes—
125C22×D52C2313yes—
126C22×D52C2313yes—
127C22×C4×D13—224no—
128C22×C4×D13C2313yes—
129C22×C4×D13C2313yes—
130C22×C4×D13C2316yes—
131C22×C4×D13C2313yes—
132C22×C4×D13C2313yes—
133C22×C4×D13C23124yes—
134C22×C4×D13C2316yes—
135C22×C4×D13C2313yes—
136C22×Dic26C2313yes—
137C22×Dic26C2313yes—
138C13×C4⋊Q8C23124yescomplemented
139C13×C22⋊Q8C23124yes—
140C13×C22⋊Q8C23124yescomplemented
141C4×Q8×C13C2318yescomplemented
142C4×D4×C13C23124yes—
143C2×C13×C4⋊C4C2313yes—
144C2×C13×C4⋊C4C2316yes—
145C2×C13×C4⋊C4C2313yes—
146C2×C13×C22⋊C4C2313yes—
147C2×C13×C22⋊C4C2313yes—
148C2×C42×C13C2313yes—
149C2×C22⋊Dic13C2313yes—
150C2×C22⋊Dic13C2311yescharacteristic
151#88201C23124yescomplemented
152#88200C23124yescomplemented
153#88200C23124yescomplemented
154Q8×Dic13C2318yescomplemented
155#88198C23124yescomplemented
156#88193C2318yes—
157#88191C23124yes—
158#88184C23124yescomplemented
159C4×C22⋊D13C23124yes—
160C4×C22⋊D13C23124yescomplemented
161C2×#6103C2313yes—
162C2×#6103C2313yes—
163C2×#6103C2311yescharacteristic
164C2×#6103C2313yes—
165C2×#6103C2316yes—
166C2×#6103C2316yes—
167C2×#6103C2313yes—
168C2×#6103C2313yes—
169C2×C4⋊Dic13C2313yes—
170C2×C4⋊Dic13C2313yes—
171#88178C23124yes—
172C2×#6101C2311yescharacteristic
173C2×#6101C2313yes—
174C2×#6101C2313yes—
175C2×#6101C2313yes—
176C2×#6101C2316yes—
177C2×C4×Dic13C2313yes—
178#88151C23124yescomplemented
179#88150C23124yescomplemented
180#88150C23148yescomplemented
181#88149C23148yescomplemented
182#88149C23124yescomplemented
183#88148C23148yescomplemented
184#88148C23148yescomplemented
185#88148C23124yescomplemented
186#88147C23124yescomplemented
187C4⋊C4×D13C23148yescomplemented
188C4⋊C4×D13C23124yescomplemented
189#88138C23124yescomplemented
190#88138C23148yescomplemented
191#88137C23124yescomplemented
192#88136C23124yes—
193C22⋊C4×D13C23148yes—
194#88132C23124yes—
195#88129C23124yescomplemented
196C4×D52C23124yescomplemented
197C4×D52C23124yescomplemented
198#88126C23124yescomplemented
199C2×#3489—131nomaximal, Sylow
200C24×C13C2411yescharacteristic
201C24×C13C2411yescharacteristic
202C23×D13—212no—
203C23×D13—212no—
204C23×D13—46no—
205C23×D13C2413yes—
206C23×D13C2411yescharacteristic
207C23×D13C24112yes—
208C23×D13C2413yes—
209C2×Q8×C13—232no—
210C2×Q8×C13—232no—
211C2×Q8×C13—212no—
212C2×Q8×C13—212no—
213C2×Q8×C13C2×D418yes—
214C2×Q8×C13C24112yes—
215C2×Q8×C13C24112yes—
216C2×Q8×C13C2414yes—
217C2×D4×C13—24no—
218C2×D4×C13C2414yes—
219C22×C4×C13—212no—
220C22×C4×C13—212no—
221C22×C4×C13C2413yes—
222C22×C4×C13C2413yes—
223C22×C4×C13C2411yescharacteristic
224C22×C4×C13C2413yes—
225C22×C4×C13C24112yes—
226C22×C4×C13C24112yes—
227C22×C4×C13C2413yes—
228C2×C22⋊D13—24no—
229C2×C22⋊D13—212no—
230C2×C22⋊D13—24no—
231C2×C22⋊D13—46no—
232C2×C22⋊D13C2414yes—
233C2×C22⋊D13C24112yes—
234C2×C22⋊D13C2414yes—
235C2×C22⋊D13C24112yes—
236C22×Dic13—24no—
237C22×Dic13C2414yes—
238C22×Dic13C2411yescharacteristic
239C22×Dic13C2413yes—
240C22×Dic13C2411yescharacteristic
241C22×Dic13C2413yes—
242C22×Dic13C2411yescharacteristic
243#6131—232no—
244#6131—296no—
245#6131—296no—
246#6131—296no—
247#6131C2×D4164yescomplemented
248Q8×D13—232no—
249Q8×D13—296no—
250#6127—296no—
251#6127—296no—
252C2×D52—224no—
253C2×D52—212no—
254C2×D52—212no—
255C2×D52—296no—
256C2×D52—46no—
257C2×D52C2×D4124yes—
258C2×D52C24112yes—
259C2×D52C24112yes—
260C2×D52C24124yes—
261C2×D52C24112yes—
262C2×D52C24112yes—
263C2×C4×D13—212no—
264C2×C4×D13—224no—
265C2×C4×D13—212no—
266C2×C4×D13—212no—
267C2×C4×D13—212no—
268C2×C4×D13—296no—
269C2×C4×D13—412no—
270C2×C4×D13C2×D4124yes—
271C2×C4×D13C24112yes—
272C2×C4×D13C24112yes—
273C2×C4×D13C24124yes—
274C2×C4×D13C24112yes—
275C2×C4×D13C24112yes—
276C2×C4×D13C24124yes—
277C2×C4×D13C24112yes—
278C2×Dic26—212no—
279C2×Dic26—212no—
280C2×Dic26C24112yes—
281C2×Dic26C24112yes—
282C13×C4⋊C4C24112yes—
283C13×C4⋊C4C24124yes—
284C13×C4⋊C4C24112yes—
285C13×C22⋊C4C24112yes—
286C13×C22⋊C4C24112yes—
287C42×C13C24112yes—
288C22⋊Dic13C24112yes—
289C22⋊Dic13C2414yes—
290#6103C24112yes—
291#6103C24112yes—
292#6103C2414yes—
293#6103C24112yes—
294#6103C24124yes—
295#6103C24124yes—
296#6103C24112yes—
297#6103C24112yes—
298C4⋊Dic13C24112yes—
299C4⋊Dic13C24112yes—
300#6101C2414yes—
301#6101C24112yes—
302#6101C24112yes—
303#6101C24112yes—
304#6101C24124yes—
305C4×Dic13C24112yes—
306C22×2−1+4—131no—
307C23×#41—131no—
308#3489—1332no—
309C2×D4×Q8—131no—
310C2×D4×Q8D1311yescharacteristic, complemented
311C2×#548—131no—
312C2×#548—131no—
313C2×#547—133no—
314C2×#547—133no—
315C2×#546—133no—
316C2×#546—133no—
317C2×#537—133no—
318C2×#536—133no—
319C2×#525—133no—
320C22×C22⋊Q8—133no—
321C2×#520—131no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C132−1+414yescomplemented
328C23×C13C2512yes—
329C23×C13C2512yes—
330C23×C13C2511yescharacteristic
331C22×D13—26no—
332C22×D13—26no—
333C22×D13—22no—
334C22×D13—26no—
335C22×D13—22no—
336C22×D13—26no—
337C22×D13—224no—
338C22×D13—22no—
339C22×D13—26no—
340C22×D13—224no—
341C22×D13—412no—
342C22×D13—448no—
343C22×D13C22×D4112yes—
344C22×D13C2516yes—
345C22×D13C2512yes—
346C22×D13C2516yes—
347Q8×C13—224no—
348Q8×C13—224no—
349Q8×C13C22×D4116yes—
350D4×C13—28no—
351C2×C4×C13—26no—
352C2×C4×C13—26no—
353C2×C4×C13—22no—
354C2×C4×C13—26no—
355C2×C4×C13—224no—
356C2×C4×C13—224no—
357C2×C4×C13C22×D4112yes—
358C2×C4×C13C2516yes—
359C2×C4×C13C2516yes—
360C2×C4×C13C2512yes—
361C2×C4×C13C2516yes—
362C2×C4×C13C2516yes—
363C22⋊D13—28no—
364C22⋊D13—224no—
365C22⋊D13—28no—
366C22⋊D13—412no—
367C2×Dic13—26no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—26no—
371C2×Dic13—28no—
372C2×Dic13C22×D414yes—
373C2×Dic13C2512yes—
374C2×Dic13C2516yes—
375C2×Dic13C2512yes—
376C2×Dic13C2516yes—
377C2×Dic13C2512yes—
378D52—248no—
379D52—224no—
380D52—224no—
381D52—412no—
382D52C22×D4148yes—
383C4×D13—224no—
384C4×D13—248no—
385C4×D13—224no—
386C4×D13—224no—
387C4×D13—224no—
388C4×D13—424no—
389C4×D13C22×D4148yes—
390Dic26—224no—
391Dic26—224no—
392C2×2−1+4—1316no—
393C2×2−1+4—2616no—
394C22×#41—131no—
395C22×#41—133no—
396C22×#41—133no—
397C22×#41—131no—
398C22×#41—1316no—
399C22×#41—133no—
400C22×#41—133no—
401C22×#41—133no—
402C22×#41—2616no—
403C23×Q8—133no—
404C23×Q8—131no—
405C23×Q8C2×D1311yescharacteristic
406C23×Q8C2×D1311yescharacteristic, complemented
407C23×D4—133no—
408C24×C4—133no—
409D4×Q8—1316no—
410D4×Q8C2×D13116yescomplemented
411#548—1316no—
412#548—1316no—
413#547—1348no—
414#547—1348no—
415#546—1348no—
416#546—1348no—
417#537—1348no—
418#536—1348no—
419C2×C4⋊Q8—133no—
420C2×C4⋊Q8C2×D1313yescomplemented
421C2×#124—133no—
422C2×#124—133no—
423#525—1348no—
424C2×#123—133no—
425C2×#123—136no—
426C2×#123—136no—
427C2×#123—133no—
428C2×C22⋊Q8—133no—
429C2×C22⋊Q8—133no—
430C2×C22⋊Q8—133no—
431C2×C22⋊Q8—1348no—
432C2×C22⋊Q8—136no—
433C2×C22⋊Q8—133no—
434C2×C22⋊Q8—133no—
435C2×C22⋊Q8—133no—
436C2×C22⋊Q8C2×D1313yes—
437C2×C22⋊Q8C2×D1313yescomplemented
438C2×#121—131no—
439C2×#121—133no—
440C2×#121—136no—
441C2×#121—133no—
442C2×#121—133no—
443C2×#121—136no—
444C2×#120—133no—
445C2×#120—133no—
446#520—1316no—
447C2×C4×Q8—131no—
448C2×C4×Q8C2×D1311yescharacteristic, complemented
449C2×C4×D4—133no—
450C2×C4×D4—133no—
451C2×C4×D4—133no—
452C2×C4×D4—133no—
453C2×C4×D4—133no—
454C2×C4×D4C2×D1313yes—
455C2×#117—133no—
456C22×C4⋊C4—133no—
457C22×C4⋊C4—136no—
458C22×C22⋊C4—136no—
459C22×C13—22no—
460C22×C13—22no—
461C22×C13—28no—
462C22×C13—22no—
463C22×C13—22no—
464C22×C13—22no—
465C22×C13—44no—
466C22×C13C23×D412yes—
467C22×C13C2×2−1+412yes—
468C22×C13C2×2−1+414yescomplemented
469C22×C13#58512yes—
470C22×C13C2611yescharacteristic
471C2×D13—26no—
472C2×D13—26no—
473C2×D13—224no—
474C2×D13—22no—
475C2×D13—26no—
476C2×D13—22no—
477C2×D13—26no—
478C2×D13—22no—
479C2×D13—26no—
480C2×D13—448no—
481C2×D13—44no—
482C2×D13—412no—
483C2×D13C23×D4112yes—
484C4×C13—26no—
485C4×C13—26no—
486C4×C13—22no—
487C4×C13—26no—
488C4×C13C23×D4112yes—
489Dic13—26no—
490Dic13—22no—
491Dic13—22no—
492Dic13—26no—
493Dic13C23×D414yes—
494C25—133no—
4952−1+4—26128no—
496C2×#41—1316no—
497C2×#41—138no—
498C2×#41—1324no—
499C2×#41—1324no—
500C2×#41—1324no—
501C2×#41—138no—
502C2×#41—1324no—
503C2×#41—1324no—
504C2×#41—2624no—
505C2×#41—2624no—
506C2×#41—2624no—
507C2×#41—2624no—
508C2×#41—2624no—
509C2×#41—26128no—
510C2×#41—268no—
511C22×Q8—28no—
512C22×Q8—28no—
513C22×Q8—1324no—
514C22×Q8—138no—
515C22×Q8—133no—
516C22×Q8—133no—
517C22×Q8—2624no—
518C22×Q8—268no—
519C22×Q8C22×D1313yes—
520C22×Q8C22×D1313yes—
521C22×Q8C22×D1318yes—
522C22×Q8C22×D1311yescharacteristic
523C22×Q8C22×D1318yescomplemented
524C22×D4—131no—
525C22×D4—133no—
526C22×D4—131no—
527C22×D4—133no—
528C22×D4—133no—
529C22×D4—133no—
530C22×D4—136no—
531C22×D4—133no—
532C22×D4—1324no—
533C22×D4—133no—
534C22×D4—2624no—
535C22×D4C22×D1311yescharacteristic
536C23×C4—133no—
537C23×C4—131no—
538C23×C4—136no—
539C23×C4—133no—
540C23×C4—133no—
541C23×C4—133no—
542C23×C4—133no—
543C23×C4—1324no—
544C23×C4—136no—
545C23×C4—2624no—
546C23×C4C22×D1313yes—
547C23×C4C22×D1313yes—
548C4⋊Q8—1324no—
549C4⋊Q8C22×D13124yescomplemented
550#124—1324no—
551#124—1324no—
552#123—1324no—
553#123—1348no—
554#123—1348no—
555#123—1324no—
556C22⋊Q8—1324no—
557C22⋊Q8—1324no—
558C22⋊Q8—1324no—
559C22⋊Q8—1348no—
560C22⋊Q8—1324no—
561C22⋊Q8—1324no—
562C22⋊Q8—1324no—
563C22⋊Q8C22×D13124yes—
564C22⋊Q8C22×D13124yescomplemented
565#121—138no—
566#121—1324no—
567#121—1348no—
568#121—1324no—
569#121—1324no—
570#121—1348no—
571#120—1324no—
572#120—1324no—
573C4×Q8—138no—
574C4×Q8C22×D1318yescomplemented
575C4×D4—1324no—
576C4×D4—1324no—
577C4×D4—1324no—
578C4×D4—1324no—
579C4×D4—1324no—
580C4×D4C22×D13124yes—
581#117—1324no—
582C2×C4⋊C4—133no—
583C2×C4⋊C4—133no—
584C2×C4⋊C4—133no—
585C2×C4⋊C4—133no—
586C2×C4⋊C4—136no—
587C2×C4⋊C4—131no—
588C2×C4⋊C4—133no—
589C2×C4⋊C4—1324no—
590C2×C4⋊C4—1348no—
591C2×C4⋊C4C22×D1313yes—
592C2×C4⋊C4C22×D1316yes—
593C2×C4⋊C4C22×D1313yes—
594C2×C22⋊C4—133no—
595C2×C22⋊C4—131no—
596C2×C22⋊C4—136no—
597C2×C22⋊C4—136no—
598C2×C22⋊C4—133no—
599C2×C22⋊C4—133no—
600C2×C22⋊C4—131no—
601C2×C22⋊C4—133no—
602C2×C22⋊C4—133no—
603C2×C22⋊C4—133no—
604C2×C22⋊C4—1348no—
605C2×C22⋊C4C22×D1313yes—
606C2×C22⋊C4C22×D1313yes—
607C2×C42—133no—
608C2×C42C22×D1313yes—
609C2×C13—24no—
610C2×C13—42no—
611C2×C13#348914yescomplemented
612C2×C13C24×D411yescharacteristic
613C2×C13C22×2−1+411yescharacteristic
614C2×C13C2×#58511yescharacteristic
615D13—212no—
616D13—42no—
617D13—46no—
618C24—133no—
619C24—133no—
620C24—131no—
621C24—1312no—
622C24—2612no—
623C24—2612no—
624C24—526no—
625C24C23×D1311yescharacteristic
626C24C23×D1311yescharacteristic
627#41—1364no—
628#41—2696no—
629#41—2696no—
630#41—2696no—
631#41—2696no—
632#41—2696no—
633#41—2632no—
634C2×Q8—232no—
635C2×Q8—232no—
636C2×Q8—212no—
637C2×Q8—212no—
638C2×Q8—1312no—
639C2×Q8—1312no—
640C2×Q8—2612no—
641C2×Q8—2696no—
642C2×Q8—2632no—
643C2×Q8—2612no—
644C2×Q8D4×D1318yes—
645C2×Q8C23×D13112yes—
646C2×Q8C23×D13112yes—
647C2×Q8C23×D1314yes—
648C2×D4—24no—
649C2×D4—134no—
650C2×D4—1312no—
651C2×D4—134no—
652C2×D4—1312no—
653C2×D4—1324no—
654C2×D4—1312no—
655C2×D4—1312no—
656C2×D4—1324no—
657C2×D4—1312no—
658C2×D4—1312no—
659C2×D4—2696no—
660C2×D4—2624no—
661C2×D4—2612no—
662C2×D4—264no—
663C2×D4—2612no—
664C2×D4—264no—
665C2×D4—2612no—
666C2×D4—526no—
667C2×D4—526no—
668C2×D4C23×D1314yes—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—131no—
672C22×C4—1324no—
673C22×C4—1312no—
674C22×C4—134no—
675C22×C4—131no—
676C22×C4—133no—
677C22×C4—133no—
678C22×C4—131no—
679C22×C4—1324no—
680C22×C4—1312no—
681C22×C4—1312no—
682C22×C4—1312no—
683C22×C4—1312no—
684C22×C4—1324no—
685C22×C4—2612no—
686C22×C4—2696no—
687C22×C4—2612no—
688C22×C4—2624no—
689C22×C4—264no—
690C22×C4—2612no—
691C22×C4—2612no—
692C22×C4—5212no—
693C22×C4C23×D13112yes—
694C22×C4C23×D13112yes—
695C22×C4C23×D1311yescharacteristic
696C22×C4C23×D1313yes—
697C22×C4C23×D1313yes—
698C22×C4C23×D1313yes—
699C22×C4C23×D1313yes—
700C4⋊C4—1312no—
701C4⋊C4—1312no—
702C4⋊C4—1312no—
703C4⋊C4—1312no—
704C4⋊C4—1324no—
705C4⋊C4—134no—
706C4⋊C4—1312no—
707C4⋊C4C23×D13112yes—
708C4⋊C4C23×D13124yes—
709C4⋊C4C23×D13112yes—
710C22⋊C4—1312no—
711C22⋊C4—134no—
712C22⋊C4—1324no—
713C22⋊C4—1324no—
714C22⋊C4—1312no—
715C22⋊C4—1312no—
716C22⋊C4—134no—
717C22⋊C4—1312no—
718C22⋊C4—1312no—
719C22⋊C4—1312no—
720C22⋊C4C23×D13112yes—
721C22⋊C4C23×D13112yes—
722C42—1312no—
723C42C23×D13112yes—
724C13C2×#348911yescharacteristic, complemented, Sylow
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—1312no—
731C23—136no—
732C23—136no—
733C23—132no—
734C23—2624no—
735C23—266no—
736C23—266no—
737C23—262no—
738C23—266no—
739C23—262no—
740C23—266no—
741C23—2624no—
742C23—262no—
743C23—266no—
744C23—5212no—
745C23—5248no—
746C23#8825414yescomplemented
747C23C24×D1312yes—
748C23C24×D1312yes—
749C23C24×D1311yescharacteristic
750Q8—224no—
751Q8—224no—
752Q8—2624no—
753Q8—2624no—
754Q8C2×D4×D13116yes—
755D4—28no—
756D4—1348no—
757D4—2648no—
758D4—2624no—
759D4—268no—
760D4—2624no—
761D4—268no—
762D4—2624no—
763D4—5212no—
764D4—5212no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—22no—
768C2×C4—26no—
769C2×C4—224no—
770C2×C4—224no—
771C2×C4—134no—
772C2×C4—132no—
773C2×C4—1348no—
774C2×C4—132no—
775C2×C4—136no—
776C2×C4—136no—
777C2×C4—132no—
778C2×C4—2624no—
779C2×C4—2624no—
780C2×C4—2648no—
781C2×C4—268no—
782C2×C4—262no—
783C2×C4—266no—
784C2×C4—262no—
785C2×C4—266no—
786C2×C4—2624no—
787C2×C4—2624no—
788C2×C4—5224no—
789C2×C4C2×D4×D13112yes—
790C2×C4C24×D1312yes—
791C2×C4C24×D1316yes—
792C2×C4C24×D1316yes—
793C2×C4C24×D1316yes—
794C2×C4C24×D1316yes—
795C22—28no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—44no—
802C22—1312no—
803C22—2624no—
804C22—266no—
805C22—266no—
806C22—262no—
807C22—266no—
808C22—262no—
809C22—266no—
810C22—262no—
811C22—266no—
812C22—5248no—
813C22—524no—
814C22—5212no—
815C22C22×D4×D1312yes—
816C22C2×#8825412yes—
817C22C2×#8825414yescomplemented
818C22#1171965212yes—
819C22C25×D1311yescharacteristic
820C4—26no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—134no—
825C4—262no—
826C4—266no—
827C4—262no—
828C4—266no—
829C4C22×D4×D13112yes—
830C2—24no—
831C2—42no—
832C2—2612no—
833C2—526no—
834C2—522no—
835C2#1312851314yesdirect product factor
836C2C23×D4×D1311yescharacteristic
837C2C22×#8825411yescharacteristic
838C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C25
hypercenterC2×D4×Q8D13
hypocenterC13C2×#3489
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#88254C2semidirect
2. C23×#6131C2semidirect
3. #13128513C2direct (N × H)
4. C2×Q8×C22⋊D13C2semidirect
5. C2×#11719281C2semidirect
6. C2×#11719522C2semidirect
7. C2×#11719431C2semidirect
8. C2×#11719336C2semidirect
9. C2×#11719255C2semidirect
10. C2×#11719335C2semidirect
11. C2×#11719334C2semidirect
12. C2×#11719429C2semidirect
13. C2×#11719252C2semidirect
14. C2×D13×C22⋊Q8C2semidirect
15. C2×#11719279C2semidirect
16. C2×D4×Q8×C13C2semidirect
18. C23×Q8×C13C22semidirect
20. C2×#88254C22semidirect
26. C22×#6131C22semidirect
27. C22×#6131C22semidirect
28. C22×Q8×D13C22semidirect
29. C22×Q8×D13C22semidirect
30. C22×#6127C22semidirect
31. C22×#6127C22semidirect
34. D4×Q8×C13C22semidirect
35. C2×C13×C4⋊Q8C22semidirect
37. C2×C13×C22⋊Q8C22semidirect
38. C2×C4×Q8×C13C22semidirect
40. #11719522C22semidirect
41. Q8×C22⋊D13C22semidirect
42. C2×#88201C22semidirect
43. C2×#88200C22semidirect
44. C2×#88200C22semidirect
45. C2×Q8×Dic13C22semidirect
46. C2×#88198C22semidirect
49. C2×#88184C22semidirect
51. C2×C4×C22⋊D13C22semidirect
53. #11719431C22semidirect
54. #11719429C22semidirect
55. #11719336C22semidirect
56. #11719335C22semidirect
57. #11719334C22semidirect
58. D13×C22⋊Q8C22semidirect
59. #11719281C22semidirect
60. #11719279C22semidirect
61. #11719255C22semidirect
62. #11719252C22semidirect
63. C2×#88151C22semidirect
64. C2×#88150C22semidirect
65. C2×#88150C22semidirect
66. C2×#88149C22semidirect
67. C2×#88149C22semidirect
68. C2×#88148C22semidirect
69. C2×#88148C22semidirect
70. C2×#88148C22semidirect
71. C2×#88147C22semidirect
72. C2×C4⋊C4×D13C22semidirect
73. C2×C4⋊C4×D13C22semidirect
74. C2×#88138C22semidirect
75. C2×#88138C22semidirect
76. C2×#88137C22semidirect
80. C2×#88129C22semidirect
81. C2×C4×D52C22semidirect
82. C2×C4×D52C22semidirect
83. C2×#88126C22semidirect
91. C22×Q8×C13C23semidirect
106. C2×#6131D4semidirect
111. C2×#6131C23semidirect
114. C2×Q8×D13C23semidirect
115. C2×Q8×D13C23semidirect
118. C2×#6127C23semidirect
119. C2×#6127C23semidirect
138. C13×C4⋊Q8C23semidirect
140. C13×C22⋊Q8C23semidirect
141. C4×Q8×C13C23semidirect
151. #88201C23semidirect
152. #88200C23semidirect
153. #88200C23semidirect
154. Q8×Dic13C23semidirect
155. #88198C23semidirect
158. #88184C23semidirect
160. C4×C22⋊D13C23semidirect
178. #88151C23semidirect
179. #88150C23semidirect
180. #88150C23semidirect
181. #88149C23semidirect
182. #88149C23semidirect
183. #88148C23semidirect
184. #88148C23semidirect
185. #88148C23semidirect
186. #88147C23semidirect
187. C4⋊C4×D13C23semidirect
188. C4⋊C4×D13C23semidirect
189. #88138C23semidirect
190. #88138C23semidirect
191. #88137C23semidirect
195. #88129C23semidirect
196. C4×D52C23semidirect
197. C4×D52C23semidirect
198. #88126C23semidirect
247. #6131C2×D4semidirect
310. C2×D4×Q8D13semidirect
327. C23×C132−1+4semidirect
406. C23×Q8C2×D13semidirect
410. D4×Q8C2×D13semidirect
420. C2×C4⋊Q8C2×D13semidirect
437. C2×C22⋊Q8C2×D13semidirect
448. C2×C4×Q8C2×D13semidirect
468. C22×C13C2×2−1+4semidirect
523. C22×Q8C22×D13semidirect
549. C4⋊Q8C22×D13semidirect
564. C22⋊Q8C22×D13semidirect
574. C4×Q8C22×D13semidirect
611. C2×C13#3489semidirect
724. C13C2×#3489semidirect
746. C23#88254semidirect
817. C22C2×#88254semidirect
835. C2#13128513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#882542
C23×#61312
#131285132
C2×Q8×C22⋊D132
C2×#117192812
C2×#117195222
C2×#117194312
C2×#117193362
C2×#117192552
C2×#117193352
C2×#117193342
C2×#117194292
C2×#117192522
C2×D13×C22⋊Q82
C2×#117192792
C2×D4×Q8×C132
C2×#348913