Finite Group Databasebeta

← C2×#13128515 #16771324

Subgroups — C2×#13128515 #16771324

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
2C22×#41×D13C211yesmaximal, characteristic, complemented
3#13128515C2132yesmaximal, direct product factor
4C2×Q8×D52C211yesmaximal, characteristic, complemented
5C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
6C2×#11719536C211yesmaximal, characteristic, complemented
7C2×#11719256C213yesmaximal, complemented
8C2×#11719336C213yesmaximal, complemented
9C2×#11719317C213yesmaximal, complemented
10C2×#11719381C213yesmaximal, complemented
11C2×#11719313C213yesmaximal, complemented
12C2×#11719380C213yesmaximal, complemented
13C2×#11719252C213yesmaximal, complemented
14C2×D13×C22⋊Q8C213yesmaximal, complemented
15C2×#11719279C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#41×D13—216no—
20C2×#41×D13C22116yescomplemented
21C2×#88254—216no—
22C2×#88254C22116yescomplemented
23C22×#6131C2211yescharacteristic
24C22×#6131C2213yescomplemented
25C22×Q8×D13C2211yescharacteristic
26C22×Q8×D13C2211yescharacteristic, complemented
27C22×Q8×D13C2213yescomplemented
28C22×#6129C2213yes—
29C22×D4×D13C2213yes—
30C22×#6127C2213yes—
31C22×#6127C2213yescomplemented
32C22×#6127C2213yescomplemented
33C23×C4×D13C2213yes—
34C13×#548C22116yescomplemented
35C2×C13×#124C2213yescomplemented
36C2×C13×C22⋊Q8C2213yescomplemented
37C2×C13×#121C2213yescomplemented
38C2×C4×Q8×C13C2211yescharacteristic, complemented
39C2×C4×D4×C13C2213yescomplemented
40#11719536C22116yescomplemented
41Q8×C22⋊D13C22116yescomplemented
42C2×#88200C2213yes—
43C2×Q8×Dic13C2211yescharacteristic, complemented
44C2×#88198C2213yescomplemented
45C2×#88193C2213yescomplemented
46C2×#88192C2213yescomplemented
47C2×#88192C2216yescomplemented
48C2×#88191C2213yes—
49C2×#88190C2213yescomplemented
50C2×C4×C22⋊D13C2213yes—
51C2×C4×C22⋊D13C2213yescomplemented
52C2×#88178C2213yescomplemented
53C2×#88178C2213yescomplemented
54#11719381C22148yescomplemented
55#11719380C22148yescomplemented
56#11719336C22148yescomplemented
57D13×C22⋊Q8C22148yescomplemented
58#11719317C22148yescomplemented
59#11719313C22148yescomplemented
60Q8×D52C22116yescomplemented
61#11719279C22116yescomplemented
62#11719256C22148yescomplemented
63#11719252C22148yescomplemented
64C2×#88151C2213yes—
65C2×#88151C2213yescomplemented
66C2×#88150C2213yes—
67C2×#88148C2213yescomplemented
68C2×#88147C2213yescomplemented
69C2×C4⋊C4×D13C2213yescomplemented
70C2×C4⋊C4×D13C2216yescomplemented
71C2×#88138C2211yescharacteristic
72C2×#88138C2216yescomplemented
73C2×#88137C2216yescomplemented
74C2×#88137C2216yescomplemented
75C2×#88137C2213yescomplemented
76C2×#88136C2213yes—
77C2×C22⋊C4×D13C2216yes—
78C2×#88132C2216yescomplemented
79C2×#88132C2213yescomplemented
80C2×C4×D52C2213yes—
81C2×C4×D52C2213yescomplemented
82C2×#88126C2213yescomplemented
83C2×#88123C2213yescomplemented
84C24×D13C2313yes—
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⋊D13C2316yes—
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2311yescharacteristic
98C22×C22⋊D13C2311yescharacteristic
99C22×C22⋊D13C2313yes—
100C23×Dic13C2313yes—
101#41×D13—2128no—
102#88254—2128no—
103C2×#6131—224no—
104C2×#6131D4116yescomplemented
105C2×#6131C2318yes—
106C2×#6131C23124yescomplemented
107C2×Q8×D13—28no—
108C2×Q8×D13—28no—
109C2×Q8×D13—224no—
110C2×Q8×D13C2318yes—
111C2×Q8×D13C2318yescomplemented
112C2×Q8×D13C23124yescomplemented
113C2×#6129—224no—
114C2×#6129C23124yes—
115C2×D4×D13—224no—
116C2×D4×D13C23124yes—
117C2×#6127—224no—
118C2×#6127—224no—
119C2×#6127—224no—
120C2×#6127C23124yes—
121C2×#6127C23124yescomplemented
122C2×#6127C23124yescomplemented
123C22×D52C2311yescharacteristic
124C22×D52C2313yes—
125C22×D52C2313yes—
126C22×C4×D13—224no—
127C22×C4×D13C2313yes—
128C22×C4×D13C2313yes—
129C22×C4×D13C2316yes—
130C22×C4×D13C2313yes—
131C22×C4×D13C2311yescharacteristic
132C22×C4×D13C23124yes—
133C22×C4×D13C2316yes—
134C22×C4×D13C2313yes—
135C22×Dic26C2313yes—
136C22×Dic26C2313yes—
137C22×Dic26C2313yes—
138C13×#124C23124yescomplemented
139C13×C22⋊Q8C23124yescomplemented
140C13×#121C23124yescomplemented
141C4×Q8×C13C2318yescomplemented
142C4×D4×C13C23124yescomplemented
143C2×C13×C4⋊C4C2313yes—
144C2×C13×C4⋊C4C2313yes—
145C2×C13×C22⋊C4C2316yes—
146C2×C13×C22⋊C4C2313yes—
147C2×C13×C22⋊C4C2311yescharacteristic
148C2×C42×C13C2313yes—
149C2×C22⋊Dic13C2316yes—
150C2×C22⋊Dic13C2313yes—
151C2×C22⋊Dic13C2313yes—
152#88200C23124yes—
153Q8×Dic13C2318yescomplemented
154#88198C23124yescomplemented
155#88193C23124yescomplemented
156#88192C23148yescomplemented
157#88192C23124yescomplemented
158#88191C23124yes—
159#88190C23124yescomplemented
160C4×C22⋊D13C23124yes—
161C4×C22⋊D13C23124yescomplemented
162C2×#6103C2313yes—
163C2×#6103C2313yes—
164C2×#6103C2313yes—
165C2×#6103C2313yes—
166C2×#6103C2313yes—
167C2×#6103C2311yescharacteristic
168C2×C4⋊Dic13C2313yes—
169C2×C4⋊Dic13C2316yes—
170C2×C4⋊Dic13C2313yes—
171#88178C23124yescomplemented
172#88178C23124yescomplemented
173C2×#6101C2311yescharacteristic
174C2×#6101C2313yes—
175C2×#6101C2313yes—
176C2×#6101C2316yes—
177C2×#6101C2313yes—
178C2×C4×Dic13C2313yes—
179#88151C23124yes—
180#88151C23124yescomplemented
181#88150C23124yes—
182#88148C23124yescomplemented
183#88147C23124yescomplemented
184C4⋊C4×D13C23148yescomplemented
185C4⋊C4×D13C23124yescomplemented
186#88138C2318yes—
187#88138C23148yescomplemented
188#88137C23124yescomplemented
189#88137C23148yescomplemented
190#88137C23148yescomplemented
191#88136C23124yes—
192C22⋊C4×D13C23148yes—
193#88132C23124yescomplemented
194#88132C23148yescomplemented
195C4×D52C23124yes—
196C4×D52C23124yescomplemented
197#88126C23124yescomplemented
198#88123C23124yescomplemented
199C2×#3489—131nomaximal, Sylow
200C24×C13C2413yes—
201C24×C13C2411yescharacteristic
202C23×D13—212no—
203C23×D13—212no—
204C23×D13—46no—
205C23×D13C2411yescharacteristic
206C23×D13C24112yes—
207C23×D13C2413yes—
208C23×D13C2411yescharacteristic
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—224no—
230C2×C22⋊D13—24no—
231C2×C22⋊D13—24no—
232C2×C22⋊D13—46no—
233C2×C22⋊D13C24124yes—
234C2×C22⋊D13C24112yes—
235C2×C22⋊D13C2414yes—
236C2×C22⋊D13C2414yes—
237C2×C22⋊D13C24112yes—
238C22×Dic13—212no—
239C22×Dic13C24112yes—
240C22×Dic13C2411yescharacteristic
241C22×Dic13C2413yes—
242C22×Dic13C2413yes—
243C22×Dic13C2413yes—
244C22×Dic13C2411yescharacteristic
245#6131—296no—
246#6131C2×D4164yescomplemented
247Q8×D13—232no—
248Q8×D13—232no—
249Q8×D13—296no—
250#6129—296no—
251D4×D13—296no—
252#6127—296no—
253#6127—296no—
254#6127—296no—
255C2×D52—212no—
256C2×D52—24no—
257C2×D52C2×D4124yes—
258C2×D52C2414yes—
259C2×D52C24112yes—
260C2×D52C24112yes—
261C2×C4×D13—212no—
262C2×C4×D13—224no—
263C2×C4×D13—212no—
264C2×C4×D13—212no—
265C2×C4×D13—24no—
266C2×C4×D13—296no—
267C2×C4×D13—412no—
268C2×C4×D13C2×D4124yes—
269C2×C4×D13C24112yes—
270C2×C4×D13C24112yes—
271C2×C4×D13C24124yes—
272C2×C4×D13C24112yes—
273C2×C4×D13C2414yes—
274C2×C4×D13C24124yes—
275C2×C4×D13C24112yes—
276C2×Dic26—212no—
277C2×Dic26—212no—
278C2×Dic26—212no—
279C2×Dic26C24112yes—
280C2×Dic26C24112yes—
281C2×Dic26C24112yes—
282C13×C4⋊C4C24112yes—
283C13×C4⋊C4C24112yes—
284C13×C22⋊C4C24124yes—
285C13×C22⋊C4C24112yes—
286C13×C22⋊C4C2414yes—
287C42×C13C24112yes—
288C22⋊Dic13C24124yes—
289C22⋊Dic13C24112yes—
290C22⋊Dic13C24112yes—
291#6103C24112yes—
292#6103C24112yes—
293#6103C24112yes—
294#6103C24112yes—
295#6103C24112yes—
296#6103C2414yes—
297C4⋊Dic13C24112yes—
298C4⋊Dic13C24124yes—
299C4⋊Dic13C24112yes—
300#6101C2414yes—
301#6101C24112yes—
302#6101C24112yes—
303#6101C24124yes—
304#6101C24112yes—
305C4×Dic13C24112yes—
306C22×2−1+4—131no—
307C23×#41—131no—
308#3489—1332no—
309C2×D4×Q8—131no—
310C2×D4×Q8—131no—
311C2×#548—131no—
312C2×#548D1311yescharacteristic, complemented
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—26no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—26no—
326C23×C13—26no—
327C23×C13—22no—
328C23×C13C2516yes—
329C23×C13C2512yes—
330C23×C13C2511yescharacteristic
331C22×D13—22no—
332C22×D13—26no—
333C22×D13—26no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—224no—
339C22×D13—224no—
340C22×D13—412no—
341C22×D13—448no—
342C22×D13C22×D4112yes—
343C22×D132−1+414yescomplemented
344C22×D13C2512yes—
345C22×D13C2516yes—
346C22×D13C2512yes—
347Q8×C13—224no—
348Q8×C13C22×D4116yes—
349D4×C13—224no—
350D4×C13—412no—
351C2×C4×C13—26no—
352C2×C4×C13—22no—
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×C13C2512yes—
360C2×C4×C13C2512yes—
361C2×C4×C13C2516yes—
362C2×C4×C13C2516yes—
363C22⋊D13—224no—
364C22⋊D13—248no—
365C22⋊D13—28no—
366C22⋊D13—28no—
367C22⋊D13—412no—
368C2×Dic13—26no—
369C2×Dic13—26no—
370C2×Dic13—22no—
371C2×Dic13—26no—
372C2×Dic13—224no—
373C2×Dic13C22×D414yes—
374C2×Dic13C2512yes—
375C2×Dic13C2516yes—
376C2×Dic13C2516yes—
377C2×Dic13C2516yes—
378C2×Dic13C2512yes—
379D52—224no—
380D52—28no—
381D52C22×D4148yes—
382C4×D13—224no—
383C4×D13—248no—
384C4×D13—224no—
385C4×D13—224no—
386C4×D13—28no—
387C4×D13—424no—
388C4×D13C22×D4148yes—
389Dic26—224no—
390Dic26—224no—
391Dic26—224no—
392C2×2−1+4—1316no—
393C2×2−1+4—2616no—
394C22×#41—1316no—
395C22×#41—131no—
396C22×#41—133no—
397C22×#41—133no—
398C22×#41—133no—
399C22×#41—133no—
400C22×#41—133no—
401C22×#41—2616no—
402C22×#41C2×D1311yescharacteristic
403C23×Q8—131no—
404C23×Q8—133no—
405C23×Q8—131no—
406C23×Q8C2×D1311yescharacteristic, complemented
407C23×D4—133no—
408C24×C4—133no—
409D4×Q8—1316no—
410D4×Q8—1316no—
411#548—1316no—
412#548C2×D13116yescomplemented
413#547—1348no—
414#547—1348no—
415#546—1348no—
416#546—1348no—
417#537—1348no—
418#536—1348no—
419C2×C4⋊Q8—133no—
420C2×C4⋊Q8—133no—
421C2×#124—133no—
422C2×#124C2×D1313yescomplemented
423#525—1348no—
424C2×#123—133no—
425C2×#123—133no—
426C2×#123—136no—
427C2×#123—136no—
428C2×C22⋊Q8—133no—
429C2×C22⋊Q8—133no—
430C2×C22⋊Q8—133no—
431C2×C22⋊Q8—1348no—
432C2×C22⋊Q8—133no—
433C2×C22⋊Q8—133no—
434C2×C22⋊Q8—133no—
435C2×C22⋊Q8—136no—
436C2×C22⋊Q8—133no—
437C2×C22⋊Q8C2×D1313yescomplemented
438C2×#121—136no—
439C2×#121—133no—
440C2×#121—133no—
441C2×#121—131no—
442C2×#121—136no—
443C2×#121C2×D1313yescomplemented
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×D1313yescomplemented
455C2×#117—133no—
456C22×C4⋊C4—133no—
457C22×C4⋊C4—136no—
458C22×C22⋊C4—136no—
459C22×C13—26no—
460C22×C13—22no—
461C22×C13—22no—
462C22×C13—26no—
463C22×C13—26no—
464C22×C13—22no—
465C22×C13—412no—
466C22×C13—44no—
467C22×C13C23×D412yes—
468C22×C13C2×2−1+412yes—
469C22×C13#58512yes—
470C22×C13C2611yescharacteristic
471C2×D13—22no—
472C2×D13—26no—
473C2×D13—26no—
474C2×D13—22no—
475C2×D13—28no—
476C2×D13—224no—
477C2×D13—22no—
478C2×D13—22no—
479C2×D13—22no—
480C2×D13—448no—
481C2×D13—44no—
482C2×D13C23×D4112yes—
483C2×D13C2×2−1+414yescomplemented
484C4×C13—26no—
485C4×C13—22no—
486C4×C13—22no—
487C4×C13—26no—
488C4×C13C23×D4112yes—
489Dic13—26no—
490Dic13—26no—
491Dic13—22no—
492Dic13—26no—
493Dic13C23×D414yes—
494C25—133no—
4952−1+4—26128no—
496C2×#41—28no—
497C2×#41—1316no—
498C2×#41—138no—
499C2×#41—1324no—
500C2×#41—1324no—
501C2×#41—1324no—
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×#41C22×D1318yes—
511C22×Q8—28no—
512C22×Q8—1324no—
513C22×Q8—138no—
514C22×Q8—138no—
515C22×Q8—133no—
516C22×Q8—133no—
517C22×Q8—133no—
518C22×Q8—2624no—
519C22×Q8—268no—
520C22×Q8—268no—
521C22×Q8C22×D1313yes—
522C22×Q8C22×D1311yescharacteristic
523C22×Q8C22×D1318yescomplemented
524C22×D4—131no—
525C22×D4—133no—
526C22×D4—131no—
527C22×D4—136no—
528C22×D4—133no—
529C22×D4—1324no—
530C22×D4—133no—
531C22×D4—131no—
532C22×D4—133no—
533C22×D4—2624no—
534C22×D4C22×D1313yes—
535C22×D4C22×D1313yes—
536C23×C4—133no—
537C23×C4—133no—
538C23×C4—136no—
539C23×C4—133no—
540C23×C4—133no—
541C23×C4—133no—
542C23×C4—131no—
543C23×C4—1324no—
544C23×C4—136no—
545C23×C4—2624no—
546C23×C4C22×D1313yes—
547C23×C4C22×D1313yes—
548C4⋊Q8—1324no—
549C4⋊Q8—1324no—
550#124—1324no—
551#124C22×D13124yescomplemented
552#123—1324no—
553#123—1324no—
554#123—1348no—
555#123—1348no—
556C22⋊Q8—1324no—
557C22⋊Q8—1324no—
558C22⋊Q8—1324no—
559C22⋊Q8—1324no—
560C22⋊Q8—1324no—
561C22⋊Q8—1324no—
562C22⋊Q8—1348no—
563C22⋊Q8—1324no—
564C22⋊Q8C22×D13124yescomplemented
565#121—1324no—
566#121—1348no—
567#121—1324no—
568#121—138no—
569#121—1348no—
570#121C22×D13124yescomplemented
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×D13124yescomplemented
581#117—1324no—
582C2×C4⋊C4—133no—
583C2×C4⋊C4—133no—
584C2×C4⋊C4—133no—
585C2×C4⋊C4—136no—
586C2×C4⋊C4—136no—
587C2×C4⋊C4—131no—
588C2×C4⋊C4—133no—
589C2×C4⋊C4—133no—
590C2×C4⋊C4—1324no—
591C2×C4⋊C4—1348no—
592C2×C4⋊C4C22×D1313yes—
593C2×C4⋊C4C22×D1313yes—
594C2×C22⋊C4—136no—
595C2×C22⋊C4—133no—
596C2×C22⋊C4—133no—
597C2×C22⋊C4—133no—
598C2×C22⋊C4—133no—
599C2×C22⋊C4—133no—
600C2×C22⋊C4—133no—
601C2×C22⋊C4—131no—
602C2×C22⋊C4—133no—
603C2×C22⋊C4—1348no—
604C2×C22⋊C4C22×D1316yes—
605C2×C22⋊C4C22×D1311yescharacteristic
606C2×C22⋊C4C22×D1313yes—
607C2×C42—133no—
608C2×C42C22×D1313yes—
609C2×C13—46no—
610C2×C13—42no—
611C2×C13#348914yescomplemented
612C2×C13C24×D411yescharacteristic
613C2×C13C22×2−1+411yescharacteristic
614C2×C13C2×#58511yescharacteristic
615D13—24no—
616D13—212no—
617D13—42no—
618C24—131no—
619C24—133no—
620C24—131no—
621C24—1312no—
622C24—2612no—
623C24—2612no—
624C24—526no—
625C24C23×D1313yes—
626C24C23×D1311yescharacteristic
627#41—232no—
628#41—1364no—
629#41—2696no—
630#41—2696no—
631#41—2696no—
632#41—2696no—
633#41—2696no—
634C2×Q8—232no—
635C2×Q8—212no—
636C2×Q8—1312no—
637C2×Q8—1312no—
638C2×Q8—1312no—
639C2×Q8—2612no—
640C2×Q8—2696no—
641C2×Q8—2632no—
642C2×Q8—2632no—
643C2×Q8—2612no—
644C2×Q8—2612no—
645C2×Q8D4×D1318yes—
646C2×Q8C23×D13112yes—
647C2×Q8C23×D1314yes—
648C2×D4—212no—
649C2×D4—46no—
650C2×D4—134no—
651C2×D4—1312no—
652C2×D4—134no—
653C2×D4—1324no—
654C2×D4—1312no—
655C2×D4—1324no—
656C2×D4—1312no—
657C2×D4—134no—
658C2×D4—1312no—
659C2×D4—2612no—
660C2×D4—264no—
661C2×D4—264no—
662C2×D4—2696no—
663C2×D4—2624no—
664C2×D4—2612no—
665C2×D4—264no—
666C2×D4—526no—
667C2×D4C23×D13112yes—
668C2×D4C23×D13112yes—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—131no—
672C22×C4—1324no—
673C22×C4—1312no—
674C22×C4—1312no—
675C22×C4—131no—
676C22×C4—133no—
677C22×C4—133no—
678C22×C4—133no—
679C22×C4—1324no—
680C22×C4—1312no—
681C22×C4—1312no—
682C22×C4—1312no—
683C22×C4—134no—
684C22×C4—1324no—
685C22×C4—264no—
686C22×C4—2696no—
687C22×C4—2612no—
688C22×C4—2624no—
689C22×C4—2612no—
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×D1311yescharacteristic
699C22×C4C23×D1313yes—
700C4⋊C4—1312no—
701C4⋊C4—1312no—
702C4⋊C4—1312no—
703C4⋊C4—1324no—
704C4⋊C4—1324no—
705C4⋊C4—134no—
706C4⋊C4—1312no—
707C4⋊C4—1312no—
708C4⋊C4C23×D13112yes—
709C4⋊C4C23×D13112yes—
710C22⋊C4—1324no—
711C22⋊C4—1312no—
712C22⋊C4—1312no—
713C22⋊C4—1312no—
714C22⋊C4—1312no—
715C22⋊C4—1312no—
716C22⋊C4—1312no—
717C22⋊C4—134no—
718C22⋊C4—1312no—
719C22⋊C4C23×D13124yes—
720C22⋊C4C23×D1314yes—
721C22⋊C4C23×D13112yes—
722C42—1312no—
723C42C23×D13112yes—
724C13C2×#348911yescharacteristic, complemented, Sylow
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—1312no—
732C23—134no—
733C23—132no—
734C23—136no—
735C23—132no—
736C23—2624no—
737C23—2624no—
738C23—262no—
739C23—266no—
740C23—262no—
741C23—266no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—5212no—
746C23—5248no—
747C23C24×D1316yes—
748C23C24×D1312yes—
749C23C24×D1311yescharacteristic
750Q8—224no—
751Q8—2624no—
752Q8—2624no—
753Q8—2624no—
754Q8C2×D4×D13116yes—
755D4—224no—
756D4—412no—
757D4—1348no—
758D4—268no—
759D4—2624no—
760D4—268no—
761D4—268no—
762D4—2648no—
763D4—2624no—
764D4—5212no—
765C2×C4—22no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—22no—
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—136no—
778C2×C4—268no—
779C2×C4—2624no—
780C2×C4—2648no—
781C2×C4—2624no—
782C2×C4—266no—
783C2×C4—266no—
784C2×C4—266no—
785C2×C4—262no—
786C2×C4—2624no—
787C2×C4—2624no—
788C2×C4—5224no—
789C2×C4C2×D4×D13112yes—
790C2×C4C24×D1312yes—
791C2×C4C24×D1316yes—
792C2×C4C24×D1316yes—
793C2×C4C24×D1312yes—
794C2×C4C24×D1316yes—
795C22—22no—
796C22—26no—
797C22—22no—
798C22—26no—
799C22—22no—
800C22—26no—
801C22—44no—
802C22—412no—
803C22—1312no—
804C22—134no—
805C22—2624no—
806C22—268no—
807C22—262no—
808C22—266no—
809C22—266no—
810C22—262no—
811C22—262no—
812C22—262no—
813C22—262no—
814C22—5248no—
815C22—524no—
816C22C22×D4×D1312yes—
817C22#1171964812yes—
818C22D13×2−1+412yes—
819C22C25×D1311yescharacteristic
820C4—22no—
821C4—26no—
822C4—22no—
823C4—26no—
824C4—134no—
825C4—266no—
826C4—266no—
827C4—262no—
828C4—266no—
829C4C22×D4×D13112yes—
830C2—46no—
831C2—42no—
832C2—264no—
833C2—2612no—
834C2—522no—
835C2#1312851514yesdirect product factor
836C2C23×D4×D1311yescharacteristic
837C2C2×D13×2−1+411yescharacteristic
838C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#548C2
socleC23×C13C25
hypercenterC2×#548D13
hypocenterC13C2×#3489
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×#41×D13C2semidirect
3. #13128515C2direct (N × H)
4. C2×Q8×D52C2semidirect
5. C2×Q8×C22⋊D13C2semidirect
6. C2×#11719536C2semidirect
7. C2×#11719256C2semidirect
8. C2×#11719336C2semidirect
9. C2×#11719317C2semidirect
10. C2×#11719381C2semidirect
11. C2×#11719313C2semidirect
12. C2×#11719380C2semidirect
13. C2×#11719252C2semidirect
14. C2×D13×C22⋊Q8C2semidirect
15. C2×#11719279C2semidirect
16. C2×C13×#548C2semidirect
18. C23×Q8×C13C22semidirect
20. C2×#41×D13C22semidirect
22. C2×#88254C22semidirect
24. 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. Q8×C22⋊D13C22semidirect
43. C2×Q8×Dic13C22semidirect
44. C2×#88198C22semidirect
45. C2×#88193C22semidirect
46. C2×#88192C22semidirect
47. C2×#88192C22semidirect
49. C2×#88190C22semidirect
51. C2×C4×C22⋊D13C22semidirect
52. C2×#88178C22semidirect
53. C2×#88178C22semidirect
54. #11719381C22semidirect
55. #11719380C22semidirect
56. #11719336C22semidirect
57. D13×C22⋊Q8C22semidirect
58. #11719317C22semidirect
59. #11719313C22semidirect
60. Q8×D52C22semidirect
61. #11719279C22semidirect
62. #11719256C22semidirect
63. #11719252C22semidirect
65. C2×#88151C22semidirect
67. C2×#88148C22semidirect
68. C2×#88147C22semidirect
69. C2×C4⋊C4×D13C22semidirect
70. C2×C4⋊C4×D13C22semidirect
72. C2×#88138C22semidirect
73. C2×#88137C22semidirect
74. C2×#88137C22semidirect
75. C2×#88137C22semidirect
78. C2×#88132C22semidirect
79. C2×#88132C22semidirect
81. C2×C4×D52C22semidirect
82. C2×#88126C22semidirect
83. C2×#88123C22semidirect
90. C22×Q8×C13C23semidirect
104. C2×#6131D4semidirect
106. C2×#6131C23semidirect
111. C2×Q8×D13C23semidirect
112. C2×Q8×D13C23semidirect
121. C2×#6127C23semidirect
122. C2×#6127C23semidirect
138. C13×#124C23semidirect
139. C13×C22⋊Q8C23semidirect
140. C13×#121C23semidirect
141. C4×Q8×C13C23semidirect
142. C4×D4×C13C23semidirect
153. Q8×Dic13C23semidirect
154. #88198C23semidirect
155. #88193C23semidirect
156. #88192C23semidirect
157. #88192C23semidirect
159. #88190C23semidirect
161. C4×C22⋊D13C23semidirect
171. #88178C23semidirect
172. #88178C23semidirect
180. #88151C23semidirect
182. #88148C23semidirect
183. #88147C23semidirect
184. C4⋊C4×D13C23semidirect
185. C4⋊C4×D13C23semidirect
187. #88138C23semidirect
188. #88137C23semidirect
189. #88137C23semidirect
190. #88137C23semidirect
193. #88132C23semidirect
194. #88132C23semidirect
196. C4×D52C23semidirect
197. #88126C23semidirect
198. #88123C23semidirect
246. #6131C2×D4semidirect
312. C2×#548D13semidirect
343. C22×D132−1+4semidirect
406. C23×Q8C2×D13semidirect
412. #548C2×D13semidirect
422. C2×#124C2×D13semidirect
437. C2×C22⋊Q8C2×D13semidirect
443. C2×#121C2×D13semidirect
448. C2×C4×Q8C2×D13semidirect
454. C2×C4×D4C2×D13semidirect
483. C2×D13C2×2−1+4semidirect
523. C22×Q8C22×D13semidirect
551. #124C22×D13semidirect
564. C22⋊Q8C22×D13semidirect
570. #121C22×D13semidirect
574. C4×Q8C22×D13semidirect
580. C4×D4C22×D13semidirect
611. C2×C13#3489semidirect
724. C13C2×#3489semidirect
835. C2#13128515direct (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×#41×D132
#131285152
C2×Q8×D522
C2×Q8×C22⋊D132
C2×#117195362
C2×#117192562
C2×#117193362
C2×#117193172
C2×#117193812
C2×#117193132
C2×#117193802
C2×#117192522
C2×D13×C22⋊Q82
C2×#117192792
C2×C13×#5482
C2×#348913