Finite Group Databasebeta

← C2×#13128486 #16771083

Subgroups — C2×#13128486 #16771083

Order 3328.

11254 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88254C211yesmaximal, characteristic, complemented
2C23×Q8×D13C211yesmaximal, characteristic, complemented
3#13128486C2132yesmaximal, direct product factor
4C2×#11719432C213yesmaximal, complemented
5C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
6C2×#11719337C213yesmaximal, complemented
7C2×#11719281C211yesmaximal, characteristic, complemented
8C2×#11719522C211yesmaximal, characteristic, complemented
9C2×#11719338C213yesmaximal, complemented
10C2×#11719257C213yesmaximal, complemented
11C2×#11719429C213yesmaximal, complemented
12C2×#11719333C213yesmaximal, complemented
13C2×#11719332C213yesmaximal, complemented
14C2×#11719252C213yesmaximal, complemented
15C2×#11719277C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C13C211yesmaximal, characteristic, complemented
17C23×Q8×C13C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic, complemented
19C2×#88254—216no—
20C2×#88254C22116yescomplemented
21C22×#6131C2213yes—
22C22×#6131C2211yescharacteristic, complemented
23C22×Q8×D13—216no—
24C22×Q8×D13C2213yes—
25C22×Q8×D13C2211yescharacteristic
26C22×Q8×D13C2213yes—
27C22×Q8×D13C2211yescharacteristic
28C22×Q8×D13C22116yescomplemented
29C22×Q8×D13C2213yescomplemented
30C22×#6127C2213yes—
31C22×#6127C2213yescomplemented
32C23×C4×D13C2213yes—
33C23×Dic26C2213yes—
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×#88200C2213yes—
44C2×#88200C2213yescomplemented
45C2×Q8×Dic13C2211yescharacteristic, complemented
46C2×#88198C2213yescomplemented
47C2×#88193C2213yes—
48C2×#88191C2211yescharacteristic
49C2×#88184C2213yes—
50C2×C4×C22⋊D13C2213yes—
51C2×C4×C22⋊D13C2213yes—
52C2×#88178C2213yescomplemented
53#11719432C22148yescomplemented
54#11719429C22148yescomplemented
55#11719338C22148yescomplemented
56#11719337C22148yescomplemented
57#11719333C22148yescomplemented
58#11719332C22148yescomplemented
59#11719281C22116yescomplemented
60#11719277C22116yescomplemented
61#11719257C22148yescomplemented
62#11719252C22148yescomplemented
63C2×#88151C2213yescomplemented
64C2×#88150C2213yes—
65C2×#88150C2216yescomplemented
66C2×#88150C2216yescomplemented
67C2×#88149C2213yes—
68C2×#88148C2213yes—
69C2×#88148C2216yes—
70C2×#88147C2216yes—
71C2×#88146C2213yes—
72C2×#88142C2216yescomplemented
73C2×#88141C2213yescomplemented
74C2×#88139C2216yescomplemented
75C2×#88138C2213yes—
76C2×#88137C2213yes—
77C2×#88136C2213yes—
78C2×#88135C2216yes—
79C2×#88132C2213yes—
80C2×#88129C2213yescomplemented
81C2×C4×D52C2213yes—
82C2×#88126C2213yes—
83C2×C4×Dic26C2213yescomplemented
84C24×D13C2311yescharacteristic
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⋊D13C2313yes—
96C22×C22⋊D13C2311yescharacteristic
97C22×C22⋊D13C2311yescharacteristic
98C22×C22⋊D13C2313yes—
99C23×Dic13C2313yes—
100#88254—2128no—
101C2×#6131—28no—
102C2×#6131—224no—
103C2×#6131C23124yes—
104C2×#6131C2318yescomplemented
105C2×Q8×D13—28no—
106C2×Q8×D13—2128no—
107C2×Q8×D13—224no—
108C2×Q8×D13—224no—
109C2×Q8×D13—224no—
110C2×Q8×D13D4116yescomplemented
111C2×Q8×D13C23124yes—
112C2×Q8×D13C23124yes—
113C2×Q8×D13C2318yes—
114C2×Q8×D13C2318yes—
115C2×Q8×D13C23124yescomplemented
116C2×#6127—224no—
117C2×#6127—224no—
118C2×#6127C23124yes—
119C2×#6127C23124yescomplemented
120C22×D52C2313yes—
121C22×D52C2313yes—
122C22×D52C2313yes—
123C22×C4×D13—224no—
124C22×C4×D13C2313yes—
125C22×C4×D13C2313yes—
126C22×C4×D13C2316yes—
127C22×C4×D13C2313yes—
128C22×C4×D13C2313yes—
129C22×C4×D13C23124yes—
130C22×C4×D13C2313yes—
131C22×Dic26—224no—
132C22×Dic26C2313yes—
133C22×Dic26C2313yes—
134C22×Dic26C2316yes—
135C22×Dic26C23124yes—
136C22×Dic26C2313yes—
137C13×C4⋊Q8C23124yescomplemented
138C13×C22⋊Q8C23124yes—
139C13×C22⋊Q8C23124yescomplemented
140C4×Q8×C13C2318yescomplemented
141C4×D4×C13C23124yes—
142C2×C13×C4⋊C4C2313yes—
143C2×C13×C4⋊C4C2316yes—
144C2×C13×C4⋊C4C2313yes—
145C2×C13×C22⋊C4C2313yes—
146C2×C13×C22⋊C4C2313yes—
147C2×C42×C13C2313yes—
148C2×C22⋊Dic13C2311yescharacteristic
149C2×C22⋊Dic13C2313yes—
150#88201C23124yescomplemented
151#88200C23124yes—
152#88200C23124yescomplemented
153Q8×Dic13C2318yescomplemented
154#88198C23124yescomplemented
155#88193C23124yes—
156#88191C2318yes—
157#88184C23124yes—
158C4×C22⋊D13C23124yes—
159C4×C22⋊D13C23124yes—
160C2×#6103C2311yescharacteristic
161C2×#6103C2313yes—
162C2×#6103C2311yescharacteristic
163C2×#6103C2313yes—
164C2×#6103C2316yes—
165C2×#6103C2313yes—
166C2×#6103C2313yes—
167C2×#6103C2316yes—
168C2×C4⋊Dic13C2313yes—
169C2×C4⋊Dic13C2313yes—
170#88178C23124yescomplemented
171C2×#6101C2313yes—
172C2×#6101C2313yes—
173C2×#6101C2313yes—
174C2×#6101C2316yes—
175C2×#6101C2313yes—
176C2×C4×Dic13C2316yes—
177C2×C4×Dic13C2313yes—
178#88151C23124yescomplemented
179#88150C23124yes—
180#88150C23148yescomplemented
181#88150C23148yescomplemented
182#88149C23124yes—
183#88148C23124yes—
184#88148C23148yes—
185#88147C23148yes—
186#88146C23124yes—
187#88142C23148yescomplemented
188#88141C23124yescomplemented
189#88139C23148yescomplemented
190#88138C23124yes—
191#88137C23124yes—
192#88136C23124yes—
193#88135C23148yes—
194#88132C23124yes—
195#88129C23124yescomplemented
196C4×D52C23124yes—
197#88126C23124yes—
198C4×Dic26C23124yescomplemented
199C2×#3486—131nomaximal, Sylow
200C24×C13C2411yescharacteristic
201C24×C13C2411yescharacteristic
202C23×D13—24no—
203C23×D13—24no—
204C23×D13—24no—
205C23×D13C2414yes—
206C23×D13C2413yes—
207C23×D13C2411yescharacteristic
208C23×D13C2411yescharacteristic
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×C13C2411yescharacteristic
223C22×C4×C13C2413yes—
224C22×C4×C13C2413yes—
225C22×C4×C13C24112yes—
226C22×C4×C13C24112yes—
227C22×C4×C13C2413yes—
228C2×C22⋊D13—212no—
229C2×C22⋊D13—24no—
230C2×C22⋊D13—24no—
231C2×C22⋊D13—212no—
232C2×C22⋊D13C24112yes—
233C2×C22⋊D13C2414yes—
234C2×C22⋊D13C2414yes—
235C2×C22⋊D13C24112yes—
236C22×Dic13—212no—
237C22×Dic13C24112yes—
238C22×Dic13C2411yescharacteristic
239C22×Dic13C2413yes—
240C22×Dic13C2411yescharacteristic
241C22×Dic13C2413yes—
242C22×Dic13C2413yes—
243#6131—232no—
244#6131—296no—
245Q8×D13—232no—
246Q8×D13—296no—
247Q8×D13—296no—
248Q8×D13—296no—
249Q8×D13C2×D4164yescomplemented
250#6127—296no—
251#6127—296no—
252C2×D52—212no—
253C2×D52—212no—
254C2×D52—212no—
255C2×D52C24112yes—
256C2×D52C24112yes—
257C2×D52C24112yes—
258C2×C4×D13—212no—
259C2×C4×D13—212no—
260C2×C4×D13—212no—
261C2×C4×D13—212no—
262C2×C4×D13—224no—
263C2×C4×D13—296no—
264C2×C4×D13C2×D4124yes—
265C2×C4×D13C24112yes—
266C2×C4×D13C24112yes—
267C2×C4×D13C24124yes—
268C2×C4×D13C24112yes—
269C2×C4×D13C24112yes—
270C2×C4×D13C24112yes—
271C2×Dic26—212no—
272C2×Dic26—224no—
273C2×Dic26—212no—
274C2×Dic26—296no—
275C2×Dic26C2×D4124yes—
276C2×Dic26C24112yes—
277C2×Dic26C24112yes—
278C2×Dic26C24124yes—
279C2×Dic26C24112yes—
280C13×C4⋊C4C24112yes—
281C13×C4⋊C4C24124yes—
282C13×C4⋊C4C24112yes—
283C13×C22⋊C4C24112yes—
284C13×C22⋊C4C24112yes—
285C42×C13C24112yes—
286C22⋊Dic13C2414yes—
287C22⋊Dic13C24112yes—
288#6103C2414yes—
289#6103C24112yes—
290#6103C2414yes—
291#6103C24112yes—
292#6103C24124yes—
293#6103C24112yes—
294#6103C24112yes—
295#6103C24124yes—
296C4⋊Dic13C24112yes—
297C4⋊Dic13C24112yes—
298#6101C24112yes—
299#6101C24112yes—
300#6101C24112yes—
301#6101C24124yes—
302#6101C24112yes—
303C4×Dic13C24124yes—
304C4×Dic13C24112yes—
305C22×2−1+4—131no—
306C24×Q8—131no—
307#3486—1332no—
308C2×D4×Q8—131no—
309C2×D4×Q8—133no—
310C2×D4×Q8—133no—
311C2×D4×Q8D1311yescharacteristic, complemented
312C2×#548—131no—
313C2×#548—133no—
314C2×#548—131no—
315C2×#548—133no—
316C2×#536—133no—
317C2×#536—133no—
318C2×#525—133no—
319C2×#525—133no—
320C2×#519—131no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C132−1+414yescomplemented
327C23×C13C2512yes—
328C23×C13C2512yes—
329C23×C13C2511yescharacteristic
330C22×D13—232no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—28no—
336C22×D13—28no—
337C22×D13—28no—
338C22×D13—26no—
339C22×D13—26no—
340C22×D13—26no—
341C22×D13C22×D414yes—
342C22×D132−1+414yescomplemented
343C22×D13C2516yes—
344C22×D13C2512yes—
345C22×D13C2512yes—
346Q8×C13—224no—
347Q8×C13—224no—
348Q8×C13C22×D4116yes—
349D4×C13—28no—
350C2×C4×C13—26no—
351C2×C4×C13—26no—
352C2×C4×C13—26no—
353C2×C4×C13—22no—
354C2×C4×C13—224no—
355C2×C4×C13—224no—
356C2×C4×C13C22×D4112yes—
357C2×C4×C13C2516yes—
358C2×C4×C13C2512yes—
359C2×C4×C13C2516yes—
360C2×C4×C13C2516yes—
361C2×C4×C13C2516yes—
362C22⋊D13—224no—
363C22⋊D13—28no—
364C22⋊D13—28no—
365C22⋊D13—224no—
366C2×Dic13—26no—
367C2×Dic13—22no—
368C2×Dic13—26no—
369C2×Dic13—22no—
370C2×Dic13—224no—
371C2×Dic13C22×D4112yes—
372C2×Dic13C2512yes—
373C2×Dic13C2516yes—
374C2×Dic13C2512yes—
375C2×Dic13C2516yes—
376C2×Dic13C2516yes—
377D52—224no—
378D52—224no—
379D52—224no—
380C4×D13—224no—
381C4×D13—224no—
382C4×D13—224no—
383C4×D13—224no—
384C4×D13—248no—
385C4×D13C22×D4148yes—
386Dic26—224no—
387Dic26—248no—
388Dic26—224no—
389Dic26C22×D4148yes—
390C2×2−1+4—1316no—
391C2×2−1+4—2616no—
392C22×#41—133no—
393C22×#41—131no—
394C22×#41—133no—
395C22×#41—133no—
396C23×Q8—131no—
397C23×Q8—133no—
398C23×Q8—133no—
399C23×Q8—131no—
400C23×Q8—1316no—
401C23×Q8—133no—
402C23×Q8—133no—
403C23×Q8—2616no—
404C23×Q8C2×D1311yescharacteristic
405C23×Q8C2×D1311yescharacteristic, complemented
406C24×C4—133no—
407D4×Q8—1316no—
408D4×Q8—1348no—
409D4×Q8—1348no—
410D4×Q8C2×D13116yescomplemented
411#548—1316no—
412#548—1348no—
413#548—1316no—
414#548—1348no—
415#536—1348no—
416#536—1348no—
417C2×C4⋊Q8—133no—
418C2×C4⋊Q8—136no—
419C2×C4⋊Q8C2×D1313yescomplemented
420C2×#124—133no—
421C2×#124—136no—
422C2×#124—133no—
423#525—1348no—
424#525—1348no—
425C2×#123—136no—
426C2×#123—133no—
427C2×#123—133no—
428C2×C22⋊Q8—133no—
429C2×C22⋊Q8—133no—
430C2×C22⋊Q8—133no—
431C2×C22⋊Q8—133no—
432C2×C22⋊Q8—136no—
433C2×C22⋊Q8—136no—
434C2×C22⋊Q8—133no—
435C2×C22⋊Q8—133no—
436C2×C22⋊Q8C2×D1313yes—
437C2×C22⋊Q8C2×D1313yescomplemented
438C2×#121—133no—
439C2×#121—133no—
440C2×#121—133no—
441C2×#121—133no—
442C2×#120—131no—
443C2×#120—133no—
444#519—1316no—
445C2×C4×Q8—131no—
446C2×C4×Q8—133no—
447C2×C4×Q8—133no—
448C2×C4×Q8C2×D1311yescharacteristic, complemented
449C2×C4×D4—133no—
450C2×C4×D4—133no—
451C2×C4×D4—136no—
452C2×C4×D4—136no—
453C2×C4×D4—133no—
454C2×C4×D4C2×D1313yes—
455C2×#117—133no—
456C2×#117—133no—
457C22×C13—22no—
458C22×C13—22no—
459C22×C13—28no—
460C22×C13—22no—
461C22×C13—22no—
462C22×C13—22no—
463C22×C13—44no—
464C22×C13C23×D412yes—
465C22×C13C2×2−1+412yes—
466C22×C13C2×2−1+412yes—
467C22×C13C2×2−1+414yescomplemented
468C22×C13C2611yescharacteristic
469C2×D13—232no—
470C2×D13—22no—
471C2×D13—22no—
472C2×D13—22no—
473C2×D13—22no—
474C2×D13—28no—
475C2×D13—28no—
476C2×D13—26no—
477C2×D13—26no—
478C2×D13—26no—
479C2×D13—412no—
480C2×D13C23×D414yes—
481C2×D13C2×2−1+414yescomplemented
482C4×C13—26no—
483C4×C13—26no—
484C4×C13—26no—
485C4×C13—22no—
486C4×C13C23×D4112yes—
487Dic13—26no—
488Dic13—22no—
489Dic13—22no—
490Dic13—26no—
491Dic13C23×D4112yes—
492C25—131no—
4932−1+4—26128no—
494C2×#41—1324no—
495C2×#41—138no—
496C2×#41—1324no—
497C2×#41—1324no—
498C2×#41—2624no—
499C2×#41—2624no—
500C2×#41—2624no—
501C2×#41—268no—
502C22×Q8—28no—
503C22×Q8—28no—
504C22×Q8—1316no—
505C22×Q8—138no—
506C22×Q8—1324no—
507C22×Q8—1324no—
508C22×Q8—138no—
509C22×Q8—1324no—
510C22×Q8—133no—
511C22×Q8—136no—
512C22×Q8—133no—
513C22×Q8—133no—
514C22×Q8—1324no—
515C22×Q8—2624no—
516C22×Q8—2624no—
517C22×Q8—26128no—
518C22×Q8—2624no—
519C22×Q8—2624no—
520C22×Q8—268no—
521C22×Q8C22×D1313yes—
522C22×Q8C22×D1313yes—
523C22×Q8C22×D1318yes—
524C22×Q8C22×D1311yescharacteristic
525C22×Q8C22×D1318yescomplemented
526C22×D4—131no—
527C22×D4—133no—
528C22×D4—131no—
529C22×D4—133no—
530C22×D4—133no—
531C22×D4—133no—
532C22×D4—133no—
533C22×D4C22×D1311yescharacteristic
534C23×C4—133no—
535C23×C4—133no—
536C23×C4—133no—
537C23×C4—133no—
538C23×C4—136no—
539C23×C4—133no—
540C23×C4—133no—
541C23×C4—1324no—
542C23×C4—2624no—
543C23×C4C22×D1313yes—
544C23×C4C22×D1313yes—
545C4⋊Q8—1324no—
546C4⋊Q8—1348no—
547C4⋊Q8C22×D13124yescomplemented
548#124—1324no—
549#124—1348no—
550#124—1324no—
551#123—1348no—
552#123—1324no—
553#123—1324no—
554C22⋊Q8—1324no—
555C22⋊Q8—1324no—
556C22⋊Q8—1324no—
557C22⋊Q8—1324no—
558C22⋊Q8—1348no—
559C22⋊Q8—1348no—
560C22⋊Q8—1324no—
561C22⋊Q8—1324no—
562C22⋊Q8C22×D13124yes—
563C22⋊Q8C22×D13124yescomplemented
564#121—1324no—
565#121—1324no—
566#121—1324no—
567#121—1324no—
568#120—138no—
569#120—1324no—
570C4×Q8—138no—
571C4×Q8—1324no—
572C4×Q8—1324no—
573C4×Q8C22×D1318yescomplemented
574C4×D4—1324no—
575C4×D4—1324no—
576C4×D4—1348no—
577C4×D4—1348no—
578C4×D4—1324no—
579C4×D4C22×D13124yes—
580#117—1324no—
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—133no—
588C2×C4⋊C4—133no—
589C2×C4⋊C4C22×D1313yes—
590C2×C4⋊C4C22×D1316yes—
591C2×C4⋊C4C22×D1313yes—
592C2×C22⋊C4—131no—
593C2×C22⋊C4—133no—
594C2×C22⋊C4—133no—
595C2×C22⋊C4—131no—
596C2×C22⋊C4—133no—
597C2×C22⋊C4—131no—
598C2×C22⋊C4—133no—
599C2×C22⋊C4—136no—
600C2×C22⋊C4—136no—
601C2×C22⋊C4—133no—
602C2×C22⋊C4C22×D1313yes—
603C2×C22⋊C4C22×D1313yes—
604C2×C42—136no—
605C2×C42—133no—
606C2×C42C22×D1313yes—
607C2×C13—24no—
608C2×C13—42no—
609C2×C13#348614yescomplemented
610C2×C13C24×D411yescharacteristic
611C2×C13C22×2−1+411yescharacteristic
612C2×C13C22×2−1+411yescharacteristic
613D13—24no—
614D13—24no—
615D13—46no—
616C24—131no—
617C24—131no—
618C24—134no—
619C24—133no—
620C24—264no—
621C24—264no—
622C24—264no—
623C24C23×D1311yescharacteristic
624C24C23×D1311yescharacteristic
625#41—2696no—
626#41—2696no—
627#41—2696no—
628#41—2632no—
629C2×Q8—232no—
630C2×Q8—232no—
631C2×Q8—212no—
632C2×Q8—212no—
633C2×Q8—1364no—
634C2×Q8—1324no—
635C2×Q8—1312no—
636C2×Q8—1324no—
637C2×Q8—1312no—
638C2×Q8—1312no—
639C2×Q8—2624no—
640C2×Q8—2612no—
641C2×Q8—2696no—
642C2×Q8—2696no—
643C2×Q8—2696no—
644C2×Q8—2696no—
645C2×Q8—2632no—
646C2×Q8—2612no—
647C2×Q8D4×D1318yes—
648C2×Q8C23×D13112yes—
649C2×Q8C23×D13112yes—
650C2×Q8C23×D1314yes—
651C2×D4—24no—
652C2×D4—134no—
653C2×D4—1312no—
654C2×D4—134no—
655C2×D4—1312no—
656C2×D4—1312no—
657C2×D4—1312no—
658C2×D4—1312no—
659C2×D4—2612no—
660C2×D4—2612no—
661C2×D4—2612no—
662C2×D4—264no—
663C2×D4—264no—
664C2×D4—2612no—
665C2×D4—2612no—
666C2×D4C23×D1314yes—
667C22×C4—212no—
668C22×C4—212no—
669C22×C4—133no—
670C22×C4—1324no—
671C22×C4—1312no—
672C22×C4—1312no—
673C22×C4—133no—
674C22×C4—131no—
675C22×C4—133no—
676C22×C4—131no—
677C22×C4—1312no—
678C22×C4—1312no—
679C22×C4—1324no—
680C22×C4—1312no—
681C22×C4—1312no—
682C22×C4—2612no—
683C22×C4—2696no—
684C22×C4—2624no—
685C22×C4—2612no—
686C22×C4—2612no—
687C22×C4—2612no—
688C22×C4—2612no—
689C22×C4C23×D13112yes—
690C22×C4C23×D13112yes—
691C22×C4C23×D1313yes—
692C22×C4C23×D1311yescharacteristic
693C22×C4C23×D1313yes—
694C22×C4C23×D1313yes—
695C22×C4C23×D1313yes—
696C4⋊C4—1312no—
697C4⋊C4—1312no—
698C4⋊C4—1312no—
699C4⋊C4—1312no—
700C4⋊C4—1324no—
701C4⋊C4—1312no—
702C4⋊C4—1312no—
703C4⋊C4C23×D13112yes—
704C4⋊C4C23×D13124yes—
705C4⋊C4C23×D13112yes—
706C22⋊C4—134no—
707C22⋊C4—1312no—
708C22⋊C4—1312no—
709C22⋊C4—134no—
710C22⋊C4—1312no—
711C22⋊C4—134no—
712C22⋊C4—1312no—
713C22⋊C4—1324no—
714C22⋊C4—1324no—
715C22⋊C4—1312no—
716C22⋊C4C23×D13112yes—
717C22⋊C4C23×D13112yes—
718C42—1324no—
719C42—1312no—
720C42C23×D13112yes—
721C13C2×#348611yescharacteristic, complemented, Sylow
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—134no—
728C23—134no—
729C23—132no—
730C23—132no—
731C23—136no—
732C23—268no—
733C23—268no—
734C23—2632no—
735C23—262no—
736C23—262no—
737C23—262no—
738C23—268no—
739C23—262no—
740C23—266no—
741C23—266no—
742C23—266no—
743C23#8825414yescomplemented
744C23C24×D1312yes—
745C23C24×D1312yes—
746C23C24×D1311yescharacteristic
747Q8—224no—
748Q8—224no—
749Q8—1348no—
750Q8—2648no—
751Q8—2624no—
752Q8—2624no—
753Q8C2×D4×D13116yes—
754D4—28no—
755D4—2624no—
756D4—2624no—
757D4—2624no—
758D4—268no—
759D4—268no—
760D4—2624no—
761D4—2624no—
762C2×C4—26no—
763C2×C4—26no—
764C2×C4—22no—
765C2×C4—26no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—1312no—
769C2×C4—136no—
770C2×C4—1348no—
771C2×C4—132no—
772C2×C4—136no—
773C2×C4—136no—
774C2×C4—132no—
775C2×C4—2624no—
776C2×C4—2648no—
777C2×C4—2624no—
778C2×C4—2624no—
779C2×C4—262no—
780C2×C4—266no—
781C2×C4—266no—
782C2×C4—262no—
783C2×C4—2624no—
784C2×C4—2624no—
785C2×C4C2×D4×D13112yes—
786C2×C4C24×D1316yes—
787C2×C4C24×D1312yes—
788C2×C4C24×D1316yes—
789C2×C4C24×D1316yes—
790C2×C4C24×D1316yes—
791C22—28no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—134no—
799C22—134no—
800C22—2632no—
801C22—268no—
802C22—268no—
803C22—262no—
804C22—262no—
805C22—262no—
806C22—262no—
807C22—266no—
808C22—266no—
809C22—266no—
810C22—5212no—
811C22C22×D4×D1312yes—
812C22C2×#8825412yes—
813C22C2×#8825414yescomplemented
814C22D13×2−1+412yes—
815C22C25×D1311yescharacteristic
816C4—26no—
817C4—26no—
818C4—26no—
819C4—22no—
820C4—1312no—
821C4—262no—
822C4—266no—
823C4—262no—
824C4—266no—
825C4C22×D4×D13112yes—
826C2—24no—
827C2—42no—
828C2—264no—
829C2—264no—
830C2—526no—
831C2#1312848614yesdirect product factor
832C2C23×D4×D1311yescharacteristic
833C2C2×D13×2−1+411yescharacteristic
834C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×D4×Q8×C13C2
socleC23×C13C25
hypercenterC2×D4×Q8D13
hypocenterC13C2×#3486
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×Q8×D13C2semidirect
3. #13128486C2direct (N × H)
4. C2×#11719432C2semidirect
5. C2×Q8×C22⋊D13C2semidirect
6. C2×#11719337C2semidirect
7. C2×#11719281C2semidirect
8. C2×#11719522C2semidirect
9. C2×#11719338C2semidirect
10. C2×#11719257C2semidirect
11. C2×#11719429C2semidirect
12. C2×#11719333C2semidirect
13. C2×#11719332C2semidirect
14. C2×#11719252C2semidirect
15. C2×#11719277C2semidirect
16. C2×D4×Q8×C13C2semidirect
18. C23×Q8×C13C22semidirect
20. C2×#88254C22semidirect
22. C22×#6131C22semidirect
28. C22×Q8×D13C22semidirect
29. C22×Q8×D13C22semidirect
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
44. C2×#88200C22semidirect
45. C2×Q8×Dic13C22semidirect
46. C2×#88198C22semidirect
52. C2×#88178C22semidirect
53. #11719432C22semidirect
54. #11719429C22semidirect
55. #11719338C22semidirect
56. #11719337C22semidirect
57. #11719333C22semidirect
58. #11719332C22semidirect
59. #11719281C22semidirect
60. #11719277C22semidirect
61. #11719257C22semidirect
62. #11719252C22semidirect
63. C2×#88151C22semidirect
65. C2×#88150C22semidirect
66. C2×#88150C22semidirect
72. C2×#88142C22semidirect
73. C2×#88141C22semidirect
74. C2×#88139C22semidirect
80. C2×#88129C22semidirect
83. C2×C4×Dic26C22semidirect
91. C22×Q8×C13C23semidirect
104. C2×#6131C23semidirect
110. C2×Q8×D13D4semidirect
115. C2×Q8×D13C23semidirect
119. C2×#6127C23semidirect
137. C13×C4⋊Q8C23semidirect
139. C13×C22⋊Q8C23semidirect
140. C4×Q8×C13C23semidirect
150. #88201C23semidirect
152. #88200C23semidirect
153. Q8×Dic13C23semidirect
154. #88198C23semidirect
170. #88178C23semidirect
178. #88151C23semidirect
180. #88150C23semidirect
181. #88150C23semidirect
187. #88142C23semidirect
188. #88141C23semidirect
189. #88139C23semidirect
195. #88129C23semidirect
198. C4×Dic26C23semidirect
249. Q8×D13C2×D4semidirect
311. C2×D4×Q8D13semidirect
326. C23×C132−1+4semidirect
342. C22×D132−1+4semidirect
405. C23×Q8C2×D13semidirect
410. D4×Q8C2×D13semidirect
419. C2×C4⋊Q8C2×D13semidirect
437. C2×C22⋊Q8C2×D13semidirect
448. C2×C4×Q8C2×D13semidirect
467. C22×C13C2×2−1+4semidirect
481. C2×D13C2×2−1+4semidirect
525. C22×Q8C22×D13semidirect
547. C4⋊Q8C22×D13semidirect
563. C22⋊Q8C22×D13semidirect
573. C4×Q8C22×D13semidirect
609. C2×C13#3486semidirect
721. C13C2×#3486semidirect
743. C23#88254semidirect
813. C22C2×#88254semidirect
831. C2#13128486direct (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×Q8×D132
#131284862
C2×#117194322
C2×Q8×C22⋊D132
C2×#117193372
C2×#117192812
C2×#117195222
C2×#117193382
C2×#117192572
C2×#117194292
C2×#117193332
C2×#117193322
C2×#117192522
C2×#117192772
C2×D4×Q8×C132
C2×#348613