Finite Group Databasebeta

← C2×#13128604 #16771093

Subgroups — C2×#13128604 #16771093

Order 3328.

11210 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
2C22×#88257C211yesmaximal, characteristic, complemented
3#13128604C2132yesmaximal, direct product factor
4C2×#11719539C211yesmaximal, characteristic, complemented
5C2×#11719304C213yesmaximal, complemented
6C2×Q8×C22⋊D13C211yesmaximal, characteristic, complemented
7C2×#11719337C213yesmaximal, complemented
8C2×#11719281C211yesmaximal, characteristic, complemented
9C2×#11719257C213yesmaximal, complemented
10C2×#11719382C213yesmaximal, complemented
11C2×#11719334C213yesmaximal, complemented
12C2×#11719313C213yesmaximal, complemented
13C2×#11719373C213yesmaximal, complemented
14C2×#11719253C213yesmaximal, complemented
15C2×C4×Q8×D13C211yesmaximal, characteristic, complemented
16C2×C13×#548C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C2×#88257—216no—
20C2×#88257C22116yescomplemented
21C2×#88254—216no—
22C2×#88254C22116yescomplemented
23C22×#6131C2211yescharacteristic
24C22×#6131C2213yes—
25C22×Q8×D13C2213yes—
26C22×Q8×D13C2211yescharacteristic
27C22×Q8×D13C2211yescharacteristic
28C22×#6129C2213yes—
29C22×#6129C2213yes—
30C22×#6127C2213yes—
31C22×#6127C2213yes—
32C22×#6127C2213yes—
33C23×Dic26C2213yes—
34C13×#548C22116yescomplemented
35C2×C13×#124C2213yes—
36C2×C13×C22⋊Q8C2213yes—
37C2×C13×#121C2213yes—
38C2×C4×Q8×C13C2211yescharacteristic
39C2×C4×D4×C13C2213yes—
40#11719539C22116yescomplemented
41Q8×C22⋊D13C22116yescomplemented
42C2×#88200C2213yes—
43C2×Q8×Dic13C2211yescharacteristic
44C2×#88198C2213yes—
45C2×#88194C2213yes—
46C2×#88194C2213yes—
47C2×#88193C2216yes—
48C2×#88192C2213yes—
49C2×#88192C2213yes—
50C2×#88184C2213yes—
51C2×C4×C22⋊D13C2213yes—
52C2×C4×C22⋊D13C2213yes—
53C2×#88178C2213yes—
54#11719382C22148yescomplemented
55#11719373C22148yescomplemented
56#11719337C22148yescomplemented
57#11719334C22148yescomplemented
58#11719313C22148yescomplemented
59#11719304C22148yescomplemented
60#11719281C22116yescomplemented
61C4×Q8×D13C22116yescomplemented
62#11719257C22148yescomplemented
63#11719253C22148yescomplemented
64C2×#88151C2213yes—
65C2×#88150C2216yes—
66C2×#88149C2213yes—
67C2×#88149C2213yes—
68C2×C4⋊C4×D13C2213yes—
69C2×#88142C2213yes—
70C2×#88141C2213yes—
71C2×#88139C2213yes—
72C2×#88139C2213yes—
73C2×#88138C2216yes—
74C2×#88138C2211yescharacteristic
75C2×#88138C2213yes—
76C2×#88138C2216yes—
77C2×#88135C2216yes—
78C2×#88135C2216yes—
79C2×#88132C2216yes—
80C2×#88129C2213yes—
81C2×C4×D52C2213yes—
82C2×C42×D13C2213yes—
83C2×C4×Dic26C2213yes—
84C2×C13×#41—28no—
85C2×C13×#41C2318yes—
86C22×Q8×C13—28no—
87C22×Q8×C13C2313yes—
88C22×Q8×C13C2318yes—
89C22×Q8×C13C2311yescharacteristic
90C22×D4×C13C2313yes—
91C22×D4×C13C2313yes—
92C23×C4×C13C2313yes—
93C23×C4×C13C2313yes—
94C22×C22⋊D13C2313yes—
95C22×C22⋊D13C2313yes—
96C22×C22⋊D13C2313yes—
97C22×C22⋊D13C2311yescharacteristic
98C22×C22⋊D13C2311yescharacteristic
99C22×C22⋊D13C2313yes—
100C22×C22⋊D13C2316yes—
101C23×Dic13C2316yes—
102#88257—2128no—
103#88254—2128no—
104C2×#6131—28no—
105C2×#6131—224no—
106C2×#6131C2318yes—
107C2×#6131C23124yes—
108C2×Q8×D13—28no—
109C2×Q8×D13—224no—
110C2×Q8×D13D4116yescomplemented
111C2×Q8×D13C2318yes—
112C2×Q8×D13C23124yes—
113C2×Q8×D13C2318yes—
114C2×#6129—224no—
115C2×#6129—224no—
116C2×#6129C23124yes—
117C2×#6129C23124yes—
118C2×#6127—224no—
119C2×#6127—224no—
120C2×#6127—224no—
121C2×#6127C23124yes—
122C2×#6127C23124yes—
123C2×#6127C23124yes—
124C22×D52C2313yes—
125C22×D52C2313yes—
126C22×D52C2311yescharacteristic
127C22×D52C2313yes—
128C22×C4×D13C2311yescharacteristic
129C22×C4×D13C2313yes—
130C22×C4×D13C2313yes—
131C22×C4×D13C2316yes—
132C22×C4×D13C2313yes—
133C22×C4×D13C2313yes—
134C22×Dic26—224no—
135C22×Dic26C2313yes—
136C22×Dic26C2313yes—
137C22×Dic26C2313yes—
138C22×Dic26C23124yes—
139C22×Dic26C2313yes—
140C13×#124C23124yes—
141C13×C22⋊Q8C23124yes—
142C13×#121C23124yes—
143C4×Q8×C13C2318yes—
144C4×D4×C13C23124yes—
145C2×C13×C4⋊C4C2313yes—
146C2×C13×C4⋊C4C2313yes—
147C2×C13×C22⋊C4C2316yes—
148C2×C13×C22⋊C4C2313yes—
149C2×C13×C22⋊C4C2311yescharacteristic
150C2×C42×C13C2313yes—
151C2×C22⋊Dic13C2313yes—
152C2×C22⋊Dic13C2313yes—
153#88200C23124yes—
154Q8×Dic13C2318yes—
155#88198C23124yes—
156#88194C23124yes—
157#88194C23124yes—
158#88193C23148yes—
159#88192C23124yes—
160#88192C23124yes—
161#88184C23124yes—
162C4×C22⋊D13C23124yes—
163C4×C22⋊D13C23124yes—
164C2×#6103C2311yescharacteristic
165C2×#6103C2313yes—
166C2×#6103C2316yes—
167C2×#6103C2313yes—
168C2×#6103C2313yes—
169C2×C4⋊Dic13C2313yes—
170C2×C4⋊Dic13C2313yes—
171#88178C23124yes—
172C2×#6101C2316yes—
173C2×#6101C2316yes—
174C2×#6101C2313yes—
175C2×#6101C2311yescharacteristic
176C2×C4×Dic13C2313yes—
177C2×C4×Dic13C2313yes—
178C2×C4×Dic13C2313yes—
179#88151C23124yes—
180#88150C23148yes—
181#88149C23124yes—
182#88149C23124yes—
183C4⋊C4×D13C23124yes—
184#88142C23124yes—
185#88141C23124yes—
186#88139C23124yes—
187#88139C23124yes—
188#88138C2318yes—
189#88138C23124yes—
190#88138C23148yes—
191#88138C23148yes—
192#88135C23148yes—
193#88135C23148yes—
194#88132C23148yes—
195#88129C23124yes—
196C4×D52C23124yes—
197C42×D13C23124yes—
198C4×Dic26C23124yes—
199C2×#3497—131nomaximal, Sylow
200C24×C13C2411yescharacteristic
201C24×C13C2413yes—
202C23×D13C2413yes—
203C23×D13C2411yescharacteristic
204C23×D13C2411yescharacteristic
205C13×#41—232no—
206C2×Q8×C13—232no—
207C2×Q8×C13—212no—
208C2×Q8×C13C2×D418yes—
209C2×Q8×C13C24112yes—
210C2×Q8×C13C2414yes—
211C2×D4×C13—212no—
212C2×D4×C13—46no—
213C2×D4×C13C24112yes—
214C2×D4×C13C24112yes—
215C22×C4×C13—212no—
216C22×C4×C13—212no—
217C22×C4×C13C2411yescharacteristic
218C22×C4×C13C2413yes—
219C22×C4×C13C2413yes—
220C22×C4×C13C2411yescharacteristic
221C22×C4×C13C24112yes—
222C22×C4×C13C24112yes—
223C22×C4×C13C2413yes—
224C2×C22⋊D13—24no—
225C2×C22⋊D13—212no—
226C2×C22⋊D13—212no—
227C2×C22⋊D13—212no—
228C2×C22⋊D13—212no—
229C2×C22⋊D13—24no—
230C2×C22⋊D13—412no—
231C2×C22⋊D13C24112yes—
232C2×C22⋊D13C24112yes—
233C2×C22⋊D13C24112yes—
234C2×C22⋊D13C2414yes—
235C2×C22⋊D13C2414yes—
236C2×C22⋊D13C24112yes—
237C2×C22⋊D13C24124yes—
238C22×Dic13—224no—
239C22×Dic13C24124yes—
240C22×Dic13C2413yes—
241C22×Dic13C2413yes—
242C22×Dic13C2411yescharacteristic
243C22×Dic13C2413yes—
244C22×Dic13C2411yescharacteristic
245#6131—232no—
246#6131—296no—
247Q8×D13—232no—
248Q8×D13—296no—
249Q8×D13C2×D4164yescomplemented
250#6129—296no—
251#6129—296no—
252#6127—296no—
253#6127—296no—
254#6127—296no—
255C2×D52—24no—
256C2×D52—212no—
257C2×D52—212no—
258C2×D52—46no—
259C2×D52C24112yes—
260C2×D52C24112yes—
261C2×D52C2414yes—
262C2×D52C24112yes—
263C2×C4×D13—212no—
264C2×C4×D13—212no—
265C2×C4×D13—224no—
266C2×C4×D13—24no—
267C2×C4×D13—46no—
268C2×C4×D13C2×D4124yes—
269C2×C4×D13C2414yes—
270C2×C4×D13C24112yes—
271C2×C4×D13C24112yes—
272C2×C4×D13C24124yes—
273C2×C4×D13C24112yes—
274C2×C4×D13C24112yes—
275C2×Dic26—212no—
276C2×Dic26—212no—
277C2×Dic26—212no—
278C2×Dic26—296no—
279C2×Dic26C2×D4124yes—
280C2×Dic26C24112yes—
281C2×Dic26C24112yes—
282C2×Dic26C24112yes—
283C2×Dic26C24112yes—
284C13×C4⋊C4C24112yes—
285C13×C4⋊C4C24112yes—
286C13×C22⋊C4C24124yes—
287C13×C22⋊C4C24112yes—
288C13×C22⋊C4C2414yes—
289C42×C13C24112yes—
290C22⋊Dic13C24112yes—
291C22⋊Dic13C24112yes—
292#6103C2414yes—
293#6103C24112yes—
294#6103C24124yes—
295#6103C24112yes—
296#6103C24112yes—
297C4⋊Dic13C24112yes—
298C4⋊Dic13C24112yes—
299#6101C24124yes—
300#6101C24124yes—
301#6101C24112yes—
302#6101C2414yes—
303C4×Dic13C24112yes—
304C4×Dic13C24112yes—
305C4×Dic13C24112yes—
306C22×2−1+4—131no—
307C22×2−1+4—131no—
308#3497—1332no—
309C2×#550—131no—
310C2×#550—133no—
311C2×D4×Q8—131no—
312C2×D4×Q8—133no—
313C2×#548—133no—
314C2×#548—131no—
315C2×#548—133no—
316C2×#548D1311yescharacteristic, complemented
317C2×#537—133no—
318C2×#537—133no—
319C2×#532—133no—
320C2×#532—133no—
321C22×C4×Q8—131no—
322C23×C13—26no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—26no—
326C23×C13—26no—
327C23×C13—22no—
328C23×C13C2512yes—
329C23×C13C2516yes—
330C23×C13C2511yescharacteristic
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—26no—
334C22×D13—22no—
335C22×D13—26no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—26no—
339C22×D13C22×D414yes—
340C22×D13C2516yes—
341C22×D13C2512yes—
342C22×D13C2512yes—
343Q8×C13—224no—
344Q8×C13C22×D4116yes—
345D4×C13—224no—
346D4×C13—412no—
347C2×C4×C13—22no—
348C2×C4×C13—26no—
349C2×C4×C13—22no—
350C2×C4×C13—26no—
351C2×C4×C13—224no—
352C2×C4×C13—224no—
353C2×C4×C13C22×D4112yes—
354C2×C4×C13C2512yes—
355C2×C4×C13C2516yes—
356C2×C4×C13C2516yes—
357C2×C4×C13C2512yes—
358C2×C4×C13C2516yes—
359C22⋊D13—28no—
360C22⋊D13—224no—
361C22⋊D13—224no—
362C22⋊D13—224no—
363C22⋊D13—224no—
364C22⋊D13—28no—
365C22⋊D13—424no—
366C2×Dic13—22no—
367C2×Dic13—26no—
368C2×Dic13—26no—
369C2×Dic13—248no—
370C2×Dic13C22×D4112yes—
371C2×Dic132−1+414yescomplemented
372C2×Dic13C2516yes—
373C2×Dic13C2516yes—
374C2×Dic13C2512yes—
375C2×Dic13C2516yes—
376C2×Dic13C2512yes—
377D52—28no—
378D52—224no—
379D52—224no—
380D52—412no—
381C4×D13—224no—
382C4×D13—224no—
383C4×D13—248no—
384C4×D13—28no—
385C4×D13—412no—
386C4×D13C22×D4148yes—
387Dic26—224no—
388Dic26—224no—
389Dic26—224no—
390Dic26C22×D4148yes—
391C2×2−1+4—1316no—
392C2×2−1+4—1316no—
393C2×2−1+4—2616no—
394C2×2−1+4—2616no—
395C22×#41—133no—
396C22×#41—131no—
397C22×#41—133no—
398C22×#41—133no—
399C22×#41—133no—
400C22×#41—133no—
401C22×#41—133no—
402C22×#41C2×D1311yescharacteristic
403C23×Q8—131no—
404C23×Q8—133no—
405C23×Q8—131no—
406C23×Q8—133no—
407C23×Q8C2×D1311yescharacteristic
408#550—1316no—
409#550—1348no—
410D4×Q8—1316no—
411D4×Q8—1348no—
412#548—1348no—
413#548—1316no—
414#548—1348no—
415#548C2×D13116yescomplemented
416#537—1348no—
417#537—1348no—
418#532—1348no—
419#532—1348no—
420C2×C4⋊Q8—133no—
421C2×C4⋊Q8—133no—
422C2×#127—133no—
423C2×#127—133no—
424C2×#124—133no—
425C2×#124—133no—
426C2×#124—133no—
427C2×#124C2×D1313yes—
428C2×C22⋊Q8—133no—
429C2×C22⋊Q8—133no—
430C2×C22⋊Q8—136no—
431C2×C22⋊Q8—133no—
432C2×C22⋊Q8—136no—
433C2×C22⋊Q8C2×D1313yes—
434C2×#121—133no—
435C2×#121—133no—
436C2×#121—136no—
437C2×#121—133no—
438C2×#121—133no—
439C2×#121—133no—
440C2×#121—133no—
441C2×#121—131no—
442C2×#121—136no—
443C2×#121—136no—
444C2×#121C2×D1313yes—
445C2×C4×Q8—131no—
446C2×C4×Q8—1316no—
447C2×C4×Q8—133no—
448C2×C4×Q8—133no—
449C2×C4×Q8C2×D1311yescharacteristic
450C2×C4×D4—133no—
451C2×C4×D4—133no—
452C2×C4×D4—136no—
453C2×C4×D4—136no—
454C2×C4×D4—133no—
455C2×C4×D4C2×D1313yes—
456C22×C4⋊C4—133no—
457C22×C42—133no—
458C22×C13—26no—
459C22×C13—22no—
460C22×C13—22no—
461C22×C13—26no—
462C22×C13—26no—
463C22×C13—22no—
464C22×C13—412no—
465C22×C13—44no—
466C22×C13C23×D412yes—
467C22×C13C2×2−1+412yes—
468C22×C13#58512yes—
469C22×C13C2611yescharacteristic
470C2×D13—22no—
471C2×D13—22no—
472C2×D13—28no—
473C2×D13—26no—
474C2×D13—22no—
475C2×D13—26no—
476C2×D13—22no—
477C2×D13—22no—
478C2×D13—26no—
479C2×D13—412no—
480C2×D13—44no—
481C2×D13C23×D414yes—
482C4×C13—22no—
483C4×C13—26no—
484C4×C13—22no—
485C4×C13—26no—
486C4×C13C23×D4112yes—
487Dic13—22no—
488Dic13—26no—
489Dic13—26no—
490Dic13C23×D4112yes—
491Dic13C2×2−1+414yescomplemented
4922−1+4—26128no—
4932−1+4—26128no—
494C2×#41—28no—
495C2×#41—1324no—
496C2×#41—138no—
497C2×#41—1324no—
498C2×#41—1324no—
499C2×#41—1324no—
500C2×#41—1324no—
501C2×#41—1324no—
502C2×#41—2624no—
503C2×#41—2624no—
504C2×#41—2624no—
505C2×#41—2624no—
506C2×#41—2624no—
507C2×#41—2624no—
508C2×#41—268no—
509C2×#41C22×D1318yes—
510C22×Q8—28no—
511C22×Q8—1316no—
512C22×Q8—138no—
513C22×Q8—1324no—
514C22×Q8—138no—
515C22×Q8—133no—
516C22×Q8—133no—
517C22×Q8—133no—
518C22×Q8—133no—
519C22×Q8—1324no—
520C22×Q8—2624no—
521C22×Q8—2624no—
522C22×Q8—268no—
523C22×Q8C22×D1313yes—
524C22×Q8C22×D1318yes—
525C22×Q8C22×D1311yescharacteristic
526C22×D4—131no—
527C22×D4—133no—
528C22×D4—131no—
529C22×D4—133no—
530C22×D4—133no—
531C22×D4—133no—
532C22×D4—136no—
533C22×D4—131no—
534C22×D4—133no—
535C22×D4—133no—
536C22×D4—133no—
537C22×D4C22×D1313yes—
538C22×D4C22×D1313yes—
539C23×C4—133no—
540C23×C4—136no—
541C23×C4—136no—
542C23×C4—133no—
543C23×C4—133no—
544C23×C4—131no—
545C23×C4—133no—
546C23×C4C22×D1313yes—
547C23×C4C22×D1313yes—
548C4⋊Q8—1324no—
549C4⋊Q8—1324no—
550#127—1324no—
551#127—1324no—
552#124—1324no—
553#124—1324no—
554#124—1324no—
555#124C22×D13124yes—
556C22⋊Q8—1324no—
557C22⋊Q8—1324no—
558C22⋊Q8—1348no—
559C22⋊Q8—1324no—
560C22⋊Q8—1348no—
561C22⋊Q8C22×D13124yes—
562#121—1324no—
563#121—1324no—
564#121—1348no—
565#121—1324no—
566#121—1324no—
567#121—1324no—
568#121—1324no—
569#121—138no—
570#121—1348no—
571#121—1348no—
572#121C22×D13124yes—
573C4×Q8—138no—
574C4×Q8—1324no—
575C4×Q8—1324no—
576C4×Q8C22×D1318yes—
577C4×D4—1324no—
578C4×D4—1324no—
579C4×D4—1348no—
580C4×D4—1348no—
581C4×D4—1324no—
582C4×D4C22×D13124yes—
583C2×C4⋊C4—136no—
584C2×C4⋊C4—133no—
585C2×C4⋊C4—131no—
586C2×C4⋊C4—133no—
587C2×C4⋊C4—136no—
588C2×C4⋊C4—133no—
589C2×C4⋊C4—1324no—
590C2×C4⋊C4C22×D1313yes—
591C2×C4⋊C4C22×D1313yes—
592C2×C22⋊C4—133no—
593C2×C22⋊C4—133no—
594C2×C22⋊C4—133no—
595C2×C22⋊C4—131no—
596C2×C22⋊C4—133no—
597C2×C22⋊C4—133no—
598C2×C22⋊C4—136no—
599C2×C22⋊C4C22×D1313yes—
600C2×C22⋊C4C22×D1316yes—
601C2×C22⋊C4C22×D1311yescharacteristic
602C2×C42—133no—
603C2×C42—133no—
604C2×C42—133no—
605C2×C42—1324no—
606C2×C42C22×D1313yes—
607C2×C13—46no—
608C2×C13—42no—
609C2×C13#349714yescomplemented
610C2×C13C24×D411yescharacteristic
611C2×C13C22×2−1+411yescharacteristic
612C2×C13C2×#58511yescharacteristic
613D13—24no—
614D13—46no—
615D13—42no—
616C24—131no—
617C24—131no—
618C24—133no—
619C24C23×D1311yescharacteristic
620C24C23×D1313yes—
621#41—232no—
622#41—2696no—
623#41—2696no—
624#41—2696no—
625#41—2696no—
626#41—2696no—
627#41—2696no—
628#41—2632no—
629C2×Q8—232no—
630C2×Q8—212no—
631C2×Q8—1364no—
632C2×Q8—1324no—
633C2×Q8—1312no—
634C2×Q8—1312no—
635C2×Q8—1312no—
636C2×Q8—1312no—
637C2×Q8—2612no—
638C2×Q8—2612no—
639C2×Q8—2696no—
640C2×Q8—2696no—
641C2×Q8—2632no—
642C2×Q8—2612no—
643C2×Q8D4×D1318yes—
644C2×Q8C23×D13112yes—
645C2×Q8C23×D1314yes—
646C2×D4—212no—
647C2×D4—46no—
648C2×D4—134no—
649C2×D4—1312no—
650C2×D4—134no—
651C2×D4—1312no—
652C2×D4—1312no—
653C2×D4—1312no—
654C2×D4—1324no—
655C2×D4—134no—
656C2×D4—1312no—
657C2×D4—1312no—
658C2×D4—1312no—
659C2×D4—264no—
660C2×D4—2612no—
661C2×D4—2612no—
662C2×D4—2612no—
663C2×D4—264no—
664C2×D4—2612no—
665C2×D4—264no—
666C2×D4—2612no—
667C2×D4—2612no—
668C2×D4—526no—
669C2×D4—5212no—
670C2×D4C23×D13112yes—
671C2×D4C23×D13112yes—
672C22×C4—212no—
673C22×C4—212no—
674C22×C4—131no—
675C22×C4—133no—
676C22×C4—1324no—
677C22×C4—1312no—
678C22×C4—1324no—
679C22×C4—133no—
680C22×C4—131no—
681C22×C4—133no—
682C22×C4—134no—
683C22×C4—1324no—
684C22×C4—1312no—
685C22×C4—1312no—
686C22×C4—1312no—
687C22×C4—2624no—
688C22×C4—264no—
689C22×C4—2624no—
690C22×C4—2612no—
691C22×C4—2612no—
692C22×C4—526no—
693C22×C4C23×D13112yes—
694C22×C4C23×D13112yes—
695C22×C4C23×D1311yescharacteristic
696C22×C4C23×D1313yes—
697C22×C4C23×D1311yescharacteristic
698C22×C4C23×D1313yes—
699C22×C4C23×D1313yes—
700C4⋊C4—1324no—
701C4⋊C4—1312no—
702C4⋊C4—134no—
703C4⋊C4—1312no—
704C4⋊C4—1324no—
705C4⋊C4—1312no—
706C4⋊C4C23×D13112yes—
707C4⋊C4C23×D13112yes—
708C22⋊C4—1312no—
709C22⋊C4—1312no—
710C22⋊C4—1312no—
711C22⋊C4—134no—
712C22⋊C4—1312no—
713C22⋊C4—1312no—
714C22⋊C4—1324no—
715C22⋊C4C23×D13112yes—
716C22⋊C4C23×D13124yes—
717C22⋊C4C23×D1314yes—
718C42—1312no—
719C42—1312no—
720C42—1312no—
721C42C23×D13112yes—
722C13C2×#349711yescharacteristic, complemented, Sylow
723C23—22no—
724C23—26no—
725C23—22no—
726C23—26no—
727C23—22no—
728C23—26no—
729C23—134no—
730C23—132no—
731C23—132no—
732C23—136no—
733C23—262no—
734C23—262no—
735C23—266no—
736C23—262no—
737C23—262no—
738C23—266no—
739C23—262no—
740C23—266no—
741C23C24×D1312yes—
742C23C24×D1316yes—
743C23C24×D1311yescharacteristic
744Q8—224no—
745Q8—1348no—
746Q8—2624no—
747Q8—2624no—
748Q8—2624no—
749Q8C2×D4×D13116yes—
750D4—224no—
751D4—412no—
752D4—268no—
753D4—2624no—
754D4—268no—
755D4—2624no—
756D4—2624no—
757D4—2624no—
758D4—268no—
759D4—2624no—
760D4—2624no—
761D4—5212no—
762D4—5224no—
763C2×C4—22no—
764C2×C4—26no—
765C2×C4—26no—
766C2×C4—22no—
767C2×C4—224no—
768C2×C4—224no—
769C2×C4—1312no—
770C2×C4—134no—
771C2×C4—132no—
772C2×C4—136no—
773C2×C4—1348no—
774C2×C4—136no—
775C2×C4—132no—
776C2×C4—136no—
777C2×C4—268no—
778C2×C4—2648no—
779C2×C4—2648no—
780C2×C4—262no—
781C2×C4—266no—
782C2×C4—266no—
783C2×C4—2624no—
784C2×C4—2624no—
785C2×C4—5212no—
786C2×C4C2×D4×D13112yes—
787C2×C4C24×D1312yes—
788C2×C4C24×D1316yes—
789C2×C4C24×D1312yes—
790C2×C4C24×D1316yes—
791C2×C4C24×D1316yes—
792C22—22no—
793C22—26no—
794C22—22no—
795C22—26no—
796C22—22no—
797C22—26no—
798C22—44no—
799C22—412no—
800C22—134no—
801C22—268no—
802C22—262no—
803C22—262no—
804C22—266no—
805C22—262no—
806C22—262no—
807C22—266no—
808C22—262no—
809C22—266no—
810C22—5212no—
811C22—524no—
812C22C22×D4×D1312yes—
813C22#1171964812yes—
814C22D13×2−1+412yes—
815C22C25×D1311yescharacteristic
816C4—22no—
817C4—26no—
818C4—22no—
819C4—26no—
820C4—1312no—
821C4—134no—
822C4—262no—
823C4—266no—
824C4—266no—
825C4C22×D4×D13112yes—
826C2—42no—
827C2—46no—
828C2—264no—
829C2—526no—
830C2—522no—
831C2#1312860414yesdirect product factor
832C2C23×D4×D1311yescharacteristic
833C2C2×D13×2−1+411yescharacteristic
834C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#548C2
socleC23×C13C25
hypercenterC2×#548D13
hypocenterC13C2×#3497
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×#88257C2semidirect
3. #13128604C2direct (N × H)
4. C2×#11719539C2semidirect
5. C2×#11719304C2semidirect
6. C2×Q8×C22⋊D13C2semidirect
7. C2×#11719337C2semidirect
8. C2×#11719281C2semidirect
9. C2×#11719257C2semidirect
10. C2×#11719382C2semidirect
11. C2×#11719334C2semidirect
12. C2×#11719313C2semidirect
13. C2×#11719373C2semidirect
14. C2×#11719253C2semidirect
15. C2×C4×Q8×D13C2semidirect
16. C2×C13×#548C2semidirect
20. C2×#88257C22semidirect
22. C2×#88254C22semidirect
34. C13×#548C22semidirect
40. #11719539C22semidirect
41. Q8×C22⋊D13C22semidirect
54. #11719382C22semidirect
55. #11719373C22semidirect
56. #11719337C22semidirect
57. #11719334C22semidirect
58. #11719313C22semidirect
59. #11719304C22semidirect
60. #11719281C22semidirect
61. C4×Q8×D13C22semidirect
62. #11719257C22semidirect
63. #11719253C22semidirect
110. C2×Q8×D13D4semidirect
249. Q8×D13C2×D4semidirect
316. C2×#548D13semidirect
371. C2×Dic132−1+4semidirect
415. #548C2×D13semidirect
491. Dic13C2×2−1+4semidirect
609. C2×C13#3497semidirect
722. C13C2×#3497semidirect
831. C2#13128604direct (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×#882572
#131286042
C2×#117195392
C2×#117193042
C2×Q8×C22⋊D132
C2×#117193372
C2×#117192812
C2×#117192572
C2×#117193822
C2×#117193342
C2×#117193132
C2×#117193732
C2×#117192532
C2×C4×Q8×D132
C2×C13×#5482
C2×#349713