Finite Group Databasebeta

← C2×#13129245 #16770727

Subgroups — C2×#13129245 #16770727

Order 3328.

7074 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129245C2132yesmaximal, direct product factor
2C2×#11719356C212yesmaximal, complemented
3C2×#11719440C212yesmaximal, complemented
4C2×#11719369C212yesmaximal, complemented
5C2×#11719427C212yesmaximal, complemented
6C2×#11719346C212yesmaximal, complemented
7C2×#11719238C212yesmaximal, complemented
8C2×Q8×C22⋊D13C212yesmaximal, complemented
9C2×#11719337C212yesmaximal, complemented
10C2×#11719367C214yesmaximal, complemented
11C2×#11719374C214yesmaximal, complemented
12C2×#11719333C212yesmaximal, complemented
13C2×#11719530C211yesmaximal, characteristic, complemented
14C2×#11719327C212yesmaximal, complemented
15C2×#11719537C211yesmaximal, characteristic
16C2×C13×#536C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C23×Q8×C13C2211yescharacteristic
19C22×Q8×D13C2212yes—
20C22×#6127C2211yescharacteristic
21C23×Dic26C2211yescharacteristic
22C13×#536C22116yescomplemented
23C2×C13×C4⋊Q8C2212yes—
24C2×C13×#124C2212yes—
25C2×C13×#123C2212yes—
26C2×C13×#123C2212yes—
27C2×C13×C22⋊Q8C2212yes—
28C2×C13×C22⋊Q8C2212yes—
29C2×C13×#117C2211yescharacteristic
30#11719537C22116yes—
31#11719530C22116yescomplemented
32Q8×C22⋊D13C22132yescomplemented
33C2×#88201C2211yescharacteristic
34C2×#88200C2214yes—
35C2×#88200C2212yes—
36C2×Q8×Dic13C2212yes—
37C2×#88198C2212yes—
38C2×#88198C2214yes—
39C2×#88198C2212yes—
40C2×#88198C2211yescharacteristic
41C2×#88194C2211yescharacteristic
42C2×#88193C2212yes—
43C2×#88193C2212yes—
44C2×#88190C2211yescharacteristic
45C2×#88190C2212yes—
46C2×#88189C2212yes—
47C2×#88189C2212yes—
48C2×C4×C22⋊D13C2214yes—
49C2×C4×C22⋊D13C2212yes—
50C2×C4×C22⋊D13C2212yes—
51C2×#88180C2211yescharacteristic
52C2×#88178C2214yes—
53C2×#88178C2212yes—
54C2×#88178C2212yes—
55C22×C4×Dic13C2211yescharacteristic
56#11719440C22132yescomplemented
57#11719427C22132yescomplemented
58#11719374C22164yescomplemented
59#11719369C22132yescomplemented
60#11719367C22164yescomplemented
61#11719356C22132yescomplemented
62#11719346C22132yescomplemented
63#11719337C22132yescomplemented
64#11719333C22132yescomplemented
65#11719327C22132yescomplemented
66#11719238C22132yescomplemented
67C2×#88152C2214yes—
68C2×#88151C2212yes—
69C2×#88150C2214yes—
70C2×#88148C2214yes—
71C2×#88146C2212yes—
72C2×#88143C2214yes—
73C2×#88142C2214yes—
74C2×#88142C2214yes—
75C2×#88142C2212yes—
76C2×#88141C2214yes—
77C2×#88141C2212yes—
78C2×#88141C2214yes—
79C2×#88139C2214yes—
80C2×#88139C2214yes—
81C2×#88139C2214yes—
82C2×#88137C2214yes—
83C2×#88135C2214yes—
84C2×#88133C2214yes—
85C2×#88133C2214yes—
86C2×#88132C2214yes—
87C2×#88132C2214yes—
88C2×#88131C2214yes—
89C2×#88130C2214yes—
90C2×C4×Dic26C2214yes—
91C2×C13×#41—44no—
92C2×C13×#41C2318yes—
93C22×Q8×C13—44no—
94C22×Q8×C13C2312yes—
95C22×Q8×C13C2311yescharacteristic
96C22×Q8×C13C2312yes—
97C22×Q8×C13C2318yes—
98C22×D4×C13C2311yescharacteristic
99C22×D4×C13C2311yescharacteristic
100C22×D4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C23×C4×C13C2312yes—
105C22×C22⋊D13C2312yes—
106C22×C22⋊D13C2312yes—
107C22×C22⋊D13C2312yes—
108C23×Dic13C2312yes—
109C23×Dic13C2312yes—
110C2×Q8×D13—48no—
111C2×Q8×D13C23116yes—
112C2×#6127—44no—
113C2×#6127C2318yes—
114C22×D52C2311yescharacteristic
115C22×C4×D13C2312yes—
116C22×C4×D13C2314yes—
117C22×Dic26—44no—
118C22×Dic26C2314yes—
119C22×Dic26C2312yes—
120C22×Dic26C2314yes—
121C22×Dic26C2311yescharacteristic
122C22×Dic26C2312yes—
123C22×Dic26C2318yes—
124C13×C4⋊Q8C23116yes—
125C13×#124C23116yes—
126C13×#123C23116yes—
127C13×#123C23116yes—
128C13×C22⋊Q8C23116yes—
129C13×C22⋊Q8C23116yes—
130C13×#117C2318yes—
131C2×C13×C4⋊C4C2314yes—
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2314yes—
134C2×C13×C22⋊C4C2314yes—
135C2×C13×C22⋊C4C2314yes—
136C2×C13×C22⋊C4C2312yes—
137C2×C42×C13C2312yes—
138C2×C22⋊Dic13C2314yes—
139C2×C22⋊Dic13C2312yes—
140C2×C22⋊Dic13C2312yes—
141C2×C22⋊Dic13C2312yes—
142C2×C22⋊Dic13C2314yes—
143#88201C2318yes—
144#88200C23132yes—
145#88200C23116yes—
146Q8×Dic13C23116yes—
147#88198C2318yes—
148#88198C23116yes—
149#88198C23132yes—
150#88198C23116yes—
151#88194C2318yes—
152#88193C23116yes—
153#88193C23116yes—
154#88190C23116yes—
155#88190C2318yes—
156#88189C23116yes—
157#88189C23116yes—
158C4×C22⋊D13C23116yes—
159C4×C22⋊D13C23132yes—
160C4×C22⋊D13C23116yes—
161C2×#6103C2312yes—
162C2×#6103C2314yes—
163C2×#6103C2314yes—
164C2×#6103C2314yes—
165C2×#6103C2312yes—
166#88180C2318yes—
167C2×C4⋊Dic13C2314yes—
168C2×C4⋊Dic13C2314yes—
169C2×C4⋊Dic13C2312yes—
170#88178C23116yes—
171#88178C23132yes—
172#88178C23116yes—
173C2×#6101C2312yes—
174C2×#6101C2314yes—
175C2×#6101C2314yes—
176C2×#6101C2314yes—
177C2×#6101C2314yes—
178C2×#6101C2314yes—
179C2×#6101C2314yes—
180C2×#6101C2312yes—
181C2×#6101C2314yes—
182C2×C4×Dic13C2314yes—
183C2×C4×Dic13C2314yes—
184C2×C4×Dic13C2314yes—
185C2×C4×Dic13C2311yescharacteristic
186C2×C4×Dic13C2312yes—
187C2×C4×Dic13C2312yes—
188C2×C4×Dic13C2311yescharacteristic
189C2×C4×Dic13C2318yes—
190#88152C23132yes—
191#88151C23116yes—
192#88150C23132yes—
193#88148C23132yes—
194#88146C23116yes—
195#88143C23132yes—
196#88142C23132yes—
197#88142C23132yes—
198#88142C23116yes—
199#88141C23132yes—
200#88141C23132yes—
201#88141C23116yes—
202#88139C23132yes—
203#88139C23132yes—
204#88139C23132yes—
205#88137C23132yes—
206#88135C23132yes—
207#88133C23132yes—
208#88133C23132yes—
209#88132C23132yes—
210#88132C23132yes—
211#88131C23132yes—
212#88130C23132yes—
213C4×Dic26C23132yes—
214C2×#3550—131nomaximal, Sylow
215C24×C13C2411yescharacteristic
216C24×C13C2411yescharacteristic
217C24×C13C2411yescharacteristic
218C23×D13C2412yes—
219C13×#41—416no—
220C2×Q8×C13—28no—
221C2×Q8×C13—44no—
222C2×Q8×C13—42no—
223C2×Q8×C13—416no—
224C2×Q8×C13C2418yes—
225C2×Q8×C13C2414yes—
226C2×Q8×C13C2418yes—
227C2×D4×C13—42no—
228C2×D4×C13—42no—
229C2×D4×C13—42no—
230C2×D4×C13C2414yes—
231C2×D4×C13C2414yes—
232C2×D4×C13C2414yes—
233C22×C4×C13—24no—
234C22×C4×C13—24no—
235C22×C4×C13—24no—
236C22×C4×C13—44no—
237C22×C4×C13C2411yescharacteristic
238C22×C4×C13C2414yes—
239C22×C4×C13C2411yescharacteristic
240C22×C4×C13C2414yes—
241C22×C4×C13C2414yes—
242C22×C4×C13C2411yescharacteristic
243C22×C4×C13C2414yes—
244C22×C4×C13C2414yes—
245C22×C4×C13C2418yes—
246C22×C4×C13C2411yescharacteristic
247C2×C22⋊D13—28no—
248C2×C22⋊D13—28no—
249C2×C22⋊D13—44no—
250C2×C22⋊D13C2418yes—
251C2×C22⋊D13C2418yes—
252C2×C22⋊D13C2418yes—
253C22×Dic13—28no—
254C22×Dic13—44no—
255C22×Dic13C2418yes—
256C22×Dic13C2414yes—
257C22×Dic13C2412yes—
258C22×Dic13C2412yes—
259C22×Dic13C2414yes—
260C22×Dic13C2418yes—
261C22×Dic13C2412yes—
262Q8×D13—432no—
263#6127—416no—
264C2×D52—42no—
265C2×D52C2414yes—
266C2×C4×D13—28no—
267C2×C4×D13—48no—
268C2×C4×D13C2418yes—
269C2×C4×D13C24116yes—
270C2×Dic26—28no—
271C2×Dic26—216no—
272C2×Dic26—416no—
273C2×Dic26—44no—
274C2×Dic26—42no—
275C2×Dic26—48no—
276C2×Dic26C24116yes—
277C2×Dic26C2418yes—
278C2×Dic26C24116yes—
279C2×Dic26C2414yes—
280C2×Dic26C2418yes—
281C13×C4⋊C4C24116yes—
282C13×C4⋊C4C2418yes—
283C13×C4⋊C4C24116yes—
284C13×C22⋊C4C24116yes—
285C13×C22⋊C4C24116yes—
286C13×C22⋊C4C2418yes—
287C42×C13C2418yes—
288C22⋊Dic13C24116yes—
289C22⋊Dic13C2418yes—
290C22⋊Dic13C2418yes—
291C22⋊Dic13C2418yes—
292C22⋊Dic13C24116yes—
293#6103C2418yes—
294#6103C24116yes—
295#6103C24116yes—
296#6103C24116yes—
297#6103C2418yes—
298C4⋊Dic13C24116yes—
299C4⋊Dic13C24116yes—
300C4⋊Dic13C2418yes—
301#6101C2418yes—
302#6101C24116yes—
303#6101C24116yes—
304#6101C24116yes—
305#6101C24116yes—
306#6101C24116yes—
307#6101C24116yes—
308#6101C2418yes—
309#6101C24116yes—
310C4×Dic13C24116yes—
311C4×Dic13C24116yes—
312C4×Dic13C24116yes—
313C4×Dic13C2414yes—
314C4×Dic13C2418yes—
315C4×Dic13C2418yes—
316C4×Dic13C2414yes—
317#3550—1332no—
318C2×#563—132no—
319C2×#563—132no—
320C2×#559—132no—
321C2×Q82—132no—
322C2×#556—132no—
323C2×#556—132no—
324C2×D4×Q8—132no—
325C2×D4×Q8—132no—
326C2×#542—134no—
327C2×#542—134no—
328C2×#536—131no—
329C2×#536—132no—
330C2×#536D1311yescharacteristic, complemented
331C2×#533—132no—
332C2×#532—131no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—24no—
337C23×C13—24no—
338C23×C13—24no—
339C23×C13C2512yes—
340C23×C13C2512yes—
341C23×C13C2512yes—
342C23×C13C2511yescharacteristic
343C22×D13—24no—
344C22×D13—24no—
345C22×D13—24no—
346C22×D13C2514yes—
347Q8×C13—216no—
348Q8×C13—48no—
349Q8×C13—44no—
350D4×C13—44no—
351D4×C13—44no—
352D4×C13—44no—
353C2×C4×C13—22no—
354C2×C4×C13—28no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—28no—
358C2×C4×C13—28no—
359C2×C4×C13—28no—
360C2×C4×C13—28no—
361C2×C4×C13—48no—
362C2×C4×C13H(5,𝔽2)14yes—
363C2×C4×C13C2512yes—
364C2×C4×C13C2518yes—
365C2×C4×C13C2512yes—
366C2×C4×C13C2518yes—
367C2×C4×C13C2512yes—
368C2×C4×C13C2512yes—
369C22⋊D13—216no—
370C22⋊D13—216no—
371C22⋊D13—48no—
372C2×Dic13—28no—
373C2×Dic13—24no—
374C2×Dic13—28no—
375C2×Dic13—24no—
376C2×Dic13—216no—
377C2×Dic13—48no—
378C2×Dic132−1+418yes—
379C2×Dic13C2518yes—
380C2×Dic13C2514yes—
381C2×Dic13C2514yes—
382C2×Dic13C2518yes—
383C2×Dic13C2514yes—
384D52—44no—
385C4×D13—216no—
386C4×D13—416no—
387Dic26—216no—
388Dic26—232no—
389Dic26—48no—
390Dic26—44no—
391Dic26—416no—
392C22×#41—131no—
393C22×#41C2×D1311yescharacteristic
394C23×Q8—132no—
395C23×Q8—131no—
396C23×Q8C2×D1311yescharacteristic
397#563—1332no—
398#563—1332no—
399#559—1332no—
400Q82—1332no—
401#556—1332no—
402#556—1332no—
403D4×Q8—1332no—
404D4×Q8—1332no—
405#542—1364no—
406#542—1364no—
407#536—1316no—
408#536—1332no—
409#536C2×D13116yescomplemented
410#533—1332no—
411#532—1316no—
412C2×C4⋊Q8—131no—
413C2×C4⋊Q8—132no—
414C2×C4⋊Q8—132no—
415C2×C4⋊Q8—134no—
416C2×C4⋊Q8—132no—
417C2×C4⋊Q8—134no—
418C2×C4⋊Q8—134no—
419C2×C4⋊Q8C2×D1312yes—
420C2×#127—131no—
421C2×#126—134no—
422C2×#126—134no—
423C2×#126—134no—
424C2×#126—134no—
425C2×#125—134no—
426C2×#124—131no—
427C2×#124—131no—
428C2×#124—132no—
429C2×#124—134no—
430C2×#124—134no—
431C2×#124—134no—
432C2×#124C2×D1312yes—
433C2×#123—132no—
434C2×#123—132no—
435C2×#123—134no—
436C2×#123—134no—
437C2×#123C2×D1312yes—
438C2×#123C2×D1312yes—
439C2×C22⋊Q8—132no—
440C2×C22⋊Q8—134no—
441C2×C22⋊Q8—132no—
442C2×C22⋊Q8—132no—
443C2×C22⋊Q8—134no—
444C2×C22⋊Q8—134no—
445C2×C22⋊Q8—132no—
446C2×C22⋊Q8—134no—
447C2×C22⋊Q8—134no—
448C2×C22⋊Q8C2×D1312yes—
449C2×C22⋊Q8C2×D1312yes—
450C2×#121—132no—
451C2×#121—132no—
452C2×C4×Q8—132no—
453C2×C4×Q8—132no—
454C2×C4×Q8—134no—
455C2×C4×Q8—134no—
456C2×C4×Q8—134no—
457C2×C4×D4—132no—
458C2×C4×D4—132no—
459C2×C4×D4—134no—
460C2×C4×D4—134no—
461C2×#117—131no—
462C2×#117—132no—
463C2×#117—134no—
464C2×#117C2×D1311yescharacteristic
465C22×C42—131no—
466C22×C13—22no—
467C22×C13—22no—
468C22×C13—22no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—24no—
472C22×C13—44no—
473C22×C13—44no—
474C22×C13—44no—
475C22×C13C2×H(5,𝔽2)12yes—
476C22×C13C2×2−1+414yes—
477C22×C13C2611yescharacteristic
478C2×D13—24no—
479C2×D13—24no—
480C2×D13—24no—
481C2×D13—48no—
482C4×C13—22no—
483C4×C13—28no—
484C4×C13—22no—
485C4×C13—22no—
486C4×C13—28no—
487C4×C13C2×H(5,𝔽2)14yes—
488Dic13—28no—
489Dic13—24no—
490Dic13—28no—
491Dic13—24no—
492Dic13C2×2−1+418yes—
493C2×#41—44no—
494C2×#41—138no—
495C2×#41—524no—
496C2×#41C22×D1318yes—
497C22×Q8—44no—
498C22×Q8—1316no—
499C22×Q8—134no—
500C22×Q8—132no—
501C22×Q8—134no—
502C22×Q8—132no—
503C22×Q8—131no—
504C22×Q8—138no—
505C22×Q8—524no—
506C22×Q8—528no—
507C22×Q8C22×D1312yes—
508C22×Q8C22×D1312yes—
509C22×Q8C22×D1311yescharacteristic
510C22×Q8C22×D1318yes—
511C22×D4—132no—
512C22×D4—132no—
513C22×D4—132no—
514C22×D4—131no—
515C22×D4C22×D1311yescharacteristic
516C22×D4C22×D1311yescharacteristic
517C22×D4C22×D1311yescharacteristic
518C23×C4—132no—
519C23×C4—132no—
520C23×C4—132no—
521C23×C4—134no—
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1312yes—
526C4⋊Q8—138no—
527C4⋊Q8—1316no—
528C4⋊Q8—1316no—
529C4⋊Q8—1332no—
530C4⋊Q8—1316no—
531C4⋊Q8—1332no—
532C4⋊Q8—1332no—
533C4⋊Q8C22×D13116yes—
534#127—138no—
535#126—1332no—
536#126—1332no—
537#126—1332no—
538#126—1332no—
539#125—1332no—
540#124—138no—
541#124—138no—
542#124—1316no—
543#124—1332no—
544#124—1332no—
545#124—1332no—
546#124C22×D13116yes—
547#123—1316no—
548#123—1316no—
549#123—1332no—
550#123—1332no—
551#123C22×D13116yes—
552#123C22×D13116yes—
553C22⋊Q8—1316no—
554C22⋊Q8—1332no—
555C22⋊Q8—1316no—
556C22⋊Q8—1316no—
557C22⋊Q8—1332no—
558C22⋊Q8—1316no—
559C22⋊Q8—1332no—
560C22⋊Q8—1332no—
561C22⋊Q8—1332no—
562C22⋊Q8C22×D13116yes—
563C22⋊Q8C22×D13116yes—
564#121—1316no—
565#121—1316no—
566C4×Q8—1316no—
567C4×Q8—1316no—
568C4×Q8—1332no—
569C4×Q8—1332no—
570C4×Q8—1332no—
571C4×D4—1316no—
572C4×D4—1316no—
573C4×D4—1332no—
574C4×D4—1332no—
575#117—138no—
576#117—1316no—
577#117—1332no—
578#117C22×D1318yes—
579C2×C4⋊C4—132no—
580C2×C4⋊C4—134no—
581C2×C4⋊C4—134no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—132no—
584C2×C4⋊C4—132no—
585C2×C4⋊C4—134no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—134no—
591C2×C4⋊C4C22×D1312yes—
592C2×C4⋊C4C22×D1314yes—
593C2×C4⋊C4C22×D1314yes—
594C2×C22⋊C4—134no—
595C2×C22⋊C4—132no—
596C2×C22⋊C4—132no—
597C2×C22⋊C4—132no—
598C2×C22⋊C4—134no—
599C2×C22⋊C4—134no—
600C2×C22⋊C4—132no—
601C2×C22⋊C4—132no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4C22×D1314yes—
605C2×C22⋊C4C22×D1312yes—
606C2×C22⋊C4C22×D1314yes—
607C2×C42—134no—
608C2×C42—134no—
609C2×C42—132no—
610C2×C42—134no—
611C2×C42—132no—
612C2×C42—131no—
613C2×C42—131no—
614C2×C42—138no—
615C2×C42C22×D1312yes—
616C2×C13—42no—
617C2×C13—42no—
618C2×C13—42no—
619C2×C13#355014yescomplemented
620C2×C13C22×H(5,𝔽2)11yescharacteristic
621C2×C13C22×2−1+412yes—
622D13—44no—
623C24—132no—
624C24C23×D1311yescharacteristic
625C24C23×D1311yescharacteristic
626C24C23×D1311yescharacteristic
627#41—416no—
628#41—5216no—
629C2×Q8—28no—
630C2×Q8—44no—
631C2×Q8—42no—
632C2×Q8—416no—
633C2×Q8—1316no—
634C2×Q8—138no—
635C2×Q8—1316no—
636C2×Q8—138no—
637C2×Q8—134no—
638C2×Q8—2616no—
639C2×Q8—268no—
640C2×Q8—524no—
641C2×Q8—528no—
642C2×Q8—522no—
643C2×Q8—5216no—
644C2×Q8—5232no—
645C2×Q8C23×D1318yes—
646C2×Q8C23×D1318yes—
647C2×Q8C23×D1314yes—
648C2×D4—42no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—138no—
652C2×D4—138no—
653C2×D4—138no—
654C2×D4—134no—
655C2×D4—268no—
656C2×D4—268no—
657C2×D4—522no—
658C2×D4—524no—
659C2×D4C23×D1314yes—
660C2×D4C23×D1314yes—
661C2×D4C23×D1314yes—
662C22×C4—24no—
663C22×C4—24no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—132no—
667C22×C4—138no—
668C22×C4—134no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—134no—
672C22×C4—138no—
673C22×C4—138no—
674C22×C4—1316no—
675C22×C4—268no—
676C22×C4—268no—
677C22×C4—528no—
678C22×C4—524no—
679C22×C4C23×D1314yes—
680C22×C4C23×D1314yes—
681C22×C4C23×D1314yes—
682C22×C4C23×D1314yes—
683C22×C4C23×D1311yescharacteristic
684C22×C4C23×D1311yescharacteristic
685C22×C4C23×D1314yes—
686C22×C4C23×D1311yescharacteristic
687C22×C4C23×D1318yes—
688C22×C4C23×D1311yescharacteristic
689C4⋊C4—138no—
690C4⋊C4—1316no—
691C4⋊C4—1316no—
692C4⋊C4—1316no—
693C4⋊C4—138no—
694C4⋊C4—138no—
695C4⋊C4—1316no—
696C4⋊C4—1316no—
697C4⋊C4—1316no—
698C4⋊C4—1316no—
699C4⋊C4—1316no—
700C4⋊C4—1316no—
701C4⋊C4C23×D1318yes—
702C4⋊C4C23×D13116yes—
703C4⋊C4C23×D13116yes—
704C22⋊C4—1316no—
705C22⋊C4—138no—
706C22⋊C4—138no—
707C22⋊C4—138no—
708C22⋊C4—1316no—
709C22⋊C4—1316no—
710C22⋊C4—138no—
711C22⋊C4—138no—
712C22⋊C4—1316no—
713C22⋊C4—1316no—
714C22⋊C4C23×D13116yes—
715C22⋊C4C23×D1318yes—
716C22⋊C4C23×D13116yes—
717C42—138no—
718C42—134no—
719C42—134no—
720C42—1316no—
721C42—1316no—
722C42—138no—
723C42—1316no—
724C42C23×D1318yes—
725C13C2×#355011yescharacteristic, complemented, Sylow
726C23—22no—
727C23—22no—
728C23—22no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—134no—
733C23—264no—
734C23—264no—
735C23—264no—
736C23C24×D1312yes—
737C23C24×D1312yes—
738C23C24×D1312yes—
739C23C24×D1311yescharacteristic
740Q8—216no—
741Q8—48no—
742Q8—44no—
743Q8—2632no—
744Q8—2616no—
745Q8—528no—
746Q8—5216no—
747Q8—524no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—2616no—
752D4—2616no—
753D4—524no—
754D4—528no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—28no—
759C2×C4—28no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—48no—
764C2×C4—138no—
765C2×C4—134no—
766C2×C4—138no—
767C2×C4—134no—
768C2×C4—134no—
769C2×C4—138no—
770C2×C4—2616no—
771C2×C4—264no—
772C2×C4—268no—
773C2×C4—264no—
774C2×C4—268no—
775C2×C4—2616no—
776C2×C4—5216no—
777C2×C4—528no—
778C2×C4#8825114yes—
779C2×C4C24×D1318yes—
780C2×C4C24×D1312yes—
781C2×C4C24×D1312yes—
782C2×C4C24×D1318yes—
783C2×C4C24×D1312yes—
784C2×C4C24×D1312yes—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—264no—
795C22—264no—
796C22—264no—
797C22—528no—
798C22C2×#8825112yes—
799C22D13×2−1+414yes—
800C22C25×D1311yescharacteristic
801C4—22no—
802C4—22no—
803C4—22no—
804C4—28no—
805C4—28no—
806C4—138no—
807C4—264no—
808C4—268no—
809C4—264no—
810C4—268no—
811C4C2×#8825114yes—
812C2—42no—
813C2—42no—
814C2—42no—
815C2—524no—
816C2#1312924514yesdirect product factor
817C2C22×#8825111yescharacteristic
818C2C2×D13×2−1+412yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#536C2
socleC23×C13C25
prime radicalC2×#11719537C2
hypercenterC2×#536D13
hypocenterC13C2×#3550
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13129245C2direct (N × H)
2. C2×#11719356C2semidirect
3. C2×#11719440C2semidirect
4. C2×#11719369C2semidirect
5. C2×#11719427C2semidirect
6. C2×#11719346C2semidirect
7. C2×#11719238C2semidirect
8. C2×Q8×C22⋊D13C2semidirect
9. C2×#11719337C2semidirect
10. C2×#11719367C2semidirect
11. C2×#11719374C2semidirect
12. C2×#11719333C2semidirect
13. C2×#11719530C2semidirect
14. C2×#11719327C2semidirect
16. C2×C13×#536C2semidirect
22. C13×#536C22semidirect
31. #11719530C22semidirect
32. Q8×C22⋊D13C22semidirect
56. #11719440C22semidirect
57. #11719427C22semidirect
58. #11719374C22semidirect
59. #11719369C22semidirect
60. #11719367C22semidirect
61. #11719356C22semidirect
62. #11719346C22semidirect
63. #11719337C22semidirect
64. #11719333C22semidirect
65. #11719327C22semidirect
66. #11719238C22semidirect
330. C2×#536D13semidirect
409. #536C2×D13semidirect
619. C2×C13#3550semidirect
725. C13C2×#3550semidirect
816. C2#13129245direct (N × H)

Maximal subgroups

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

subgroupindex
#131292452
C2×#117193562
C2×#117194402
C2×#117193692
C2×#117194272
C2×#117193462
C2×#117192382
C2×Q8×C22⋊D132
C2×#117193372
C2×#117193672
C2×#117193742
C2×#117193332
C2×#117195302
C2×#117193272
C2×#117195372
C2×C13×#5362
C2×#355013