Finite Group Databasebeta

← C2×#13125733 #16733622

Subgroups — C2×#13125733 #16733622

Order 3328.

2250 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719538C211yesmaximal, characteristic, complemented
2#13125733C2116yesmaximal, direct product factor
3C2×#11718631C211yesmaximal, characteristic, complemented
4C2×#11718705C211yesmaximal, characteristic, complemented
5C2×#11718628C211yesmaximal, characteristic, complemented
6C2×#11718694C211yesmaximal, characteristic, complemented
7C2×#11718710C211yesmaximal, characteristic, complemented
8C2×#11718703C211yesmaximal, characteristic, complemented
9C2×#11718712C211yesmaximal, characteristic, complemented
10C2×#11718699C211yesmaximal, characteristic, complemented
11C2×#11718900C211yesmaximal, characteristic, complemented
12C2×#11718708C211yesmaximal, characteristic, complemented
13C2×#11718899C211yesmaximal, characteristic, complemented
14C2×#11718698C211yesmaximal, characteristic, complemented
15C2×#11718895C211yesmaximal, characteristic, complemented
16C2×C13×#537C211yesmaximal, characteristic, complemented
17C22×C13×#41C2211yescharacteristic
18C22×C13×#41C2211yescharacteristic
19C22×#6127C2211yescharacteristic
20C13×#537—24no—
21C13×#537C2218yescomplemented
22C2×C13×C22⋊Q8—21no—
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121—21no—
26C2×C13×#121—21no—
27C2×C13×#121—21no—
28C2×C13×#121C2211yescharacteristic
29C2×C13×#121C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31#11719538—24no—
32#11719538C2218yescomplemented
33C2×#88200—21no—
34C22×#6107C2211yescharacteristic
35C22×#6106C2211yescharacteristic
36C2×#88193—21no—
37C2×#88193—21no—
38C2×#88192—21no—
39C22×#6105C2211yescharacteristic
40C22×#6104C2211yescharacteristic
41C2×#88184C2211yescharacteristic
42C2×#88184C2211yescharacteristic
43C22×C4⋊Dic13C2211yescharacteristic
44C2×#88178C2211yescharacteristic
45C2×#88178C2211yescharacteristic
46C22×#6099C2211yescharacteristic
47C23×#1055C2211yescharacteristic
48#11718900C2218yescomplemented
49#11718899C2218yescomplemented
50#11718895C2218yescomplemented
51C2×#88075C2211yescharacteristic
52C2×#88075C2211yescharacteristic
53C2×#88072C2211yescharacteristic
54C2×#88072C2211yescharacteristic
55C2×C22⋊#1055C2211yescharacteristic
56C2×C22⋊#1055C2211yescharacteristic
57C2×C22⋊#1055C2211yescharacteristic
58C2×C22⋊#1055C2211yescharacteristic
59#11718712C2218yescomplemented
60#11718710C2218yescomplemented
61#11718708C2218yescomplemented
62#11718705C2218yescomplemented
63#11718703C2218yescomplemented
64#11718699C2218yescomplemented
65#11718698C2218yescomplemented
66#11718694C2218yescomplemented
67#11718631C2218yescomplemented
68C2×#88050C2211yescharacteristic
69C2×#88050C2211yescharacteristic
70#11718628C2218yescomplemented
71C2×#88049C2211yescharacteristic
72C2×#88049C2211yescharacteristic
73C2×#88047C2211yescharacteristic
74C2×#88047C2211yescharacteristic
75C2×#88047C2211yescharacteristic
76C2×#88047C2211yescharacteristic
77C2×C13×#41—22no—
78C2×C13×#41—42no—
79C2×C13×#41—42no—
80C2×C13×#41—42no—
81C2×C13×#41—42no—
82C2×C13×#41D414yes—
83C2×C13×#41C2314yes—
84C2×C13×#41C2314yes—
85C22×Q8×C13D411yescharacteristic
86C22×Q8×C13C2311yescharacteristic
87C22×D4×C13—21no—
88C22×D4×C13—21no—
89C22×D4×C13—21no—
90C22×D4×C13D411yescharacteristic
91C22×D4×C13D411yescharacteristic
92C22×D4×C13D411yescharacteristic
93C22×D4×C13C2311yescharacteristic
94C23×C4×C13—21no—
95C23×C4×C13—21no—
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C22×C22⋊D13—21no—
100C22×C22⋊D13—21no—
101C22×C22⋊D13—21no—
102C23×Dic13—21no—
103C2×#6127—22no—
104C2×#6127—42no—
105C2×#6127—42no—
106C2×#6127C2314yes—
107C22×D52C2311yescharacteristic
108C22×C4×D13—21no—
109C22×Dic26C2311yescharacteristic
110C13×C22⋊Q8—28no—
111C13×C22⋊Q8—22no—
112C13×C22⋊Q8—22no—
113C13×C22⋊Q8C2314yes—
114C13×C22⋊Q8C2314yes—
115C13×#121—28no—
116C13×#121—28no—
117C13×#121—28no—
118C13×#121—22no—
119C13×#121—22no—
120C13×#121C2314yes—
121C13×#121C2314yes—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—22no—
124C2×C13×C4⋊C4—21no—
125C2×C13×C4⋊C4—21no—
126C2×C13×C4⋊C4C2311yescharacteristic
127C2×C13×C4⋊C4C2311yescharacteristic
128C2×C13×C4⋊C4C2314yes—
129C2×C13×C22⋊C4—21no—
130C2×C13×C22⋊C4—21no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4—21no—
133C2×C22⋊Dic13—21no—
134C2×C22⋊Dic13—21no—
135#88200—28no—
136C2×#6107—42no—
137C2×#6107C2314yes—
138C2×#6106—42no—
139C2×#6106C2314yes—
140#88193—28no—
141#88193—28no—
142#88192—28no—
143C2×#6105—42no—
144C2×#6105C2314yes—
145C2×#6104—42no—
146C2×#6104C2314yes—
147#88184—22no—
148#88184—22no—
149#88184C2314yes—
150#88184C2314yes—
151C2×#6103—21no—
152C2×#6103—21no—
153C2×C4⋊Dic13—21no—
154C2×C4⋊Dic13—22no—
155C2×C4⋊Dic13C2314yes—
156C2×C4⋊Dic13C2311yescharacteristic
157C2×C4⋊Dic13C2311yescharacteristic
158#88178—22no—
159#88178—22no—
160#88178C2314yes—
161#88178C2314yes—
162C2×#6101—21no—
163C2×#6101—21no—
164C2×#6099—42no—
165C2×#6099C2314yes—
166C22×#1055—42no—
167C22×#1055C2311yescharacteristic
168C22×#1055C2311yescharacteristic
169C22×#1055C2311yescharacteristic
170C22×#1055C2311yescharacteristic
171C22×#1055C2314yes—
172#88075C2314yes—
173#88075C2314yes—
174#88072C2314yes—
175#88072C2314yes—
176C22⋊#1055C2314yes—
177C22⋊#1055C2314yes—
178C22⋊#1055C2314yes—
179C22⋊#1055C2314yes—
180#88050C2314yes—
181#88050C2314yes—
182#88049C2314yes—
183#88049C2314yes—
184#88047C2314yes—
185#88047C2314yes—
186#88047C2314yes—
187#88047C2314yes—
188C2×#3203—131nomaximal, Sylow
189C24×C13—21no—
190C24×C13C2×D411yescharacteristic
191C24×C13C2×D411yescharacteristic
192C24×C13C2×D411yescharacteristic
193C23×D13—21no—
194C13×#41—48no—
195C13×#41—44no—
196C13×#41—44no—
197C13×#41—44no—
198C13×#41—44no—
199C13×#41—48no—
200C2×Q8×C13—21no—
201C2×Q8×C13—22no—
202C2×Q8×C13—22no—
203C2×Q8×C13—42no—
204C2×Q8×C13C2×D414yes—
205C2×Q8×C13C2412yes—
206C2×D4×C13—24no—
207C2×D4×C13—24no—
208C2×D4×C13—24no—
209C2×D4×C13—21no—
210C2×D4×C13—22no—
211C2×D4×C13—22no—
212C2×D4×C13—42no—
213C2×D4×C13—42no—
214C2×D4×C13—42no—
215C2×D4×C13—44no—
216C2×D4×C13—82no—
217C2×D4×C13—82no—
218C2×D4×C13C2×D414yes—
219C2×D4×C13C2×D414yes—
220C2×D4×C13C2×D414yes—
221C2×D4×C13C2412yes—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—22no—
227C22×C4×C13—22no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—24no—
232C22×C4×C13—24no—
233C22×C4×C13—44no—
234C22×C4×C13—82no—
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D412yes—
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D412yes—
241C22×C4×C13C2412yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C2412yes—
244C22×C4×C13C2411yescharacteristic
245C2×C22⋊D13—24no—
246C2×C22⋊D13—24no—
247C2×C22⋊D13—24no—
248C2×C22⋊D13—44no—
249C2×C22⋊D13—82no—
250C2×C22⋊D13—82no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—24no—
255C22×Dic13—82no—
256#6127—44no—
257#6127—44no—
258#6127—48no—
259C2×D52—22no—
260C2×D52—22no—
261C2×D52—21no—
262C2×D52C2412yes—
263C2×C4×D13—24no—
264C2×C4×D13—44no—
265C2×Dic26—22no—
266C2×Dic26—22no—
267C2×Dic26—21no—
268C2×Dic26C2412yes—
269C13×C4⋊C4—24no—
270C13×C4⋊C4—21no—
271C13×C4⋊C4—21no—
272C13×C4⋊C4—24no—
273C13×C4⋊C4—24no—
274C13×C4⋊C4C2412yes—
275C13×C4⋊C4C2412yes—
276C13×C22⋊C4—24no—
277C13×C22⋊C4—24no—
278C13×C22⋊C4—24no—
279C13×C22⋊C4—24no—
280C22⋊Dic13—24no—
281C22⋊Dic13—24no—
282#6107—44no—
283#6106—44no—
284#6105—44no—
285#6104—44no—
286#6103—24no—
287#6103—24no—
288C4⋊Dic13—21no—
289C4⋊Dic13—21no—
290C4⋊Dic13—24no—
291C4⋊Dic13C2412yes—
292C4⋊Dic13C2412yes—
293#6101—24no—
294#6101—24no—
295#6099—44no—
296C2×#1055—22no—
297C2×#1055—22no—
298C2×#1055—22no—
299C2×#1055—22no—
300C2×#1055—44no—
301C2×#1055C2412yes—
302C2×#1055C2412yes—
303C2×#1055C2412yes—
304C2×#1055C2412yes—
305C2×#537—131no—
306C2×#537D1311yescharacteristic, complemented
307#3203—1316no—
308C2×#484—131no—
309C2×#484—131no—
310C2×#480—131no—
311C2×#480—131no—
312C2×#468—131no—
313C2×#468—131no—
314C2×#467—131no—
315C2×#466—131no—
316C2×#452—131no—
317C2×#452—131no—
318C2×#449—131no—
319C2×#449—131no—
320C2×#408—131no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—42no—
332C23×C13—42no—
333C23×C13—42no—
334C23×C13C22×D412yes—
335C23×C13C22×D412yes—
336C23×C13C22×D412yes—
337C23×C13C22×D411yescharacteristic
338C22×D13—22no—
339C22×D13—42no—
340C22×D13—42no—
341C22×D13—42no—
342Q8×C13—22no—
343Q8×C13—22no—
344Q8×C13—44no—
345Q8×C13—42no—
346D4×C13—22no—
347D4×C13—22no—
348D4×C13—44no—
349D4×C13—44no—
350D4×C13—44no—
351D4×C13—48no—
352D4×C13—42no—
353D4×C13—84no—
354D4×C13—84no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—24no—
359C2×C4×C13—24no—
360C2×C4×C13—24no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—48no—
371C2×C4×C13—42no—
372C2×C4×C13—42no—
373C2×C4×C13—42no—
374C2×C4×C13—84no—
375C2×C4×C13C22×D412yes—
376C2×C4×C13C22×D412yes—
377C2×C4×C13C22×D412yes—
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13H(5,𝔽2)12yes—
380C2×C4×C13H(5,𝔽2)12yes—
381C2×C4×C13C2511yescharacteristic
382C22⋊D13—48no—
383C22⋊D13—84no—
384C22⋊D13—84no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—42no—
389C2×Dic13—42no—
390C2×Dic13—42no—
391C2×Dic13—84no—
392D52—22no—
393D52—22no—
394D52—42no—
395C4×D13—48no—
396Dic26—22no—
397Dic26—22no—
398Dic26—42no—
399#1055—22no—
400#1055—22no—
401#1055—22no—
402#1055—22no—
403C22×#41—131no—
404C22×#41C2×D1311yescharacteristic
405C22×#41C2×D1311yescharacteristic
406C22×Q16—131no—
407C22×SD16—131no—
408C22×SD16—131no—
409C22×D8—131no—
410C22×M16—131no—
411C23×C8—131no—
412#537—24no—
413#537—138no—
414#537—264no—
415#537C2×D1318yescomplemented
416C2×C22⋊Q8—21no—
417C2×C22⋊Q8—131no—
418C2×C22⋊Q8—131no—
419C2×C22⋊Q8—261no—
420C2×C22⋊Q8C2×D1311yescharacteristic
421C2×C22⋊Q8C2×D1311yescharacteristic
422C2×#121—21no—
423C2×#121—21no—
424C2×#121—21no—
425C2×#121—131no—
426C2×#121—131no—
427C2×#121—261no—
428C2×#121—261no—
429C2×#121—261no—
430C2×#121C2×D1311yescharacteristic
431C2×#121C2×D1311yescharacteristic
432C22×C4⋊C4—131no—
433C22×C4⋊C4C2×D1311yescharacteristic
434#484—138no—
435#484—138no—
436#480—138no—
437#480—138no—
438#468—138no—
439#468—138no—
440#467—138no—
441#466—138no—
442#452—138no—
443#452—138no—
444#449—138no—
445#449—138no—
446C2×#107—131no—
447C2×#107—131no—
448C2×#107—131no—
449C2×#107—131no—
450C2×#103—131no—
451C2×#103—131no—
452C2×#103—131no—
453C2×#103—131no—
454C2×#102—131no—
455C2×#102—131no—
456C2×#102—131no—
457C2×#102—131no—
458#408—138no—
459C2×C22⋊C8—131no—
460C2×C22⋊C8—131no—
461C2×C22⋊C8—131no—
462C2×C22⋊C8—131no—
463C22×C13—22no—
464C22×C13—22no—
465C22×C13—22no—
466C22×C13—22no—
467C22×C13—22no—
468C22×C13—22no—
469C22×C13—22no—
470C22×C13—22no—
471C22×C13—22no—
472C22×C13—44no—
473C22×C13—44no—
474C22×C13—44no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—84no—
479C22×C13#53412yes—
480C22×C13#57612yes—
481C22×C13#57812yes—
482C22×C13C23×D411yescharacteristic
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—42no—
486C2×D13—84no—
487C4×C13—22no—
488C4×C13—22no—
489C4×C13—22no—
490C4×C13—42no—
491C4×C13—42no—
492C4×C13—42no—
493C4×C13#53412yes—
494C4×C13C2×H(5,𝔽2)11yescharacteristic
495C4×C13C2×H(5,𝔽2)11yescharacteristic
496Dic13—42no—
497Dic13—42no—
498Dic13—42no—
499C2×#41—22no—
500C2×#41—42no—
501C2×#41—42no—
502C2×#41—42no—
503C2×#41—42no—
504C2×#41—134no—
505C2×#41—262no—
506C2×#41—522no—
507C2×#41—522no—
508C2×#41C22⋊D1314yes—
509C2×#41C22×D1314yes—
510C2×#41C22×D1314yes—
511C22×Q8—131no—
512C22×Q8C22⋊D1311yescharacteristic
513C22×Q8C22×D1311yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—131no—
518C22×D4—261no—
519C22×D4—261no—
520C22×D4—261no—
521C22×D4C22⋊D1311yescharacteristic
522C22×D4C22⋊D1311yescharacteristic
523C22×D4C22⋊D1311yescharacteristic
524C22×D4C22×D1311yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—261no—
528C23×C4—261no—
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C2×Q16—134no—
533C2×Q16—522no—
534C2×SD16—134no—
535C2×SD16—134no—
536C2×SD16—522no—
537C2×SD16—522no—
538C2×D8—134no—
539C2×D8—522no—
540C2×M16—134no—
541C2×M16—522no—
542C22×C8—131no—
543C22×C8—131no—
544C22×C8—131no—
545C22×C8—131no—
546C22×C8—134no—
547C22×C8—522no—
548C22⋊Q8—28no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—134no—
552C22⋊Q8—134no—
553C22⋊Q8—268no—
554C22⋊Q8—262no—
555C22⋊Q8—262no—
556C22⋊Q8C22×D1314yes—
557C22⋊Q8C22×D1314yes—
558#121—28no—
559#121—28no—
560#121—28no—
561#121—22no—
562#121—22no—
563#121—134no—
564#121—134no—
565#121—268no—
566#121—268no—
567#121—268no—
568#121—262no—
569#121—262no—
570#121C22×D1314yes—
571#121C22×D1314yes—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—131no—
577C2×C4⋊C4—131no—
578C2×C4⋊C4—134no—
579C2×C4⋊C4—261no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—261no—
582C2×C4⋊C4—261no—
583C2×C4⋊C4C22×D1311yescharacteristic
584C2×C4⋊C4C22×D1311yescharacteristic
585C2×C4⋊C4C22×D1314yes—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—261no—
591C2×C22⋊C4—261no—
592C2×C22⋊C4—261no—
593C2×C22⋊C4—261no—
594#107—134no—
595#107—134no—
596#107—134no—
597#107—134no—
598#103—134no—
599#103—134no—
600#103—134no—
601#103—134no—
602#102—134no—
603#102—134no—
604#102—134no—
605#102—134no—
606C22⋊C8—134no—
607C22⋊C8—134no—
608C22⋊C8—134no—
609C22⋊C8—134no—
610C2×C13—42no—
611C2×C13—42no—
612C2×C13—42no—
613C2×C13—82no—
614C2×C13#320314yescomplemented
615C2×C13C2×#53411yescharacteristic
616C2×C13C2×#57611yescharacteristic
617C2×C13C2×#57811yescharacteristic
618D13—82no—
619C24—21no—
620C24—261no—
621C24C2×C22⋊D1311yescharacteristic
622C24C2×C22⋊D1311yescharacteristic
623C24C2×C22⋊D1311yescharacteristic
624#41—48no—
625#41—44no—
626#41—44no—
627#41—44no—
628#41—44no—
629#41—48no—
630#41—524no—
631#41—524no—
632#41—528no—
633C2×Q8—21no—
634C2×Q8—22no—
635C2×Q8—22no—
636C2×Q8—42no—
637C2×Q8—132no—
638C2×Q8—261no—
639C2×Q8—262no—
640C2×Q8—262no—
641C2×Q8C2×C22⋊D1314yes—
642C2×Q8C23×D1312yes—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—44no—
653C2×D4—82no—
654C2×D4—82no—
655C2×D4—132no—
656C2×D4—264no—
657C2×D4—264no—
658C2×D4—264no—
659C2×D4—262no—
660C2×D4—262no—
661C2×D4—261no—
662C2×D4—524no—
663C2×D4—1042no—
664C2×D4—1042no—
665C2×D4C2×C22⋊D1314yes—
666C2×D4C2×C22⋊D1314yes—
667C2×D4C2×C22⋊D1314yes—
668C2×D4C23×D1312yes—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—44no—
681C22×C4—82no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—264no—
686C22×C4—264no—
687C22×C4—524no—
688C22×C4—1042no—
689C22×C4C2×C22⋊D1312yes—
690C22×C4C2×C22⋊D1312yes—
691C22×C4C2×C22⋊D1312yes—
692C22×C4C2×C22⋊D1311yescharacteristic
693C22×C4C2×C22⋊D1311yescharacteristic
694C22×C4C2×C22⋊D1311yescharacteristic
695C22×C4C23×D1312yes—
696C22×C4C23×D1312yes—
697C22×C4C23×D1312yes—
698C22×C4C23×D1311yescharacteristic
699Q16—524no—
700SD16—524no—
701SD16—524no—
702D8—524no—
703M16—524no—
704C2×C8—132no—
705C2×C8—132no—
706C2×C8—132no—
707C2×C8—132no—
708C2×C8—262no—
709C2×C8—262no—
710C2×C8—262no—
711C2×C8—262no—
712C2×C8—524no—
713C4⋊C4—24no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—24no—
717C4⋊C4—24no—
718C4⋊C4—132no—
719C4⋊C4—132no—
720C4⋊C4—264no—
721C4⋊C4—261no—
722C4⋊C4—261no—
723C4⋊C4—264no—
724C4⋊C4—264no—
725C4⋊C4C23×D1312yes—
726C4⋊C4C23×D1312yes—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—264no—
732C22⋊C4—264no—
733C22⋊C4—264no—
734C22⋊C4—264no—
735C13C2×#320311yescharacteristic, complemented, Sylow
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—262no—
750C23—522no—
751C23—522no—
752C23—522no—
753C23C22×C22⋊D1312yes—
754C23C22×C22⋊D1312yes—
755C23C22×C22⋊D1312yes—
756C23C22×C22⋊D1311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—44no—
760Q8—42no—
761Q8—262no—
762Q8—262no—
763Q8—522no—
764D4—22no—
765D4—22no—
766D4—44no—
767D4—44no—
768D4—44no—
769D4—48no—
770D4—42no—
771D4—84no—
772D4—84no—
773D4—262no—
774D4—262no—
775D4—528no—
776D4—522no—
777D4—1044no—
778D4—1044no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—48no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—262no—
800C2×C4—262no—
801C2×C4—262no—
802C2×C4—528no—
803C2×C4—522no—
804C2×C4—522no—
805C2×C4—522no—
806C2×C4—1044no—
807C2×C4#8825112yes—
808C2×C4#8825112yes—
809C2×C4C22×C22⋊D1312yes—
810C2×C4C22×C22⋊D1312yes—
811C2×C4C22×C22⋊D1312yes—
812C2×C4C22×C22⋊D1311yescharacteristic
813C2×C4C24×D1311yescharacteristic
814C8—262no—
815C8—262no—
816C8—262no—
817C8—262no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—84no—
834C22—522no—
835C22—522no—
836C22—522no—
837C22—1044no—
838C22#1171950912yes—
839C22#1171954012yes—
840C22#1171954312yes—
841C22C23×C22⋊D1311yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—522no—
849C4—522no—
850C4—522no—
851C4#1171950912yes—
852C4C2×#8825111yescharacteristic
853C4C2×#8825111yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—82no—
858C2—1042no—
859C2#1312573314yesdirect product factor
860C2C2×#1171950911yescharacteristic
861C2C2×#1171954011yescharacteristic
862C2C2×#1171954311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#537C2
socleC23×C13C22×D4
hypercenterC2×#537D13
hypocenterC13C2×#3203
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#11719538C2semidirect
2. #13125733C2direct (N × H)
3. C2×#11718631C2semidirect
4. C2×#11718705C2semidirect
5. C2×#11718628C2semidirect
6. C2×#11718694C2semidirect
7. C2×#11718710C2semidirect
8. C2×#11718703C2semidirect
9. C2×#11718712C2semidirect
10. C2×#11718699C2semidirect
11. C2×#11718900C2semidirect
12. C2×#11718708C2semidirect
13. C2×#11718899C2semidirect
14. C2×#11718698C2semidirect
15. C2×#11718895C2semidirect
16. C2×C13×#537C2semidirect
21. C13×#537C22semidirect
32. #11719538C22semidirect
48. #11718900C22semidirect
49. #11718899C22semidirect
50. #11718895C22semidirect
59. #11718712C22semidirect
60. #11718710C22semidirect
61. #11718708C22semidirect
62. #11718705C22semidirect
63. #11718703C22semidirect
64. #11718699C22semidirect
65. #11718698C22semidirect
66. #11718694C22semidirect
67. #11718631C22semidirect
70. #11718628C22semidirect
306. C2×#537D13semidirect
415. #537C2×D13semidirect
614. C2×C13#3203semidirect
735. C13C2×#3203semidirect
859. C2#13125733direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#117195382
#131257332
C2×#117186312
C2×#117187052
C2×#117186282
C2×#117186942
C2×#117187102
C2×#117187032
C2×#117187122
C2×#117186992
C2×#117189002
C2×#117187082
C2×#117188992
C2×#117186982
C2×#117188952
C2×C13×#5372
C2×#320313