Finite Group Databasebeta

← C2×#13129076 #16770164

Subgroups — C2×#13129076 #16770164

Order 3328.

7162 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129076C2132yesmaximal, direct product factor
2C2×#11719356C211yesmaximal, characteristic, complemented
3C2×#11719417C212yesmaximal, complemented
4C2×#11719377C211yesmaximal, characteristic, complemented
5C2×#11719355C212yesmaximal, complemented
6C2×#11719236C212yesmaximal, complemented
7C2×#11719292C211yesmaximal, characteristic, complemented
8C2×#11719200C212yesmaximal, complemented
9C2×D4×Dic26C212yesmaximal, complemented
10C2×#11719337C212yesmaximal, complemented
11C2×#11719328C212yesmaximal, complemented
12C2×#11719224C212yesmaximal, complemented
13C2×#11719406C212yesmaximal, complemented
14C2×#11719370C212yesmaximal, complemented
15C2×#11719269C212yesmaximal, complemented
16C2×#11719353C211yesmaximal, characteristic, complemented
17C2×#11719380C211yesmaximal, characteristic, complemented
18C2×#11719291C211yesmaximal, characteristic
19C22×#88132C212yesmaximal, complemented
20C2×C13×#551C211yesmaximal, characteristic, complemented
21C24×Dic13C2211yescharacteristic
22C22×Q8×D13C2211yescharacteristic, complemented
23C22×#6129C2211yescharacteristic
24C23×Dic26C2212yes—
25C23×Dic26C2211yescharacteristic, complemented
26C13×#551C22116yescomplemented
27C2×C13×#126C2212yes—
28C2×C13×#124C2211yescharacteristic
29C2×C13×#123C2211yescharacteristic
30C2×C13×#123C2212yes—
31C2×C13×C22⋊Q8C2212yes—
32C2×C13×#120C2211yescharacteristic
33C2×C4×D4×C13C2212yes—
34C2×C13×#117C2212yes—
35C22×C13×C22⋊C4C2212yes—
36C2×#88207C2211yescharacteristic
37C22×C22⋊Dic13C2212yes—
38C2×#88198C2212yescomplemented
39C2×#88198C2211yescharacteristic, complemented
40C2×#88193C2212yes—
41C2×#88190C2211yescharacteristic
42C2×#88189C2211yescharacteristic
43C2×#88189C2211yescharacteristic
44C2×#88189C2212yes—
45C2×D4×Dic13C2212yes—
46C2×D4×Dic13C2212yes—
47C2×#88183C2212yes—
48C2×#88183C2211yescharacteristic, complemented
49C2×C4×C22⋊D13C2212yes—
50C2×#88180C2212yes—
51C22×C4⋊Dic13C2212yes—
52C2×#88178C2212yes—
53C2×#88178C2212yescomplemented
54C22×#6101C2212yes—
55C22×#6101C2212yes—
56#11719417C22132yescomplemented
57#11719406C22132yescomplemented
58#11719380C22116yescomplemented
59#11719377C22116yescomplemented
60#11719370C22132yescomplemented
61#11719356C22116yescomplemented
62#11719355C22132yescomplemented
63#11719353C22116yescomplemented
64#11719337C22132yescomplemented
65#11719328C22132yescomplemented
66#11719292C22116yescomplemented
67#11719291C22116yes—
68#11719269C22132yescomplemented
69D4×Dic26C22132yescomplemented
70#11719236C22132yescomplemented
71#11719224C22132yescomplemented
72C2×#88152C2212yescomplemented
73C2×#88151C2212yescomplemented
74C2×#88150C2212yescomplemented
75C2×#88150C2212yescomplemented
76C2×#88144C2212yescomplemented
77C2×#88144C2212yescomplemented
78C2×#88143C2212yescomplemented
79C2×#88143C2212yescomplemented
80C2×#88143C2212yescomplemented
81C2×#88143C2212yescomplemented
82C2×#88143C2212yescomplemented
83C2×#88142C2212yescomplemented
84C2×#88142C2212yescomplemented
85C2×#88142C2212yescomplemented
86C2×#88142C2212yescomplemented
87C2×#88141C2212yescomplemented
88#11719200C22132yescomplemented
89C2×#88140C2211yescharacteristic
90C2×#88140C2212yes—
91C2×#88140C2211yescharacteristic, complemented
92C2×#88139C2212yes—
93C2×#88137C2212yes—
94C2×#88137C2212yescomplemented
95C2×#88135C2212yes—
96C2×#88135C2212yes—
97C2×#88133C2212yes—
98C2×#88133C2212yes—
99C2×#88133C2212yes—
100C2×#88133C2212yescomplemented
101C2×#88133C2212yescomplemented
102C2×#88132C2212yes—
103C2×#88132C2212yes—
104C2×#88132C2212yes—
105C2×#88132C2212yes—
106C2×#88132C2212yes—
107C2×#88132C2212yes—
108C2×#88132C2212yes—
109C2×#88132C2212yes—
110C2×#88132C2212yes—
111C2×#88132C2212yes—
112C2×#88132C2212yes—
113C2×#88132C22132yescomplemented
114C2×#88132C2212yescomplemented
115C2×#88132C2212yescomplemented
116C2×#88131C2211yescharacteristic
117C2×#88131C2212yes—
118C2×#88131C2212yes—
119C2×#88131C2211yescharacteristic, complemented
120C2×#88130C2212yescomplemented
121C2×#88126C2211yescharacteristic, complemented
122C2×#88124C2212yescomplemented
123C2×#88124C2212yescomplemented
124C2×#88123C2212yescomplemented
125C2×#88123C2211yescharacteristic, complemented
126C2×C4×Dic26C2212yescomplemented
127C25×C13C2311yescharacteristic
128C22×Q8×C13C2311yescharacteristic
129C22×D4×C13C2312yes—
130C22×D4×C13C2311yescharacteristic
131C23×C4×C13C2312yes—
132C23×C4×C13C2312yes—
133C23×C4×C13C2311yescharacteristic
134C22×C22⋊D13C2312yes—
135C22×C22⋊D13C2311yescharacteristic
136C22×C22⋊D13C2311yescharacteristic
137C23×Dic13—44no—
138C23×Dic13C2312yes—
139C23×Dic13C2311yescharacteristic
140C23×Dic13C2311yescharacteristic
141C23×Dic13C2312yes—
142C23×Dic13C2311yescharacteristic
143C23×Dic13C2312yes—
144C23×Dic13C2312yes—
145C23×Dic13C2318yes—
146C23×Dic13C2311yescharacteristic
147C2×Q8×D13—44no—
148C2×Q8×D13C2318yescomplemented
149C2×#6129—44no—
150C2×#6129C2318yes—
151C22×C4×D13C2311yescharacteristic
152C22×C4×D13C2312yes—
153C22×Dic26—48no—
154C22×Dic26—44no—
155C22×Dic26C2312yes—
156C22×Dic26C2312yes—
157C22×Dic26C2311yescharacteristic
158C22×Dic26C2311yescharacteristic
159C22×Dic26C2312yes—
160C22×Dic26C2312yes—
161C22×Dic26C2312yes—
162C22×Dic26C23116yes—
163C22×Dic26C2318yescomplemented
164C13×#126C23116yes—
165C13×#124C2318yes—
166C13×#123C2318yes—
167C13×#123C23116yes—
168C13×C22⋊Q8C23116yes—
169C13×#120C2318yes—
170C4×D4×C13C23116yes—
171C13×#117C23116yes—
172C2×C13×C4⋊C4C2312yes—
173C2×C13×C4⋊C4C2312yes—
174C2×C13×C4⋊C4C2312yes—
175C2×C13×C4⋊C4C2312yes—
176C2×C13×C22⋊C4C2312yes—
177C2×C13×C22⋊C4C2312yes—
178C2×C13×C22⋊C4C2311yescharacteristic
179C2×C13×C22⋊C4C2311yescharacteristic
180C2×C13×C22⋊C4C2312yes—
181C2×C13×C22⋊C4C2312yes—
182C2×C13×C22⋊C4C2312yes—
183C2×C13×C22⋊C4C2312yes—
184C2×C13×C22⋊C4C23116yes—
185C2×C42×C13C2312yes—
186C2×C42×C13C2311yescharacteristic
187#88207C2318yes—
188C2×C22⋊Dic13C2312yes—
189C2×C22⋊Dic13C2312yes—
190C2×C22⋊Dic13C2311yescharacteristic
191C2×C22⋊Dic13C2311yescharacteristic
192C2×C22⋊Dic13C2312yes—
193C2×C22⋊Dic13C2312yes—
194C2×C22⋊Dic13C2312yes—
195C2×C22⋊Dic13C23116yes—
196C2×C22⋊Dic13C2312yes—
197C2×C22⋊Dic13C2312yes—
198#88198C2318yescomplemented
199#88198C23116yescomplemented
200#88193C23116yes—
201#88190C2318yes—
202#88189C23116yes—
203#88189C2318yes—
204#88189C2318yes—
205D4×Dic13C23116yes—
206D4×Dic13C23116yes—
207#88183C23116yes—
208#88183C2318yescomplemented
209C4×C22⋊D13C23116yes—
210C2×#6103C2312yes—
211C2×#6103C2312yes—
212C2×#6103C2312yes—
213C2×#6103C2312yes—
214#88180C23116yes—
215C2×C4⋊Dic13C2312yes—
216C2×C4⋊Dic13C2312yes—
217C2×C4⋊Dic13C2312yes—
218C2×C4⋊Dic13C2312yes—
219C2×C4⋊Dic13C2312yes—
220C2×C4⋊Dic13C2312yes—
221C2×C4⋊Dic13C2312yes—
222C2×C4⋊Dic13C2312yes—
223C2×C4⋊Dic13C2312yes—
224C2×C4⋊Dic13C23116yes—
225#88178C23116yes—
226#88178C23116yescomplemented
227C2×#6101C2312yes—
228C2×#6101C2312yes—
229C2×#6101C2312yes—
230C2×#6101C2312yes—
231C2×#6101C2312yes—
232C2×#6101C2312yes—
233C2×#6101C2312yes—
234C2×#6101C2312yes—
235C2×#6101C2312yes—
236C2×#6101C2312yes—
237C2×#6101C2312yes—
238C2×#6101C2312yes—
239C2×#6101C2312yes—
240C2×#6101C2312yes—
241C2×#6101C2312yes—
242C2×#6101C2312yes—
243C2×#6101C2312yes—
244C2×#6101C23116yes—
245C2×#6101C23116yes—
246C2×#6101C2312yes—
247C2×C4×Dic13C2312yes—
248C2×C4×Dic13C2312yes—
249C2×C4×Dic13C2311yescharacteristic
250C2×C4×Dic13C2312yes—
251C2×C4×Dic13C2312yes—
252C2×C4×Dic13C2312yes—
253#88152C23116yescomplemented
254#88151C23116yescomplemented
255#88150C23116yescomplemented
256#88150C23116yescomplemented
257#88144C23116yescomplemented
258#88144C23116yescomplemented
259#88143C23116yescomplemented
260#88143C23116yescomplemented
261#88143C23116yescomplemented
262#88143C23116yescomplemented
263#88143C23116yescomplemented
264#88142C23116yescomplemented
265#88142C23116yescomplemented
266#88142C23116yescomplemented
267#88142C23116yescomplemented
268#88141C23116yescomplemented
269#88140C23116yes—
270#88140C2318yes—
271#88140C2318yescomplemented
272#88139C23116yes—
273#88137C23116yes—
274#88137C23116yescomplemented
275#88135C23116yes—
276#88135C23116yes—
277#88133C23116yes—
278#88133C23116yes—
279#88133C23116yes—
280#88133C23116yescomplemented
281#88133C23116yescomplemented
282#88132C23116yes—
283#88132C23116yes—
284#88132C23116yes—
285#88132C23116yes—
286#88132C23116yes—
287#88132C23116yes—
288#88132C23116yes—
289#88132C23116yes—
290#88132C23116yes—
291#88132C23116yes—
292#88132C23116yes—
293#88132C23116yescomplemented
294#88132C23116yescomplemented
295#88131C23116yes—
296#88131C23116yes—
297#88131C2318yes—
298#88131C2318yescomplemented
299#88130C23116yescomplemented
300#88126C2318yescomplemented
301#88124C23116yescomplemented
302#88124C23116yescomplemented
303#88123C2318yescomplemented
304#88123C23116yescomplemented
305C4×Dic26C23116yescomplemented
306C2×#3538—131nomaximal, Sylow
307C24×C13—28no—
308C24×C13—42no—
309C24×C13C2411yescharacteristic
310C24×C13C2411yescharacteristic
311C24×C13C2414yes—
312C24×C13C2412yes—
313C23×D13C2411yescharacteristic
314C2×Q8×C13—42no—
315C2×Q8×C13C2414yes—
316C2×D4×C13—28no—
317C2×D4×C13—42no—
318C2×D4×C13C2418yes—
319C2×D4×C13C2414yes—
320C22×C4×C13—28no—
321C22×C4×C13—42no—
322C22×C4×C13—44no—
323C22×C4×C13C2412yes—
324C22×C4×C13C2412yes—
325C22×C4×C13C2411yescharacteristic
326C22×C4×C13C2412yes—
327C22×C4×C13C2412yes—
328C22×C4×C13C2412yes—
329C22×C4×C13C2418yes—
330C22×C4×C13C2418yes—
331C22×C4×C13C2414yes—
332C2×C22⋊D13—28no—
333C2×C22⋊D13—42no—
334C2×C22⋊D13—42no—
335C2×C22⋊D13C2418yes—
336C2×C22⋊D13C2414yes—
337C2×C22⋊D13C2414yes—
338C22×Dic13—28no—
339C22×Dic13—24no—
340C22×Dic13—28no—
341C22×Dic13—24no—
342C22×Dic13—416no—
343C22×Dic13—44no—
344C22×Dic13—42no—
345C22×Dic13—42no—
346C22×Dic13—44no—
347C22×Dic13C2418yes—
348C22×Dic13C2414yes—
349C22×Dic13C2414yes—
350C22×Dic13C2418yes—
351C22×Dic13C2412yes—
352C22×Dic13C2412yes—
353C22×Dic13C2412yes—
354C22×Dic13C2411yescharacteristic
355C22×Dic13C2412yes—
356C22×Dic13C2412yes—
357C22×Dic13C2411yescharacteristic
358C22×Dic13C2412yes—
359C22×Dic13C2414yes—
360C22×Dic13C2418yes—
361C22×Dic13C2418yes—
362C22×Dic13C2414yes—
363C22×Dic13C2411yescharacteristic
364Q8×D13—416no—
365#6129—416no—
366C2×C4×D13—24no—
367C2×C4×D13—44no—
368C2×C4×D13C2414yes—
369C2×C4×D13C2418yes—
370C2×Dic26—28no—
371C2×Dic26—28no—
372C2×Dic26—432no—
373C2×Dic26—416no—
374C2×Dic26—44no—
375C2×Dic26—44no—
376C2×Dic26—44no—
377C2×Dic26—42no—
378C2×Dic26—42no—
379C2×Dic26C2418yes—
380C2×Dic26C2418yes—
381C2×Dic26C2414yes—
382C2×Dic26C2414yes—
383C2×Dic26C2418yes—
384C2×Dic26C2418yes—
385C2×Dic26C2418yes—
386C13×C4⋊C4C2418yes—
387C13×C4⋊C4C2418yes—
388C13×C4⋊C4C2418yes—
389C13×C4⋊C4C2418yes—
390C13×C22⋊C4C2418yes—
391C13×C22⋊C4C2418yes—
392C13×C22⋊C4C2414yes—
393C13×C22⋊C4C2414yes—
394C13×C22⋊C4C2418yes—
395C13×C22⋊C4C2418yes—
396C13×C22⋊C4C2418yes—
397C13×C22⋊C4C2418yes—
398C42×C13C2418yes—
399C42×C13C2414yes—
400C22⋊Dic13C2418yes—
401C22⋊Dic13C2418yes—
402C22⋊Dic13C2414yes—
403C22⋊Dic13C2414yes—
404C22⋊Dic13C2418yes—
405C22⋊Dic13C2418yes—
406C22⋊Dic13C2418yes—
407C22⋊Dic13C2418yes—
408C22⋊Dic13C2418yes—
409#6103C2418yes—
410#6103C2418yes—
411#6103C2418yes—
412#6103C2418yes—
413C4⋊Dic13C2418yes—
414C4⋊Dic13C2418yes—
415C4⋊Dic13C2418yes—
416C4⋊Dic13C2418yes—
417C4⋊Dic13C2418yes—
418C4⋊Dic13C2418yes—
419C4⋊Dic13C2418yes—
420C4⋊Dic13C2418yes—
421C4⋊Dic13C2418yes—
422#6101C2418yes—
423#6101C2418yes—
424#6101C2418yes—
425#6101C2418yes—
426#6101C2418yes—
427#6101C2418yes—
428#6101C2418yes—
429#6101C2418yes—
430#6101C2418yes—
431#6101C2418yes—
432#6101C2418yes—
433#6101C2418yes—
434#6101C2418yes—
435#6101C2418yes—
436#6101C2418yes—
437#6101C2418yes—
438#6101C2418yes—
439#6101C2418yes—
440C4×Dic13C2418yes—
441C4×Dic13C2418yes—
442C4×Dic13C2414yes—
443C4×Dic13C2418yes—
444C4×Dic13C2418yes—
445C4×Dic13C2418yes—
446#3538—1332no—
447C2×#563—132no—
448C2×#563—131no—
449C2×#563—131no—
450C2×#552—132no—
451C2×#552—132no—
452C2×#551—131no—
453C2×#551—132no—
454C2×#551D1311yescharacteristic, complemented
455C2×D4×Q8—132no—
456C2×D4×Q8—132no—
457C2×#544—132no—
458C2×#544—132no—
459C2×#541—132no—
460C2×#539—132no—
461C2×#539—132no—
462C2×#536—131no—
463C2×#536—131no—
464C2×#525—131no—
465C22×C22⋊Q8—132no—
466C23×C13—24no—
467C23×C13—24no—
468C23×C13—22no—
469C23×C13—22no—
470C23×C13—24no—
471C23×C13—216no—
472C23×C13—24no—
473C23×C13—44no—
474C23×C13—416no—
475C23×C132−1+418yes—
476C23×C13C2512yes—
477C23×C13C2512yes—
478C23×C13C2514yes—
479C23×C13C2511yescharacteristic
480C22×D13—22no—
481C22×D13—24no—
482C22×D13C2512yes—
483Q8×C13—44no—
484D4×C13—216no—
485D4×C13—44no—
486C2×C4×C13—24no—
487C2×C4×C13—24no—
488C2×C4×C13—22no—
489C2×C4×C13—216no—
490C2×C4×C13—24no—
491C2×C4×C13—24no—
492C2×C4×C13—24no—
493C2×C4×C13—44no—
494C2×C4×C13—48no—
495C2×C4×C13C2514yes—
496C2×C4×C13C2514yes—
497C2×C4×C13C2512yes—
498C2×C4×C13C2514yes—
499C2×C4×C13C2514yes—
500C2×C4×C13C2514yes—
501C22⋊D13—216no—
502C22⋊D13—44no—
503C22⋊D13—44no—
504C2×Dic13—24no—
505C2×Dic13—24no—
506C2×Dic13—22no—
507C2×Dic13—24no—
508C2×Dic13—22no—
509C2×Dic13—216no—
510C2×Dic13—24no—
511C2×Dic13—24no—
512C2×Dic13—24no—
513C2×Dic13—28no—
514C2×Dic13—216no—
515C2×Dic13—28no—
516C2×Dic13—48no—
517C2×Dic13—44no—
518C2×Dic13—44no—
519C2×Dic13—48no—
520C2×Dic13H(5,𝔽2)14yes—
521C2×Dic13C2514yes—
522C2×Dic13C2514yes—
523C2×Dic13C2514yes—
524C2×Dic13C2512yes—
525C2×Dic13C2514yes—
526C2×Dic13C2514yes—
527C2×Dic13C2512yes—
528C2×Dic13C2514yes—
529C2×Dic13C2512yes—
530C4×D13—28no—
531C4×D13—48no—
532Dic26—216no—
533Dic26—216no—
534Dic26—48no—
535Dic26—48no—
536Dic26—48no—
537Dic26—44no—
538Dic26—44no—
539C22×#41—131no—
540C23×Q8—131no—
541C23×Q8—132no—
542C23×Q8—131no—
543C24×C4—131no—
544#563—1332no—
545#563—1316no—
546#563—1316no—
547#552—1332no—
548#552—1332no—
549#551—1316no—
550#551—1332no—
551#551C2×D13116yescomplemented
552D4×Q8—1332no—
553D4×Q8—1332no—
554#544—1332no—
555#544—1332no—
556#541—1332no—
557#539—1332no—
558#539—1332no—
559#536—1316no—
560#536—1316no—
561C2×C4⋊Q8—131no—
562C2×C4⋊Q8—132no—
563C2×C4⋊Q8—132no—
564C2×C4⋊Q8—132no—
565C2×C4⋊Q8—132no—
566C2×C4⋊Q8—132no—
567C2×C4⋊Q8—131no—
568C2×C4⋊Q8—132no—
569C2×#126—132no—
570C2×#126—132no—
571C2×#126—132no—
572C2×#126—132no—
573C2×#126—132no—
574C2×#126—132no—
575C2×#126—132no—
576C2×#126C2×D1312yes—
577C2×#125—132no—
578C2×#125—132no—
579C2×#125—132no—
580C2×#125—132no—
581C2×#125—132no—
582C2×#125—132no—
583C2×#125—132no—
584C2×#125—132no—
585C2×#125—132no—
586C2×#124—131no—
587C2×#124—132no—
588C2×#124C2×D1311yescharacteristic
589#525—1316no—
590C2×#123—131no—
591C2×#123—131no—
592C2×#123—132no—
593C2×#123—132no—
594C2×#123—131no—
595C2×#123—132no—
596C2×#123—132no—
597C2×#123—131no—
598C2×#123—132no—
599C2×#123—131no—
600C2×#123C2×D1311yescharacteristic
601C2×#123C2×D1312yes—
602C2×C22⋊Q8—132no—
603C2×C22⋊Q8—132no—
604C2×C22⋊Q8—132no—
605C2×C22⋊Q8—132no—
606C2×C22⋊Q8—132no—
607C2×C22⋊Q8—132no—
608C2×C22⋊Q8—132no—
609C2×C22⋊Q8—132no—
610C2×C22⋊Q8—132no—
611C2×C22⋊Q8—132no—
612C2×C22⋊Q8—132no—
613C2×C22⋊Q8—132no—
614C2×C22⋊Q8—132no—
615C2×C22⋊Q8—132no—
616C2×C22⋊Q8—132no—
617C2×C22⋊Q8—132no—
618C2×C22⋊Q8—1332no—
619C2×C22⋊Q8—132no—
620C2×C22⋊Q8—132no—
621C2×C22⋊Q8C2×D1312yes—
622C2×#121—132no—
623C2×#120—131no—
624C2×#120C2×D1311yescharacteristic
625C2×C4×Q8—132no—
626C2×C4×Q8—132no—
627C2×C4×D4—132no—
628C2×C4×D4—132no—
629C2×C4×D4—132no—
630C2×C4×D4—132no—
631C2×C4×D4—132no—
632C2×C4×D4C2×D1312yes—
633C2×#117—132no—
634C2×#117—131no—
635C2×#117—132no—
636C2×#117—132no—
637C2×#117—131no—
638C2×#117—131no—
639C2×#117C2×D1312yes—
640C22×C4⋊C4—132no—
641C22×C4⋊C4—132no—
642C22×C4⋊C4—132no—
643C22×C22⋊C4—132no—
644C22×C22⋊C4C2×D1312yes—
645C22×C13—24no—
646C22×C13—24no—
647C22×C13—216no—
648C22×C13—22no—
649C22×C13—22no—
650C22×C13—24no—
651C22×C13—24no—
652C22×C13—416no—
653C22×C13—44no—
654C22×C13—44no—
655C22×C13C2×H(5,𝔽2)12yes—
656C22×C13C2×2−1+418yes—
657C22×C13C2×2−1+414yes—
658C22×C13C2611yescharacteristic
659C2×D13—22no—
660C2×D13—24no—
661C2×D13—44no—
662C4×C13—24no—
663C4×C13—24no—
664C4×C13—22no—
665C4×C13—24no—
666C4×C13—24no—
667C4×C13—24no—
668Dic13—24no—
669Dic13—24no—
670Dic13—22no—
671Dic13—24no—
672Dic13—22no—
673Dic13—24no—
674Dic13—24no—
675Dic13—24no—
676Dic13C2×H(5,𝔽2)14yes—
677C25C22×D1311yescharacteristic
678C2×#41—138no—
679C2×#41—524no—
680C22×Q8—138no—
681C22×Q8—132no—
682C22×Q8—132no—
683C22×Q8—132no—
684C22×Q8—132no—
685C22×Q8—132no—
686C22×Q8—131no—
687C22×Q8—131no—
688C22×Q8—1316no—
689C22×Q8—138no—
690C22×Q8—528no—
691C22×Q8—524no—
692C22×Q8—524no—
693C22×Q8C22×D1311yescharacteristic
694C22×D4—132no—
695C22×D4—131no—
696C22×D4—131no—
697C22×D4C22×D1312yes—
698C22×D4C22×D1311yescharacteristic
699C23×C4—132no—
700C23×C4—132no—
701C23×C4—131no—
702C23×C4—131no—
703C23×C4—132no—
704C23×C4—132no—
705C23×C4—131no—
706C23×C4—131no—
707C23×C4—138no—
708C23×C4—131no—
709C23×C4—132no—
710C23×C4—524no—
711C23×C4C22×D1312yes—
712C23×C4C22×D1312yes—
713C23×C4C22×D1311yescharacteristic
714C4⋊Q8—138no—
715C4⋊Q8—1316no—
716C4⋊Q8—1316no—
717C4⋊Q8—1316no—
718C4⋊Q8—1316no—
719C4⋊Q8—1316no—
720C4⋊Q8—138no—
721C4⋊Q8—1316no—
722#126—1316no—
723#126—1316no—
724#126—1316no—
725#126—1316no—
726#126—1316no—
727#126—1316no—
728#126—1316no—
729#126C22×D13116yes—
730#125—1316no—
731#125—1316no—
732#125—1316no—
733#125—1316no—
734#125—1316no—
735#125—1316no—
736#125—1316no—
737#125—1316no—
738#125—1316no—
739#124—138no—
740#124—1316no—
741#124C22×D1318yes—
742#123—138no—
743#123—138no—
744#123—1316no—
745#123—138no—
746#123—1316no—
747#123—138no—
748#123—1316no—
749#123—138no—
750#123—1316no—
751#123—1316no—
752#123C22×D1318yes—
753#123C22×D13116yes—
754C22⋊Q8—1316no—
755C22⋊Q8—1316no—
756C22⋊Q8—1316no—
757C22⋊Q8—1316no—
758C22⋊Q8—1316no—
759C22⋊Q8—1316no—
760C22⋊Q8—1316no—
761C22⋊Q8—1316no—
762C22⋊Q8—1316no—
763C22⋊Q8—1316no—
764C22⋊Q8—1316no—
765C22⋊Q8—1316no—
766C22⋊Q8—1316no—
767C22⋊Q8—1316no—
768C22⋊Q8—1316no—
769C22⋊Q8—1316no—
770C22⋊Q8—1316no—
771C22⋊Q8—1316no—
772C22⋊Q8C22×D13116yes—
773#121—1316no—
774#120—138no—
775#120C22×D1318yes—
776C4×Q8—1316no—
777C4×Q8—1316no—
778C4×D4—1316no—
779C4×D4—1316no—
780C4×D4—1316no—
781C4×D4—1316no—
782C4×D4—1316no—
783C4×D4C22×D13116yes—
784#117—1316no—
785#117—138no—
786#117—138no—
787#117—1316no—
788#117—1316no—
789#117—138no—
790#117C22×D13116yes—
791C2×C4⋊C4—132no—
792C2×C4⋊C4—132no—
793C2×C4⋊C4—132no—
794C2×C4⋊C4—132no—
795C2×C4⋊C4—132no—
796C2×C4⋊C4—132no—
797C2×C4⋊C4—132no—
798C2×C4⋊C4—132no—
799C2×C4⋊C4—132no—
800C2×C4⋊C4—132no—
801C2×C4⋊C4—132no—
802C2×C4⋊C4—132no—
803C2×C4⋊C4—1316no—
804C2×C4⋊C4—1316no—
805C2×C4⋊C4—1316no—
806C2×C4⋊C4—132no—
807C2×C4⋊C4—132no—
808C2×C4⋊C4—132no—
809C2×C4⋊C4—132no—
810C2×C4⋊C4—132no—
811C2×C4⋊C4—132no—
812C2×C4⋊C4—132no—
813C2×C4⋊C4—132no—
814C2×C4⋊C4—132no—
815C2×C4⋊C4—132no—
816C2×C4⋊C4—132no—
817C2×C4⋊C4—132no—
818C2×C4⋊C4—132no—
819C2×C4⋊C4—132no—
820C2×C4⋊C4—132no—
821C2×C4⋊C4C22×D1312yes—
822C2×C4⋊C4C22×D1312yes—
823C2×C4⋊C4C22×D1312yes—
824C2×C4⋊C4C22×D1312yes—
825C2×C22⋊C4—132no—
826C2×C22⋊C4—132no—
827C2×C22⋊C4—132no—
828C2×C22⋊C4—132no—
829C2×C22⋊C4—1316no—
830C2×C22⋊C4—132no—
831C2×C22⋊C4—131no—
832C2×C22⋊C4—131no—
833C2×C22⋊C4—132no—
834C2×C22⋊C4—132no—
835C2×C22⋊C4—132no—
836C2×C22⋊C4—132no—
837C2×C22⋊C4—132no—
838C2×C22⋊C4—132no—
839C2×C22⋊C4C22×D1312yes—
840C2×C22⋊C4C22×D1312yes—
841C2×C22⋊C4C22×D1312yes—
842C2×C22⋊C4C22×D1312yes—
843C2×C22⋊C4C22×D13116yes—
844C2×C22⋊C4C22×D1312yes—
845C2×C22⋊C4C22×D1311yescharacteristic
846C2×C22⋊C4C22×D1311yescharacteristic
847C2×C22⋊C4C22×D1312yes—
848C2×C42—131no—
849C2×C42—132no—
850C2×C42—132no—
851C2×C42—132no—
852C2×C42—132no—
853C2×C42—132no—
854C2×C42C22×D1311yescharacteristic
855C2×C42C22×D1312yes—
856C2×C13—28no—
857C2×C13—42no—
858C2×C13—42no—
859C2×C13#353814yescomplemented
860C2×C13C22×H(5,𝔽2)11yescharacteristic
861C2×C13C22×2−1+412yes—
862D13—42no—
863C24—28no—
864C24—42no—
865C24—131no—
866C24C23×D1311yescharacteristic
867C24C23×D1311yescharacteristic
868C24C23×D1314yes—
869C24C23×D1312yes—
870#41—5216no—
871C2×Q8—42no—
872C2×Q8—138no—
873C2×Q8—138no—
874C2×Q8—138no—
875C2×Q8—138no—
876C2×Q8—138no—
877C2×Q8—134no—
878C2×Q8—134no—
879C2×Q8—268no—
880C2×Q8—268no—
881C2×Q8—524no—
882C2×Q8—524no—
883C2×Q8—524no—
884C2×Q8—522no—
885C2×Q8—522no—
886C2×Q8—5232no—
887C2×Q8—5216no—
888C2×Q8—5216no—
889C2×Q8C23×D1314yes—
890C2×D4—28no—
891C2×D4—42no—
892C2×D4—138no—
893C2×D4—134no—
894C2×D4—134no—
895C2×D4—268no—
896C2×D4—522no—
897C2×D4—522no—
898C2×D4C23×D1318yes—
899C2×D4C23×D1314yes—
900C22×C4—28no—
901C22×C4—42no—
902C22×C4—44no—
903C22×C4—131no—
904C22×C4—138no—
905C22×C4—138no—
906C22×C4—134no—
907C22×C4—134no—
908C22×C4—132no—
909C22×C4—132no—
910C22×C4—132no—
911C22×C4—131no—
912C22×C4—132no—
913C22×C4—132no—
914C22×C4—132no—
915C22×C4—131no—
916C22×C4—138no—
917C22×C4—138no—
918C22×C4—134no—
919C22×C4—134no—
920C22×C4—134no—
921C22×C4—138no—
922C22×C4—264no—
923C22×C4—268no—
924C22×C4—264no—
925C22×C4—264no—
926C22×C4—268no—
927C22×C4—524no—
928C22×C4—5216no—
929C22×C4—524no—
930C22×C4—522no—
931C22×C4—524no—
932C22×C4—522no—
933C22×C4C23×D1318yes—
934C22×C4C23×D1312yes—
935C22×C4C23×D1312yes—
936C22×C4C23×D1311yescharacteristic
937C22×C4C23×D1312yes—
938C22×C4C23×D1312yes—
939C22×C4C23×D1312yes—
940C22×C4C23×D1318yes—
941C22×C4C23×D1314yes—
942C4⋊C4—138no—
943C4⋊C4—138no—
944C4⋊C4—138no—
945C4⋊C4—138no—
946C4⋊C4—138no—
947C4⋊C4—138no—
948C4⋊C4—138no—
949C4⋊C4—138no—
950C4⋊C4—138no—
951C4⋊C4—138no—
952C4⋊C4—138no—
953C4⋊C4—138no—
954C4⋊C4—138no—
955C4⋊C4—138no—
956C4⋊C4—138no—
957C4⋊C4—138no—
958C4⋊C4—138no—
959C4⋊C4—138no—
960C4⋊C4—138no—
961C4⋊C4—138no—
962C4⋊C4—138no—
963C4⋊C4—138no—
964C4⋊C4—138no—
965C4⋊C4—138no—
966C4⋊C4—138no—
967C4⋊C4—138no—
968C4⋊C4—138no—
969C4⋊C4C23×D1318yes—
970C4⋊C4C23×D1318yes—
971C4⋊C4C23×D1318yes—
972C4⋊C4C23×D1318yes—
973C22⋊C4—138no—
974C22⋊C4—138no—
975C22⋊C4—138no—
976C22⋊C4—138no—
977C22⋊C4—138no—
978C22⋊C4—134no—
979C22⋊C4—134no—
980C22⋊C4—138no—
981C22⋊C4—138no—
982C22⋊C4—138no—
983C22⋊C4—138no—
984C22⋊C4—138no—
985C22⋊C4—138no—
986C22⋊C4C23×D1318yes—
987C22⋊C4C23×D1318yes—
988C22⋊C4C23×D1318yes—
989C22⋊C4C23×D1318yes—
990C22⋊C4C23×D1318yes—
991C22⋊C4C23×D1314yes—
992C22⋊C4C23×D1314yes—
993C22⋊C4C23×D1318yes—
994C42—134no—
995C42—138no—
996C42—138no—
997C42—138no—
998C42—138no—
999C42—138no—
1000C42C23×D1314yes—
1001C42C23×D1318yes—
1002C13C2×#353811yescharacteristic, complemented, Sylow
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—216no—
1007C23—24no—
1008C23—22no—
1009C23—22no—
1010C23—44no—
1011C23—416no—
1012C23—132no—
1013C23—264no—
1014C23—262no—
1015C23#8825718yes—
1016C23C24×D1312yes—
1017C23C24×D1312yes—
1018C23C24×D1314yes—
1019C23C24×D1311yescharacteristic
1020Q8—44no—
1021Q8—2616no—
1022Q8—2616no—
1023Q8—528no—
1024Q8—528no—
1025Q8—528no—
1026Q8—524no—
1027Q8—524no—
1028D4—216no—
1029D4—44no—
1030D4—2616no—
1031D4—524no—
1032D4—524no—
1033C2×C4—216no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—44no—
1041C2×C4—48no—
1042C2×C4—134no—
1043C2×C4—132no—
1044C2×C4—134no—
1045C2×C4—134no—
1046C2×C4—134no—
1047C2×C4—132no—
1048C2×C4—134no—
1049C2×C4—134no—
1050C2×C4—134no—
1051C2×C4—132no—
1052C2×C4—268no—
1053C2×C4—2616no—
1054C2×C4—268no—
1055C2×C4—268no—
1056C2×C4—2616no—
1057C2×C4—264no—
1058C2×C4—264no—
1059C2×C4—264no—
1060C2×C4—262no—
1061C2×C4—264no—
1062C2×C4—262no—
1063C2×C4—264no—
1064C2×C4—264no—
1065C2×C4—528no—
1066C2×C4—528no—
1067C2×C4—524no—
1068C2×C4—528no—
1069C2×C4—524no—
1070C2×C4C24×D1314yes—
1071C2×C4C24×D1314yes—
1072C2×C4C24×D1312yes—
1073C2×C4C24×D1314yes—
1074C2×C4C24×D1314yes—
1075C2×C4C24×D1314yes—
1076C22—216no—
1077C22—24no—
1078C22—24no—
1079C22—22no—
1080C22—22no—
1081C22—24no—
1082C22—24no—
1083C22—416no—
1084C22—44no—
1085C22—44no—
1086C22—262no—
1087C22—264no—
1088C22—524no—
1089C22C2×#8825718yes—
1090C22C2×#8825714yes—
1091C22D13×H(5,𝔽2)12yes—
1092C22C25×D1311yescharacteristic
1093C4—24no—
1094C4—24no—
1095C4—22no—
1096C4—24no—
1097C4—24no—
1098C4—24no—
1099C4—134no—
1100C4—262no—
1101C4—264no—
1102C4—262no—
1103C4—264no—
1104C4—264no—
1105C4—264no—
1106C4—264no—
1107C4—264no—
1108C2—28no—
1109C2—42no—
1110C2—42no—
1111C2—522no—
1112C2#1312907614yesdirect product factor
1113C2C2×D13×H(5,𝔽2)11yescharacteristic
1114C2C22×#8825712yes—
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#551C2
socleC23×C13C25
prime radicalC2×#11719291C2
hypercenterC2×#551D13
hypocenterC13C2×#3538
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#551

Complements

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

NH ≅ G/Ntype
1. #13129076C2direct (N × H)
2. C2×#11719356C2semidirect
3. C2×#11719417C2semidirect
4. C2×#11719377C2semidirect
5. C2×#11719355C2semidirect
6. C2×#11719236C2semidirect
7. C2×#11719292C2semidirect
8. C2×#11719200C2semidirect
9. C2×D4×Dic26C2semidirect
10. C2×#11719337C2semidirect
11. C2×#11719328C2semidirect
12. C2×#11719224C2semidirect
13. C2×#11719406C2semidirect
14. C2×#11719370C2semidirect
15. C2×#11719269C2semidirect
16. C2×#11719353C2semidirect
17. C2×#11719380C2semidirect
19. C22×#88132C2semidirect
20. C2×C13×#551C2semidirect
22. C22×Q8×D13C22semidirect
25. C23×Dic26C22semidirect
26. C13×#551C22semidirect
38. C2×#88198C22semidirect
39. C2×#88198C22semidirect
48. C2×#88183C22semidirect
53. C2×#88178C22semidirect
56. #11719417C22semidirect
57. #11719406C22semidirect
58. #11719380C22semidirect
59. #11719377C22semidirect
60. #11719370C22semidirect
61. #11719356C22semidirect
62. #11719355C22semidirect
63. #11719353C22semidirect
64. #11719337C22semidirect
65. #11719328C22semidirect
66. #11719292C22semidirect
68. #11719269C22semidirect
69. D4×Dic26C22semidirect
70. #11719236C22semidirect
71. #11719224C22semidirect
72. C2×#88152C22semidirect
73. C2×#88151C22semidirect
74. C2×#88150C22semidirect
75. C2×#88150C22semidirect
76. C2×#88144C22semidirect
77. C2×#88144C22semidirect
78. C2×#88143C22semidirect
79. C2×#88143C22semidirect
80. C2×#88143C22semidirect
81. C2×#88143C22semidirect
82. C2×#88143C22semidirect
83. C2×#88142C22semidirect
84. C2×#88142C22semidirect
85. C2×#88142C22semidirect
86. C2×#88142C22semidirect
87. C2×#88141C22semidirect
88. #11719200C22semidirect
91. C2×#88140C22semidirect
94. C2×#88137C22semidirect
100. C2×#88133C22semidirect
101. C2×#88133C22semidirect
113. C2×#88132C22semidirect
114. C2×#88132C22semidirect
115. C2×#88132C22semidirect
119. C2×#88131C22semidirect
120. C2×#88130C22semidirect
121. C2×#88126C22semidirect
122. C2×#88124C22semidirect
123. C2×#88124C22semidirect
124. C2×#88123C22semidirect
125. C2×#88123C22semidirect
126. C2×C4×Dic26C22semidirect
148. C2×Q8×D13C23semidirect
163. C22×Dic26C23semidirect
198. #88198C23semidirect
199. #88198C23semidirect
208. #88183C23semidirect
226. #88178C23semidirect
253. #88152C23semidirect
254. #88151C23semidirect
255. #88150C23semidirect
256. #88150C23semidirect
257. #88144C23semidirect
258. #88144C23semidirect
259. #88143C23semidirect
260. #88143C23semidirect
261. #88143C23semidirect
262. #88143C23semidirect
263. #88143C23semidirect
264. #88142C23semidirect
265. #88142C23semidirect
266. #88142C23semidirect
267. #88142C23semidirect
268. #88141C23semidirect
271. #88140C23semidirect
274. #88137C23semidirect
280. #88133C23semidirect
281. #88133C23semidirect
293. #88132C23semidirect
294. #88132C23semidirect
298. #88131C23semidirect
299. #88130C23semidirect
300. #88126C23semidirect
301. #88124C23semidirect
302. #88124C23semidirect
303. #88123C23semidirect
304. #88123C23semidirect
305. C4×Dic26C23semidirect
454. C2×#551D13semidirect
551. #551C2×D13semidirect
859. C2×C13#3538semidirect
1002. C13C2×#3538semidirect
1112. C2#13129076direct (N × H)

Maximal subgroups

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

subgroupindex
#131290762
C2×#117193562
C2×#117194172
C2×#117193772
C2×#117193552
C2×#117192362
C2×#117192922
C2×#117192002
C2×D4×Dic262
C2×#117193372
C2×#117193282
C2×#117192242
C2×#117194062
C2×#117193702
C2×#117192692
C2×#117193532
C2×#117193802
C2×#117192912
C22×#881322
C2×C13×#5512
C2×#353813