Finite Group Databasebeta

← C2×#13129233 #16770710

Subgroups — C2×#13129233 #16770710

Order 3328.

7810 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129233C2132yesmaximal, direct product factor
2C2×#11719372C214yesmaximal, complemented
3C2×#11719340C212yesmaximal, complemented
4C2×#11719216C212yesmaximal, complemented
5C2×#11719539C212yesmaximal, complemented
6C2×#11719304C212yesmaximal, complemented
7C2×#11719256C211yesmaximal, characteristic, complemented
8C2×#11719260C211yesmaximal, characteristic, complemented
9C2×#11719431C211yesmaximal, characteristic, complemented
10C2×#11719368C214yesmaximal, complemented
11C2×#11719215C212yesmaximal, complemented
12C2×#11719334C212yesmaximal, complemented
13C2×#11719313C212yesmaximal, complemented
14C2×#11719538C212yesmaximal, complemented
15C2×#11719433C211yesmaximal, characteristic, complemented
16C2×#11719253C211yesmaximal, characteristic, complemented
17C2×#11719253C211yesmaximal, characteristic, complemented
18C2×C13×#547C211yesmaximal, characteristic, complemented
19C22×C13×#41C2212yes—
20C22×#6131C2212yes—
21C22×#6129C2212yes—
22C22×#6127C2212yes—
23C22×#6127C2212yes—
24C22×#6127C2212yes—
25C13×#547C22116yescomplemented
26C2×C13×C4⋊Q8C2211yescharacteristic
27C2×C13×#123C2214yes—
28C2×C13×C22⋊Q8C2212yes—
29C2×C13×#121C2212yes—
30C2×C4×D4×C13C2211yescharacteristic
31C2×C4×D4×C13C2211yescharacteristic
32C22×C13×C4⋊C4C2212yes—
33#11719539C22132yescomplemented
34#11719538C22132yescomplemented
35C2×#88200C2212yes—
36C2×#88200C2212yes—
37C2×Q8×Dic13C2212yes—
38C2×#88194C2214yes—
39C2×#88194C2211yescharacteristic
40C2×#88194C2211yescharacteristic
41C2×#88193C2214yes—
42C2×#88193C2214yes—
43C2×#88192C2214yes—
44C2×#88192C2212yes—
45C2×#88192C2211yescharacteristic
46C2×#88192C2211yescharacteristic
47C2×#88184C2214yes—
48C2×#88184C2214yes—
49C2×#88184C2212yes—
50C2×C4×C22⋊D13C2214yes—
51C2×C4×C22⋊D13C2212yes—
52C2×C4×C22⋊D13C2212yes—
53C22×C4⋊Dic13C2212yes—
54C2×#88178C2214yes—
55C2×#88178C2212yes—
56#11719433C22116yescomplemented
57#11719431C22116yescomplemented
58#11719372C22164yescomplemented
59#11719368C22164yescomplemented
60#11719340C22132yescomplemented
61#11719334C22132yescomplemented
62#11719313C22132yescomplemented
63#11719304C22132yescomplemented
64#11719260C22116yescomplemented
65#11719256C22116yescomplemented
66#11719253C22116yescomplemented
67#11719253C22116yescomplemented
68#11719216C22132yescomplemented
69#11719215C22132yescomplemented
70C2×#88151C2214yes—
71C2×#88151C2212yes—
72C2×#88151C2212yes—
73C2×#88150C2214yes—
74C2×#88149C2214yes—
75C2×#88149C2212yes—
76C2×#88149C2211yescharacteristic
77C2×#88149C2211yescharacteristic
78C2×#88148C2214yes—
79C2×#88146C2212yes—
80C2×C4⋊C4×D13C2212yes—
81C2×C4⋊C4×D13C2212yes—
82C2×#88144C2212yes—
83C2×#88143C2214yes—
84C2×#88142C2211yescharacteristic
85C2×#88142C2211yescharacteristic
86C2×#88141C2212yes—
87C2×#88140C2214yes—
88C2×#88139C2212yes—
89C2×#88139C2212yes—
90C2×#88138C2212yes—
91C2×#88138C2212yes—
92C2×#88138C2214yes—
93C2×#88138C2214yes—
94C2×#88137C2214yes—
95C2×#88135C2214yes—
96C2×#88132C2214yes—
97C2×C4×D52C2211yescharacteristic
98C2×C4×D52C2211yescharacteristic
99C2×C42×D13C2211yescharacteristic
100C2×#88123C2211yescharacteristic
101C2×C13×#41—48no—
102C2×C13×#41C23116yes—
103C22×Q8×C13C2312yes—
104C22×D4×C13C2311yescharacteristic
105C22×D4×C13C2311yescharacteristic
106C22×D4×C13C2314yes—
107C23×C4×C13C2312yes—
108C23×C4×C13C2312yes—
109C23×C4×C13C2314yes—
110C22×C22⋊D13C2312yes—
111C22×C22⋊D13C2312yes—
112C22×C22⋊D13C2314yes—
113C22×C22⋊D13C2312yes—
114C22×C22⋊D13C2312yes—
115C22×C22⋊D13C2314yes—
116C22×C22⋊D13C2312yes—
117C22×C22⋊D13C2312yes—
118C23×Dic13C2314yes—
119C2×#6131—48no—
120C2×#6131C23116yes—
121C2×#6129—48no—
122C2×#6129C23116yes—
123C2×#6127—48no—
124C2×#6127—48no—
125C2×#6127—48no—
126C2×#6127C23116yes—
127C2×#6127C23116yes—
128C2×#6127C23116yes—
129C22×D52C2311yescharacteristic
130C22×D52C2311yescharacteristic
131C22×D52C2312yes—
132C22×D52C2314yes—
133C22×D52C2312yes—
134C22×C4×D13C2311yescharacteristic
135C22×C4×D13C2311yescharacteristic
136C22×C4×D13C2311yescharacteristic
137C22×C4×D13C2312yes—
138C22×C4×D13C2312yes—
139C22×C4×D13C2314yes—
140C22×C4×D13C2314yes—
141C22×Dic26C2312yes—
142C22×Dic26C2312yes—
143C22×Dic26C2312yes—
144C13×C4⋊Q8C2318yes—
145C13×#123C23132yes—
146C13×C22⋊Q8C23116yes—
147C13×#121C23116yes—
148C4×D4×C13C2318yes—
149C4×D4×C13C2318yes—
150C2×C13×C4⋊C4C2312yes—
151C2×C13×C4⋊C4C2311yescharacteristic
152C2×C13×C4⋊C4C2311yescharacteristic
153C2×C13×C4⋊C4C2314yes—
154C2×C13×C4⋊C4C2312yes—
155C2×C13×C4⋊C4C23116yes—
156C2×C13×C22⋊C4C2314yes—
157C2×C13×C22⋊C4C2312yes—
158C2×C13×C22⋊C4C2312yes—
159C2×C42×C13C2311yescharacteristic
160C2×C22⋊Dic13C2312yes—
161C2×C22⋊Dic13C2314yes—
162C2×C22⋊Dic13C2312yes—
163#88200C23116yes—
164#88200C23116yes—
165Q8×Dic13C23116yes—
166#88194C2318yes—
167#88194C2318yes—
168#88194C23132yes—
169#88193C23132yes—
170#88193C23132yes—
171#88192C2318yes—
172#88192C2318yes—
173#88192C23116yes—
174#88192C23132yes—
175#88184C23132yes—
176#88184C23132yes—
177#88184C23116yes—
178C4×C22⋊D13C23116yes—
179C4×C22⋊D13C23132yes—
180C4×C22⋊D13C23116yes—
181C2×#6103C2312yes—
182C2×#6103C2312yes—
183C2×#6103C2314yes—
184C2×#6103C2312yes—
185C2×#6103C2314yes—
186C2×#6103C2312yes—
187C2×#6103C2314yes—
188C2×C4⋊Dic13C2312yes—
189C2×C4⋊Dic13C2312yes—
190C2×C4⋊Dic13C2311yescharacteristic
191C2×C4⋊Dic13C2311yescharacteristic
192C2×C4⋊Dic13C2314yes—
193C2×C4⋊Dic13C2314yes—
194C2×C4⋊Dic13C23116yes—
195#88178C23116yes—
196#88178C23132yes—
197C2×#6101C2314yes—
198C2×#6101C2314yes—
199C2×#6101C2312yes—
200C2×#6101C2314yes—
201C2×#6101C2312yes—
202C2×C4×Dic13C2311yescharacteristic
203C2×C4×Dic13C2311yescharacteristic
204C2×C4×Dic13C2311yescharacteristic
205C2×C4×Dic13C2314yes—
206#88151C23116yes—
207#88151C23116yes—
208#88151C23132yes—
209#88150C23132yes—
210#88149C23116yes—
211#88149C2318yes—
212#88149C23132yes—
213#88149C2318yes—
214#88148C23132yes—
215#88146C23116yes—
216C4⋊C4×D13C23116yes—
217C4⋊C4×D13C23116yes—
218#88144C23116yes—
219#88143C23132yes—
220#88142C2318yes—
221#88142C2318yes—
222#88141C23116yes—
223#88140C23132yes—
224#88139C23116yes—
225#88139C23116yes—
226#88138C23116yes—
227#88138C23116yes—
228#88138C23132yes—
229#88138C23132yes—
230#88137C23132yes—
231#88135C23132yes—
232#88132C23132yes—
233C4×D52C2318yes—
234C4×D52C2318yes—
235C42×D13C2318yes—
236#88123C2318yes—
237C2×#3548—131nomaximal, Sylow
238C24×C13C2412yes—
239C24×C13C2412yes—
240C23×D13C2412yes—
241C23×D13C2411yescharacteristic
242C23×D13C2412yes—
243C13×#41—432no—
244C2×Q8×C13—28no—
245C2×Q8×C13C2418yes—
246C2×D4×C13—24no—
247C2×D4×C13—24no—
248C2×D4×C13—48no—
249C2×D4×C13C2414yes—
250C2×D4×C13C2414yes—
251C2×D4×C13C24116yes—
252C22×C4×C13—28no—
253C22×C4×C13—28no—
254C22×C4×C13—48no—
255C22×C4×C13C2414yes—
256C22×C4×C13C2411yescharacteristic
257C22×C4×C13C2412yes—
258C22×C4×C13C2412yes—
259C22×C4×C13C2418yes—
260C22×C4×C13C2418yes—
261C22×C4×C13C24116yes—
262C22×C4×C13C2411yescharacteristic
263C22×C4×C13C2411yescharacteristic
264C2×C22⋊D13—28no—
265C2×C22⋊D13—28no—
266C2×C22⋊D13—48no—
267C2×C22⋊D13—44no—
268C2×C22⋊D13—44no—
269C2×C22⋊D13—44no—
270C2×C22⋊D13—44no—
271C2×C22⋊D13—48no—
272C2×C22⋊D13C2418yes—
273C2×C22⋊D13C2418yes—
274C2×C22⋊D13C24116yes—
275C2×C22⋊D13C2418yes—
276C2×C22⋊D13C2418yes—
277C2×C22⋊D13C24116yes—
278C2×C22⋊D13C2418yes—
279C2×C22⋊D13C2418yes—
280C22×Dic13—48no—
281C22×Dic13C2411yescharacteristic
282C22×Dic13C2411yescharacteristic
283C22×Dic13C2414yes—
284C22×Dic13C2412yes—
285C22×Dic13C2412yes—
286C22×Dic13C24116yes—
287C22×Dic13C2411yescharacteristic
288#6131—432no—
289#6129—432no—
290#6127—432no—
291#6127—432no—
292#6127—432no—
293C2×D52—24no—
294C2×D52—24no—
295C2×D52—44no—
296C2×D52—44no—
297C2×D52—48no—
298C2×D52C2414yes—
299C2×D52C2414yes—
300C2×D52C2418yes—
301C2×D52C24116yes—
302C2×D52C2418yes—
303C2×C4×D13—24no—
304C2×C4×D13—24no—
305C2×C4×D13—28no—
306C2×C4×D13—28no—
307C2×C4×D13—24no—
308C2×C4×D13—48no—
309C2×C4×D13—48no—
310C2×C4×D13C2414yes—
311C2×C4×D13C2414yes—
312C2×C4×D13C2414yes—
313C2×C4×D13C2418yes—
314C2×C4×D13C2418yes—
315C2×C4×D13C24116yes—
316C2×C4×D13C24116yes—
317C2×Dic26—28no—
318C2×Dic26—44no—
319C2×Dic26—44no—
320C2×Dic26C2418yes—
321C2×Dic26C2418yes—
322C2×Dic26C2418yes—
323C13×C4⋊C4C2418yes—
324C13×C4⋊C4C2414yes—
325C13×C4⋊C4C2414yes—
326C13×C4⋊C4C24116yes—
327C13×C4⋊C4C2418yes—
328C13×C22⋊C4C24116yes—
329C13×C22⋊C4C2418yes—
330C13×C22⋊C4C2418yes—
331C42×C13C2414yes—
332C22⋊Dic13C2418yes—
333C22⋊Dic13C24116yes—
334C22⋊Dic13C2418yes—
335#6103C2418yes—
336#6103C2418yes—
337#6103C24116yes—
338#6103C2418yes—
339#6103C24116yes—
340#6103C2418yes—
341#6103C24116yes—
342C4⋊Dic13C2418yes—
343C4⋊Dic13C2418yes—
344C4⋊Dic13C2414yes—
345C4⋊Dic13C2414yes—
346C4⋊Dic13C24116yes—
347C4⋊Dic13C24116yes—
348#6101C24116yes—
349#6101C24116yes—
350#6101C2418yes—
351#6101C24116yes—
352#6101C2418yes—
353C4×Dic13C2414yes—
354C4×Dic13C2414yes—
355C4×Dic13C2414yes—
356C4×Dic13C24116yes—
357#3548—1332no—
358C2×#562—134no—
359C2×#554—132no—
360C2×#554—132no—
361C2×#550—132no—
362C2×#550—132no—
363C2×#547—131no—
364C2×#547—131no—
365C2×#547—131no—
366C2×#547D1311yescharacteristic, complemented
367C2×#540—134no—
368C2×#537—132no—
369C2×#537—132no—
370C2×#537—132no—
371C2×#537—132no—
372C2×#533—131no—
373C2×#532—131no—
374C2×#532—131no—
375C23×C13—24no—
376C23×C13—24no—
377C23×C13—24no—
378C23×C13—24no—
379C23×C13—24no—
380C23×C13—24no—
381C23×C13C2514yes—
382C23×C13C2514yes—
383C23×C13C2511yescharacteristic
384C22×D13—24no—
385C22×D13—22no—
386C22×D13—22no—
387C22×D13—24no—
388C22×D13—24no—
389C22×D13—24no—
390C22×D13—22no—
391C22×D13—24no—
392C22×D13—24no—
393C22×D13C2514yes—
394C22×D13C2512yes—
395C22×D13C2514yes—
396Q8×C13—216no—
397D4×C13—28no—
398D4×C13—28no—
399D4×C13—416no—
400C2×C4×C13—24no—
401C2×C4×C13—24no—
402C2×C4×C13—28no—
403C2×C4×C13—22no—
404C2×C4×C13—216no—
405C2×C4×C13—216no—
406C2×C4×C13—416no—
407C2×C4×C13H(5,𝔽2)14yes—
408C2×C4×C13H(5,𝔽2)14yes—
409C2×C4×C13C2518yes—
410C2×C4×C13C2512yes—
411C2×C4×C13C2514yes—
412C2×C4×C13C2514yes—
413C2×C4×C13C2512yes—
414C2×C4×C13C2512yes—
415C22⋊D13—216no—
416C22⋊D13—216no—
417C22⋊D13—416no—
418C22⋊D13—48no—
419C22⋊D13—48no—
420C22⋊D13—48no—
421C22⋊D13—48no—
422C22⋊D13—416no—
423C2×Dic13—28no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—24no—
427C2×Dic13—24no—
428C2×Dic13—416no—
429C2×Dic132−1+414yes—
430C2×Dic13C2512yes—
431C2×Dic13C2512yes—
432C2×Dic13C2518yes—
433C2×Dic13C2514yes—
434C2×Dic13C2514yes—
435C2×Dic13C2512yes—
436D52—28no—
437D52—28no—
438D52—48no—
439D52—48no—
440D52—416no—
441C4×D13—28no—
442C4×D13—28no—
443C4×D13—216no—
444C4×D13—216no—
445C4×D13—28no—
446C4×D13—416no—
447C4×D13—416no—
448Dic26—216no—
449Dic26—48no—
450Dic26—48no—
451C22×#41—132no—
452C22×#41—132no—
453C22×#41—132no—
454C22×#41—132no—
455C22×#41—132no—
456C22×#41C2×D1312yes—
457#562—1364no—
458#554—1332no—
459#554—1332no—
460#550—1332no—
461#550—1332no—
462#547—1316no—
463#547—1316no—
464#547—1316no—
465#547C2×D13116yescomplemented
466#540—1364no—
467#537—1332no—
468#537—1332no—
469#537—1332no—
470#537—1332no—
471#533—1316no—
472#532—1316no—
473#532—1316no—
474C2×C4⋊Q8—131no—
475C2×C4⋊Q8—131no—
476C2×C4⋊Q8—131no—
477C2×C4⋊Q8C2×D1311yescharacteristic
478C2×#127—131no—
479C2×#127—131no—
480C2×#127—134no—
481C2×#125—134no—
482C2×#125—132no—
483C2×#124—132no—
484C2×#124—132no—
485C2×#123—134no—
486C2×#123—134no—
487C2×#123—134no—
488C2×#123C2×D1314yes—
489C2×C22⋊Q8—132no—
490C2×C22⋊Q8—132no—
491C2×C22⋊Q8—132no—
492C2×C22⋊Q8—134no—
493C2×C22⋊Q8—134no—
494C2×C22⋊Q8—132no—
495C2×C22⋊Q8—132no—
496C2×C22⋊Q8—134no—
497C2×C22⋊Q8—134no—
498C2×C22⋊Q8C2×D1312yes—
499C2×#121—131no—
500C2×#121—131no—
501C2×#121—132no—
502C2×#121—134no—
503C2×#121—134no—
504C2×#121—134no—
505C2×#121—134no—
506C2×#121—132no—
507C2×#121—134no—
508C2×#121—131no—
509C2×#121—131no—
510C2×#121—134no—
511C2×#121—132no—
512C2×#121—132no—
513C2×#121—132no—
514C2×#121—134no—
515C2×#121—134no—
516C2×#121C2×D1312yes—
517C2×C4×Q8—132no—
518C2×C4×Q8—132no—
519C2×C4×D4—132no—
520C2×C4×D4—132no—
521C2×C4×D4—134no—
522C2×C4×D4—134no—
523C2×C4×D4—131no—
524C2×C4×D4—131no—
525C2×C4×D4C2×D1311yescharacteristic
526C2×C4×D4C2×D1311yescharacteristic
527C2×#117—132no—
528C22×C4⋊C4—132no—
529C22×C4⋊C4—132no—
530C22×C4⋊C4—132no—
531C22×C4⋊C4C2×D1312yes—
532C22×C42—131no—
533C22×C13—24no—
534C22×C13—24no—
535C22×C13—24no—
536C22×C13—24no—
537C22×C13—24no—
538C22×C13—24no—
539C22×C13—48no—
540C22×C13—48no—
541C22×C13C2×H(5,𝔽2)12yes—
542C22×C13C2×H(5,𝔽2)12yes—
543C22×C13C2×2−1+412yes—
544C22×C13C2611yescharacteristic
545C2×D13—24no—
546C2×D13—22no—
547C2×D13—22no—
548C2×D13—24no—
549C2×D13—24no—
550C2×D13—24no—
551C2×D13—22no—
552C2×D13—24no—
553C2×D13—24no—
554C2×D13—48no—
555C2×D13—44no—
556C2×D13—48no—
557C4×C13—24no—
558C4×C13—24no—
559C4×C13—28no—
560C4×C13—22no—
561C4×C13C2×H(5,𝔽2)14yes—
562C4×C13C2×H(5,𝔽2)14yes—
563Dic13—28no—
564Dic13—22no—
565Dic13—22no—
566Dic13—24no—
567Dic13—24no—
568Dic13C2×2−1+414yes—
569C2×#41—48no—
570C2×#41—1316no—
571C2×#41—1316no—
572C2×#41—1316no—
573C2×#41—1316no—
574C2×#41—1316no—
575C2×#41—528no—
576C2×#41—528no—
577C2×#41—528no—
578C2×#41—528no—
579C2×#41—528no—
580C2×#41C22×D13116yes—
581C22×Q8—132no—
582C22×Q8—132no—
583C22×Q8—132no—
584C22×Q8C22×D1312yes—
585C22×D4—132no—
586C22×D4—132no—
587C22×D4—132no—
588C22×D4—132no—
589C22×D4—134no—
590C22×D4—134no—
591C22×D4—132no—
592C22×D4—132no—
593C22×D4—131no—
594C22×D4—131no—
595C22×D4—132no—
596C22×D4—132no—
597C22×D4—134no—
598C22×D4C22×D1311yescharacteristic
599C22×D4C22×D1311yescharacteristic
600C22×D4C22×D1314yes—
601C23×C4—134no—
602C23×C4—132no—
603C23×C4—132no—
604C23×C4—131no—
605C23×C4—131no—
606C23×C4—131no—
607C23×C4—134no—
608C23×C4—134no—
609C23×C4C22×D1312yes—
610C23×C4C22×D1312yes—
611C23×C4C22×D1314yes—
612C4⋊Q8—138no—
613C4⋊Q8—138no—
614C4⋊Q8—138no—
615C4⋊Q8C22×D1318yes—
616#127—138no—
617#127—138no—
618#127—1332no—
619#125—1316no—
620#125—1332no—
621#124—1316no—
622#124—1316no—
623#123—1332no—
624#123—1332no—
625#123—1332no—
626#123C22×D13132yes—
627C22⋊Q8—1316no—
628C22⋊Q8—1316no—
629C22⋊Q8—1316no—
630C22⋊Q8—1332no—
631C22⋊Q8—1316no—
632C22⋊Q8—1316no—
633C22⋊Q8—1332no—
634C22⋊Q8—1332no—
635C22⋊Q8—1332no—
636C22⋊Q8C22×D13116yes—
637#121—138no—
638#121—138no—
639#121—1332no—
640#121—1316no—
641#121—1332no—
642#121—1332no—
643#121—1332no—
644#121—1316no—
645#121—1332no—
646#121—138no—
647#121—138no—
648#121—1332no—
649#121—1316no—
650#121—1316no—
651#121—1316no—
652#121—1332no—
653#121—1332no—
654#121C22×D13116yes—
655C4×Q8—1316no—
656C4×Q8—1316no—
657C4×D4—1316no—
658C4×D4—1316no—
659C4×D4—1332no—
660C4×D4—1332no—
661C4×D4—138no—
662C4×D4—138no—
663C4×D4C22×D1318yes—
664C4×D4C22×D1318yes—
665#117—1316no—
666C2×C4⋊C4—131no—
667C2×C4⋊C4—131no—
668C2×C4⋊C4—132no—
669C2×C4⋊C4—134no—
670C2×C4⋊C4—134no—
671C2×C4⋊C4—134no—
672C2×C4⋊C4—1316no—
673C2×C4⋊C4—132no—
674C2×C4⋊C4—132no—
675C2×C4⋊C4—132no—
676C2×C4⋊C4—134no—
677C2×C4⋊C4—134no—
678C2×C4⋊C4—1316no—
679C2×C4⋊C4—1316no—
680C2×C4⋊C4C22×D1311yescharacteristic
681C2×C4⋊C4C22×D1312yes—
682C2×C4⋊C4C22×D1311yescharacteristic
683C2×C4⋊C4C22×D1314yes—
684C2×C4⋊C4C22×D13116yes—
685C2×C4⋊C4C22×D1312yes—
686C2×C22⋊C4—134no—
687C2×C22⋊C4—132no—
688C2×C22⋊C4—132no—
689C2×C22⋊C4—134no—
690C2×C22⋊C4—134no—
691C2×C22⋊C4—134no—
692C2×C22⋊C4—132no—
693C2×C22⋊C4—132no—
694C2×C22⋊C4—132no—
695C2×C22⋊C4—132no—
696C2×C22⋊C4C22×D1314yes—
697C2×C22⋊C4C22×D1312yes—
698C2×C22⋊C4C22×D1312yes—
699C2×C42—134no—
700C2×C42—131no—
701C2×C42—131no—
702C2×C42—131no—
703C2×C42—138no—
704C2×C42C22×D1311yescharacteristic
705C2×C13—44no—
706C2×C13—44no—
707C2×C13#354814yescomplemented
708C2×C13C22×H(5,𝔽2)11yescharacteristic
709C2×C13C22×H(5,𝔽2)11yescharacteristic
710C2×C13C22×2−1+411yescharacteristic
711D13—44no—
712D13—42no—
713D13—44no—
714C24—131no—
715C24—132no—
716C24—132no—
717C24C23×D1312yes—
718C24C23×D1312yes—
719#41—432no—
720#41—5232no—
721#41—5232no—
722#41—5232no—
723#41—5232no—
724#41—5232no—
725C2×Q8—28no—
726C2×Q8—138no—
727C2×Q8—138no—
728C2×Q8—138no—
729C2×Q8—268no—
730C2×Q8—524no—
731C2×Q8—524no—
732C2×Q8C23×D1318yes—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—48no—
736C2×D4—138no—
737C2×D4—138no—
738C2×D4—138no—
739C2×D4—138no—
740C2×D4—1316no—
741C2×D4—1316no—
742C2×D4—138no—
743C2×D4—138no—
744C2×D4—134no—
745C2×D4—134no—
746C2×D4—138no—
747C2×D4—138no—
748C2×D4—1316no—
749C2×D4—268no—
750C2×D4—268no—
751C2×D4—264no—
752C2×D4—264no—
753C2×D4—524no—
754C2×D4—528no—
755C2×D4—524no—
756C2×D4—524no—
757C2×D4—524no—
758C2×D4—524no—
759C2×D4—524no—
760C2×D4—528no—
761C2×D4—528no—
762C2×D4C23×D1314yes—
763C2×D4C23×D1314yes—
764C2×D4C23×D13116yes—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—48no—
768C22×C4—131no—
769C22×C4—131no—
770C22×C4—131no—
771C22×C4—134no—
772C22×C4—132no—
773C22×C4—132no—
774C22×C4—1316no—
775C22×C4—134no—
776C22×C4—134no—
777C22×C4—134no—
778C22×C4—138no—
779C22×C4—138no—
780C22×C4—1316no—
781C22×C4—1316no—
782C22×C4—264no—
783C22×C4—268no—
784C22×C4—264no—
785C22×C4—268no—
786C22×C4—264no—
787C22×C4—528no—
788C22×C4—528no—
789C22×C4—528no—
790C22×C4C23×D1318yes—
791C22×C4C23×D1318yes—
792C22×C4C23×D1311yescharacteristic
793C22×C4C23×D1314yes—
794C22×C4C23×D1312yes—
795C22×C4C23×D1312yes—
796C22×C4C23×D13116yes—
797C22×C4C23×D1311yescharacteristic
798C22×C4C23×D1311yescharacteristic
799C4⋊C4—134no—
800C4⋊C4—134no—
801C4⋊C4—138no—
802C4⋊C4—1316no—
803C4⋊C4—1316no—
804C4⋊C4—1316no—
805C4⋊C4—138no—
806C4⋊C4—138no—
807C4⋊C4—138no—
808C4⋊C4—1316no—
809C4⋊C4—1316no—
810C4⋊C4C23×D1314yes—
811C4⋊C4C23×D1318yes—
812C4⋊C4C23×D1314yes—
813C4⋊C4C23×D13116yes—
814C4⋊C4C23×D1318yes—
815C22⋊C4—1316no—
816C22⋊C4—138no—
817C22⋊C4—138no—
818C22⋊C4—1316no—
819C22⋊C4—1316no—
820C22⋊C4—1316no—
821C22⋊C4—138no—
822C22⋊C4—138no—
823C22⋊C4—138no—
824C22⋊C4—138no—
825C22⋊C4C23×D13116yes—
826C22⋊C4C23×D1318yes—
827C22⋊C4C23×D1318yes—
828C42—134no—
829C42—134no—
830C42—134no—
831C42—1316no—
832C42C23×D1314yes—
833C13C2×#354811yescharacteristic, complemented, Sylow
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—24no—
839C23—24no—
840C23—132no—
841C23—134no—
842C23—134no—
843C23—264no—
844C23—262no—
845C23—264no—
846C23—262no—
847C23—264no—
848C23—264no—
849C23—262no—
850C23—264no—
851C23—264no—
852C23C24×D1314yes—
853C23C24×D1314yes—
854C23C24×D1311yescharacteristic
855Q8—216no—
856Q8—2616no—
857Q8—528no—
858Q8—528no—
859D4—28no—
860D4—28no—
861D4—416no—
862D4—2616no—
863D4—2616no—
864D4—268no—
865D4—268no—
866D4—528no—
867D4—5216no—
868D4—528no—
869D4—528no—
870D4—528no—
871D4—528no—
872D4—528no—
873D4—5216no—
874D4—5216no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—22no—
879C2×C4—216no—
880C2×C4—216no—
881C2×C4—416no—
882C2×C4—134no—
883C2×C4—132no—
884C2×C4—132no—
885C2×C4—132no—
886C2×C4—138no—
887C2×C4—134no—
888C2×C4—134no—
889C2×C4—268no—
890C2×C4—264no—
891C2×C4—262no—
892C2×C4—264no—
893C2×C4—262no—
894C2×C4—268no—
895C2×C4—2616no—
896C2×C4—268no—
897C2×C4—2616no—
898C2×C4—268no—
899C2×C4—5216no—
900C2×C4—5216no—
901C2×C4—5216no—
902C2×C4#8825114yes—
903C2×C4#8825614yes—
904C2×C4C24×D1312yes—
905C2×C4C24×D1318yes—
906C2×C4C24×D1314yes—
907C2×C4C24×D1314yes—
908C2×C4C24×D1312yes—
909C2×C4C24×D1312yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—48no—
917C22—48no—
918C22—264no—
919C22—262no—
920C22—264no—
921C22—262no—
922C22—264no—
923C22—264no—
924C22—262no—
925C22—264no—
926C22—264no—
927C22—524no—
928C22—528no—
929C22—528no—
930C22C2×#8825112yes—
931C22C2×#8825612yes—
932C22D13×2−1+412yes—
933C22C25×D1311yescharacteristic
934C4—24no—
935C4—28no—
936C4—24no—
937C4—22no—
938C4—134no—
939C4—264no—
940C4—262no—
941C4—264no—
942C4—262no—
943C4—268no—
944C4C2×#8825114yes—
945C4C2×#8825614yes—
946C2—44no—
947C2—44no—
948C2—522no—
949C2—524no—
950C2—524no—
951C2#1312923314yesdirect product factor
952C2C22×#8825111yescharacteristic
953C2C22×#8825611yescharacteristic
954C2C2×D13×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#547C2
socleC23×C13C25
hypercenterC2×#547D13
hypocenterC13C2×#3548
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #13129233C2direct (N × H)
2. C2×#11719372C2semidirect
3. C2×#11719340C2semidirect
4. C2×#11719216C2semidirect
5. C2×#11719539C2semidirect
6. C2×#11719304C2semidirect
7. C2×#11719256C2semidirect
8. C2×#11719260C2semidirect
9. C2×#11719431C2semidirect
10. C2×#11719368C2semidirect
11. C2×#11719215C2semidirect
12. C2×#11719334C2semidirect
13. C2×#11719313C2semidirect
14. C2×#11719538C2semidirect
15. C2×#11719433C2semidirect
16. C2×#11719253C2semidirect
17. C2×#11719253C2semidirect
18. C2×C13×#547C2semidirect
25. C13×#547C22semidirect
33. #11719539C22semidirect
34. #11719538C22semidirect
56. #11719433C22semidirect
57. #11719431C22semidirect
58. #11719372C22semidirect
59. #11719368C22semidirect
60. #11719340C22semidirect
61. #11719334C22semidirect
62. #11719313C22semidirect
63. #11719304C22semidirect
64. #11719260C22semidirect
65. #11719256C22semidirect
66. #11719253C22semidirect
67. #11719253C22semidirect
68. #11719216C22semidirect
69. #11719215C22semidirect
366. C2×#547D13semidirect
465. #547C2×D13semidirect
707. C2×C13#3548semidirect
833. C13C2×#3548semidirect
951. C2#13129233direct (N × H)

Maximal subgroups

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

subgroupindex
#131292332
C2×#117193722
C2×#117193402
C2×#117192162
C2×#117195392
C2×#117193042
C2×#117192562
C2×#117192602
C2×#117194312
C2×#117193682
C2×#117192152
C2×#117193342
C2×#117193132
C2×#117195382
C2×#117194332
C2×#117192532
C2×C13×#5472
C2×#354813