Finite Group Databasebeta

← C2×#13128582 #16771339

Subgroups — C2×#13128582 #16771339

Order 3328.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128582C2132yesmaximal, direct product factor
2C2×#11719346C212yesmaximal, complemented
3C2×#11719340C212yesmaximal, complemented
4C2×#11719347C212yesmaximal, complemented
5C2×#11719218C214yesmaximal, complemented
6C2×#11719344C212yesmaximal, complemented
7C2×#11719200C214yesmaximal, complemented
8C2×#11719205C211yesmaximal, characteristic, complemented
9C2×#11719348C212yesmaximal, complemented
10C2×#11719330C212yesmaximal, complemented
11C2×#11719521C211yesmaximal, characteristic, complemented
12C2×#11719327C212yesmaximal, complemented
13C2×#11719329C212yesmaximal, complemented
14C2×#11719496C211yesmaximal, characteristic
15C2×#11719209C211yesmaximal, characteristic, complemented
16C2×#11719517C211yesmaximal, characteristic, complemented
17C22×#88180C211yesmaximal, characteristic, complemented
18C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
19C23×Q8×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C22×#6127C2211yescharacteristic
22C2×C13×C22⋊Q8C2212yes—
23C2×C13×C22⋊Q8C2212yes—
24C2×C13×C22⋊Q8C2212yes—
25C2×C13×C22⋊Q8C2212yes—
26C2×C13×C22⋊Q8C22116yescomplemented
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2212yes—
29C22×C13×C22⋊C4C2212yes—
30C2×#88207C2212yes—
31C22×C22⋊Dic13C2212yes—
32#11719521C22116yescomplemented
33C2×#88201C2212yescomplemented
34C2×#88200C2212yescomplemented
35C2×#88200C2212yescomplemented
36#11719517C22116yescomplemented
37C2×Q8×Dic13C2212yescomplemented
38C2×Q8×Dic13C2212yescomplemented
39C2×Q8×Dic13C2212yescomplemented
40C2×Q8×Dic13C2212yescomplemented
41C2×#88198C2212yescomplemented
42#11719496C22116yes—
43C2×#88184C2211yescharacteristic
44C2×#88184C2211yescharacteristic
45C2×#88183C2214yes—
46C2×#88183C2212yes—
47C2×C4×C22⋊D13C2214yes—
48C2×C4×C22⋊D13C2212yes—
49C2×C4×C22⋊D13C2212yes—
50C2×#88180C2212yes—
51C2×#88180C2211yescharacteristic
52C2×#88180C2211yescharacteristic
53C2×#88180C2211yescharacteristic
54C2×#88180C2211yescharacteristic
55C2×#88180C2212yes—
56C2×#88180C2211yescharacteristic
57C2×#88180C2214yes—
58C2×#88180C22116yescomplemented
59C22×C4⋊Dic13C2211yescharacteristic
60C22×C4⋊Dic13C2211yescharacteristic
61C2×#88178C2211yescharacteristic
62C2×#88178C2214yes—
63C2×#88178C2211yescharacteristic
64C22×C4×Dic13C2212yes—
65#11719348C22132yescomplemented
66#11719347C22132yescomplemented
67#11719346C22132yescomplemented
68#11719344C22132yescomplemented
69#11719340C22132yescomplemented
70#11719330C22132yescomplemented
71#11719329C22132yescomplemented
72#11719327C22132yescomplemented
73#11719218C22164yescomplemented
74C2×#88152C2214yescomplemented
75C2×#88152C2214yescomplemented
76C2×#88151C2214yescomplemented
77#11719209C22116yescomplemented
78C2×#88147C2212yescomplemented
79C2×#88146C2212yescomplemented
80C2×#88146C2214yescomplemented
81C2×C4⋊C4×D13C2212yescomplemented
82#11719205C22116yescomplemented
83C2×#88144C2212yescomplemented
84C2×#88144C2214yescomplemented
85C2×#88144C2212yescomplemented
86C2×#88143C2214yescomplemented
87C2×#88143C2214yescomplemented
88C2×#88142C2212yescomplemented
89C2×#88142C2212yescomplemented
90C2×#88141C2212yescomplemented
91C2×#88141C2214yescomplemented
92#11719200C22164yescomplemented
93C2×#88140C2214yes—
94C2×#88139C2214yes—
95C2×#88137C2214yes—
96C2×#88135C2214yes—
97C2×#88133C2214yes—
98C2×#88133C2214yes—
99C2×#88132C2214yes—
100C2×#88131C2214yes—
101C25×C13C2311yescharacteristic
102C22×Q8×C13—28no—
103C22×Q8×C13C2312yes—
104C22×Q8×C13C2312yes—
105C22×Q8×C13C2318yes—
106C23×C4×C13—28no—
107C23×C4×C13C2311yescharacteristic
108C23×C4×C13C2311yescharacteristic
109C23×C4×C13C2311yescharacteristic
110C23×C4×C13C2311yescharacteristic
111C23×C4×C13C2312yes—
112C23×C4×C13C2311yescharacteristic
113C23×C4×C13C2318yes—
114C23×C4×C13C2312yes—
115C23×C4×C13C2311yescharacteristic
116C22×C22⋊D13C2312yes—
117C22×C22⋊D13C2312yes—
118C22×C22⋊D13C2312yes—
119C23×Dic13C2312yes—
120C23×Dic13C2312yes—
121C2×#6127—28no—
122C2×#6127C2318yes—
123C22×D52C2311yescharacteristic
124C22×C4×D13C2312yes—
125C22×C4×D13C2314yes—
126C22×Dic26C2311yescharacteristic
127C22×Dic26C2314yes—
128C13×C22⋊Q8C23116yes—
129C13×C22⋊Q8C23116yes—
130C13×C22⋊Q8C23116yes—
131C13×C22⋊Q8C23116yes—
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2314yes—
134C2×C13×C4⋊C4C2312yes—
135C2×C13×C4⋊C4C2314yes—
136C2×C13×C4⋊C4C2318yes—
137C2×C13×C4⋊C4C23116yes—
138C2×C13×C22⋊C4C2314yes—
139C2×C13×C22⋊C4C2314yes—
140C2×C13×C22⋊C4C23116yes—
141#88207C23116yes—
142C2×C22⋊Dic13C2312yes—
143C2×C22⋊Dic13C2312yes—
144C2×C22⋊Dic13C2312yes—
145C2×C22⋊Dic13C2312yes—
146C2×C22⋊Dic13C23116yes—
147C2×C22⋊Dic13C2312yes—
148C2×C22⋊Dic13C2312yes—
149C2×C22⋊Dic13C2312yes—
150#88201C23116yescomplemented
151#88200C23116yescomplemented
152#88200C23116yescomplemented
153Q8×Dic13C23116yescomplemented
154Q8×Dic13C23116yescomplemented
155Q8×Dic13C23116yescomplemented
156Q8×Dic13C23116yescomplemented
157#88198C23116yescomplemented
158#88184C2318yes—
159#88184C2318yes—
160#88183C23132yes—
161#88183C23116yes—
162C4×C22⋊D13C23132yes—
163C4×C22⋊D13C23116yes—
164C4×C22⋊D13C23116yes—
165C2×#6103C2314yes—
166C2×#6103C2314yes—
167C2×#6103C2314yes—
168C2×#6103C2312yes—
169C2×#6103C2312yes—
170#88180C23132yes—
171#88180C2318yes—
172#88180C2318yes—
173#88180C2318yes—
174#88180C23116yes—
175#88180C23116yes—
176#88180C2318yes—
177#88180C2318yes—
178C2×C4⋊Dic13C2314yes—
179C2×C4⋊Dic13C2314yes—
180C2×C4⋊Dic13C2314yes—
181C2×C4⋊Dic13C2311yescharacteristic
182C2×C4⋊Dic13C2311yescharacteristic
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2312yes—
185C2×C4⋊Dic13C2311yescharacteristic
186C2×C4⋊Dic13C2311yescharacteristic
187C2×C4⋊Dic13C2311yescharacteristic
188C2×C4⋊Dic13C2311yescharacteristic
189C2×C4⋊Dic13C2318yes—
190C2×C4⋊Dic13C2318yes—
191#88178C23132yes—
192#88178C2318yes—
193#88178C2318yes—
194C2×#6101C2314yes—
195C2×#6101C2314yes—
196C2×#6101C2314yes—
197C2×#6101C2314yes—
198C2×#6101C2314yes—
199C2×#6101C2312yes—
200C2×#6101C2312yes—
201C2×C4×Dic13C2314yes—
202C2×C4×Dic13C2314yes—
203C2×C4×Dic13C2314yes—
204C2×C4×Dic13C2312yes—
205C2×C4×Dic13C2312yes—
206C2×C4×Dic13C2312yes—
207C2×C4×Dic13C2312yes—
208C2×C4×Dic13C2312yes—
209C2×C4×Dic13C23116yes—
210#88152C23132yescomplemented
211#88152C23132yescomplemented
212#88151C23132yescomplemented
213#88147C23116yescomplemented
214#88146C23116yescomplemented
215#88146C23132yescomplemented
216C4⋊C4×D13C23116yescomplemented
217#88144C23116yescomplemented
218#88144C23116yescomplemented
219#88144C23132yescomplemented
220#88143C23132yescomplemented
221#88143C23132yescomplemented
222#88142C23116yescomplemented
223#88142C23116yescomplemented
224#88141C23116yescomplemented
225#88141C23132yescomplemented
226#88140C23132yes—
227#88139C23132yes—
228#88137C23132yes—
229#88135C23132yes—
230#88133C23132yes—
231#88133C23132yes—
232#88132C23132yes—
233#88131C23132yes—
234C2×#3495—131nomaximal, Sylow
235C24×C13—24no—
236C24×C13—24no—
237C24×C13—42no—
238C24×C13C2411yescharacteristic
239C24×C13C2414yes—
240C24×C13C2411yescharacteristic
241C24×C13C2411yescharacteristic
242C23×D13C2412yes—
243C2×Q8×C13—28no—
244C2×Q8×C13—28no—
245C2×Q8×C13—232no—
246C2×Q8×C13C2418yes—
247C2×Q8×C13C2418yes—
248C22×C4×C13—24no—
249C22×C4×C13—28no—
250C22×C4×C13—24no—
251C22×C4×C13—24no—
252C22×C4×C13—24no—
253C22×C4×C13—24no—
254C22×C4×C13—232no—
255C22×C4×C13—44no—
256C22×C4×C13#4118yes—
257C22×C4×C13C2411yescharacteristic
258C22×C4×C13C2414yes—
259C22×C4×C13C2414yes—
260C22×C4×C13C2414yes—
261C22×C4×C13C2411yescharacteristic
262C22×C4×C13C2414yes—
263C22×C4×C13C2414yes—
264C22×C4×C13C2414yes—
265C22×C4×C13C2418yes—
266C22×C4×C13C2414yes—
267C22×C4×C13C2418yes—
268C22×C4×C13C2411yescharacteristic
269C22×C4×C13C2411yescharacteristic
270C22×C4×C13C2414yes—
271C2×C22⋊D13—28no—
272C2×C22⋊D13—28no—
273C2×C22⋊D13—44no—
274C2×C22⋊D13C2418yes—
275C2×C22⋊D13C2418yes—
276C2×C22⋊D13C2418yes—
277C22×Dic13—28no—
278C22×Dic13—44no—
279C22×Dic13C2418yes—
280C22×Dic13C2412yes—
281C22×Dic13C2412yes—
282C22×Dic13C2412yes—
283C22×Dic13C2412yes—
284C22×Dic13C2412yes—
285C22×Dic13C2412yes—
286C22×Dic13C2412yes—
287C22×Dic13C2418yes—
288#6127—232no—
289C2×D52—24no—
290C2×D52C2414yes—
291C2×C4×D13—28no—
292C2×C4×D13—48no—
293C2×C4×D13C2418yes—
294C2×C4×D13C24116yes—
295C2×Dic26—24no—
296C2×Dic26—48no—
297C2×Dic26C2414yes—
298C2×Dic26C24116yes—
299C13×C4⋊C4C2418yes—
300C13×C4⋊C4C24116yes—
301C13×C4⋊C4C2418yes—
302C13×C4⋊C4C24116yes—
303C13×C22⋊C4C24116yes—
304C13×C22⋊C4C24116yes—
305C22⋊Dic13C2418yes—
306C22⋊Dic13C2418yes—
307C22⋊Dic13C2418yes—
308C22⋊Dic13C2418yes—
309C22⋊Dic13C2418yes—
310C22⋊Dic13C2418yes—
311C22⋊Dic13C2418yes—
312#6103C24116yes—
313#6103C24116yes—
314#6103C24116yes—
315#6103C2418yes—
316#6103C2418yes—
317C4⋊Dic13C24116yes—
318C4⋊Dic13C24116yes—
319C4⋊Dic13C24116yes—
320C4⋊Dic13C2414yes—
321C4⋊Dic13C2414yes—
322C4⋊Dic13C2418yes—
323C4⋊Dic13C2418yes—
324C4⋊Dic13C2414yes—
325C4⋊Dic13C2414yes—
326C4⋊Dic13C2414yes—
327C4⋊Dic13C2414yes—
328#6101C24116yes—
329#6101C24116yes—
330#6101C24116yes—
331#6101C24116yes—
332#6101C24116yes—
333#6101C2418yes—
334#6101C2418yes—
335C4×Dic13C24116yes—
336C4×Dic13C24116yes—
337C4×Dic13C24116yes—
338C4×Dic13C2418yes—
339C4×Dic13C2418yes—
340C4×Dic13C2418yes—
341C4×Dic13C2418yes—
342C4×Dic13C2418yes—
343#3495—1332no—
344C2×#556—132no—
345C2×#554—132no—
346C2×#552—132no—
347C2×#552—132no—
348C2×#552—134no—
349C2×#551—134no—
350C2×#544—131no—
351C2×#542—132no—
352C2×#541—132no—
353C2×#536—131no—
354C2×#533—132no—
355C2×#529—132no—
356C2×#525—131no—
357C22×C22⋊Q8D1311yescharacteristic, complemented
358C2×#520—131no—
359C2×#519—131no—
360C22×#117—131no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—28no—
366C23×C13—22no—
367C23×C13—28no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—44no—
371C23×C13—416no—
372C23×C13C2×#4114yes—
373C23×C132−1+414yes—
374C23×C13C2512yes—
375C23×C13C2512yes—
376C23×C13C2512yes—
377C23×C13C2511yescharacteristic
378C22×D13—24no—
379C22×D13—24no—
380C22×D13—24no—
381C22×D13C2514yes—
382Q8×C13—216no—
383Q8×C13—216no—
384C2×C4×C13—28no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—216no—
388C2×C4×C13—28no—
389C2×C4×C13—28no—
390C2×C4×C13—28no—
391C2×C4×C13—28no—
392C2×C4×C13—28no—
393C2×C4×C13—28no—
394C2×C4×C13—48no—
395C2×C4×C13C2×#4114yes—
396C2×C4×C13C2×#4114yes—
397C2×C4×C13C2×#41116yes—
398C2×C4×C13C2512yes—
399C2×C4×C13C2518yes—
400C2×C4×C13C2518yes—
401C2×C4×C13C2512yes—
402C2×C4×C13C2512yes—
403C2×C4×C13C2512yes—
404C22⋊D13—216no—
405C22⋊D13—216no—
406C22⋊D13—48no—
407C2×Dic13—24no—
408C2×Dic13—216no—
409C2×Dic13—24no—
410C2×Dic13—24no—
411C2×Dic13—24no—
412C2×Dic13—24no—
413C2×Dic13—24no—
414C2×Dic13—24no—
415C2×Dic13—48no—
416C2×Dic13C2514yes—
417C2×Dic13C2514yes—
418C2×Dic13C2514yes—
419C2×Dic13C2514yes—
420C2×Dic13C2514yes—
421C2×Dic13C2514yes—
422C2×Dic13C2514yes—
423D52—28no—
424C4×D13—216no—
425C4×D13—416no—
426Dic26—28no—
427Dic26—416no—
428C22×#41—131no—
429C23×Q8C2×D1311yescharacteristic
430C24×C4C2×D1311yescharacteristic
431#556—1332no—
432#554—1332no—
433#552—1332no—
434#552—1332no—
435#552—1364no—
436#551—1364no—
437#544—1316no—
438#542—1332no—
439#541—1332no—
440#536—1316no—
441#533—1332no—
442C2×C4⋊Q8—132no—
443C2×C4⋊Q8—132no—
444C2×C4⋊Q8—132no—
445#529—1332no—
446C2×#126—134no—
447C2×#126—134no—
448C2×#126—134no—
449C2×#126—134no—
450C2×#125—134no—
451C2×#125—134no—
452C2×#125—132no—
453C2×#125—134no—
454C2×#125—132no—
455C2×#124—132no—
456C2×#124—134no—
457#525—1316no—
458C2×#123—132no—
459C2×#123—134no—
460C2×#123—134no—
461C2×#123—134no—
462C2×C22⋊Q8—132no—
463C2×C22⋊Q8—132no—
464C2×C22⋊Q8—131no—
465C2×C22⋊Q8—131no—
466C2×C22⋊Q8—134no—
467C2×C22⋊Q8—134no—
468C2×C22⋊Q8—134no—
469C2×C22⋊Q8C2×D1312yes—
470C2×C22⋊Q8C2×D1312yes—
471C2×C22⋊Q8C2×D1312yes—
472C2×C22⋊Q8C2×D1312yes—
473C2×C22⋊Q8C2×D13116yescomplemented
474C2×#121—131no—
475C2×#121—131no—
476C2×#120—132no—
477#520—1316no—
478#519—1316no—
479C2×C4×Q8—132no—
480C2×C4×Q8—132no—
481C2×C4×Q8—132no—
482C2×C4×Q8—132no—
483C2×C4×Q8—132no—
484C2×C4×Q8—134no—
485C2×C4×D4—134no—
486C2×C4×D4—132no—
487C2×C4×D4—132no—
488C2×C4×D4—132no—
489C2×C4×D4—134no—
490C2×#117—131no—
491C2×#117—131no—
492C2×#117—132no—
493C2×#117—131no—
494C2×#117—132no—
495C2×#117—131no—
496C2×#117—131no—
497C2×#117—134no—
498C2×#117—1316no—
499C2×#117—132no—
500C2×#117—134no—
501C2×#117—134no—
502C22×C4⋊C4—131no—
503C22×C4⋊C4—131no—
504C22×C4⋊C4—132no—
505C22×C4⋊C4C2×D1311yescharacteristic
506C22×C4⋊C4C2×D1312yes—
507C22×C22⋊C4—132no—
508C22×C22⋊C4C2×D1312yes—
509C22×C42—132no—
510C22×C13—22no—
511C22×C13—22no—
512C22×C13—22no—
513C22×C13—22no—
514C22×C13—28no—
515C22×C13—28no—
516C22×C13—22no—
517C22×C13—22no—
518C22×C13—22no—
519C22×C13—416no—
520C22×C13—44no—
521C22×C13C22×#4114yes—
522C22×C13C22×#4112yes—
523C22×C13C2×2−1+414yes—
524C22×C13C2×2−1+412yes—
525C22×C13#58512yes—
526C22×C13C2611yescharacteristic
527C2×D13—24no—
528C2×D13—24no—
529C2×D13—24no—
530C2×D13—48no—
531C4×C13—22no—
532C4×C13—22no—
533C4×C13—28no—
534C4×C13—28no—
535C4×C13C22×#4114yes—
536C4×C13C22×#4114yes—
537Dic13—24no—
538Dic13—24no—
539Dic13—24no—
540Dic13—24no—
541Dic13—24no—
542Dic13—24no—
543Dic13—24no—
544C25C22×D1311yescharacteristic
545C2×#41—138no—
546C2×#41—268no—
547C22×Q8—28no—
548C22×Q8—131no—
549C22×Q8—134no—
550C22×Q8C22×D1312yes—
551C22×Q8C22×D1312yes—
552C22×Q8C22×D1318yes—
553C22×D4—132no—
554C22×D4—132no—
555C22×D4—132no—
556C22×D4—131no—
557C23×C4—28no—
558C23×C4—132no—
559C23×C4—132no—
560C23×C4—132no—
561C23×C4—134no—
562C23×C4C22×D1312yes—
563C23×C4C22×D1311yescharacteristic
564C23×C4C22×D1311yescharacteristic
565C23×C4C22×D1311yescharacteristic
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1318yes—
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1312yes—
570C23×C4C22×D1311yescharacteristic
571C4⋊Q8—1316no—
572C4⋊Q8—1316no—
573C4⋊Q8—1316no—
574#126—1332no—
575#126—1332no—
576#126—1332no—
577#126—1332no—
578#125—1316no—
579#125—1332no—
580#125—1332no—
581#125—1332no—
582#125—1316no—
583#124—1316no—
584#124—1332no—
585#123—1316no—
586#123—1332no—
587#123—1332no—
588#123—1332no—
589C22⋊Q8—1316no—
590C22⋊Q8—1316no—
591C22⋊Q8—138no—
592C22⋊Q8—138no—
593C22⋊Q8—1332no—
594C22⋊Q8—1332no—
595C22⋊Q8—1332no—
596C22⋊Q8C22×D13116yes—
597C22⋊Q8C22×D13116yes—
598C22⋊Q8C22×D13116yes—
599C22⋊Q8C22×D13116yes—
600#121—138no—
601#121—138no—
602#120—1316no—
603C4×Q8—1316no—
604C4×Q8—1316no—
605C4×Q8—1316no—
606C4×Q8—1316no—
607C4×Q8—1316no—
608C4×Q8—1332no—
609C4×D4—1332no—
610C4×D4—1316no—
611C4×D4—1316no—
612C4×D4—1316no—
613C4×D4—1332no—
614#117—138no—
615#117—138no—
616#117—1316no—
617#117—138no—
618#117—1316no—
619#117—138no—
620#117—138no—
621#117—1332no—
622#117—1316no—
623#117—1332no—
624#117—1332no—
625C2×C4⋊C4—131no—
626C2×C4⋊C4—131no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—131no—
629C2×C4⋊C4—131no—
630C2×C4⋊C4—132no—
631C2×C4⋊C4—138no—
632C2×C4⋊C4—138no—
633C2×C4⋊C4—134no—
634C2×C4⋊C4—131no—
635C2×C4⋊C4—131no—
636C2×C4⋊C4—134no—
637C2×C4⋊C4—134no—
638C2×C4⋊C4—134no—
639C2×C4⋊C4—134no—
640C2×C4⋊C4—134no—
641C2×C4⋊C4—132no—
642C2×C4⋊C4—132no—
643C2×C4⋊C4—134no—
644C2×C4⋊C4—134no—
645C2×C4⋊C4—1316no—
646C2×C4⋊C4C22×D1312yes—
647C2×C4⋊C4C22×D1314yes—
648C2×C4⋊C4C22×D1312yes—
649C2×C4⋊C4C22×D1318yes—
650C2×C4⋊C4C22×D1314yes—
651C2×C4⋊C4C22×D13116yes—
652C2×C22⋊C4—132no—
653C2×C22⋊C4—132no—
654C2×C22⋊C4—132no—
655C2×C22⋊C4—132no—
656C2×C22⋊C4—1316no—
657C2×C22⋊C4—132no—
658C2×C22⋊C4—132no—
659C2×C22⋊C4—132no—
660C2×C22⋊C4—132no—
661C2×C22⋊C4—134no—
662C2×C22⋊C4—134no—
663C2×C22⋊C4—132no—
664C2×C22⋊C4—134no—
665C2×C22⋊C4C22×D1314yes—
666C2×C22⋊C4C22×D1314yes—
667C2×C22⋊C4C22×D13116yes—
668C2×C42—132no—
669C2×C42—132no—
670C2×C42—134no—
671C2×C42—134no—
672C2×C42—134no—
673C2×C42—132no—
674C2×C42—132no—
675C2×C42—1316no—
676C2×C42—132no—
677C2×C13—24no—
678C2×C13—24no—
679C2×C13—42no—
680C2×C13#349514yescomplemented
681C2×C13C23×#4111yescharacteristic
682C2×C13C22×2−1+411yescharacteristic
683C2×C13C2×#58511yescharacteristic
684D13—44no—
685C24—24no—
686C24—24no—
687C24—42no—
688C24—132no—
689C24C23×D1311yescharacteristic
690C24C23×D1314yes—
691C24C23×D1311yescharacteristic
692C24C23×D1311yescharacteristic
693#41—2632no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—232no—
697C2×Q8—134no—
698C2×Q8—1316no—
699C2×Q8—264no—
700C2×Q8—528no—
701C2×Q8C23×D1318yes—
702C2×Q8C23×D1318yes—
703C2×D4—138no—
704C2×D4—138no—
705C2×D4—138no—
706C2×D4—134no—
707C2×D4—268no—
708C2×D4—268no—
709C2×D4—264no—
710C2×D4—524no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—232no—
718C22×C4—44no—
719C22×C4—138no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—138no—
728C22×C4—138no—
729C22×C4—1316no—
730C22×C4—268no—
731C22×C4—268no—
732C22×C4—528no—
733C22×C4—524no—
734C22×C4#612918yes—
735C22×C4C23×D1314yes—
736C22×C4C23×D1318yes—
737C22×C4C23×D1314yes—
738C22×C4C23×D1314yes—
739C22×C4C23×D1314yes—
740C22×C4C23×D1314yes—
741C22×C4C23×D1311yescharacteristic
742C22×C4C23×D1314yes—
743C22×C4C23×D1314yes—
744C22×C4C23×D1311yescharacteristic
745C22×C4C23×D1318yes—
746C22×C4C23×D1314yes—
747C22×C4C23×D1311yescharacteristic
748C22×C4C23×D1311yescharacteristic
749C4⋊C4—134no—
750C4⋊C4—134no—
751C4⋊C4—138no—
752C4⋊C4—134no—
753C4⋊C4—134no—
754C4⋊C4—138no—
755C4⋊C4—1316no—
756C4⋊C4—134no—
757C4⋊C4—134no—
758C4⋊C4—1316no—
759C4⋊C4—1316no—
760C4⋊C4—1316no—
761C4⋊C4—1316no—
762C4⋊C4—1316no—
763C4⋊C4—138no—
764C4⋊C4—138no—
765C4⋊C4—1316no—
766C4⋊C4—1316no—
767C4⋊C4C23×D1318yes—
768C4⋊C4C23×D13116yes—
769C4⋊C4C23×D1318yes—
770C4⋊C4C23×D13116yes—
771C22⋊C4—138no—
772C22⋊C4—138no—
773C22⋊C4—138no—
774C22⋊C4—138no—
775C22⋊C4—138no—
776C22⋊C4—138no—
777C22⋊C4—138no—
778C22⋊C4—138no—
779C22⋊C4—1316no—
780C22⋊C4—1316no—
781C22⋊C4—138no—
782C22⋊C4—1316no—
783C22⋊C4C23×D13116yes—
784C22⋊C4C23×D13116yes—
785C42—138no—
786C42—138no—
787C42—138no—
788C42—138no—
789C42—1316no—
790C42—1316no—
791C42—1316no—
792C42—138no—
793C13C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—28no—
799C23—22no—
800C23—28no—
801C23—22no—
802C23—22no—
803C23—44no—
804C23—416no—
805C23—134no—
806C23—264no—
807C23—264no—
808C23—264no—
809C23C2×#612914yes—
810C23#8825414yes—
811C23C24×D1312yes—
812C23C24×D1312yes—
813C23C24×D1312yes—
814C23C24×D1311yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—268no—
818Q8—5216no—
819D4—2616no—
820D4—2616no—
821D4—268no—
822D4—528no—
823C2×C4—28no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—216no—
827C2×C4—28no—
828C2×C4—28no—
829C2×C4—28no—
830C2×C4—28no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—48no—
834C2×C4—134no—
835C2×C4—134no—
836C2×C4—134no—
837C2×C4—134no—
838C2×C4—134no—
839C2×C4—134no—
840C2×C4—134no—
841C2×C4—264no—
842C2×C4—2616no—
843C2×C4—264no—
844C2×C4—264no—
845C2×C4—264no—
846C2×C4—264no—
847C2×C4—264no—
848C2×C4—264no—
849C2×C4—2616no—
850C2×C4—5216no—
851C2×C4—528no—
852C2×C4C2×#612914yes—
853C2×C4C2×#612914yes—
854C2×C4C2×#6129116yes—
855C2×C4C24×D1312yes—
856C2×C4C24×D1318yes—
857C2×C4C24×D1318yes—
858C2×C4C24×D1312yes—
859C2×C4C24×D1312yes—
860C2×C4C24×D1312yes—
861C22—28no—
862C22—28no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—416no—
871C22—44no—
872C22—264no—
873C22—264no—
874C22—264no—
875C22—528no—
876C22C22×#612914yes—
877C22C22×#612912yes—
878C22C2×#8825414yes—
879C22C2×#8825412yes—
880C22#1171964812yes—
881C22C25×D1311yescharacteristic
882C4—22no—
883C4—22no—
884C4—28no—
885C4—28no—
886C4—264no—
887C4—264no—
888C4—264no—
889C4—264no—
890C4—264no—
891C4—264no—
892C4—264no—
893C4C22×#612914yes—
894C4C22×#612914yes—
895C2—24no—
896C2—24no—
897C2—42no—
898C2—524no—
899C2#1312858214yesdirect product factor
900C2C23×#612911yescharacteristic
901C2C22×#8825411yescharacteristic
902C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC22×C13×C22⋊Q8C2
socleC23×C13C25
prime radicalC2×#11719496C2
hypercenterC22×C22⋊Q8D13
hypocenterC13C2×#3495
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13128582C2direct (N × H)
2. C2×#11719346C2semidirect
3. C2×#11719340C2semidirect
4. C2×#11719347C2semidirect
5. C2×#11719218C2semidirect
6. C2×#11719344C2semidirect
7. C2×#11719200C2semidirect
8. C2×#11719205C2semidirect
9. C2×#11719348C2semidirect
10. C2×#11719330C2semidirect
11. C2×#11719521C2semidirect
12. C2×#11719327C2semidirect
13. C2×#11719329C2semidirect
15. C2×#11719209C2semidirect
16. C2×#11719517C2semidirect
17. C22×#88180C2semidirect
18. C22×C13×C22⋊Q8C2semidirect
26. C2×C13×C22⋊Q8C22semidirect
32. #11719521C22semidirect
33. C2×#88201C22semidirect
34. C2×#88200C22semidirect
35. C2×#88200C22semidirect
36. #11719517C22semidirect
37. C2×Q8×Dic13C22semidirect
38. C2×Q8×Dic13C22semidirect
39. C2×Q8×Dic13C22semidirect
40. C2×Q8×Dic13C22semidirect
41. C2×#88198C22semidirect
58. C2×#88180C22semidirect
65. #11719348C22semidirect
66. #11719347C22semidirect
67. #11719346C22semidirect
68. #11719344C22semidirect
69. #11719340C22semidirect
70. #11719330C22semidirect
71. #11719329C22semidirect
72. #11719327C22semidirect
73. #11719218C22semidirect
74. C2×#88152C22semidirect
75. C2×#88152C22semidirect
76. C2×#88151C22semidirect
77. #11719209C22semidirect
78. C2×#88147C22semidirect
79. C2×#88146C22semidirect
80. C2×#88146C22semidirect
81. C2×C4⋊C4×D13C22semidirect
82. #11719205C22semidirect
83. C2×#88144C22semidirect
84. C2×#88144C22semidirect
85. C2×#88144C22semidirect
86. C2×#88143C22semidirect
87. C2×#88143C22semidirect
88. C2×#88142C22semidirect
89. C2×#88142C22semidirect
90. C2×#88141C22semidirect
91. C2×#88141C22semidirect
92. #11719200C22semidirect
150. #88201C23semidirect
151. #88200C23semidirect
152. #88200C23semidirect
153. Q8×Dic13C23semidirect
154. Q8×Dic13C23semidirect
155. Q8×Dic13C23semidirect
156. Q8×Dic13C23semidirect
157. #88198C23semidirect
210. #88152C23semidirect
211. #88152C23semidirect
212. #88151C23semidirect
213. #88147C23semidirect
214. #88146C23semidirect
215. #88146C23semidirect
216. C4⋊C4×D13C23semidirect
217. #88144C23semidirect
218. #88144C23semidirect
219. #88144C23semidirect
220. #88143C23semidirect
221. #88143C23semidirect
222. #88142C23semidirect
223. #88142C23semidirect
224. #88141C23semidirect
225. #88141C23semidirect
357. C22×C22⋊Q8D13semidirect
473. C2×C22⋊Q8C2×D13semidirect
680. C2×C13#3495semidirect
793. C13C2×#3495semidirect
899. C2#13128582direct (N × H)

Maximal subgroups

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

subgroupindex
#131285822
C2×#117193462
C2×#117193402
C2×#117193472
C2×#117192182
C2×#117193442
C2×#117192002
C2×#117192052
C2×#117193482
C2×#117193302
C2×#117195212
C2×#117193272
C2×#117193292
C2×#117194962
C2×#117192092
C2×#117195172
C22×#881802
C22×C13×C22⋊Q82
C2×#349513