Finite Group Databasebeta

← C2×#13128585 #16771346

Subgroups — C2×#13128585 #16771346

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#13128585C2132yesmaximal, direct product factor
2C2×#11719346C212yesmaximal, complemented
3C2×#11719340C212yesmaximal, complemented
4C2×#11719347C212yesmaximal, complemented
5C2×#11719355C214yesmaximal, complemented
6C2×#11719344C212yesmaximal, complemented
7C2×#11719363C214yesmaximal, complemented
8C2×#11719224C211yesmaximal, characteristic, complemented
9C2×#11719387C212yesmaximal, complemented
10C2×#11719436C212yesmaximal, complemented
11C2×#11719433C212yesmaximal, complemented
12C2×#11719385C212yesmaximal, complemented
13C2×#11719533C211yesmaximal, characteristic
14C22×#88200C211yesmaximal, characteristic, complemented
15C2×#11719532C211yesmaximal, characteristic, complemented
16C2×#11719517C211yesmaximal, characteristic, complemented
17C2×D13×#117C211yesmaximal, characteristic, complemented
18C2×C13×#536C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C23×Q8×C13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C13×#536C22116yescomplemented
23C2×C13×C4⋊Q8C2212yescomplemented
24C2×C13×#124C2212yescomplemented
25C2×C13×#123C2214yes—
26C2×C13×C22⋊Q8C2212yescomplemented
27C2×C13×C22⋊Q8C2212yescomplemented
28C2×C13×#117C2211yescharacteristic
29#11719533C22116yes—
30#11719532C22116yescomplemented
31C2×#88200C2211yescharacteristic
32C2×#88200C2212yes—
33C2×#88200C2212yes—
34C2×#88200C2212yes—
35C2×#88200C2212yes—
36C2×#88200C2211yescharacteristic
37C2×#88200C22116yescomplemented
38#11719517C22116yescomplemented
39C2×Q8×Dic13C2212yescomplemented
40C2×Q8×Dic13C2212yescomplemented
41C2×Q8×Dic13C2212yescomplemented
42C2×Q8×Dic13C2212yescomplemented
43C2×Q8×Dic13C2212yescomplemented
44C2×#88192C2211yescharacteristic
45C2×#88192C2211yescharacteristic
46C2×#88191C2212yes—
47C2×#88189C2212yes—
48C2×D4×Dic13C2214yes—
49C2×D4×Dic13C2212yescomplemented
50C2×C4×C22⋊D13C2212yes—
51C2×C4×C22⋊D13C2212yes—
52C22×#6103C2212yes—
53C2×#88180C2211yescharacteristic
54C2×#88180C2211yescharacteristic
55C2×#88180C2214yes—
56C2×#88180C2212yescomplemented
57C22×C4⋊Dic13C2211yescharacteristic
58C22×C4⋊Dic13C2212yescomplemented
59C22×#6101C2212yes—
60#11719436C22132yescomplemented
61#11719433C22132yescomplemented
62#11719387C22132yescomplemented
63#11719385C22132yescomplemented
64#11719363C22164yescomplemented
65#11719355C22164yescomplemented
66#11719347C22132yescomplemented
67#11719346C22132yescomplemented
68#11719344C22132yescomplemented
69#11719340C22132yescomplemented
70D13×#117C22116yescomplemented
71#11719224C22116yescomplemented
72C2×#88152C2214yes—
73C2×#88152C2214yes—
74C2×#88151C2214yes—
75C2×#88146C2211yescharacteristic
76C2×#88146C2211yescharacteristic
77C2×#88146C2214yes—
78C2×C4⋊C4×D13C2211yescharacteristic
79C2×C4⋊C4×D13C2211yescharacteristic
80C2×#88144C2212yescomplemented
81C2×#88144C2214yescomplemented
82C2×#88143C2214yescomplemented
83C2×#88143C2214yescomplemented
84C2×#88142C2212yescomplemented
85C2×#88141C2214yescomplemented
86C2×#88140C2214yes—
87C2×#88139C2214yes—
88C2×#88137C2214yes—
89C2×#88135C2214yes—
90C2×C22⋊C4×D13C2212yes—
91C2×#88133C2214yescomplemented
92C2×#88133C2214yescomplemented
93C2×#88132C2214yes—
94C2×#88132C2214yescomplemented
95C2×#88131C2212yes—
96C2×#88131C2214yescomplemented
97C2×#88126C2212yes—
98C2×C42×D13C2212yes—
99C2×#88124C2212yescomplemented
100C2×#88123C2212yescomplemented
101C24×D13C2311yescharacteristic
102C2×C13×#41—28no—
103C2×C13×#41C2318yes—
104C22×Q8×C13—28no—
105C22×Q8×C13C2312yes—
106C22×Q8×C13C2312yes—
107C22×Q8×C13C2311yescharacteristic
108C22×Q8×C13C2318yes—
109C22×D4×C13C2312yes—
110C22×D4×C13C2311yescharacteristic
111C23×C4×C13C2312yes—
112C23×C4×C13C2312yes—
113C23×C4×C13C2311yescharacteristic
114C22×C22⋊D13C2312yes—
115C22×C22⋊D13C2312yes—
116C23×Dic13C2311yescharacteristic
117C23×Dic13C2314yes—
118C23×Dic13C2312yes—
119C22×C4×D13—28no—
120C22×C4×D13C2311yescharacteristic
121C22×C4×D13C2312yes—
122C22×C4×D13C2311yescharacteristic
123C22×C4×D13C2311yescharacteristic
124C22×C4×D13C2311yescharacteristic
125C22×C4×D13C2318yes—
126C22×C4×D13C2312yes—
127C22×Dic26C2314yes—
128C13×C4⋊Q8C23116yescomplemented
129C13×#124C23116yescomplemented
130C13×#123C23132yes—
131C13×C22⋊Q8C23116yescomplemented
132C13×C22⋊Q8C23116yescomplemented
133C13×#117C2318yes—
134C2×C13×C4⋊C4C2314yes—
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C4⋊C4C2314yes—
137C2×C13×C4⋊C4C2311yescharacteristic
138C2×C13×C22⋊C4C2312yes—
139C2×C13×C22⋊C4C2314yes—
140C2×C13×C22⋊C4C2314yes—
141C2×C42×C13C2312yes—
142C2×C22⋊Dic13C2312yes—
143C2×C22⋊Dic13C2312yes—
144C2×C22⋊Dic13C2312yes—
145C2×C22⋊Dic13C2312yes—
146C2×C22⋊Dic13C2314yes—
147#88200C2318yes—
148#88200C23116yes—
149#88200C2318yes—
150#88200C23116yes—
151#88200C23116yes—
152#88200C23116yes—
153Q8×Dic13C23116yescomplemented
154Q8×Dic13C23116yescomplemented
155Q8×Dic13C23116yescomplemented
156Q8×Dic13C23116yescomplemented
157Q8×Dic13C23116yescomplemented
158#88192C2318yes—
159#88192C2318yes—
160#88191C23116yes—
161#88189C23116yes—
162D4×Dic13C23132yes—
163D4×Dic13C23116yescomplemented
164C4×C22⋊D13C23116yes—
165C4×C22⋊D13C23116yes—
166C2×#6103C2312yes—
167C2×#6103C2312yes—
168C2×#6103C2314yes—
169C2×#6103C2314yes—
170C2×#6103C2312yes—
171C2×#6103C2312yes—
172C2×#6103C23116yes—
173#88180C2318yes—
174#88180C2318yes—
175#88180C23132yes—
176#88180C23116yescomplemented
177C2×C4⋊Dic13C2311yescharacteristic
178C2×C4⋊Dic13C2312yes—
179C2×C4⋊Dic13C2314yes—
180C2×C4⋊Dic13C2311yescharacteristic
181C2×C4⋊Dic13C2314yes—
182C2×C4⋊Dic13C2314yes—
183C2×C4⋊Dic13C2312yes—
184C2×C4⋊Dic13C2314yes—
185C2×C4⋊Dic13C2311yescharacteristic
186C2×C4⋊Dic13C2311yescharacteristic
187C2×C4⋊Dic13C2318yes—
188C2×C4⋊Dic13C23116yescomplemented
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2312yes—
192C2×#6101C2312yes—
193C2×#6101C2314yes—
194C2×#6101C2314yes—
195C2×#6101C2312yes—
196C2×#6101C2312yes—
197C2×#6101C23116yes—
198C2×C4×Dic13C2312yes—
199C2×C4×Dic13C2312yes—
200C2×C4×Dic13C2312yes—
201C2×C4×Dic13C2314yes—
202C2×C4×Dic13C2314yes—
203C2×C4×Dic13C2314yes—
204C2×C4×Dic13C2312yes—
205#88152C23132yes—
206#88152C23132yes—
207#88151C23132yes—
208#88146C23132yes—
209#88146C2318yes—
210#88146C2318yes—
211C4⋊C4×D13C2318yes—
212C4⋊C4×D13C2318yes—
213#88144C23132yescomplemented
214#88144C23116yescomplemented
215#88143C23132yescomplemented
216#88143C23132yescomplemented
217#88142C23116yescomplemented
218#88141C23132yescomplemented
219#88140C23132yes—
220#88139C23132yes—
221#88137C23132yes—
222#88135C23132yes—
223C22⋊C4×D13C23116yes—
224#88133C23132yescomplemented
225#88133C23132yescomplemented
226#88132C23132yes—
227#88132C23132yescomplemented
228#88131C23116yes—
229#88131C23132yescomplemented
230#88126C23116yes—
231C42×D13C23116yes—
232#88124C23116yescomplemented
233#88123C23116yescomplemented
234C2×#3495—131nomaximal, Sylow
235C24×C13C2412yes—
236C24×C13C2411yescharacteristic
237C23×D13—24no—
238C23×D13—24no—
239C23×D13—42no—
240C23×D13C2411yescharacteristic
241C23×D13C2414yes—
242C23×D13C2411yescharacteristic
243C13×#41—232no—
244C2×Q8×C13—28no—
245C2×Q8×C13—28no—
246C2×Q8×C13—232no—
247C2×Q8×C13—24no—
248C2×Q8×C13C2418yes—
249C2×Q8×C13C2418yes—
250C2×Q8×C13C2414yes—
251C2×D4×C13—28no—
252C2×D4×C13—24no—
253C2×D4×C13C2418yes—
254C2×D4×C13C2414yes—
255C22×C4×C13—28no—
256C22×C4×C13—28no—
257C22×C4×C13#4118yes—
258C22×C4×C13C2414yes—
259C22×C4×C13C2412yes—
260C22×C4×C13C2412yes—
261C22×C4×C13C2412yes—
262C22×C4×C13C2418yes—
263C22×C4×C13C2418yes—
264C22×C4×C13C2411yescharacteristic
265C22×C4×C13C2411yescharacteristic
266C22×C4×C13C2414yes—
267C2×C22⋊D13—28no—
268C2×C22⋊D13—44no—
269C2×C22⋊D13C2418yes—
270C2×C22⋊D13C2418yes—
271C22×Dic13—24no—
272C22×Dic13—44no—
273C22×Dic13—48no—
274C22×Dic13C2414yes—
275C22×Dic13C2412yes—
276C22×Dic13C2411yescharacteristic
277C22×Dic13C2412yes—
278C22×Dic13C2412yes—
279C22×Dic13C2412yes—
280C22×Dic13C2414yes—
281C22×Dic13C2411yescharacteristic
282C22×Dic13C24116yes—
283C22×Dic13C2418yes—
284C2×C4×D13—28no—
285C2×C4×D13—24no—
286C2×C4×D13—24no—
287C2×C4×D13—24no—
288C2×C4×D13—24no—
289C2×C4×D13—232no—
290C2×C4×D13—44no—
291C2×C4×D13C2414yes—
292C2×C4×D13C2418yes—
293C2×C4×D13C2414yes—
294C2×C4×D13C2414yes—
295C2×C4×D13C2414yes—
296C2×C4×D13C2418yes—
297C2×Dic26—48no—
298C2×Dic26C24116yes—
299C13×C4⋊C4C24116yes—
300C13×C4⋊C4C2414yes—
301C13×C4⋊C4C24116yes—
302C13×C4⋊C4C2414yes—
303C13×C22⋊C4C2418yes—
304C13×C22⋊C4C24116yes—
305C13×C22⋊C4C24116yes—
306C42×C13C2418yes—
307C22⋊Dic13C2418yes—
308C22⋊Dic13C2418yes—
309C22⋊Dic13C2418yes—
310C22⋊Dic13C2418yes—
311C22⋊Dic13C24116yes—
312#6103C2418yes—
313#6103C2418yes—
314#6103C24116yes—
315#6103C24116yes—
316#6103C2418yes—
317#6103C2418yes—
318C4⋊Dic13C2414yes—
319C4⋊Dic13C2418yes—
320C4⋊Dic13C24116yes—
321C4⋊Dic13C2414yes—
322C4⋊Dic13C24116yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C2418yes—
325C4⋊Dic13C24116yes—
326C4⋊Dic13C2414yes—
327C4⋊Dic13C2414yes—
328#6101C24116yes—
329#6101C24116yes—
330#6101C2418yes—
331#6101C2418yes—
332#6101C24116yes—
333#6101C24116yes—
334#6101C2418yes—
335#6101C2418yes—
336C4×Dic13C2418yes—
337C4×Dic13C2418yes—
338C4×Dic13C2418yes—
339C4×Dic13C24116yes—
340C4×Dic13C24116yes—
341C4×Dic13C24116yes—
342C4×Dic13C2418yes—
343#3495—1332no—
344C2×#556—132no—
345C2×#554—132no—
346C2×#552—134no—
347C2×#552—132no—
348C2×#552—132no—
349C2×#551—134no—
350C2×#544—131no—
351C2×#542—132no—
352C2×#541—132no—
353C2×#536D1311yescharacteristic, complemented
354C2×#533—132no—
355C2×#529—132no—
356C2×#525—131no—
357C22×C22⋊Q8—131no—
358C2×#520—131no—
359C2×#519—131no—
360C22×#117—131no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—24no—
364C23×C13—24no—
365C23×C13—24no—
366C23×C13C2×#4114yes—
367C23×C13C2514yes—
368C23×C13C2512yes—
369C23×C13C2511yescharacteristic
370C22×D13—22no—
371C22×D13—22no—
372C22×D13—28no—
373C22×D13—22no—
374C22×D13—22no—
375C22×D13—22no—
376C22×D13—28no—
377C22×D13—44no—
378C22×D13—416no—
379C22×D132−1+414yes—
380C22×D13C2512yes—
381C22×D13C2512yes—
382Q8×C13—216no—
383Q8×C13—216no—
384Q8×C13—28no—
385D4×C13—216no—
386D4×C13—28no—
387C2×C4×C13—24no—
388C2×C4×C13—216no—
389C2×C4×C13—28no—
390C2×C4×C13—24no—
391C2×C4×C13—24no—
392C2×C4×C13—216no—
393C2×C4×C13C2×#4114yes—
394C2×C4×C13C2×#4114yes—
395C2×C4×C13C2×#41116yes—
396C2×C4×C13C2518yes—
397C2×C4×C13C2514yes—
398C2×C4×C13C2514yes—
399C2×C4×C13C2514yes—
400C2×C4×C13C2512yes—
401C2×C4×C13C2512yes—
402C22⋊D13—216no—
403C22⋊D13—48no—
404C2×Dic13—28no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—24no—
408C2×Dic13—24no—
409C2×Dic13—24no—
410C2×Dic13—28no—
411C2×Dic13—24no—
412C2×Dic13—48no—
413C2×Dic13—416no—
414C2×Dic13C2514yes—
415C2×Dic13C2512yes—
416C2×Dic13C2514yes—
417C2×Dic13C2514yes—
418C2×Dic13C2514yes—
419C2×Dic13C2518yes—
420C2×Dic13C2512yes—
421C4×D13—216no—
422C4×D13—28no—
423C4×D13—28no—
424C4×D13—28no—
425C4×D13—28no—
426C4×D13—48no—
427Dic26—416no—
428C22×#41C2×D1311yescharacteristic
429C23×Q8C2×D1311yescharacteristic
430C24×C4—131no—
431#556—1332no—
432#554—1332no—
433#552—1364no—
434#552—1332no—
435#552—1332no—
436#551—1364no—
437#544—1316no—
438#542—1332no—
439#541—1332no—
440#536C2×D13116yescomplemented
441#533—1332no—
442C2×C4⋊Q8—132no—
443C2×C4⋊Q8—132no—
444C2×C4⋊Q8C2×D1312yescomplemented
445#529—1332no—
446C2×#126—134no—
447C2×#126—134no—
448C2×#126—134no—
449C2×#126—134no—
450C2×#125—134no—
451C2×#125—134no—
452C2×#125—134no—
453C2×#125—132no—
454C2×#125—132no—
455C2×#124—134no—
456C2×#124C2×D1312yescomplemented
457#525—1316no—
458C2×#123—132no—
459C2×#123—134no—
460C2×#123—134no—
461C2×#123C2×D1314yes—
462C2×C22⋊Q8—132no—
463C2×C22⋊Q8—132no—
464C2×C22⋊Q8—132no—
465C2×C22⋊Q8—132no—
466C2×C22⋊Q8—131no—
467C2×C22⋊Q8—131no—
468C2×C22⋊Q8—1316no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—134no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8C2×D1312yescomplemented
473C2×C22⋊Q8C2×D1312yescomplemented
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—134no—
493C2×#117—132no—
494C2×#117—1316no—
495C2×#117—131no—
496C2×#117—131no—
497C2×#117—134no—
498C2×#117—132no—
499C2×#117—134no—
500C2×#117—132no—
501C2×#117C2×D1311yescharacteristic
502C22×C4⋊C4—132no—
503C22×C4⋊C4—131no—
504C22×C4⋊C4—132no—
505C22×C4⋊C4—131no—
506C22×C4⋊C4—131no—
507C22×C22⋊C4—132no—
508C22×C22⋊C4—132no—
509C22×C42—132no—
510C22×C13—22no—
511C22×C13—22no—
512C22×C13—28no—
513C22×C13—24no—
514C22×C13—24no—
515C22×C13—24no—
516C22×C13—48no—
517C22×C13C22×#4114yes—
518C22×C13C22×#4112yes—
519C22×C13C2×2−1+412yes—
520C22×C13#58512yes—
521C22×C13C2611yescharacteristic
522C2×D13—22no—
523C2×D13—22no—
524C2×D13—28no—
525C2×D13—22no—
526C2×D13—22no—
527C2×D13—22no—
528C2×D13—416no—
529C2×D13—44no—
530C2×D13C2×2−1+414yes—
531C4×C13—24no—
532C4×C13—28no—
533C4×C13—24no—
534C4×C13—24no—
535C4×C13C22×#4114yes—
536C4×C13C22×#4114yes—
537Dic13—22no—
538Dic13—22no—
539Dic13—24no—
540Dic13—24no—
541Dic13—24no—
542Dic13—28no—
543Dic13—24no—
544C25—131no—
545C2×#41—28no—
546C2×#41C22×D1318yes—
547C22×Q8—28no—
548C22×Q8—134no—
549C22×Q8C22×D1312yes—
550C22×Q8C22×D1312yes—
551C22×Q8C22×D1311yescharacteristic
552C22×Q8C22×D1318yes—
553C22×D4—132no—
554C22×D4—132no—
555C22×D4C22×D1312yes—
556C22×D4C22×D1311yescharacteristic
557C23×C4—131no—
558C23×C4—132no—
559C23×C4—134no—
560C23×C4—132no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—138no—
565C23×C4—131no—
566C23×C4—132no—
567C23×C4—268no—
568C23×C4C22×D1312yes—
569C23×C4C22×D1312yes—
570C23×C4C22×D1311yescharacteristic
571C4⋊Q8—1316no—
572C4⋊Q8—1316no—
573C4⋊Q8C22×D13116yescomplemented
574#126—1332no—
575#126—1332no—
576#126—1332no—
577#126—1332no—
578#125—1332no—
579#125—1332no—
580#125—1332no—
581#125—1316no—
582#125—1316no—
583#124—1332no—
584#124C22×D13116yescomplemented
585#123—1316no—
586#123—1332no—
587#123—1332no—
588#123C22×D13132yes—
589C22⋊Q8—1316no—
590C22⋊Q8—1316no—
591C22⋊Q8—1316no—
592C22⋊Q8—1316no—
593C22⋊Q8—138no—
594C22⋊Q8—138no—
595C22⋊Q8—1332no—
596C22⋊Q8—1332no—
597C22⋊Q8—1332no—
598C22⋊Q8C22×D13116yescomplemented
599C22⋊Q8C22×D13116yescomplemented
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—1316no—
610C4×D4—1332no—
611C4×D4—1316no—
612C4×D4—1316no—
613C4×D4—1332no—
614#117—138no—
615#117—138no—
616#117—1332no—
617#117—1316no—
618#117—138no—
619#117—138no—
620#117—1332no—
621#117—1316no—
622#117—1332no—
623#117—1316no—
624#117C22×D1318yes—
625C2×C4⋊C4—131no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—131no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—132no—
630C2×C4⋊C4—134no—
631C2×C4⋊C4—132no—
632C2×C4⋊C4—134no—
633C2×C4⋊C4—138no—
634C2×C4⋊C4—1316no—
635C2×C4⋊C4—134no—
636C2×C4⋊C4—1316no—
637C2×C4⋊C4—131no—
638C2×C4⋊C4—131no—
639C2×C4⋊C4—134no—
640C2×C4⋊C4—134no—
641C2×C4⋊C4—134no—
642C2×C4⋊C4—134no—
643C2×C4⋊C4—132no—
644C2×C4⋊C4—132no—
645C2×C4⋊C4—134no—
646C2×C4⋊C4—138no—
647C2×C4⋊C4—138no—
648C2×C4⋊C4C22×D1311yescharacteristic
649C2×C4⋊C4C22×D1311yescharacteristic
650C2×C4⋊C4C22×D1314yes—
651C2×C4⋊C4C22×D1314yes—
652C2×C22⋊C4—132no—
653C2×C22⋊C4—132no—
654C2×C22⋊C4—132no—
655C2×C22⋊C4—134no—
656C2×C22⋊C4—132no—
657C2×C22⋊C4—132no—
658C2×C22⋊C4—132no—
659C2×C22⋊C4—134no—
660C2×C22⋊C4—134no—
661C2×C22⋊C4—1316no—
662C2×C22⋊C4—132no—
663C2×C22⋊C4—132no—
664C2×C22⋊C4—1316no—
665C2×C22⋊C4C22×D1312yes—
666C2×C22⋊C4C22×D1314yes—
667C2×C22⋊C4C22×D1314yes—
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×C42C22×D1312yes—
677C2×C13—24no—
678C2×C13—44no—
679C2×C13#349514yescomplemented
680C2×C13C23×#4111yescharacteristic
681C2×C13C22×2−1+411yescharacteristic
682C2×C13C2×#58511yescharacteristic
683D13—24no—
684D13—42no—
685C24—131no—
686C24—131no—
687C24—134no—
688C24—264no—
689C24—264no—
690C24—522no—
691C24C23×D1312yes—
692C24C23×D1311yescharacteristic
693#41—232no—
694C2×Q8—28no—
695C2×Q8—28no—
696C2×Q8—232no—
697C2×Q8—24no—
698C2×Q8—1316no—
699C2×Q8—528no—
700C2×Q8C23×D1318yes—
701C2×Q8C23×D1318yes—
702C2×Q8C23×D1314yes—
703C2×D4—28no—
704C2×D4—24no—
705C2×D4—138no—
706C2×D4—138no—
707C2×D4—268no—
708C2×D4—524no—
709C2×D4C23×D1318yes—
710C2×D4C23×D1314yes—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—134no—
714C22×C4—132no—
715C22×C4—131no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—134no—
720C22×C4—131no—
721C22×C4—138no—
722C22×C4—1316no—
723C22×C4—134no—
724C22×C4—138no—
725C22×C4—134no—
726C22×C4—134no—
727C22×C4—134no—
728C22×C4—138no—
729C22×C4—268no—
730C22×C4—264no—
731C22×C4—264no—
732C22×C4—264no—
733C22×C4—264no—
734C22×C4—264no—
735C22×C4—2632no—
736C22×C4—524no—
737C22×C4—528no—
738C22×C4—524no—
739C22×C4#612918yes—
740C22×C4C23×D1318yes—
741C22×C4C23×D1318yes—
742C22×C4C23×D1314yes—
743C22×C4C23×D1312yes—
744C22×C4C23×D1312yes—
745C22×C4C23×D1312yes—
746C22×C4C23×D1314yes—
747C22×C4C23×D1311yescharacteristic
748C22×C4C23×D1311yescharacteristic
749C4⋊C4—134no—
750C4⋊C4—138no—
751C4⋊C4—134no—
752C4⋊C4—138no—
753C4⋊C4—138no—
754C4⋊C4—1316no—
755C4⋊C4—138no—
756C4⋊C4—1316no—
757C4⋊C4—1316no—
758C4⋊C4—134no—
759C4⋊C4—134no—
760C4⋊C4—1316no—
761C4⋊C4—1316no—
762C4⋊C4—1316no—
763C4⋊C4—1316no—
764C4⋊C4—138no—
765C4⋊C4—138no—
766C4⋊C4—1316no—
767C4⋊C4C23×D1314yes—
768C4⋊C4C23×D1314yes—
769C4⋊C4C23×D13116yes—
770C4⋊C4C23×D13116yes—
771C22⋊C4—138no—
772C22⋊C4—138no—
773C22⋊C4—138no—
774C22⋊C4—1316no—
775C22⋊C4—138no—
776C22⋊C4—138no—
777C22⋊C4—138no—
778C22⋊C4—1316no—
779C22⋊C4—1316no—
780C22⋊C4—138no—
781C22⋊C4—138no—
782C22⋊C4C23×D1318yes—
783C22⋊C4C23×D13116yes—
784C22⋊C4C23×D13116yes—
785C42—138no—
786C42—138no—
787C42—138no—
788C42—1316no—
789C42—1316no—
790C42—1316no—
791C42—138no—
792C42C23×D1318yes—
793C13C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—24no—
797C23—24no—
798C23—24no—
799C23—134no—
800C23—132no—
801C23—132no—
802C23—268no—
803C23—262no—
804C23—262no—
805C23—268no—
806C23—262no—
807C23—262no—
808C23—262no—
809C23—524no—
810C23—5216no—
811C23C2×#612914yes—
812C23C24×D1314yes—
813C23C24×D1312yes—
814C23C24×D1311yescharacteristic
815Q8—216no—
816Q8—216no—
817Q8—28no—
818Q8—5216no—
819D4—216no—
820D4—28no—
821D4—2616no—
822D4—528no—
823C2×C4—24no—
824C2×C4—216no—
825C2×C4—28no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—216no—
829C2×C4—134no—
830C2×C4—132no—
831C2×C4—134no—
832C2×C4—134no—
833C2×C4—134no—
834C2×C4—138no—
835C2×C4—132no—
836C2×C4—2616no—
837C2×C4—268no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—264no—
841C2×C4—264no—
842C2×C4—264no—
843C2×C4—268no—
844C2×C4—264no—
845C2×C4—268no—
846C2×C4—268no—
847C2×C4—268no—
848C2×C4—268no—
849C2×C4—528no—
850C2×C4—5216no—
851C2×C4—528no—
852C2×C4C2×#612914yes—
853C2×C4C2×#612914yes—
854C2×C4C2×#6129116yes—
855C2×C4C24×D1318yes—
856C2×C4C24×D1314yes—
857C2×C4C24×D1314yes—
858C2×C4C24×D1314yes—
859C2×C4C24×D1312yes—
860C2×C4C24×D1312yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—48no—
868C22—134no—
869C22—268no—
870C22—262no—
871C22—262no—
872C22—262no—
873C22—262no—
874C22—262no—
875C22—5216no—
876C22—524no—
877C22C22×#612914yes—
878C22C22×#612912yes—
879C22D13×2−1+412yes—
880C22#1171965212yes—
881C22C25×D1311yescharacteristic
882C4—24no—
883C4—28no—
884C4—24no—
885C4—24no—
886C4—262no—
887C4—262no—
888C4—264no—
889C4—264no—
890C4—264no—
891C4—268no—
892C4—264no—
893C4C22×#612914yes—
894C4C22×#612914yes—
895C2—24no—
896C2—44no—
897C2—264no—
898C2—522no—
899C2#1312858514yesdirect product factor
900C2C23×#612911yescharacteristic
901C2C2×D13×2−1+411yescharacteristic
902C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#536C2
socleC23×C13C25
prime radicalC2×#11719533C2
hypercenterC2×#536D13
hypocenterC13C2×#3495
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13128585C2direct (N × H)
2. C2×#11719346C2semidirect
3. C2×#11719340C2semidirect
4. C2×#11719347C2semidirect
5. C2×#11719355C2semidirect
6. C2×#11719344C2semidirect
7. C2×#11719363C2semidirect
8. C2×#11719224C2semidirect
9. C2×#11719387C2semidirect
10. C2×#11719436C2semidirect
11. C2×#11719433C2semidirect
12. C2×#11719385C2semidirect
14. C22×#88200C2semidirect
15. C2×#11719532C2semidirect
16. C2×#11719517C2semidirect
17. C2×D13×#117C2semidirect
18. C2×C13×#536C2semidirect
22. C13×#536C22semidirect
23. C2×C13×C4⋊Q8C22semidirect
24. C2×C13×#124C22semidirect
26. C2×C13×C22⋊Q8C22semidirect
27. C2×C13×C22⋊Q8C22semidirect
30. #11719532C22semidirect
37. C2×#88200C22semidirect
38. #11719517C22semidirect
39. C2×Q8×Dic13C22semidirect
40. C2×Q8×Dic13C22semidirect
41. C2×Q8×Dic13C22semidirect
42. C2×Q8×Dic13C22semidirect
43. C2×Q8×Dic13C22semidirect
49. C2×D4×Dic13C22semidirect
56. C2×#88180C22semidirect
58. C22×C4⋊Dic13C22semidirect
60. #11719436C22semidirect
61. #11719433C22semidirect
62. #11719387C22semidirect
63. #11719385C22semidirect
64. #11719363C22semidirect
65. #11719355C22semidirect
66. #11719347C22semidirect
67. #11719346C22semidirect
68. #11719344C22semidirect
69. #11719340C22semidirect
70. D13×#117C22semidirect
71. #11719224C22semidirect
80. C2×#88144C22semidirect
81. C2×#88144C22semidirect
82. C2×#88143C22semidirect
83. C2×#88143C22semidirect
84. C2×#88142C22semidirect
85. C2×#88141C22semidirect
91. C2×#88133C22semidirect
92. C2×#88133C22semidirect
94. C2×#88132C22semidirect
96. C2×#88131C22semidirect
99. C2×#88124C22semidirect
100. C2×#88123C22semidirect
128. C13×C4⋊Q8C23semidirect
129. C13×#124C23semidirect
131. C13×C22⋊Q8C23semidirect
132. C13×C22⋊Q8C23semidirect
153. Q8×Dic13C23semidirect
154. Q8×Dic13C23semidirect
155. Q8×Dic13C23semidirect
156. Q8×Dic13C23semidirect
157. Q8×Dic13C23semidirect
163. D4×Dic13C23semidirect
176. #88180C23semidirect
188. C2×C4⋊Dic13C23semidirect
213. #88144C23semidirect
214. #88144C23semidirect
215. #88143C23semidirect
216. #88143C23semidirect
217. #88142C23semidirect
218. #88141C23semidirect
224. #88133C23semidirect
225. #88133C23semidirect
227. #88132C23semidirect
229. #88131C23semidirect
232. #88124C23semidirect
233. #88123C23semidirect
353. C2×#536D13semidirect
440. #536C2×D13semidirect
444. C2×C4⋊Q8C2×D13semidirect
456. C2×#124C2×D13semidirect
472. C2×C22⋊Q8C2×D13semidirect
473. C2×C22⋊Q8C2×D13semidirect
573. C4⋊Q8C22×D13semidirect
584. #124C22×D13semidirect
598. C22⋊Q8C22×D13semidirect
599. C22⋊Q8C22×D13semidirect
679. C2×C13#3495semidirect
793. C13C2×#3495semidirect
899. C2#13128585direct (N × H)

Maximal subgroups

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

subgroupindex
#131285852
C2×#117193462
C2×#117193402
C2×#117193472
C2×#117193552
C2×#117193442
C2×#117193632
C2×#117192242
C2×#117193872
C2×#117194362
C2×#117194332
C2×#117193852
C2×#117195332
C22×#882002
C2×#117195322
C2×#117195172
C2×D13×#1172
C2×C13×#5362
C2×#349513