Finite Group Databasebeta

← C2×#13128719 #16771358

Subgroups — C2×#13128719 #16771358

Order 3328.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128719C2132yesmaximal, direct product factor
2C2×#11719272C211yesmaximal, characteristic, complemented
3C2×#11719426C212yesmaximal, complemented
4C2×#11719437C211yesmaximal, characteristic, complemented
5C2×#11719289C211yesmaximal, characteristic, complemented
6C2×#11719273C212yesmaximal, complemented
7C2×#11719286C212yesmaximal, complemented
8C2×#11719399C212yesmaximal, complemented
9C2×#11719398C214yesmaximal, complemented
10C2×#11719401C214yesmaximal, complemented
11C2×#11719429C212yesmaximal
12C2×#11719393C212yesmaximal, complemented
13C2×#11719283C212yesmaximal, complemented
14C2×#11719283C211yesmaximal, characteristic, complemented
15C2×D13×C4⋊Q8C211yesmaximal, characteristic, complemented
16C2×#11719277C212yesmaximal, complemented
17C2×C4×#6131C211yesmaximal, characteristic
18C2×C13×#557C211yesmaximal, characteristic, complemented
19C22×#6131C2211yescharacteristic
20C22×Q8×D13C2212yes—
21C13×#557C22116yescomplemented
22C2×C13×C4⋊Q8C2211yescharacteristic
23C2×C13×C4⋊Q8C2212yes—
24C2×C13×#125C2214yes—
25C2×C13×#125C2212yes—
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2212yes—
28C2×C4×Q8×C13C2212yes—
29C2×C4×Q8×C13C2211yescharacteristic
30C2×#88201C2212yes—
31C2×#88200C2211yescharacteristic
32C2×#88200C2212yes—
33C2×Q8×Dic13C2211yescharacteristic
34C2×Q8×Dic13C2212yes—
35C2×#88198C2212yes—
36C2×#88198C2211yescharacteristic
37C2×#88198C2212yes—
38#11719437C22116yescomplemented
39#11719429C22132yes—
40D13×C4⋊Q8C22116yescomplemented
41#11719426C22132yescomplemented
42#11719401C22164yescomplemented
43#11719399C22132yescomplemented
44#11719398C22164yescomplemented
45#11719393C22132yescomplemented
46#11719289C22116yescomplemented
47#11719286C22132yescomplemented
48#11719283C22116yescomplemented
49#11719283C22132yescomplemented
50C4×#6131C22116yes—
51#11719277C22132yescomplemented
52#11719273C22132yescomplemented
53#11719272C22116yescomplemented
54C2×#88152C2214yes—
55C2×#88152C2214yes—
56C2×#88152C2214yes—
57C2×#88151C2211yescharacteristic
58C2×#88151C2212yes—
59C2×#88150C2214yes—
60C2×#88150C2214yes—
61C2×#88150C2212yes—
62C2×#88150C2214yes—
63C2×#88148C2214yes—
64C2×#88148C2214yes—
65C2×#88147C2212yes—
66C2×#88147C2211yescharacteristic
67C2×#88146C2212yes—
68C2×#88146C2211yescharacteristic
69C2×#88146C2214yes—
70C2×#88146C2212yes—
71C2×#88146C2212yes—
72C2×C4⋊C4×D13C2212yes—
73C2×C4⋊C4×D13C2212yes—
74C2×#88144C2214yes—
75C2×#88143C2212yes—
76C2×#88143C2214yes—
77C2×#88143C2214yes—
78C2×#88143C2214yes—
79C2×#88142C2212yes—
80C2×#88142C2212yes—
81C2×#88142C2211yescharacteristic
82C2×#88141C2214yes—
83C2×#88141C2212yes—
84C2×#88141C2214yes—
85C2×#88130C2214yes—
86C2×#88129C2212yes—
87C2×C4×D52C2212yes—
88C2×C4×D52C2211yescharacteristic
89C2×#88126C2214yes—
90C2×#88126C2212yes—
91C2×#88126C2214yes—
92C2×C42×D13C2211yescharacteristic
93C2×C42×D13C2212yes—
94C2×#88124C2212yes—
95C2×#88123C2211yescharacteristic
96C2×C4×Dic26C2214yes—
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2312yes—
103C22×Q8×C13C2311yescharacteristic
104C2×#6131—28no—
105C2×#6131C2318yes—
106C2×Q8×D13—216no—
107C2×Q8×D13C23116yes—
108C22×D52C2311yescharacteristic
109C22×D52C2312yes—
110C22×C4×D13C2312yes—
111C22×C4×D13C2311yescharacteristic
112C22×C4×D13C2312yes—
113C22×C4×D13C2311yescharacteristic
114C22×C4×D13C2312yes—
115C22×C4×D13C2314yes—
116C22×C4×D13C2311yescharacteristic
117C22×Dic26C2311yescharacteristic
118C22×Dic26C2312yes—
119C22×Dic26C2312yes—
120C22×Dic26C2314yes—
121C13×C4⋊Q8C23116yes—
122C13×C4⋊Q8C2318yes—
123C13×#125C23116yes—
124C13×#125C23132yes—
125C4×Q8×C13C2318yes—
126C4×Q8×C13C23116yes—
127C4×Q8×C13C23116yes—
128C4×Q8×C13C2318yes—
129C2×C13×C4⋊C4C2311yescharacteristic
130C2×C13×C4⋊C4C2314yes—
131C2×C13×C4⋊C4C2314yes—
132C2×C13×C4⋊C4C2312yes—
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2314yes—
137C2×C13×C4⋊C4C2312yes—
138C2×C42×C13C2312yes—
139C2×C42×C13C2311yescharacteristic
140C2×C42×C13C2312yes—
141C2×C42×C13C2314yes—
142#88201C23116yes—
143#88200C2318yes—
144#88200C23116yes—
145Q8×Dic13C2318yes—
146Q8×Dic13C23116yes—
147#88198C23116yes—
148#88198C23116yes—
149#88198C2318yes—
150C2×#6103C2312yes—
151C2×#6103C2312yes—
152C2×#6103C2314yes—
153C2×#6103C2312yes—
154C2×#6103C2314yes—
155C2×#6103C2312yes—
156C2×#6103C2312yes—
157C2×#6103C2314yes—
158C2×#6103C2314yes—
159C2×C4⋊Dic13C2311yescharacteristic
160C2×C4⋊Dic13C2312yes—
161C2×C4⋊Dic13C2311yescharacteristic
162C2×C4⋊Dic13C2312yes—
163C2×C4⋊Dic13C2314yes—
164C2×C4⋊Dic13C2312yes—
165C2×C4⋊Dic13C2312yes—
166C2×#6101C2314yes—
167C2×#6101C2312yes—
168C2×#6101C2312yes—
169C2×#6101C2312yes—
170C2×#6101C2312yes—
171C2×#6101C2314yes—
172C2×#6101C2314yes—
173C2×#6101C2314yes—
174C2×#6101C2312yes—
175C2×#6101C2314yes—
176C2×#6101C2314yes—
177C2×C4×Dic13C2312yes—
178C2×C4×Dic13C2311yescharacteristic
179C2×C4×Dic13C2314yes—
180C2×C4×Dic13C2312yes—
181C2×C4×Dic13C2314yes—
182C2×C4×Dic13C2311yescharacteristic
183C2×C4×Dic13C2312yes—
184C2×C4×Dic13C2311yescharacteristic
185C2×C4×Dic13C2314yes—
186#88152C23132yes—
187#88152C23132yes—
188#88152C23132yes—
189#88151C23116yes—
190#88151C2318yes—
191#88150C23132yes—
192#88150C23132yes—
193#88150C23132yes—
194#88150C23116yes—
195#88148C23132yes—
196#88148C23132yes—
197#88147C2318yes—
198#88147C23116yes—
199#88146C23116yes—
200#88146C2318yes—
201#88146C23132yes—
202#88146C23116yes—
203#88146C23116yes—
204C4⋊C4×D13C23116yes—
205C4⋊C4×D13C23116yes—
206#88144C23132yes—
207#88143C23132yes—
208#88143C23132yes—
209#88143C23132yes—
210#88143C23116yes—
211#88142C23116yes—
212#88142C23116yes—
213#88142C2318yes—
214#88141C23132yes—
215#88141C23116yes—
216#88141C23132yes—
217#88130C23132yes—
218#88129C23116yes—
219C4×D52C2318yes—
220C4×D52C23116yes—
221#88126C23116yes—
222#88126C23132yes—
223#88126C23132yes—
224C42×D13C2318yes—
225C42×D13C23116yes—
226#88124C23116yes—
227#88123C2318yes—
228C4×Dic26C23116yes—
229C4×Dic26C23116yes—
230C4×Dic26C2318yes—
231C4×Dic26C23116yes—
232C4×Dic26C23132yes—
233C2×#3509—131nomaximal, Sylow
234C23×D13C2412yes—
235C23×D13C2411yescharacteristic
236C2×Q8×C13—28no—
237C2×Q8×C13—24no—
238C2×Q8×C13—24no—
239C2×Q8×C13C2414yes—
240C2×Q8×C13C2418yes—
241C2×Q8×C13C2414yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C2412yes—
244C22×C4×C13C2412yes—
245C22×C4×C13C2411yescharacteristic
246C22×C4×C13C2414yes—
247C22×C4×C13C2412yes—
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2411yescharacteristic
250C22×Dic13C2412yes—
251C22×Dic13C2412yes—
252C22×Dic13C2412yes—
253C22×Dic13C2411yescharacteristic
254C22×Dic13C2414yes—
255C22×Dic13C2411yescharacteristic
256C22×Dic13C2411yescharacteristic
257#6131—232no—
258Q8×D13—264no—
259C2×D52—28no—
260C2×D52—24no—
261C2×D52C2414yes—
262C2×D52C2418yes—
263C2×C4×D13—216no—
264C2×C4×D13—24no—
265C2×C4×D13—28no—
266C2×C4×D13—28no—
267C2×C4×D13—24no—
268C2×C4×D13—28no—
269C2×C4×D13#4118yes—
270C2×C4×D13C2418yes—
271C2×C4×D13C2414yes—
272C2×C4×D13C2418yes—
273C2×C4×D13C2414yes—
274C2×C4×D13C2418yes—
275C2×C4×D13C24116yes—
276C2×C4×D13C2414yes—
277C2×Dic26—28no—
278C2×Dic26—24no—
279C2×Dic26—216no—
280C2×Dic26—28no—
281C2×Dic26C2414yes—
282C2×Dic26C2418yes—
283C2×Dic26C2418yes—
284C2×Dic26C24116yes—
285C13×C4⋊C4C2414yes—
286C13×C4⋊C4C24116yes—
287C13×C4⋊C4C24116yes—
288C13×C4⋊C4C2418yes—
289C13×C4⋊C4C2418yes—
290C13×C4⋊C4C2414yes—
291C13×C4⋊C4C2418yes—
292C13×C4⋊C4C24116yes—
293C13×C4⋊C4C2418yes—
294C42×C13C2418yes—
295C42×C13C2414yes—
296C42×C13C2418yes—
297C42×C13C24116yes—
298#6103C2418yes—
299#6103C2418yes—
300#6103C24116yes—
301#6103C2418yes—
302#6103C24116yes—
303#6103C2418yes—
304#6103C2418yes—
305#6103C24116yes—
306#6103C24116yes—
307C4⋊Dic13C2414yes—
308C4⋊Dic13C2418yes—
309C4⋊Dic13C2414yes—
310C4⋊Dic13C2418yes—
311C4⋊Dic13C24116yes—
312C4⋊Dic13C2418yes—
313C4⋊Dic13C2418yes—
314#6101C24116yes—
315#6101C2418yes—
316#6101C2418yes—
317#6101C2418yes—
318#6101C2418yes—
319#6101C24116yes—
320#6101C24116yes—
321#6101C24116yes—
322#6101C2418yes—
323#6101C24116yes—
324#6101C24116yes—
325C4×Dic13C2418yes—
326C4×Dic13C2414yes—
327C4×Dic13C24116yes—
328C4×Dic13C2418yes—
329C4×Dic13C24116yes—
330C4×Dic13C2414yes—
331C4×Dic13C2418yes—
332C4×Dic13C2414yes—
333C4×Dic13C24116yes—
334#3509—1332no—
335C2×#557—132no—
336C2×#557—131no—
337C2×#557D1311yescharacteristic, complemented
338C2×#556—131no—
339C2×#556—132no—
340C2×#556—131no—
341C2×#552—134no—
342C2×#552—132no—
343C2×#552—132no—
344C2×#541—134no—
345C2×#536—132no—
346C2×#533—132no—
347C2×#533—131no—
348C2×#533—132no—
349C22×C4⋊Q8—131no—
350C2×#519—132no—
351C2×C4×#41—131no—
352C23×C13C2511yescharacteristic
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—24no—
356C22×D13—24no—
357C22×D13—24no—
358C22×D13C2×#4114yes—
359C22×D13C2514yes—
360C22×D13C2512yes—
361Q8×C13—216no—
362Q8×C13—28no—
363Q8×C13—28no—
364C2×C4×C13—28no—
365C2×C4×C13—24no—
366C2×C4×C13—24no—
367C2×C4×C13—24no—
368C2×C4×C13—22no—
369C2×C4×C13—24no—
370C2×C4×C13C2×#4114yes—
371C2×C4×C132−1+414yes—
372C2×C4×C13C2514yes—
373C2×C4×C13C2514yes—
374C2×C4×C13C2514yes—
375C2×C4×C13C2512yes—
376C2×C4×C13C2518yes—
377C2×C4×C13C2514yes—
378C2×C4×C13C2512yes—
379C2×C4×C13C2512yes—
380C2×Dic13—28no—
381C2×Dic13—24no—
382C2×Dic13—24no—
383C2×Dic13—24no—
384C2×Dic13—22no—
385C2×Dic13C2×#4114yes—
386C2×Dic132−1+414yes—
387C2×Dic13C2514yes—
388C2×Dic13C2514yes—
389C2×Dic13C2514yes—
390C2×Dic13C2512yes—
391C2×Dic13C2518yes—
392C2×Dic13C2512yes—
393C2×Dic13C2512yes—
394D52—216no—
395D52—28no—
396C4×D13—232no—
397C4×D13—28no—
398C4×D13—216no—
399C4×D13—216no—
400C4×D13—28no—
401C4×D13—216no—
402C4×D13C2×#41116yes—
403Dic26—216no—
404Dic26—28no—
405Dic26—232no—
406Dic26—216no—
407C22×#41—131no—
408C23×Q8—132no—
409#557—1332no—
410#557—1316no—
411#557C2×D13116yescomplemented
412#556—1316no—
413#556—1332no—
414#556—1316no—
415#552—1364no—
416#552—1332no—
417#552—1332no—
418#541—1364no—
419#536—1332no—
420#533—1332no—
421#533—1316no—
422#533—1332no—
423C2×C4⋊Q8—132no—
424C2×C4⋊Q8—131no—
425C2×C4⋊Q8—132no—
426C2×C4⋊Q8—1316no—
427C2×C4⋊Q8—132no—
428C2×C4⋊Q8—132no—
429C2×C4⋊Q8—131no—
430C2×C4⋊Q8—131no—
431C2×C4⋊Q8C2×D1311yescharacteristic
432C2×C4⋊Q8C2×D1312yes—
433C2×#126—134no—
434C2×#126—134no—
435C2×#126—134no—
436C2×#126—134no—
437C2×#125—132no—
438C2×#125—134no—
439C2×#125—134no—
440C2×#125—134no—
441C2×#125—134no—
442C2×#125—132no—
443C2×#125C2×D1312yes—
444C2×#125C2×D1314yes—
445C2×#124—132no—
446C2×#124—132no—
447C2×#123—134no—
448C2×#123—134no—
449C2×C22⋊Q8—131no—
450C2×C22⋊Q8—132no—
451C2×C22⋊Q8—134no—
452C2×C22⋊Q8—134no—
453C2×C22⋊Q8—132no—
454C2×C22⋊Q8—134no—
455C2×C22⋊Q8—131no—
456C2×C22⋊Q8—132no—
457#519—1332no—
458C4×#41—1316no—
459C2×C4×Q8—131no—
460C2×C4×Q8—132no—
461C2×C4×Q8—134no—
462C2×C4×Q8—132no—
463C2×C4×Q8—134no—
464C2×C4×Q8—134no—
465C2×C4×Q8—132no—
466C2×C4×Q8—132no—
467C2×C4×Q8—131no—
468C2×C4×Q8—132no—
469C2×C4×Q8C2×D1311yescharacteristic
470C2×C4×Q8C2×D1312yes—
471C2×C4×Q8C2×D1312yes—
472C2×C4×Q8C2×D1311yescharacteristic
473C2×C4×D4—132no—
474C2×C4×D4—131no—
475C2×C4×D4—132no—
476C2×C4×D4—131no—
477C2×#117—131no—
478C2×#117—132no—
479C2×#117—134no—
480C2×#117—132no—
481C2×#117—132no—
482C2×#117—132no—
483C2×#117—134no—
484C2×#117—134no—
485C22×C4⋊C4—132no—
486C22×C4⋊C4—132no—
487C22×C42—131no—
488C22×C42—132no—
489C22×C13C22×#4112yes—
490C22×C13C2×2−1+412yes—
491C22×C13C2×2−1+412yes—
492C22×C13C2611yescharacteristic
493C2×D13—22no—
494C2×D13—22no—
495C2×D13—28no—
496C2×D13—24no—
497C2×D13—24no—
498C2×D13—24no—
499C2×D13—48no—
500C2×D13C22×#4114yes—
501C4×C13—28no—
502C4×C13—24no—
503C4×C13—24no—
504C4×C13—24no—
505C4×C13—22no—
506C4×C13—24no—
507C4×C13C22×#4114yes—
508C4×C13C2×2−1+414yes—
509Dic13—28no—
510Dic13—24no—
511Dic13—24no—
512Dic13—24no—
513Dic13—22no—
514Dic13C22×#4114yes—
515Dic13C2×2−1+414yes—
516C2×#41—138no—
517C2×#41—268no—
518C22×Q8—1316no—
519C22×Q8—132no—
520C22×Q8—131no—
521C22×Q8—134no—
522C22×Q8—132no—
523C22×Q8—2616no—
524C22×Q8C22×D1312yes—
525C22×Q8C22×D1311yescharacteristic
526C22×Q8C22×D1311yescharacteristic
527C22×D4—132no—
528C22×D4—131no—
529C23×C4—131no—
530C23×C4—134no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—132no—
534C23×C4—132no—
535C23×C4—132no—
536C4⋊Q8—1316no—
537C4⋊Q8—138no—
538C4⋊Q8—1316no—
539C4⋊Q8—1316no—
540C4⋊Q8—1316no—
541C4⋊Q8—138no—
542C4⋊Q8—138no—
543C4⋊Q8C22×D1318yes—
544C4⋊Q8C22×D13116yes—
545#126—1332no—
546#126—1332no—
547#126—1332no—
548#126—1332no—
549#125—1316no—
550#125—1332no—
551#125—1332no—
552#125—1332no—
553#125—1332no—
554#125—1316no—
555#125C22×D13116yes—
556#125C22×D13132yes—
557#124—1316no—
558#124—1316no—
559#123—1332no—
560#123—1332no—
561C22⋊Q8—138no—
562C22⋊Q8—1316no—
563C22⋊Q8—1332no—
564C22⋊Q8—1332no—
565C22⋊Q8—1316no—
566C22⋊Q8—138no—
567C22⋊Q8—1332no—
568C22⋊Q8—1316no—
569C4×Q8—138no—
570C4×Q8—1316no—
571C4×Q8—1332no—
572C4×Q8—1316no—
573C4×Q8—1332no—
574C4×Q8—1332no—
575C4×Q8—1316no—
576C4×Q8—1316no—
577C4×Q8—1316no—
578C4×Q8—138no—
579C4×Q8C22×D1318yes—
580C4×Q8C22×D13116yes—
581C4×Q8C22×D13116yes—
582C4×Q8C22×D1318yes—
583C4×D4—1316no—
584C4×D4—138no—
585C4×D4—1316no—
586C4×D4—138no—
587#117—138no—
588#117—1316no—
589#117—1332no—
590#117—1316no—
591#117—1316no—
592#117—1316no—
593#117—1332no—
594#117—1332no—
595C2×C4⋊C4—134no—
596C2×C4⋊C4—132no—
597C2×C4⋊C4—134no—
598C2×C4⋊C4—132no—
599C2×C4⋊C4—132no—
600C2×C4⋊C4—131no—
601C2×C4⋊C4—131no—
602C2×C4⋊C4—132no—
603C2×C4⋊C4—132no—
604C2×C4⋊C4—132no—
605C2×C4⋊C4—134no—
606C2×C4⋊C4—134no—
607C2×C4⋊C4—134no—
608C2×C4⋊C4—134no—
609C2×C4⋊C4—134no—
610C2×C4⋊C4—132no—
611C2×C4⋊C4—132no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—1316no—
614C2×C4⋊C4—1316no—
615C2×C4⋊C4C22×D1312yes—
616C2×C4⋊C4C22×D1312yes—
617C2×C4⋊C4C22×D1311yescharacteristic
618C2×C4⋊C4C22×D1311yescharacteristic
619C2×C4⋊C4C22×D1312yes—
620C2×C4⋊C4C22×D1314yes—
621C2×C4⋊C4C22×D1314yes—
622C2×C4⋊C4C22×D1314yes—
623C2×C4⋊C4C22×D1312yes—
624C2×C22⋊C4—132no—
625C2×C22⋊C4—132no—
626C2×C22⋊C4—132no—
627C2×C22⋊C4—132no—
628C2×C22⋊C4—132no—
629C2×C22⋊C4—134no—
630C2×C22⋊C4—134no—
631C2×C22⋊C4—134no—
632C2×C22⋊C4—134no—
633C2×C42—132no—
634C2×C42—134no—
635C2×C42—134no—
636C2×C42—134no—
637C2×C42—131no—
638C2×C42—132no—
639C2×C42—132no—
640C2×C42—131no—
641C2×C42—131no—
642C2×C42—138no—
643C2×C42—1316no—
644C2×C42C22×D1314yes—
645C2×C42C22×D1312yes—
646C2×C42C22×D1312yes—
647C2×C42C22×D1311yescharacteristic
648C2×C13#350914yescomplemented
649C2×C13C23×#4111yescharacteristic
650C2×C13C22×2−1+411yescharacteristic
651C2×C13C22×2−1+411yescharacteristic
652D13—24no—
653D13—44no—
654C24—131no—
655C24—132no—
656#41—2632no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—138no—
661C2×Q8—134no—
662C2×Q8—1316no—
663C2×Q8—138no—
664C2×Q8—2616no—
665C2×Q8—268no—
666C2×Q8—2664no—
667C2×Q8—264no—
668C2×Q8—268no—
669C2×Q8C23×D1318yes—
670C2×Q8C23×D1314yes—
671C2×Q8C23×D1314yes—
672C2×D4—138no—
673C2×D4—134no—
674C2×D4—268no—
675C2×D4—264no—
676C22×C4—131no—
677C22×C4—131no—
678C22×C4—138no—
679C22×C4—134no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—131no—
684C22×C4—134no—
685C22×C4—134no—
686C22×C4—134no—
687C22×C4—138no—
688C22×C4—138no—
689C22×C4—138no—
690C22×C4—1316no—
691C22×C4—268no—
692C22×C4—264no—
693C22×C4—268no—
694C22×C4—2616no—
695C22×C4—264no—
696C22×C4—268no—
697C22×C4C23×D1312yes—
698C22×C4C23×D1312yes—
699C22×C4C23×D1311yescharacteristic
700C22×C4C23×D1314yes—
701C22×C4C23×D1312yes—
702C22×C4C23×D1312yes—
703C22×C4C23×D1311yescharacteristic
704C22×C4C23×D1311yescharacteristic
705C4⋊C4—1316no—
706C4⋊C4—138no—
707C4⋊C4—1316no—
708C4⋊C4—138no—
709C4⋊C4—138no—
710C4⋊C4—134no—
711C4⋊C4—134no—
712C4⋊C4—138no—
713C4⋊C4—138no—
714C4⋊C4—138no—
715C4⋊C4—1316no—
716C4⋊C4—1316no—
717C4⋊C4—1316no—
718C4⋊C4—1316no—
719C4⋊C4—1316no—
720C4⋊C4—138no—
721C4⋊C4—138no—
722C4⋊C4—138no—
723C4⋊C4C23×D1318yes—
724C4⋊C4C23×D1318yes—
725C4⋊C4C23×D1314yes—
726C4⋊C4C23×D1314yes—
727C4⋊C4C23×D1318yes—
728C4⋊C4C23×D13116yes—
729C4⋊C4C23×D13116yes—
730C4⋊C4C23×D13116yes—
731C4⋊C4C23×D1318yes—
732C22⋊C4—138no—
733C22⋊C4—138no—
734C22⋊C4—138no—
735C22⋊C4—138no—
736C22⋊C4—138no—
737C22⋊C4—1316no—
738C22⋊C4—1316no—
739C22⋊C4—1316no—
740C22⋊C4—1316no—
741C42—134no—
742C42—138no—
743C42—134no—
744C42—138no—
745C42—134no—
746C42—1316no—
747C42—1316no—
748C42—1316no—
749C42—138no—
750C42C23×D1318yes—
751C42C23×D1314yes—
752C42C23×D13116yes—
753C42C23×D1318yes—
754C13C2×#350911yescharacteristic, complemented, Sylow
755C23—134no—
756C23—132no—
757C23—134no—
758C23—262no—
759C23—262no—
760C23—264no—
761C23—264no—
762C23—264no—
763C23C24×D1311yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—28no—
767Q8—2616no—
768Q8—2632no—
769Q8—268no—
770Q8—2616no—
771D4—2616no—
772D4—268no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—134no—
780C2×C4—134no—
781C2×C4—132no—
782C2×C4—132no—
783C2×C4—1316no—
784C2×C4—134no—
785C2×C4—134no—
786C2×C4—134no—
787C2×C4—132no—
788C2×C4—138no—
789C2×C4—268no—
790C2×C4—2616no—
791C2×C4—2616no—
792C2×C4—2632no—
793C2×C4—264no—
794C2×C4—262no—
795C2×C4—264no—
796C2×C4—268no—
797C2×C4—264no—
798C2×C4—268no—
799C2×C4—2616no—
800C2×C4#8825414yes—
801C2×C4#41×D1314yes—
802C2×C4C24×D1314yes—
803C2×C4C24×D1314yes—
804C2×C4C24×D1312yes—
805C2×C4C24×D1318yes—
806C2×C4C24×D1314yes—
807C2×C4C24×D1314yes—
808C2×C4C24×D1312yes—
809C2×C4C24×D1312yes—
810C22—134no—
811C22—268no—
812C22—262no—
813C22—262no—
814C22—264no—
815C22—264no—
816C22—264no—
817C22—528no—
818C22C2×#8825412yes—
819C22C2×#41×D1312yes—
820C22D13×2−1+412yes—
821C22C25×D1311yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—134no—
829C4—134no—
830C4—268no—
831C4—264no—
832C4—264no—
833C4—262no—
834C4—264no—
835C4C2×#8825414yes—
836C4C2×#41×D1314yes—
837C2—264no—
838C2—524no—
839C2#1312871914yesdirect product factor
840C2C22×#41×D1311yescharacteristic
841C2C2×D13×2−1+411yescharacteristic
842C2C22×#8825411yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#557C2
socleC23×C13C25
prime radicalC22×#6131C22
hypercenterC2×#557D13
hypocenterC13C2×#3509
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #13128719C2direct (N × H)
2. C2×#11719272C2semidirect
3. C2×#11719426C2semidirect
4. C2×#11719437C2semidirect
5. C2×#11719289C2semidirect
6. C2×#11719273C2semidirect
7. C2×#11719286C2semidirect
8. C2×#11719399C2semidirect
9. C2×#11719398C2semidirect
10. C2×#11719401C2semidirect
12. C2×#11719393C2semidirect
13. C2×#11719283C2semidirect
14. C2×#11719283C2semidirect
15. C2×D13×C4⋊Q8C2semidirect
16. C2×#11719277C2semidirect
18. C2×C13×#557C2semidirect
21. C13×#557C22semidirect
38. #11719437C22semidirect
40. D13×C4⋊Q8C22semidirect
41. #11719426C22semidirect
42. #11719401C22semidirect
43. #11719399C22semidirect
44. #11719398C22semidirect
45. #11719393C22semidirect
46. #11719289C22semidirect
47. #11719286C22semidirect
48. #11719283C22semidirect
49. #11719283C22semidirect
51. #11719277C22semidirect
52. #11719273C22semidirect
53. #11719272C22semidirect
337. C2×#557D13semidirect
411. #557C2×D13semidirect
648. C2×C13#3509semidirect
754. C13C2×#3509semidirect
839. C2#13128719direct (N × H)

Maximal subgroups

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

subgroupindex
#131287192
C2×#117192722
C2×#117194262
C2×#117194372
C2×#117192892
C2×#117192732
C2×#117192862
C2×#117193992
C2×#117193982
C2×#117194012
C2×#117194292
C2×#117193932
C2×#117192832
C2×D13×C4⋊Q82
C2×#117192772
C2×C4×#61312
C2×C13×#5572
C2×#350913