Finite Group Databasebeta

← C2×#13129324 #16770639

Subgroups — C2×#13129324 #16770639

Order 3328.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129324C2132yesmaximal, direct product factor
2C2×#11719351C214yesmaximal, complemented
3C2×Q8×Dic26C211yesmaximal, characteristic, complemented
4C2×#11719275C211yesmaximal, characteristic, complemented
5C2×#11719272C212yesmaximal, complemented
6C2×#11719289C211yesmaximal, characteristic, complemented
7C2×#11719289C212yesmaximal, complemented
8C2×#11719346C212yesmaximal, complemented
9C2×#11719284C211yesmaximal, characteristic, complemented
10C2×#11719344C212yesmaximal, complemented
11C2×#11719434C212yesmaximal, complemented
12C2×#11719239C212yesmaximal
13C2×#11719223C212yesmaximal, complemented
14C2×#11719436C212yesmaximal, complemented
15C2×#11719401C214yesmaximal, complemented
16C2×#11719175C211yesmaximal, characteristic, complemented
17C2×#11719184C211yesmaximal, characteristic
18C2×C13×#533C211yesmaximal, characteristic, complemented
19C13×#533C22116yescomplemented
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×C4⋊Q8C2211yescharacteristic
22C2×C13×#125C2212yes—
23C2×C13×C22⋊Q8C2212yes—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×C22⋊Q8C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×Q8×C13C2212yes—
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C13×#117C2212yes—
30C22×C42×C13C2211yescharacteristic
31C2×#88200C2214yes—
32C2×#88200C2212yes—
33C2×#88200C2212yes—
34C2×Q8×Dic13C2212yes—
35C2×Q8×Dic13C2212yes—
36C2×#88198C2214yes—
37C2×#88184C2211yescharacteristic
38C2×#88183C2212yes—
39C2×C4×C22⋊D13C2212yes—
40C2×#88180C2212yes—
41C2×#88178C2212yes—
42C2×#88178C2211yescharacteristic
43C2×#88178C2212yes—
44#11719436C22132yescomplemented
45#11719434C22132yescomplemented
46#11719401C22164yescomplemented
47#11719351C22164yescomplemented
48#11719346C22132yescomplemented
49#11719344C22132yescomplemented
50#11719289C22132yescomplemented
51#11719289C22116yescomplemented
52#11719284C22116yescomplemented
53#11719275C22116yescomplemented
54#11719272C22132yescomplemented
55Q8×Dic26C22116yescomplemented
56#11719239C22132yes—
57#11719223C22132yescomplemented
58C2×#88152C2214yes—
59C2×#88152C2214yes—
60C2×#88152C2214yes—
61C2×#88152C2214yes—
62C2×#88150C2214yes—
63C2×#88150C2214yes—
64C2×#88146C2214yes—
65C2×#88146C2212yes—
66C2×C4⋊C4×D13C2212yes—
67C2×#88144C2214yes—
68C2×#88144C2212yes—
69C2×#88143C2214yes—
70C2×#88143C2214yes—
71C2×#88143C2214yes—
72C2×#88143C2214yes—
73C2×#88142C2214yes—
74C2×#88142C2212yes—
75C2×#88141C2214yes—
76C2×#88139C2214yes—
77C2×#88137C2214yes—
78C2×#88133C2214yes—
79C2×#88133C2214yes—
80#11719184C22116yes—
81C2×#88130C2212yes—
82C2×#88129C2212yes—
83C2×#88129C2211yescharacteristic
84C2×C4×D52C2212yes—
85C2×C4×D52C2211yescharacteristic
86C2×#88126C2212yes—
87#11719175C22116yescomplemented
88C2×#88124C2212yes—
89C2×#88124C2212yes—
90C2×#88124C2211yescharacteristic
91C2×#88123C2212yes—
92C2×#88123C2212yes—
93C2×#88123C2211yescharacteristic
94C2×#88123C2211yescharacteristic
95C2×C4×Dic26C2212yes—
96C2×C4×Dic26C2212yes—
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2311yescharacteristic
103C22×Q8×C13C2312yes—
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C22×C22⋊D13C2312yes—
108C22×D52C2311yescharacteristic
109C22×C4×D13C2312yes—
110C22×C4×D13C2314yes—
111C22×Dic26C2312yes—
112C22×Dic26C2311yescharacteristic
113C22×Dic26C2312yes—
114C22×Dic26C2314yes—
115C13×C4⋊Q8C2318yes—
116C13×C4⋊Q8C2318yes—
117C13×#125C23116yes—
118C13×C22⋊Q8C2318yes—
119C13×C22⋊Q8C2318yes—
120C13×C22⋊Q8C23116yes—
121C4×Q8×C13C2318yes—
122C4×Q8×C13C23116yes—
123C4×Q8×C13C2318yes—
124C13×#117C23116yes—
125C2×C13×C4⋊C4C2312yes—
126C2×C13×C4⋊C4C2311yescharacteristic
127C2×C13×C4⋊C4C2312yes—
128C2×C13×C4⋊C4C2312yes—
129C2×C13×C4⋊C4C2312yes—
130C2×C13×C4⋊C4C2312yes—
131C2×C13×C4⋊C4C2312yes—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C22⋊C4C2312yes—
135C2×C13×C22⋊C4C2312yes—
136C2×C42×C13C2312yes—
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139C2×C42×C13C2311yescharacteristic
140C2×C42×C13C2312yes—
141C2×C42×C13C2311yescharacteristic
142C2×C42×C13C2318yes—
143C2×C22⋊Dic13C2312yes—
144C2×C22⋊Dic13C2314yes—
145#88200C23132yes—
146#88200C23116yes—
147#88200C23116yes—
148Q8×Dic13C23116yes—
149Q8×Dic13C23116yes—
150#88198C23132yes—
151#88184C2318yes—
152#88183C23116yes—
153C4×C22⋊D13C23116yes—
154C2×#6103C2312yes—
155C2×#6103C2312yes—
156C2×#6103C2312yes—
157C2×#6103C2314yes—
158C2×#6103C2312yes—
159C2×#6103C2314yes—
160C2×#6103C2314yes—
161#88180C23116yes—
162C2×C4⋊Dic13C2311yescharacteristic
163C2×C4⋊Dic13C2312yes—
164C2×C4⋊Dic13C2311yescharacteristic
165C2×C4⋊Dic13C2312yes—
166C2×C4⋊Dic13C2312yes—
167C2×C4⋊Dic13C2312yes—
168C2×C4⋊Dic13C2314yes—
169C2×C4⋊Dic13C2314yes—
170C2×C4⋊Dic13C2314yes—
171#88178C23116yes—
172#88178C23116yes—
173#88178C2318yes—
174C2×#6101C2314yes—
175C2×#6101C2314yes—
176C2×#6101C2312yes—
177C2×#6101C2314yes—
178C2×#6101C2314yes—
179C2×#6101C2314yes—
180C2×#6101C2312yes—
181C2×#6101C2312yes—
182C2×#6101C2314yes—
183C2×#6101C2314yes—
184C2×#6101C2312yes—
185C2×C4×Dic13C2314yes—
186C2×C4×Dic13C2312yes—
187C2×C4×Dic13C2314yes—
188C2×C4×Dic13C2314yes—
189C2×C4×Dic13C2314yes—
190#88152C23132yes—
191#88152C23132yes—
192#88152C23132yes—
193#88152C23132yes—
194#88150C23132yes—
195#88150C23132yes—
196#88146C23116yes—
197#88146C23132yes—
198C4⋊C4×D13C23116yes—
199#88144C23116yes—
200#88144C23132yes—
201#88143C23132yes—
202#88143C23132yes—
203#88143C23132yes—
204#88143C23132yes—
205#88142C23116yes—
206#88142C23132yes—
207#88141C23132yes—
208#88139C23132yes—
209#88137C23132yes—
210#88133C23132yes—
211#88133C23132yes—
212#88130C23116yes—
213#88129C2318yes—
214#88129C23116yes—
215C4×D52C2318yes—
216C4×D52C23116yes—
217#88126C23116yes—
218#88124C23116yes—
219#88124C2318yes—
220#88124C23116yes—
221#88123C2318yes—
222#88123C2318yes—
223#88123C23116yes—
224#88123C23116yes—
225C4×Dic26C23116yes—
226C4×Dic26C23116yes—
227C4×Dic26C2318yes—
228C4×Dic26C23116yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C2×#3555—131nomaximal, Sylow
232C24×C13C2411yescharacteristic
233C23×D13C2412yes—
234C2×Q8×C13—24no—
235C2×Q8×C13—24no—
236C2×Q8×C13—44no—
237C2×Q8×C13C2414yes—
238C2×Q8×C13C2414yes—
239C2×Q8×C13C2418yes—
240C22×C4×C13—24no—
241C22×C4×C13—24no—
242C22×C4×C13—42no—
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2412yes—
245C22×C4×C13C2412yes—
246C22×C4×C13C2412yes—
247C22×C4×C13C2411yescharacteristic
248C22×C4×C13C2411yescharacteristic
249C22×C4×C13C2412yes—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2414yes—
252C22×C4×C13C2414yes—
253C22×C4×C13C2414yes—
254C22×C4×C13C2411yescharacteristic
255C22×C4×C13C2411yescharacteristic
256C2×C22⋊D13—44no—
257C2×C22⋊D13C2418yes—
258C22×Dic13C2412yes—
259C22×Dic13C2414yes—
260C22×Dic13C2412yes—
261C22×Dic13C2412yes—
262C22×Dic13C2414yes—
263C2×D52—24no—
264C2×D52C2414yes—
265C2×C4×D13—28no—
266C2×C4×D13—48no—
267C2×C4×D13C2418yes—
268C2×C4×D13C24116yes—
269C2×Dic26—28no—
270C2×Dic26—24no—
271C2×Dic26—44no—
272C2×Dic26—48no—
273C2×Dic26C2418yes—
274C2×Dic26C2414yes—
275C2×Dic26C2418yes—
276C2×Dic26C24116yes—
277C13×C4⋊C4C2418yes—
278C13×C4⋊C4C2414yes—
279C13×C4⋊C4C2418yes—
280C13×C4⋊C4C2418yes—
281C13×C4⋊C4C2418yes—
282C13×C4⋊C4C2418yes—
283C13×C4⋊C4C2418yes—
284C13×C4⋊C4C2414yes—
285C13×C4⋊C4C2418yes—
286C13×C22⋊C4C2418yes—
287C13×C22⋊C4C2418yes—
288C42×C13C2418yes—
289C42×C13C2414yes—
290C42×C13C2414yes—
291C42×C13C2414yes—
292C42×C13C2418yes—
293C42×C13C2414yes—
294C22⋊Dic13C2418yes—
295C22⋊Dic13C24116yes—
296#6103C2418yes—
297#6103C2418yes—
298#6103C2418yes—
299#6103C24116yes—
300#6103C2418yes—
301#6103C24116yes—
302#6103C24116yes—
303C4⋊Dic13C2414yes—
304C4⋊Dic13C2418yes—
305C4⋊Dic13C2414yes—
306C4⋊Dic13C2418yes—
307C4⋊Dic13C2418yes—
308C4⋊Dic13C2418yes—
309C4⋊Dic13C24116yes—
310C4⋊Dic13C24116yes—
311C4⋊Dic13C24116yes—
312#6101C24116yes—
313#6101C24116yes—
314#6101C2418yes—
315#6101C24116yes—
316#6101C24116yes—
317#6101C24116yes—
318#6101C2418yes—
319#6101C2418yes—
320#6101C24116yes—
321#6101C24116yes—
322#6101C2418yes—
323C4×Dic13C24116yes—
324C4×Dic13C2418yes—
325C4×Dic13C24116yes—
326C4×Dic13C24116yes—
327C4×Dic13C24116yes—
328#3555—1332no—
329C2×#563—134no—
330C2×Q82—131no—
331C2×#557—132no—
332C2×#557—131no—
333C2×#556—132no—
334C2×#556—132no—
335C2×#556—131no—
336C2×#554—131no—
337C2×#552—132no—
338C2×#544—132no—
339C2×#542—132no—
340C2×#541—132no—
341C2×#541—134no—
342C2×#541—132no—
343C2×#533—131no—
344C2×#533D1311yescharacteristic, complemented
345C2×#529—131no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13C2512yes—
350C23×C13C2511yescharacteristic
351C22×D13—24no—
352C22×D13—24no—
353C22×D13—24no—
354C22×D13C2514yes—
355Q8×C13—28no—
356Q8×C13—28no—
357Q8×C13—48no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—24no—
361C2×C4×C13—24no—
362C2×C4×C13—22no—
363C2×C4×C13—24no—
364C2×C4×C13—24no—
365C2×C4×C13—22no—
366C2×C4×C13—28no—
367C2×C4×C13—28no—
368C2×C4×C13—44no—
369C2×C4×C132−1+414yes—
370C2×C4×C132−1+414yes—
371C2×C4×C13C2512yes—
372C2×C4×C13C2514yes—
373C2×C4×C13C2514yes—
374C2×C4×C13C2514yes—
375C2×C4×C13C2512yes—
376C2×C4×C13C2512yes—
377C2×C4×C13C2514yes—
378C2×C4×C13C2512yes—
379C2×C4×C13C2512yes—
380C2×C4×C13C2512yes—
381C22⋊D13—48no—
382C2×Dic13—28no—
383C2×Dic13—24no—
384C2×Dic13—24no—
385C2×Dic13—28no—
386C2×Dic13—24no—
387C2×Dic13C2514yes—
388C2×Dic13C2518yes—
389C2×Dic13C2514yes—
390C2×Dic13C2514yes—
391C2×Dic13C2518yes—
392D52—28no—
393C4×D13—216no—
394C4×D13—416no—
395Dic26—216no—
396Dic26—28no—
397Dic26—48no—
398Dic26—416no—
399#563—1364no—
400Q82—1316no—
401#557—1332no—
402#557—1316no—
403#556—1332no—
404#556—1332no—
405#556—1316no—
406#554—1316no—
407#552—1332no—
408#544—1332no—
409#542—1332no—
410#541—1332no—
411#541—1364no—
412#541—1332no—
413#533—1316no—
414#533C2×D13116yescomplemented
415C2×C4⋊Q8—134no—
416C2×C4⋊Q8—134no—
417C2×C4⋊Q8—132no—
418C2×C4⋊Q8—131no—
419C2×C4⋊Q8—131no—
420C2×C4⋊Q8—132no—
421C2×C4⋊Q8—132no—
422C2×C4⋊Q8C2×D1311yescharacteristic
423C2×C4⋊Q8C2×D1311yescharacteristic
424#529—1316no—
425C2×#126—134no—
426C2×#126—134no—
427C2×#126—134no—
428C2×#126—134no—
429C2×#126—134no—
430C2×#126—134no—
431C2×#126—132no—
432C2×#125—134no—
433C2×#125—134no—
434C2×#125—134no—
435C2×#125—134no—
436C2×#125—134no—
437C2×#125—132no—
438C2×#125—131no—
439C2×#125—132no—
440C2×#125—132no—
441C2×#125C2×D1312yes—
442C2×#124—134no—
443C2×#124—131no—
444C2×#124—132no—
445C2×#123—132no—
446C2×#123—134no—
447C2×C22⋊Q8—132no—
448C2×C22⋊Q8—132no—
449C2×C22⋊Q8—134no—
450C2×C22⋊Q8—131no—
451C2×C22⋊Q8—132no—
452C2×C22⋊Q8—132no—
453C2×C22⋊Q8—134no—
454C2×C22⋊Q8—134no—
455C2×C22⋊Q8C2×D1311yescharacteristic
456C2×C22⋊Q8C2×D1311yescharacteristic
457C2×C22⋊Q8C2×D1312yes—
458C2×#121—131no—
459C2×C4×Q8—132no—
460C2×C4×Q8—132no—
461C2×C4×Q8—134no—
462C2×C4×Q8—131no—
463C2×C4×Q8—132no—
464C2×C4×Q8—132no—
465C2×C4×Q8—132no—
466C2×C4×Q8—132no—
467C2×C4×Q8—132no—
468C2×C4×Q8C2×D1311yescharacteristic
469C2×C4×Q8C2×D1312yes—
470C2×C4×Q8C2×D1311yescharacteristic
471C2×C4×D4—132no—
472C2×C4×D4—131no—
473C2×C4×D4—132no—
474C2×#117—132no—
475C2×#117—134no—
476C2×#117—132no—
477C2×#117—132no—
478C2×#117C2×D1312yes—
479C22×C4⋊C4—132no—
480C22×C42C2×D1311yescharacteristic
481C22×C13—22no—
482C22×C13—22no—
483C22×C13—22no—
484C22×C13—44no—
485C22×C13C2×2−1+412yes—
486C22×C13C2×2−1+412yes—
487C22×C13#58512yes—
488C22×C13C2611yescharacteristic
489C2×D13—24no—
490C2×D13—24no—
491C2×D13—24no—
492C2×D13—48no—
493C4×C13—22no—
494C4×C13—22no—
495C4×C13—24no—
496C4×C13—24no—
497C4×C13—22no—
498C4×C13—24no—
499C4×C13—24no—
500C4×C13—22no—
501C4×C13C2×2−1+414yes—
502C4×C13C2×2−1+414yes—
503Dic13—28no—
504Dic13—24no—
505Dic13—24no—
506Dic13—28no—
507Dic13—24no—
508C22×Q8—131no—
509C22×Q8—132no—
510C22×Q8—132no—
511C22×Q8—134no—
512C22×Q8C22×D1311yescharacteristic
513C22×Q8C22×D1311yescharacteristic
514C22×Q8C22×D1312yes—
515C22×D4—132no—
516C22×D4—131no—
517C23×C4—132no—
518C23×C4—134no—
519C23×C4C22×D1311yescharacteristic
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C4⋊Q8—1332no—
523C4⋊Q8—1332no—
524C4⋊Q8—1316no—
525C4⋊Q8—138no—
526C4⋊Q8—138no—
527C4⋊Q8—1316no—
528C4⋊Q8—1316no—
529C4⋊Q8C22×D1318yes—
530C4⋊Q8C22×D1318yes—
531#126—1332no—
532#126—1332no—
533#126—1332no—
534#126—1332no—
535#126—1332no—
536#126—1332no—
537#126—1316no—
538#125—1332no—
539#125—1332no—
540#125—1332no—
541#125—1332no—
542#125—1332no—
543#125—1316no—
544#125—138no—
545#125—1316no—
546#125—1316no—
547#125C22×D13116yes—
548#124—1332no—
549#124—138no—
550#124—1316no—
551#123—1316no—
552#123—1332no—
553C22⋊Q8—1316no—
554C22⋊Q8—1316no—
555C22⋊Q8—1332no—
556C22⋊Q8—138no—
557C22⋊Q8—1316no—
558C22⋊Q8—1316no—
559C22⋊Q8—1332no—
560C22⋊Q8—1332no—
561C22⋊Q8C22×D1318yes—
562C22⋊Q8C22×D1318yes—
563C22⋊Q8C22×D13116yes—
564#121—138no—
565C4×Q8—1316no—
566C4×Q8—1316no—
567C4×Q8—1332no—
568C4×Q8—138no—
569C4×Q8—1316no—
570C4×Q8—1316no—
571C4×Q8—1316no—
572C4×Q8—1316no—
573C4×Q8—1316no—
574C4×Q8C22×D1318yes—
575C4×Q8C22×D13116yes—
576C4×Q8C22×D1318yes—
577C4×D4—1316no—
578C4×D4—138no—
579C4×D4—1316no—
580#117—1316no—
581#117—1332no—
582#117—1316no—
583#117—1316no—
584#117C22×D13116yes—
585C2×C4⋊C4—132no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—132no—
588C2×C4⋊C4—132no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—132no—
591C2×C4⋊C4—131no—
592C2×C4⋊C4—132no—
593C2×C4⋊C4—132no—
594C2×C4⋊C4—131no—
595C2×C4⋊C4—134no—
596C2×C4⋊C4—134no—
597C2×C4⋊C4—134no—
598C2×C4⋊C4—134no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—132no—
601C2×C4⋊C4—134no—
602C2×C4⋊C4—132no—
603C2×C4⋊C4—134no—
604C2×C4⋊C4—134no—
605C2×C4⋊C4—1316no—
606C2×C4⋊C4C22×D1311yescharacteristic
607C2×C4⋊C4C22×D1312yes—
608C2×C4⋊C4C22×D1311yescharacteristic
609C2×C4⋊C4C22×D1312yes—
610C2×C4⋊C4C22×D1312yes—
611C2×C4⋊C4C22×D1312yes—
612C2×C4⋊C4C22×D1312yes—
613C2×C4⋊C4C22×D1312yes—
614C2×C4⋊C4C22×D1312yes—
615C2×C22⋊C4—134no—
616C2×C22⋊C4—132no—
617C2×C22⋊C4—132no—
618C2×C22⋊C4—132no—
619C2×C22⋊C4—132no—
620C2×C22⋊C4—134no—
621C2×C22⋊C4—134no—
622C2×C22⋊C4—132no—
623C2×C22⋊C4—134no—
624C2×C22⋊C4C22×D1312yes—
625C2×C22⋊C4C22×D1312yes—
626C2×C42—134no—
627C2×C42—132no—
628C2×C42—134no—
629C2×C42—134no—
630C2×C42—134no—
631C2×C42C22×D1311yescharacteristic
632C2×C42C22×D1312yes—
633C2×C42C22×D1312yes—
634C2×C42C22×D1311yescharacteristic
635C2×C42C22×D1311yescharacteristic
636C2×C42C22×D1311yescharacteristic
637C2×C42C22×D1318yes—
638C2×C13—42no—
639C2×C13#355514yescomplemented
640C2×C13C22×2−1+411yescharacteristic
641C2×C13C22×2−1+411yescharacteristic
642C2×C13C2×#58511yescharacteristic
643D13—44no—
644C24—132no—
645C24C23×D1311yescharacteristic
646C2×Q8—24no—
647C2×Q8—24no—
648C2×Q8—44no—
649C2×Q8—134no—
650C2×Q8—138no—
651C2×Q8—138no—
652C2×Q8—1316no—
653C2×Q8—264no—
654C2×Q8—268no—
655C2×Q8—524no—
656C2×Q8—528no—
657C2×Q8C23×D1314yes—
658C2×Q8C23×D1314yes—
659C2×Q8C23×D1318yes—
660C2×D4—138no—
661C2×D4—134no—
662C2×D4—264no—
663C2×D4—524no—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—42no—
667C22×C4—134no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—134no—
672C22×C4—138no—
673C22×C4—1316no—
674C22×C4—268no—
675C22×C4—528no—
676C22×C4C23×D1314yes—
677C22×C4C23×D1314yes—
678C22×C4C23×D1311yescharacteristic
679C22×C4C23×D1312yes—
680C22×C4C23×D1312yes—
681C22×C4C23×D1312yes—
682C22×C4C23×D1311yescharacteristic
683C22×C4C23×D1311yescharacteristic
684C22×C4C23×D1311yescharacteristic
685C22×C4C23×D1312yes—
686C22×C4C23×D1314yes—
687C22×C4C23×D1311yescharacteristic
688C22×C4C23×D1311yescharacteristic
689C4⋊C4—138no—
690C4⋊C4—1316no—
691C4⋊C4—138no—
692C4⋊C4—138no—
693C4⋊C4—1316no—
694C4⋊C4—138no—
695C4⋊C4—134no—
696C4⋊C4—138no—
697C4⋊C4—138no—
698C4⋊C4—134no—
699C4⋊C4—1316no—
700C4⋊C4—1316no—
701C4⋊C4—1316no—
702C4⋊C4—1316no—
703C4⋊C4—1316no—
704C4⋊C4—138no—
705C4⋊C4—1316no—
706C4⋊C4—138no—
707C4⋊C4—1316no—
708C4⋊C4—1316no—
709C4⋊C4C23×D1314yes—
710C4⋊C4C23×D1318yes—
711C4⋊C4C23×D1314yes—
712C4⋊C4C23×D1318yes—
713C4⋊C4C23×D1318yes—
714C4⋊C4C23×D1318yes—
715C4⋊C4C23×D1318yes—
716C4⋊C4C23×D1318yes—
717C4⋊C4C23×D1318yes—
718C22⋊C4—1316no—
719C22⋊C4—138no—
720C22⋊C4—138no—
721C22⋊C4—138no—
722C22⋊C4—138no—
723C22⋊C4—1316no—
724C22⋊C4—1316no—
725C22⋊C4—138no—
726C22⋊C4—1316no—
727C22⋊C4C23×D1318yes—
728C22⋊C4C23×D1318yes—
729C42—1316no—
730C42—138no—
731C42—1316no—
732C42—1316no—
733C42—1316no—
734C42C23×D1314yes—
735C42C23×D1314yes—
736C42C23×D1314yes—
737C42C23×D1314yes—
738C42C23×D1318yes—
739C42C23×D1318yes—
740C13C2×#355511yescharacteristic, complemented, Sylow
741C23—22no—
742C23—22no—
743C23—22no—
744C23—134no—
745C23—264no—
746C23—264no—
747C23—264no—
748C23C24×D1312yes—
749C23C24×D1311yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—268no—
754Q8—2616no—
755Q8—528no—
756Q8—5216no—
757D4—268no—
758D4—528no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—138no—
771C2×C4—134no—
772C2×C4—134no—
773C2×C4—134no—
774C2×C4—138no—
775C2×C4—268no—
776C2×C4—264no—
777C2×C4—264no—
778C2×C4—268no—
779C2×C4—264no—
780C2×C4—2616no—
781C2×C4—5216no—
782C2×C4#8825414yes—
783C2×C4#8825714yes—
784C2×C4C24×D1312yes—
785C2×C4C24×D1314yes—
786C2×C4C24×D1314yes—
787C2×C4C24×D1314yes—
788C2×C4C24×D1312yes—
789C2×C4C24×D1312yes—
790C2×C4C24×D1312yes—
791C2×C4C24×D1314yes—
792C2×C4C24×D1312yes—
793C2×C4C24×D1312yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—264no—
799C22—264no—
800C22—264no—
801C22—528no—
802C22C2×#8825412yes—
803C22C2×#8825712yes—
804C22#1171964812yes—
805C22C25×D1311yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—264no—
815C4—268no—
816C4—264no—
817C4—268no—
818C4—264no—
819C4C2×#8825414yes—
820C4C2×#8825714yes—
821C2—42no—
822C2—524no—
823C2#1312932414yesdirect product factor
824C2C22×#8825711yescharacteristic
825C2C22×#8825411yescharacteristic
826C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#533C2
socleC23×C13C25
prime radicalC2×#88184C22
hypercenterC2×#533D13
hypocenterC13C2×#3555
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #13129324C2direct (N × H)
2. C2×#11719351C2semidirect
3. C2×Q8×Dic26C2semidirect
4. C2×#11719275C2semidirect
5. C2×#11719272C2semidirect
6. C2×#11719289C2semidirect
7. C2×#11719289C2semidirect
8. C2×#11719346C2semidirect
9. C2×#11719284C2semidirect
10. C2×#11719344C2semidirect
11. C2×#11719434C2semidirect
13. C2×#11719223C2semidirect
14. C2×#11719436C2semidirect
15. C2×#11719401C2semidirect
16. C2×#11719175C2semidirect
18. C2×C13×#533C2semidirect
19. C13×#533C22semidirect
44. #11719436C22semidirect
45. #11719434C22semidirect
46. #11719401C22semidirect
47. #11719351C22semidirect
48. #11719346C22semidirect
49. #11719344C22semidirect
50. #11719289C22semidirect
51. #11719289C22semidirect
52. #11719284C22semidirect
53. #11719275C22semidirect
54. #11719272C22semidirect
55. Q8×Dic26C22semidirect
57. #11719223C22semidirect
87. #11719175C22semidirect
344. C2×#533D13semidirect
414. #533C2×D13semidirect
639. C2×C13#3555semidirect
740. C13C2×#3555semidirect
823. C2#13129324direct (N × H)

Maximal subgroups

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

subgroupindex
#131293242
C2×#117193512
C2×Q8×Dic262
C2×#117192752
C2×#117192722
C2×#117192892
C2×#117193462
C2×#117192842
C2×#117193442
C2×#117194342
C2×#117192392
C2×#117192232
C2×#117194362
C2×#117194012
C2×#117191752
C2×#117191842
C2×C13×#5332
C2×#355513