Finite Group Databasebeta

← C2×#13129312 #16770634

Subgroups — C2×#13129312 #16770634

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#13129312C2132yesmaximal, direct product factor
2C2×#11719417C214yesmaximal, complemented
3C2×Q8×Dic26C211yesmaximal, characteristic, complemented
4C2×#11719275C212yesmaximal, complemented
5C2×#11719426C211yesmaximal, characteristic, complemented
6C2×#11719376C212yesmaximal, complemented
7C2×#11719238C212yesmaximal, complemented
8C2×#11719248C211yesmaximal, characteristic, complemented
9C2×#11719347C212yesmaximal, complemented
10C2×#11719224C212yesmaximal, complemented
11C2×#11719387C212yesmaximal
12C2×#11719330C212yesmaximal, complemented
13C2×#11719288C212yesmaximal, complemented
14C2×#11719406C214yesmaximal, complemented
15C2×#11719433C211yesmaximal, characteristic, complemented
16C2×#11719283C211yesmaximal, characteristic, complemented
17C2×#11719262C211yesmaximal, characteristic
18C2×C13×#556C211yesmaximal, characteristic, complemented
19C13×#556C22116yescomplemented
20C2×C13×C4⋊Q8C2211yescharacteristic
21C2×C13×#126C2214yes—
22C2×C13×#124C2212yes—
23C2×C13×C22⋊Q8C2212yes—
24C2×C4×Q8×C13C2212yes—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2212yes—
28C2×#88200C2212yes—
29C2×#88200C2211yescharacteristic
30C2×Q8×Dic13C2212yes—
31C2×Q8×Dic13C2212yes—
32C2×Q8×Dic13C2212yes—
33C2×#88198C2212yes—
34C2×#88198C2211yescharacteristic
35C2×#88192C2211yescharacteristic
36C2×#88190C2211yescharacteristic
37C2×D4×Dic13C2212yes—
38C2×C4×C22⋊D13C2212yes—
39C2×#88180C2212yes—
40C22×C4⋊Dic13C2212yes—
41C2×#88178C2212yes—
42#11719433C22116yescomplemented
43#11719426C22116yescomplemented
44#11719417C22164yescomplemented
45#11719406C22164yescomplemented
46#11719387C22132yes—
47#11719376C22132yescomplemented
48#11719347C22132yescomplemented
49#11719330C22132yescomplemented
50#11719288C22132yescomplemented
51#11719283C22116yescomplemented
52#11719275C22132yescomplemented
53Q8×Dic26C22116yescomplemented
54#11719262C22116yes—
55#11719248C22116yescomplemented
56#11719238C22132yescomplemented
57#11719224C22132yescomplemented
58C2×#88152C2214yes—
59C2×#88151C2211yescharacteristic
60C2×#88151C2212yes—
61C2×#88151C2211yescharacteristic
62C2×#88150C2212yes—
63C2×#88146C2212yes—
64C2×#88144C2214yes—
65C2×#88144C2212yes—
66C2×#88144C2214yes—
67C2×#88144C2212yes—
68C2×#88144C2212yes—
69C2×#88144C2211yescharacteristic
70C2×#88143C2212yes—
71C2×#88143C2214yes—
72C2×#88143C2214yes—
73C2×#88142C2214yes—
74C2×#88142C2211yescharacteristic
75C2×#88142C2212yes—
76C2×#88141C2212yes—
77C2×#88141C2212yes—
78C2×#88140C2214yes—
79C2×#88139C2214yes—
80C2×#88137C2212yes—
81C2×#88133C2212yes—
82C2×#88133C2214yes—
83C2×#88133C2214yes—
84C2×#88133C2214yes—
85C2×#88132C2214yes—
86C2×#88132C2214yes—
87C2×#88132C2214yes—
88C2×#88131C2214yes—
89C2×#88130C2214yes—
90C2×#88126C2212yes—
91C2×C42×D13C2211yescharacteristic
92C2×#88124C2214yes—
93C2×#88123C2214yes—
94C2×#88123C2212yes—
95C2×#88123C2211yescharacteristic
96C2×C4×Dic26C2214yes—
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2211yescharacteristic
99C2×C4×Dic26C2211yescharacteristic
100C2×C4×Dic26C2212yes—
101C22×Q8×C13C2311yescharacteristic
102C22×Q8×C13C2312yes—
103C22×D4×C13C2311yescharacteristic
104C23×C4×C13C2312yes—
105C22×C22⋊D13C2312yes—
106C23×Dic13C2314yes—
107C22×C4×D13C2311yescharacteristic
108C22×C4×D13C2311yescharacteristic
109C22×C4×D13C2311yescharacteristic
110C22×Dic26C2311yescharacteristic
111C22×Dic26C2311yescharacteristic
112C22×Dic26C2312yes—
113C22×Dic26C2314yes—
114C22×Dic26C2312yes—
115C13×C4⋊Q8C2318yes—
116C13×#126C23132yes—
117C13×#124C23116yes—
118C13×C22⋊Q8C23116yes—
119C4×Q8×C13C2318yes—
120C4×Q8×C13C23116yes—
121C4×D4×C13C2318yes—
122C13×#117C23116yes—
123C2×C13×C4⋊C4C2312yes—
124C2×C13×C4⋊C4C2312yes—
125C2×C13×C4⋊C4C2311yescharacteristic
126C2×C13×C4⋊C4C2312yes—
127C2×C13×C4⋊C4C2314yes—
128C2×C13×C4⋊C4C2311yescharacteristic
129C2×C13×C22⋊C4C2314yes—
130C2×C13×C22⋊C4C2312yes—
131C2×C13×C22⋊C4C2314yes—
132C2×C42×C13C2311yescharacteristic
133C2×C42×C13C2312yes—
134C2×C42×C13C2314yes—
135C2×C22⋊Dic13C2312yes—
136C2×C22⋊Dic13C2312yes—
137C2×C22⋊Dic13C2312yes—
138C2×C22⋊Dic13C2314yes—
139#88200C23116yes—
140#88200C2318yes—
141Q8×Dic13C23116yes—
142Q8×Dic13C23116yes—
143Q8×Dic13C23116yes—
144#88198C23116yes—
145#88198C2318yes—
146#88192C2318yes—
147#88190C2318yes—
148D4×Dic13C23116yes—
149C4×C22⋊D13C23116yes—
150C2×#6103C2312yes—
151C2×#6103C2312yes—
152C2×#6103C2312yes—
153C2×#6103C2314yes—
154#88180C23116yes—
155C2×C4⋊Dic13C2312yes—
156C2×C4⋊Dic13C2312yes—
157C2×C4⋊Dic13C2311yescharacteristic
158C2×C4⋊Dic13C2311yescharacteristic
159C2×C4⋊Dic13C2312yes—
160C2×C4⋊Dic13C2314yes—
161C2×C4⋊Dic13C2314yes—
162C2×C4⋊Dic13C2314yes—
163C2×C4⋊Dic13C2314yes—
164C2×C4⋊Dic13C2312yes—
165C2×C4⋊Dic13C2312yes—
166C2×C4⋊Dic13C23116yes—
167#88178C23116yes—
168C2×#6101C2312yes—
169C2×#6101C2314yes—
170C2×#6101C2314yes—
171C2×#6101C2312yes—
172C2×#6101C2312yes—
173C2×#6101C2312yes—
174C2×#6101C2312yes—
175C2×#6101C2312yes—
176C2×#6101C2314yes—
177C2×#6101C2314yes—
178C2×#6101C2312yes—
179C2×#6101C2314yes—
180C2×C4×Dic13C2311yescharacteristic
181C2×C4×Dic13C2312yes—
182C2×C4×Dic13C2314yes—
183C2×C4×Dic13C2314yes—
184C2×C4×Dic13C2314yes—
185C2×C4×Dic13C2312yes—
186C2×C4×Dic13C2311yescharacteristic
187C2×C4×Dic13C2311yescharacteristic
188#88152C23132yes—
189#88151C23116yes—
190#88151C2318yes—
191#88151C2318yes—
192#88150C23116yes—
193#88146C23116yes—
194#88144C23116yes—
195#88144C23116yes—
196#88144C23116yes—
197#88144C2318yes—
198#88144C23132yes—
199#88144C23132yes—
200#88143C23132yes—
201#88143C23116yes—
202#88143C23132yes—
203#88142C2318yes—
204#88142C23116yes—
205#88142C23132yes—
206#88141C23116yes—
207#88141C23116yes—
208#88140C23132yes—
209#88139C23132yes—
210#88137C23116yes—
211#88133C23132yes—
212#88133C23116yes—
213#88133C23132yes—
214#88133C23132yes—
215#88132C23132yes—
216#88132C23132yes—
217#88132C23132yes—
218#88131C23132yes—
219#88130C23132yes—
220#88126C23116yes—
221C42×D13C2318yes—
222#88124C23132yes—
223#88123C2318yes—
224#88123C23132yes—
225#88123C23116yes—
226C4×Dic26C2318yes—
227C4×Dic26C2318yes—
228C4×Dic26C23132yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C2×#3555—131nomaximal, Sylow
232C24×C13C2412yes—
233C23×D13C2411yescharacteristic
234C2×Q8×C13—24no—
235C2×Q8×C13—28no—
236C2×Q8×C13C2414yes—
237C2×Q8×C13C2418yes—
238C2×D4×C13—24no—
239C2×D4×C13C2414yes—
240C22×C4×C13—28no—
241C22×C4×C13C2414yes—
242C22×C4×C13C2412yes—
243C22×C4×C13C2411yescharacteristic
244C22×C4×C13C2412yes—
245C22×C4×C13C2412yes—
246C22×C4×C13C2418yes—
247C22×C4×C13C2411yescharacteristic
248C22×C4×C13C2411yescharacteristic
249C2×C22⋊D13—44no—
250C2×C22⋊D13C2418yes—
251C22×Dic13—48no—
252C22×Dic13C2411yescharacteristic
253C22×Dic13C2412yes—
254C22×Dic13C2412yes—
255C22×Dic13C2412yes—
256C22×Dic13C2411yescharacteristic
257C22×Dic13C2414yes—
258C22×Dic13C2411yescharacteristic
259C22×Dic13C2412yes—
260C22×Dic13C24116yes—
261C2×C4×D13—24no—
262C2×C4×D13—24no—
263C2×C4×D13—42no—
264C2×C4×D13C2414yes—
265C2×C4×D13C2414yes—
266C2×C4×D13C2414yes—
267C2×Dic26—24no—
268C2×Dic26—24no—
269C2×Dic26—44no—
270C2×Dic26—44no—
271C2×Dic26—48no—
272C2×Dic26C2414yes—
273C2×Dic26C2414yes—
274C2×Dic26C2418yes—
275C2×Dic26C24116yes—
276C2×Dic26C2418yes—
277C13×C4⋊C4C2418yes—
278C13×C4⋊C4C2418yes—
279C13×C4⋊C4C2414yes—
280C13×C4⋊C4C2418yes—
281C13×C4⋊C4C24116yes—
282C13×C4⋊C4C2414yes—
283C13×C22⋊C4C24116yes—
284C13×C22⋊C4C2418yes—
285C13×C22⋊C4C24116yes—
286C42×C13C2414yes—
287C42×C13C2418yes—
288C42×C13C24116yes—
289C22⋊Dic13C2418yes—
290C22⋊Dic13C2418yes—
291C22⋊Dic13C2418yes—
292C22⋊Dic13C24116yes—
293#6103C2418yes—
294#6103C2418yes—
295#6103C2418yes—
296#6103C24116yes—
297C4⋊Dic13C2418yes—
298C4⋊Dic13C2418yes—
299C4⋊Dic13C2414yes—
300C4⋊Dic13C2414yes—
301C4⋊Dic13C2418yes—
302C4⋊Dic13C24116yes—
303C4⋊Dic13C24116yes—
304C4⋊Dic13C24116yes—
305C4⋊Dic13C24116yes—
306C4⋊Dic13C2418yes—
307C4⋊Dic13C2418yes—
308#6101C2418yes—
309#6101C24116yes—
310#6101C24116yes—
311#6101C2418yes—
312#6101C2418yes—
313#6101C2418yes—
314#6101C2418yes—
315#6101C2418yes—
316#6101C24116yes—
317#6101C24116yes—
318#6101C2418yes—
319#6101C24116yes—
320C4×Dic13C2414yes—
321C4×Dic13C2418yes—
322C4×Dic13C24116yes—
323C4×Dic13C24116yes—
324C4×Dic13C24116yes—
325C4×Dic13C2418yes—
326C4×Dic13C2414yes—
327C4×Dic13C2414yes—
328#3555—1332no—
329C2×#563—134no—
330C2×Q82—131no—
331C2×#557—131no—
332C2×#557—132no—
333C2×#556—132no—
334C2×#556—132no—
335C2×#556D1311yescharacteristic, complemented
336C2×#554—131no—
337C2×#552—132no—
338C2×#544—132no—
339C2×#542—132no—
340C2×#541—134no—
341C2×#541—132no—
342C2×#541—132no—
343C2×#533—131no—
344C2×#533—131no—
345C2×#529—131no—
346C23×C13—24no—
347C23×C13—24no—
348C23×C13—24no—
349C23×C13C2514yes—
350C23×C13C2511yescharacteristic
351C22×D13—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13C2512yes—
355Q8×C13—28no—
356Q8×C13—216no—
357D4×C13—28no—
358C2×C4×C13—24no—
359C2×C4×C13—24no—
360C2×C4×C13—28no—
361C2×C4×C13—24no—
362C2×C4×C13—22no—
363C2×C4×C13—216no—
364C2×C4×C132−1+414yes—
365C2×C4×C132−1+414yes—
366C2×C4×C13C2518yes—
367C2×C4×C13C2514yes—
368C2×C4×C13C2512yes—
369C2×C4×C13C2514yes—
370C2×C4×C13C2514yes—
371C2×C4×C13C2512yes—
372C2×C4×C13C2512yes—
373C22⋊D13—48no—
374C2×Dic13—24no—
375C2×Dic13—24no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—28no—
380C2×Dic13—24no—
381C2×Dic13—24no—
382C2×Dic13—416no—
383C2×Dic13C2512yes—
384C2×Dic13C2514yes—
385C2×Dic13C2514yes—
386C2×Dic13C2514yes—
387C2×Dic13C2512yes—
388C2×Dic13C2518yes—
389C2×Dic13C2512yes—
390C2×Dic13C2514yes—
391C4×D13—28no—
392C4×D13—28no—
393C4×D13—44no—
394Dic26—28no—
395Dic26—28no—
396Dic26—48no—
397Dic26—48no—
398Dic26—416no—
399#563—1364no—
400Q82—1316no—
401#557—1316no—
402#557—1332no—
403#556—1332no—
404#556—1332no—
405#556C2×D13116yescomplemented
406#554—1316no—
407#552—1332no—
408#544—1332no—
409#542—1332no—
410#541—1364no—
411#541—1332no—
412#541—1332no—
413#533—1316no—
414#533—1316no—
415C2×C4⋊Q8—131no—
416C2×C4⋊Q8—132no—
417C2×C4⋊Q8—131no—
418C2×C4⋊Q8—134no—
419C2×C4⋊Q8—132no—
420C2×C4⋊Q8—131no—
421C2×C4⋊Q8—132no—
422C2×C4⋊Q8—134no—
423C2×C4⋊Q8C2×D1311yescharacteristic
424#529—1316no—
425C2×#126—134no—
426C2×#126—132no—
427C2×#126—134no—
428C2×#126—134no—
429C2×#126—134no—
430C2×#126—134no—
431C2×#126C2×D1314yes—
432C2×#125—132no—
433C2×#125—134no—
434C2×#125—134no—
435C2×#125—131no—
436C2×#125—132no—
437C2×#125—134no—
438C2×#125—132no—
439C2×#125—134no—
440C2×#125—132no—
441C2×#125—134no—
442C2×#124—131no—
443C2×#124—134no—
444C2×#124C2×D1312yes—
445C2×#123—132no—
446C2×#123—134no—
447C2×C22⋊Q8—132no—
448C2×C22⋊Q8—131no—
449C2×C22⋊Q8—132no—
450C2×C22⋊Q8—132no—
451C2×C22⋊Q8—131no—
452C2×C22⋊Q8—131no—
453C2×C22⋊Q8—132no—
454C2×C22⋊Q8—134no—
455C2×C22⋊Q8—134no—
456C2×C22⋊Q8—134no—
457C2×C22⋊Q8C2×D1312yes—
458C2×#121—131no—
459C2×C4×Q8—132no—
460C2×C4×Q8—132no—
461C2×C4×Q8—132no—
462C2×C4×Q8—132no—
463C2×C4×Q8—132no—
464C2×C4×Q8—131no—
465C2×C4×Q8—131no—
466C2×C4×Q8—132no—
467C2×C4×Q8—134no—
468C2×C4×Q8—132no—
469C2×C4×Q8C2×D1311yescharacteristic
470C2×C4×Q8C2×D1312yes—
471C2×C4×D4—132no—
472C2×C4×D4—132no—
473C2×C4×D4C2×D1311yescharacteristic
474C2×#117—132no—
475C2×#117—132no—
476C2×#117—134no—
477C2×#117—132no—
478C2×#117C2×D1312yes—
479C22×C4⋊C4—132no—
480C22×C42—131no—
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—48no—
485C22×C13C2×2−1+412yes—
486C22×C13C2×2−1+412yes—
487C22×C13#58512yes—
488C22×C13C2611yescharacteristic
489C2×D13—22no—
490C2×D13—22no—
491C2×D13—22no—
492C2×D13—44no—
493C4×C13—24no—
494C4×C13—24no—
495C4×C13—28no—
496C4×C13—24no—
497C4×C13—22no—
498C4×C13C2×2−1+414yes—
499C4×C13C2×2−1+414yes—
500Dic13—24no—
501Dic13—24no—
502Dic13—22no—
503Dic13—22no—
504Dic13—22no—
505Dic13—28no—
506Dic13—24no—
507Dic13—24no—
508C22×Q8—131no—
509C22×Q8—131no—
510C22×Q8—132no—
511C22×Q8—132no—
512C22×Q8—134no—
513C22×Q8C22×D1311yescharacteristic
514C22×Q8C22×D1312yes—
515C22×D4—132no—
516C22×D4C22×D1311yescharacteristic
517C23×C4—134no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4—131no—
521C23×C4C22×D1312yes—
522C4⋊Q8—138no—
523C4⋊Q8—1316no—
524C4⋊Q8—138no—
525C4⋊Q8—1332no—
526C4⋊Q8—1316no—
527C4⋊Q8—138no—
528C4⋊Q8—1316no—
529C4⋊Q8—1332no—
530C4⋊Q8C22×D1318yes—
531#126—1332no—
532#126—1316no—
533#126—1332no—
534#126—1332no—
535#126—1332no—
536#126—1332no—
537#126C22×D13132yes—
538#125—138no—
539#125—1316no—
540#125—1316no—
541#125—1332no—
542#125—1332no—
543#125—1316no—
544#125—1332no—
545#125—1332no—
546#125—1316no—
547#125—1332no—
548#124—138no—
549#124—1332no—
550#124C22×D13116yes—
551#123—1316no—
552#123—1332no—
553C22⋊Q8—1316no—
554C22⋊Q8—138no—
555C22⋊Q8—1316no—
556C22⋊Q8—138no—
557C22⋊Q8—138no—
558C22⋊Q8—1316no—
559C22⋊Q8—1316no—
560C22⋊Q8—1332no—
561C22⋊Q8—1332no—
562C22⋊Q8—1332no—
563C22⋊Q8C22×D13116yes—
564#121—138no—
565C4×Q8—1316no—
566C4×Q8—1316no—
567C4×Q8—1316no—
568C4×Q8—1316no—
569C4×Q8—1316no—
570C4×Q8—138no—
571C4×Q8—138no—
572C4×Q8—1316no—
573C4×Q8—1332no—
574C4×Q8—1316no—
575C4×Q8C22×D1318yes—
576C4×Q8C22×D13116yes—
577C4×D4—1316no—
578C4×D4—1316no—
579C4×D4C22×D1318yes—
580#117—1316no—
581#117—1316no—
582#117—1332no—
583#117—1316no—
584#117C22×D13116yes—
585C2×C4⋊C4—131no—
586C2×C4⋊C4—132no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—1316no—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—132no—
591C2×C4⋊C4—132no—
592C2×C4⋊C4—134no—
593C2×C4⋊C4—132no—
594C2×C4⋊C4—132no—
595C2×C4⋊C4—132no—
596C2×C4⋊C4—132no—
597C2×C4⋊C4—131no—
598C2×C4⋊C4—132no—
599C2×C4⋊C4—132no—
600C2×C4⋊C4—134no—
601C2×C4⋊C4—134no—
602C2×C4⋊C4—134no—
603C2×C4⋊C4—134no—
604C2×C4⋊C4—132no—
605C2×C4⋊C4—134no—
606C2×C4⋊C4—132no—
607C2×C4⋊C4—134no—
608C2×C4⋊C4—134no—
609C2×C4⋊C4C22×D1312yes—
610C2×C4⋊C4C22×D1311yescharacteristic
611C2×C4⋊C4C22×D1311yescharacteristic
612C2×C4⋊C4C22×D1312yes—
613C2×C4⋊C4C22×D1312yes—
614C2×C4⋊C4C22×D1314yes—
615C2×C22⋊C4—132no—
616C2×C22⋊C4—132no—
617C2×C22⋊C4—132no—
618C2×C22⋊C4—134no—
619C2×C22⋊C4—132no—
620C2×C22⋊C4—134no—
621C2×C22⋊C4—132no—
622C2×C22⋊C4—132no—
623C2×C22⋊C4C22×D1314yes—
624C2×C22⋊C4C22×D1314yes—
625C2×C22⋊C4C22×D1312yes—
626C2×C42—134no—
627C2×C42—131no—
628C2×C42—132no—
629C2×C42—132no—
630C2×C42—134no—
631C2×C42—131no—
632C2×C42—134no—
633C2×C42—131no—
634C2×C42—138no—
635C2×C42C22×D1312yes—
636C2×C42C22×D1314yes—
637C2×C42C22×D1311yescharacteristic
638C2×C13—44no—
639C2×C13#355514yescomplemented
640C2×C13C22×2−1+411yescharacteristic
641C2×C13C22×2−1+411yescharacteristic
642C2×C13C2×#58511yescharacteristic
643D13—42no—
644C24—131no—
645C24C23×D1312yes—
646C2×Q8—24no—
647C2×Q8—28no—
648C2×Q8—134no—
649C2×Q8—134no—
650C2×Q8—138no—
651C2×Q8—138no—
652C2×Q8—1316no—
653C2×Q8—264no—
654C2×Q8—264no—
655C2×Q8—524no—
656C2×Q8—524no—
657C2×Q8—528no—
658C2×Q8C23×D1314yes—
659C2×Q8C23×D1318yes—
660C2×D4—24no—
661C2×D4—138no—
662C2×D4—524no—
663C2×D4C23×D1314yes—
664C22×C4—28no—
665C22×C4—131no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—131no—
670C22×C4—134no—
671C22×C4—131no—
672C22×C4—132no—
673C22×C4—1316no—
674C22×C4—134no—
675C22×C4—134no—
676C22×C4—134no—
677C22×C4—264no—
678C22×C4—264no—
679C22×C4—522no—
680C22×C4—528no—
681C22×C4C23×D1318yes—
682C22×C4C23×D1314yes—
683C22×C4C23×D1312yes—
684C22×C4C23×D1311yescharacteristic
685C22×C4C23×D1312yes—
686C22×C4C23×D1312yes—
687C22×C4C23×D1311yescharacteristic
688C22×C4C23×D1311yescharacteristic
689C4⋊C4—134no—
690C4⋊C4—138no—
691C4⋊C4—1316no—
692C4⋊C4—138no—
693C4⋊C4—138no—
694C4⋊C4—138no—
695C4⋊C4—1316no—
696C4⋊C4—138no—
697C4⋊C4—138no—
698C4⋊C4—138no—
699C4⋊C4—138no—
700C4⋊C4—134no—
701C4⋊C4—138no—
702C4⋊C4—138no—
703C4⋊C4—1316no—
704C4⋊C4—1316no—
705C4⋊C4—1316no—
706C4⋊C4—1316no—
707C4⋊C4—138no—
708C4⋊C4—1316no—
709C4⋊C4—138no—
710C4⋊C4—1316no—
711C4⋊C4—1316no—
712C4⋊C4C23×D1318yes—
713C4⋊C4C23×D1314yes—
714C4⋊C4C23×D1314yes—
715C4⋊C4C23×D1318yes—
716C4⋊C4C23×D1318yes—
717C4⋊C4C23×D13116yes—
718C22⋊C4—138no—
719C22⋊C4—138no—
720C22⋊C4—138no—
721C22⋊C4—1316no—
722C22⋊C4—138no—
723C22⋊C4—1316no—
724C22⋊C4—138no—
725C22⋊C4—138no—
726C22⋊C4C23×D13116yes—
727C22⋊C4C23×D13116yes—
728C22⋊C4C23×D1318yes—
729C42—134no—
730C42—134no—
731C42—134no—
732C42—1316no—
733C42—138no—
734C42—138no—
735C42—1316no—
736C42—1316no—
737C42C23×D1314yes—
738C42C23×D1318yes—
739C42C23×D13116yes—
740C13C2×#355511yescharacteristic, complemented, Sylow
741C23—24no—
742C23—24no—
743C23—24no—
744C23—132no—
745C23—262no—
746C23—262no—
747C23—262no—
748C23C24×D1314yes—
749C23C24×D1311yescharacteristic
750Q8—28no—
751Q8—216no—
752Q8—268no—
753Q8—268no—
754Q8—528no—
755Q8—528no—
756Q8—5216no—
757D4—28no—
758D4—528no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—216no—
765C2×C4—132no—
766C2×C4—134no—
767C2×C4—134no—
768C2×C4—134no—
769C2×C4—132no—
770C2×C4—132no—
771C2×C4—138no—
772C2×C4—134no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—264no—
776C2×C4—264no—
777C2×C4—264no—
778C2×C4—262no—
779C2×C4—268no—
780C2×C4—264no—
781C2×C4—268no—
782C2×C4—268no—
783C2×C4—524no—
784C2×C4—5216no—
785C2×C4#8825714yes—
786C2×C4#8825714yes—
787C2×C4C24×D1318yes—
788C2×C4C24×D1314yes—
789C2×C4C24×D1312yes—
790C2×C4C24×D1314yes—
791C2×C4C24×D1314yes—
792C2×C4C24×D1312yes—
793C2×C4C24×D1312yes—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—262no—
799C22—262no—
800C22—262no—
801C22—524no—
802C22C2×#8825712yes—
803C22C2×#8825712yes—
804C22#1171965212yes—
805C22C25×D1311yescharacteristic
806C4—24no—
807C4—24no—
808C4—28no—
809C4—22no—
810C4—24no—
811C4—262no—
812C4—262no—
813C4—264no—
814C4—264no—
815C4—264no—
816C4—262no—
817C4—268no—
818C4—264no—
819C4C2×#8825714yes—
820C4C2×#8825714yes—
821C2—44no—
822C2—522no—
823C2#1312931214yesdirect product factor
824C2C22×#8825711yescharacteristic
825C2C22×#8825711yescharacteristic
826C2C2×#1171965211yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#556C2
socleC23×C13C25
prime radicalC2×#88192C22
hypercenterC2×#556D13
hypocenterC13C2×#3555
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13129312C2direct (N × H)
2. C2×#11719417C2semidirect
3. C2×Q8×Dic26C2semidirect
4. C2×#11719275C2semidirect
5. C2×#11719426C2semidirect
6. C2×#11719376C2semidirect
7. C2×#11719238C2semidirect
8. C2×#11719248C2semidirect
9. C2×#11719347C2semidirect
10. C2×#11719224C2semidirect
12. C2×#11719330C2semidirect
13. C2×#11719288C2semidirect
14. C2×#11719406C2semidirect
15. C2×#11719433C2semidirect
16. C2×#11719283C2semidirect
18. C2×C13×#556C2semidirect
19. C13×#556C22semidirect
42. #11719433C22semidirect
43. #11719426C22semidirect
44. #11719417C22semidirect
45. #11719406C22semidirect
47. #11719376C22semidirect
48. #11719347C22semidirect
49. #11719330C22semidirect
50. #11719288C22semidirect
51. #11719283C22semidirect
52. #11719275C22semidirect
53. Q8×Dic26C22semidirect
55. #11719248C22semidirect
56. #11719238C22semidirect
57. #11719224C22semidirect
335. C2×#556D13semidirect
405. #556C2×D13semidirect
639. C2×C13#3555semidirect
740. C13C2×#3555semidirect
823. C2#13129312direct (N × H)

Maximal subgroups

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

subgroupindex
#131293122
C2×#117194172
C2×Q8×Dic262
C2×#117192752
C2×#117194262
C2×#117193762
C2×#117192382
C2×#117192482
C2×#117193472
C2×#117192242
C2×#117193872
C2×#117193302
C2×#117192882
C2×#117194062
C2×#117194332
C2×#117192832
C2×#117192622
C2×C13×#5562
C2×#355513