Finite Group Databasebeta

← C2×#13129176 #16770601

Subgroups — C2×#13129176 #16770601

Order 3328.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13129176C2132yesmaximal, direct product factor
2C2×#11719417C214yesmaximal, complemented
3C2×Q8×Dic26C211yesmaximal, characteristic, complemented
4C2×#11719268C211yesmaximal, characteristic, complemented
5C2×#11719284C211yesmaximal, characteristic, complemented
6C2×#11719248C211yesmaximal, characteristic, complemented
7C2×#11719347C212yesmaximal, complemented
8C2×#11719246C212yesmaximal, complemented
9C2×#11719260C212yesmaximal, complemented
10C2×#11719316C212yesmaximal, complemented
11C2×#11719394C212yesmaximal, complemented
12C2×#11719224C212yesmaximal, complemented
13C2×#11719239C212yesmaximal, complemented
14C2×#11719387C212yesmaximal, complemented
15C2×#11719353C214yesmaximal, complemented
16C22×#88123C211yesmaximal, characteristic, complemented
17C2×#11719184C211yesmaximal, characteristic, complemented
18C2×C13×#529C211yesmaximal, characteristic, complemented
19C22×#6129C2214yes—
20C23×Dic26C2212yes—
21C13×#529C22116yescomplemented
22C2×C13×#126C2212yes—
23C2×C13×#125C2211yescharacteristic
24C2×C13×#124C2211yescharacteristic
25C2×C13×#123C2212yes—
26C2×C13×C22⋊Q8C2211yescharacteristic
27C2×C13×#121C2211yescharacteristic
28C2×C4×Q8×C13C2211yescharacteristic
29C2×C4×D4×C13C2212yes—
30C2×C4×D4×C13C2211yescharacteristic
31C2×C13×#117C2212yes—
32C22×C42×C13C2211yescharacteristic
33C2×#88200C2212yes—
34C2×Q8×Dic13C2212yes—
35C2×#88192C2212yes—
36C2×#88189C2214yes—
37C2×D4×Dic13C2212yes—
38C2×#88184C2212yes—
39C2×#88184C2211yescharacteristic
40C2×#88183C2212yes—
41C2×C4×C22⋊D13C2212yes—
42C2×#88180C2212yes—
43C22×C4⋊Dic13C2212yes—
44C22×C4⋊Dic13C2212yes—
45C22×C4⋊Dic13C2212yes—
46C2×#88178C2212yes—
47C2×#88178C2211yescharacteristic
48#11719417C22164yescomplemented
49#11719394C22132yescomplemented
50#11719387C22132yescomplemented
51#11719353C22164yescomplemented
52#11719347C22132yescomplemented
53#11719316C22132yescomplemented
54#11719284C22116yescomplemented
55Q8×Dic26C22116yescomplemented
56#11719268C22116yescomplemented
57#11719260C22132yescomplemented
58#11719248C22116yescomplemented
59#11719246C22132yescomplemented
60#11719239C22132yescomplemented
61#11719224C22132yescomplemented
62C2×#88152C2214yes—
63C2×#88151C2214yes—
64C2×#88150C2214yes—
65C2×#88150C2214yes—
66C2×#88146C2212yes—
67C2×C4⋊C4×D13C2212yes—
68C2×#88144C2214yes—
69C2×#88144C2212yes—
70C2×#88143C2214yes—
71C2×#88142C2214yes—
72C2×#88142C2214yes—
73C2×#88142C2212yes—
74C2×#88140C2214yes—
75C2×#88140C2214yes—
76C2×#88139C2214yes—
77C2×#88139C2214yes—
78C2×#88137C2214yes—
79C2×#88133C2214yes—
80C2×#88132C2214yes—
81C2×#88132C2214yes—
82C2×#88132C2214yes—
83C2×#88131C2214yes—
84#11719184C22116yescomplemented
85C2×#88130C2212yes—
86C2×#88129C2211yescharacteristic
87C2×C4×D52C2212yes—
88C2×C4×D52C2211yescharacteristic
89C2×#88126C2212yes—
90C2×#88124C2211yescharacteristic
91C2×#88124C2212yes—
92C2×#88123C2212yes—
93C2×#88123C2212yes—
94C2×#88123C2212yes—
95C2×#88123C2212yes—
96C2×#88123C2211yescharacteristic
97C2×#88123C2211yescharacteristic
98C2×#88123C22116yescomplemented
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C22×Q8×C13C2311yescharacteristic
102C22×D4×C13C2311yescharacteristic
103C22×D4×C13C2312yes—
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2312yes—
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C22×C22⋊D13C2312yes—
109C22×C22⋊D13C2314yes—
110C23×Dic13C2314yes—
111C23×Dic13C2314yes—
112C2×#6129—416no—
113C2×#6129C23132yes—
114C22×D52C2311yescharacteristic
115C22×C4×D13C2312yes—
116C22×C4×D13C2314yes—
117C22×Dic26—48no—
118C22×Dic26C2311yescharacteristic
119C22×Dic26C2312yes—
120C22×Dic26C2314yes—
121C22×Dic26C2312yes—
122C22×Dic26C2314yes—
123C22×Dic26C23116yes—
124C13×#126C23116yes—
125C13×#125C2318yes—
126C13×#124C2318yes—
127C13×#123C23116yes—
128C13×C22⋊Q8C2318yes—
129C13×#121C2318yes—
130C4×Q8×C13C2318yes—
131C4×D4×C13C23116yes—
132C4×D4×C13C2318yes—
133C13×#117C23116yes—
134C2×C13×C4⋊C4C2311yescharacteristic
135C2×C13×C4⋊C4C2312yes—
136C2×C13×C4⋊C4C2312yes—
137C2×C13×C4⋊C4C2312yes—
138C2×C13×C4⋊C4C2311yescharacteristic
139C2×C13×C4⋊C4C2312yes—
140C2×C13×C22⋊C4C2312yes—
141C2×C13×C22⋊C4C2312yes—
142C2×C13×C22⋊C4C2312yes—
143C2×C13×C22⋊C4C2312yes—
144C2×C13×C22⋊C4C2312yes—
145C2×C42×C13C2311yescharacteristic
146C2×C42×C13C2312yes—
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2311yescharacteristic
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2318yes—
151C2×C22⋊Dic13C2312yes—
152C2×C22⋊Dic13C2314yes—
153C2×C22⋊Dic13C2314yes—
154#88200C23116yes—
155Q8×Dic13C23116yes—
156#88192C23116yes—
157#88189C23132yes—
158D4×Dic13C23116yes—
159#88184C2318yes—
160#88184C23116yes—
161#88183C23116yes—
162C4×C22⋊D13C23116yes—
163C2×#6103C2312yes—
164C2×#6103C2312yes—
165C2×#6103C2312yes—
166C2×#6103C2314yes—
167C2×#6103C2312yes—
168C2×#6103C2314yes—
169#88180C23116yes—
170C2×C4⋊Dic13C2312yes—
171C2×C4⋊Dic13C2311yescharacteristic
172C2×C4⋊Dic13C2312yes—
173C2×C4⋊Dic13C2314yes—
174C2×C4⋊Dic13C2314yes—
175C2×C4⋊Dic13C2312yes—
176C2×C4⋊Dic13C2312yes—
177C2×C4⋊Dic13C2314yes—
178C2×C4⋊Dic13C23116yes—
179C2×C4⋊Dic13C23116yes—
180C2×C4⋊Dic13C2311yescharacteristic
181C2×C4⋊Dic13C2314yes—
182C2×C4⋊Dic13C23116yes—
183#88178C2318yes—
184#88178C23116yes—
185C2×#6101C2312yes—
186C2×#6101C2314yes—
187C2×#6101C2312yes—
188C2×#6101C2312yes—
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2312yes—
192C2×#6101C2314yes—
193C2×C4×Dic13C2312yes—
194C2×C4×Dic13C2314yes—
195C2×C4×Dic13C2314yes—
196#88152C23132yes—
197#88151C23132yes—
198#88150C23132yes—
199#88150C23132yes—
200#88146C23116yes—
201C4⋊C4×D13C23116yes—
202#88144C23132yes—
203#88144C23116yes—
204#88143C23132yes—
205#88142C23132yes—
206#88142C23116yes—
207#88142C23132yes—
208#88140C23132yes—
209#88140C23132yes—
210#88139C23132yes—
211#88139C23132yes—
212#88137C23132yes—
213#88133C23132yes—
214#88132C23132yes—
215#88132C23132yes—
216#88132C23132yes—
217#88131C23132yes—
218#88130C23116yes—
219#88129C2318yes—
220C4×D52C2318yes—
221C4×D52C23116yes—
222#88126C23116yes—
223#88124C2318yes—
224#88124C23116yes—
225#88123C23116yes—
226#88123C2318yes—
227#88123C2318yes—
228#88123C23116yes—
229#88123C23116yes—
230#88123C23116yes—
231C4×Dic26C2318yes—
232C4×Dic26C23116yes—
233C2×#3544—131nomaximal, Sylow
234C24×C13C2412yes—
235C24×C13C2411yescharacteristic
236C23×D13C2412yes—
237C2×Q8×C13—24no—
238C2×Q8×C13C2414yes—
239C2×D4×C13—28no—
240C2×D4×C13—24no—
241C2×D4×C13C2414yes—
242C2×D4×C13C2418yes—
243C22×C4×C13—24no—
244C22×C4×C13—24no—
245C22×C4×C13—28no—
246C22×C4×C13—24no—
247C22×C4×C13C2412yes—
248C22×C4×C13C2412yes—
249C22×C4×C13C2412yes—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2414yes—
255C22×C4×C13C2418yes—
256C22×C4×C13C2414yes—
257C22×C4×C13C2414yes—
258C22×C4×C13C2411yescharacteristic
259C22×C4×C13C2411yescharacteristic
260C2×C22⋊D13—28no—
261C2×C22⋊D13—48no—
262C2×C22⋊D13C2418yes—
263C2×C22⋊D13C24116yes—
264C22×Dic13—216no—
265C22×Dic13—48no—
266C22×Dic13C24116yes—
267C22×Dic13C2412yes—
268C22×Dic13C2412yes—
269C22×Dic13C2414yes—
270C22×Dic13C2412yes—
271C22×Dic13C2414yes—
272C22×Dic13C24116yes—
273#6129—464no—
274C2×D52—24no—
275C2×D52C2414yes—
276C2×C4×D13—28no—
277C2×C4×D13—48no—
278C2×C4×D13C2418yes—
279C2×C4×D13C24116yes—
280C2×Dic26—24no—
281C2×Dic26—44no—
282C2×Dic26—48no—
283C2×Dic26—44no—
284C2×Dic26—432no—
285C2×Dic26—48no—
286C2×Dic26C2414yes—
287C2×Dic26C2418yes—
288C2×Dic26C24116yes—
289C2×Dic26C2418yes—
290C2×Dic26C24116yes—
291C13×C4⋊C4C2414yes—
292C13×C4⋊C4C2418yes—
293C13×C4⋊C4C2418yes—
294C13×C4⋊C4C2418yes—
295C13×C4⋊C4C2414yes—
296C13×C4⋊C4C2418yes—
297C13×C22⋊C4C2418yes—
298C13×C22⋊C4C2418yes—
299C13×C22⋊C4C2418yes—
300C13×C22⋊C4C2418yes—
301C13×C22⋊C4C2418yes—
302C42×C13C2414yes—
303C42×C13C2418yes—
304C42×C13C2414yes—
305C42×C13C2414yes—
306C42×C13C2414yes—
307C22⋊Dic13C2418yes—
308C22⋊Dic13C24116yes—
309C22⋊Dic13C24116yes—
310#6103C2418yes—
311#6103C2418yes—
312#6103C2418yes—
313#6103C24116yes—
314#6103C2418yes—
315#6103C24116yes—
316C4⋊Dic13C2418yes—
317C4⋊Dic13C2414yes—
318C4⋊Dic13C2418yes—
319C4⋊Dic13C24116yes—
320C4⋊Dic13C24116yes—
321C4⋊Dic13C2418yes—
322C4⋊Dic13C2418yes—
323C4⋊Dic13C24116yes—
324C4⋊Dic13C2414yes—
325C4⋊Dic13C24116yes—
326#6101C2418yes—
327#6101C24116yes—
328#6101C2418yes—
329#6101C2418yes—
330#6101C24116yes—
331#6101C24116yes—
332#6101C2418yes—
333#6101C24116yes—
334C4×Dic13C2418yes—
335C4×Dic13C24116yes—
336C4×Dic13C24116yes—
337#3544—1332no—
338C2×#563—134no—
339C2×Q82—131no—
340C2×#555—131no—
341C2×#554—131no—
342C2×#554—131no—
343C2×#552—132no—
344C2×#552—132no—
345C2×#547—132no—
346C2×#547—132no—
347C2×#544—132no—
348C2×#544—132no—
349C2×#542—132no—
350C2×#542—132no—
351C2×#536—134no—
352C22×C4⋊Q8—131no—
353C2×#529—131no—
354C2×#529D1311yescharacteristic, complemented
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—24no—
358C23×C13—24no—
359C23×C13—24no—
360C23×C13H(5,𝔽2)14yes—
361C23×C13C2514yes—
362C23×C13C2512yes—
363C23×C13C2511yescharacteristic
364C22×D13—24no—
365C22×D13—24no—
366C22×D13—24no—
367C22×D13C2514yes—
368Q8×C13—28no—
369D4×C13—216no—
370D4×C13—28no—
371C2×C4×C13—28no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—24no—
375C2×C4×C13—24no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—24no—
379C2×C4×C13—28no—
380C2×C4×C13—216no—
381C2×C4×C13—28no—
382C2×C4×C132−1+414yes—
383C2×C4×C132−1+414yes—
384C2×C4×C13C2514yes—
385C2×C4×C13C2514yes—
386C2×C4×C13C2514yes—
387C2×C4×C13C2512yes—
388C2×C4×C13C2512yes—
389C2×C4×C13C2512yes—
390C2×C4×C13C2512yes—
391C2×C4×C13C2512yes—
392C2×C4×C13C2512yes—
393C22⋊D13—216no—
394C22⋊D13—416no—
395C2×Dic13—28no—
396C2×Dic13—28no—
397C2×Dic13—232no—
398C2×Dic13—24no—
399C2×Dic13—24no—
400C2×Dic13—24no—
401C2×Dic13—416no—
402C2×Dic13C2514yes—
403C2×Dic13C2514yes—
404C2×Dic13C2518yes—
405C2×Dic13C2514yes—
406C2×Dic13C2518yes—
407D52—28no—
408C4×D13—216no—
409C4×D13—416no—
410Dic26—28no—
411Dic26—48no—
412Dic26—416no—
413Dic26—48no—
414Dic26—416no—
415C22×#41—134no—
416C23×Q8—132no—
417#563—1364no—
418Q82—1316no—
419#555—1316no—
420#554—1316no—
421#554—1316no—
422#552—1332no—
423#552—1332no—
424#547—1332no—
425#547—1332no—
426#544—1332no—
427#544—1332no—
428#542—1332no—
429#542—1332no—
430#536—1364no—
431C2×C4⋊Q8—134no—
432C2×C4⋊Q8—134no—
433C2×C4⋊Q8—132no—
434C2×C4⋊Q8—132no—
435C2×C4⋊Q8—132no—
436C2×C4⋊Q8—131no—
437C2×C4⋊Q8—131no—
438C2×C4⋊Q8—132no—
439C2×C4⋊Q8—132no—
440C2×C4⋊Q8—1316no—
441#529—1316no—
442#529C2×D13116yescomplemented
443C2×#126—134no—
444C2×#126—134no—
445C2×#126—132no—
446C2×#126C2×D1312yes—
447C2×#125—134no—
448C2×#125—132no—
449C2×#125—134no—
450C2×#125—131no—
451C2×#125—132no—
452C2×#125C2×D1311yescharacteristic
453C2×#124—134no—
454C2×#124—134no—
455C2×#124—131no—
456C2×#124C2×D1311yescharacteristic
457C2×#123—134no—
458C2×#123—132no—
459C2×#123—134no—
460C2×#123—134no—
461C2×#123—134no—
462C2×#123C2×D1312yes—
463C2×C22⋊Q8—132no—
464C2×C22⋊Q8—131no—
465C2×C22⋊Q8—132no—
466C2×C22⋊Q8—134no—
467C2×C22⋊Q8—134no—
468C2×C22⋊Q8—134no—
469C2×C22⋊Q8—134no—
470C2×C22⋊Q8—134no—
471C2×C22⋊Q8—134no—
472C2×C22⋊Q8C2×D1311yescharacteristic
473C2×#121—132no—
474C2×#121—131no—
475C2×#121—132no—
476C2×#121C2×D1311yescharacteristic
477C2×C4×Q8—132no—
478C2×C4×Q8—131no—
479C2×C4×Q8—132no—
480C2×C4×Q8C2×D1311yescharacteristic
481C2×C4×D4—132no—
482C2×C4×D4—132no—
483C2×C4×D4—131no—
484C2×C4×D4—132no—
485C2×C4×D4C2×D1312yes—
486C2×C4×D4C2×D1311yescharacteristic
487C2×#117—132no—
488C2×#117—132no—
489C2×#117—134no—
490C2×#117—132no—
491C2×#117C2×D1312yes—
492C22×C4⋊C4—132no—
493C22×C4⋊C4—132no—
494C22×C4⋊C4—132no—
495C22×C4⋊C4—132no—
496C22×C42C2×D1311yescharacteristic
497C22×C13—22no—
498C22×C13—22no—
499C22×C13—28no—
500C22×C13—24no—
501C22×C13—24no—
502C22×C13—24no—
503C22×C13—48no—
504C22×C13C2×H(5,𝔽2)14yes—
505C22×C13C2×H(5,𝔽2)12yes—
506C22×C13C2×2−1+412yes—
507C22×C13C2×2−1+412yes—
508C22×C13C2611yescharacteristic
509C2×D13—24no—
510C2×D13—24no—
511C2×D13—24no—
512C2×D13—48no—
513C4×C13—22no—
514C4×C13—22no—
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—22no—
518C4×C13—22no—
519C4×C13—24no—
520C4×C13C2×2−1+414yes—
521C4×C13C2×2−1+414yes—
522Dic13—28no—
523Dic13—28no—
524Dic13—24no—
525Dic13—24no—
526Dic13—24no—
527C2×#41—1332no—
528C2×#41—5216no—
529C22×Q8—131no—
530C22×Q8—132no—
531C22×Q8—134no—
532C22×Q8—134no—
533C22×Q8—132no—
534C22×Q8—1316no—
535C22×Q8—528no—
536C22×Q8C22×D1311yescharacteristic
537C22×D4—132no—
538C22×D4—134no—
539C22×D4—131no—
540C22×D4C22×D1311yescharacteristic
541C22×D4C22×D1312yes—
542C23×C4—134no—
543C23×C4—134no—
544C23×C4—132no—
545C23×C4—134no—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1312yes—
549C23×C4C22×D1311yescharacteristic
550C4⋊Q8—1332no—
551C4⋊Q8—1332no—
552C4⋊Q8—1316no—
553C4⋊Q8—1316no—
554C4⋊Q8—1316no—
555C4⋊Q8—138no—
556C4⋊Q8—138no—
557C4⋊Q8—1316no—
558C4⋊Q8—1316no—
559#126—1332no—
560#126—1332no—
561#126—1316no—
562#126C22×D13116yes—
563#125—1316no—
564#125—1332no—
565#125—1332no—
566#125—138no—
567#125—1316no—
568#125C22×D1318yes—
569#124—1332no—
570#124—1332no—
571#124—138no—
572#124C22×D1318yes—
573#123—1332no—
574#123—1316no—
575#123—1332no—
576#123—1332no—
577#123—1332no—
578#123C22×D13116yes—
579C22⋊Q8—1316no—
580C22⋊Q8—138no—
581C22⋊Q8—1316no—
582C22⋊Q8—1332no—
583C22⋊Q8—1332no—
584C22⋊Q8—1332no—
585C22⋊Q8—1332no—
586C22⋊Q8—1332no—
587C22⋊Q8—1332no—
588C22⋊Q8C22×D1318yes—
589#121—1316no—
590#121—138no—
591#121—1316no—
592#121C22×D1318yes—
593C4×Q8—1316no—
594C4×Q8—138no—
595C4×Q8—1316no—
596C4×Q8C22×D1318yes—
597C4×D4—1316no—
598C4×D4—1316no—
599C4×D4—138no—
600C4×D4—1316no—
601C4×D4C22×D13116yes—
602C4×D4C22×D1318yes—
603#117—1316no—
604#117—1316no—
605#117—1332no—
606#117—1316no—
607#117C22×D13116yes—
608C2×C4⋊C4—132no—
609C2×C4⋊C4—132no—
610C2×C4⋊C4—131no—
611C2×C4⋊C4—132no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—134no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—134no—
617C2×C4⋊C4—1316no—
618C2×C4⋊C4—1316no—
619C2×C4⋊C4—1316no—
620C2×C4⋊C4—131no—
621C2×C4⋊C4—134no—
622C2×C4⋊C4—134no—
623C2×C4⋊C4—132no—
624C2×C4⋊C4—132no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—132no—
627C2×C4⋊C4—134no—
628C2×C4⋊C4—134no—
629C2×C4⋊C4—1316no—
630C2×C4⋊C4C22×D1311yescharacteristic
631C2×C4⋊C4C22×D1311yescharacteristic
632C2×C4⋊C4C22×D1312yes—
633C2×C4⋊C4C22×D1312yes—
634C2×C4⋊C4C22×D1312yes—
635C2×C4⋊C4C22×D1312yes—
636C2×C22⋊C4—132no—
637C2×C22⋊C4—134no—
638C2×C22⋊C4—134no—
639C2×C22⋊C4—132no—
640C2×C22⋊C4—134no—
641C2×C22⋊C4—132no—
642C2×C22⋊C4—134no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4—132no—
645C2×C22⋊C4C22×D1312yes—
646C2×C22⋊C4C22×D1312yes—
647C2×C22⋊C4C22×D1312yes—
648C2×C22⋊C4C22×D1312yes—
649C2×C22⋊C4C22×D1312yes—
650C2×C42—134no—
651C2×C42—132no—
652C2×C42—134no—
653C2×C42C22×D1311yescharacteristic
654C2×C42C22×D1311yescharacteristic
655C2×C42C22×D1312yes—
656C2×C42C22×D1311yescharacteristic
657C2×C42C22×D1311yescharacteristic
658C2×C42C22×D1318yes—
659C2×C13—24no—
660C2×C13—44no—
661C2×C13#354414yescomplemented
662C2×C13C22×H(5,𝔽2)11yescharacteristic
663C2×C13C22×2−1+411yescharacteristic
664C2×C13C22×2−1+411yescharacteristic
665D13—44no—
666C24—132no—
667C24C23×D1312yes—
668C24C23×D1311yescharacteristic
669#41—5264no—
670C2×Q8—24no—
671C2×Q8—134no—
672C2×Q8—138no—
673C2×Q8—1316no—
674C2×Q8—1316no—
675C2×Q8—138no—
676C2×Q8—264no—
677C2×Q8—524no—
678C2×Q8—528no—
679C2×Q8—524no—
680C2×Q8—5232no—
681C2×Q8—528no—
682C2×Q8C23×D1314yes—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—138no—
686C2×D4—1316no—
687C2×D4—134no—
688C2×D4—268no—
689C2×D4—264no—
690C2×D4—528no—
691C2×D4C23×D1314yes—
692C2×D4C23×D1318yes—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—28no—
696C22×C4—24no—
697C22×C4—1316no—
698C22×C4—132no—
699C22×C4—132no—
700C22×C4—134no—
701C22×C4—132no—
702C22×C4—134no—
703C22×C4—1316no—
704C22×C4—138no—
705C22×C4—1316no—
706C22×C4—2616no—
707C22×C4—268no—
708C22×C4—528no—
709C22×C4—528no—
710C22×C4C23×D1314yes—
711C22×C4C23×D1314yes—
712C22×C4C23×D1314yes—
713C22×C4C23×D1318yes—
714C22×C4C23×D1312yes—
715C22×C4C23×D1312yes—
716C22×C4C23×D1311yescharacteristic
717C22×C4C23×D1311yescharacteristic
718C22×C4C23×D1311yescharacteristic
719C22×C4C23×D1311yescharacteristic
720C22×C4C23×D1312yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1311yescharacteristic
723C4⋊C4—138no—
724C4⋊C4—138no—
725C4⋊C4—134no—
726C4⋊C4—138no—
727C4⋊C4—138no—
728C4⋊C4—1316no—
729C4⋊C4—1316no—
730C4⋊C4—1316no—
731C4⋊C4—1316no—
732C4⋊C4—134no—
733C4⋊C4—1316no—
734C4⋊C4—1316no—
735C4⋊C4—138no—
736C4⋊C4—138no—
737C4⋊C4—138no—
738C4⋊C4—138no—
739C4⋊C4—1316no—
740C4⋊C4—1316no—
741C4⋊C4C23×D1314yes—
742C4⋊C4C23×D1314yes—
743C4⋊C4C23×D1318yes—
744C4⋊C4C23×D1318yes—
745C4⋊C4C23×D1318yes—
746C4⋊C4C23×D1318yes—
747C22⋊C4—138no—
748C22⋊C4—1316no—
749C22⋊C4—1316no—
750C22⋊C4—138no—
751C22⋊C4—1316no—
752C22⋊C4—138no—
753C22⋊C4—1316no—
754C22⋊C4—138no—
755C22⋊C4—138no—
756C22⋊C4C23×D1318yes—
757C22⋊C4C23×D1318yes—
758C22⋊C4C23×D1318yes—
759C22⋊C4C23×D1318yes—
760C22⋊C4C23×D1318yes—
761C42—1316no—
762C42—138no—
763C42—1316no—
764C42C23×D1314yes—
765C42C23×D1314yes—
766C42C23×D1314yes—
767C42C23×D1314yes—
768C42C23×D1318yes—
769C13C2×#354411yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—134no—
776C23—264no—
777C23—264no—
778C23—264no—
779C23#8825614yes—
780C23C24×D1314yes—
781C23C24×D1312yes—
782C23C24×D1311yescharacteristic
783Q8—28no—
784Q8—268no—
785Q8—528no—
786Q8—5216no—
787Q8—528no—
788Q8—5216no—
789D4—216no—
790D4—28no—
791D4—2616no—
792D4—268no—
793D4—5216no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—134no—
806C2×C4—134no—
807C2×C4—138no—
808C2×C4—134no—
809C2×C4—138no—
810C2×C4—268no—
811C2×C4—268no—
812C2×C4—2632no—
813C2×C4—264no—
814C2×C4—264no—
815C2×C4—264no—
816C2×C4—2616no—
817C2×C4—5216no—
818C2×C4—5216no—
819C2×C4#8825714yes—
820C2×C4#8825714yes—
821C2×C4C24×D1314yes—
822C2×C4C24×D1314yes—
823C2×C4C24×D1312yes—
824C2×C4C24×D1312yes—
825C2×C4C24×D1312yes—
826C2×C4C24×D1312yes—
827C2×C4C24×D1314yes—
828C2×C4C24×D1312yes—
829C2×C4C24×D1312yes—
830C22—22no—
831C22—22no—
832C22—28no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—264no—
838C22—264no—
839C22—264no—
840C22—528no—
841C22C2×#8825614yes—
842C22C2×#8825612yes—
843C22C2×#8825712yes—
844C22C2×#8825712yes—
845C22C25×D1311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—268no—
854C4—268no—
855C4—264no—
856C4—264no—
857C4—264no—
858C4C2×#8825714yes—
859C4C2×#8825714yes—
860C2—24no—
861C2—44no—
862C2—524no—
863C2#1312917614yesdirect product factor
864C2C22×#8825611yescharacteristic
865C2C22×#8825711yescharacteristic
866C2C22×#8825711yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C13×#529C2
socleC23×C13C25
hypercenterC2×#529D13
hypocenterC13C2×#3544
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #13129176C2direct (N × H)
2. C2×#11719417C2semidirect
3. C2×Q8×Dic26C2semidirect
4. C2×#11719268C2semidirect
5. C2×#11719284C2semidirect
6. C2×#11719248C2semidirect
7. C2×#11719347C2semidirect
8. C2×#11719246C2semidirect
9. C2×#11719260C2semidirect
10. C2×#11719316C2semidirect
11. C2×#11719394C2semidirect
12. C2×#11719224C2semidirect
13. C2×#11719239C2semidirect
14. C2×#11719387C2semidirect
15. C2×#11719353C2semidirect
16. C22×#88123C2semidirect
17. C2×#11719184C2semidirect
18. C2×C13×#529C2semidirect
21. C13×#529C22semidirect
48. #11719417C22semidirect
49. #11719394C22semidirect
50. #11719387C22semidirect
51. #11719353C22semidirect
52. #11719347C22semidirect
53. #11719316C22semidirect
54. #11719284C22semidirect
55. Q8×Dic26C22semidirect
56. #11719268C22semidirect
57. #11719260C22semidirect
58. #11719248C22semidirect
59. #11719246C22semidirect
60. #11719239C22semidirect
61. #11719224C22semidirect
84. #11719184C22semidirect
98. C2×#88123C22semidirect
354. C2×#529D13semidirect
442. #529C2×D13semidirect
661. C2×C13#3544semidirect
769. C13C2×#3544semidirect
863. C2#13129176direct (N × H)

Maximal subgroups

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

subgroupindex
#131291762
C2×#117194172
C2×Q8×Dic262
C2×#117192682
C2×#117192842
C2×#117192482
C2×#117193472
C2×#117192462
C2×#117192602
C2×#117193162
C2×#117193942
C2×#117192242
C2×#117192392
C2×#117193872
C2×#117193532
C22×#881232
C2×#117191842
C2×C13×#5292
C2×#354413