Finite Group Databasebeta

← C2×#13128814 #16771033

Subgroups — C2×#13128814 #16771033

Order 3328.

7142 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#13128814C2132yesmaximal, direct product factor
2C2×#11719272C211yesmaximal, characteristic, complemented
3C2×#11719284C211yesmaximal, characteristic, complemented
4C2×#11719248C211yesmaximal, characteristic, complemented
5C2×#11719270C212yesmaximal, complemented
6C2×#11719246C212yesmaximal, complemented
7C2×#11719234C212yesmaximal, complemented
8C2×#11719236C214yesmaximal, complemented
9C2×#11719260C211yesmaximal, characteristic, complemented
10C2×#11719529C212yesmaximal, complemented
11C2×#11719288C212yesmaximal, complemented
12C2×#11719269C214yesmaximal, complemented
13C2×#11719175C211yesmaximal, characteristic, complemented
14C2×#11719184C212yesmaximal, complemented
15C2×#11719184C211yesmaximal, characteristic, complemented
16C22×#88124C212yesmaximal, complemented
17C2×#11719251C212yesmaximal, complemented
18C2×C4×C13×#41C211yesmaximal, characteristic, complemented
19C22×C13×#41C2211yescharacteristic
20C22×#6129C2212yes—
21C4×C13×#41C22116yescomplemented
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2212yes—
27C2×C4×D4×C13C2212yes—
28C2×C13×#117C2212yes—
29C2×C13×#117C2211yescharacteristic
30C22×C42×C13C2212yes—
31C22×C42×C13C2211yescharacteristic
32#11719529C22132yescomplemented
33C2×#88200C2212yes—
34C2×#88198C2212yes—
35C2×#88193C2214yes—
36C2×#88189C2214yes—
37C2×D4×Dic13C2212yes—
38C2×#88184C2212yes—
39C2×#88184C2211yescharacteristic
40C2×#88183C2214yes—
41C2×#88183C2212yes—
42C2×C4×C22⋊D13C2214yes—
43C2×C4×C22⋊D13C2212yes—
44C2×#88180C2212yes—
45C22×C4⋊Dic13C2212yes—
46C22×C4⋊Dic13C2212yes—
47C2×#88178C2212yes—
48C2×#88178C2211yescharacteristic
49C2×#88178C2212yes—
50C2×#88178C2212yes—
51C22×#6101C2214yes—
52C22×#6101C2214yes—
53#11719288C22132yescomplemented
54#11719284C22116yescomplemented
55#11719272C22116yescomplemented
56#11719270C22132yescomplemented
57#11719269C22164yescomplemented
58#11719260C22116yescomplemented
59#11719251C22132yescomplemented
60#11719248C22116yescomplemented
61#11719246C22132yescomplemented
62#11719236C22164yescomplemented
63#11719234C22132yescomplemented
64C2×#88152C2214yes—
65C2×#88151C2212yes—
66C2×#88150C2214yes—
67C2×C4⋊C4×D13C2212yes—
68C2×#88144C2212yes—
69C2×#88143C2214yes—
70C2×#88143C2214yes—
71C2×#88141C2212yes—
72C2×#88140C2214yes—
73C2×#88137C2214yes—
74C2×#88135C2214yes—
75C2×#88133C2214yes—
76C2×#88132C2214yes—
77C2×#88131C2214yes—
78#11719184C22132yescomplemented
79#11719184C22116yescomplemented
80C2×#88130C2214yes—
81C2×#88130C2212yes—
82C2×#88129C2211yescharacteristic
83C2×C4×D52C2211yescharacteristic
84C2×C4×D52C2212yes—
85C2×#88126C2212yes—
86C2×#88126C2214yes—
87#11719175C22116yescomplemented
88C2×#88124C2214yes—
89C2×#88124C2214yes—
90C2×#88124C2211yescharacteristic
91C2×#88124C2212yes—
92C2×#88124C2212yes—
93C2×#88124C2212yes—
94C2×#88124C22132yescomplemented
95C2×#88123C2211yescharacteristic
96C2×#88123C2211yescharacteristic
97C2×C4×Dic26C2212yes—
98C2×C4×Dic26C2212yes—
99C2×C4×Dic26C2212yes—
100C2×C4×Dic26C2211yescharacteristic
101C2×C13×#41—28no—
102C2×C13×#41C2318yes—
103C22×Q8×C13C2311yescharacteristic
104C22×D4×C13C2312yes—
105C22×D4×C13C2311yescharacteristic
106C23×C4×C13C2312yes—
107C23×C4×C13C2311yescharacteristic
108C23×C4×C13C2312yes—
109C23×C4×C13C2311yescharacteristic
110C23×C4×C13C2312yes—
111C23×C4×C13C2311yescharacteristic
112C22×C22⋊D13C2314yes—
113C22×C22⋊D13C2312yes—
114C23×Dic13C2314yes—
115C23×Dic13C2314yes—
116C2×#6129—216no—
117C2×#6129C23116yes—
118C22×D52C2311yescharacteristic
119C22×C4×D13C2312yes—
120C22×C4×D13C2314yes—
121C22×Dic26C2311yescharacteristic
122C22×Dic26C2312yes—
123C22×Dic26C2312yes—
124C4×Q8×C13C2318yes—
125C4×Q8×C13C2318yes—
126C4×D4×C13C23116yes—
127C4×D4×C13C2318yes—
128C4×D4×C13C2318yes—
129C4×D4×C13C23116yes—
130C13×#117C2318yes—
131C13×#117C23116yes—
132C2×C13×C4⋊C4C2311yescharacteristic
133C2×C13×C4⋊C4C2312yes—
134C2×C13×C4⋊C4C2312yes—
135C2×C13×C4⋊C4C2311yescharacteristic
136C2×C13×C22⋊C4C2312yes—
137C2×C13×C22⋊C4C2312yes—
138C2×C13×C22⋊C4C2312yes—
139C2×C42×C13C2311yescharacteristic
140C2×C42×C13C2311yescharacteristic
141C2×C42×C13C2311yescharacteristic
142C2×C42×C13C2312yes—
143C2×C42×C13C2311yescharacteristic
144C2×C42×C13C2312yes—
145C2×C42×C13C2312yes—
146C2×C42×C13C23116yes—
147C2×C42×C13C2318yes—
148C2×C22⋊Dic13C2314yes—
149C2×C22⋊Dic13C2312yes—
150C2×C22⋊Dic13C2314yes—
151#88200C23116yes—
152#88198C23116yes—
153#88193C23132yes—
154#88189C23132yes—
155D4×Dic13C23116yes—
156#88184C23116yes—
157#88184C2318yes—
158#88183C23132yes—
159#88183C23116yes—
160C4×C22⋊D13C23116yes—
161C4×C22⋊D13C23132yes—
162C2×#6103C2312yes—
163C2×#6103C2312yes—
164C2×#6103C2312yes—
165C2×#6103C2314yes—
166C2×#6103C2312yes—
167C2×#6103C2314yes—
168#88180C23116yes—
169C2×C4⋊Dic13C2312yes—
170C2×C4⋊Dic13C2312yes—
171C2×C4⋊Dic13C2312yes—
172C2×C4⋊Dic13C2311yescharacteristic
173C2×C4⋊Dic13C2312yes—
174C2×C4⋊Dic13C2311yescharacteristic
175C2×C4⋊Dic13C2314yes—
176C2×C4⋊Dic13C2314yes—
177C2×C4⋊Dic13C23116yes—
178C2×C4⋊Dic13C23116yes—
179#88178C23116yes—
180#88178C23116yes—
181#88178C2318yes—
182#88178C23116yes—
183C2×#6101C2314yes—
184C2×#6101C2314yes—
185C2×#6101C2312yes—
186C2×#6101C2314yes—
187C2×#6101C2312yes—
188C2×#6101C2312yes—
189C2×#6101C2314yes—
190C2×#6101C2314yes—
191C2×#6101C2314yes—
192C2×#6101C2314yes—
193C2×#6101C23132yes—
194C2×#6101C23132yes—
195C2×#6101C2312yes—
196C2×#6101C2314yes—
197C2×C4×Dic13C2314yes—
198C2×C4×Dic13C2314yes—
199C2×C4×Dic13C2312yes—
200#88152C23132yes—
201#88151C23116yes—
202#88150C23132yes—
203C4⋊C4×D13C23116yes—
204#88144C23116yes—
205#88143C23132yes—
206#88143C23132yes—
207#88141C23116yes—
208#88140C23132yes—
209#88137C23132yes—
210#88135C23132yes—
211#88133C23132yes—
212#88132C23132yes—
213#88131C23132yes—
214#88130C23116yes—
215#88130C23132yes—
216#88129C2318yes—
217C4×D52C2318yes—
218C4×D52C23116yes—
219#88126C23132yes—
220#88126C23116yes—
221#88124C2318yes—
222#88124C23116yes—
223#88124C23132yes—
224#88124C23116yes—
225#88124C23132yes—
226#88124C23116yes—
227#88123C2318yes—
228#88123C2318yes—
229C4×Dic26C23116yes—
230C4×Dic26C23116yes—
231C4×Dic26C23116yes—
232C4×Dic26C2318yes—
233C2×#3515—131nomaximal, Sylow
234C24×C13C2411yescharacteristic
235C24×C13C2412yes—
236C23×D13C2412yes—
237C13×#41—232no—
238C2×Q8×C13—24no—
239C2×Q8×C13C2414yes—
240C2×D4×C13—28no—
241C2×D4×C13#4118yes—
242C2×D4×C13C2418yes—
243C2×D4×C13C2414yes—
244C22×C4×C13—28no—
245C22×C4×C13—24no—
246C22×C4×C13—28no—
247C22×C4×C13—24no—
248C22×C4×C13—42no—
249C22×C4×C13—44no—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2412yes—
252C22×C4×C13C2411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×C4×C13C2412yes—
255C22×C4×C13C2418yes—
256C22×C4×C13C2412yes—
257C22×C4×C13C2411yescharacteristic
258C22×C4×C13C2414yes—
259C22×C4×C13C2418yes—
260C22×C4×C13C2414yes—
261C22×C4×C13C2418yes—
262C22×C4×C13C2414yes—
263C22×C4×C13C2411yescharacteristic
264C22×C4×C13C2411yescharacteristic
265C2×C22⋊D13—216no—
266C2×C22⋊D13—44no—
267C2×C22⋊D13C24116yes—
268C2×C22⋊D13C2418yes—
269C22×Dic13—216no—
270C22×Dic13—48no—
271C22×Dic13C24116yes—
272C22×Dic13C2412yes—
273C22×Dic13C2414yes—
274C22×Dic13C2412yes—
275C22×Dic13C2414yes—
276C22×Dic13C2412yes—
277C22×Dic13C24116yes—
278#6129—264no—
279C2×D52—24no—
280C2×D52C2414yes—
281C2×C4×D13—28no—
282C2×C4×D13—48no—
283C2×C4×D13C2418yes—
284C2×C4×D13C24116yes—
285C2×Dic26—28no—
286C2×Dic26—24no—
287C2×Dic26—44no—
288C2×Dic26C2414yes—
289C2×Dic26C2418yes—
290C2×Dic26C2418yes—
291C13×C4⋊C4C2414yes—
292C13×C4⋊C4C2418yes—
293C13×C4⋊C4C2418yes—
294C13×C4⋊C4C2414yes—
295C13×C22⋊C4C2418yes—
296C13×C22⋊C4C2418yes—
297C13×C22⋊C4C2418yes—
298C42×C13C2414yes—
299C42×C13C2414yes—
300C42×C13C2414yes—
301C42×C13C2418yes—
302C42×C13C2414yes—
303C42×C13C2418yes—
304C42×C13C2418yes—
305C22⋊Dic13C24116yes—
306C22⋊Dic13C2418yes—
307C22⋊Dic13C24116yes—
308#6103C2418yes—
309#6103C2418yes—
310#6103C2418yes—
311#6103C24116yes—
312#6103C2418yes—
313#6103C24116yes—
314C4⋊Dic13C2418yes—
315C4⋊Dic13C2418yes—
316C4⋊Dic13C2418yes—
317C4⋊Dic13C2414yes—
318C4⋊Dic13C2418yes—
319C4⋊Dic13C2414yes—
320C4⋊Dic13C24116yes—
321C4⋊Dic13C24116yes—
322#6101C24116yes—
323#6101C24116yes—
324#6101C2418yes—
325#6101C24116yes—
326#6101C2418yes—
327#6101C2418yes—
328#6101C24116yes—
329#6101C24116yes—
330#6101C24116yes—
331#6101C24116yes—
332#6101C2418yes—
333#6101C24116yes—
334C4×Dic13C24116yes—
335C4×Dic13C24116yes—
336C4×Dic13C2418yes—
337#3515—1332no—
338C2×#557—131no—
339C2×#554—131no—
340C2×#554—131no—
341C2×#553—132no—
342C2×#552—132no—
343C2×#552—134no—
344C2×#552—132no—
345C2×#547—132no—
346C2×#547—131no—
347C2×#541—132no—
348C2×#539—134no—
349C2×#533—131no—
350C2×#529—131no—
351C2×#529—132no—
352C22×#125—132no—
353C2×#520—132no—
354C2×C4×#41D1311yescharacteristic, complemented
355C23×C13—24no—
356C23×C13—24no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13C2×#4118yes—
361C23×C13C2512yes—
362C23×C13C2514yes—
363C23×C13C2511yescharacteristic
364C22×D13—24no—
365C22×D13—24no—
366C22×D13—24no—
367C22×D13C2514yes—
368Q8×C13—28no—
369D4×C13—216no—
370D4×C13C2×#41116yes—
371C2×C4×C13—22no—
372C2×C4×C13—24no—
373C2×C4×C13—216no—
374C2×C4×C13—22no—
375C2×C4×C13—24no—
376C2×C4×C13—22no—
377C2×C4×C13—24no—
378C2×C4×C13—22no—
379C2×C4×C13—28no—
380C2×C4×C13—216no—
381C2×C4×C13—28no—
382C2×C4×C13—44no—
383C2×C4×C13—48no—
384C2×C4×C13C2×#4114yes—
385C2×C4×C132−1+414yes—
386C2×C4×C13C2512yes—
387C2×C4×C13C2514yes—
388C2×C4×C13C2512yes—
389C2×C4×C13C2512yes—
390C2×C4×C13C2514yes—
391C2×C4×C13C2514yes—
392C2×C4×C13C2512yes—
393C2×C4×C13C2512yes—
394C2×C4×C13C2512yes—
395C22⋊D13—232no—
396C22⋊D13—48no—
397C2×Dic13—28no—
398C2×Dic13—24no—
399C2×Dic13—232no—
400C2×Dic13—24no—
401C2×Dic13—28no—
402C2×Dic13—24no—
403C2×Dic13—416no—
404C2×Dic13C2514yes—
405C2×Dic13C2518yes—
406C2×Dic13C2514yes—
407C2×Dic13C2518yes—
408C2×Dic13C2514yes—
409D52—28no—
410C4×D13—216no—
411C4×D13—416no—
412Dic26—216no—
413Dic26—28no—
414Dic26—48no—
415C22×#41—132no—
416C22×#41C2×D1311yescharacteristic
417#557—1316no—
418#554—1316no—
419#554—1316no—
420#553—1332no—
421#552—1332no—
422#552—1332no—
423#552—1364no—
424#547—1332no—
425#547—1316no—
426#541—1332no—
427#539—1364no—
428#533—1316no—
429C2×C4⋊Q8—132no—
430C2×C4⋊Q8—131no—
431C2×C4⋊Q8—131no—
432#529—1332no—
433#529—1316no—
434C2×#126—134no—
435C2×#126—134no—
436C2×#126—134no—
437C2×#126—132no—
438C2×#125—134no—
439C2×#125—134no—
440C2×#125—132no—
441C2×#125—131no—
442C2×#125—132no—
443C2×#125—134no—
444C2×#125—134no—
445C2×#125—132no—
446C2×#125—132no—
447C2×#125—1332no—
448C2×#124—131no—
449C2×#123—134no—
450C2×#123—132no—
451C2×#123—134no—
452C2×#123—134no—
453C2×#123—134no—
454C2×C22⋊Q8—132no—
455C2×C22⋊Q8—131no—
456C2×C22⋊Q8—132no—
457C2×C22⋊Q8—132no—
458C2×C22⋊Q8—132no—
459C2×C22⋊Q8—134no—
460C2×C22⋊Q8—132no—
461C2×C22⋊Q8—134no—
462C2×#121—134no—
463C2×#121—132no—
464C2×#121—131no—
465#520—1332no—
466C4×#41C2×D13116yescomplemented
467C2×C4×Q8—132no—
468C2×C4×Q8—132no—
469C2×C4×Q8—132no—
470C2×C4×Q8—131no—
471C2×C4×Q8—132no—
472C2×C4×Q8C2×D1311yescharacteristic
473C2×C4×Q8C2×D1311yescharacteristic
474C2×C4×D4—132no—
475C2×C4×D4—134no—
476C2×C4×D4—132no—
477C2×C4×D4—134no—
478C2×C4×D4—131no—
479C2×C4×D4—132no—
480C2×C4×D4C2×D1311yescharacteristic
481C2×C4×D4C2×D1312yes—
482C2×C4×D4C2×D1311yescharacteristic
483C2×C4×D4C2×D1312yes—
484C2×#117—132no—
485C2×#117—134no—
486C2×#117—132no—
487C2×#117—134no—
488C2×#117C2×D1311yescharacteristic
489C2×#117C2×D1312yes—
490C22×C4⋊C4—134no—
491C22×C4⋊C4—134no—
492C22×C4⋊C4—132no—
493C22×C4⋊C4—132no—
494C22×C4⋊C4—132no—
495C22×C42C2×D1312yes—
496C22×C42C2×D1311yescharacteristic
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—216no—
500C22×C13—22no—
501C22×C13—22no—
502C22×C13—22no—
503C22×C13—44no—
504C22×C13C22×#4118yes—
505C22×C13C22×#4112yes—
506C22×C13C2×2−1+412yes—
507C22×C13#58512yes—
508C22×C13C2611yescharacteristic
509C2×D13—24no—
510C2×D13—24no—
511C2×D13—24no—
512C2×D13—48no—
513C4×C13—22no—
514C4×C13—24no—
515C4×C13—22no—
516C4×C13—24no—
517C4×C13—22no—
518C4×C13—24no—
519C4×C13—22no—
520C4×C13C22×#4114yes—
521C4×C13C2×2−1+414yes—
522Dic13—28no—
523Dic13—24no—
524Dic13—24no—
525Dic13—28no—
526Dic13—24no—
527C2×#41—28no—
528C2×#41—1316no—
529C2×#41—2616no—
530C2×#41C22×D1318yes—
531C22×Q8—131no—
532C22×Q8—132no—
533C22×Q8—132no—
534C22×Q8C22×D1311yescharacteristic
535C22×D4—134no—
536C22×D4—132no—
537C22×D4—131no—
538C22×D4C22×D1312yes—
539C22×D4C22×D1311yescharacteristic
540C23×C4—134no—
541C23×C4—134no—
542C23×C4—132no—
543C23×C4—134no—
544C23×C4C22×D1312yes—
545C23×C4C22×D1312yes—
546C23×C4C22×D1311yescharacteristic
547C23×C4C22×D1311yescharacteristic
548C23×C4C22×D1312yes—
549C23×C4C22×D1311yescharacteristic
550C4⋊Q8—1316no—
551C4⋊Q8—138no—
552C4⋊Q8—138no—
553#126—1332no—
554#126—1332no—
555#126—1332no—
556#126—1316no—
557#125—1332no—
558#125—1332no—
559#125—1316no—
560#125—138no—
561#125—1316no—
562#125—1332no—
563#125—1332no—
564#125—1316no—
565#125—1316no—
566#124—138no—
567#123—1332no—
568#123—1316no—
569#123—1332no—
570#123—1332no—
571#123—1332no—
572C22⋊Q8—1316no—
573C22⋊Q8—138no—
574C22⋊Q8—1316no—
575C22⋊Q8—1316no—
576C22⋊Q8—1316no—
577C22⋊Q8—1332no—
578C22⋊Q8—1316no—
579C22⋊Q8—1332no—
580#121—1332no—
581#121—1316no—
582#121—138no—
583C4×Q8—1316no—
584C4×Q8—1316no—
585C4×Q8—1316no—
586C4×Q8—138no—
587C4×Q8—1316no—
588C4×Q8C22×D1318yes—
589C4×Q8C22×D1318yes—
590C4×D4—1316no—
591C4×D4—1332no—
592C4×D4—1316no—
593C4×D4—1332no—
594C4×D4—138no—
595C4×D4—1316no—
596C4×D4C22×D1318yes—
597C4×D4C22×D13116yes—
598C4×D4C22×D1318yes—
599C4×D4C22×D13116yes—
600#117—1316no—
601#117—1332no—
602#117—1316no—
603#117—1332no—
604#117C22×D1318yes—
605#117C22×D13116yes—
606C2×C4⋊C4—134no—
607C2×C4⋊C4—132no—
608C2×C4⋊C4—131no—
609C2×C4⋊C4—132no—
610C2×C4⋊C4—131no—
611C2×C4⋊C4—132no—
612C2×C4⋊C4—132no—
613C2×C4⋊C4—134no—
614C2×C4⋊C4—132no—
615C2×C4⋊C4—134no—
616C2×C4⋊C4—134no—
617C2×C4⋊C4—1332no—
618C2×C4⋊C4—134no—
619C2×C4⋊C4—134no—
620C2×C4⋊C4—134no—
621C2×C4⋊C4—134no—
622C2×C4⋊C4—1332no—
623C2×C4⋊C4—1316no—
624C2×C4⋊C4—1316no—
625C2×C4⋊C4—132no—
626C2×C4⋊C4—134no—
627C2×C4⋊C4—132no—
628C2×C4⋊C4—132no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—1316no—
631C2×C4⋊C4C22×D1311yescharacteristic
632C2×C4⋊C4C22×D1312yes—
633C2×C4⋊C4C22×D1311yescharacteristic
634C2×C4⋊C4C22×D1312yes—
635C2×C22⋊C4—134no—
636C2×C22⋊C4—134no—
637C2×C22⋊C4—132no—
638C2×C22⋊C4—132no—
639C2×C22⋊C4—132no—
640C2×C22⋊C4—132no—
641C2×C22⋊C4—134no—
642C2×C22⋊C4—134no—
643C2×C22⋊C4—132no—
644C2×C22⋊C4C22×D1312yes—
645C2×C22⋊C4C22×D1312yes—
646C2×C22⋊C4C22×D1312yes—
647C2×C42—134no—
648C2×C42—134no—
649C2×C42—132no—
650C2×C42C22×D1312yes—
651C2×C42C22×D1311yescharacteristic
652C2×C42C22×D1311yescharacteristic
653C2×C42C22×D1312yes—
654C2×C42C22×D1311yescharacteristic
655C2×C42C22×D1312yes—
656C2×C42C22×D13116yes—
657C2×C42C22×D1318yes—
658C2×C42C22×D1311yescharacteristic
659C2×C13—28no—
660C2×C13—42no—
661C2×C13#351514yescomplemented
662C2×C13C23×#4111yescharacteristic
663C2×C13C22×2−1+411yescharacteristic
664C2×C13C2×#58511yescharacteristic
665D13—44no—
666C24—132no—
667C24C23×D1311yescharacteristic
668C24C23×D1312yes—
669#41—232no—
670#41—2664no—
671C2×Q8—24no—
672C2×Q8—134no—
673C2×Q8—138no—
674C2×Q8—138no—
675C2×Q8—268no—
676C2×Q8—264no—
677C2×Q8—524no—
678C2×Q8C23×D1314yes—
679C2×D4—28no—
680C2×D4—1316no—
681C2×D4—138no—
682C2×D4—134no—
683C2×D4—2616no—
684C2×D4—264no—
685C2×D4—524no—
686C2×D4#612718yes—
687C2×D4C23×D1318yes—
688C2×D4C23×D1314yes—
689C22×C4—28no—
690C22×C4—24no—
691C22×C4—28no—
692C22×C4—24no—
693C22×C4—44no—
694C22×C4—42no—
695C22×C4—1316no—
696C22×C4—132no—
697C22×C4—134no—
698C22×C4—134no—
699C22×C4—132no—
700C22×C4—132no—
701C22×C4—1316no—
702C22×C4—138no—
703C22×C4—1316no—
704C22×C4—2616no—
705C22×C4—268no—
706C22×C4—528no—
707C22×C4—528no—
708C22×C4C23×D1318yes—
709C22×C4C23×D1318yes—
710C22×C4C23×D1314yes—
711C22×C4C23×D1314yes—
712C22×C4C23×D1311yescharacteristic
713C22×C4C23×D1312yes—
714C22×C4C23×D1311yescharacteristic
715C22×C4C23×D1311yescharacteristic
716C22×C4C23×D1312yes—
717C22×C4C23×D1311yescharacteristic
718C22×C4C23×D1312yes—
719C22×C4C23×D1318yes—
720C22×C4C23×D1314yes—
721C22×C4C23×D1311yescharacteristic
722C22×C4C23×D1311yescharacteristic
723C4⋊C4—1316no—
724C4⋊C4—138no—
725C4⋊C4—134no—
726C4⋊C4—138no—
727C4⋊C4—134no—
728C4⋊C4—138no—
729C4⋊C4—138no—
730C4⋊C4—1316no—
731C4⋊C4—138no—
732C4⋊C4—1316no—
733C4⋊C4—1316no—
734C4⋊C4—1316no—
735C4⋊C4—1316no—
736C4⋊C4—1316no—
737C4⋊C4—1316no—
738C4⋊C4—138no—
739C4⋊C4—1316no—
740C4⋊C4—138no—
741C4⋊C4—138no—
742C4⋊C4—1316no—
743C4⋊C4C23×D1314yes—
744C4⋊C4C23×D1318yes—
745C4⋊C4C23×D1314yes—
746C4⋊C4C23×D1318yes—
747C22⋊C4—1316no—
748C22⋊C4—1316no—
749C22⋊C4—138no—
750C22⋊C4—138no—
751C22⋊C4—138no—
752C22⋊C4—138no—
753C22⋊C4—1316no—
754C22⋊C4—1316no—
755C22⋊C4—138no—
756C22⋊C4C23×D1318yes—
757C22⋊C4C23×D1318yes—
758C22⋊C4C23×D1318yes—
759C42—1316no—
760C42—1316no—
761C42—138no—
762C42C23×D1314yes—
763C42C23×D1318yes—
764C42C23×D1314yes—
765C42C23×D1314yes—
766C42C23×D1318yes—
767C42C23×D1314yes—
768C42C23×D1318yes—
769C13C2×#351511yescharacteristic, complemented, Sylow
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—134no—
776C23—264no—
777C23—264no—
778C23—264no—
779C23C2×#612718yes—
780C23C24×D1312yes—
781C23C24×D1314yes—
782C23C24×D1311yescharacteristic
783Q8—28no—
784Q8—2616no—
785Q8—268no—
786Q8—528no—
787D4—216no—
788D4—2632no—
789D4—268no—
790D4—528no—
791D4C2×#6127116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—134no—
806C2×C4—138no—
807C2×C4—138no—
808C2×C4—134no—
809C2×C4—134no—
810C2×C4—264no—
811C2×C4—268no—
812C2×C4—2632no—
813C2×C4—264no—
814C2×C4—264no—
815C2×C4—268no—
816C2×C4—2616no—
817C2×C4—5216no—
818C2×C4—5216no—
819C2×C4C2×#612714yes—
820C2×C4#8825714yes—
821C2×C4C24×D1312yes—
822C2×C4C24×D1314yes—
823C2×C4C24×D1312yes—
824C2×C4C24×D1312yes—
825C2×C4C24×D1314yes—
826C2×C4C24×D1312yes—
827C2×C4C24×D1314yes—
828C2×C4C24×D1312yes—
829C2×C4C24×D1312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—264no—
838C22—264no—
839C22—264no—
840C22—528no—
841C22C22×#612718yes—
842C22C22×#612712yes—
843C22C2×#8825712yes—
844C22#1171964812yes—
845C22C25×D1311yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—264no—
854C4—268no—
855C4—264no—
856C4—264no—
857C4—268no—
858C4C22×#612714yes—
859C4C2×#8825714yes—
860C2—28no—
861C2—42no—
862C2—524no—
863C2#1312881414yesdirect product factor
864C2C23×#612711yescharacteristic
865C2C22×#8825711yescharacteristic
866C2C2×#1171964811yescharacteristic
subgroupG/H
centerC23C24×D13
commutator, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC2×C4×C13×#41C2
socleC23×C13C25
hypercenterC2×C4×#41D13
hypocenterC13C2×#3515
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13128814C2direct (N × H)
2. C2×#11719272C2semidirect
3. C2×#11719284C2semidirect
4. C2×#11719248C2semidirect
5. C2×#11719270C2semidirect
6. C2×#11719246C2semidirect
7. C2×#11719234C2semidirect
8. C2×#11719236C2semidirect
9. C2×#11719260C2semidirect
10. C2×#11719529C2semidirect
11. C2×#11719288C2semidirect
12. C2×#11719269C2semidirect
13. C2×#11719175C2semidirect
14. C2×#11719184C2semidirect
15. C2×#11719184C2semidirect
16. C22×#88124C2semidirect
17. C2×#11719251C2semidirect
18. C2×C4×C13×#41C2semidirect
21. C4×C13×#41C22semidirect
32. #11719529C22semidirect
53. #11719288C22semidirect
54. #11719284C22semidirect
55. #11719272C22semidirect
56. #11719270C22semidirect
57. #11719269C22semidirect
58. #11719260C22semidirect
59. #11719251C22semidirect
60. #11719248C22semidirect
61. #11719246C22semidirect
62. #11719236C22semidirect
63. #11719234C22semidirect
78. #11719184C22semidirect
79. #11719184C22semidirect
87. #11719175C22semidirect
94. C2×#88124C22semidirect
354. C2×C4×#41D13semidirect
466. C4×#41C2×D13semidirect
661. C2×C13#3515semidirect
769. C13C2×#3515semidirect
863. C2#13128814direct (N × H)

Maximal subgroups

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

subgroupindex
#131288142
C2×#117192722
C2×#117192842
C2×#117192482
C2×#117192702
C2×#117192462
C2×#117192342
C2×#117192362
C2×#117192602
C2×#117195292
C2×#117192882
C2×#117192692
C2×#117191752
C2×#117191842
C22×#881242
C2×#117192512
C2×C4×C13×#412
C2×#351513