Finite Group Databasebeta

← #16731367

Subgroups — #16731367

Order 3328.

2148 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2#13124998C214yesmaximal, complemented
3#13124966C212yesmaximal, complemented
4#13124935C212yesmaximal, complemented
5#13124907C214yesmaximal, complemented
6#13124875C212yesmaximal, complemented
7#13124844C212yesmaximal, complemented
8#13124784C212yesmaximal, complemented
9#13124651C212yesmaximal, complemented
10#13124323C212yesmaximal, complemented
11#13124096C212yesmaximal
12C4×#88205C214yesmaximal, complemented
13#13123469C211yesmaximal, characteristic, complemented
14C2×C4×C13×#41C211yesmaximal, characteristic
15C22×C13×#41C2211yescharacteristic
16C4×C13×#41—21no—
17C4×C13×#41—21no—
18C4×C13×#41—21no—
19C4×C13×#41—21no—
20C4×C13×#41C2212yes—
21C4×C13×#41C2212yes—
22C4×C13×#41C2212yes—
23C4×C13×#41C2212yes—
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13—21no—
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×C4×D4×C13C2211yescharacteristic
30C2×C13×#117—21no—
31C2×C13×#117C2211yescharacteristic
32C22×C42×C13—21no—
33C22×C42×C13C2211yescharacteristic
34C2×#88205C2214yes—
35C2×#88180—21no—
36C2×#88178—21no—
37C2×#88178C2212yes—
38#11719175—21no—
39#11719175—21no—
40#11719175—21no—
41#11719175—21no—
42#11719175C2212yes—
43#11719175C2212yes—
44#11719175C2212yescomplemented
45#11719175C2212yescomplemented
46C2×#88124—21no—
47C2×#88123C2211yescharacteristic, complemented
48C2×#88123C2211yescharacteristic, complemented
49C2×C4×Dic26—21no—
50C2×C4×Dic26C2212yescomplemented
51#11718900C2218yes—
52#11718893C2214yes—
53#11718889C2214yes—
54#11718879C2214yes—
55#11718868C2212yes—
56#11718692C2214yescomplemented
57#11718692C2214yescomplemented
58#11718691C2218yescomplemented
59C4×#6107C2218yescomplemented
60#11718682C2214yescomplemented
61#11718681C2214yescomplemented
62#11718680C2214yescomplemented
63#11718680C2214yescomplemented
64#11718679C2218yescomplemented
65C4×#6105C2218yescomplemented
66#11718669C2214yescomplemented
67#11718668C2214yescomplemented
68#11718665C2214yescomplemented
69#11718657C2218yescomplemented
70#11718656C2214yescomplemented
71#11718632C2214yes—
72#11718631C2214yes—
73#11718587C2212yes—
74#11718587C2212yescomplemented
75#11718586C2212yes—
76#11718586C2212yescomplemented
77#11718585C2212yescomplemented
78C4×#6099C2212yescomplemented
79C2×C13×#41—28no—
80C2×C13×#41—21no—
81C2×C13×#41—21no—
82C2×C13×#41C2312yes—
83C2×C13×#41C2312yes—
84C22×Q8×C13C2311yescharacteristic
85C22×D4×C13—21no—
86C22×D4×C13C2311yescharacteristic
87C23×C4×C13—21no—
88C23×C4×C13—21no—
89C23×C4×C13—21no—
90C23×C4×C13D411yescharacteristic
91C23×C4×C13D411yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C22×Dic26—21no—
94C22×Dic26C2312yes—
95C4×Q8×C13—21no—
96C4×Q8×C13—21no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13C2312yes—
100C4×Q8×C13C2312yes—
101C4×Q8×C13C2312yes—
102C4×Q8×C13C2312yes—
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—22no—
106C4×D4×C13—22no—
107C4×D4×C13—22no—
108C4×D4×C13—22no—
109C4×D4×C13—22no—
110C4×D4×C13—22no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13—21no—
115C4×D4×C13C2312yes—
116C4×D4×C13C2312yes—
117C4×D4×C13C2312yes—
118C4×D4×C13C2312yes—
119C13×#117—21no—
120C13×#117—21no—
121C13×#117—22no—
122C13×#117—22no—
123C13×#117—22no—
124C13×#117—22no—
125C13×#117C2312yes—
126C13×#117C2312yes—
127C2×C13×C4⋊C4—21no—
128C2×C13×C4⋊C4—21no—
129C2×C13×C4⋊C4C2311yescharacteristic
130C2×C13×C4⋊C4C2311yescharacteristic
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4—21no—
133C2×C13×C22⋊C4—21no—
134C2×C42×C13—21no—
135C2×C42×C13—21no—
136C2×C42×C13—21no—
137C2×C42×C13—22no—
138C2×C42×C13—22no—
139C2×C42×C13—22no—
140C2×C42×C13—22no—
141C2×C42×C13D411yescharacteristic
142C2×C42×C13D411yescharacteristic
143C2×C42×C13D411yescharacteristic
144C2×C42×C13D411yescharacteristic
145C2×C42×C13D411yescharacteristic
146C2×C42×C13D411yescharacteristic
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2311yescharacteristic
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2311yescharacteristic
152C2×C42×C13C2311yescharacteristic
153C2×C22⋊Dic13—22no—
154#88205—216no—
155C2×#6107C2318yes—
156C2×#6105C2318yes—
157#88180—22no—
158#88180—22no—
159#88180—22no—
160#88180—22no—
161C2×C4⋊Dic13—21no—
162C2×C4⋊Dic13—21no—
163C2×C4⋊Dic13—21no—
164C2×C4⋊Dic13C2312yes—
165#88178—22no—
166#88178—22no—
167#88178—22no—
168#88178—22no—
169#88178—22no—
170#88178—22no—
171#88178C2314yes—
172#88178C2314yes—
173C2×#6101—22no—
174C2×#6101—22no—
175C2×C4×Dic13—22no—
176C2×#6099C2314yes—
177#88124—22no—
178#88124—22no—
179#88124—22no—
180#88124—22no—
181#88123—21no—
182#88123—21no—
183#88123—21no—
184#88123—21no—
185#88123C2312yes—
186#88123C2312yes—
187#88123C2312yes—
188#88123C2312yes—
189C4×Dic26—22no—
190C4×Dic26—22no—
191C4×Dic26—22no—
192C4×Dic26—22no—
193C4×Dic26—22no—
194C4×Dic26—22no—
195C4×Dic26C2314yes—
196C4×Dic26C2314yes—
197#88075C2318yes—
198#88072C2318yes—
199C22⋊#1055C2314yes—
200C22⋊#1055C2314yes—
201#88050C2318yes—
202#88050C2318yes—
203#88048C2318yes—
204#88047C2318yes—
205C4⋊#1055C2314yes—
206C4⋊#1055C2314yes—
207#88043C2314yes—
208C4×#1055C2314yes—
209#60562—131nomaximal, Sylow
210C24×C13—21no—
211C24×C13C2×D411yescharacteristic
212C13×#41—28no—
213C13×#41—28no—
214C13×#41—24no—
215C13×#41—24no—
216C13×#41—24no—
217C13×#41#4118yes—
218C2×Q8×C13—24no—
219C2×Q8×C13—21no—
220C2×Q8×C13C2412yes—
221C2×D4×C13—28no—
222C2×D4×C13—22no—
223C2×D4×C13—22no—
224C2×D4×C13—24no—
225C2×D4×C13—21no—
226C2×D4×C13C2412yes—
227C22×C4×C13—28no—
228C22×C4×C13—21no—
229C22×C4×C13—24no—
230C22×C4×C13—22no—
231C22×C4×C13—22no—
232C22×C4×C13—24no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—22no—
236C22×C4×C13—22no—
237C22×C4×C13—22no—
238C22×C4×C13—22no—
239C22×C4×C13—42no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13C2×D411yescharacteristic
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D411yescharacteristic
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D411yescharacteristic
251C22×C4×C13C2×D411yescharacteristic
252C22×C4×C13C2×D411yescharacteristic
253C22×C4×C13C2×D411yescharacteristic
254C22×C4×C13C2×D411yescharacteristic
255C22×C4×C13C2×D411yescharacteristic
256C22×C4×C13C2×D411yescharacteristic
257C22×C4×C13C2411yescharacteristic
258C22×C4×C13C2411yescharacteristic
259C22×C4×C13C2411yescharacteristic
260C22×Dic13—22no—
261C22×Dic13—22no—
262C2×Dic26—28no—
263C2×Dic26—22no—
264C2×Dic26—22no—
265C2×Dic26—22no—
266C2×Dic26—44no—
267C2×Dic26C2414yes—
268C13×C4⋊C4—22no—
269C13×C4⋊C4—22no—
270C13×C4⋊C4—22no—
271C13×C4⋊C4—22no—
272C13×C4⋊C4—21no—
273C13×C4⋊C4—21no—
274C13×C4⋊C4C2412yes—
275C13×C4⋊C4C2412yes—
276C13×C22⋊C4—22no—
277C13×C22⋊C4—22no—
278C13×C22⋊C4—22no—
279C13×C22⋊C4—22no—
280C13×C22⋊C4—22no—
281C13×C22⋊C4—22no—
282C42×C13—22no—
283C42×C13—22no—
284C42×C13—22no—
285C42×C13—22no—
286C42×C13—22no—
287C42×C13—22no—
288C42×C13C2×D411yescharacteristic
289C42×C13C2×D411yescharacteristic
290C42×C13C2×D411yescharacteristic
291C42×C13C2×D411yescharacteristic
292C42×C13C2×D411yescharacteristic
293C42×C13C2×D411yescharacteristic
294C42×C13C2×D411yescharacteristic
295C42×C13C2×D411yescharacteristic
296C42×C13C2×D411yescharacteristic
297C42×C13C2×D411yescharacteristic
298C42×C13C2×D411yescharacteristic
299C42×C13C2×D411yescharacteristic
300C42×C13C2411yescharacteristic
301C42×C13C2411yescharacteristic
302C42×C13C2411yescharacteristic
303C42×C13C2411yescharacteristic
304C22⋊Dic13—24no—
305C22⋊Dic13—24no—
306#6107—216no—
307#6105—216no—
308C4⋊Dic13—22no—
309C4⋊Dic13—22no—
310C4⋊Dic13—22no—
311C4⋊Dic13—22no—
312C4⋊Dic13—22no—
313C4⋊Dic13—22no—
314C4⋊Dic13—22no—
315C4⋊Dic13C2414yes—
316#6101—24no—
317#6101—24no—
318#6101—24no—
319#6101—24no—
320C4×Dic13—24no—
321C4×Dic13—24no—
322#6099—28no—
323C2×#1055C2418yes—
324C2×#533—131no—
325C2×C4×#41D1311yescharacteristic
326#3116—134no—
327#3113—132no—
328#3110—132no—
329#3107—134no—
330#3104—132no—
331#3101—132no—
332#3095—132no—
333#3079—132no—
334#3039—132no—
335#3007—132no—
336C4×#137—134no—
337#2920—131no—
338C23×C13—24no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—41no—
343C23×C13—42no—
344C23×C13—42no—
345C23×C13C22×D411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348Q8×C13—24no—
349Q8×C13—22no—
350Q8×C13C2×#4114yes—
351D4×C13—28no—
352D4×C13—24no—
353D4×C13—28no—
354D4×C13—22no—
355D4×C13C2×#4114yes—
356C2×C4×C13—24no—
357C2×C4×C13—28no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—28no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—44no—
379C2×C4×C13—42no—
380C2×C4×C13—42no—
381C2×C4×C13—44no—
382C2×C4×C13—44no—
383C2×C4×C13—44no—
384C2×C4×C13#13714yescomplemented
385C2×C4×C13C22×D411yescharacteristic
386C2×C4×C13C22×D411yescharacteristic
387C2×C4×C13C22×D411yescharacteristic
388C2×C4×C13C22×D411yescharacteristic
389C2×C4×C13C22×D411yescharacteristic
390C2×C4×C13C22×D411yescharacteristic
391C2×C4×C13C22×D411yescharacteristic
392C2×C4×C13C22×D411yescharacteristic
393C2×C4×C13C22×D411yescharacteristic
394C2×C4×C13C22×D411yescharacteristic
395C2×C4×C13C22×D411yescharacteristic
396C2×C4×C13C2×#4114yes—
397C2×C4×C13C2511yescharacteristic
398C2×Dic13—24no—
399C2×Dic13—24no—
400C2×Dic13—44no—
401C2×Dic13—44no—
402Dic26—28no—
403Dic26—44no—
404Dic26—44no—
405Dic26—44no—
406#1055—28no—
407C22×#41C2×D1311yescharacteristic
408C2×#137—134no—
409#533—132no—
410#533—132no—
411#533—132no—
412#533—132no—
413#533—261no—
414#533—261no—
415#533—261no—
416#533—261no—
417C2×C4⋊Q8—131no—
418C2×C4⋊Q8—131no—
419C2×#125—261no—
420C2×C22⋊Q8—132no—
421C2×C22⋊Q8—261no—
422C4×#41—21no—
423C4×#41—21no—
424C4×#41—21no—
425C4×#41—21no—
426C4×#41C2×D1312yes—
427C4×#41C2×D1312yes—
428C4×#41C2×D1312yes—
429C4×#41C2×D1312yes—
430C2×C4×Q8—132no—
431C2×C4×Q8—261no—
432C2×C4×Q8C2×D1311yescharacteristic
433C2×C4×Q8C2×D1311yescharacteristic
434C2×C4×D4—21no—
435C2×C4×D4—21no—
436C2×C4×D4C2×D1311yescharacteristic
437C2×C4×D4C2×D1311yescharacteristic
438C2×#117—21no—
439C2×#117—261no—
440C2×#117C2×D1311yescharacteristic
441C22×C42—21no—
442C22×C42C2×D1311yescharacteristic
443#485—138no—
444#484—134no—
445#483—134no—
446#477—134no—
447#476—134no—
448#475—134no—
449#474—134no—
450#462—134no—
451#462—134no—
452#461—134no—
453#461—134no—
454#452—138no—
455#451—134no—
456#450—134no—
457#441—138no—
458#440—138no—
459C4×Q16—138no—
460C4×SD16—138no—
461#432—132no—
462#432—132no—
463#431—132no—
464#431—132no—
465#428—134no—
466#423—132no—
467#419—134no—
468#417—134no—
469#407—132no—
470C4×M16—132no—
471C22×C13—21no—
472C22×C13—21no—
473C22×C13—21no—
474C22×C13—21no—
475C22×C13—21no—
476C22×C13—24no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—44no—
480C22×C13—48no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13#52512yes—
484C22×C13C2×#13712yes—
485C22×C13C23×D411yescharacteristic
486C4×C13—21no—
487C4×C13—24no—
488C4×C13—21no—
489C4×C13—21no—
490C4×C13—21no—
491C4×C13—21no—
492C4×C13—21no—
493C4×C13—21no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13#52512yes—
497C4×C13C2×#13712yes—
498C4×C13C2×#13712yes—
499C4×C13#57512yes—
500C4×C13C22×#4112yes—
501Dic13—44no—
502Dic13—44no—
503C2×#41—28no—
504C2×#41—21no—
505C2×#41—21no—
506C2×#41C22×D1312yes—
507C2×#41C22×D1312yes—
508C22×Q8—132no—
509C22×Q8—261no—
510C22×Q8C22×D1311yescharacteristic
511C22×D4—21no—
512C22×D4C22×D1311yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C22⋊D1311yescharacteristic
517C23×C4C22⋊D1311yescharacteristic
518C23×C4C22×D1311yescharacteristic
519#137—2616no—
520C2×Q16—138no—
521C2×SD16—138no—
522C2×M16—134no—
523C4⋊Q8—132no—
524C4⋊Q8—132no—
525C4⋊Q8—132no—
526C4⋊Q8—132no—
527C4⋊Q8—261no—
528C4⋊Q8—261no—
529C4⋊Q8—261no—
530C4⋊Q8—261no—
531#125—262no—
532#125—262no—
533#125—262no—
534#125—262no—
535C22⋊Q8—134no—
536C22⋊Q8—134no—
537C22⋊Q8—262no—
538C22⋊Q8—262no—
539C22⋊Q8—262no—
540C22⋊Q8—262no—
541C22⋊Q8—262no—
542C22⋊Q8—262no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8—21no—
547C4×Q8—134no—
548C4×Q8—134no—
549C4×Q8—262no—
550C4×Q8—262no—
551C4×Q8—262no—
552C4×Q8—262no—
553C4×Q8—262no—
554C4×Q8—262no—
555C4×Q8C22×D1312yes—
556C4×Q8C22×D1312yes—
557C4×Q8C22×D1312yes—
558C4×Q8C22×D1312yes—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4C22×D1312yes—
572C4×D4C22×D1312yes—
573C4×D4C22×D1312yes—
574C4×D4C22×D1312yes—
575#117—21no—
576#117—21no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—262no—
582#117—262no—
583#117—262no—
584#117—262no—
585#117C22×D1312yes—
586#117C22×D1312yes—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—132no—
590C2×C4⋊C4—261no—
591C2×C4⋊C4—261no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—261no—
595C2×C4⋊C4C22×D1311yescharacteristic
596C2×C4⋊C4C22×D1311yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—262no—
601C2×C42—21no—
602C2×C42—21no—
603C2×C42—21no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—262no—
609C2×C42C22⋊D1311yescharacteristic
610C2×C42C22⋊D1311yescharacteristic
611C2×C42C22⋊D1311yescharacteristic
612C2×C42C22⋊D1311yescharacteristic
613C2×C42C22⋊D1311yescharacteristic
614C2×C42C22⋊D1311yescharacteristic
615C2×C42C22×D1311yescharacteristic
616C2×C42C22×D1311yescharacteristic
617C2×C42C22×D1311yescharacteristic
618C2×C42C22×D1311yescharacteristic
619C2×C42C22×D1311yescharacteristic
620C2×C42C22×D1311yescharacteristic
621#107—138no—
622#106—138no—
623C4⋊C8—134no—
624C4⋊C8—134no—
625#103—138no—
626#103—138no—
627#103—138no—
628#102—138no—
629C22⋊C8—134no—
630C22⋊C8—134no—
631#97—134no—
632C4×C8—134no—
633C2×C13—22no—
634C2×C13—22no—
635C2×C13—41no—
636C2×C13—44no—
637C2×C13C2×#52511yescharacteristic
638C2×C13C22×#13711yescharacteristic
639C2×C13C2×#57511yescharacteristic
640C24—21no—
641C24C2×C22⋊D1311yescharacteristic
642#41—28no—
643#41—28no—
644#41—24no—
645#41—24no—
646#41—24no—
647#41#612718yes—
648C2×Q8—24no—
649C2×Q8—21no—
650C2×Q8—134no—
651C2×Q8—262no—
652C2×Q8—262no—
653C2×Q8—262no—
654C2×Q8—268no—
655C2×Q8—524no—
656C2×Q8C23×D1312yes—
657C2×D4—28no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—24no—
661C2×D4—21no—
662C2×D4C23×D1312yes—
663C22×C4—28no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—42no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4C2×C22⋊D1311yescharacteristic
681C22×C4C2×C22⋊D1311yescharacteristic
682C22×C4C2×C22⋊D1311yescharacteristic
683C22×C4C2×C22⋊D1311yescharacteristic
684C22×C4C2×C22⋊D1311yescharacteristic
685C22×C4C2×C22⋊D1311yescharacteristic
686C22×C4C2×C22⋊D1311yescharacteristic
687C22×C4C2×C22⋊D1311yescharacteristic
688C22×C4C2×C22⋊D1311yescharacteristic
689C22×C4C2×C22⋊D1311yescharacteristic
690C22×C4C2×C22⋊D1311yescharacteristic
691C22×C4C2×C22⋊D1311yescharacteristic
692C22×C4C2×C22⋊D1311yescharacteristic
693C22×C4C2×C22⋊D1311yescharacteristic
694C22×C4C2×C22⋊D1311yescharacteristic
695C22×C4C23×D1311yescharacteristic
696C22×C4C23×D1311yescharacteristic
697C22×C4C23×D1311yescharacteristic
698Q16—2616no—
699SD16—2616no—
700M16—268no—
701C2×C8—138no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—134no—
709C4⋊C4—262no—
710C4⋊C4—262no—
711C4⋊C4—262no—
712C4⋊C4—262no—
713C4⋊C4—262no—
714C4⋊C4—264no—
715C4⋊C4—264no—
716C4⋊C4—264no—
717C4⋊C4—264no—
718C4⋊C4—262no—
719C4⋊C4—262no—
720C4⋊C4C23×D1312yes—
721C4⋊C4C23×D1312yes—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—264no—
729C22⋊C4—264no—
730C42—22no—
731C42—22no—
732C42—22no—
733C42—22no—
734C42—22no—
735C42—22no—
736C42—264no—
737C42—264no—
738C42C2×C22⋊D1311yescharacteristic
739C42C2×C22⋊D1311yescharacteristic
740C42C2×C22⋊D1311yescharacteristic
741C42C2×C22⋊D1311yescharacteristic
742C42C2×C22⋊D1311yescharacteristic
743C42C2×C22⋊D1311yescharacteristic
744C42C2×C22⋊D1311yescharacteristic
745C42C2×C22⋊D1311yescharacteristic
746C42C2×C22⋊D1311yescharacteristic
747C42C2×C22⋊D1311yescharacteristic
748C42C2×C22⋊D1311yescharacteristic
749C42C2×C22⋊D1311yescharacteristic
750C42C23×D1311yescharacteristic
751C42C23×D1311yescharacteristic
752C42C23×D1311yescharacteristic
753C42C23×D1311yescharacteristic
754C13#6056211yescharacteristic, complemented, Sylow
755C23—24no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23C22×C22⋊D1311yescharacteristic
763C23C22×C22⋊D1311yescharacteristic
764C23C22×C22⋊D1311yescharacteristic
765Q8—24no—
766Q8—22no—
767Q8—268no—
768Q8—524no—
769Q8—524no—
770Q8—524no—
771Q8C2×#612714yes—
772D4—28no—
773D4—24no—
774D4—28no—
775D4—22no—
776D4C2×#612714yes—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—28no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—264no—
806C2×C4—264no—
807C2×C4—524no—
808C2×C4—524no—
809C2×C4#8820514yescomplemented
810C2×C4C2×#612714yes—
811C2×C4C22×C22⋊D1311yescharacteristic
812C2×C4C22×C22⋊D1311yescharacteristic
813C2×C4C22×C22⋊D1311yescharacteristic
814C2×C4C22×C22⋊D1311yescharacteristic
815C2×C4C22×C22⋊D1311yescharacteristic
816C2×C4C22×C22⋊D1311yescharacteristic
817C2×C4C22×C22⋊D1311yescharacteristic
818C2×C4C22×C22⋊D1311yescharacteristic
819C2×C4C22×C22⋊D1311yescharacteristic
820C2×C4C22×C22⋊D1311yescharacteristic
821C2×C4C22×C22⋊D1311yescharacteristic
822C2×C4C24×D1311yescharacteristic
823C8—268no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—24no—
832C22—44no—
833C22—48no—
834C22—42no—
835C22—42no—
836C22#1171949612yes—
837C22C2×#8820512yes—
838C22C23×C22⋊D1311yescharacteristic
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—24no—
846C4—21no—
847C4—42no—
848C4—42no—
849C4—524no—
850C4—524no—
851C4#1171949612yes—
852C4#1171952712yes—
853C4C2×#8820512yes—
854C4C2×#8820512yes—
855C4C22×#612712yes—
856C2—22no—
857C2—22no—
858C2—41no—
859C2—44no—
860C2C2×#1171949611yescharacteristic
861C2C22×#8820511yescharacteristic
862C2C2×#1171952711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C4×C13×#41C2
socleC22×C13C23×D4
prime radicalC22×C13×#41C22
hypercenterC2×C4×#41D13
hypocenterC13#60562
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. #13124998C2semidirect
3. #13124966C2semidirect
4. #13124935C2semidirect
5. #13124907C2semidirect
6. #13124875C2semidirect
7. #13124844C2semidirect
8. #13124784C2semidirect
9. #13124651C2semidirect
10. #13124323C2semidirect
12. C4×#88205C2semidirect
13. #13123469C2semidirect
44. #11719175C22semidirect
45. #11719175C22semidirect
47. C2×#88123C22semidirect
48. C2×#88123C22semidirect
50. C2×C4×Dic26C22semidirect
56. #11718692C22semidirect
57. #11718692C22semidirect
58. #11718691C22semidirect
59. C4×#6107C22semidirect
60. #11718682C22semidirect
61. #11718681C22semidirect
62. #11718680C22semidirect
63. #11718680C22semidirect
64. #11718679C22semidirect
65. C4×#6105C22semidirect
66. #11718669C22semidirect
67. #11718668C22semidirect
68. #11718665C22semidirect
69. #11718657C22semidirect
70. #11718656C22semidirect
74. #11718587C22semidirect
76. #11718586C22semidirect
77. #11718585C22semidirect
78. C4×#6099C22semidirect
384. C2×C4×C13#137semidirect
754. C13#60562semidirect
809. C2×C4#88205semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
#131249982
#131249662
#131249352
#131249072
#131248752
#131248442
#131247842
#131246512
#131243232
#131240962
C4×#882052
#131234692
C2×C4×C13×#412
#6056213