Finite Group Databasebeta

← #15878444

Subgroups — #15878444

Order 3328.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic, complemented
3C2×#11718894C211yesmaximal, characteristic, complemented
4#13117765C211yesmaximal, characteristic, complemented
5#13115764C211yesmaximal, characteristic, complemented
6#13115661C211yesmaximal, characteristic, complemented
7#13115275C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic, complemented
9#13115159C211yesmaximal, characteristic, complemented
10#13115154C211yesmaximal, characteristic, complemented
11#13114851C211yesmaximal, characteristic, complemented
12#13114776C211yesmaximal, characteristic, complemented
13#13114776C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C2×C13×#550C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C22×C13×#41C2211yescharacteristic
18C13×#550—24no—
19C13×#550C418yescomplemented
20C2×C13×#127—21no—
21C2×C13×#127C2211yescharacteristic
22C2×C13×#121—21no—
23C2×C13×#121—21no—
24C2×C13×#121C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13—21no—
28C2×C4×D4×C13C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33#11718894—24no—
34#11718893—24no—
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39#11718881—21no—
40C2×#88072C2211yescharacteristic
41C2×#88072C2211yescharacteristic
42C2×#88072C2211yescharacteristic
43C2×#88072C2211yescharacteristic
44C2×#88072C2211yescharacteristic
45C2×#88072C2211yescharacteristic
46C2×#88072C2211yescharacteristic
47C2×#88072C2211yescharacteristic
48#11718873C2211yescharacteristic
49#11718873C2211yescharacteristic
50C2×C22⋊#1055C2211yescharacteristic
51C2×C22⋊#1055C2211yescharacteristic
52#11718672—24no—
53#11718642—21no—
54#11718612—21no—
55C22⋊C4×Dic13—21no—
56#11718597C2211yescharacteristic
57C4×C4⋊Dic13C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×#88043C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—22no—
69C2×C13×#41—22no—
70C2×C13×#41—41no—
71C2×C13×#41—41no—
72C2×C13×#41—41no—
73C2×C13×#41—41no—
74C2×C13×#41C2×C414yes—
75C2×C13×#41C2×C414yescomplemented
76C22×Q8×C13C2311yescharacteristic
77C22×D4×C13—21no—
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13—21no—
82C22×D4×C13—21no—
83C22×D4×C13D411yescharacteristic
84C22×D4×C13C2311yescharacteristic
85C22×D4×C13C2311yescharacteristic
86C23×C4×C13—21no—
87C23×C4×C13—21no—
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×Dic13—21no—
91C13×#127—28no—
92C13×#127—22no—
93C13×#127C2×C414yescomplemented
94C13×#121—22no—
95C13×#121—22no—
96C13×#121—28no—
97C13×#121—28no—
98C13×#121C2×C414yes—
99C13×#121C2×C414yescomplemented
100C4×Q8×C13—22no—
101C4×Q8×C13C2×C414yescomplemented
102C4×D4×C13—28no—
103C4×D4×C13C2×C414yes—
104C4×D4×C13D414yes—
105C2×C13×C4⋊C4—21no—
106C2×C13×C4⋊C4D411yescharacteristic
107C2×C13×C4⋊C4C2311yescharacteristic
108C2×C13×C22⋊C4—21no—
109C2×C13×C22⋊C4—21no—
110C2×C13×C22⋊C4D411yescharacteristic
111C2×C13×C22⋊C4D411yescharacteristic
112C2×C42×C13—21no—
113C2×C42×C13C2311yescharacteristic
114C2×C22⋊Dic13—21no—
115C2×C22⋊Dic13—21no—
116C2×C22⋊Dic13—21no—
117#88180—22no—
118#88180—41no—
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—21no—
121C2×C4⋊Dic13—41no—
122C2×C4⋊Dic13C2311yescharacteristic
123C2×C4⋊Dic13C2311yescharacteristic
124C2×C4⋊Dic13C2311yescharacteristic
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C2×#6099—22no—
129C2×#6099—22no—
130C2×#6099—41no—
131C22×#1055—22no—
132C22×#1055—22no—
133C22×#1055—41no—
134C22×#1055C2311yescharacteristic
135C22×#1055C2311yescharacteristic
136C22×#1055C2311yescharacteristic
137C22×#1055C2311yescharacteristic
138#88075—22no—
139#88075—22no—
140#88075—22no—
141#88075D414yescomplemented
142#88072—22no—
143#88072—22no—
144#88072—22no—
145#88072—22no—
146#88072—41no—
147#88072—41no—
148#88072—41no—
149#88072—41no—
150#88071—21no—
151#88071—21no—
152#88071—21no—
153#88071—21no—
154#88071—21no—
155C22⋊#1055—22no—
156C22⋊#1055—22no—
157C4⋊#1055—22no—
158#88043—22no—
159#22422—131nomaximal, Sylow
160C24×C13—21no—
161C24×C13—21no—
162C24×C13C2×D411yescharacteristic
163C24×C13C2×D411yescharacteristic
164C13×#41—28no—
165C13×#41—28no—
166C13×#41—44no—
167C13×#41—44no—
168C13×#41—44no—
169C13×#41—44no—
170C13×#41—44no—
171C13×#41—44no—
172C2×Q8×C13—21no—
173C2×Q8×C13—21no—
174C2×Q8×C13—21no—
175C2×Q8×C13C22×C412yes—
176C2×Q8×C13C2×D412yes—
177C2×Q8×C13#4112yes—
178C2×D4×C13—24no—
179C2×D4×C13—24no—
180C2×D4×C13—24no—
181C2×D4×C13—24no—
182C2×D4×C13—24no—
183C2×D4×C13—24no—
184C2×D4×C13—21no—
185C2×D4×C13—21no—
186C2×D4×C13—21no—
187C2×D4×C13—21no—
188C2×D4×C13—21no—
189C2×D4×C13—21no—
190C2×D4×C13—21no—
191C2×D4×C13—21no—
192C2×D4×C13—21no—
193C2×D4×C13—21no—
194C2×D4×C13—41no—
195C2×D4×C13—41no—
196C2×D4×C13—42no—
197C2×D4×C13—42no—
198C2×D4×C13—42no—
199C2×D4×C13—42no—
200C2×D4×C13—42no—
201C2×D4×C13—42no—
202C2×D4×C13—81no—
203C2×D4×C13—81no—
204C2×D4×C13—81no—
205C2×D4×C13—81no—
206C2×D4×C13—81no—
207C2×D4×C13—81no—
208C2×D4×C13C22⋊C414yes—
209C2×D4×C13C22×C412yes—
210C2×D4×C13C22×C412yes—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—24no—
222C22×C4×C13—24no—
223C22×C4×C13—42no—
224C22×C4×C13—42no—
225C22×C4×C13—42no—
226C22×C4×C13—42no—
227C22×C4×C13C22×C412yes—
228C22×C4×C13C22×C412yes—
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D412yes—
234C22×C4×C13C2×D412yes—
235C22×C4×C13C2411yescharacteristic
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—42no—
241C22×Dic13—42no—
242C22×Dic13—81no—
243C13×C4⋊C4—24no—
244C13×C4⋊C4—21no—
245C13×C4⋊C4C22⋊C414yes—
246C13×C4⋊C4C22×C412yes—
247C13×C22⋊C4—24no—
248C13×C22⋊C4—24no—
249C13×C22⋊C4C22⋊C414yes—
250C13×C22⋊C4C22⋊C414yes—
251C42×C13—24no—
252C42×C13C22×C412yes—
253C42×C13C2×D412yes—
254C22⋊Dic13—42no—
255C22⋊Dic13—42no—
256C22⋊Dic13—81no—
257C4⋊Dic13—21no—
258C4⋊Dic13—21no—
259C4⋊Dic13—21no—
260C4⋊Dic13—21no—
261C4⋊Dic13—21no—
262C4⋊Dic13—21no—
263C4⋊Dic13—21no—
264C4⋊Dic13—42no—
265C4⋊Dic13C2×D412yes—
266C4×Dic13—42no—
267C4×Dic13—81no—
268#6099—44no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—21no—
272C2×#1055—21no—
273C2×#1055—21no—
274C2×#1055—21no—
275C2×#1055—21no—
276C2×#1055—21no—
277C2×#1055—21no—
278C2×#1055—21no—
279C2×#1055—21no—
280C2×#1055—44no—
281C2×#1055C2×D412yes—
282C2×#550D1311yescharacteristic
283C2×#435—131no—
284C2×#417—131no—
285C2×#416—131no—
286#2352—131no—
287#1982—131no—
288#1961—131no—
289#1895—131no—
290#1893—131no—
291#1875—131no—
292#1874—131no—
293#1805—131no—
294#1788—131no—
295#1788—131no—
296#1763—131no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13—21no—
300C23×C13—21no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—21no—
304C23×C13—21no—
305C23×C13—21no—
306C23×C13—21no—
307C23×C13—21no—
308C23×C13—21no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13C2×C22⋊C412yes—
324C23×C13C2×C22⋊C412yes—
325C23×C13C22×D411yescharacteristic
326Q8×C13—22no—
327Q8×C13—22no—
328Q8×C13—22no—
329Q8×C13C4×D414yes—
330D4×C13—22no—
331D4×C13—22no—
332D4×C13—22no—
333D4×C13—22no—
334D4×C13—44no—
335D4×C13—48no—
336D4×C13—48no—
337D4×C13—48no—
338D4×C13—41no—
339D4×C13—41no—
340D4×C13—41no—
341D4×C13—41no—
342D4×C13—84no—
343D4×C13—84no—
344D4×C13—84no—
345C2×C4×C13—22no—
346C2×C4×C13—21no—
347C2×C4×C13—21no—
348C2×C4×C13—22no—
349C2×C4×C13—21no—
350C2×C4×C13—21no—
351C2×C4×C13—22no—
352C2×C4×C13—21no—
353C2×C4×C13—21no—
354C2×C4×C13—21no—
355C2×C4×C13—21no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—48no—
366C2×C4×C13—48no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13C2×C22⋊C412yes—
370C2×C4×C13C2×C22⋊C412yes—
371C2×C4×C13C2×C22⋊C412yes—
372C2×C4×C13C2×C22⋊C412yes—
373C2×C4×C13C23×C411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C2×#4111yescharacteristic
377C2×C4×C13H(5,𝔽2)11yescharacteristic
378C2×C4×C13H(5,𝔽2)11yescharacteristic
379C2×Dic13—22no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—84no—
392#1055—22no—
393#1055—41no—
394#1055—41no—
395#1055—41no—
396C22×#41C2×D1311yescharacteristic
397C22×#41C2×D1311yescharacteristic
398C22×M16—131no—
399C23×C8—131no—
400#550—24no—
401#550Dic1318yescomplemented
402C2×#127—21no—
403C2×#127C2×D1311yescharacteristic
404C2×#121—21no—
405C2×#121—21no—
406C2×#121C2×D1311yescharacteristic
407C2×#121C2×D1311yescharacteristic
408C2×C4×Q8C2×D1311yescharacteristic
409C2×C4×D4—21no—
410C2×C4×D4C2×D1311yescharacteristic
411C2×#117—131no—
412C22×C4⋊C4—131no—
413#435—264no—
414C2×C4⋊C8—131no—
415#417—264no—
416#416—264no—
417C2×#103—131no—
418C2×#103—131no—
419C2×#103—131no—
420C2×#103—131no—
421C2×#102—131no—
422C2×#102—131no—
423C2×#102—131no—
424C2×#102—131no—
425C2×#102—131no—
426C2×#102—131no—
427C2×#102—131no—
428C2×#102—131no—
429C2×C22⋊C8—131no—
430C2×C22⋊C8—131no—
431C2×#97—131no—
432#388—261no—
433#387—261no—
434#386—261no—
435#382—131no—
436#380—131no—
437#380—131no—
438C4×C4⋊C4—131no—
439C4×C22⋊C4—261no—
440#340—131no—
441#340—131no—
442#340—131no—
443#340—131no—
444C22×C13—22no—
445C22×C13—22no—
446C22×C13—22no—
447C22×C13—22no—
448C22×C13—22no—
449C22×C13—22no—
450C22×C13—41no—
451C22×C13—41no—
452C22×C13—41no—
453C22×C13—41no—
454C22×C13—41no—
455C22×C13—41no—
456C22×C13—41no—
457C22×C13—41no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—81no—
465C22×C13—81no—
466C22×C13—81no—
467C22×C13—81no—
468C22×C13—81no—
469C22×C13—81no—
470C22×C13—81no—
471C22×C13—81no—
472C22×C13C22×C22⋊C411yescharacteristic
473C22×C13D4211yescharacteristic
474C22×C13#54611yescharacteristic
475C22×C13#57511yescharacteristic
476C22×C13#57511yescharacteristic
477C22×C13#57611yescharacteristic
478C22×C13#57711yescharacteristic
479C4×C13—22no—
480C4×C13—22no—
481C4×C13—24no—
482C4×C13—22no—
483C4×C13—22no—
484C4×C13—42no—
485C4×C13C2×C4×D411yescharacteristic
486C4×C13#51811yescharacteristic
487C4×C13D4211yescharacteristic
488C4×C13#54611yescharacteristic
489Dic13—42no—
490Dic13—81no—
491Dic13—81no—
492Dic13—81no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41C2×Dic1314yes—
504C2×#41C2×Dic1314yescomplemented
505C22×Q8C22×D1311yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C22⋊D1311yescharacteristic
513C22×D4C22×D1311yescharacteristic
514C22×D4C22×D1311yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—261no—
518C23×C4C22×D1311yescharacteristic
519C23×C4C22×D1311yescharacteristic
520C2×M16—262no—
521C2×M16—262no—
522C2×M16—521no—
523C22×C8—131no—
524C22×C8—131no—
525C22×C8—131no—
526C22×C8—131no—
527C22×C8—262no—
528C22×C8—262no—
529C22×C8—521no—
530#127—28no—
531#127—22no—
532#127C2×Dic1314yescomplemented
533#121—22no—
534#121—22no—
535#121—28no—
536#121—28no—
537#121C2×Dic1314yes—
538#121C2×Dic1314yescomplemented
539C4×Q8—22no—
540C4×Q8C2×Dic1314yescomplemented
541C4×D4—28no—
542C4×D4C2×Dic1314yes—
543C4×D4C22⋊D1314yes—
544#117—262no—
545#117—521no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—131no—
548C2×C4⋊C4—131no—
549C2×C4⋊C4—131no—
550C2×C4⋊C4—131no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4—261no—
553C2×C4⋊C4—521no—
554C2×C4⋊C4C22⋊D1311yescharacteristic
555C2×C4⋊C4C22×D1311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—261no—
559C2×C22⋊C4—261no—
560C2×C22⋊C4—261no—
561C2×C22⋊C4C22⋊D1311yescharacteristic
562C2×C22⋊C4C22⋊D1311yescharacteristic
563C2×C42—21no—
564C2×C42—261no—
565C2×C42—261no—
566C2×C42C22×D1311yescharacteristic
567C4⋊C8—262no—
568#103—134no—
569#103—262no—
570#103—262no—
571#103—262no—
572#102—262no—
573#102—262no—
574#102—262no—
575#102—262no—
576#102—521no—
577#102—521no—
578#102—521no—
579#102—521no—
580C22⋊C8—262no—
581C22⋊C8—262no—
582#97—262no—
583#95—261no—
584#95—261no—
585#95—261no—
586#95—261no—
587#95—261no—
588C2×C13—42no—
589C2×C13—42no—
590C2×C13—82no—
591C2×C13—82no—
592C2×C13D4×C22⋊C411yescharacteristic
593C2×C13#289611yescharacteristic
594C2×C13#289711yescharacteristic
595C2×C13#326811yescharacteristic
596C2×C13#327111yescharacteristic
597C2×C13#330911yescharacteristic
598C2×C13#331711yescharacteristic
599C24—21no—
600C24—21no—
601C24C2×C22⋊D1311yescharacteristic
602C24C2×C22⋊D1311yescharacteristic
603#41—28no—
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—44no—
609#41—44no—
610#41—44no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8D4×D1312yes—
615C2×Q8#612912yes—
616C2×Q8C22×Dic1312yes—
617C2×D4—24no—
618C2×D4—24no—
619C2×D4—24no—
620C2×D4—24no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—81no—
642C2×D4—81no—
643C2×D4—81no—
644C2×D4—81no—
645C2×D4—81no—
646C2×D4—81no—
647C2×D4C22⋊Dic1314yes—
648C2×D4C22×Dic1312yes—
649C2×D4C22×Dic1312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—24no—
661C22×C4—24no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—522no—
671C22×C4—522no—
672C22×C4—1041no—
673C22×C4C22×Dic1312yes—
674C22×C4C22×Dic1312yes—
675C22×C4C2×C22⋊D1311yescharacteristic
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C2×C22⋊D1312yes—
680C22×C4C2×C22⋊D1312yes—
681C22×C4C23×D1311yescharacteristic
682M16—524no—
683C2×C8—132no—
684C2×C8—261no—
685C2×C8—261no—
686C2×C8—261no—
687C2×C8—261no—
688C2×C8—261no—
689C2×C8—261no—
690C2×C8—261no—
691C2×C8—261no—
692C2×C8—261no—
693C2×C8—261no—
694C2×C8—261no—
695C2×C8—524no—
696C4⋊C4—24no—
697C4⋊C4—21no—
698C4⋊C4—132no—
699C4⋊C4—261no—
700C4⋊C4—261no—
701C4⋊C4—261no—
702C4⋊C4—261no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—522no—
707C4⋊C4C22⋊Dic1314yes—
708C4⋊C4C22×Dic1312yes—
709C22⋊C4—24no—
710C22⋊C4—24no—
711C22⋊C4—522no—
712C22⋊C4—522no—
713C22⋊C4—1041no—
714C22⋊C4C22⋊Dic1314yes—
715C22⋊C4C22⋊Dic1314yes—
716C42—24no—
717C42—522no—
718C42—1041no—
719C42C22×Dic1312yes—
720C42C2×C22⋊D1312yes—
721C13#2242211yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23C2×C22⋊Dic1312yes—
749C23C2×C22⋊Dic1312yes—
750C23C22×C22⋊D1311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8D4×Dic1314yes—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—44no—
760D4—48no—
761D4—48no—
762D4—48no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—84no—
768D4—84no—
769D4—84no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—262no—
795C2×C4—521no—
796C2×C4—521no—
797C2×C4—521no—
798C2×C4—521no—
799C2×C4—521no—
800C2×C4—521no—
801C2×C4—521no—
802C2×C4—521no—
803C2×C4—521no—
804C2×C4—521no—
805C2×C4—521no—
806C2×C4—1044no—
807C2×C4C2×C22⋊Dic1312yes—
808C2×C4C2×C22⋊Dic1312yes—
809C2×C4C2×C22⋊Dic1312yes—
810C2×C4C2×C22⋊Dic1312yes—
811C2×C4C2×D4×D1311yescharacteristic
812C2×C4C2×#612911yescharacteristic
813C2×C4#8825111yescharacteristic
814C2×C4#8825111yescharacteristic
815C2×C4C23×Dic1311yescharacteristic
816C2×C4C22×C22⋊D1311yescharacteristic
817C8—262no—
818C8—521no—
819C8—521no—
820C8—521no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22D4×C22⋊D1311yescharacteristic
850C22#1171951111yescharacteristic
851C22#1171952711yescharacteristic
852C22#1171952711yescharacteristic
853C22#1171954011yescharacteristic
854C22#1171954111yescharacteristic
855C22C22×C22⋊Dic1311yescharacteristic
856C4—22no—
857C4—22no—
858C4—22no—
859C4—22no—
860C4—24no—
861C4—42no—
862C4—522no—
863C4—1041no—
864C4—1041no—
865C4—1041no—
866C4C2×D4×Dic1311yescharacteristic
867C4#1171950311yescharacteristic
868C4D4×C22⋊D1311yescharacteristic
869C4#1171951111yescharacteristic
870C2—42no—
871C2—42no—
872C2—82no—
873C2—82no—
874C2D4×C22⋊Dic1311yescharacteristic
875C2#1312335511yescharacteristic
876C2#1312336211yescharacteristic
877C2#1312637711yescharacteristic
878C2#1312641711yescharacteristic
879C2#1312684211yescharacteristic
880C2#1312696211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#550C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#550D13
hypocenterC13#22422
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. C2×#11718893C2semidirect
3. C2×#11718894C2semidirect
4. #13117765C2semidirect
5. #13115764C2semidirect
6. #13115661C2semidirect
7. #13115275C2semidirect
8. #13115265C2semidirect
9. #13115159C2semidirect
10. #13115154C2semidirect
11. #13114851C2semidirect
12. #13114776C2semidirect
13. #13114776C2semidirect
14. #13114666C2semidirect
19. C13×#550C4semidirect
75. C2×C13×#41C2×C4semidirect
93. C13×#127C2×C4semidirect
99. C13×#121C2×C4semidirect
101. C4×Q8×C13C2×C4semidirect
141. #88075D4semidirect
401. #550Dic13semidirect
504. C2×#41C2×Dic13semidirect
532. #127C2×Dic13semidirect
538. #121C2×Dic13semidirect
540. C4×Q8C2×Dic13semidirect
721. C13#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
C2×#117188932
C2×#117188942
#131177652
#131157642
#131156612
#131152752
#131152652
#131151592
#131151542
#131148512
#131147762
#131146662
C2×C13×#5502
#2242213