Finite Group Databasebeta

← #15868668

Subgroups — #15868668

Order 3328.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718899C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic, complemented
3C2×C4×#6104C211yesmaximal, characteristic, complemented
4#13117529C211yesmaximal, characteristic, complemented
5#13115191C211yesmaximal, characteristic, complemented
6#13115184C211yesmaximal, characteristic, complemented
7#13115153C211yesmaximal, characteristic, complemented
8#13115090C211yesmaximal, characteristic, complemented
9#13115083C211yesmaximal, characteristic, complemented
10#13115024C211yesmaximal, characteristic, complemented
11#13114776C211yesmaximal, characteristic, complemented
12#13114661C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C2×C13×#520C211yesmaximal, characteristic, complemented
16C22×C13×#41C2211yescharacteristic
17C13×#520—24no—
18C13×#520—24no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117C2211yescharacteristic
27C22×C13×C4⋊C4—21no—
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×#6106C2211yescharacteristic
30C22×#6104C2211yescharacteristic
31C2×#88184C2211yescharacteristic
32C2×C4×D52C2211yescharacteristic
33#11718899C418yescomplemented
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40#11718873C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718687—24no—
44C4×#6104—24no—
45#11718651—21no—
46#11718650—21no—
47C2×#88049C2211yescharacteristic
48C2×#88049C2211yescharacteristic
49C2×#88047C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51#11718618—21no—
52#11718617—21no—
53#11718600C2211yescharacteristic
54C4×C4⋊Dic13C2211yescharacteristic
55#11718589C2211yescharacteristic
56C2×#88043C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718116C2211yescharacteristic
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—22no—
69C2×C13×#41C2×C414yescomplemented
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13—21no—
72C22×D4×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C22×C22⋊D13—21no—
79C22×D52C2311yescharacteristic
80C22×C4×D13—21no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13D414yescomplemented
85C4×D4×C13—28no—
86C4×D4×C13—28no—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13—22no—
90C4×D4×C13D414yescomplemented
91C13×#117—28no—
92C13×#117—22no—
93C13×#117—22no—
94C2×C13×C4⋊C4—28no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4D411yescharacteristic
101C2×C13×C4⋊C4D411yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C22⋊C4—21no—
105C2×C13×C22⋊C4—21no—
106C2×C13×C22⋊C4D411yescharacteristic
107C2×C13×C22⋊C4D411yescharacteristic
108C2×C42×C13—21no—
109C2×C42×C13—21no—
110C2×C42×C13C2311yescharacteristic
111C2×C42×C13C2311yescharacteristic
112C2×C22⋊Dic13—21no—
113C2×#6106—22no—
114C2×#6106—22no—
115C2×#6106C2×C414yescomplemented
116C2×#6104—22no—
117C2×#6104—22no—
118C2×#6104C2×C414yescomplemented
119#88184—22no—
120#88184C2×C414yescomplemented
121C2×#6103—21no—
122C2×#6103—21no—
123C2×#6103—21no—
124C2×#6103—21no—
125C2×C4⋊Dic13C2311yescharacteristic
126C2×C4⋊Dic13C2311yescharacteristic
127C2×C4⋊Dic13C2311yescharacteristic
128C2×#6101—21no—
129C2×C4×Dic13—21no—
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134C4×D52—22no—
135C4×D52—22no—
136#88075—22no—
137#88075—22no—
138#88075C2×C414yescomplemented
139#88072—22no—
140#88072—22no—
141#88072C2×C414yescomplemented
142#88071—21no—
143#88071—21no—
144#88071—21no—
145C22⋊#1055—22no—
146C22⋊#1055C2×C414yescomplemented
147#88049—22no—
148#88049—22no—
149#88047—22no—
150#88047—22no—
151#88043—22no—
152C4×#1055—22no—
153#21460—131nomaximal, Sylow
154C24×C13—21no—
155C24×C13C2×D411yescharacteristic
156C23×D13—21no—
157C13×#41—28no—
158C13×#41—28no—
159C13×#41—28no—
160C13×#41—28no—
161C2×Q8×C13—21no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13C22×C412yes—
165C2×Q8×C13C2×D412yes—
166C2×Q8×C13#4112yes—
167C2×D4×C13—24no—
168C2×D4×C13—24no—
169C2×D4×C13—24no—
170C2×D4×C13—21no—
171C2×D4×C13—21no—
172C2×D4×C13—21no—
173C2×D4×C13C22×C412yes—
174C2×D4×C13C2×D412yes—
175C2×D4×C13#4112yes—
176C22×C4×C13—24no—
177C22×C4×C13—24no—
178C22×C4×C13—21no—
179C22×C4×C13—24no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—24no—
187C22×C4×C13—24no—
188C22×C4×C13—24no—
189C22×C4×C13—81no—
190C22×C4×C13—81no—
191C22×C4×C13—81no—
192C22×C4×C13—81no—
193C22×C4×C13—81no—
194C22×C4×C13—81no—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13#4112yes—
202C22×C4×C13C2411yescharacteristic
203C2×C22⋊D13—24no—
204C2×C22⋊D13—81no—
205C2×C22⋊D13—81no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C2×D52—21no—
210C2×D52—21no—
211C2×D52—21no—
212C2×D52—21no—
213C2×D52—21no—
214C2×D52C22×C412yes—
215C2×C4×D13—42no—
216C2×C4×D13—81no—
217C2×C4×D13—81no—
218C13×C4⋊C4—24no—
219C13×C4⋊C4—24no—
220C13×C4⋊C4—22no—
221C13×C4⋊C4—24no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—21no—
224C13×C4⋊C4—21no—
225C13×C4⋊C4C2×D412yes—
226C13×C4⋊C4C2×D412yes—
227C13×C22⋊C4—24no—
228C13×C22⋊C4—24no—
229C13×C22⋊C4—22no—
230C13×C22⋊C4—22no—
231C42×C13—24no—
232C42×C13—24no—
233C42×C13—21no—
234C42×C13—21no—
235C42×C13C2×D412yes—
236C42×C13C2×D412yes—
237C22⋊Dic13—81no—
238#6106—28no—
239#6104—28no—
240#6103—24no—
241#6103—42no—
242#6103—81no—
243#6103—81no—
244C4⋊Dic13—21no—
245C4⋊Dic13—21no—
246C4⋊Dic13—21no—
247C4⋊Dic13—21no—
248C4⋊Dic13—21no—
249C4⋊Dic13C22×C412yes—
250#6101—81no—
251C4×Dic13—81no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055—21no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055C22×C412yes—
263C2×#1055C22×C412yes—
264C2×#520D1311yescharacteristic, complemented
265C2×#449—131no—
266C2×#440—131no—
267C2×C4×D8—131no—
268#2324—131no—
269#1880—131no—
270#1879—131no—
271#1874—131no—
272#1863—131no—
273#1862—131no—
274#1852—131no—
275#1788—131no—
276#1762—131no—
277C4×#103—131no—
278#1750—131no—
279C23×C13—22no—
280C23×C13—21no—
281C23×C13—22no—
282C23×C13—21no—
283C23×C13—22no—
284C23×C13—21no—
285C23×C13—21no—
286C23×C13—21no—
287C23×C13—21no—
288C23×C13—41no—
289C23×C13—41no—
290C23×C13—41no—
291C23×C13—41no—
292C23×C13C4×D412yes—
293C23×C13C22×D411yescharacteristic
294C22×D13—22no—
295C22×D13—41no—
296C22×D13—41no—
297C22×D13—41no—
298C22×D13—41no—
299C22×D13—41no—
300C22×D13—41no—
301Q8×C13—22no—
302Q8×C13—22no—
303Q8×C13—22no—
304Q8×C13C4×D414yes—
305D4×C13—216no—
306D4×C13—22no—
307D4×C13—22no—
308D4×C13—22no—
309D4×C13C4×D414yes—
310C2×C4×C13—216no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—22no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—21no—
325C2×C4×C13—21no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—21no—
329C2×C4×C13—21no—
330C2×C4×C13—21no—
331C2×C4×C13—21no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—84no—
337C2×C4×C13—84no—
338C2×C4×C13—84no—
339C2×C4×C13C4×D412yes—
340C2×C4×C13#12012yes—
341C2×C4×C13#12012yes—
342C2×C4×C13C23×C411yescharacteristic
343C2×C4×C13C22×D411yescharacteristic
344C2×C4×C13C22×D411yescharacteristic
345C2×C4×C13C2×#4111yescharacteristic
346C2×C4×C13C2×#4111yescharacteristic
347C2×C4×C13C2×#4111yescharacteristic
348C22⋊D13—84no—
349C2×Dic13—22no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358D52—22no—
359D52—22no—
360D52—41no—
361D52—41no—
362C4×D13—84no—
363#1055—22no—
364#1055—22no—
365#1055—41no—
366#1055—41no—
367C22×#41C2×D1311yescharacteristic
368C22×SD16—131no—
369C22×D8—131no—
370C2×#121—131no—
371#520—24no—
372#520—24no—
373C2×C4×Q8C2×D1311yescharacteristic
374C2×C4×Q8C2×D1311yescharacteristic
375C2×C4×D4—21no—
376C2×C4×D4—21no—
377C2×C4×D4—131no—
378C2×C4×D4C2×D1311yescharacteristic
379C2×C4×D4C2×D1311yescharacteristic
380C2×#117—21no—
381C2×#117C2×D1311yescharacteristic
382C22×C4⋊C4—21no—
383C22×C4⋊C4C2×D1311yescharacteristic
384#449—138no—
385#440—264no—
386C4×D8—264no—
387C2×#107—131no—
388C2×#107—131no—
389C2×#103—131no—
390C2×#103—131no—
391C2×#103—131no—
392C2×#102—131no—
393C2×#102—131no—
394C2×#102—131no—
395C2×#102—131no—
396C2×#102—131no—
397C2×C22⋊C8—131no—
398C2×C22⋊C8—131no—
399C2×#97—131no—
400C2×C4×C8—131no—
401#390—131no—
402#390—261no—
403#389—131no—
404#388—261no—
405#386—261no—
406#385—261no—
407#380—131no—
408C4×C4⋊C4—131no—
409#340—131no—
410#340—131no—
411#340—131no—
412#340—131no—
413#336—131no—
414#336—131no—
415C22×C13—22no—
416C22×C13—22no—
417C22×C13—22no—
418C22×C13—24no—
419C22×C13—41no—
420C22×C13—42no—
421C22×C13—41no—
422C22×C13—42no—
423C22×C13—42no—
424C22×C13—42no—
425C22×C13—41no—
426C22×C13—42no—
427C22×C13—41no—
428C22×C13—42no—
429C22×C13C2×C4×D411yescharacteristic
430C22×C13C2×#12011yescharacteristic
431C22×C13#52511yescharacteristic
432C22×C13#57611yescharacteristic
433C22×C13#57611yescharacteristic
434C22×C13#57711yescharacteristic
435C22×C13#57811yescharacteristic
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—81no—
440C2×D13—81no—
441C2×D13—81no—
442C2×D13—81no—
443C4×C13—22no—
444C4×C13—22no—
445C4×C13—22no—
446C4×C13—24no—
447C4×C13—41no—
448C4×C13—42no—
449C4×C13—42no—
450C4×C13—41no—
451C4×C13C2×C4×D411yescharacteristic
452C4×C13C2×C4×D411yescharacteristic
453C4×C13#52511yescharacteristic
454C4×C13#52511yescharacteristic
455Dic13—42no—
456Dic13—81no—
457Dic13—81no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41C4×D1314yescomplemented
464C22×Q8C22×D1311yescharacteristic
465C22×D4—21no—
466C22×D4—131no—
467C22×D4—261no—
468C22×D4C22×D1311yescharacteristic
469C23×C4—21no—
470C23×C4—21no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—261no—
474C23×C4C22×D1311yescharacteristic
475C2×SD16—134no—
476C2×SD16—262no—
477C2×SD16—262no—
478C2×D8—134no—
479C2×D8—262no—
480C2×D8—262no—
481C22×C8—131no—
482C22×C8—131no—
483C22×C8—131no—
484C22×C8—131no—
485#121—134no—
486#121—262no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8C22⋊D1314yescomplemented
491C4×D4—28no—
492C4×D4—28no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—262no—
497C4×D4—262no—
498C4×D4C22⋊D1314yescomplemented
499#117—28no—
500#117—22no—
501#117—22no—
502C2×C4⋊C4—28no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4—131no—
509C2×C4⋊C4—131no—
510C2×C4⋊C4—131no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4C22⋊D1311yescharacteristic
513C2×C4⋊C4C22⋊D1311yescharacteristic
514C2×C4⋊C4C22×D1311yescharacteristic
515C2×C4⋊C4C22×D1311yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—261no—
519C2×C22⋊C4—261no—
520C2×C22⋊C4—261no—
521C2×C22⋊C4—261no—
522C2×C22⋊C4—261no—
523C2×C22⋊C4C22⋊D1311yescharacteristic
524C2×C22⋊C4C22⋊D1311yescharacteristic
525C2×C42—21no—
526C2×C42—21no—
527C2×C42—261no—
528C2×C42C22×D1311yescharacteristic
529C2×C42C22×D1311yescharacteristic
530#107—262no—
531#107—262no—
532#103—134no—
533#103—262no—
534#103—262no—
535#102—134no—
536#102—262no—
537#102—262no—
538#102—262no—
539#102—262no—
540C22⋊C8—134no—
541C22⋊C8—262no—
542#97—262no—
543C4×C8—262no—
544#95—261no—
545#95—261no—
546#95—261no—
547C2×C13—42no—
548C2×C13—44no—
549C2×C13C4×#12011yescharacteristic
550C2×C13#294611yescharacteristic
551C2×C13#295111yescharacteristic
552C2×C13#300811yescharacteristic
553C2×C13#301311yescharacteristic
554C2×C13#311911yescharacteristic
555C2×C13#312411yescharacteristic
556D13—82no—
557C24—21no—
558C24—261no—
559C24C2×C22⋊D1311yescharacteristic
560#41—28no—
561#41—28no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C2×C4×D1312yes—
568C2×Q8#612712yes—
569C2×Q8C2×C22⋊D1312yes—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—132no—
577C2×D4—264no—
578C2×D4—261no—
579C2×D4—261no—
580C2×D4—261no—
581C2×D4—261no—
582C2×D4—261no—
583C2×D4—1041no—
584C2×D4—1041no—
585C2×D4C2×C4×D1312yes—
586C2×D4#612712yes—
587C2×D4C2×C22⋊D1312yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—81no—
602C22×C4—81no—
603C22×C4—81no—
604C22×C4—81no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—522no—
611C22×C4—1041no—
612C22×C4—1041no—
613C22×C4C2×C4×D1312yes—
614C22×C4#612712yes—
615C22×C4C2×C22⋊D1311yescharacteristic
616C22×C4C2×C22⋊D1311yescharacteristic
617C22×C4C2×C22⋊D1311yescharacteristic
618C22×C4C2×C22⋊D1311yescharacteristic
619C22×C4C2×C22⋊D1311yescharacteristic
620C22×C4C23×D1311yescharacteristic
621SD16—268no—
622D8—268no—
623C2×C8—132no—
624C2×C8—132no—
625C2×C8—261no—
626C2×C8—261no—
627C2×C8—261no—
628C2×C8—261no—
629C2×C8—261no—
630C2×C8—261no—
631C2×C8—261no—
632C2×C8—261no—
633C2×C8—261no—
634C2×C8—261no—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—132no—
643C4⋊C4—261no—
644C4⋊C4—261no—
645C4⋊C4—261no—
646C4⋊C4—261no—
647C4⋊C4—261no—
648C4⋊C4—1041no—
649C4⋊C4C2×C22⋊D1312yes—
650C4⋊C4C2×C22⋊D1312yes—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—264no—
656C22⋊C4—522no—
657C22⋊C4—1041no—
658C22⋊C4—1041no—
659C22⋊C4—1041no—
660C42—24no—
661C42—24no—
662C42—21no—
663C42—21no—
664C42—1041no—
665C42C2×C22⋊D1312yes—
666C42C2×C22⋊D1312yes—
667C13#2146011yescharacteristic, complemented, Sylow
668C23—22no—
669C23—21no—
670C23—22no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—262no—
682C23—521no—
683C23—521no—
684C23—521no—
685C23—521no—
686C23—521no—
687C23—521no—
688C23C4×C22⋊D1312yes—
689C23C22×C22⋊D1311yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8C4×C22⋊D1314yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—262no—
699D4—262no—
700D4—521no—
701D4—521no—
702D4—1044no—
703D4C4×C22⋊D1314yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—262no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—521no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—1044no—
743C2×C4C4×C22⋊D1312yes—
744C2×C4#8820712yes—
745C2×C4#8820712yes—
746C2×C4C22×C4×D1311yescharacteristic
747C2×C4C2×#612711yescharacteristic
748C2×C4C2×#612711yescharacteristic
749C2×C4C2×#612711yescharacteristic
750C2×C4C22×C22⋊D1311yescharacteristic
751C2×C4C22×C22⋊D1311yescharacteristic
752C8—262no—
753C8—262no—
754C8—521no—
755C8—521no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—522no—
771C22—522no—
772C22—522no—
773C22—1041no—
774C22—1041no—
775C22—1041no—
776C22—1041no—
777C22C2×C4×C22⋊D1311yescharacteristic
778C22#1171949611yescharacteristic
779C22#1171954011yescharacteristic
780C22#1171954011yescharacteristic
781C22#1171954211yescharacteristic
782C22#1171954311yescharacteristic
783C22C2×#8820711yescharacteristic
784C4—22no—
785C4—22no—
786C4—22no—
787C4—24no—
788C4—41no—
789C4—42no—
790C4—42no—
791C4—41no—
792C4—522no—
793C4—1041no—
794C4—1041no—
795C4C2×C4×C22⋊D1311yescharacteristic
796C4C2×C4×C22⋊D1311yescharacteristic
797C4#1171949611yescharacteristic
798C4#1171949611yescharacteristic
799C2—42no—
800C2—44no—
801C2—1042no—
802C2C4×#8820711yescharacteristic
803C2#1312366411yescharacteristic
804C2#1312370911yescharacteristic
805C2#1312410411yescharacteristic
806C2#1312415111yescharacteristic
807C2#1312503511yescharacteristic
808C2#1312509811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC2×#11718899C2
cosocleC22×C4×C13C24
hypercenterC2×#520D13
hypocenterC13#21460
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
3. C2×C4×#6104C2semidirect
4. #13117529C2semidirect
5. #13115191C2semidirect
6. #13115184C2semidirect
7. #13115153C2semidirect
8. #13115090C2semidirect
9. #13115083C2semidirect
10. #13115024C2semidirect
11. #13114776C2semidirect
12. #13114661C2semidirect
13. C4×#88075C2semidirect
14. #13114602C2semidirect
15. C2×C13×#520C2semidirect
33. #11718899C4semidirect
69. C2×C13×#41C2×C4semidirect
84. C4×Q8×C13D4semidirect
90. C4×D4×C13D4semidirect
115. C2×#6106C2×C4semidirect
118. C2×#6104C2×C4semidirect
120. #88184C2×C4semidirect
138. #88075C2×C4semidirect
141. #88072C2×C4semidirect
146. C22⋊#1055C2×C4semidirect
264. C2×#520D13semidirect
463. C2×#41C4×D13semidirect
490. C4×Q8C22⋊D13semidirect
498. C4×D4C22⋊D13semidirect
667. C13#21460semidirect

Maximal subgroups

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

subgroupindex
C2×#117188992
C2×#117186872
C2×C4×#61042
#131175292
#131151912
#131151842
#131151532
#131150902
#131150832
#131150242
#131147762
#131146612
C4×#880752
#131146022
C2×C13×#5202
#2146013