Finite Group Databasebeta

← #15883177

Subgroups — #15883177

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718707C211yesmaximal, characteristic
2C2×#11718687C211yesmaximal, characteristic, complemented
3C22×#88049C211yesmaximal, characteristic
4C22⋊C4×D52C211yesmaximal, characteristic
5#13115720C211yesmaximal, characteristic, complemented
6#13115532C211yesmaximal, characteristic, complemented
7#13115456C211yesmaximal, characteristic, complemented
8#13115260C211yesmaximal, characteristic, complemented
9#13115191C211yesmaximal, characteristic, complemented
10#13115173C211yesmaximal, characteristic, complemented
11#13115082C211yesmaximal, characteristic, complemented
12#13115024C211yesmaximal, characteristic, complemented
13#13114664C211yesmaximal, characteristic, complemented
14#13114614C211yesmaximal, characteristic, complemented
15C13×#2360C211yesmaximal, characteristic, complemented
16C23×D52C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic, complemented
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×#6106C2211yescharacteristic
21C22×#6106C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C22⋊C4×D13—21no—
24C2×C4×D52C2211yescharacteristic
25C2×C4×D52C2211yescharacteristic
26C13×#391C2211yescharacteristic, complemented
27C13×#389—21no—
28C13×#389C2211yescharacteristic, complemented
29C13×#387—21no—
30C13×#385—21no—
31C4×C13×C4⋊C4C2211yescharacteristic, complemented
32C4×C13×C22⋊C4—21no—
33C4×C13×C22⋊C4C2211yescharacteristic
34C2×#88075C2211yescharacteristic, complemented
35C2×#88075C2211yescharacteristic, complemented
36#11718873C2211yescharacteristic
37C2×C22⋊#1055C2211yescharacteristic
38#11718707C418yescomplemented
39#11718687—24no—
40C2×#88049—24no—
41C2×#88049C2211yescharacteristic
42C2×#88049C2211yescharacteristic
43C2×#88049C2211yescharacteristic
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88047C2211yescharacteristic, complemented
48C2×#88047C2211yescharacteristic, complemented
49#11718616—21no—
50#11718600C2211yescharacteristic
51#11718600C2211yescharacteristic
52C2×#88043C2211yescharacteristic, complemented
53C2×#88043C2211yescharacteristic, complemented
54#11718326—21no—
55#11718326—21no—
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718121C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61#11718116C2211yescharacteristic, complemented
62C24×D13—21no—
63C22×Q8×C13C2311yescharacteristic
64C23×C4×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C22×D52—22no—
67C22×D52—22no—
68C22×D52—21no—
69C22×D52—22no—
70C22×D52—41no—
71C22×D52—41no—
72C22×D52C2×C414yes—
73C22×D52C2311yescharacteristic
74C22×D52C2311yescharacteristic
75C22×C4×D13—21no—
76C22×C4×D13—21no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8C2×C414yescomplemented
79C4×Q8×C13—22no—
80C4×Q8×C13—41no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C42×C13—21no—
94C2×C42×C13—21no—
95C2×C42×C13C2311yescharacteristic
96C2×C42×C13C2311yescharacteristic
97C2×C22⋊Dic13—21no—
98C2×#6106—22no—
99C2×#6106—22no—
100C2×#6106—41no—
101C2×#6106—41no—
102C2×#6106C2×C414yescomplemented
103C2×#6106C2×C414yescomplemented
104C2×#6103—21no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103—21no—
108C2×#6103—21no—
109C2×#6103—21no—
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C22×#1055—22no—
113C22×#1055—22no—
114C22×#1055—41no—
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C22⋊C4×D13—44no—
120C4×D52—22no—
121C4×D52—22no—
122C4×D52—41no—
123C4×D52—41no—
124C13×#95—21no—
125C13×#95—21no—
126C13×#95—21no—
127C13×#95—21no—
128C13×#95D411yescharacteristic
129C13×#95D411yescharacteristic
130#88075—22no—
131#88075—41no—
132#88071—21no—
133C22⋊#1055C2×C414yescomplemented
134#88049—22no—
135#88049—22no—
136#88049—22no—
137#88049C2×C414yescomplemented
138#88049C2×C414yescomplemented
139#88049D414yes—
140#88047—22no—
141#88047—41no—
142#88043—22no—
143#88043—41no—
144#22854—131nomaximal, Sylow
145C24×C13C2×D411yescharacteristic
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—24no—
149C23×D13—42no—
150C23×D13—42no—
151C23×D13—42no—
152C23×D13—42no—
153C23×D13—81no—
154C23×D13—81no—
155C2×Q8×C13—21no—
156C2×Q8×C13—21no—
157C2×Q8×C13—21no—
158C2×Q8×C13—21no—
159C2×Q8×C13—21no—
160C2×Q8×C13C22×C412yes—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—42no—
170C22×C4×C13—42no—
171C22×C4×C13—81no—
172C22×C4×C13C22×C412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13#4112yes—
179C22×C4×C13C2411yescharacteristic
180C22×Dic13—21no—
181C22×Dic13—21no—
182C2×D52—21no—
183C2×D52—21no—
184C2×D52—21no—
185C2×D52—21no—
186C2×D52—21no—
187C2×D52—21no—
188C2×D52—21no—
189C2×D52—28no—
190C2×D52—24no—
191C2×D52—21no—
192C2×D52—44no—
193C2×D52—44no—
194C2×D52—44no—
195C2×D52—42no—
196C2×D52—42no—
197C2×D52C22×C412yes—
198C2×D52C22×C412yes—
199C2×D52C2×D412yes—
200C2×D52#4112yes—
201C2×C4×D13—42no—
202C2×C4×D13—42no—
203C2×C4×D13—42no—
204C2×C4×D13—42no—
205C2×C4×D13—81no—
206C2×C4×D13—81no—
207C13×C4⋊C4—24no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4—21no—
212C13×C4⋊C4—42no—
213C13×C4⋊C4—42no—
214C13×C4⋊C4—81no—
215C13×C4⋊C4C22×C412yes—
216C13×C4⋊C4C2×D412yes—
217C13×C22⋊C4—24no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C42×C13—21no—
221C42×C13—21no—
222C42×C13—21no—
223C42×C13—21no—
224C42×C13—42no—
225C42×C13—81no—
226C22⋊Dic13—42no—
227#6106—28no—
228#6106—44no—
229#6103—42no—
230#6103—42no—
231#6103—42no—
232#6103—42no—
233#6103—81no—
234#6103—81no—
235C4⋊Dic13—21no—
236C4⋊Dic13—21no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—44no—
249C2×#1055C22×C412yes—
250C2×#1055C22×C412yes—
251C2×#1055C2×D412yes—
252C2×#450—131no—
253C2×#440—131no—
254C22×#102—131no—
255#2360D1311yescharacteristic, complemented
256D4×C22⋊C4—131no—
257#1973—131no—
258#1936—131no—
259#1925—131no—
260#1892—131no—
261#1880—131no—
262#1877—131no—
263#1862—131no—
264#1852—131no—
265#1762—131no—
266#1752—131no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13C4×D412yes—
272C23×C13AGL(1,ℤ/8)12yes—
273C23×C13#13712yes—
274C23×C13C22×D411yescharacteristic
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—48no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288C22×D13—41no—
289C22×D13—41no—
290C22×D13—48no—
291C22×D13—84no—
292C22×D13—84no—
293C22×D13—84no—
294C22×D13—84no—
295C22×D13—84no—
296Q8×C13—22no—
297Q8×C13—22no—
298Q8×C13—41no—
299Q8×C13—41no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—22no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—84no—
331C2×C4×C13C4×D412yes—
332C2×C4×C13C23×C411yescharacteristic
333C2×C4×C13C22×D411yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13H(5,𝔽2)11yescharacteristic
337C2×C4×C13H(5,𝔽2)11yescharacteristic
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344D52—22no—
345D52—22no—
346D52—22no—
347D52—22no—
348D52—22no—
349D52—48no—
350D52—41no—
351D52—41no—
352D52C4×D414yes—
353C4×D13—84no—
354C4×D13—84no—
355#1055—22no—
356#1055—22no—
357#1055—22no—
358#1055—41no—
359C23×D4—131no—
360C22×SD16—131no—
361C22×SD16—131no—
362C23×C8—131no—
363C2×C22⋊Q8C2×D1311yescharacteristic
364C2×C4×Q8C2×D1311yescharacteristic, complemented
365C2×C4×D4—131no—
366C2×C4×D4—131no—
367C22×C4⋊C4C2×D1311yescharacteristic
368C22×C22⋊C4—261no—
369#450—138no—
370#440—264no—
371C2×#107—131no—
372C2×#107—131no—
373C2×#103—131no—
374C2×#103—131no—
375C2×#102—131no—
376C2×#102—131no—
377C2×#102—131no—
378C2×#102—131no—
379C2×#102—131no—
380C2×#102—131no—
381C2×#102—264no—
382C2×C22⋊C8—131no—
383C2×#97—131no—
384C2×#97—131no—
385#391C2×D1311yescharacteristic, complemented
386#390—131no—
387#390—131no—
388#389—21no—
389#389C2×D1311yescharacteristic, complemented
390#387—21no—
391#386—261no—
392#386—261no—
393#385—21no—
394#380—131no—
395#379—261no—
396C4×C4⋊C4C2×D1311yescharacteristic, complemented
397C4×C22⋊C4—21no—
398C4×C22⋊C4C2×D1311yescharacteristic
399#340—131no—
400#340—131no—
401#340—131no—
402#340—131no—
403#336—131no—
404#336—131no—
405C22×C13—22no—
406C22×C13—22no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—22no—
411C22×C13#44014yescomplemented
412C22×C13C2×C4×D411yescharacteristic
413C22×C13D4211yescharacteristic
414C22×C13#54611yescharacteristic
415C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C13C2×#13711yescharacteristic
417C22×C13#57611yescharacteristic
418C22×C13#57711yescharacteristic
419C2×D13—24no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—42no—
429C2×D13—816no—
430C2×D13—81no—
431C2×D13—81no—
432C2×D13—81no—
433C2×D13—81no—
434C4×C13—22no—
435C4×C13—42no—
436C4×C13—42no—
437C4×C13—41no—
438C4×C13—42no—
439C4×C13—41no—
440C4×C13—41no—
441C4×C13—41no—
442C4×C13—81no—
443C4×C13C2×C4×D411yescharacteristic
444C4×C13#51811yescharacteristic
445C4×C13#54611yescharacteristic
446C4×C13#55111yescharacteristic
447Dic13—81no—
448Dic13—81no—
449C25—261no—
450C22×Q8C22×D1311yescharacteristic
451C22×D4—134no—
452C22×D4—131no—
453C22×D4—131no—
454C22×D4—262no—
455C22×D4—262no—
456C22×D4—262no—
457C22×D4—261no—
458C22×D4—521no—
459C22×D4—521no—
460C23×C4—21no—
461C23×C4—261no—
462C23×C4—261no—
463C23×C4C22×D1311yescharacteristic
464C2×SD16—134no—
465C2×SD16—134no—
466C2×SD16—262no—
467C2×SD16—262no—
468C2×SD16—521no—
469C2×SD16—521no—
470C22×C8—131no—
471C22×C8—131no—
472C22×C8—131no—
473C22×C8—131no—
474C22×C8—262no—
475C22×C8—262no—
476C22×C8—521no—
477C22⋊Q8—22no—
478C22⋊Q8C4×D1314yescomplemented
479C4×Q8—22no—
480C4×Q8—41no—
481C4×D4—262no—
482C4×D4—262no—
483C4×D4—521no—
484C4×D4—521no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—131no—
493C2×C4⋊C4C22×D1311yescharacteristic
494C2×C4⋊C4C22×D1311yescharacteristic
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4—261no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4—261no—
503C2×C22⋊C4—261no—
504C2×C22⋊C4—524no—
505C2×C22⋊C4C22⋊D1311yescharacteristic
506C2×C22⋊C4C22⋊D1311yescharacteristic
507C2×C42—21no—
508C2×C42—21no—
509C2×C42C22×D1311yescharacteristic
510C2×C42C22×D1311yescharacteristic
511#107—262no—
512#107—521no—
513#103—262no—
514#103—521no—
515#102—134no—
516#102—134no—
517#102—134no—
518#102—262no—
519#102—262no—
520#102—262no—
521C22⋊C8—134no—
522#97—262no—
523#97—521no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—261no—
529#95C22⋊D1311yescharacteristic
530#95C22⋊D1311yescharacteristic
531C2×C13—24no—
532C2×C13#235811yescharacteristic
533C2×C13C2×#44011yescharacteristic
534C2×C13#294611yescharacteristic
535C2×C13#326411yescharacteristic
536C2×C13#326611yescharacteristic
537C2×C13#331011yescharacteristic
538C2×C13#331411yescharacteristic
539D13—44no—
540D13—82no—
541C24—261no—
542C24—261no—
543C24—264no—
544C24—522no—
545C24—522no—
546C24—522no—
547C24—522no—
548C24—1041no—
549C24—1041no—
550C24C2×C22⋊D1311yescharacteristic
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8C2×C4×D1312yes—
557C2×D4—132no—
558C2×D4—132no—
559C2×D4—132no—
560C2×D4—132no—
561C2×D4—268no—
562C2×D4—264no—
563C2×D4—261no—
564C2×D4—261no—
565C2×D4—261no—
566C2×D4—261no—
567C2×D4—261no—
568C2×D4—261no—
569C2×D4—261no—
570C2×D4—261no—
571C2×D4—524no—
572C2×D4—524no—
573C2×D4—524no—
574C2×D4—522no—
575C2×D4—522no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—522no—
590C22×C4—522no—
591C22×C4—522no—
592C22×C4—522no—
593C22×C4—1041no—
594C22×C4—1041no—
595C22×C4C2×C4×D1312yes—
596C22×C4#612712yes—
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C23×D1311yescharacteristic
603SD16—268no—
604SD16—524no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—261no—
611C2×C8—261no—
612C2×C8—261no—
613C2×C8—261no—
614C2×C8—261no—
615C2×C8—261no—
616C2×C8—261no—
617C2×C8—524no—
618C4⋊C4—24no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—81no—
626C4⋊C4—261no—
627C4⋊C4—261no—
628C4⋊C4—261no—
629C4⋊C4—261no—
630C4⋊C4C2×C4×D1312yes—
631C4⋊C4D4×D1312yes—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—522no—
636C22⋊C4—522no—
637C22⋊C4—522no—
638C22⋊C4—522no—
639C22⋊C4—522no—
640C22⋊C4—1041no—
641C22⋊C4—1041no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—42no—
647C42—81no—
648C13#2285411yescharacteristic, complemented, Sylow
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—262no—
654C23—262no—
655C23—262no—
656C23—262no—
657C23—528no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—528no—
663C23—521no—
664C23—521no—
665C23—521no—
666C23—521no—
667C23—521no—
668C23—521no—
669C23—1044no—
670C23—1044no—
671C23—1044no—
672C23—1044no—
673C23—1044no—
674C23C4×C22⋊D1312yes—
675C23#8819612yes—
676C23#8820312yes—
677C23C22×C22⋊D1311yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—134no—
683D4—262no—
684D4—262no—
685D4—262no—
686D4—262no—
687D4—262no—
688D4—528no—
689D4—521no—
690D4—521no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—84no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—1044no—
729C2×C4—1044no—
730C2×C4C4×C22⋊D1312yes—
731C2×C4C22×C4×D1311yescharacteristic
732C2×C4C2×#612711yescharacteristic
733C2×C4C2×D4×D1311yescharacteristic
734C2×C4#8825111yescharacteristic
735C2×C4#41×D1311yescharacteristic
736C2×C4#8825611yescharacteristic
737C8—262no—
738C8—262no—
739C8—262no—
740C8—521no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—264no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—10416no—
758C22—1041no—
759C22—1041no—
760C22—1041no—
761C22—1041no—
762C22#1171868714yescomplemented
763C22C2×C4×C22⋊D1311yescharacteristic
764C22D4×C22⋊D1311yescharacteristic
765C22C2×#8819611yescharacteristic
766C22C2×#8820311yescharacteristic
767C22#1171953411yescharacteristic
768C22#1171954011yescharacteristic
769C22#1171954211yescharacteristic
770C4—22no—
771C4—42no—
772C4—42no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—81no—
779C4—1041no—
780C4—1041no—
781C4C4×D4×D1311yescharacteristic
782C4#1171925011yescharacteristic
783C4#1171925511yescharacteristic
784C4#1171926111yescharacteristic
785C2—24no—
786C2—524no—
787C2—1042no—
788C2#1311781311yescharacteristic
789C2C2×#1171868711yescharacteristic
790C2#1312366411yescharacteristic
791C2#1312631711yescharacteristic
792C2#1312634711yescharacteristic
793C2#1312685111yescharacteristic
794C2#1312691111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2360C2
socleC23×C13C22×D4
prime radicalC23×D52C22
cosocleC22×C4×C13C24
hypercenter#2360D13
hypocenterC13#22854
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. C2×#11718687C2semidirect
5. #13115720C2semidirect
6. #13115532C2semidirect
7. #13115456C2semidirect
8. #13115260C2semidirect
9. #13115191C2semidirect
10. #13115173C2semidirect
11. #13115082C2semidirect
12. #13115024C2semidirect
13. #13114664C2semidirect
14. #13114614C2semidirect
15. C13×#2360C2semidirect
18. C2×C4×Q8×C13C22semidirect
26. C13×#391C22semidirect
28. C13×#389C22semidirect
31. C4×C13×C4⋊C4C22semidirect
34. C2×#88075C22semidirect
35. C2×#88075C22semidirect
38. #11718707C4semidirect
47. C2×#88047C22semidirect
48. C2×#88047C22semidirect
52. C2×#88043C22semidirect
53. C2×#88043C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718121C22semidirect
60. #11718116C22semidirect
61. #11718116C22semidirect
78. C13×C22⋊Q8C2×C4semidirect
102. C2×#6106C2×C4semidirect
103. C2×#6106C2×C4semidirect
133. C22⋊#1055C2×C4semidirect
137. #88049C2×C4semidirect
138. #88049C2×C4semidirect
255. #2360D13semidirect
364. C2×C4×Q8C2×D13semidirect
385. #391C2×D13semidirect
389. #389C2×D13semidirect
396. C4×C4⋊C4C2×D13semidirect
411. C22×C13#440semidirect
478. C22⋊Q8C4×D13semidirect
648. C13#22854semidirect
762. C22#11718687semidirect

Maximal subgroups

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

subgroupindex
C2×#117187072
C2×#117186872
C22×#880492
C22⋊C4×D522
#131157202
#131155322
#131154562
#131152602
#131151912
#131151732
#131150822
#131150242
#131146642
#131146142
C13×#23602
#2285413