Finite Group Databasebeta

← #15920096

Subgroups — #15920096

Order 3328.

1206 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718669C211yesmaximal, characteristic, complemented
2C22×#88072C211yesmaximal, characteristic
3#13118538C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic, complemented
5#13116210C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13115972C211yesmaximal, characteristic, complemented
8#13115097C211yesmaximal, characteristic, complemented
9#13115097C211yesmaximal, characteristic, complemented
10#13115028C211yesmaximal, characteristic, complemented
11#13115016C211yesmaximal, characteristic, complemented
12#13114859C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic, complemented
14#13114767C211yesmaximal, characteristic
15D4×C13×C22⋊C4C211yesmaximal, characteristic
16C23×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C22⋊C4—21no—
20C22×C4⋊Dic13C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88132—21no—
23C2×#88123C2211yescharacteristic, complemented
24C13×#390C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C13×#386—21no—
27C13×#386—21no—
28C13×#380C2211yescharacteristic
29C13×#379—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88072—24no—
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40#11718873C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718669—24no—
43C2×#88048C2211yescharacteristic, complemented
44C2×#88048C2211yescharacteristic, complemented
45C2×#88048C2211yescharacteristic, complemented
46C2×#88048C2211yescharacteristic, complemented
47#11718611—21no—
48#11718596C2211yescharacteristic, complemented
49#11718589C2211yescharacteristic, complemented
50#11718589C2211yescharacteristic, complemented
51C2×C4⋊#1055C2211yescharacteristic, complemented
52C2×C4⋊#1055C2211yescharacteristic, complemented
53#11718322—21no—
54#11718317—21no—
55#11718121C2211yescharacteristic, complemented
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718116C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61C25×C13—21no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—21no—
65C22×D4×C13—22no—
66C22×D4×C13—41no—
67C22×D4×C13—41no—
68C22×D4×C13Q814yescomplemented
69C22×D4×C13C2311yescharacteristic
70C22×D4×C13C2311yescharacteristic
71C23×C4×C13—21no—
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C23×Dic13—21no—
75C22×Dic26—21no—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C4×D4×C13—41no—
79C4×D4×C13—41no—
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—44no—
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C22⋊Dic13—21no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13—21no—
100C2×C4⋊Dic13—41no—
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4⋊Dic13C2311yescharacteristic
105C2×#6101—21no—
106C2×#6101—21no—
107C22×#1055—22no—
108C22×#1055—22no—
109C22×#1055—41no—
110C22×#1055C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114#88132—44no—
115#88123—22no—
116#88123—41no—
117C13×#95—21no—
118C13×#95D411yescharacteristic
119C13×#95D411yescharacteristic
120#88072—22no—
121#88072—22no—
122#88072—22no—
123#88072—22no—
124#88072—22no—
125#88072—41no—
126#88072—41no—
127#88072D414yes—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131C22⋊#1055—22no—
132#88048—22no—
133#88048—22no—
134#88048—41no—
135#88048—41no—
136C4⋊#1055—22no—
137C4⋊#1055—41no—
138#25958—131nomaximal, Sylow
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—24no—
142C24×C13—42no—
143C24×C13—42no—
144C24×C13—42no—
145C24×C13—42no—
146C24×C13—81no—
147C24×C13—81no—
148C24×C13C2×D411yescharacteristic
149C2×D4×C13—28no—
150C2×D4×C13—24no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—44no—
160C2×D4×C13—44no—
161C2×D4×C13—44no—
162C2×D4×C13—42no—
163C2×D4×C13—42no—
164C2×D4×C13C2×D412yes—
165C2×D4×C13C2×Q812yes—
166C2×D4×C13C2×Q812yes—
167C2×D4×C13#4112yes—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—42no—
175C22×C4×C13—42no—
176C22×C4×C13—42no—
177C22×C4×C13—42no—
178C22×C4×C13—81no—
179C22×C4×C13—81no—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×Q812yes—
186C22×C4×C13#4112yes—
187C22×C4×C13C2411yescharacteristic
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—42no—
193C22×Dic13—42no—
194C22×Dic13—81no—
195C2×Dic26—42no—
196C2×Dic26—42no—
197C2×Dic26—81no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—42no—
204C13×C22⋊C4—42no—
205C13×C22⋊C4—42no—
206C13×C22⋊C4—42no—
207C13×C22⋊C4—42no—
208C13×C22⋊C4—81no—
209C13×C22⋊C4—81no—
210C13×C22⋊C4SD1614yes—
211C42×C13—21no—
212C42×C13—21no—
213C42×C13—21no—
214C42×C13—21no—
215C22⋊Dic13—42no—
216C4⋊Dic13—21no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—42no—
224C4⋊Dic13—42no—
225C4⋊Dic13—42no—
226C4⋊Dic13—81no—
227C4⋊Dic13C2×D412yes—
228#6101—42no—
229#6101—42no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—44no—
242C2×#1055C2×D412yes—
243C2×#476—131no—
244C22×#102—131no—
245#2440—131no—
246D4×C22⋊C4D1311yescharacteristic
247#2094—131no—
248#2065—131no—
249#2065—131no—
250#2023—131no—
251#1864—131no—
252#1864—131no—
253#1853—131no—
254#1850—131no—
255#1807—131no—
256#1802—131no—
257#1786—131no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—48no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—48no—
278C23×C13—84no—
279C23×C13—84no—
280C23×C13—84no—
281C23×C13—84no—
282C23×C13—84no—
283C23×C13C22⋊Q812yes—
284C23×C13C2×SD1612yes—
285C23×C13AGL(1,ℤ/8)12yes—
286C23×C13C22×D411yescharacteristic
287D4×C13—22no—
288D4×C13—22no—
289D4×C13—22no—
290D4×C13—22no—
291D4×C13—22no—
292D4×C13—48no—
293D4×C13—41no—
294D4×C13—41no—
295D4×C13C22⋊Q814yescomplemented
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
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—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—84no—
319C2×C4×C13—84no—
320C2×C4×C13C22⋊Q812yes—
321C2×C4×C13C2×SD1612yes—
322C2×C4×C13C2×SD1612yes—
323C2×C4×C13C22×D411yescharacteristic
324C2×C4×C13C22×Q811yescharacteristic
325C2×C4×C13C2×#4111yescharacteristic
326C2×C4×C13C2×#4111yescharacteristic
327C2×C4×C13H(5,𝔽2)11yescharacteristic
328C2×C4×C13H(5,𝔽2)11yescharacteristic
329C2×Dic13—22no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—84no—
342Dic26—84no—
343#1055—22no—
344#1055—41no—
345#1055—41no—
346#1055—41no—
347C23×D4C2×D1311yescharacteristic
348C23×C8—131no—
349C2×C4⋊Q8—131no—
350C2×C22⋊Q8—261no—
351C2×C4×D4C2×D1311yescharacteristic
352C2×C4×D4C2×D1311yescharacteristic
353C22×C4⋊C4—131no—
354C22×C22⋊C4—21no—
355#476—264no—
356C2×#106—131no—
357C2×#106—131no—
358C2×#106—131no—
359C2×#106—131no—
360C2×C4⋊C8—131no—
361C2×C4⋊C8—131no—
362C2×#102—131no—
363C2×#102—131no—
364C2×#102—131no—
365C2×#102—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×#102—131no—
369C2×#102—131no—
370C2×#102—264no—
371C2×C22⋊C8—131no—
372#398—261no—
373#395—261no—
374#390C2×D1311yescharacteristic
375#390C2×D1311yescharacteristic
376#389—131no—
377#389—131no—
378#386—21no—
379#386—21no—
380#385—261no—
381#384—131no—
382#380—131no—
383#380C2×D1311yescharacteristic
384#379—21no—
385C4×C22⋊C4C2×D1311yescharacteristic
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#336—131no—
391#336—131no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—24no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—816no—
409C22×C13—81no—
410C22×C13—81no—
411C22×C13—81no—
412C22×C13—81no—
413C22×C13#47614yescomplemented
414C22×C13C2×C22⋊Q811yescharacteristic
415C22×C13D4211yescharacteristic
416C22×C13#54611yescharacteristic
417C22×C13C22×SD1611yescharacteristic
418C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
419C22×C13#57611yescharacteristic
420C22×C13#57711yescharacteristic
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—41no—
425C4×C13—41no—
426C4×C13—81no—
427C4×C13—81no—
428C4×C13C2×C22⋊Q811yescharacteristic
429C4×C13#54311yescharacteristic
430C4×C13#54611yescharacteristic
431C4×C13#55111yescharacteristic
432Dic13—42no—
433Dic13—81no—
434Dic13—81no—
435Dic13—81no—
436C25—21no—
437C22×Q8—261no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—21no—
442C22×D4—41no—
443C22×D4—41no—
444C22×D4Dic2614yescomplemented
445C22×D4C22×D1311yescharacteristic
446C22×D4C22×D1311yescharacteristic
447C23×C4—21no—
448C23×C4—21no—
449C23×C4—261no—
450C23×C4C22×D1311yescharacteristic
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—262no—
456C22×C8—262no—
457C22×C8—521no—
458C4⋊Q8—262no—
459C4⋊Q8—521no—
460C22⋊Q8—524no—
461C4×D4—22no—
462C4×D4—22no—
463C4×D4—41no—
464C4×D4—41no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4—261no—
475C2×C4⋊C4—261no—
476C2×C4⋊C4—521no—
477C2×C4⋊C4C22×D1311yescharacteristic
478C2×C4⋊C4C22×D1311yescharacteristic
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—44no—
487C2×C22⋊C4—261no—
488C2×C22⋊C4C22⋊D1311yescharacteristic
489C2×C22⋊C4C22⋊D1311yescharacteristic
490C2×C42C22×D1311yescharacteristic
491C2×C42C22×D1311yescharacteristic
492#106—262no—
493#106—262no—
494#106—521no—
495#106—521no—
496C4⋊C8—262no—
497C4⋊C8—521no—
498#102—134no—
499#102—262no—
500#102—262no—
501#102—262no—
502#102—262no—
503#102—262no—
504#102—521no—
505#102—521no—
506C22⋊C8—262no—
507#95—21no—
508#95—261no—
509#95—261no—
510#95—261no—
511#95C22⋊D1311yescharacteristic
512#95C22⋊D1311yescharacteristic
513C2×C13—24no—
514C2×C13—44no—
515C2×C13—82no—
516C2×C13#243711yescharacteristic
517C2×C13C2×#47611yescharacteristic
518C2×C13#308111yescharacteristic
519C2×C13#326411yescharacteristic
520C2×C13D4×SD1611yescharacteristic
521C2×C13#329511yescharacteristic
522C2×C13#330611yescharacteristic
523C24—21no—
524C24—21no—
525C24—24no—
526C24—42no—
527C24—42no—
528C24—42no—
529C24—42no—
530C24—81no—
531C24—81no—
532C24C2×C22⋊D1311yescharacteristic
533C2×Q8—522no—
534C2×Q8—522no—
535C2×Q8—1041no—
536C2×D4—28no—
537C2×D4—24no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—42no—
550C2×D4—42no—
551C2×D4C2×Dic2612yes—
552C2×D4C2×Dic2612yes—
553C2×D4D4×D1312yes—
554C2×D4#612912yes—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—81no—
566C22×C4—81no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—522no—
572C22×C4—522no—
573C22×C4—1041no—
574C22×C4C2×Dic2612yes—
575C22×C4#612712yes—
576C22×C4C2×C22⋊D1311yescharacteristic
577C22×C4C2×C22⋊D1311yescharacteristic
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C23×D1311yescharacteristic
582C2×C8—132no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—524no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—132no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—261no—
606C4⋊C4—261no—
607C4⋊C4—522no—
608C4⋊C4—522no—
609C4⋊C4—522no—
610C4⋊C4—522no—
611C4⋊C4—522no—
612C4⋊C4—1041no—
613C22⋊C4—22no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—81no—
620C22⋊C4—81no—
621C22⋊C4—522no—
622C22⋊C4#610514yes—
623C42—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C13#2595811yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—48no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—48no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#8817812yes—
654C23C2×#610512yes—
655C23#8820312yes—
656C23C22×C22⋊D1311yescharacteristic
657Q8—1044no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—41no—
665D4—41no—
666D4#8813214yescomplemented
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4—262no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—521no—
695C2×C4—521no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—1044no—
704C2×C4#8817812yes—
705C2×C4C2×#610512yes—
706C2×C4C2×#610512yes—
707C2×C4C22×Dic2611yescharacteristic
708C2×C4C2×#612711yescharacteristic
709C2×C4C2×D4×D1311yescharacteristic
710C2×C4C2×#612911yescharacteristic
711C2×C4#8825111yescharacteristic
712C2×C4#8825111yescharacteristic
713C8—262no—
714C8—521no—
715C8—521no—
716C8—521no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—816no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22#1171866914yescomplemented
739C22C2×#8817811yescharacteristic
740C22C22×#610511yescharacteristic
741C22D4×C22⋊D1311yescharacteristic
742C22#1171951111yescharacteristic
743C22C2×#8820311yescharacteristic
744C22#1171954011yescharacteristic
745C22#1171954111yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—41no—
750C4—41no—
751C4—81no—
752C4—81no—
753C4—522no—
754C4—1041no—
755C4—1041no—
756C4—1041no—
757C4C2×#8813211yescharacteristic
758C4#1171918811yescharacteristic
759C4#1171919511yescharacteristic
760C4#1171920011yescharacteristic
761C2—24no—
762C2—44no—
763C2—82no—
764C2#1311849711yescharacteristic
765C2C2×#1171866911yescharacteristic
766C2#1312466711yescharacteristic
767C2#1312631711yescharacteristic
768C2D4×#610511yescharacteristic
769C2#1312666011yescharacteristic
770C2#1312679711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
hypercenterD4×C22⋊C4D13
hypocenterC13#25958
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718669C2semidirect
3. #13118538C2semidirect
4. #13116369C2semidirect
5. #13116210C2semidirect
6. #13116210C2semidirect
7. #13115972C2semidirect
8. #13115097C2semidirect
9. #13115097C2semidirect
10. #13115028C2semidirect
11. #13115016C2semidirect
12. #13114859C2semidirect
13. #13114836C2semidirect
23. C2×#88123C22semidirect
43. C2×#88048C22semidirect
44. C2×#88048C22semidirect
45. C2×#88048C22semidirect
46. C2×#88048C22semidirect
48. #11718596C22semidirect
49. #11718589C22semidirect
50. #11718589C22semidirect
51. C2×C4⋊#1055C22semidirect
52. C2×C4⋊#1055C22semidirect
55. #11718121C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718116C22semidirect
60. #11718116C22semidirect
68. C22×D4×C13Q8semidirect
295. D4×C13C22⋊Q8semidirect
413. C22×C13#476semidirect
444. C22×D4Dic26semidirect
627. C13#25958semidirect
666. D4#88132semidirect
738. C22#11718669semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
C22×#880722
#131185382
#131163692
#131162102
#131159722
#131150972
#131150282
#131150162
#131148592
#131148362
#131147672
D4×C13×C22⋊C42
#2595813