Finite Group Databasebeta

← #15896939

Subgroups — #15896939

Order 3328.

1088 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718724C211yesmaximal, characteristic, complemented
2C2×C4×#6107C211yesmaximal, characteristic, complemented
3#13119745C211yesmaximal, characteristic
4#13116036C211yesmaximal, characteristic, complemented
5#13116029C211yesmaximal, characteristic, complemented
6#13115844C211yesmaximal, characteristic, complemented
7#13115844C211yesmaximal, characteristic, complemented
8#13115802C211yesmaximal, characteristic, complemented
9#13115631C211yesmaximal, characteristic
10#13115148C211yesmaximal, characteristic, complemented
11#13115143C211yesmaximal, characteristic, complemented
12#13115035C211yesmaximal, characteristic, complemented
13#13115024C211yesmaximal, characteristic, complemented
14#13114851C211yesmaximal, characteristic, complemented
15C2×C13×#552C211yesmaximal, characteristic
16C13×#552—24no—
17C13×#552—24no—
18C2×C13×#126—21no—
19C2×C13×#125—21no—
20C2×C13×#125C2211yescharacteristic
21C2×C13×#123—21no—
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C2×#88178C2211yescharacteristic
31C2×#88178C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36#11718883—21no—
37#11718873C2211yescharacteristic
38#11718873C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718724—24no—
44C4×#6107—24no—
45#11718641—21no—
46C2×#88050C2211yescharacteristic
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51C2×#88047C2211yescharacteristic
52#11718605—21no—
53#11718605—21no—
54#11718597C2211yescharacteristic
55C2×C4⋊#1055C2211yescharacteristic
56C2×C4×#1055C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63C22×Q8×C13C2311yescharacteristic
64C22×D4×C13D411yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C22×Dic26C2311yescharacteristic
69C13×#126—28no—
70C13×#125—28no—
71C13×#125—22no—
72C13×#125D414yes—
73C13×#123—28no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—22no—
78C4×Q8×C13—22no—
79C4×Q8×C13D414yes—
80C4×D4×C13—22no—
81C4×D4×C13—22no—
82C13×#117—28no—
83C13×#117—22no—
84C13×#117—22no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C42×C13—21no—
103C2×C42×C13—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13—21no—
109C2×#6107—22no—
110C2×#6107—22no—
111C2×#6107—22no—
112C2×C4⋊Dic13C2311yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115#88178—22no—
116#88178—22no—
117#88178—41no—
118#88178—41no—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×C4×Dic13—21no—
123C22×#1055C2311yescharacteristic
124C22×#1055C2311yescharacteristic
125C22×#1055C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C4×Dic26—22no—
128C4×Dic26—22no—
129#88075—22no—
130#88075—41no—
131#88075—41no—
132#88071—21no—
133#88071—21no—
134#88071—21no—
135#88071—21no—
136C22⋊#1055—22no—
137C22⋊#1055—22no—
138C22⋊#1055—41no—
139C22⋊#1055—41no—
140#88050—22no—
141#88050—22no—
142#88050—22no—
143#88048—22no—
144#88047—22no—
145#88047—22no—
146C4⋊#1055—22no—
147C4×#1055—22no—
148#24127—131nomaximal, Sylow
149C24×C13C2×D411yescharacteristic
150C24×C13C2×D411yescharacteristic
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13C2×D412yes—
157C2×D4×C13—22no—
158C2×D4×C13—22no—
159C2×D4×C13—41no—
160C22×C4×C13—24no—
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—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—42no—
178C22×C4×C13—42no—
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2411yescharacteristic
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C2×Dic26—21no—
189C2×Dic26—21no—
190C2×Dic26—21no—
191C2×Dic26—21no—
192C2×Dic26—21no—
193C2×Dic26#4112yes—
194C13×C4⋊C4—24no—
195C13×C4⋊C4—24no—
196C13×C4⋊C4—24no—
197C13×C4⋊C4—24no—
198C13×C4⋊C4—24no—
199C13×C4⋊C4—24no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4C2×D412yes—
205C13×C4⋊C4C2×D412yes—
206C13×C4⋊C4C2×D412yes—
207C13×C22⋊C4—24no—
208C13×C22⋊C4—24no—
209C13×C22⋊C4—24no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C42×C13—24no—
213C42×C13—24no—
214C42×C13C2×D412yes—
215C42×C13C2×D412yes—
216C22⋊Dic13—42no—
217C22⋊Dic13—42no—
218C22⋊Dic13—42no—
219C22⋊Dic13—42no—
220#6107—28no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227#6101—42no—
228#6101—42no—
229#6101—42no—
230C4×Dic13—42no—
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—21no—
242C2×#1055#4112yes—
243C2×#552D1311yescharacteristic
244C2×#479—131no—
245C2×C4×Q16—131no—
246#2536—131no—
247#2036—131no—
248#2035—131no—
249#2001—131no—
250#2001—131no—
251#1991—131no—
252#1954—131no—
253#1873—131no—
254#1872—131no—
255#1854—131no—
256#1852—131no—
257#1805—131no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13#13512yes—
272C23×C13C22×D411yescharacteristic
273Q8×C13—22no—
274Q8×C13—22no—
275Q8×C13—41no—
276Q8×C13—41no—
277D4×C13—44no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—21no—
287C2×C4×C13—22no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—48no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13#12012yes—
310C2×C4×C13#12012yes—
311C2×C4×C13C22×D411yescharacteristic
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C2×#4111yescharacteristic
314C2×C4×C13C2×#4111yescharacteristic
315C2×C4×C13H(5,𝔽2)11yescharacteristic
316C2×C4×C132−1+411yescharacteristic
317C2×Dic13—22no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329Dic26—22no—
330Dic26—22no—
331Dic26—41no—
332Dic26—41no—
333#1055—22no—
334#1055—41no—
335#1055—41no—
336#1055—41no—
337C22×Q16—131no—
338#552—24no—
339#552—24no—
340C2×#126—21no—
341C2×#125—21no—
342C2×#125C2×D1311yescharacteristic
343C2×#123—21no—
344C2×C22⋊Q8—131no—
345C2×C22⋊Q8—131no—
346C2×C22⋊Q8C2×D1311yescharacteristic
347C2×C22⋊Q8C2×D1311yescharacteristic
348C2×C4×Q8—131no—
349C2×C4×Q8C2×D1311yescharacteristic
350C2×C4×D4C2×D1311yescharacteristic
351C2×#117—21no—
352C2×#117C2×D1311yescharacteristic
353C22×C4⋊C4C2×D1311yescharacteristic
354#479—264no—
355C4×Q16—264no—
356C2×#107—131no—
357C2×#107—131no—
358C2×#106—131no—
359C2×C4⋊C8—131no—
360C2×#103—131no—
361C2×#103—131no—
362C2×#103—131no—
363C2×#103—131no—
364C2×#103—131no—
365C2×#103—131no—
366C2×C22⋊C8—131no—
367C2×C22⋊C8—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×C4×C8—131no—
371#398—261no—
372#394—261no—
373#388—261no—
374#388—261no—
375#382—131no—
376#380—131no—
377#380—131no—
378#340—131no—
379#340—131no—
380#340—131no—
381#340—131no—
382#340—131no—
383#340—131no—
384C22×C13—22no—
385C22×C13—22no—
386C22×C13—22no—
387C22×C13—41no—
388C22×C13—41no—
389C22×C13—41no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—41no—
398C22×C13C2×#12011yescharacteristic
399C22×C13#54611yescharacteristic
400C22×C13#54711yescharacteristic
401C22×C13C2×#13511yescharacteristic
402C22×C13#57511yescharacteristic
403C22×C13#57811yescharacteristic
404C22×C13#57811yescharacteristic
405C4×C13—22no—
406C4×C13—22no—
407C4×C13—41no—
408C4×C13—41no—
409C4×C13—42no—
410C4×C13—42no—
411C4×C13—42no—
412C4×C13—42no—
413C4×C13#52511yescharacteristic
414C4×C13#53711yescharacteristic
415C4×C13#54811yescharacteristic
416C4×C13#55011yescharacteristic
417Dic13—42no—
418Dic13—81no—
419Dic13—81no—
420Dic13—81no—
421C22×Q8—131no—
422C22×Q8C22×D1311yescharacteristic
423C22×D4C22⋊D1311yescharacteristic
424C23×C4—21no—
425C23×C4C22×D1311yescharacteristic
426C23×C4C22×D1311yescharacteristic
427C2×Q16—262no—
428C2×Q16—262no—
429C2×Q16—262no—
430C22×C8—131no—
431C22×C8—131no—
432C22×C8—131no—
433C22×C8—131no—
434#126—28no—
435#125—28no—
436#125—22no—
437#125C22⋊D1314yes—
438#123—28no—
439C22⋊Q8—22no—
440C22⋊Q8—22no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—262no—
444C22⋊Q8—262no—
445C22⋊Q8—521no—
446C22⋊Q8—521no—
447C4×Q8—22no—
448C4×Q8—262no—
449C4×Q8—262no—
450C4×Q8C22⋊D1314yes—
451C4×D4—22no—
452C4×D4—22no—
453#117—28no—
454#117—22no—
455#117—22no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—131no—
466C2×C4⋊C4—131no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4—261no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4C22⋊D1311yescharacteristic
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C4⋊C4C22×D1311yescharacteristic
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—261no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4—261no—
481C2×C22⋊C4C22⋊D1311yescharacteristic
482C2×C22⋊C4C22⋊D1311yescharacteristic
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—261no—
486C2×C42C22×D1311yescharacteristic
487#107—262no—
488#107—262no—
489#106—262no—
490C4⋊C8—262no—
491#103—262no—
492#103—262no—
493#103—262no—
494#103—262no—
495#103—521no—
496#103—521no—
497C22⋊C8—262no—
498C22⋊C8—262no—
499C22⋊C8—521no—
500C22⋊C8—521no—
501C4×C8—262no—
502#95—261no—
503#95—261no—
504#95—261no—
505#95—261no—
506C2×C13—42no—
507C2×C13—81no—
508C2×C13#240711yescharacteristic
509C2×C13#300211yescharacteristic
510C2×C13#301111yescharacteristic
511C2×C13#330011yescharacteristic
512C2×C13#332711yescharacteristic
513C2×C13#333611yescharacteristic
514C2×C13#335211yescharacteristic
515C24C2×C22⋊D1311yescharacteristic
516C24C2×C22⋊D1311yescharacteristic
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—132no—
523C2×Q8—261no—
524C2×Q8—261no—
525C2×Q8—261no—
526C2×Q8—261no—
527C2×Q8—261no—
528C2×Q8C2×C22⋊D1312yes—
529C2×D4—22no—
530C2×D4—22no—
531C2×D4—41no—
532C22×C4—24no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4C2×C22⋊D1311yescharacteristic
556C22×C4C2×C22⋊D1311yescharacteristic
557C22×C4C2×C22⋊D1311yescharacteristic
558C22×C4C2×C22⋊D1311yescharacteristic
559C22×C4C23×D1311yescharacteristic
560Q16—268no—
561C2×C8—132no—
562C2×C8—261no—
563C2×C8—261no—
564C2×C8—261no—
565C2×C8—261no—
566C2×C8—261no—
567C2×C8—261no—
568C2×C8—261no—
569C2×C8—261no—
570C2×C8—261no—
571C2×C8—261no—
572C2×C8—261no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—261no—
584C4⋊C4—261no—
585C4⋊C4—261no—
586C4⋊C4—261no—
587C4⋊C4—261no—
588C4⋊C4—261no—
589C4⋊C4—522no—
590C4⋊C4—522no—
591C4⋊C4—522no—
592C4⋊C4C2×C22⋊D1312yes—
593C4⋊C4C2×C22⋊D1312yes—
594C4⋊C4C2×C22⋊D1312yes—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—522no—
601C22⋊C4—522no—
602C22⋊C4—522no—
603C22⋊C4—522no—
604C42—24no—
605C42—24no—
606C42—522no—
607C42C2×C22⋊D1312yes—
608C42C2×C22⋊D1312yes—
609C13#2412711yescharacteristic, complemented, Sylow
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23#8820412yes—
624C23C22×C22⋊D1311yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—262no—
630Q8—262no—
631Q8—521no—
632Q8—521no—
633D4—44no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—48no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—262no—
666C2×C4—521no—
667C2×C4—521no—
668C2×C4—521no—
669C2×C4—521no—
670C2×C4—521no—
671C2×C4—521no—
672C2×C4—521no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—521no—
676C2×C4—521no—
677C2×C4#8820712yes—
678C2×C4#8820712yes—
679C2×C4#41×D1311yescharacteristic
680C2×C4#41×D1311yescharacteristic
681C2×C4#8825611yescharacteristic
682C2×C4#8825711yescharacteristic
683C2×C4C22×C22⋊D1311yescharacteristic
684C2×C4C22×C22⋊D1311yescharacteristic
685C8—262no—
686C8—521no—
687C8—521no—
688C8—521no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22C2×#8820411yescharacteristic
704C22#1171952711yescharacteristic
705C22#1171952911yescharacteristic
706C22#1171953411yescharacteristic
707C22#1171954311yescharacteristic
708C22#1171954311yescharacteristic
709C22C2×#8820711yescharacteristic
710C4—22no—
711C4—22no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—41no—
716C4—41no—
717C4—42no—
718C4—522no—
719C4—1041no—
720C4—1041no—
721C4—1041no—
722C4#1171953311yescharacteristic
723C4#1171953611yescharacteristic
724C4#1171953811yescharacteristic
725C4#1171953911yescharacteristic
726C2—42no—
727C2—81no—
728C2#1311817511yescharacteristic
729C2#1312405411yescharacteristic
730C2#1312413111yescharacteristic
731C2#1312671711yescharacteristic
732C2#1312709811yescharacteristic
733C2#1312719811yescharacteristic
734C2#1312740511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#552C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
hypercenterC2×#552D13
hypocenterC13#24127
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#11718724C2semidirect
2. C2×C4×#6107C2semidirect
4. #13116036C2semidirect
5. #13116029C2semidirect
6. #13115844C2semidirect
7. #13115844C2semidirect
8. #13115802C2semidirect
10. #13115148C2semidirect
11. #13115143C2semidirect
12. #13115035C2semidirect
13. #13115024C2semidirect
14. #13114851C2semidirect
609. C13#24127semidirect

Maximal subgroups

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

subgroupindex
C2×#117187242
C2×C4×#61072
#131197452
#131160362
#131160292
#131158442
#131158022
#131156312
#131151482
#131151432
#131150352
#131150242
#131148512
C2×C13×#5522
#2412713