Finite Group Databasebeta

← #15874200

Subgroups — #15874200

Order 3328.

1080 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718879C211yesmaximal, characteristic
2#13117518C211yesmaximal, characteristic, complemented
3#13115716C211yesmaximal, characteristic, complemented
4#13115689C211yesmaximal, characteristic, complemented
5#13115536C211yesmaximal, characteristic, complemented
6#13115522C211yesmaximal, characteristic, complemented
7#13115460C211yesmaximal, characteristic, complemented
8#13115453C211yesmaximal, characteristic, complemented
9#13115194C211yesmaximal, characteristic, complemented
10#13115194C211yesmaximal, characteristic, complemented
11#13115148C211yesmaximal, characteristic, complemented
12#13115035C211yesmaximal, characteristic, complemented
13#13114767C211yesmaximal, characteristic
14#13114602C211yesmaximal, characteristic, complemented
15C13×#2309C211yesmaximal, characteristic
16C23×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6105C2211yescharacteristic
20C22×#6105C2211yescharacteristic
21C2×#88178C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic, complemented
23C13×#390—21no—
24C13×#390—21no—
25C13×#390C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#390C2211yescharacteristic
28C13×#390C2211yescharacteristic
29C13×#379—21no—
30C13×#379—21no—
31#11718879C418yescomplemented
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38#11718873C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718639—21no—
42#11718633—21no—
43C2×#88050C2211yescharacteristic, complemented
44C2×#88050C2211yescharacteristic, complemented
45C2×#88048C2211yescharacteristic, complemented
46C2×#88047C2211yescharacteristic, complemented
47#11718606—21no—
48#11718605—21no—
49C4×C4⋊Dic13C2211yescharacteristic, complemented
50#11718590C2211yescharacteristic, complemented
51#11718589C2211yescharacteristic, complemented
52C2×#88043C2211yescharacteristic, complemented
53C2×C4×#1055C2211yescharacteristic, complemented
54#11718121C2211yescharacteristic, complemented
55#11718121C2211yescharacteristic, complemented
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718116C2211yescharacteristic, complemented
59#11718116C2211yescharacteristic, complemented
60C25×C13—21no—
61C22×D4×C13—21no—
62C22×D4×C13—22no—
63C22×D4×C13—41no—
64C22×D4×C13—41no—
65C22×D4×C13—41no—
66C22×D4×C13—41no—
67C22×D4×C13C2×C414yes—
68C22×D4×C13C2311yescharacteristic
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C22×Dic26C2311yescharacteristic
72C13×#117—41no—
73C13×#117—41no—
74C13×#117—41no—
75C13×#117—41no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
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⋊C4D411yescharacteristic
90C2×C13×C22⋊C4D411yescharacteristic
91C2×C42×C13—21no—
92C2×C42×C13C2311yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C22⋊Dic13—21no—
95C2×C22⋊Dic13—21no—
96C2×#6105—41no—
97C2×#6105—41no—
98C2×#6105—41no—
99C2×#6105—41no—
100C2×#6105C2×C414yes—
101C2×#6105C2×C414yes—
102C2×C4⋊Dic13C2311yescharacteristic
103C2×C4⋊Dic13C2311yescharacteristic
104C2×C4⋊Dic13C2311yescharacteristic
105#88178—22no—
106#88178C2×C414yes—
107C2×#6101—21no—
108C2×#6101—21no—
109C2×#6101—21no—
110C2×C4×Dic13—21no—
111C2×C4×Dic13—21no—
112C22×#1055C2311yescharacteristic
113C22×#1055C2311yescharacteristic
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C4×Dic26—41no—
117C4×Dic26—41no—
118#88072—41no—
119#88072—41no—
120#88072—41no—
121#88072—41no—
122#88072C2×C414yes—
123#88072C2×C414yes—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130C22⋊#1055C2×C414yes—
131#88050—41no—
132#88050—41no—
133#88048—41no—
134#88047—41no—
135#88043—41no—
136C4×#1055—41no—
137#22052—131nomaximal, Sylow
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—24no—
141C24×C13—42no—
142C24×C13—42no—
143C24×C13—81no—
144C24×C13—81no—
145C24×C13—81no—
146C24×C13—81no—
147C24×C13C2×D411yescharacteristic
148C2×D4×C13—24no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
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—42no—
162C2×D4×C13—42no—
163C2×D4×C13—44no—
164C2×D4×C13—44no—
165C2×D4×C13C22×C412yes—
166C2×D4×C13C22×C412yes—
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×C13C22×C412yes—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13#4112yes—
180C22×C4×C13C2411yescharacteristic
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C2×Dic26—21no—
186C2×Dic26—21no—
187C2×Dic26—21no—
188C2×Dic26—21no—
189C2×Dic26—21no—
190C2×Dic26C22×C412yes—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—41no—
196C13×C4⋊C4—41no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—42no—
200C13×C22⋊C4—81no—
201C13×C22⋊C4—81no—
202C13×C22⋊C4—81no—
203C13×C22⋊C4—81no—
204C13×C22⋊C4—81no—
205C13×C22⋊C4—81no—
206C13×C22⋊C4—81no—
207C13×C22⋊C4—81no—
208C42×C13—21no—
209C42×C13—21no—
210C42×C13—21no—
211C42×C13—21no—
212C42×C13—42no—
213C22⋊Dic13—24no—
214C22⋊Dic13—81no—
215#6105—44no—
216#6105—44no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13C22×C412yes—
223#6101—24no—
224#6101—42no—
225#6101—81no—
226C4×Dic13—42no—
227C4×Dic13—81no—
228C2×#1055—21no—
229C2×#1055—21no—
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×#1055C22×C412yes—
239C2×#1055C22×C412yes—
240C2×#450—131no—
241#2323—131no—
242#2309D1311yescharacteristic
243#1973—131no—
244#1968—131no—
245#1936—131no—
246#1934—131no—
247#1926—131no—
248#1925—131no—
249#1880—131no—
250#1880—131no—
251#1873—131no—
252#1854—131no—
253#1786—131no—
254#1750—131no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—48no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
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—84no—
277C23×C13—84no—
278C23×C13—84no—
279C23×C13—84no—
280C23×C13—84no—
281C23×C13—84no—
282C23×C13C4×D412yes—
283C23×C13C22×D411yescharacteristic
284D4×C13—22no—
285D4×C13—22no—
286D4×C13—22no—
287D4×C13—22no—
288D4×C13—48no—
289D4×C13—41no—
290D4×C13—41no—
291D4×C13—41no—
292D4×C13—41no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13C4×D412yes—
318C2×C4×C13C23×C411yescharacteristic
319C2×C4×C13C2×#4111yescharacteristic
320C2×C4×C13H(5,𝔽2)11yescharacteristic
321C2×C4×C13H(5,𝔽2)11yescharacteristic
322C2×C4×C13H(5,𝔽2)11yescharacteristic
323C2×C4×C13H(5,𝔽2)11yescharacteristic
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336Dic26—22no—
337Dic26—22no—
338Dic26—41no—
339Dic26—41no—
340#1055—22no—
341#1055—22no—
342#1055—41no—
343#1055—41no—
344C23×D4C2×D1311yescharacteristic
345C22×SD16—131no—
346C22×SD16—131no—
347C2×C22⋊Q8—131no—
348C2×C4×Q8—131no—
349C2×#117C2×D1311yescharacteristic
350C2×#117C2×D1311yescharacteristic
351#450—138no—
352C2×#107—131no—
353C2×#106—131no—
354C2×#103—131no—
355C2×#103—131no—
356C2×#102—131no—
357C2×#102—131no—
358C2×#102—131no—
359C2×#102—131no—
360C2×#102—131no—
361C2×#102—131no—
362C2×C22⋊C8—131no—
363C2×C22⋊C8—131no—
364C2×#97—131no—
365C2×C4×C8—131no—
366#391—131no—
367#390—21no—
368#390—21no—
369#390C2×D1311yescharacteristic
370#390C2×D1311yescharacteristic
371#390C2×D1311yescharacteristic
372#390C2×D1311yescharacteristic
373#389—131no—
374#389—261no—
375#388—261no—
376#388—261no—
377#387—261no—
378#380—131no—
379#379—21no—
380#379—21no—
381C4×C4⋊C4—131no—
382#340—131no—
383#340—131no—
384#340—131no—
385#340—131no—
386#336—131no—
387#336—131no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—42no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—816no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13—81no—
405C22×C13—81no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13C2×C4×D411yescharacteristic
411C22×C13#53411yescharacteristic
412C22×C13#53511yescharacteristic
413C22×C13#57611yescharacteristic
414C22×C13#57711yescharacteristic
415C22×C13#57711yescharacteristic
416C22×C13#57711yescharacteristic
417C4×C13—22no—
418C4×C13—41no—
419C4×C13—41no—
420C4×C13—41no—
421C4×C13—41no—
422C4×C13—81no—
423C4×C13—81no—
424C4×C13#51811yescharacteristic
425C4×C13#51811yescharacteristic
426C4×C13#53811yescharacteristic
427C4×C13#53811yescharacteristic
428Dic13—42no—
429Dic13—42no—
430Dic13—81no—
431Dic13—81no—
432C25—21no—
433C22×Q8—131no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—41no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4—41no—
440C22×D4C4×D1314yes—
441C22×D4C22×D1311yescharacteristic
442C22×D4C22×D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C2×SD16—134no—
445C2×SD16—134no—
446C2×SD16—521no—
447C2×SD16—521no—
448C2×SD16—521no—
449C2×SD16—521no—
450C22×C8—131no—
451C22×C8—131no—
452C22×C8—131no—
453C22×C8—131no—
454C22⋊Q8—134no—
455C22⋊Q8—262no—
456C4×Q8—521no—
457C4×Q8—521no—
458#117—41no—
459#117—41no—
460#117—41no—
461#117—41no—
462C2×C4⋊C4—131no—
463C2×C4⋊C4—131no—
464C2×C4⋊C4—131no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4C22⋊D1311yescharacteristic
469C2×C4⋊C4C22⋊D1311yescharacteristic
470C2×C4⋊C4C22×D1311yescharacteristic
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—261no—
482C2×C22⋊C4—261no—
483C2×C22⋊C4C22⋊D1311yescharacteristic
484C2×C22⋊C4C22⋊D1311yescharacteristic
485C2×C42—21no—
486C2×C42—261no—
487C2×C42—261no—
488C2×C42C22×D1311yescharacteristic
489C2×C42C22×D1311yescharacteristic
490#107—521no—
491#106—521no—
492#103—521no—
493#103—521no—
494#102—134no—
495#102—134no—
496#102—521no—
497#102—521no—
498#102—521no—
499#102—521no—
500C22⋊C8—134no—
501C22⋊C8—262no—
502#97—521no—
503C4×C8—521no—
504#95—261no—
505#95—261no—
506#95—261no—
507#95—261no—
508#95—261no—
509C2×C13—42no—
510C2×C13—82no—
511C2×C13—82no—
512C2×C13#232111yescharacteristic
513C2×C13#294611yescharacteristic
514C2×C13#294911yescharacteristic
515C2×C13#319811yescharacteristic
516C2×C13#320011yescharacteristic
517C2×C13#322211yescharacteristic
518C2×C13#322411yescharacteristic
519C24—21no—
520C24—21no—
521C24—24no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24C2×C22⋊D1311yescharacteristic
529C2×Q8—132no—
530C2×Q8—261no—
531C2×Q8—261no—
532C2×Q8—261no—
533C2×Q8—261no—
534C2×Q8—261no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
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—42no—
549C2×D4—42no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4C2×C4×D1312yes—
553C2×D4C2×C4×D1312yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4C2×C4×D1312yes—
565C22×C4#612712yes—
566C22×C4C2×C22⋊D1311yescharacteristic
567C22×C4C2×C22⋊D1311yescharacteristic
568C22×C4C2×C22⋊D1311yescharacteristic
569C22×C4C2×C22⋊D1311yescharacteristic
570C22×C4C2×C22⋊D1311yescharacteristic
571C22×C4C23×D1311yescharacteristic
572SD16—524no—
573SD16—524no—
574C2×C8—132no—
575C2×C8—132no—
576C2×C8—261no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4—132no—
593C4⋊C4—264no—
594C4⋊C4—261no—
595C4⋊C4—261no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—522no—
600C4⋊C4—1041no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—81no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C22⋊C4—81no—
610C22⋊C4—81no—
611C22⋊C4—81no—
612C22⋊C4—264no—
613C22⋊C4—1041no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—42no—
619C42—522no—
620C42—1041no—
621C13#2205211yescharacteristic, complemented, Sylow
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—22no—
629C23—22no—
630C23—48no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23C4×C22⋊D1312yes—
650C23C22×C22⋊D1311yescharacteristic
651Q8—262no—
652Q8—262no—
653Q8—521no—
654Q8—521no—
655D4—22no—
656D4—22no—
657D4—22no—
658D4—22no—
659D4—48no—
660D4—41no—
661D4—41no—
662D4—41no—
663D4—41no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—521no—
691C2×C4—521no—
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×C4C4×C22⋊D1312yes—
701C2×C4C22×C4×D1311yescharacteristic
702C2×C4C2×#612711yescharacteristic
703C2×C4#8825111yescharacteristic
704C2×C4#8825111yescharacteristic
705C2×C4#8825111yescharacteristic
706C2×C4#8825111yescharacteristic
707C8—262no—
708C8—262no—
709C8—521no—
710C8—521no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—816no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×C22⋊D1311yescharacteristic
734C22#1171950911yescharacteristic
735C22#1171951011yescharacteristic
736C22#1171954011yescharacteristic
737C22#1171954111yescharacteristic
738C22#1171954111yescharacteristic
739C22#1171954111yescharacteristic
740C4—22no—
741C4—41no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—81no—
746C4—81no—
747C4—522no—
748C4—522no—
749C4—1041no—
750C4—1041no—
751C4#1171919111yescharacteristic
752C4#1171919111yescharacteristic
753C4#1171919911yescharacteristic
754C4#1171919911yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2#1311749411yescharacteristic
759C2#1312366811yescharacteristic
760C2#1312369311yescharacteristic
761C2#1312568811yescharacteristic
762C2#1312570811yescharacteristic
763C2#1312590811yescharacteristic
764C2#1312593011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2309C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
cosocleC22×C4×C13C24
hypercenter#2309D13
hypocenterC13#22052
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #13117518C2semidirect
3. #13115716C2semidirect
4. #13115689C2semidirect
5. #13115536C2semidirect
6. #13115522C2semidirect
7. #13115460C2semidirect
8. #13115453C2semidirect
9. #13115194C2semidirect
10. #13115194C2semidirect
11. #13115148C2semidirect
12. #13115035C2semidirect
14. #13114602C2semidirect
22. C2×C4×Dic26C22semidirect
31. #11718879C4semidirect
43. C2×#88050C22semidirect
44. C2×#88050C22semidirect
45. C2×#88048C22semidirect
46. C2×#88047C22semidirect
49. C4×C4⋊Dic13C22semidirect
50. #11718590C22semidirect
51. #11718589C22semidirect
52. C2×#88043C22semidirect
53. C2×C4×#1055C22semidirect
54. #11718121C22semidirect
55. #11718121C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718116C22semidirect
59. #11718116C22semidirect
621. C13#22052semidirect

Maximal subgroups

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

subgroupindex
C2×#117188792
#131175182
#131157162
#131156892
#131155362
#131155222
#131154602
#131154532
#131151942
#131151482
#131150352
#131147672
#131146022
C13×#23092
#2205213