Finite Group Databasebeta

← #15879164

Subgroups — #15879164

Order 3328.

1226 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719270C211yesmaximal, characteristic
2C2×D4×#1055C211yesmaximal, characteristic, complemented
3#13115800C211yesmaximal, characteristic, complemented
4#13115793C211yesmaximal, characteristic, complemented
5#13115262C211yesmaximal, characteristic, complemented
6#13115262C211yesmaximal, characteristic, complemented
7#13115158C211yesmaximal, characteristic, complemented
8#13115153C211yesmaximal, characteristic, complemented
9#13114928C211yesmaximal, characteristic, complemented
10#13114924C211yesmaximal, characteristic, complemented
11#13114843C211yesmaximal, characteristic, complemented
12C4×#88049C211yesmaximal, characteristic, complemented
13#13114552C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88193—21no—
20C2×#88184C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C2×#88180C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C23×#1055C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26#11719270—24no—
27#11719270C418yescomplemented
28C2×#88152—21no—
29C2×#88137—21no—
30C2×#88135—21no—
31C2×C4×D52C2211yescharacteristic
32C2×#88124C2211yescharacteristic
33C13×#388—21no—
34C13×#387—21no—
35C13×#386—21no—
36C13×#382C2211yescharacteristic
37C13×#380C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C4×C13×C4⋊C4C2211yescharacteristic
40C4×C13×C22⋊C4—21no—
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43D4×#1055—24no—
44C2×#88049C2211yescharacteristic
45C2×#88049C2211yescharacteristic
46C2×#88049C2211yescharacteristic
47C2×#88049C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13D411yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C22×C22⋊D13—21no—
67C22×C22⋊D13—21no—
68C23×Dic13—21no—
69C22×D52C2311yescharacteristic
70C22×C4×D13—21no—
71C4×D4×C13C2×C414yes—
72C4×D4×C13D414yes—
73C13×#117—22no—
74C13×#117—41no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C13×C22⋊C4D411yescharacteristic
88C2×C42×C13—21no—
89C2×C42×C13—21no—
90C2×C42×C13C2311yescharacteristic
91C2×C22⋊Dic13—21no—
92#88193—28no—
93#88184—22no—
94#88184—22no—
95#88184C2×C414yes—
96#88184C2×C414yescomplemented
97C2×#6103—21no—
98C2×#6103—21no—
99C2×#6103—21no—
100#88180—22no—
101#88180C2×C414yescomplemented
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13C2×C414yes—
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4⋊Dic13C2311yescharacteristic
107C2×C4⋊Dic13C2311yescharacteristic
108C2×#6101—21no—
109C2×#6101—21no—
110C2×C4×Dic13—21no—
111C22×#1055—22no—
112C22×#1055—22no—
113C22×#1055—22no—
114C22×#1055—22no—
115C22×#1055—41no—
116C22×#1055—41no—
117C22×#1055C2311yescharacteristic
118C22×#1055C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121#88152—28no—
122#88137—28no—
123#88135—28no—
124C4×D52—22no—
125C4×D52C2×C414yescomplemented
126#88124—22no—
127#88124C2×C414yescomplemented
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95—21no—
133C22⋊#1055—22no—
134C22⋊#1055—22no—
135#88049—22no—
136#88049—22no—
137#88049—41no—
138#88049—41no—
139C4⋊#1055—22no—
140C4×#1055—22no—
141#22488—131nomaximal, Sylow
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C23×D13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13C22⋊C414yes—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—81no—
163C22×C4×C13C22×C412yes—
164C22×C4×C13C22×C412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2411yescharacteristic
172C2×C22⋊D13—24no—
173C2×C22⋊D13—24no—
174C2×C22⋊D13—42no—
175C2×C22⋊D13—42no—
176C2×C22⋊D13—81no—
177C2×C22⋊D13—81no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—24no—
182C22×Dic13—81no—
183C22×Dic13—81no—
184C2×D52—21no—
185C2×D52—21no—
186C2×D52—21no—
187C2×D52—21no—
188C2×D52—21no—
189C2×D52C22×C412yes—
190C2×C4×D13—24no—
191C2×C4×D13—81no—
192C2×C4×D13—81no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—21no—
198C13×C4⋊C4—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—42no—
201C13×C4⋊C4C22⋊C414yes—
202C13×C4⋊C4#4112yes—
203C13×C22⋊C4—42no—
204C13×C22⋊C4—42no—
205C13×C22⋊C4—81no—
206C13×C22⋊C4C22⋊C414yes—
207C13×C22⋊C4C22⋊C414yes—
208C42×C13—42no—
209C42×C13—81no—
210C42×C13C22×C412yes—
211C42×C13C2×D412yes—
212C22⋊Dic13—24no—
213#6103—24no—
214#6103—24no—
215#6103—24no—
216C4⋊Dic13—24no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4⋊Dic13C22×C412yes—
221C4⋊Dic13C22×C412yes—
222C4⋊Dic13C22×C412yes—
223#6101—24no—
224#6101—24no—
225C4×Dic13—24no—
226C2×#1055—21no—
227C2×#1055—21no—
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—44no—
238C2×#1055—44no—
239C2×#1055#4112yes—
240C2×#553—131no—
241C2×C8×D4—131no—
242#2352D1311yescharacteristic, complemented
243#1991—131no—
244#1989—131no—
245#1893—131no—
246#1893—131no—
247#1875—131no—
248#1874—131no—
249#1825—131no—
250#1824—131no—
251#1804—131no—
252C4×#102—131no—
253#1735—131no—
254C2×#340—131no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13C2×C22⋊C412yes—
266C23×C13C2×C22⋊C412yes—
267C23×C13#13512yes—
268C23×C13#13512yes—
269C23×C13C22×D411yescharacteristic
270C22×D13—22no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277D4×C13—28no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
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—84no—
307C2×C4×C13C2×C22⋊C412yes—
308C2×C4×C13C2×C22⋊C412yes—
309C2×C4×C13C2×C22⋊C412yes—
310C2×C4×C13C2×C22⋊C412yes—
311C2×C4×C13C23×C411yescharacteristic
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C2×#4111yescharacteristic
314C2×C4×C13C2×#4111yescharacteristic
315C2×C4×C13H(5,𝔽2)11yescharacteristic
316C2×C4×C132−1+411yescharacteristic
317C22⋊D13—48no—
318C22⋊D13—84no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—84no—
329D52—22no—
330D52—22no—
331D52—41no—
332D52—41no—
333C4×D13—84no—
334#1055—22no—
335#1055—41no—
336#1055—41no—
337#1055—41no—
338C23×C8—131no—
339C23×C8—131no—
340#553—138no—
341#553—264no—
342C2×#126—261no—
343C2×#125—131no—
344C2×#123—261no—
345C2×#121—131no—
346C2×#121—131no—
347C2×#121—261no—
348C2×C4×D4—131no—
349C2×C4×D4—261no—
350C2×C4×D4C2×D1311yescharacteristic
351C2×#117—131no—
352C2×#117C2×D1311yescharacteristic
353C22×C4⋊C4—131no—
354C22×C4⋊C4C2×D1311yescharacteristic
355C8×D4—264no—
356C2×C4⋊C8—131no—
357C2×#102—131no—
358C2×#102—131no—
359C2×#102—131no—
360C2×#102—131no—
361C2×C22⋊C8—131no—
362C2×C22⋊C8—131no—
363C2×C4×C8—131no—
364#388—21no—
365#387—21no—
366#386—21no—
367#382C2×D1311yescharacteristic
368#380C2×D1311yescharacteristic
369#380C2×D1311yescharacteristic
370C4×C4⋊C4C2×D1311yescharacteristic
371C4×C22⋊C4—21no—
372#340—131no—
373#340—131no—
374#340—131no—
375#340—131no—
376#340—131no—
377#340—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—22no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13#41614yes—
398C22×C13C22×C22⋊C411yescharacteristic
399C22×C13#54611yescharacteristic
400C22×C13#54711yescharacteristic
401C22×C13C2×#13511yescharacteristic
402C22×C13C2×#13511yescharacteristic
403C22×C13#57611yescharacteristic
404C22×C13#57711yescharacteristic
405C2×D13—42no—
406C2×D13—42no—
407C2×D13—42no—
408C2×D13—81no—
409C2×D13—81no—
410C2×D13—81no—
411C2×D13—81no—
412C4×C13—22no—
413C4×C13—22no—
414C4×C13—22no—
415C4×C13—22no—
416C4×C13—42no—
417C4×C13—81no—
418C4×C13—81no—
419C4×C13—81no—
420C4×C13C4×#4111yescharacteristic
421C4×C13#52011yescharacteristic
422C4×C13#54611yescharacteristic
423C4×C13#54711yescharacteristic
424Dic13—42no—
425Dic13—42no—
426Dic13—42no—
427C22×D4—131no—
428C22×D4—261no—
429C22×D4—261no—
430C22×D4C22⋊D1311yescharacteristic
431C23×C4—21no—
432C23×C4—261no—
433C23×C4—261no—
434C23×C4C22×D1311yescharacteristic
435C23×C4C22×D1311yescharacteristic
436C22×C8—131no—
437C22×C8—131no—
438C22×C8—131no—
439C22×C8—131no—
440C22×C8—262no—
441C22×C8—262no—
442C22×C8—262no—
443C22×C8—262no—
444C22×C8—521no—
445C22×C8—521no—
446#126—268no—
447#125—134no—
448#125—262no—
449#123—268no—
450#121—134no—
451#121—134no—
452#121—268no—
453#121—262no—
454#121—262no—
455C4×D4—134no—
456C4×D4—268no—
457C4×D4—262no—
458C4×D4C4×D1314yes—
459C4×D4D5214yes—
460#117—22no—
461#117—41no—
462#117—134no—
463#117—262no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—134no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4—261no—
475C2×C4⋊C4C22⋊D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C4⋊C4C22×D1311yescharacteristic
478C2×C4⋊C4C22×D1311yescharacteristic
479C2×C4⋊C4C22×D1311yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—261no—
484C2×C22⋊C4—261no—
485C2×C22⋊C4—261no—
486C2×C22⋊C4—261no—
487C2×C22⋊C4C22⋊D1311yescharacteristic
488C2×C22⋊C4C22⋊D1311yescharacteristic
489C2×C42—21no—
490C2×C42—21no—
491C2×C42—261no—
492C2×C42C22×D1311yescharacteristic
493C4⋊C8—262no—
494#102—262no—
495#102—262no—
496#102—521no—
497#102—521no—
498C22⋊C8—262no—
499C22⋊C8—262no—
500C4×C8—262no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C2×C13—24no—
507C2×C13—42no—
508C2×C13#233911yescharacteristic
509C2×C13C2×#41611yescharacteristic
510C2×C13#289711yescharacteristic
511C2×C13#329711yescharacteristic
512C2×C13#330111yescharacteristic
513C2×C13#333711yescharacteristic
514C2×C13#333911yescharacteristic
515D13—82no—
516C24—261no—
517C24C2×C22⋊D1311yescharacteristic
518C24C2×C22⋊D1311yescharacteristic
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—132no—
522C2×D4—264no—
523C2×D4—264no—
524C2×D4—261no—
525C2×D4—261no—
526C2×D4—261no—
527C2×D4—261no—
528C2×D4—261no—
529C2×D4—522no—
530C2×D4—522no—
531C2×D4—1041no—
532C2×D4—1041no—
533C2×D4#610314yes—
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—42no—
547C22×C4—42no—
548C22×C4—81no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—264no—
553C22×C4—264no—
554C22×C4—1041no—
555C22×C4—1041no—
556C22×C4—1041no—
557C22×C4—1041no—
558C22×C4C2×C4×D1312yes—
559C22×C4C2×C4×D1312yes—
560C22×C4C2×D5212yes—
561C22×C4C2×D5212yes—
562C22×C4C2×C22⋊D1311yescharacteristic
563C22×C4C2×C22⋊D1311yescharacteristic
564C22×C4C2×C22⋊D1311yescharacteristic
565C22×C4C2×C22⋊D1311yescharacteristic
566C22×C4C23×D1311yescharacteristic
567C2×C8—132no—
568C2×C8—261no—
569C2×C8—261no—
570C2×C8—261no—
571C2×C8—261no—
572C2×C8—261no—
573C2×C8—261no—
574C2×C8—261no—
575C2×C8—261no—
576C2×C8—261no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—524no—
580C2×C8—524no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—132no—
590C4⋊C4—132no—
591C4⋊C4—132no—
592C4⋊C4—264no—
593C4⋊C4—264no—
594C4⋊C4—264no—
595C4⋊C4—261no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4#610314yes—
599C4⋊C4#612912yes—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—264no—
604C22⋊C4—264no—
605C22⋊C4—264no—
606C22⋊C4—264no—
607C22⋊C4#610314yes—
608C22⋊C4#610314yes—
609C42—42no—
610C42—81no—
611C42—264no—
612C42C2×C4×D1312yes—
613C42C2×D5212yes—
614C13#2248811yescharacteristic, complemented, Sylow
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—262no—
626C23—521no—
627C23—521no—
628C23—521no—
629C23—521no—
630C23—521no—
631C23—521no—
632C23C2×#610312yes—
633C23C2×#610312yes—
634C23#8820412yes—
635C23#8820412yes—
636C23C22×C22⋊D1311yescharacteristic
637D4—28no—
638D4—262no—
639D4—262no—
640D4—528no—
641D4—521no—
642D4—521no—
643D4—1044no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—84no—
673C2×C4—262no—
674C2×C4—262no—
675C2×C4—262no—
676C2×C4—521no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—521no—
682C2×C4—1044no—
683C2×C4—1044no—
684C2×C4C2×#610312yes—
685C2×C4C2×#610312yes—
686C2×C4C2×#610312yes—
687C2×C4C2×#610312yes—
688C2×C4C22×C4×D1311yescharacteristic
689C2×C4C22×D5211yescharacteristic
690C2×C4C2×#612911yescharacteristic
691C2×C4#8825111yescharacteristic
692C2×C4#41×D1311yescharacteristic
693C2×C4#8825711yescharacteristic
694C8—262no—
695C8—521no—
696C8—521no—
697C8—521no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—522no—
712C22—522no—
713C22—522no—
714C22—1041no—
715C22—1041no—
716C22—1041no—
717C22—1041no—
718C22#1171866314yes—
719C22C22×#610311yescharacteristic
720C22#1171951111yescharacteristic
721C22C2×#8820411yescharacteristic
722C22C2×#8820411yescharacteristic
723C22#1171952911yescharacteristic
724C22#1171954011yescharacteristic
725C22#1171954211yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—522no—
735C4—522no—
736C4—522no—
737C4C4×#612911yescharacteristic
738C4#1171925111yescharacteristic
739C4#1171925911yescharacteristic
740C4#1171926011yescharacteristic
741C2—24no—
742C2—42no—
743C2—1042no—
744C2#1311766111yescharacteristic
745C2C2×#1171866311yescharacteristic
746C2#1312335911yescharacteristic
747C2#1312668611yescharacteristic
748C2#1312673811yescharacteristic
749C2#1312721511yescharacteristic
750C2#1312723211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radicalC2×#11719270C2
cosocleC22×C4×C13C24
hypercenter#2352D13
hypocenterC13#22488
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×D4×#1055C2semidirect
3. #13115800C2semidirect
4. #13115793C2semidirect
5. #13115262C2semidirect
6. #13115262C2semidirect
7. #13115158C2semidirect
8. #13115153C2semidirect
9. #13114928C2semidirect
10. #13114924C2semidirect
11. #13114843C2semidirect
12. C4×#88049C2semidirect
13. #13114552C2semidirect
14. C2×#11718121C2semidirect
15. C13×#2352C2semidirect
27. #11719270C4semidirect
96. #88184C2×C4semidirect
101. #88180C2×C4semidirect
125. C4×D52C2×C4semidirect
127. #88124C2×C4semidirect
242. #2352D13semidirect
614. C13#22488semidirect

Maximal subgroups

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

subgroupindex
C2×#117192702
C2×D4×#10552
#131158002
#131157932
#131152622
#131151582
#131151532
#131149282
#131149242
#131148432
C4×#880492
#131145522
C2×#117181212
C13×#23522
#2248813