Finite Group Databasebeta

← #15879252

Subgroups — #15879252

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic
2#13117765C211yesmaximal, characteristic
3#13115810C211yesmaximal, characteristic, complemented
4#13115785C211yesmaximal, characteristic, complemented
5#13115270C211yesmaximal, characteristic, complemented
6#13115260C211yesmaximal, characteristic, complemented
7#13115149C211yesmaximal, characteristic, complemented
8#13115144C211yesmaximal, characteristic, complemented
9#13114931C211yesmaximal, characteristic, complemented
10#13114931C211yesmaximal, characteristic, complemented
11#13114851C211yesmaximal, characteristic, complemented
12#13114666C211yesmaximal, characteristic, complemented
13#13114557C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C2×C13×#556C211yesmaximal, characteristic
16C13×#556—24no—
17C13×#556C418yescomplemented
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C13×#126—21no—
20C2×C13×#126—21no—
21C2×C13×#124—21no—
22C2×C13×C22⋊Q8C2211yescharacteristic
23C2×C13×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C13—21no—
25C2×C4×Q8×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37#11718881—21no—
38#11718873C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718672—24no—
43#11718642—21no—
44#11718612—21no—
45C22⋊C4×Dic13—21no—
46#11718597C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
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×Q8×C13—21no—
63C22×Q8×C13C2311yescharacteristic
64C22×D4×C13D411yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8C2×C414yescomplemented
70C13×#126—28no—
71C13×#126—28no—
72C13×#124—28no—
73C13×C22⋊Q8—22no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8C2×C414yes—
76C13×C22⋊Q8C2×C414yescomplemented
77C4×Q8×C13—28no—
78C4×Q8×C13—22no—
79C4×Q8×C13C2×C414yescomplemented
80C4×D4×C13C2×C414yes—
81C4×D4×C13D414yes—
82C13×#117—22no—
83C13×#117—22no—
84C13×#117C2×C414yes—
85C13×#117C2×C414yescomplemented
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13—21no—
102C2×C42×C13—21no—
103C2×C42×C13C2311yescharacteristic
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107#88180—22no—
108#88180—41no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—41no—
112C2×C4⋊Dic13C2311yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4×Dic13—21no—
117C2×C4×Dic13—21no—
118C2×#6099—22no—
119C2×#6099—22no—
120C2×#6099—41no—
121C22×#1055—22no—
122C22×#1055—22no—
123C22×#1055—41no—
124C22×#1055C2311yescharacteristic
125C22×#1055C2311yescharacteristic
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128#88075—22no—
129#88075—22no—
130#88075—41no—
131#88075—41no—
132#88071—21no—
133#88071—21no—
134#88071—21no—
135#88071—21no—
136#88071—21no—
137C22⋊#1055—22no—
138C22⋊#1055—22no—
139C4⋊#1055—22no—
140#88043—22no—
141#22494—131nomaximal, Sylow
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C2×Q8×C13—24no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13—42no—
151C2×Q8×C13—42no—
152C2×Q8×C13C22×C412yes—
153C2×D4×C13—41no—
154C2×D4×C13—41no—
155C2×D4×C13C22⋊C414yes—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
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×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D412yes—
176C22×C4×C13C2411yescharacteristic
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—42no—
182C22×Dic13—42no—
183C22×Dic13—81no—
184C13×C4⋊C4—24no—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—24no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4C22⋊C414yes—
192C13×C4⋊C4C22×C412yes—
193C13×C4⋊C4C22×C412yes—
194C13×C4⋊C4C22×C412yes—
195C13×C22⋊C4—24no—
196C13×C22⋊C4—24no—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4C22⋊C414yes—
200C13×C22⋊C4C22⋊C414yes—
201C42×C13—24no—
202C42×C13—24no—
203C42×C13—24no—
204C42×C13C22×C412yes—
205C42×C13C2×D412yes—
206C22⋊Dic13—42no—
207C22⋊Dic13—42no—
208C22⋊Dic13—81no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—21no—
216C4⋊Dic13—42no—
217C4⋊Dic13#4112yes—
218C4×Dic13—42no—
219C4×Dic13—81no—
220#6099—44no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055—21no—
229C2×#1055—21no—
230C2×#1055—21no—
231C2×#1055—21no—
232C2×#1055—44no—
233C2×#1055#4112yes—
234C2×#556D1311yescharacteristic
235C2×#435—131no—
236#2352—131no—
237#1993—131no—
238#1987—131no—
239#1894—131no—
240#1892—131no—
241#1873—131no—
242#1872—131no—
243#1825—131no—
244#1825—131no—
245#1805—131no—
246#1763—131no—
247#1736—131no—
248#1735—131no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—21no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13C2×C22⋊C412yes—
262C23×C13C2×C22⋊C412yes—
263C23×C13C22×D411yescharacteristic
264Q8×C13—22no—
265Q8×C13—22no—
266Q8×C13—48no—
267Q8×C13—41no—
268Q8×C13—41no—
269D4×C13—44no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13C2×C22⋊C412yes—
299C2×C4×C13C2×C22⋊C412yes—
300C2×C4×C13C2×C22⋊C412yes—
301C2×C4×C13C2×C22⋊C412yes—
302C2×C4×C13C23×C411yescharacteristic
303C2×C4×C13C22×D411yescharacteristic
304C2×C4×C13C2×#4111yescharacteristic
305C2×C4×C13C2×#4111yescharacteristic
306C2×C4×C13H(5,𝔽2)11yescharacteristic
307C2×C4×C132−1+411yescharacteristic
308C2×Dic13—22no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—84no—
321#1055—22no—
322#1055—41no—
323#1055—41no—
324#1055—41no—
325C22×M16—131no—
326C23×C8—131no—
327#556—24no—
328#556Dic1318yescomplemented
329C2×C4⋊Q8C2×D1311yescharacteristic
330C2×#126—21no—
331C2×#126—21no—
332C2×#124—21no—
333C2×C22⋊Q8C2×D1311yescharacteristic
334C2×C22⋊Q8C2×D1311yescharacteristic
335C2×C4×Q8—21no—
336C2×C4×Q8C2×D1311yescharacteristic
337C2×C4×D4C2×D1311yescharacteristic
338C2×#117—131no—
339C2×#117C2×D1311yescharacteristic
340C2×#117C2×D1311yescharacteristic
341C22×C4⋊C4—131no—
342#435—264no—
343C2×C4⋊C8—131no—
344C2×#103—131no—
345C2×#103—131no—
346C2×#103—131no—
347C2×#103—131no—
348C2×C22⋊C8—131no—
349C2×C22⋊C8—131no—
350C2×#97—131no—
351#388—261no—
352#387—261no—
353#386—261no—
354#382—131no—
355#380—131no—
356#380—131no—
357C4×C4⋊C4—131no—
358C4×C22⋊C4—261no—
359#340—131no—
360#340—131no—
361#340—131no—
362#340—131no—
363#340—131no—
364#340—131no—
365#340—131no—
366#340—131no—
367#340—131no—
368#340—131no—
369#340—131no—
370#340—131no—
371C22×C13—22no—
372C22×C13—22no—
373C22×C13—22no—
374C22×C13—22no—
375C22×C13—22no—
376C22×C13—22no—
377C22×C13—41no—
378C22×C13—41no—
379C22×C13—41no—
380C22×C13—41no—
381C22×C13—41no—
382C22×C13—41no—
383C22×C13—41no—
384C22×C13—41no—
385C22×C13C22×C22⋊C411yescharacteristic
386C22×C13#54611yescharacteristic
387C22×C13#54711yescharacteristic
388C22×C13#57511yescharacteristic
389C22×C13#57511yescharacteristic
390C22×C13#57711yescharacteristic
391C22×C13#57811yescharacteristic
392C4×C13—22no—
393C4×C13—22no—
394C4×C13—22no—
395C4×C13—22no—
396C4×C13—42no—
397C4×C13—42no—
398C4×C13—42no—
399C4×C13—42no—
400C4×C13C4×#4111yescharacteristic
401C4×C13#52011yescharacteristic
402C4×C13#54611yescharacteristic
403C4×C13#54711yescharacteristic
404Dic13—42no—
405Dic13—81no—
406Dic13—81no—
407Dic13—81no—
408C22×Q8—21no—
409C22×Q8C22×D1311yescharacteristic
410C22×D4C22⋊D1311yescharacteristic
411C23×C4—261no—
412C23×C4C22×D1311yescharacteristic
413C23×C4C22×D1311yescharacteristic
414C2×M16—262no—
415C2×M16—262no—
416C2×M16—521no—
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—131no—
420C22×C8—131no—
421C22×C8—262no—
422C22×C8—262no—
423C22×C8—521no—
424C4⋊Q8—22no—
425C4⋊Q8C2×Dic1314yescomplemented
426#126—28no—
427#126—28no—
428#124—28no—
429C22⋊Q8—22no—
430C22⋊Q8—22no—
431C22⋊Q8C2×Dic1314yes—
432C22⋊Q8C2×Dic1314yescomplemented
433C4×Q8—28no—
434C4×Q8—22no—
435C4×Q8C2×Dic1314yescomplemented
436C4×D4C2×Dic1314yes—
437C4×D4C22⋊D1314yes—
438#117—22no—
439#117—22no—
440#117—262no—
441#117—521no—
442#117C2×Dic1314yes—
443#117C2×Dic1314yescomplemented
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—131no—
449C2×C4⋊C4—131no—
450C2×C4⋊C4—131no—
451C2×C4⋊C4—131no—
452C2×C4⋊C4—262no—
453C2×C4⋊C4—261no—
454C2×C4⋊C4—521no—
455C2×C4⋊C4C22⋊D1311yescharacteristic
456C2×C4⋊C4C22×D1311yescharacteristic
457C2×C4⋊C4C22×D1311yescharacteristic
458C2×C4⋊C4C22×D1311yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—261no—
464C2×C22⋊C4—261no—
465C2×C22⋊C4—261no—
466C2×C22⋊C4C22⋊D1311yescharacteristic
467C2×C22⋊C4C22⋊D1311yescharacteristic
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—261no—
472C2×C42—261no—
473C2×C42C22×D1311yescharacteristic
474C4⋊C8—262no—
475#103—262no—
476#103—262no—
477#103—521no—
478#103—521no—
479C22⋊C8—262no—
480C22⋊C8—262no—
481#97—262no—
482#95—261no—
483#95—261no—
484#95—261no—
485#95—261no—
486#95—261no—
487C2×C13—42no—
488C2×C13—42no—
489C2×C13#233911yescharacteristic
490C2×C13#289611yescharacteristic
491C2×C13#289811yescharacteristic
492C2×C13#331111yescharacteristic
493C2×C13#331311yescharacteristic
494C2×C13#334911yescharacteristic
495C2×C13#335011yescharacteristic
496C24C2×C22⋊D1311yescharacteristic
497C24C2×C22⋊D1311yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8C22×Dic1312yes—
507C2×D4—41no—
508C2×D4—41no—
509C2×D4C22⋊Dic1314yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—261no—
523C22×C4—261no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—522no—
527C22×C4—522no—
528C22×C4—1041no—
529C22×C4C22×Dic1312yes—
530C22×C4C22×Dic1312yes—
531C22×C4C2×C22⋊D1311yescharacteristic
532C22×C4C2×C22⋊D1311yescharacteristic
533C22×C4C2×C22⋊D1311yescharacteristic
534C22×C4C2×C22⋊D1311yescharacteristic
535C22×C4C2×C22⋊D1312yes—
536C22×C4C2×C22⋊D1312yes—
537C22×C4C23×D1311yescharacteristic
538M16—524no—
539C2×C8—132no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C2×C8—261no—
547C2×C8—261no—
548C2×C8—261no—
549C2×C8—261no—
550C2×C8—261no—
551C2×C8—524no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—24no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—132no—
560C4⋊C4—261no—
561C4⋊C4—261no—
562C4⋊C4—261no—
563C4⋊C4—261no—
564C4⋊C4—261no—
565C4⋊C4—261no—
566C4⋊C4—261no—
567C4⋊C4—522no—
568C4⋊C4C22⋊Dic1314yes—
569C4⋊C4C22×Dic1312yes—
570C4⋊C4C22×Dic1312yes—
571C4⋊C4C22×Dic1312yes—
572C22⋊C4—24no—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—522no—
577C22⋊C4—522no—
578C22⋊C4—1041no—
579C22⋊C4C22⋊Dic1314yes—
580C22⋊C4C22⋊Dic1314yes—
581C42—24no—
582C42—24no—
583C42—24no—
584C42—522no—
585C42—1041no—
586C42C22×Dic1312yes—
587C42C2×C22⋊D1312yes—
588C13#2249411yescharacteristic, complemented, Sylow
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23C2×C22⋊Dic1312yes—
602C23C2×C22⋊Dic1312yes—
603C23C22×C22⋊D1311yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—48no—
607Q8—41no—
608Q8—41no—
609D4—44no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—262no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—521no—
649C2×C4—521no—
650C2×C4—1044no—
651C2×C4C2×C22⋊Dic1312yes—
652C2×C4C2×C22⋊Dic1312yes—
653C2×C4C2×C22⋊Dic1312yes—
654C2×C4C2×C22⋊Dic1312yes—
655C2×C4#41×D1311yescharacteristic
656C2×C4#41×D1311yescharacteristic
657C2×C4#8825611yescharacteristic
658C2×C4#8825711yescharacteristic
659C2×C4C23×Dic1311yescharacteristic
660C2×C4C22×C22⋊D1311yescharacteristic
661C8—262no—
662C8—521no—
663C8—521no—
664C8—521no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22#1171952711yescharacteristic
680C22#1171952711yescharacteristic
681C22#1171952911yescharacteristic
682C22#1171953411yescharacteristic
683C22#1171954211yescharacteristic
684C22#1171954311yescharacteristic
685C22C22×C22⋊Dic1311yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—522no—
695C4—1041no—
696C4—1041no—
697C4—1041no—
698C4#1171952911yescharacteristic
699C4#41×Dic1311yescharacteristic
700C4#1171953211yescharacteristic
701C4#1171953411yescharacteristic
702C2—42no—
703C2—42no—
704C2#1311766611yescharacteristic
705C2#1312335511yescharacteristic
706C2#1312336911yescharacteristic
707C2#1312686611yescharacteristic
708C2#1312689611yescharacteristic
709C2#1312736011yescharacteristic
710C2#1312738111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#556C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenterC2×#556D13
hypocenterC13#22494
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
3. #13115810C2semidirect
4. #13115785C2semidirect
5. #13115270C2semidirect
6. #13115260C2semidirect
7. #13115149C2semidirect
8. #13115144C2semidirect
9. #13114931C2semidirect
10. #13114931C2semidirect
11. #13114851C2semidirect
12. #13114666C2semidirect
13. #13114557C2semidirect
14. #13114552C2semidirect
17. C13×#556C4semidirect
69. C13×C4⋊Q8C2×C4semidirect
76. C13×C22⋊Q8C2×C4semidirect
79. C4×Q8×C13C2×C4semidirect
85. C13×#117C2×C4semidirect
328. #556Dic13semidirect
425. C4⋊Q8C2×Dic13semidirect
432. C22⋊Q8C2×Dic13semidirect
435. C4×Q8C2×Dic13semidirect
443. #117C2×Dic13semidirect
588. C13#22494semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
#131177652
#131158102
#131157852
#131152702
#131152602
#131151492
#131151442
#131149312
#131148512
#131146662
#131145572
#131145522
C2×C13×#5562
#2249413