Finite Group Databasebeta

← #15868067

Subgroups — #15868067

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718661C211yesmaximal, characteristic, complemented
2#13117192C211yesmaximal, characteristic, complemented
3#13115789C211yesmaximal, characteristic, complemented
4#13115785C211yesmaximal, characteristic, complemented
5#13115769C211yesmaximal, characteristic, complemented
6#13115769C211yesmaximal, characteristic, complemented
7#13115159C211yesmaximal, characteristic
8#13115154C211yesmaximal, characteristic
9#13115149C211yesmaximal, characteristic, complemented
10#13115144C211yesmaximal, characteristic, complemented
11#13114666C211yesmaximal, characteristic, complemented
12#13114661C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C2×C13×#542C211yesmaximal, characteristic
16C13×#542—24no—
17C13×#542C418yescomplemented
18C2×C13×C4⋊Q8C2211yescharacteristic
19C2×C13×#126—21no—
20C2×C13×#124—21no—
21C2×C13×#124C2211yescharacteristic
22C2×C13×#123—21no—
23C2×C13×C22⋊Q8—21no—
24C2×C13×C22⋊Q8C2211yescharacteristic
25C2×C13×#121C2211yescharacteristic
26C2×C4×Q8×C13C2211yescharacteristic
27C2×C4×D4×C13C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718661—24no—
42C4⋊C4×Dic13—21no—
43C4⋊C4×Dic13—21no—
44C22⋊C4×Dic13—21no—
45C22⋊C4×Dic13—21no—
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C4×C4⋊Dic13C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×C4×#1055C2211yescharacteristic
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×C13—21no—
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13C2311yescharacteristic
68C23×Dic13—21no—
69C13×C4⋊Q8—22no—
70C13×C4⋊Q8C2×C414yescomplemented
71C13×#126—28no—
72C13×#124—28no—
73C13×#124—22no—
74C13×#124C2×C414yescomplemented
75C13×#123—28no—
76C13×C22⋊Q8—22no—
77C13×C22⋊Q8—28no—
78C13×C22⋊Q8C2×C414yes—
79C13×#121—22no—
80C13×#121C2×C414yes—
81C4×Q8×C13—22no—
82C4×Q8×C13C2×C414yescomplemented
83C4×D4×C13—22no—
84C4×D4×C13C2×C414yescomplemented
85C13×#117C2×C414yes—
86C13×#117D414yes—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4D411yescharacteristic
91C2×C13×C4⋊C4D411yescharacteristic
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⋊C4—21no—
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C13×C22⋊C4D411yescharacteristic
101C2×C42×C13—21no—
102C2×C42×C13C2311yescharacteristic
103C2×C42×C13C2311yescharacteristic
104C2×C22⋊Dic13—21no—
105#88180—22no—
106#88180—22no—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13C2311yescharacteristic
111C2×C4⋊Dic13C2311yescharacteristic
112C2×C4⋊Dic13C2311yescharacteristic
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4×Dic13—21no—
115C2×C4×Dic13—21no—
116C2×C4×Dic13—21no—
117C2×C4×Dic13—21no—
118C2×C4×Dic13—21no—
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123#88075—22no—
124#88075—22no—
125#88075—22no—
126#88075—22no—
127#88072—22no—
128#88072—22no—
129#88072—22no—
130#88072—22no—
131#88071—21no—
132#88071—21no—
133#88071—21no—
134#88071—21no—
135C22⋊#1055—22no—
136C22⋊#1055—22no—
137C4⋊#1055—22no—
138C4⋊#1055—22no—
139#88043—22no—
140C4×#1055—22no—
141#21397—131nomaximal, Sylow
142C24×C13—21no—
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—81no—
151C2×Q8×C13—81no—
152C2×Q8×C13C22×C412yes—
153C2×D4×C13—24no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—81no—
160C2×D4×C13—81no—
161C2×D4×C13C22×C412yes—
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—24no—
170C22×C4×C13—81no—
171C22×C4×C13—81no—
172C22×C4×C13C22×C412yes—
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D412yes—
179C22×C4×C13C2411yescharacteristic
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—24no—
185C22×Dic13—81no—
186C22×Dic13—81no—
187C13×C4⋊C4—24no—
188C13×C4⋊C4—24no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4C22⋊C414yes—
193C13×C4⋊C4C22⋊C414yes—
194C13×C4⋊C4C22×C412yes—
195C13×C4⋊C4C22×C412yes—
196C13×C22⋊C4—24no—
197C13×C22⋊C4—24no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4—24no—
200C13×C22⋊C4—24no—
201C13×C22⋊C4C22⋊C414yes—
202C13×C22⋊C4C22⋊C414yes—
203C42×C13—24no—
204C42×C13C22×C412yes—
205C42×C13C22×C412yes—
206C42×C13C2×D412yes—
207C42×C13C2×D412yes—
208C22⋊Dic13—24no—
209C4⋊Dic13—24no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212C4⋊Dic13—21no—
213C4⋊Dic13—21no—
214C4⋊Dic13#4112yes—
215C4⋊Dic13#4112yes—
216C4⋊Dic13#4112yes—
217C4⋊Dic13#4112yes—
218C4×Dic13—24no—
219C4×Dic13—81no—
220C4×Dic13—81no—
221C4×Dic13—81no—
222C4×Dic13—81no—
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—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#542D1311yescharacteristic
236C2×#433—131no—
237#2274—131no—
238#1988—131no—
239#1987—131no—
240#1983—131no—
241#1983—131no—
242#1875—131no—
243#1874—131no—
244#1873—131no—
245#1872—131no—
246#1763—131no—
247#1762—131no—
248C4×#103—131no—
249C4×#102—131no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—21no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—22no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13C2×C22⋊C412yes—
264C23×C13C22×D411yescharacteristic
265Q8×C13—22no—
266Q8×C13—22no—
267Q8×C13—41no—
268Q8×C13—41no—
269Q8×C13—84no—
270D4×C13—22no—
271D4×C13—22no—
272D4×C13—41no—
273D4×C13—41no—
274D4×C13—84no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
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—22no—
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—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—84no—
299C2×C4×C13C2×C22⋊C412yes—
300C2×C4×C13C2×C22⋊C412yes—
301C2×C4×C13C2×C22⋊C412yes—
302C2×C4×C13C2×C22⋊C412yes—
303C2×C4×C13C2×C22⋊C412yes—
304C2×C4×C13C23×C411yescharacteristic
305C2×C4×C13C22×D411yescharacteristic
306C2×C4×C13C2×#4111yescharacteristic
307C2×C4×C13C2×#4111yescharacteristic
308C2×C4×C13C2×#4111yescharacteristic
309C2×C4×C13C2×#4111yescharacteristic
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—84no—
323#1055—41no—
324#1055—41no—
325#1055—41no—
326#1055—41no—
327#542—24no—
328#542Dic1318yescomplemented
329C2×C4⋊Q8C2×D1311yescharacteristic
330C2×#126—21no—
331C2×#124—21no—
332C2×#124C2×D1311yescharacteristic
333C2×#123—21no—
334C2×C22⋊Q8—21no—
335C2×C22⋊Q8C2×D1311yescharacteristic
336C2×#121C2×D1311yescharacteristic
337C2×C4×Q8C2×D1311yescharacteristic
338C2×C4×D4C2×D1311yescharacteristic
339C2×#117—131no—
340C2×#117C2×D1311yescharacteristic
341C22×C4⋊C4—131no—
342#433—264no—
343C2×C4⋊C8—131no—
344C2×C4⋊C8—131no—
345C2×#103—131no—
346C2×#103—131no—
347C2×#103—131no—
348C2×#103—131no—
349C2×#102—131no—
350C2×#102—131no—
351C2×#102—131no—
352C2×#102—131no—
353C2×C22⋊C8—131no—
354C2×C22⋊C8—131no—
355C2×#97—131no—
356C2×C4×C8—131no—
357C4×C4⋊C4—131no—
358C4×C4⋊C4—131no—
359C4×C4⋊C4—131no—
360C4×C4⋊C4—131no—
361C4×C4⋊C4—261no—
362C4×C4⋊C4—261no—
363C4×C22⋊C4—261no—
364C4×C22⋊C4—261no—
365#340—131no—
366#340—131no—
367#340—131no—
368#340—131no—
369#340—131no—
370#340—131no—
371#340—131no—
372#340—131no—
373C22×C13—22no—
374C22×C13—22no—
375C22×C13—22no—
376C22×C13—41no—
377C22×C13—41no—
378C22×C13—41no—
379C22×C13—41no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—81no—
384C22×C13—81no—
385C22×C13—81no—
386C22×C13—81no—
387C22×C13C22×C22⋊C411yescharacteristic
388C22×C13#52511yescharacteristic
389C22×C13#52511yescharacteristic
390C22×C13#57611yescharacteristic
391C22×C13#57711yescharacteristic
392C22×C13#57711yescharacteristic
393C22×C13#57811yescharacteristic
394C4×C13—22no—
395C4×C13—22no—
396C4×C13—22no—
397C4×C13—22no—
398C4×C13—22no—
399C4×C13—42no—
400C4×C13—42no—
401C4×C13—42no—
402C4×C13C4×#4111yescharacteristic
403C4×C13C4×#4111yescharacteristic
404C4×C13#53211yescharacteristic
405C4×C13#53211yescharacteristic
406Dic13—42no—
407Dic13—42no—
408Dic13—42no—
409Dic13—42no—
410C22×Q8—21no—
411C22×Q8C22×D1311yescharacteristic
412C22×D4—21no—
413C22×D4C22×D1311yescharacteristic
414C23×C4—21no—
415C23×C4—261no—
416C23×C4C22×D1311yescharacteristic
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—131no—
420C22×C8—131no—
421C4⋊Q8—22no—
422C4⋊Q8C2×Dic1314yescomplemented
423#126—28no—
424#124—28no—
425#124—22no—
426#124C2×Dic1314yescomplemented
427#123—28no—
428C22⋊Q8—22no—
429C22⋊Q8—28no—
430C22⋊Q8C2×Dic1314yes—
431#121—22no—
432#121C2×Dic1314yes—
433C4×Q8—22no—
434C4×Q8C2×Dic1314yescomplemented
435C4×D4—22no—
436C4×D4C2×Dic1314yescomplemented
437#117—262no—
438#117—262no—
439#117C2×Dic1314yes—
440#117C22⋊D1314yes—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—131no—
445C2×C4⋊C4—131no—
446C2×C4⋊C4—131no—
447C2×C4⋊C4—131no—
448C2×C4⋊C4—262no—
449C2×C4⋊C4—262no—
450C2×C4⋊C4—261no—
451C2×C4⋊C4C22⋊D1311yescharacteristic
452C2×C4⋊C4C22⋊D1311yescharacteristic
453C2×C4⋊C4C22×D1311yescharacteristic
454C2×C4⋊C4C22×D1311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—261no—
461C2×C22⋊C4C22⋊D1311yescharacteristic
462C2×C22⋊C4C22⋊D1311yescharacteristic
463C2×C42—21no—
464C2×C42—261no—
465C2×C42—261no—
466C2×C42—261no—
467C2×C42—261no—
468C2×C42—261no—
469C2×C42C22×D1311yescharacteristic
470C2×C42C22×D1311yescharacteristic
471C4⋊C8—262no—
472C4⋊C8—262no—
473#103—262no—
474#103—262no—
475#103—262no—
476#103—262no—
477#102—262no—
478#102—262no—
479#102—262no—
480#102—262no—
481C22⋊C8—262no—
482C22⋊C8—262no—
483#97—262no—
484C4×C8—262no—
485#95—261no—
486#95—261no—
487#95—261no—
488#95—261no—
489C2×C13—42no—
490C2×C13—82no—
491C2×C13#229711yescharacteristic
492C2×C13#289711yescharacteristic
493C2×C13#289811yescharacteristic
494C2×C13#311811yescharacteristic
495C2×C13#312111yescharacteristic
496C2×C13#312411yescharacteristic
497C2×C13#312511yescharacteristic
498C24—21no—
499C24C2×C22⋊D1311yescharacteristic
500C2×Q8—24no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—81no—
507C2×Q8—81no—
508C2×Q8C22×Dic1312yes—
509C2×D4—24no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—81no—
516C2×D4—81no—
517C2×D4C22×Dic1312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—81no—
527C22×C4—81no—
528C22×C4—261no—
529C22×C4—261no—
530C22×C4—261no—
531C22×C4—261no—
532C22×C4—264no—
533C22×C4—1041no—
534C22×C4—1041no—
535C22×C4C22×Dic1312yes—
536C22×C4C2×C22⋊D1311yescharacteristic
537C22×C4C2×C22⋊D1311yescharacteristic
538C22×C4C2×C22⋊D1311yescharacteristic
539C22×C4C2×C22⋊D1311yescharacteristic
540C22×C4C2×C22⋊D1311yescharacteristic
541C22×C4C2×C22⋊D1312yes—
542C22×C4C23×D1311yescharacteristic
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—261no—
552C2×C8—261no—
553C2×C8—261no—
554C2×C8—261no—
555C4⋊C4—24no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—132no—
561C4⋊C4—132no—
562C4⋊C4—132no—
563C4⋊C4—132no—
564C4⋊C4—264no—
565C4⋊C4—261no—
566C4⋊C4—261no—
567C4⋊C4—261no—
568C4⋊C4—261no—
569C4⋊C4C22⋊Dic1314yes—
570C4⋊C4C22⋊Dic1314yes—
571C4⋊C4C22×Dic1312yes—
572C4⋊C4C22×Dic1312yes—
573C22⋊C4—24no—
574C22⋊C4—24no—
575C22⋊C4—24no—
576C22⋊C4—24no—
577C22⋊C4—24no—
578C22⋊C4—264no—
579C22⋊C4C22⋊Dic1314yes—
580C22⋊C4C22⋊Dic1314yes—
581C42—24no—
582C42—264no—
583C42—1041no—
584C42—1041no—
585C42—1041no—
586C42—1041no—
587C42C22×Dic1312yes—
588C42C22×Dic1312yes—
589C42C2×C22⋊D1312yes—
590C42C2×C22⋊D1312yes—
591C13#2139711yescharacteristic, complemented, Sylow
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—22no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23C2×C22⋊Dic1312yes—
606C23C22×C22⋊D1311yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—84no—
612D4—22no—
613D4—22no—
614D4—41no—
615D4—41no—
616D4—84no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—84no—
641C2×C4—262no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—521no—
646C2×C4—521no—
647C2×C4—521no—
648C2×C4—521no—
649C2×C4—521no—
650C2×C4—521no—
651C2×C4—521no—
652C2×C4—521no—
653C2×C4—1044no—
654C2×C4C2×C22⋊Dic1312yes—
655C2×C4C2×C22⋊Dic1312yes—
656C2×C4C2×C22⋊Dic1312yes—
657C2×C4C2×C22⋊Dic1312yes—
658C2×C4C2×C22⋊Dic1312yes—
659C2×C4#41×D1311yescharacteristic
660C2×C4#41×D1311yescharacteristic
661C2×C4#41×D1311yescharacteristic
662C2×C4#41×D1311yescharacteristic
663C2×C4C23×Dic1311yescharacteristic
664C2×C4C22×C22⋊D1311yescharacteristic
665C8—521no—
666C8—521no—
667C8—521no—
668C8—521no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—42no—
677C22—42no—
678C22—42no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22#1171953311yescharacteristic
684C22#1171953311yescharacteristic
685C22#1171954011yescharacteristic
686C22#1171954111yescharacteristic
687C22#1171954211yescharacteristic
688C22#1171954311yescharacteristic
689C22C22×C22⋊Dic1311yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—522no—
699C4—522no—
700C4—522no—
701C4—522no—
702C4#41×Dic1311yescharacteristic
703C4#41×Dic1311yescharacteristic
704C4#1171953711yescharacteristic
705C4#1171953711yescharacteristic
706C2—42no—
707C2—82no—
708C2#1311732711yescharacteristic
709C2#1312336211yescharacteristic
710C2#1312336911yescharacteristic
711C2#1312501411yescharacteristic
712C2#1312505911yescharacteristic
713C2#1312509211yescharacteristic
714C2#1312510711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#542C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenterC2×#542D13
hypocenterC13#21397
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#11718661C2semidirect
2. #13117192C2semidirect
3. #13115789C2semidirect
4. #13115785C2semidirect
5. #13115769C2semidirect
6. #13115769C2semidirect
9. #13115149C2semidirect
10. #13115144C2semidirect
11. #13114666C2semidirect
12. #13114661C2semidirect
13. C4×#88075C2semidirect
14. C4×#88072C2semidirect
17. C13×#542C4semidirect
70. C13×C4⋊Q8C2×C4semidirect
74. C13×#124C2×C4semidirect
82. C4×Q8×C13C2×C4semidirect
84. C4×D4×C13C2×C4semidirect
328. #542Dic13semidirect
422. C4⋊Q8C2×Dic13semidirect
426. #124C2×Dic13semidirect
434. C4×Q8C2×Dic13semidirect
436. C4×D4C2×Dic13semidirect
591. C13#21397semidirect

Maximal subgroups

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

subgroupindex
C2×#117186612
#131171922
#131157892
#131157852
#131157692
#131151592
#131151542
#131151492
#131151442
#131146662
#131146612
C4×#880752
C4×#880722
C2×C13×#5422
#2139713