Finite Group Databasebeta

← #15879267

Subgroups — #15879267

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic, complemented
2#13117765C211yesmaximal, characteristic, complemented
3#13115810C211yesmaximal, characteristic, complemented
4#13115785C211yesmaximal, characteristic, complemented
5#13115275C211yesmaximal, characteristic, complemented
6#13115265C211yesmaximal, characteristic, complemented
7#13115159C211yesmaximal, characteristic, complemented
8#13115154C211yesmaximal, characteristic, complemented
9#13114926C211yesmaximal, characteristic, complemented
10#13114922C211yesmaximal, characteristic, complemented
11#13114846C211yesmaximal, characteristic, complemented
12#13114661C211yesmaximal, characteristic, complemented
13#13114555C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C2×C13×#547C211yesmaximal, characteristic
16C22×C13×#41—21no—
17C13×#547—24no—
18C13×#547C418yescomplemented
19C2×C13×C4⋊Q8C2211yescharacteristic
20C2×C13×#123—21no—
21C2×C13×#123—21no—
22C2×C13×C22⋊Q8—21no—
23C2×C13×#121C2211yescharacteristic
24C2×C13×#121C2211yescharacteristic
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33#11718881—21no—
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
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
62C2×C13×#41—28no—
63C2×C13×#41—44no—
64C2×C13×#41—44no—
65C22×Q8×C13—21no—
66C22×D4×C13—21no—
67C22×D4×C13—21no—
68C22×D4×C13D411yescharacteristic
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13—21no—
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×Dic13—21no—
76C13×C4⋊Q8—22no—
77C13×C4⋊Q8C2×C414yescomplemented
78C13×#123—28no—
79C13×#123—28no—
80C13×C22⋊Q8—28no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121C2×C414yes—
84C13×#121C2×C414yescomplemented
85C4×D4×C13—22no—
86C4×D4×C13C2×C414yes—
87C4×D4×C13C2×C414yescomplemented
88C4×D4×C13D414yes—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4C2×C414yes—
95C2×C13×C4⋊C4C2×C414yescomplemented
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4D411yescharacteristic
104C2×C13×C22⋊C4D411yescharacteristic
105C2×C42×C13C2311yescharacteristic
106C2×C22⋊Dic13—21no—
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13—21no—
109#88180—22no—
110#88180—41no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13—41no—
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117C2×C4⋊Dic13C2311yescharacteristic
118C2×C4×Dic13—21no—
119C2×C4×Dic13—21no—
120C2×#6099—22no—
121C2×#6099—22no—
122C2×#6099—41no—
123C22×#1055—22no—
124C22×#1055—22no—
125C22×#1055—41no—
126C22×#1055C2311yescharacteristic
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130#88072—22no—
131#88072—22no—
132#88072—41no—
133#88072—41no—
134#88071—21no—
135#88071—21no—
136#88071—21no—
137#88071—21no—
138#88071—21no—
139C22⋊#1055—22no—
140C22⋊#1055—22no—
141C4⋊#1055—22no—
142#88043—22no—
143#22495—131nomaximal, Sylow
144C24×C13—21no—
145C24×C13C2×D411yescharacteristic
146C24×C13C2×D411yescharacteristic
147C13×#41—432no—
148C2×Q8×C13—24no—
149C2×Q8×C13—42no—
150C2×Q8×C13—42no—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13—24no—
154C2×D4×C13—24no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—42no—
161C2×D4×C13—42no—
162C2×D4×C13—42no—
163C2×D4×C13—42no—
164C2×D4×C13C22⋊C414yes—
165C2×D4×C13C22×C412yes—
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—24no—
175C22×C4×C13—24no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—24no—
180C22×C4×C13—42no—
181C22×C4×C13—42no—
182C22×C4×C13—42no—
183C22×C4×C13—42no—
184C22×C4×C13—42no—
185C22×C4×C13—42no—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2411yescharacteristic
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—42no—
200C22×Dic13—42no—
201C22×Dic13—81no—
202C13×C4⋊C4—24no—
203C13×C4⋊C4—24no—
204C13×C4⋊C4—24no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4C22⋊C414yes—
209C13×C4⋊C4C22×C412yes—
210C13×C4⋊C4C22×C412yes—
211C13×C4⋊C4C22×C412yes—
212C13×C22⋊C4—24no—
213C13×C22⋊C4—24no—
214C13×C22⋊C4—24no—
215C13×C22⋊C4C22⋊C414yes—
216C13×C22⋊C4C22⋊C414yes—
217C42×C13C22×C412yes—
218C42×C13C2×D412yes—
219C22⋊Dic13—42no—
220C22⋊Dic13—42no—
221C22⋊Dic13—81no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—42no—
230C4⋊Dic13#4112yescomplemented
231C4×Dic13—42no—
232C4×Dic13—81no—
233#6099—44no—
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—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—44no—
246C2×#1055#4112yescomplemented
247C2×#547D1311yescharacteristic
248C2×#435—131no—
249#2352—131no—
250#1993—131no—
251#1987—131no—
252#1895—131no—
253#1893—131no—
254#1875—131no—
255#1874—131no—
256#1824—131no—
257#1823—131no—
258#1804—131no—
259#1762—131no—
260#1736—131no—
261C2×#340—131no—
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—21no—
272C23×C13—22no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13—41no—
279C23×C13C2×C22⋊C412yes—
280C23×C13C2×C22⋊C412yes—
281C23×C13AGL(1,ℤ/8)12yes—
282C23×C13AGL(1,ℤ/8)12yes—
283C23×C13C22×D411yescharacteristic
284Q8×C13—48no—
285D4×C13—28no—
286D4×C13—22no—
287D4×C13—22no—
288D4×C13—48no—
289D4×C13—48no—
290D4×C13—41no—
291D4×C13—41no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—48no—
312C2×C4×C13—48no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—48no—
320C2×C4×C13C2×C22⋊C412yes—
321C2×C4×C13C2×C22⋊C412yes—
322C2×C4×C13C2×C22⋊C412yes—
323C2×C4×C13C2×C22⋊C412yes—
324C2×C4×C13C23×C411yescharacteristic
325C2×C4×C13C22×D411yescharacteristic
326C2×C4×C13C2×#4111yescharacteristic
327C2×C4×C13C2×#4111yescharacteristic
328C2×C4×C13H(5,𝔽2)11yescharacteristic
329C2×C4×C132−1+411yescharacteristic
330C2×Dic13—22no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—84no—
343#1055—22no—
344#1055—41no—
345#1055—41no—
346#1055—41no—
347C22×#41—21no—
348C22×M16—131no—
349C23×C8—131no—
350#547—24no—
351#547Dic1318yescomplemented
352C2×C4⋊Q8C2×D1311yescharacteristic
353C2×#123—21no—
354C2×#123—21no—
355C2×C22⋊Q8—21no—
356C2×#121C2×D1311yescharacteristic
357C2×#121C2×D1311yescharacteristic
358C2×C4×D4C2×D1311yescharacteristic
359C2×C4×D4C2×D1311yescharacteristic
360C2×#117—131no—
361C22×C4⋊C4—131no—
362C22×C4⋊C4C2×D1311yescharacteristic
363C22×C4⋊C4C2×D1311yescharacteristic
364#435—264no—
365C2×C4⋊C8—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×#102—131no—
369C2×#102—131no—
370C2×C22⋊C8—131no—
371C2×C22⋊C8—131no—
372C2×#97—131no—
373#388—261no—
374#387—261no—
375#386—261no—
376#382—131no—
377#380—131no—
378#380—131no—
379C4×C4⋊C4—131no—
380C4×C22⋊C4—261no—
381#340—131no—
382#340—131no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390#340—131no—
391#340—131no—
392#340—131no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—22no—
401C22×C13—22no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13—81no—
410C22×C13—81no—
411C22×C13—81no—
412C22×C13—81no—
413C22×C13#41814yes—
414C22×C13C22×C22⋊C411yescharacteristic
415C22×C13#54611yescharacteristic
416C22×C13#54711yescharacteristic
417C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
418C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
419C22×C13#57711yescharacteristic
420C22×C13#57811yescharacteristic
421C4×C13—22no—
422C4×C13—22no—
423C4×C13—22no—
424C4×C13—22no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13—42no—
428C4×C13C4×#4111yescharacteristic
429C4×C13#52011yescharacteristic
430C4×C13#54611yescharacteristic
431C4×C13#54711yescharacteristic
432Dic13—42no—
433Dic13—81no—
434Dic13—81no—
435Dic13—81no—
436C2×#41—28no—
437C2×#41—44no—
438C2×#41—44no—
439C22×Q8—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C22⋊D1311yescharacteristic
443C22×D4C22×D1311yescharacteristic
444C23×C4—21no—
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—261no—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C2×M16—262no—
451C2×M16—262no—
452C2×M16—521no—
453C22×C8—131no—
454C22×C8—131no—
455C22×C8—131no—
456C22×C8—131no—
457C22×C8—262no—
458C22×C8—262no—
459C22×C8—521no—
460C4⋊Q8—22no—
461C4⋊Q8C2×Dic1314yescomplemented
462#123—28no—
463#123—28no—
464C22⋊Q8—28no—
465#121—22no—
466#121—22no—
467#121C2×Dic1314yes—
468#121C2×Dic1314yescomplemented
469C4×D4—22no—
470C4×D4C2×Dic1314yes—
471C4×D4C2×Dic1314yescomplemented
472C4×D4C22⋊D1314yes—
473#117—262no—
474#117—521no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—131no—
481C2×C4⋊C4—131no—
482C2×C4⋊C4—131no—
483C2×C4⋊C4—131no—
484C2×C4⋊C4—262no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—521no—
487C2×C4⋊C4C2×Dic1314yes—
488C2×C4⋊C4C2×Dic1314yescomplemented
489C2×C4⋊C4C22⋊D1311yescharacteristic
490C2×C4⋊C4C22×D1311yescharacteristic
491C2×C4⋊C4C22×D1311yescharacteristic
492C2×C4⋊C4C22×D1311yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4C22⋊D1311yescharacteristic
500C2×C22⋊C4C22⋊D1311yescharacteristic
501C2×C42—261no—
502C2×C42—261no—
503C2×C42C22×D1311yescharacteristic
504C4⋊C8—262no—
505#102—262no—
506#102—262no—
507#102—521no—
508#102—521no—
509C22⋊C8—262no—
510C22⋊C8—262no—
511#97—262no—
512#95—261no—
513#95—261no—
514#95—261no—
515#95—261no—
516#95—261no—
517C2×C13—24no—
518C2×C13—42no—
519C2×C13—82no—
520C2×C13#233911yescharacteristic
521C2×C13C2×#41811yescharacteristic
522C2×C13#289811yescharacteristic
523C2×C13#330611yescharacteristic
524C2×C13#330811yescharacteristic
525C2×C13#334311yescharacteristic
526C2×C13#334511yescharacteristic
527C24—21no—
528C24C2×C22⋊D1311yescharacteristic
529C24C2×C22⋊D1311yescharacteristic
530#41—432no—
531C2×Q8—24no—
532C2×Q8—42no—
533C2×Q8—42no—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—24no—
537C2×D4—24no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4C22⋊Dic1314yes—
548C2×D4C22×Dic1312yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—522no—
574C22×C4—522no—
575C22×C4—1041no—
576C22×C4C22×Dic1312yes—
577C22×C4C22×Dic1312yes—
578C22×C4C2×C22⋊D1311yescharacteristic
579C22×C4C2×C22⋊D1311yescharacteristic
580C22×C4C2×C22⋊D1311yescharacteristic
581C22×C4C2×C22⋊D1311yescharacteristic
582C22×C4C2×C22⋊D1312yes—
583C22×C4C2×C22⋊D1312yes—
584C22×C4C23×D1311yescharacteristic
585M16—524no—
586C2×C8—132no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—261no—
591C2×C8—261no—
592C2×C8—261no—
593C2×C8—261no—
594C2×C8—261no—
595C2×C8—261no—
596C2×C8—261no—
597C2×C8—261no—
598C2×C8—524no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—132no—
606C4⋊C4—261no—
607C4⋊C4—261no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—261no—
611C4⋊C4—261no—
612C4⋊C4—261no—
613C4⋊C4—522no—
614C4⋊C4C22⋊Dic1314yes—
615C4⋊C4C22×Dic1312yes—
616C4⋊C4C22×Dic1312yes—
617C4⋊C4C22×Dic1312yes—
618C22⋊C4—24no—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—522no—
622C22⋊C4—522no—
623C22⋊C4—1041no—
624C22⋊C4C22⋊Dic1314yes—
625C22⋊C4C22⋊Dic1314yes—
626C42—522no—
627C42—1041no—
628C42C22×Dic1312yes—
629C42C2×C22⋊D1312yes—
630C13#2249511yescharacteristic, complemented, Sylow
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23#8818612yes—
649C23#8818612yes—
650C23C2×C22⋊Dic1312yes—
651C23C2×C22⋊Dic1312yes—
652C23C22×C22⋊D1311yescharacteristic
653Q8—48no—
654D4—28no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—48no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—48no—
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×C4—521no—
701C2×C4—1044no—
702C2×C4C2×C22⋊Dic1312yes—
703C2×C4C2×C22⋊Dic1312yes—
704C2×C4C2×C22⋊Dic1312yes—
705C2×C4C2×C22⋊Dic1312yes—
706C2×C4#41×D1311yescharacteristic
707C2×C4#41×D1311yescharacteristic
708C2×C4#8825611yescharacteristic
709C2×C4#8825711yescharacteristic
710C2×C4C23×Dic1311yescharacteristic
711C2×C4C22×C22⋊D1311yescharacteristic
712C8—262no—
713C8—521no—
714C8—521no—
715C8—521no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#1171887614yes—
737C22C2×#8818611yescharacteristic
738C22C2×#8818611yescharacteristic
739C22#1171952911yescharacteristic
740C22#1171953411yescharacteristic
741C22#1171954211yescharacteristic
742C22#1171954311yescharacteristic
743C22C22×C22⋊Dic1311yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—522no—
752C4—1041no—
753C4—1041no—
754C4—1041no—
755C4#1171952911yescharacteristic
756C4#41×Dic1311yescharacteristic
757C4#1171953211yescharacteristic
758C4#1171953411yescharacteristic
759C2—24no—
760C2—42no—
761C2—82no—
762C2#1311766611yescharacteristic
763C2C2×#1171887611yescharacteristic
764C2#1312336911yescharacteristic
765C2#1312679111yescharacteristic
766C2#1312682111yescharacteristic
767C2#1312727011yescharacteristic
768C2#1312730611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#547C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#547D13
hypocenterC13#22495
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. #13117765C2semidirect
3. #13115810C2semidirect
4. #13115785C2semidirect
5. #13115275C2semidirect
6. #13115265C2semidirect
7. #13115159C2semidirect
8. #13115154C2semidirect
9. #13114926C2semidirect
10. #13114922C2semidirect
11. #13114846C2semidirect
12. #13114661C2semidirect
13. #13114555C2semidirect
14. C2×#11718121C2semidirect
18. C13×#547C4semidirect
77. C13×C4⋊Q8C2×C4semidirect
84. C13×#121C2×C4semidirect
87. C4×D4×C13C2×C4semidirect
95. C2×C13×C4⋊C4C2×C4semidirect
230. C4⋊Dic13#41semidirect
246. C2×#1055#41semidirect
351. #547Dic13semidirect
461. C4⋊Q8C2×Dic13semidirect
468. #121C2×Dic13semidirect
471. C4×D4C2×Dic13semidirect
488. C2×C4⋊C4C2×Dic13semidirect
630. C13#22495semidirect

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
#131152752
#131152652
#131151592
#131151542
#131149262
#131149222
#131148462
#131146612
#131145552
C2×#117181212
C2×C13×#5472
#2249513