Finite Group Databasebeta

← #15879312

Subgroups — #15879312

Order 3328.

1186 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic, complemented
2#13117785C211yesmaximal, characteristic, complemented
3#13115806C211yesmaximal, characteristic, complemented
4#13115794C211yesmaximal, characteristic, complemented
5#13115275C211yesmaximal, characteristic, complemented
6#13115265C211yesmaximal, characteristic, complemented
7#13115159C211yesmaximal, characteristic, complemented
8#13115159C211yesmaximal, characteristic, complemented
9#13114931C211yesmaximal, characteristic, complemented
10#13114922C211yesmaximal, characteristic, complemented
11#13114836C211yesmaximal, characteristic, complemented
12#13114661C211yesmaximal, characteristic, complemented
13#13114555C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C2×C13×#553C211yesmaximal, characteristic
16C13×#553—24no—
17C13×#553C418yescomplemented
18C2×C13×#126—21no—
19C2×C13×#125C2211yescharacteristic
20C2×C13×#123—21no—
21C2×C13×#121—21no—
22C2×C13×#121C2211yescharacteristic
23C2×C13×#121C2211yescharacteristic
24C2×C4×D4×C13—21no—
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×#88180C2211yescharacteristic
30C2×#88180C2211yescharacteristic
31C22×#6099C2211yescharacteristic
32C23×#1055C2211yescharacteristic
33#11718882—21no—
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38#11718873C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718672—24no—
43C4⋊C4×Dic13—21no—
44#11718612—21no—
45#11718612—21no—
46#11718596C2211yescharacteristic
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×D4×C13—21no—
63C22×D4×C13—21no—
64C22×D4×C13D411yescharacteristic
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C13×#126—28no—
71C13×#125—22no—
72C13×#125C2×C414yes—
73C13×#123—28no—
74C13×#121—28no—
75C13×#121—22no—
76C13×#121—22no—
77C13×#121C2×C414yes—
78C13×#121C2×C414yes—
79C4×D4×C13—28no—
80C4×D4×C13—22no—
81C4×D4×C13C2×C414yes—
82C4×D4×C13C2×C414yes—
83C4×D4×C13D414yes—
84C13×#117—22no—
85C13×#117C2×C414yes—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—21no—
90C2×C13×C4⋊C4C2×C414yes—
91C2×C13×C4⋊C4D411yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
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×C22⋊Dic13—21no—
104C2×C22⋊Dic13—21no—
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107#88180—22no—
108#88180—22no—
109#88180—41no—
110#88180—41no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13C2311yescharacteristic
114C2×C4⋊Dic13C2311yescharacteristic
115C2×C4⋊Dic13C2311yescharacteristic
116C2×C4⋊Dic13C2311yescharacteristic
117C2×C4×Dic13—21no—
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—
137C22⋊#1055—22no—
138C22⋊#1055—22no—
139C4⋊#1055—22no—
140#88043—22no—
141#22498—131nomaximal, Sylow
142C24×C13—21no—
143C24×C13C2×D411yescharacteristic
144C24×C13C2×D411yescharacteristic
145C2×D4×C13—24no—
146C2×D4×C13—24no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—41no—
153C2×D4×C13—41no—
154C2×D4×C13—42no—
155C2×D4×C13—42no—
156C2×D4×C13—81no—
157C2×D4×C13—81no—
158C2×D4×C13C22⋊C414yes—
159C2×D4×C13C22×C412yes—
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×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—24no—
172C22×C4×C13—24no—
173C22×C4×C13—81no—
174C22×C4×C13—81no—
175C22×C4×C13—81no—
176C22×C4×C13—81no—
177C22×C4×C13C22×C412yes—
178C22×C4×C13C22×C412yes—
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D412yes—
184C22×C4×C13C2×D412yes—
185C22×C4×C13C2411yescharacteristic
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C13×C4⋊C4—24no—
191C13×C4⋊C4—24no—
192C13×C4⋊C4—24no—
193C13×C4⋊C4—21no—
194C13×C4⋊C4—21no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4C22⋊C414yes—
197C13×C4⋊C4C22×C412yes—
198C13×C4⋊C4C22×C412yes—
199C13×C4⋊C4C22×C412yes—
200C13×C22⋊C4—24no—
201C13×C22⋊C4—24no—
202C13×C22⋊C4—24no—
203C13×C22⋊C4—24no—
204C13×C22⋊C4C22⋊C414yes—
205C13×C22⋊C4C22⋊C414yes—
206C42×C13—24no—
207C42×C13C22×C412yes—
208C42×C13C2×D412yes—
209C22⋊Dic13—42no—
210C22⋊Dic13—42no—
211C22⋊Dic13—81no—
212C22⋊Dic13—81no—
213C4⋊Dic13—21no—
214C4⋊Dic13—21no—
215C4⋊Dic13—21no—
216C4⋊Dic13—21no—
217C4⋊Dic13—21no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4⋊Dic13—42no—
221C4⋊Dic13—81no—
222C4⋊Dic13#4112yes—
223C4×Dic13—42no—
224C4×Dic13—42no—
225C4×Dic13—42no—
226#6099—44no—
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—21no—
238C2×#1055—44no—
239C2×#1055#4112yes—
240C2×#553D1311yescharacteristic
241C2×#435—131no—
242#2354—131no—
243#1992—131no—
244#1989—131no—
245#1895—131no—
246#1893—131no—
247#1875—131no—
248#1875—131no—
249#1825—131no—
250#1823—131no—
251#1802—131no—
252#1762—131no—
253#1736—131no—
254#1735—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×C13—21no—
266C23×C13—21no—
267C23×C13—22no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13C2×C22⋊C412yes—
275C23×C13C2×C22⋊C412yes—
276C23×C13C22×D411yescharacteristic
277D4×C13—22no—
278D4×C13—22no—
279D4×C13—44no—
280D4×C13—48no—
281D4×C13—41no—
282D4×C13—41no—
283D4×C13—84no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—21no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—84no—
310C2×C4×C13—84no—
311C2×C4×C13C2×C22⋊C412yes—
312C2×C4×C13C2×C22⋊C412yes—
313C2×C4×C13C2×C22⋊C412yes—
314C2×C4×C13C2×C22⋊C412yes—
315C2×C4×C13C23×C411yescharacteristic
316C2×C4×C13C22×D411yescharacteristic
317C2×C4×C13C2×#4111yescharacteristic
318C2×C4×C13C2×#4111yescharacteristic
319C2×C4×C13H(5,𝔽2)11yescharacteristic
320C2×C4×C132−1+411yescharacteristic
321C2×Dic13—22no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333#1055—22no—
334#1055—41no—
335#1055—41no—
336#1055—41no—
337C22×M16—131no—
338C23×C8—131no—
339#553—24no—
340#553Dic1318yescomplemented
341C2×#126—21no—
342C2×#125C2×D1311yescharacteristic
343C2×#123—21no—
344C2×#121—21no—
345C2×#121C2×D1311yescharacteristic
346C2×#121C2×D1311yescharacteristic
347C2×C4×D4—21no—
348C2×C4×D4C2×D1311yescharacteristic
349C2×C4×D4C2×D1311yescharacteristic
350C2×#117—131no—
351C2×#117—131no—
352C2×#117C2×D1311yescharacteristic
353C22×C4⋊C4C2×D1311yescharacteristic
354#435—264no—
355C2×C4⋊C8—131no—
356C2×#102—131no—
357C2×#102—131no—
358C2×#102—131no—
359C2×#102—131no—
360C2×C22⋊C8—131no—
361C2×C22⋊C8—131no—
362C2×#97—131no—
363#390—261no—
364#388—261no—
365#388—261no—
366#384—131no—
367#380—131no—
368#380—131no—
369C4×C4⋊C4—131no—
370C4×C4⋊C4—261no—
371#340—131no—
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—
383C22×C13—22no—
384C22×C13—22no—
385C22×C13—22no—
386C22×C13—22no—
387C22×C13—22no—
388C22×C13—22no—
389C22×C13—41no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13—41no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—81no—
401C22×C13—81no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13C22×C22⋊C411yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13#54711yescharacteristic
407C22×C13#57511yescharacteristic
408C22×C13#57511yescharacteristic
409C22×C13#57611yescharacteristic
410C22×C13#57711yescharacteristic
411C4×C13—22no—
412C4×C13—22no—
413C4×C13—22no—
414C4×C13—22no—
415C4×C13—42no—
416C4×C13—42no—
417C4×C13—42no—
418C4×C13C4×#4111yescharacteristic
419C4×C13#52011yescharacteristic
420C4×C13#54611yescharacteristic
421C4×C13#54711yescharacteristic
422Dic13—42no—
423Dic13—81no—
424Dic13—81no—
425Dic13—81no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4C22⋊D1311yescharacteristic
429C22×D4C22×D1311yescharacteristic
430C23×C4—21no—
431C23×C4—21no—
432C23×C4C22×D1311yescharacteristic
433C23×C4C22×D1311yescharacteristic
434C2×M16—262no—
435C2×M16—262no—
436C2×M16—521no—
437C22×C8—131no—
438C22×C8—131no—
439C22×C8—131no—
440C22×C8—131no—
441C22×C8—262no—
442C22×C8—262no—
443C22×C8—521no—
444#126—28no—
445#125—22no—
446#125C2×Dic1314yes—
447#123—28no—
448#121—28no—
449#121—22no—
450#121—22no—
451#121C2×Dic1314yes—
452#121C2×Dic1314yes—
453C4×D4—28no—
454C4×D4—22no—
455C4×D4C2×Dic1314yes—
456C4×D4C2×Dic1314yes—
457C4×D4C22⋊D1314yes—
458#117—22no—
459#117—262no—
460#117—262no—
461#117—521no—
462#117—521no—
463#117C2×Dic1314yes—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—131no—
471C2×C4⋊C4—131no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4—261no—
474C2×C4⋊C4C2×Dic1314yes—
475C2×C4⋊C4C22⋊D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C4⋊C4C22×D1311yescharacteristic
478C2×C4⋊C4C22×D1311yescharacteristic
479C2×C22⋊C4—21no—
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—261no—
491C2×C42—261no—
492C2×C42—261no—
493C2×C42C22×D1311yescharacteristic
494C4⋊C8—262no—
495#102—262no—
496#102—262no—
497#102—521no—
498#102—521no—
499C22⋊C8—262no—
500C22⋊C8—262no—
501#97—262no—
502#95—261no—
503#95—261no—
504#95—261no—
505C2×C13—42no—
506C2×C13—42no—
507C2×C13—82no—
508C2×C13#233911yescharacteristic
509C2×C13#289611yescharacteristic
510C2×C13#289711yescharacteristic
511C2×C13#330711yescharacteristic
512C2×C13#330911yescharacteristic
513C2×C13#334711yescharacteristic
514C2×C13#335011yescharacteristic
515C24—21no—
516C24C2×C22⋊D1311yescharacteristic
517C24C2×C22⋊D1311yescharacteristic
518C2×D4—24no—
519C2×D4—24no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—81no—
530C2×D4—81no—
531C2×D4C22⋊Dic1314yes—
532C2×D4C22×Dic1312yes—
533C22×C4—21no—
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—24no—
545C22×C4—24no—
546C22×C4—81no—
547C22×C4—81no—
548C22×C4—81no—
549C22×C4—81no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4C22×Dic1312yes—
555C22×C4C22×Dic1312yes—
556C22×C4C2×C22⋊D1311yescharacteristic
557C22×C4C2×C22⋊D1311yescharacteristic
558C22×C4C2×C22⋊D1311yescharacteristic
559C22×C4C2×C22⋊D1311yescharacteristic
560C22×C4C2×C22⋊D1312yes—
561C22×C4C2×C22⋊D1312yes—
562C22×C4C23×D1311yescharacteristic
563M16—524no—
564C2×C8—132no—
565C2×C8—261no—
566C2×C8—261no—
567C2×C8—261no—
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—524no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—132no—
584C4⋊C4—261no—
585C4⋊C4—261no—
586C4⋊C4—261no—
587C4⋊C4—261no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4—522no—
592C4⋊C4—1041no—
593C4⋊C4C22⋊Dic1314yes—
594C4⋊C4C22×Dic1312yes—
595C4⋊C4C22×Dic1312yes—
596C4⋊C4C22×Dic1312yes—
597C22⋊C4—24no—
598C22⋊C4—24no—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—522no—
602C22⋊C4—522no—
603C22⋊C4—1041no—
604C22⋊C4—1041no—
605C22⋊C4C22⋊Dic1314yes—
606C22⋊C4C22⋊Dic1314yes—
607C42—24no—
608C42—522no—
609C42—522no—
610C42—522no—
611C42C22×Dic1312yes—
612C42C2×C22⋊D1312yes—
613C13#2249811yescharacteristic, complemented, Sylow
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23C2×C22⋊Dic1312yes—
634C23C2×C22⋊Dic1312yes—
635C23C22×C22⋊D1311yescharacteristic
636D4—22no—
637D4—22no—
638D4—44no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—84no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
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—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—84no—
670C2×C4—262no—
671C2×C4—521no—
672C2×C4—521no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—521no—
676C2×C4—521no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4—521no—
680C2×C4—521no—
681C2×C4—521no—
682C2×C4C2×C22⋊Dic1312yes—
683C2×C4C2×C22⋊Dic1312yes—
684C2×C4C2×C22⋊Dic1312yes—
685C2×C4C2×C22⋊Dic1312yes—
686C2×C4#41×D1311yescharacteristic
687C2×C4#41×D1311yescharacteristic
688C2×C4#8825611yescharacteristic
689C2×C4#8825711yescharacteristic
690C2×C4C23×Dic1311yescharacteristic
691C2×C4C22×C22⋊D1311yescharacteristic
692C8—262no—
693C8—521no—
694C8—521no—
695C8—521no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22#1171952711yescharacteristic
718C22#1171952711yescharacteristic
719C22#1171952911yescharacteristic
720C22#1171953411yescharacteristic
721C22#1171954011yescharacteristic
722C22#1171954111yescharacteristic
723C22C22×C22⋊Dic1311yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—522no—
732C4—1041no—
733C4—1041no—
734C4—1041no—
735C4#1171952911yescharacteristic
736C4#41×Dic1311yescharacteristic
737C4#1171953211yescharacteristic
738C4#1171953411yescharacteristic
739C2—42no—
740C2—42no—
741C2—82no—
742C2#1311766611yescharacteristic
743C2#1312335511yescharacteristic
744C2#1312336211yescharacteristic
745C2#1312680611yescharacteristic
746C2#1312683611yescharacteristic
747C2#1312733011yescharacteristic
748C2#1312737511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#553D13
hypocenterC13#22498
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. #13117785C2semidirect
3. #13115806C2semidirect
4. #13115794C2semidirect
5. #13115275C2semidirect
6. #13115265C2semidirect
7. #13115159C2semidirect
8. #13115159C2semidirect
9. #13114931C2semidirect
10. #13114922C2semidirect
11. #13114836C2semidirect
12. #13114661C2semidirect
13. #13114555C2semidirect
14. #13114552C2semidirect
17. C13×#553C4semidirect
340. #553Dic13semidirect
613. C13#22498semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
#131177852
#131158062
#131157942
#131152752
#131152652
#131151592
#131149312
#131149222
#131148362
#131146612
#131145552
#131145522
C2×C13×#5532
#2249813