Finite Group Databasebeta

← #15883154

Subgroups — #15883154

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718789C211yesmaximal, characteristic, complemented
2C2×#11718390C211yesmaximal, characteristic, complemented
3C2×#11718868C211yesmaximal, characteristic, complemented
4C4×#88207C211yesmaximal, characteristic
5#13115632C211yesmaximal, characteristic, complemented
6#13115445C211yesmaximal, characteristic, complemented
7#13115439C211yesmaximal, characteristic, complemented
8#13115133C211yesmaximal, characteristic, complemented
9#13115131C211yesmaximal, characteristic, complemented
10#13115130C211yesmaximal, characteristic, complemented
11#13115019C211yesmaximal, characteristic, complemented
12#13115018C211yesmaximal, characteristic, complemented
13#13114622C211yesmaximal, characteristic, complemented
14#13114617C211yesmaximal, characteristic, complemented
15C2×C13×#407C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C22×C13×M16C2211yescharacteristic
18C22×C13×M16C2211yescharacteristic
19C2×#88207C411yescharacteristic
20C2×C4×C22⋊D13C2211yescharacteristic
21C2×C4×C22⋊D13C2211yescharacteristic
22C2×C4×C22⋊D13C2211yescharacteristic
23C22×#6099C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C22×#6094C2211yescharacteristic, complemented
26C13×#407—24no—
27C2×C13×C22⋊C8C2211yescharacteristic
28C2×C13×C22⋊C8C2211yescharacteristic
29C2×C13×C22⋊C8C2211yescharacteristic
30C2×C13×C22⋊C8C2211yescharacteristic
31#11718908C411yescharacteristic
32#11718874C411yescharacteristic
33#11718874C411yescharacteristic
34#11718874C411yescharacteristic
35#11718871C411yescharacteristic
36#11718871C411yescharacteristic
37#11718871C411yescharacteristic
38C4×C22⋊Dic13C2211yescharacteristic
39C4×C22⋊Dic13C2211yescharacteristic
40C4×C22⋊Dic13C2211yescharacteristic
41#11718868—24no—
42C2×C22⋊#1055C2211yescharacteristic
43C2×C22⋊#1055C2211yescharacteristic
44C2×C22⋊#1055C2211yescharacteristic
45C2×C22⋊#1055C2211yescharacteristic
46#11718789—24no—
47C2×#88060C2211yescharacteristic, complemented
48C2×#88060C2211yescharacteristic, complemented
49C2×#88060C2211yescharacteristic, complemented
50C2×#88055C2211yescharacteristic, complemented
51C2×#88054C2211yescharacteristic, complemented
52C2×#88054C2211yescharacteristic, complemented
53C2×#88054C2211yescharacteristic, complemented
54C2×C8×Dic13C2211yescharacteristic, complemented
55C2×C8×Dic13C2211yescharacteristic, complemented
56#11718390—24no—
57#11718142C2211yescharacteristic, complemented
58#11718142C2211yescharacteristic, complemented
59#11718142C2211yescharacteristic, complemented
60#11718142C2211yescharacteristic, complemented
61#11718142C2211yescharacteristic, complemented
62#11718142C2211yescharacteristic, complemented
63C25×C13C2×C411yescharacteristic
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—41no—
69C23×C4×C13—41no—
70C23×C4×C13C2×C411yescharacteristic
71C23×C4×C13C2×C411yescharacteristic
72C23×C4×C13C2×C411yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C22×C22⋊D13C2×C411yescharacteristic
77C22×C22⋊D13C2×C411yescharacteristic
78C22×C22⋊D13C2×C411yescharacteristic
79C22×C4×D13C2311yescharacteristic
80C2×C13×M16—22no—
81C2×C13×M16—22no—
82C2×C13×M16—22no—
83C2×C13×M16—22no—
84C2×C13×M16—41no—
85C2×C13×M16—41no—
86C22×C8×C13C2311yescharacteristic
87C22×C8×C13C2311yescharacteristic
88C22×C8×C13C2311yescharacteristic
89C22×C8×C13C2311yescharacteristic
90#88207—24no—
91C2×C22⋊Dic13C2×C411yescharacteristic
92C2×C22⋊Dic13C2×C411yescharacteristic
93C2×C22⋊Dic13C2×C411yescharacteristic
94C2×C22⋊Dic13C2×C411yescharacteristic
95C2×C22⋊Dic13C2×C411yescharacteristic
96C2×C22⋊Dic13C2×C411yescharacteristic
97C2×C22⋊Dic13C2×C411yescharacteristic
98C2×C22⋊Dic13C2×C411yescharacteristic
99C2×C22⋊Dic13C2×C411yescharacteristic
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C4×C22⋊D13—22no—
104C4×C22⋊D13—41no—
105C4×C22⋊D13—41no—
106C2×#6103C2×C411yescharacteristic
107C2×#6103C2×C411yescharacteristic
108C2×#6103C2×C411yescharacteristic
109C2×#6101C2×C411yescharacteristic
110C2×#6101C2×C411yescharacteristic
111C2×#6101C2×C411yescharacteristic
112C2×C4×Dic13C2311yescharacteristic
113C2×C4×Dic13C2311yescharacteristic
114C2×C4×Dic13C2311yescharacteristic
115C2×#6099—22no—
116C2×#6099—22no—
117C2×#6099—22no—
118C2×#6099—22no—
119C2×#6099—41no—
120C2×#6099—41no—
121C22×#1055C2311yescharacteristic
122C22×#1055C2311yescharacteristic
123C22×#1055C2311yescharacteristic
124C22×#1055C2311yescharacteristic
125C2×#6094—22no—
126C2×#6094—22no—
127C2×#6094—41no—
128C13×C22⋊C8—22no—
129C13×C22⋊C8—22no—
130C13×C22⋊C8—22no—
131C13×C22⋊C8D414yescomplemented
132#88071C2×C411yescharacteristic
133#88071C2×C411yescharacteristic
134#88071C2×C411yescharacteristic
135#88071C2×C411yescharacteristic
136#88071C2×C411yescharacteristic
137#88071C2×C411yescharacteristic
138C22⋊#1055—22no—
139C22⋊#1055—22no—
140C22⋊#1055—22no—
141C22⋊#1055D414yescomplemented
142#88060—22no—
143#88060—22no—
144#88060—41no—
145#88055—41no—
146#88054—22no—
147#88054—22no—
148#88054—41no—
149C8×Dic13—22no—
150C8×Dic13—22no—
151#22852—131nomaximal, Sylow
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—41no—
156C24×C13—41no—
157C24×C13—41no—
158C24×C13—41no—
159C24×C13C22×C411yescharacteristic
160C24×C13C22×C411yescharacteristic
161C24×C13C22×C411yescharacteristic
162C23×D13C22×C411yescharacteristic
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—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—41no—
184C22×C4×C13—41no—
185C22×C4×C13—41no—
186C22×C4×C13—44no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13C22×C411yescharacteristic
191C22×C4×C13C22×C411yescharacteristic
192C22×C4×C13C22×C411yescharacteristic
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13C2411yescharacteristic
198C2×C22⋊D13—22no—
199C2×C22⋊D13—22no—
200C2×C22⋊D13—22no—
201C2×C22⋊D13—22no—
202C2×C22⋊D13—22no—
203C2×C22⋊D13—41no—
204C2×C22⋊D13—41no—
205C2×C22⋊D13—41no—
206C2×C22⋊D13—41no—
207C22×Dic13C22×C411yescharacteristic
208C22×Dic13C22×C411yescharacteristic
209C22×Dic13C22×C411yescharacteristic
210C22×Dic13C22×C411yescharacteristic
211C22×Dic13C22×C411yescharacteristic
212C22×Dic13C22×C411yescharacteristic
213C22×Dic13C22×C411yescharacteristic
214C2×C4×D13—21no—
215C2×C4×D13—21no—
216C2×C4×D13—21no—
217C2×C4×D13—21no—
218C2×C4×D13—21no—
219C2×C4×D13—21no—
220C13×M16—44no—
221C13×M16—44no—
222C2×C8×C13—21no—
223C2×C8×C13—21no—
224C2×C8×C13—21no—
225C2×C8×C13—21no—
226C2×C8×C13—21no—
227C2×C8×C13—21no—
228C2×C8×C13—21no—
229C2×C8×C13—21no—
230C2×C8×C13—21no—
231C2×C8×C13—21no—
232C2×C8×C13C2×D412yes—
233C2×C8×C13C2×D412yes—
234C22⋊Dic13—22no—
235C22⋊Dic13—22no—
236C22⋊Dic13—22no—
237C22⋊Dic13—22no—
238C22⋊Dic13—41no—
239C22⋊Dic13—41no—
240C22⋊Dic13—41no—
241C22⋊Dic13—41no—
242C22⋊Dic13M1614yescomplemented
243#6103—22no—
244#6103—22no—
245#6103—41no—
246#6101—22no—
247#6101—22no—
248#6101—41no—
249C4×Dic13—21no—
250C4×Dic13—21no—
251C4×Dic13—21no—
252C4×Dic13—21no—
253C4×Dic13—21no—
254C4×Dic13—21no—
255#6099—44no—
256#6099—44no—
257C2×#1055—21no—
258C2×#1055—21no—
259C2×#1055—21no—
260C2×#1055—21no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055C2×D412yes—
268C2×#1055C2×D412yes—
269#6094—44no—
270C2×#436—131no—
271C2×#436—131no—
272C2×#407—131no—
273C2×#407D1311yescharacteristic, complemented
274C4×#120—131no—
275#1955—131no—
276#1923—131no—
277#1923—131no—
278#1870—131no—
279#1870—131no—
280#1870—131no—
281#1851—131no—
282#1851—131no—
283#1753—131no—
284#1753—131no—
285C23×C13—21no—
286C23×C13—21no—
287C23×C13—21no—
288C23×C13—21no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13—21no—
300C23×C13—21no—
301C23×C13—21no—
302C23×C13—21no—
303C23×C13—44no—
304C23×C13—44no—
305C23×C13—44no—
306C23×C13—44no—
307C23×C13—44no—
308C23×C13—44no—
309C23×C13—44no—
310C23×C13C4×D412yes—
311C23×C13C4×D412yes—
312C23×C13C2×M1612yes—
313C23×C13C23×C411yescharacteristic
314C22×D13—21no—
315C22×D13—21no—
316C22×D13—21no—
317C22×D13—21no—
318C22×D13—21no—
319C22×D13—21no—
320C22×D13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—21no—
324C2×C4×C13—21no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—21no—
334C2×C4×C13—21no—
335C2×C4×C13—21no—
336C2×C4×C13—44no—
337C2×C4×C13—44no—
338C2×C4×C13—44no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13C4×D412yes—
344C2×C4×C13C4×D412yes—
345C2×C4×C13C22×D411yescharacteristic
346C2×C4×C13C22×D411yescharacteristic
347C2×C4×C13C2×#4111yescharacteristic
348C2×C4×C13C2×#4111yescharacteristic
349C2×C4×C13H(5,𝔽2)11yescharacteristic
350C2×C4×C13H(5,𝔽2)11yescharacteristic
351C22⋊D13—44no—
352C22⋊D13—44no—
353C22⋊D13—44no—
354C2×Dic13—21no—
355C2×Dic13—21no—
356C2×Dic13—21no—
357C2×Dic13—21no—
358C2×Dic13—21no—
359C2×Dic13—21no—
360C2×Dic13—21no—
361C2×Dic13—21no—
362C2×Dic13—21no—
363C2×Dic13—21no—
364C2×Dic13—21no—
365C2×Dic13—21no—
366C2×Dic13—21no—
367C2×Dic13—21no—
368C2×Dic13—21no—
369C2×Dic13—21no—
370C2×Dic13—21no—
371C2×Dic13—21no—
372C2×Dic13—21no—
373C2×Dic13C2×M1612yes—
374C2×Dic13C2×M1612yes—
375C4×D13—41no—
376C4×D13—41no—
377C4×D13—41no—
378C4×D13—41no—
379C8×C13—22no—
380C8×C13—22no—
381C8×C13—41no—
382C8×C13—41no—
383#1055—22no—
384#1055—22no—
385#1055—41no—
386#1055—41no—
387C24×C4C2×D1311yescharacteristic
388C22×M16—131no—
389C22×M16—131no—
390C22×M16—131no—
391C22×M16C2×D1311yescharacteristic
392C22×M16C2×D1311yescharacteristic
393C2×#120—131no—
394C2×C4×D4—131no—
395C2×C4×D4—131no—
396C2×C4×D4—131no—
397#436—264no—
398#436—264no—
399C2×C4⋊C8—131no—
400C2×C4⋊C8—131no—
401C2×C4⋊C8—131no—
402#407—24no—
403#407—264no—
404C2×C22⋊C8—131no—
405C2×C22⋊C8—131no—
406C2×C22⋊C8—131no—
407C2×C22⋊C8—131no—
408C2×C22⋊C8—131no—
409C2×C22⋊C8—131no—
410C2×C22⋊C8—131no—
411C2×C22⋊C8C2×D1311yescharacteristic
412C2×C22⋊C8C2×D1311yescharacteristic
413C2×C22⋊C8C2×D1311yescharacteristic
414C2×C22⋊C8C2×D1311yescharacteristic
415C2×#97—131no—
416C2×C4×C8—131no—
417C2×C4×C8—131no—
418#386—131no—
419#386—131no—
420#386—131no—
421#385—131no—
422#385—131no—
423#385—131no—
424#379—131no—
425C4×C22⋊C4—131no—
426C4×C22⋊C4—131no—
427C4×C22⋊C4—131no—
428#336—131no—
429#336—131no—
430#336—131no—
431#336—131no—
432#336—131no—
433#336—131no—
434C22×C13—22no—
435C22×C13—22no—
436C22×C13—22no—
437C22×C13—22no—
438C22×C13—22no—
439C22×C13—22no—
440C22×C13—22no—
441C22×C13—22no—
442C22×C13—22no—
443C22×C13—416no—
444C22×C13—41no—
445C22×C13—41no—
446C22×C13—41no—
447C22×C13—41no—
448C22×C13—41no—
449C22×C13—41no—
450C22×C13—41no—
451C22×C13—41no—
452C22×C13—41no—
453C22×C13—41no—
454C22×C13—41no—
455C22×C13—41no—
456C22×C13C2×C4×D411yescharacteristic
457C22×C13C2×C4×D411yescharacteristic
458C22×C13#51811yescharacteristic
459C22×C13C22×M1611yescharacteristic
460C22×C13#56811yescharacteristic
461C22×C13#56811yescharacteristic
462C22×C13#56811yescharacteristic
463C2×D13—41no—
464C2×D13—41no—
465C2×D13—41no—
466C2×D13—41no—
467C2×D13—41no—
468C2×D13—41no—
469C2×D13—41no—
470C4×C13—22no—
471C4×C13—22no—
472C4×C13—41no—
473C4×C13D4211yescharacteristic
474C4×C13#54611yescharacteristic
475C4×C13#54611yescharacteristic
476C4×C13#55111yescharacteristic
477Dic13—22no—
478Dic13—22no—
479Dic13—41no—
480Dic13—41no—
481Dic13—41no—
482Dic13—41no—
483Dic13—41no—
484C25C4×D1311yescharacteristic
485C22×D4—131no—
486C22×D4—131no—
487C22×D4—131no—
488C23×C4—22no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—22no—
492C23×C4—41no—
493C23×C4—41no—
494C23×C4—131no—
495C23×C4C4×D1311yescharacteristic
496C23×C4C4×D1311yescharacteristic
497C23×C4C4×D1311yescharacteristic
498C23×C4C22×D1311yescharacteristic
499C23×C4C22×D1311yescharacteristic
500C23×C4C22×D1311yescharacteristic
501C2×M16—22no—
502C2×M16—22no—
503C2×M16—22no—
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C2×M16—262no—
508C2×M16—262no—
509C2×M16—262no—
510C2×M16—262no—
511C2×M16—262no—
512C2×M16—262no—
513C2×M16—521no—
514C2×M16—521no—
515C2×M16—521no—
516C22×C8—131no—
517C22×C8—131no—
518C22×C8—131no—
519C22×C8—131no—
520C22×C8C22×D1311yescharacteristic
521C22×C8C22×D1311yescharacteristic
522C22×C8C22×D1311yescharacteristic
523C22×C8C22×D1311yescharacteristic
524#120—264no—
525C4×D4—262no—
526C4×D4—262no—
527C4×D4—262no—
528C4×D4—262no—
529C4×D4—521no—
530C4×D4—521no—
531C2×C4⋊C4—131no—
532C2×C4⋊C4—131no—
533C2×C4⋊C4—131no—
534C2×C22⋊C4—131no—
535C2×C22⋊C4—131no—
536C2×C22⋊C4—131no—
537C2×C22⋊C4—131no—
538C2×C22⋊C4—131no—
539C2×C22⋊C4—131no—
540C2×C22⋊C4—131no—
541C2×C22⋊C4—131no—
542C2×C22⋊C4—131no—
543C2×C22⋊C4—131no—
544C2×C22⋊C4—131no—
545C2×C22⋊C4—131no—
546C2×C42—131no—
547C2×C42—131no—
548C2×C42—131no—
549C4⋊C8—262no—
550C4⋊C8—262no—
551C4⋊C8—521no—
552C22⋊C8—22no—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C22⋊C8—134no—
556C22⋊C8—262no—
557C22⋊C8—262no—
558C22⋊C8—262no—
559C22⋊C8—262no—
560C22⋊C8—262no—
561C22⋊C8—521no—
562C22⋊C8C22⋊D1314yescomplemented
563#97—521no—
564C4×C8—262no—
565C4×C8—262no—
566#95—131no—
567#95—131no—
568#95—131no—
569#95—131no—
570#95—131no—
571#95—131no—
572C2×C13—42no—
573C2×C13—42no—
574C2×C13—42no—
575C2×C13#235811yescharacteristic
576C2×C13#293011yescharacteristic
577C2×C13#293011yescharacteristic
578C2×C13D4×M1611yescharacteristic
579C2×C13D4×M1611yescharacteristic
580C2×C13#297511yescharacteristic
581C2×C13#297811yescharacteristic
582D13—81no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—41no—
587C24—41no—
588C24—41no—
589C24—41no—
590C24—131no—
591C24C2×C4×D1311yescharacteristic
592C24C2×C4×D1311yescharacteristic
593C24C2×C4×D1311yescharacteristic
594C2×D4—262no—
595C2×D4—262no—
596C2×D4—262no—
597C2×D4—262no—
598C2×D4—262no—
599C2×D4—521no—
600C2×D4—521no—
601C2×D4—521no—
602C2×D4—521no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—131no—
631C22×C4—131no—
632C22×C4—131no—
633C22×C4—131no—
634C22×C4—131no—
635C22×C4—131no—
636C22×C4—131no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4C2×C4×D1311yescharacteristic
644C22×C4C2×C4×D1311yescharacteristic
645C22×C4C2×C4×D1311yescharacteristic
646C22×C4#612712yes—
647C22×C4D4×D1312yes—
648C22×C4#612912yes—
649C22×C4C2×C22⋊D1312yes—
650C22×C4C23×D1311yescharacteristic
651M16—44no—
652M16—44no—
653M16—524no—
654M16—524no—
655M16—524no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—132no—
667C2×C8—132no—
668C2×C8—261no—
669C2×C8—261no—
670C2×C8—261no—
671C2×C8—261no—
672C2×C8—261no—
673C2×C8—261no—
674C2×C8—261no—
675C2×C8—261no—
676C2×C8—261no—
677C2×C8—261no—
678C2×C8C2×C22⋊D1312yes—
679C2×C8C2×C22⋊D1312yes—
680C4⋊C4—262no—
681C4⋊C4—262no—
682C4⋊C4—521no—
683C22⋊C4—134no—
684C22⋊C4—262no—
685C22⋊C4—262no—
686C22⋊C4—262no—
687C22⋊C4—262no—
688C22⋊C4—262no—
689C22⋊C4—262no—
690C22⋊C4—521no—
691C22⋊C4—521no—
692C22⋊C4—521no—
693C22⋊C4—521no—
694C22⋊C4—521no—
695C42—261no—
696C42—261no—
697C42—261no—
698C42—261no—
699C42—261no—
700C42—261no—
701C13#2285211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—261no—
728C23—261no—
729C23—261no—
730C23—261no—
731C23—261no—
732C23—261no—
733C23—261no—
734C23#8813512yes—
735C23M16×D1312yes—
736C23C4×C22⋊D1312yes—
737C23C22×C4×D1311yescharacteristic
738D4—524no—
739D4—524no—
740D4—524no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—132no—
764C2×C4—132no—
765C2×C4—261no—
766C2×C4—261no—
767C2×C4—261no—
768C2×C4—261no—
769C2×C4—261no—
770C2×C4—261no—
771C2×C4—261no—
772C2×C4—261no—
773C2×C4—261no—
774C2×C4—261no—
775C2×C4—261no—
776C2×C4—261no—
777C2×C4—261no—
778C2×C4—261no—
779C2×C4—261no—
780C2×C4—261no—
781C2×C4—261no—
782C2×C4—261no—
783C2×C4—261no—
784C2×C4—521no—
785C2×C4—521no—
786C2×C4—521no—
787C2×C4—521no—
788C2×C4#8813512yes—
789C2×C4C4×C22⋊D1312yes—
790C2×C4C2×#612711yescharacteristic
791C2×C4C2×D4×D1311yescharacteristic
792C2×C4C2×#612911yescharacteristic
793C2×C4#8825111yescharacteristic
794C2×C4#8825111yescharacteristic
795C2×C4C22×C22⋊D1311yescharacteristic
796C8—22no—
797C8—22no—
798C8—41no—
799C8—41no—
800C8—262no—
801C8—262no—
802C8—521no—
803C8—521no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—416no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—521no—
827C22—521no—
828C22—521no—
829C22—521no—
830C22—521no—
831C22—521no—
832C22—521no—
833C22C2×#8813511yescharacteristic
834C22#1171919111yescharacteristic
835C22C2×M16×D1311yescharacteristic
836C22#1171945011yescharacteristic
837C22#1171945011yescharacteristic
838C22#1171945011yescharacteristic
839C22C2×C4×C22⋊D1311yescharacteristic
840C4—22no—
841C4—22no—
842C4—41no—
843C4—262no—
844C4—262no—
845C4—521no—
846C4—521no—
847C4—521no—
848C4—521no—
849C4—521no—
850C4#1171919511yescharacteristic
851C4#1171920011yescharacteristic
852C4D4×C22⋊D1311yescharacteristic
853C4#1171951111yescharacteristic
854C2—42no—
855C2—42no—
856C2—42no—
857C2—1041no—
858C2#1311781511yescharacteristic
859C2#1312353511yescharacteristic
860C2#1312353911yescharacteristic
861C2#1312356811yescharacteristic
862C2M16×C22⋊D1311yescharacteristic
863C2#1312387511yescharacteristic
864C2#1312389611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#407C2
prime radicalC2×#88207C4
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13#22852
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#11718789C2semidirect
2. C2×#11718390C2semidirect
3. C2×#11718868C2semidirect
5. #13115632C2semidirect
6. #13115445C2semidirect
7. #13115439C2semidirect
8. #13115133C2semidirect
9. #13115131C2semidirect
10. #13115130C2semidirect
11. #13115019C2semidirect
12. #13115018C2semidirect
13. #13114622C2semidirect
14. #13114617C2semidirect
15. C2×C13×#407C2semidirect
25. C22×#6094C22semidirect
47. C2×#88060C22semidirect
48. C2×#88060C22semidirect
49. C2×#88060C22semidirect
50. C2×#88055C22semidirect
51. C2×#88054C22semidirect
52. C2×#88054C22semidirect
53. C2×#88054C22semidirect
54. C2×C8×Dic13C22semidirect
55. C2×C8×Dic13C22semidirect
57. #11718142C22semidirect
58. #11718142C22semidirect
59. #11718142C22semidirect
60. #11718142C22semidirect
61. #11718142C22semidirect
62. #11718142C22semidirect
131. C13×C22⋊C8D4semidirect
141. C22⋊#1055D4semidirect
242. C22⋊Dic13M16semidirect
273. C2×#407D13semidirect
562. C22⋊C8C22⋊D13semidirect
701. C13#22852semidirect

Maximal subgroups

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

subgroupindex
C2×#117187892
C2×#117183902
C2×#117188682
C4×#882072
#131156322
#131154452
#131154392
#131151332
#131151312
#131151302
#131150192
#131150182
#131146222
#131146172
C2×C13×#4072
#2285213