Finite Group Databasebeta

← #15794158

Subgroups — #15794158

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D13C211yesmaximal, characteristic
2C2×#11718634C211yesmaximal, characteristic, complemented
3C2×#11718650C212yesmaximal
4C2×#11718648C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6#13113068C212yesmaximal, complemented
7#13113067C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C23×C4×D13C2211yescharacteristic
14C23×C4×D13C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C13×C4⋊C4C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C2×C42×D13—24no—
28C2×C42×D13—24no—
29C2×C42×D13—24no—
30C13×#389—24no—
31C2×C13×#95C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39#11718650—28no—
40#11718648—24no—
41#11718648C418yescomplemented
42#11718634—24no—
43C24×D13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—22no—
61C22×C4×D13—22no—
62C22×C4×D13—22no—
63C22×C4×D13—22no—
64C22×C4×D13—22no—
65C22×C4×D13—22no—
66C22×C4×D13—22no—
67C22×C4×D13—22no—
68C22×C4×D13—22no—
69C22×C4×D13—22no—
70C22×C4×D13C2×C414yes—
71C22×C4×D13D414yes—
72C22×C4×D13D414yes—
73C22×C4×D13Q814yes—
74C22×C4×D13Q814yes—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—24no—
82C2×C13×C4⋊C4—24no—
83C2×C13×C4⋊C4C2×C414yescomplemented
84C2×C42×C13—22no—
85C2×C42×C13—22no—
86C2×C42×C13D414yes—
87C2×#6103—24no—
88C2×#6103—24no—
89C2×#6103—24no—
90C2×#6103—24no—
91C2×#6103—24no—
92C2×#6103C2×C418yes—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13C2×C414yescomplemented
99C2×#6101—24no—
100C2×#6101—24no—
101C2×#6101—24no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13D414yes—
111C42×D13—232no—
112C13×#95—24no—
113#88071—24no—
114#88071—24no—
115#88071—24no—
116#88071—24no—
117#88071—24no—
118#88071—24no—
119#88071C2×C418yescomplemented
120#14697—131nomaximal, Sylow
121C24×C13C2411yescharacteristic
122C23×D13—21no—
123C23×D13—21no—
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—21no—
129C23×D13—21no—
130C23×D13C22×C412yes—
131C23×D13C2×D412yes—
132C23×D13C2×D412yes—
133C23×D13C2×Q812yes—
134C23×D13C2×Q812yes—
135C23×D13#4112yes—
136C23×D13#4112yes—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13C22×C414yes—
159C22×C4×C13C22×C412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×Q812yes—
167C22×C4×C13C2×Q812yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×C4×C13#4112yes—
171C22×C4×C13#4112yes—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13C22×C414yes—
198C22×Dic13C22×C412yes—
199C22×Dic13C2×D412yes—
200C22×Dic13C2×D412yes—
201C22×Dic13C2×D412yes—
202C22×Dic13C2×D412yes—
203C22×Dic13C2×Q812yes—
204C22×Dic13C2×Q812yes—
205C22×Dic13#4112yes—
206C22×Dic13#4112yes—
207C2×C4×D13—28no—
208C2×C4×D13—28no—
209C2×C4×D13—28no—
210C2×C4×D13—28no—
211C2×C4×D13—28no—
212C2×C4×D13—28no—
213C2×C4×D13—28no—
214C2×C4×D13—28no—
215C2×C4×D13—28no—
216C2×C4×D13—28no—
217C2×C4×D13—28no—
218C2×C4×D13—28no—
219C2×C4×D13—28no—
220C2×C4×D13—28no—
221C2×C4×D13—28no—
222C2×C4×D13—28no—
223C2×C4×D13—28no—
224C2×C4×D13—28no—
225C2×C4×D13—28no—
226C2×C4×D13—28no—
227C2×C4×D13C4⋊C4116yescomplemented
228C13×C4⋊C4—28no—
229C13×C4⋊C4—44no—
230C13×C4⋊C4—48no—
231C42×C13—28no—
232#6103—216no—
233#6103—48no—
234C4⋊Dic13—28no—
235C4⋊Dic13—44no—
236#6101—48no—
237C4×Dic13—28no—
238C4×Dic13—28no—
239C4×Dic13—28no—
240C23×C42—131no—
241C2×#389—131no—
242C2×#389D1311yescharacteristic, complemented
243C2×#385—132no—
244C2×#380—131no—
245C2×#380—131no—
246#1436—132no—
247#1436—132no—
248C4⋊#95—131no—
249C4⋊#95—131no—
250C22⋊#95—132no—
251C23×C13C23×C411yescharacteristic
252C23×C13C22×D411yescharacteristic
253C23×C13C22×D411yescharacteristic
254C23×C13C22×D411yescharacteristic
255C23×C13C22×D411yescharacteristic
256C23×C13C22×Q811yescharacteristic
257C23×C13C22×Q811yescharacteristic
258C23×C13C2×#4111yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—22no—
281C22×D13—22no—
282C22×D13—22no—
283C22×D13—22no—
284C22×D13—22no—
285C22×D13—22no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13C2×C4⋊C414yes—
295C22×D13C4×D414yes—
296C22×D13C4×Q814yes—
297C22×D13#12114yes—
298C22×D13C22⋊Q814yes—
299C22×D13#12514yes—
300C22×D13C4⋊Q814yes—
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—22no—
312C2×C4×C13—22no—
313C2×C4×C13—24no—
314C2×C4×C13—24no—
315C2×C4×C13—24no—
316C2×C4×C13—42no—
317C2×C4×C13—42no—
318C2×C4×C13—42no—
319C2×C4×C13—42no—
320C2×C4×C13—42no—
321C2×C4×C13—42no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—42no—
325C2×C4×C13—42no—
326C2×C4×C13—42no—
327C2×C4×C13C2×C4⋊C414yes—
328C2×C4×C13C4×D414yes—
329C2×C4×C13C4×D414yes—
330C2×C4×C13#12014yes—
331C2×C4×C13#12114yes—
332C2×C4×C13C22⋊Q814yes—
333C2×C4×C13C22⋊Q814yes—
334C2×C4×C13C22⋊Q814yes—
335C2×C4×C13#12314yes—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—22no—
351C2×Dic13—22no—
352C2×Dic13—22no—
353C2×Dic13—22no—
354C2×Dic13—24no—
355C2×Dic13—24no—
356C2×Dic13—24no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13—42no—
362C2×Dic13—42no—
363C2×Dic13—42no—
364C2×Dic13—42no—
365C2×Dic13—42no—
366C2×Dic13—42no—
367C2×Dic13—42no—
368C2×Dic13C2×C4⋊C414yes—
369C2×Dic13#12114yes—
370C2×Dic13C22⋊Q814yes—
371C4×D13—232no—
372C4×D13—232no—
373C4×D13—232no—
374C24×C4—131no—
375C24×C4—131no—
376C24×C4—131no—
377C22×C4⋊C4—131no—
378C22×C4⋊C4—132no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4C2×D1312yes—
381C22×C4⋊C4C2×D1311yescharacteristic
382C22×C4⋊C4C2×D1311yescharacteristic
383C22×C22⋊C4—132no—
384C22×C22⋊C4—132no—
385C22×C42—131no—
386C22×C42—131no—
387C22×C42—131no—
388C22×C42—264no—
389C22×C42—264no—
390C22×C42—264no—
391C22×C42C2×D1311yescharacteristic
392#389—24no—
393#389—264no—
394#385—268no—
395#380—138no—
396#380—264no—
397C2×#95—132no—
398C2×#95—132no—
399C2×#95—132no—
400C2×#95—132no—
401C2×#95—132no—
402C2×#95—132no—
403C2×#95—132no—
404C2×#95C2×D1312yes—
405C22×C13C22×C4⋊C411yescharacteristic
406C22×C13C2×C4×D411yescharacteristic
407C22×C13C2×C4×D411yescharacteristic
408C22×C13C2×C4×D411yescharacteristic
409C22×C13C2×C4×Q811yescharacteristic
410C22×C13C4×#4111yescharacteristic
411C22×C13C4×#4111yescharacteristic
412C22×C13C2×#12011yescharacteristic
413C22×C13C2×#12111yescharacteristic
414C22×C13C2×#12111yescharacteristic
415C22×C13C2×#12111yescharacteristic
416C22×C13C2×C22⋊Q811yescharacteristic
417C22×C13C2×C22⋊Q811yescharacteristic
418C22×C13C2×C22⋊Q811yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13C2×C22⋊Q811yescharacteristic
421C22×C13C2×#12311yescharacteristic
422C22×C13#52511yescharacteristic
423C22×C13#52511yescharacteristic
424C22×C13#52511yescharacteristic
425C22×C13#52511yescharacteristic
426C22×C13#52511yescharacteristic
427C22×C13#52511yescharacteristic
428C22×C13C2×#12511yescharacteristic
429C22×C13#52911yescharacteristic
430C22×C13#52911yescharacteristic
431C22×C13#52911yescharacteristic
432C22×C13#52911yescharacteristic
433C22×C13C2×C4⋊Q811yescharacteristic
434C22×C13#53211yescharacteristic
435C22×C13#53211yescharacteristic
436C22×C13#53311yescharacteristic
437C22×C13#53311yescharacteristic
438C22×C13#53311yescharacteristic
439C22×C13#53311yescharacteristic
440C2×D13—24no—
441C2×D13—24no—
442C2×D13—24no—
443C2×D13—24no—
444C2×D13—24no—
445C2×D13—24no—
446C2×D13—24no—
447C2×D13—24no—
448C2×D13—24no—
449C2×D13—24no—
450C2×D13—24no—
451C2×D13—24no—
452C2×D13—24no—
453C2×D13—24no—
454C2×D13#38918yescomplemented
455C4×C13—24no—
456C4×C13—24no—
457C4×C13—44no—
458C4×C13—82no—
459C4×C13#38518yescomplemented
460Dic13—24no—
461Dic13—24no—
462Dic13—24no—
463Dic13—44no—
464Dic13—82no—
465C25—131no—
466C23×C4—131no—
467C23×C4—131no—
468C23×C4—131no—
469C23×C4—134no—
470C23×C4—134no—
471C23×C4—134no—
472C23×C4—132no—
473C23×C4—134no—
474C23×C4—134no—
475C23×C4—132no—
476C23×C4—262no—
477C23×C4—262no—
478C23×C4—262no—
479C23×C4—262no—
480C23×C4—262no—
481C23×C4—262no—
482C23×C4—262no—
483C23×C4—262no—
484C23×C4—262no—
485C23×C4—262no—
486C23×C4—262no—
487C23×C4—262no—
488C23×C4—262no—
489C23×C4—262no—
490C23×C4—262no—
491C23×C4—262no—
492C23×C4C22×D1312yes—
493C23×C4C22×D1312yes—
494C23×C4C22×D1311yescharacteristic
495C23×C4C22×D1311yescharacteristic
496C23×C4C22×D1311yescharacteristic
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—134no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—264no—
509C2×C4⋊C4—264no—
510C2×C4⋊C4—264no—
511C2×C4⋊C4—262no—
512C2×C4⋊C4—262no—
513C2×C4⋊C4—262no—
514C2×C4⋊C4C4×D1314yescomplemented
515C2×C22⋊C4—138no—
516C2×C22⋊C4—264no—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—134no—
524C2×C42—2632no—
525C2×C42—262no—
526C2×C42—262no—
527C2×C42—262no—
528C2×C42—262no—
529C2×C42—262no—
530C2×C42—262no—
531C2×C42—262no—
532C2×C42—262no—
533C2×C42C22⋊D1314yes—
534#95—24no—
535#95—138no—
536#95—264no—
537#95—264no—
538#95—264no—
539#95—264no—
540#95—264no—
541#95—264no—
542C2×C13C2×#38511yescharacteristic
543C2×C13C2×#38911yescharacteristic
544C2×C13#229611yescharacteristic
545C2×C13C4×#12111yescharacteristic
546C2×C13C4×#12111yescharacteristic
547C2×C13C4×C22⋊Q811yescharacteristic
548C2×C13C4×C22⋊Q811yescharacteristic
549C2×C13#284711yescharacteristic
550C2×C13#284811yescharacteristic
551C2×C13#285111yescharacteristic
552C2×C13#285111yescharacteristic
553C2×C13#285411yescharacteristic
554C2×C13#285511yescharacteristic
555C2×C13#285711yescharacteristic
556C2×C13#285711yescharacteristic
557D13—28no—
558C24—132no—
559C24—132no—
560C24—132no—
561C24—132no—
562C24—132no—
563C24—132no—
564C24—132no—
565C24—261no—
566C24—261no—
567C24—261no—
568C24—261no—
569C24—261no—
570C24—261no—
571C24—261no—
572C24—261no—
573C24C23×D1311yescharacteristic
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—132no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—132no—
600C22×C4—132no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—1316no—
605C22×C4—134no—
606C22×C4—268no—
607C22×C4—268no—
608C22×C4—268no—
609C22×C4—268no—
610C22×C4—268no—
611C22×C4—268no—
612C22×C4—268no—
613C22×C4—268no—
614C22×C4—268no—
615C22×C4—268no—
616C22×C4—268no—
617C22×C4—268no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—268no—
631C22×C4—268no—
632C22×C4—268no—
633C22×C4—268no—
634C22×C4—268no—
635C22×C4—268no—
636C22×C4—268no—
637C22×C4—268no—
638C22×C4—262no—
639C22×C4—262no—
640C22×C4—262no—
641C22×C4—262no—
642C22×C4—262no—
643C22×C4—262no—
644C22×C4—262no—
645C22×C4—262no—
646C22×C4—262no—
647C22×C4—262no—
648C22×C4—262no—
649C22×C4—262no—
650C22×C4—262no—
651C22×C4C2×C4×D1314yes—
652C22×C4C2×C4×D1312yes—
653C22×C4#612712yes—
654C22×C4D4×D1312yes—
655C22×C4D4×D1312yes—
656C22×C4D4×D1312yes—
657C22×C4#612912yes—
658C22×C4Q8×D1312yes—
659C22×C4Q8×D1312yes—
660C22×C4#613112yes—
661C22×C4#613112yes—
662C22×C4C2×C22⋊D1312yes—
663C22×C4C2×C22⋊D1312yes—
664C22×C4C2×C22⋊D1312yes—
665C4⋊C4—28no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—268no—
669C4⋊C4—528no—
670C4⋊C4—524no—
671C22⋊C4—2616no—
672C22⋊C4—528no—
673C42—28no—
674C42—268no—
675C42—268no—
676C42—268no—
677C13#1469711yescharacteristic, complemented, Sylow
678C23—134no—
679C23—134no—
680C23—134no—
681C23—134no—
682C23—134no—
683C23—134no—
684C23—134no—
685C23—262no—
686C23—262no—
687C23—262no—
688C23—262no—
689C23—262no—
690C23—262no—
691C23—262no—
692C23—262no—
693C23—262no—
694C23—262no—
695C23—262no—
696C23—262no—
697C23—262no—
698C23—262no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—262no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23—262no—
708C23—262no—
709C23—262no—
710C23—262no—
711C23—262no—
712C23—262no—
713C23C22×C4×D1311yescharacteristic
714C23C2×#612711yescharacteristic
715C23C2×D4×D1311yescharacteristic
716C23C2×D4×D1311yescharacteristic
717C23C2×D4×D1311yescharacteristic
718C23C2×#612911yescharacteristic
719C23C2×Q8×D1311yescharacteristic
720C23C2×Q8×D1311yescharacteristic
721C23C2×#613111yescharacteristic
722C23C2×#613111yescharacteristic
723C23#41×D1311yescharacteristic
724C23#41×D1311yescharacteristic
725C23#41×D1311yescharacteristic
726C23#41×D1311yescharacteristic
727C23C22×C22⋊D1311yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—134no—
755C2×C4—134no—
756C2×C4—134no—
757C2×C4—2632no—
758C2×C4—2632no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—262no—
764C2×C4—262no—
765C2×C4—262no—
766C2×C4—262no—
767C2×C4—262no—
768C2×C4—262no—
769C2×C4—262no—
770C2×C4—262no—
771C2×C4—262no—
772C2×C4—262no—
773C2×C4—262no—
774C2×C4—262no—
775C2×C4—262no—
776C2×C4—262no—
777C2×C4—2632no—
778C2×C4—264no—
779C2×C4—264no—
780C2×C4—264no—
781C2×C4—522no—
782C2×C4—522no—
783C2×C4—522no—
784C2×C4—522no—
785C2×C4—522no—
786C2×C4—522no—
787C2×C4—522no—
788C2×C4—522no—
789C2×C4—522no—
790C2×C4—522no—
791C2×C4—522no—
792C2×C4C4⋊C4×D1314yes—
793C2×C4#8814714yes—
794C2×C4#8814814yes—
795C2×C4#8815014yes—
796C2×C4C4×C22⋊D1314yes—
797C2×C4#8819114yes—
798C2×C4#8819214yes—
799C2×C4#8820014yes—
800C2×C4#8820014yes—
801C22—138no—
802C22—264no—
803C22—264no—
804C22—264no—
805C22—264no—
806C22—264no—
807C22—264no—
808C22—264no—
809C22—264no—
810C22—264no—
811C22—264no—
812C22—264no—
813C22—264no—
814C22—264no—
815C22—264no—
816C22C2×C4⋊C4×D1311yescharacteristic
817C22C2×#8814711yescharacteristic
818C22C2×#8814811yescharacteristic
819C22C2×#8815011yescharacteristic
820C22C4×#612911yescharacteristic
821C22C4×D4×D1311yescharacteristic
822C22#1171925311yescharacteristic
823C22#1171926211yescharacteristic
824C22C4×Q8×D1311yescharacteristic
825C22C4×#613111yescharacteristic
826C22#1171928311yescharacteristic
827C22#1171928511yescharacteristic
828C22D13×#12111yescharacteristic
829C22D13×#12111yescharacteristic
830C22#1171931111yescharacteristic
831C22#1171931111yescharacteristic
832C22D13×C22⋊Q811yescharacteristic
833C22D13×C22⋊Q811yescharacteristic
834C22#1171933211yescharacteristic
835C22#1171933211yescharacteristic
836C22D13×#12511yescharacteristic
837C22#1171939311yescharacteristic
838C22#1171939611yescharacteristic
839C22#1171939611yescharacteristic
840C22D13×C4⋊Q811yescharacteristic
841C22#1171943011yescharacteristic
842C22#1171943311yescharacteristic
843C22#1171943311yescharacteristic
844C22C2×C4×C22⋊D1311yescharacteristic
845C22C2×#8819111yescharacteristic
846C22C2×#8819211yescharacteristic
847C22C2×#8820011yescharacteristic
848C22C2×#8820011yescharacteristic
849C22#1171953311yescharacteristic
850C22#1171953311yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—264no—
856C4—264no—
857C4—264no—
858C4—524no—
859C4—1042no—
860C4#1171865018yescomplemented
861C2—268no—
862C2C2×#1171865011yescharacteristic
863C2D13×#38911yescharacteristic
864C2#1311731711yescharacteristic
865C2C4×#8819211yescharacteristic
866C2#1311734411yescharacteristic
867C2C4×#8820011yescharacteristic
868C2#1311736611yescharacteristic
869C2#1312311511yescharacteristic
870C2#1312312011yescharacteristic
871C2#1312314111yescharacteristic
872C2#1312314511yescharacteristic
873C2#1312316911yescharacteristic
874C2#1312317411yescharacteristic
875C2#1312318311yescharacteristic
876C2#1312318711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#14697
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718634C2semidirect
6. #13113068C2semidirect
7. #13113067C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
11. C2×C13×#389C2semidirect
41. #11718648C4semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
98. C2×C4⋊Dic13C2×C4semidirect
119. #88071C2×C4semidirect
227. C2×C4×D13C4⋊C4semidirect
242. C2×#389D13semidirect
454. C2×D13#389semidirect
459. C4×C13#385semidirect
514. C2×C4⋊C4C4×D13semidirect
677. C13#14697semidirect
860. C4#11718650semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D132
C2×#117186342
C2×#117186502
C2×#117186482
#131130682
#131130672
#131130662
#131130652
#131130572
C2×C13×#3892
#1469713