Finite Group Databasebeta

← #15787408

Subgroups — #15787408

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718314C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic13C211yesmaximal, characteristic
6#13113106C211yesmaximal, characteristic, complemented
7#13113086C211yesmaximal, characteristic, complemented
8#13113079C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113071C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113067C211yesmaximal, characteristic, complemented
14#13113058C211yesmaximal, characteristic
15C13×#1439C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×#88132—24no—
34C2×#88132—24no—
35C2×#88132C418yescomplemented
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C4⋊C4×Dic13—24no—
55C22⋊C4×Dic13—24no—
56#11718314—24no—
57#11718307—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—22no—
69C23×Dic13—41no—
70C23×Dic13—41no—
71C23×Dic13C2×C414yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—22no—
83C22×Dic26—22no—
84C22×Dic26—41no—
85C22×Dic26—41no—
86C22×Dic26C2×C414yes—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—41no—
98C2×C13×C22⋊C4C2×C414yes—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—22no—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—41no—
106C2×C22⋊Dic13C2×C414yes—
107C2×C22⋊Dic13Q814yescomplemented
108C2×C4⋊Dic13C2×C414yes—
109C2×C4⋊Dic13D414yes—
110C2×C4⋊Dic13D414yes—
111C2×#6101—22no—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—41no—
118C2×#6101C2×C414yes—
119C2×#6101C2×C414yes—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—22no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—41no—
130C2×C4×Dic13—41no—
131C2×C4×Dic13—41no—
132#88132—232no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—41no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—41no—
150#88071D414yes—
151#14099—131nomaximal, Sylow
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13C22×C412yes—
165C24×C13C2×Q812yes—
166C24×C13#4112yes—
167C24×C13C2411yescharacteristic
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—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
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—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—28no—
245C22×Dic13—28no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—44no—
254C22×Dic13—44no—
255C22×Dic13—44no—
256C22×Dic13—44no—
257C22×Dic13—44no—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×D412yes—
268C22×Dic13C2×Q812yes—
269C22×Dic13C2×Q812yes—
270C22×Dic13#4112yes—
271C22×Dic13#4112yes—
272C22×Dic13#4112yes—
273C2×Dic26—28no—
274C2×Dic26—28no—
275C2×Dic26—44no—
276C2×Dic26—44no—
277C2×Dic26—44no—
278C2×Dic26—44no—
279C2×Dic26—44no—
280C13×C4⋊C4—28no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—44no—
284C22⋊Dic13—28no—
285C22⋊Dic13—28no—
286C22⋊Dic13—44no—
287C4⋊Dic13C22⋊C4116yescomplemented
288#6101—28no—
289#6101—28no—
290#6101—44no—
291C4×Dic13—28no—
292C4×Dic13—44no—
293C4×Dic13—44no—
294C4×Dic13—44no—
295C22×C22⋊Q8—131no—
296C2×#391—131no—
297C2×#387—131no—
298C2×C4×C4⋊C4—131no—
299C2×C4×C22⋊C4—131no—
300#1446—131no—
301#1441—131no—
302#1439—131no—
303#1439D1311yescharacteristic
304#1437—131no—
305#1437—131no—
306#1436—131no—
307#1436—131no—
308#1436—131no—
309C22⋊#95—131no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13C4×Q814yes—
345C23×C13C23×C411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×Q811yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13C2×#4111yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C13H(5,𝔽2)11yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13C2×C22⋊C414yes—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
434C2×Dic13—22no—
435C2×Dic13—416no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13C2×C22⋊C414yes—
456C2×Dic13C2×C22⋊C414yes—
457C2×Dic13C4×D414yes—
458C2×Dic13C22⋊Q814yescomplemented
459Dic26—416no—
460C23×Q8—131no—
461C24×C4—131no—
462C2×C22⋊Q8—138no—
463C2×C22⋊Q8—264no—
464C2×C22⋊Q8—264no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4C2×D1311yescharacteristic
470C22×C22⋊C4—131no—
471C22×C22⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4C2×D1311yescharacteristic
474C22×C22⋊C4C2×D1311yescharacteristic
475C22×C22⋊C4C2×D1311yescharacteristic
476C22×C42—131no—
477C22×C42—131no—
478C22×C42—131no—
479C22×C42—131no—
480#391—264no—
481#387—264no—
482C4×C4⋊C4—264no—
483C4×C22⋊C4—264no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95C2×D1311yescharacteristic
500C2×#95C2×D1311yescharacteristic
501C2×#95C2×D1311yescharacteristic
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13C22×C22⋊C411yescharacteristic
518C22×C13C2×C4×D411yescharacteristic
519C22×C13C2×C4×Q811yescharacteristic
520C22×C13C4×#4111yescharacteristic
521C22×C13C4×#4111yescharacteristic
522C22×C13#51811yescharacteristic
523C22×C13#51911yescharacteristic
524C22×C13C2×C22⋊Q811yescharacteristic
525C22×C13#52511yescharacteristic
526C22×C13#52511yescharacteristic
527C22×C13#52511yescharacteristic
528C22×C13#52911yescharacteristic
529C22×C13#53211yescharacteristic
530C22×C13#53211yescharacteristic
531C22×C13#53311yescharacteristic
532C22×C13#53911yescharacteristic
533C22×C13#53911yescharacteristic
534C22×C13#54211yescharacteristic
535C22×C13#54211yescharacteristic
536C22×C13D4211yescharacteristic
537C22×C13D4211yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54711yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13#54811yescharacteristic
544C22×C13D4×Q811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13#55111yescharacteristic
547C22×C13#55111yescharacteristic
548C22×C13#55211yescharacteristic
549C22×C13#55411yescharacteristic
550C22×C13#55411yescharacteristic
551C22×C13#55611yescharacteristic
552C4×C13—24no—
553C4×C13—42no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—81no—
558Dic13—24no—
559Dic13—24no—
560Dic13—24no—
561Dic13—24no—
562Dic13—42no—
563Dic13—42no—
564Dic13—42no—
565Dic13—81no—
566C25C22×D1311yescharacteristic
567C22×Q8—134no—
568C22×Q8—262no—
569C22×Q8—262no—
570C22×Q8—262no—
571C22×Q8—262no—
572C22×Q8—521no—
573C22×Q8—521no—
574C23×C4—131no—
575C23×C4—131no—
576C23×C4—131no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—131no—
580C23×C4—131no—
581C23×C4—134no—
582C23×C4—131no—
583C23×C4—262no—
584C23×C4—262no—
585C23×C4—262no—
586C23×C4—262no—
587C23×C4—521no—
588C23×C4—521no—
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C22⋊Q8—2632no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—134no—
600C2×C4⋊C4—134no—
601C2×C4⋊C4—134no—
602C2×C4⋊C4—134no—
603C2×C4⋊C4—134no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—262no—
609C2×C4⋊C4—262no—
610C2×C4⋊C4—521no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4—134no—
620C2×C22⋊C4—134no—
621C2×C22⋊C4—262no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—521no—
628C2×C22⋊C4C4×D1314yes—
629C2×C42—262no—
630C2×C42—262no—
631C2×C42—262no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—262no—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638C2×C42—521no—
639C2×C42—521no—
640C2×C42—521no—
641#95—22no—
642#95—22no—
643#95—41no—
644#95—134no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—262no—
654#95—262no—
655#95—262no—
656#95—262no—
657#95—262no—
658#95—521no—
659C2×C13—44no—
660C2×C13#229711yescharacteristic
661C2×C13C4×C22⋊Q811yescharacteristic
662C2×C13#233211yescharacteristic
663C2×C13D4×C22⋊C411yescharacteristic
664C2×C13Q8×C22⋊C411yescharacteristic
665C2×C13#236211yescharacteristic
666C2×C13#236811yescharacteristic
667C2×C13#244911yescharacteristic
668C2×C13#245211yescharacteristic
669C2×C13#246111yescharacteristic
670C2×C13#246311yescharacteristic
671C2×C13#246511yescharacteristic
672C2×C13#247711yescharacteristic
673C2×C13#255611yescharacteristic
674C2×C13#256011yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C2×C4×D1312yes—
688C24#612912yes—
689C24Q8×D1312yes—
690C24C23×D1311yescharacteristic
691C2×Q8—268no—
692C2×Q8—268no—
693C2×Q8—524no—
694C2×Q8—524no—
695C2×Q8—524no—
696C2×Q8—524no—
697C2×Q8—524no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—132no—
734C22×C4—132no—
735C22×C4—132no—
736C22×C4—132no—
737C22×C4—132no—
738C22×C4—132no—
739C22×C4—132no—
740C22×C4—132no—
741C22×C4—132no—
742C22×C4—132no—
743C22×C4—132no—
744C22×C4—132no—
745C22×C4—132no—
746C22×C4—132no—
747C22×C4—132no—
748C22×C4—268no—
749C22×C4—268no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—524no—
792C22×C4—524no—
793C22×C4—524no—
794C22×C4—524no—
795C22×C4—524no—
796C22×C4C2×C4×D1312yes—
797C22×C4C2×C4×D1312yes—
798C22×C4D4×D1312yes—
799C22×C4D4×D1312yes—
800C22×C4D4×D1312yes—
801C22×C4#612912yes—
802C22×C4#612912yes—
803C4⋊C4—28no—
804C4⋊C4—1316no—
805C4⋊C4—268no—
806C4⋊C4—268no—
807C4⋊C4—524no—
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—44no—
811C22⋊C4—268no—
812C22⋊C4—268no—
813C22⋊C4—524no—
814C42—268no—
815C42—524no—
816C42—524no—
817C42—524no—
818C13#1409911yescharacteristic, complemented, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23#8814114yes—
854C23C22×C4×D1311yescharacteristic
855C23C2×D4×D1311yescharacteristic
856C23C2×D4×D1311yescharacteristic
857C23C2×D4×D1311yescharacteristic
858C23C2×#612911yescharacteristic
859C23C2×#612911yescharacteristic
860C23C2×#612911yescharacteristic
861C23#8825111yescharacteristic
862C23C2×Q8×D1311yescharacteristic
863C23#41×D1311yescharacteristic
864C23#41×D1311yescharacteristic
865C23#41×D1311yescharacteristic
866C23#8825611yescharacteristic
867C23#8825711yescharacteristic
868C23#8825711yescharacteristic
869Q8—5216no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—134no—
912C2×C4—134no—
913C2×C4—134no—
914C2×C4—134no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—262no—
926C2×C4—262no—
927C2×C4—262no—
928C2×C4—262no—
929C2×C4—262no—
930C2×C4—262no—
931C2×C4—262no—
932C2×C4—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—262no—
936C2×C4—262no—
937C2×C4—262no—
938C2×C4—262no—
939C2×C4—262no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—262no—
943C2×C4—262no—
944C2×C4—262no—
945C2×C4—262no—
946C2×C4—262no—
947C2×C4—262no—
948C2×C4—5216no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4—521no—
956C2×C4—521no—
957C2×C4—521no—
958C2×C4—521no—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4—521no—
968C2×C4C22⋊C4×D1314yes—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C2×C22⋊C4×D1311yescharacteristic
985C22C2×#8814111yescharacteristic
986C22#1171922111yescharacteristic
987C22C4×#612911yescharacteristic
988C22C4×#612911yescharacteristic
989C22C4×D4×D1311yescharacteristic
990C22#1171925011yescharacteristic
991C22#1171929111yescharacteristic
992C22#1171929111yescharacteristic
993C22#1171929211yescharacteristic
994C22#1171930111yescharacteristic
995C22#1171930111yescharacteristic
996C22#1171930311yescharacteristic
997C22#1171930311yescharacteristic
998C22#1171930311yescharacteristic
999C22#1171930711yescharacteristic
1000C22#1171931411yescharacteristic
1001C22#1171931711yescharacteristic
1002C22#1171932711yescharacteristic
1003C22D13×C22⋊Q811yescharacteristic
1004C22#1171933711yescharacteristic
1005C22#1171933711yescharacteristic
1006C22#1171934011yescharacteristic
1007C22#1171934111yescharacteristic
1008C22#1171935411yescharacteristic
1009C22#1171936011yescharacteristic
1010C22#1171936111yescharacteristic
1011C22#1171936311yescharacteristic
1012C22#1171936511yescharacteristic
1013C22#1171937611yescharacteristic
1014C22#1171938111yescharacteristic
1015C22#1171938711yescharacteristic
1016C22#1171941311yescharacteristic
1017C22#1171941511yescharacteristic
1018C22#1171942211yescharacteristic
1019C4—24no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—81no—
1025C4—264no—
1026C4—264no—
1027C4—264no—
1028C4—264no—
1029C4—522no—
1030C4—522no—
1031C4—522no—
1032C4—1041no—
1033C2—44no—
1034C2#1311732111yescharacteristic
1035C2#1311736811yescharacteristic
1036C2#1311758611yescharacteristic
1037C2#1311765711yescharacteristic
1038C2#1311766811yescharacteristic
1039C2#1311786611yescharacteristic
1040C2#1311791711yescharacteristic
1041C2#1311864811yescharacteristic
1042C2#1311867911yescharacteristic
1043C2#1311879611yescharacteristic
1044C2#1311882611yescharacteristic
1045C2#1311885011yescharacteristic
1046C2#1311903011yescharacteristic
1047C2#1311991311yescharacteristic
1048C2#1311997311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1439C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1439D13
hypocenterC13#14099
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
3. C2×#11718314C2semidirect
4. C2×C4⋊C4×Dic13C2semidirect
6. #13113106C2semidirect
7. #13113086C2semidirect
11. #13113071C2semidirect
12. #13113067C2semidirect
13. #13113067C2semidirect
35. C2×#88132C4semidirect
107. C2×C22⋊Dic13Q8semidirect
287. C4⋊Dic13C22⋊C4semidirect
458. C2×Dic13C22⋊Q8semidirect
818. C13#14099semidirect

Maximal subgroups

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

subgroupindex
C22×#881322
C2×#117183072
C2×#117183142
C2×C4⋊C4×Dic132
C2×C22⋊C4×Dic132
#131131062
#131130862
#131130792
#131130732
#131130712
#131130672
#131130582
C13×#14392
#1409913