Finite Group Databasebeta

← #15790270

Subgroups — #15790270

Order 3328.

1910 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
1C2×#11718891C211yesmaximal, characteristic, complemented
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718642C211yesmaximal, characteristic, complemented
4C2×#11718873C211yesmaximal, characteristic
5#13113107C211yesmaximal, characteristic, complemented
6#13113089C211yesmaximal, characteristic, complemented
7#13113089C211yesmaximal, characteristic, complemented
8#13113089C211yesmaximal, characteristic, complemented
9#13113081C211yesmaximal, characteristic
10#13113081C211yesmaximal, characteristic
11#13113073C211yesmaximal, characteristic
12#13113073C211yesmaximal, characteristic
13#13113068C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C22×C13×C22⋊Q8C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×C22⋊Q8—24no—
19C2×C13×C22⋊Q8—24no—
20C2×C13×C22⋊Q8C418yescomplemented
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36#11718891—24no—
37#11718873—24no—
38C2×#88071C2211yescharacteristic
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
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718646—24no—
57#11718642—24no—
58C25×C13C2311yescharacteristic
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C22×Q8×C13C2×C414yes—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13C2×C414yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C13×C22⋊Q8—232no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4C2×C414yes—
93C2×C13×C4⋊C4C2×C414yes—
94C2×C13×C4⋊C4C2×C414yes—
95C2×C13×C4⋊C4D414yes—
96C2×C13×C4⋊C4D414yes—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4C2×C414yes—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—22no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—22no—
108C2×C22⋊Dic13—41no—
109C2×C22⋊Dic13—41no—
110C2×C22⋊Dic13—41no—
111C2×C22⋊Dic13—41no—
112C2×C22⋊Dic13—41no—
113C2×C22⋊Dic13—41no—
114C2×C22⋊Dic13Q814yescomplemented
115C2×C4⋊Dic13—22no—
116C2×C4⋊Dic13—22no—
117C2×C4⋊Dic13—22no—
118C2×C4⋊Dic13—22no—
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—22no—
121C2×C4⋊Dic13—22no—
122C2×C4⋊Dic13—41no—
123C2×C4⋊Dic13—41no—
124C2×C4⋊Dic13—41no—
125C2×C4⋊Dic13—41no—
126C2×C4⋊Dic13—41no—
127C2×C4×Dic13—22no—
128C2×C4×Dic13—22no—
129C2×C4×Dic13—22no—
130C2×C4×Dic13—41no—
131C2×C4×Dic13—41no—
132C2×C4×Dic13—41no—
133#88071—22no—
134#88071—22no—
135#88071—22no—
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—41no—
145#88071—41no—
146#88071—41no—
147#88071—41no—
148#88071—41no—
149#88071—41no—
150#88071D414yes—
151#14362—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
168C2×Q8×C13—28no—
169C2×Q8×C13—28no—
170C2×Q8×C13—44no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—44no—
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×C13—28no—
204C22×C4×C13—28no—
205C22×C4×C13—44no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13—44no—
209C22×C4×C13—44no—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C22×C412yes—
212C22×C4×C13C22×C412yes—
213C22×C4×C13C22×C412yes—
214C22×C4×C13C22×C412yes—
215C22×C4×C13C22×C412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×D412yes—
218C22×C4×C13C2×D412yes—
219C22×C4×C13C2×D412yes—
220C22×C4×C13C2×D412yes—
221C22×C4×C13C2×D412yes—
222C22×C4×C13C2×D412yes—
223C22×C4×C13#4112yes—
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—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13—21no—
264C22×Dic13—21no—
265C22×Dic13—21no—
266C22×Dic13—21no—
267C22×Dic13—21no—
268C22×Dic13—21no—
269C22×Dic13—21no—
270C22×Dic13—21no—
271C22×Dic13—21no—
272C22×Dic13—21no—
273C22×Dic13—21no—
274C22×Dic13—21no—
275C22×Dic13—21no—
276C22×Dic13C2×D412yes—
277C22×Dic13C2×D412yes—
278C22×Dic13C2×Q812yes—
279C22×Dic13C2×Q812yes—
280C13×C4⋊C4—28no—
281C13×C4⋊C4—28no—
282C13×C4⋊C4C22⋊C4116yescomplemented
283C13×C22⋊C4—28no—
284C13×C22⋊C4—28no—
285C22⋊Dic13—44no—
286C22⋊Dic13—44no—
287C22⋊Dic13—44no—
288C22⋊Dic13—44no—
289C4⋊Dic13—44no—
290C4⋊Dic13—44no—
291C4⋊Dic13—44no—
292C4⋊Dic13—44no—
293C4×Dic13—44no—
294C4×Dic13—44no—
295C22×C22⋊Q8D1311yescharacteristic
296C2×#391—131no—
297C2×#389—131no—
298C2×#387—131no—
299C2×#380—131no—
300#1446—131no—
301#1441—131no—
302#1441—131no—
303#1441—131no—
304#1439—131no—
305#1439—131no—
306#1437—131no—
307#1437—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×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
354C23×C13H(5,𝔽2)11yescharacteristic
355C23×C13H(5,𝔽2)11yescharacteristic
356C23×C132−1+411yescharacteristic
357C23×C132−1+411yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
360Q8×C13—416no—
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—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—416no—
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×C13C2×C22⋊C414yes—
401C2×C4×C13C2×C22⋊C414yes—
402C2×C4×C13C2×C22⋊C414yes—
403C2×C4×C13C4×D414yes—
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—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
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×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C23×Q8C2×D1311yescharacteristic
461C24×C4C2×D1311yescharacteristic
462C2×C22⋊Q8—24no—
463C2×C22⋊Q8—24no—
464C2×C22⋊Q8Dic1318yescomplemented
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4C2×D1311yescharacteristic
470C22×C4⋊C4C2×D1311yescharacteristic
471C22×C4⋊C4C2×D1311yescharacteristic
472C22×C22⋊C4—131no—
473C22×C22⋊C4—131no—
474C22×C22⋊C4—131no—
475C22×C22⋊C4—131no—
476C22×C22⋊C4C2×D1311yescharacteristic
477C22×C22⋊C4C2×D1311yescharacteristic
478C22×C42—131no—
479C22×C42—131no—
480#391—264no—
481#389—264no—
482#387—264no—
483#380—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×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
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×C13#51811yescharacteristic
521C22×C13#51911yescharacteristic
522C22×C13#52011yescharacteristic
523C22×C13#52011yescharacteristic
524C22×C13#53511yescharacteristic
525C22×C13#53611yescharacteristic
526C22×C13#53611yescharacteristic
527C22×C13#53711yescharacteristic
528C22×C13#53711yescharacteristic
529C22×C13#53711yescharacteristic
530C22×C13#53811yescharacteristic
531C22×C13#53911yescharacteristic
532C22×C13#54111yescharacteristic
533C22×C13#54211yescharacteristic
534C22×C13#54311yescharacteristic
535C22×C13#54411yescharacteristic
536C22×C13D4211yescharacteristic
537C22×C13D4211yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54611yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13D4×Q811yescharacteristic
544C22×C13D4×Q811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13#55211yescharacteristic
547C22×C13#55411yescharacteristic
548C22×C13#56211yescharacteristic
549C22×C13#56211yescharacteristic
550C22×C13#56311yescharacteristic
551C22×C13#56311yescharacteristic
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—24no—
555C4×C13—24no—
556C4×C13—42no—
557C4×C13—42no—
558Dic13—42no—
559Dic13—42no—
560Dic13—42no—
561Dic13—42no—
562Dic13—81no—
563Dic13—81no—
564Dic13—81no—
565Dic13—81no—
566C25C22×D1311yescharacteristic
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—22no—
570C22×Q8—22no—
571C22×Q8—41no—
572C22×Q8—41no—
573C22×Q8C2×Dic1314yes—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4—131no—
581C23×C4—131no—
582C23×C4—131no—
583C23×C4—131no—
584C23×C4—131no—
585C23×C4—131no—
586C23×C4—131no—
587C23×C4—131no—
588C23×C4C2×Dic1314yes—
589C23×C4C22×D1311yescharacteristic
590C23×C4C22×D1311yescharacteristic
591C23×C4C22×D1311yescharacteristic
592C23×C4C22×D1311yescharacteristic
593C23×C4C22×D1311yescharacteristic
594C23×C4C22×D1311yescharacteristic
595C22⋊Q8—232no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4—262no—
603C2×C4⋊C4—262no—
604C2×C4⋊C4—262no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—521no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4—521no—
612C2×C4⋊C4C2×Dic1314yes—
613C2×C4⋊C4C2×Dic1314yes—
614C2×C4⋊C4C2×Dic1314yes—
615C2×C4⋊C4C22⋊D1314yes—
616C2×C4⋊C4C22⋊D1314yes—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—134no—
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⋊C4—521no—
629C2×C22⋊C4—521no—
630C2×C22⋊C4—521no—
631C2×C22⋊C4—521no—
632C2×C22⋊C4—521no—
633C2×C22⋊C4C2×Dic1314yes—
634C2×C22⋊C4C2×Dic1314yes—
635C2×C42—262no—
636C2×C42—262no—
637C2×C42—262no—
638C2×C42—521no—
639C2×C42—521no—
640C2×C42—521no—
641#95—134no—
642#95—262no—
643#95—262no—
644#95—262no—
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—521no—
654#95—521no—
655#95—521no—
656#95—521no—
657#95—521no—
658#95—521no—
659C2×C13—44no—
660C2×C13#231111yescharacteristic
661C2×C13#232311yescharacteristic
662C2×C13#232911yescharacteristic
663C2×C13D4×C22⋊C411yescharacteristic
664C2×C13Q8×C22⋊C411yescharacteristic
665C2×C13#236011yescharacteristic
666C2×C13#237811yescharacteristic
667C2×C13#267611yescharacteristic
668C2×C13#267711yescharacteristic
669C2×C13#268111yescharacteristic
670C2×C13#268311yescharacteristic
671C2×C13#269011yescharacteristic
672C2×C13#269211yescharacteristic
673C2×C13#270211yescharacteristic
674C2×C13#270411yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24Q8×D1312yes—
688C24#613112yes—
689C24C22×Dic1312yes—
690C24C23×D1311yescharacteristic
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
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—28no—
727C22×C4—28no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—132no—
734C22×C4—132no—
735C22×C4—132no—
736C22×C4—132no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
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×C4D4×D1312yes—
790C22×C4#612912yes—
791C22×C4C22×Dic1312yes—
792C22×C4C22×Dic1312yes—
793C22×C4C22×Dic1312yes—
794C22×C4C22×Dic1312yes—
795C22×C4C22×Dic1312yes—
796C22×C4C22×Dic1312yes—
797C22×C4C2×C22⋊D1312yes—
798C22×C4C2×C22⋊D1312yes—
799C22×C4C2×C22⋊D1312yes—
800C22×C4C2×C22⋊D1312yes—
801C22×C4C2×C22⋊D1312yes—
802C22×C4C2×C22⋊D1312yes—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—524no—
806C4⋊C4—524no—
807C4⋊C4—524no—
808C4⋊C4—524no—
809C4⋊C4C22⋊Dic13116yescomplemented
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—524no—
813C22⋊C4—524no—
814C22⋊C4—524no—
815C22⋊C4—524no—
816C42—524no—
817C42—524no—
818C13#1436211yescharacteristic, 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—
853C23Q8×Dic1314yes—
854C23C2×D4×D1311yescharacteristic
855C23C2×#612911yescharacteristic
856C23#8825111yescharacteristic
857C23#8825111yescharacteristic
858C23C2×Q8×D1311yescharacteristic
859C23C2×#613111yescharacteristic
860C23#8825411yescharacteristic
861C23#8825411yescharacteristic
862C23#8825611yescharacteristic
863C23#8825611yescharacteristic
864C23#8825711yescharacteristic
865C23#8825711yescharacteristic
866C23C23×Dic1311yescharacteristic
867C23C22×C22⋊D1311yescharacteristic
868C23C22×C22⋊D1311yescharacteristic
869Q8—416no—
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—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
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—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
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×C4D4×Dic1314yes—
966C2×C4C2×C22⋊Dic1314yes—
967C2×C4C2×C22⋊Dic1314yes—
968C2×C4C2×C22⋊Dic1314yes—
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—
984C22#1171932811yescharacteristic
985C22#1171933011yescharacteristic
986C22#1171933311yescharacteristic
987C22#1171933411yescharacteristic
988C22#1171933511yescharacteristic
989C22#1171933711yescharacteristic
990C22#1171933911yescharacteristic
991C22#1171934011yescharacteristic
992C22#1171934711yescharacteristic
993C22#1171934811yescharacteristic
994C22#1171934911yescharacteristic
995C22#1171935011yescharacteristic
996C22#1171935111yescharacteristic
997C22#1171935111yescharacteristic
998C22#1171935211yescharacteristic
999C22#1171935211yescharacteristic
1000C22C2×D4×Dic1311yescharacteristic
1001C22#1171950311yescharacteristic
1002C22D4×C22⋊D1311yescharacteristic
1003C22D4×C22⋊D1311yescharacteristic
1004C22#1171951111yescharacteristic
1005C22#1171951111yescharacteristic
1006C22C2×Q8×Dic1311yescharacteristic
1007C22#1171951711yescharacteristic
1008C22Q8×C22⋊D1311yescharacteristic
1009C22Q8×C22⋊D1311yescharacteristic
1010C22#1171952211yescharacteristic
1011C22#1171952211yescharacteristic
1012C22#1171953011yescharacteristic
1013C22#1171953211yescharacteristic
1014C22#1171953211yescharacteristic
1015C22#1171953511yescharacteristic
1016C22#1171953811yescharacteristic
1017C22#1171953811yescharacteristic
1018C22C22×C22⋊Dic1311yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—522no—
1026C4—522no—
1027C4—522no—
1028C4—522no—
1029C4—1041no—
1030C4—1041no—
1031C4—1041no—
1032C4—1041no—
1033C2—44no—
1034C2#1311742811yescharacteristic
1035C2#1311752011yescharacteristic
1036C2#1311757111yescharacteristic
1037C2D4×C22⋊Dic1311yescharacteristic
1038C2Q8×C22⋊Dic1311yescharacteristic
1039C2#1311784511yescharacteristic
1040C2#1311800211yescharacteristic
1041C2#1312113311yescharacteristic
1042C2#1312114711yescharacteristic
1043C2#1312119111yescharacteristic
1044C2#1312120611yescharacteristic
1045C2#1312129811yescharacteristic
1046C2#1312132811yescharacteristic
1047C2#1312146011yescharacteristic
1048C2#1312149011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×C22⋊Q8C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13#14362
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#11718891C2semidirect
2. C2×#11718646C2semidirect
3. C2×#11718642C2semidirect
5. #13113107C2semidirect
6. #13113089C2semidirect
7. #13113089C2semidirect
8. #13113089C2semidirect
13. #13113068C2semidirect
20. C2×C13×C22⋊Q8C4semidirect
114. C2×C22⋊Dic13Q8semidirect
282. C13×C4⋊C4C22⋊C4semidirect
464. C2×C22⋊Q8Dic13semidirect
809. C4⋊C4C22⋊Dic13semidirect
818. C13#14362semidirect

Maximal subgroups

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

subgroupindex
C2×#117188912
C2×#117186462
C2×#117186422
C2×#117188732
#131131072
#131130892
#131130812
#131130732
#131130682
#131130592
C22×C13×C22⋊Q82
#1436213