Finite Group Databasebeta

← #15785715

Subgroups — #15785715

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic13C211yesmaximal, characteristic, complemented
2C2×#11718891C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113089C212yesmaximal, complemented
6#13113081C212yesmaximal
7#13113073C212yesmaximal
8#13113068C212yesmaximal, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C22×C13×C22⋊Q8C211yesmaximal, characteristic
12C23×Q8×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C2×C13×C22⋊Q8—24no—
15C2×C13×C22⋊Q8—24no—
16C2×C13×C22⋊Q8C418yescomplemented
17C22×C13×C4⋊C4C2212yes—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2212yes—
22C22×C22⋊Dic13C2211yescharacteristic
23C2×Q8×Dic13—24no—
24C2×Q8×Dic13—24no—
25C2×Q8×Dic13—24no—
26C22×C4⋊Dic13C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4×Dic13C2212yes—
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32#11718891—24no—
33#11718873—24no—
34C4×C22⋊Dic13—24no—
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2212yes—
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43C2×#88071C2212yes—
44C25×C13C2311yescharacteristic
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—22no—
48C22×Q8×C13—22no—
49C22×Q8×C13C2×C414yes—
50C22×Q8×C13D414yes—
51C22×Q8×C13D414yes—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13C2×C414yes—
59C23×C4×C13C2312yes—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2312yes—
62C23×C4×C13C2311yescharacteristic
63C23×Dic13C2312yes—
64C23×Dic13C2312yes—
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C13×C22⋊Q8—232no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C13×C4⋊C4C2×C418yes—
76C2×C13×C22⋊C4—24no—
77C2×C13×C22⋊C4—24no—
78C2×C13×C22⋊C4C2×C418yes—
79C2×C22⋊Dic13—22no—
80C2×C22⋊Dic13—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—24no—
85C2×C22⋊Dic13—24no—
86C2×C22⋊Dic13—42no—
87C2×C22⋊Dic13Q814yescomplemented
88Q8×Dic13—232no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—22no—
97C2×C4⋊Dic13D414yes—
98C2×C4×Dic13—22no—
99C2×C4×Dic13—24no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—24no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13D414yes—
107#88071—24no—
108#88071—24no—
109#88071—22no—
110#88071—22no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—42no—
115#88071—42no—
116#13969—131nomaximal, Sylow
117C24×C13—21no—
118C24×C13—21no—
119C24×C13—21no—
120C24×C13—21no—
121C24×C13—21no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13—21no—
126C24×C13—21no—
127C24×C13—21no—
128C24×C13—21no—
129C24×C13C22×C412yes—
130C24×C13C2×Q812yes—
131C24×C13#4112yes—
132C24×C13C2411yescharacteristic
133C2×Q8×C13—28no—
134C2×Q8×C13—28no—
135C2×Q8×C13—28no—
136C2×Q8×C13—28no—
137C2×Q8×C13—28no—
138C2×Q8×C13—28no—
139C2×Q8×C13C22⋊C4116yescomplemented
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—28no—
157C22×C4×C13—28no—
158C22×C4×C13—28no—
159C22×C4×C13—44no—
160C22×C4×C13—44no—
161C22×C4×C13—44no—
162C22×C4×C13—44no—
163C22×C4×C13C22×C414yes—
164C22×C4×C13C22×C412yes—
165C22×C4×C13C22×C414yes—
166C22×C4×C13C22×C412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D414yes—
170C22×C4×C13C2×D414yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13C2×D412yes—
173C22×C4×C13#4112yes—
174C22×C4×C13#4112yes—
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—22no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—22no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—22no—
198C22×Dic13—21no—
199C22×Dic13—22no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—22no—
204C22×Dic13—22no—
205C22×Dic13—22no—
206C22×Dic13—22no—
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—22no—
210C22×Dic13C2×D414yes—
211C22×Dic13C2×D412yes—
212C22×Dic13C2×D412yes—
213C22×Dic13C2×Q812yes—
214C22×Dic13C2×Q812yes—
215C22×Dic13#4112yes—
216C22×Dic13#4112yes—
217C13×C4⋊C4—28no—
218C13×C4⋊C4—216no—
219C13×C22⋊C4—216no—
220C22⋊Dic13—28no—
221C22⋊Dic13—28no—
222C22⋊Dic13—48no—
223C4⋊Dic13—216no—
224C4⋊Dic13—28no—
225C4⋊Dic13—44no—
226C4×Dic13—216no—
227C4×Dic13—28no—
228C4×Dic13—44no—
229C22×C22⋊Q8D1311yescharacteristic
230C22×C4×Q8—131no—
231C2×#391—131no—
232C2×#380—131no—
233C2×C4×C22⋊C4—131no—
234#1441—132no—
235#1439—132no—
236#1437—132no—
237#1436—132no—
238C4⋊#95—131no—
239C4⋊#95—131no—
240C23×C13—22no—
241C23×C13—22no—
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—22no—
247C23×C13—22no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13C4×Q814yescomplemented
275C23×C13C23×C411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C23×C13C22×D411yescharacteristic
278C23×C13C22×D411yescharacteristic
279C23×C13C22×D411yescharacteristic
280C23×C13C22×Q811yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13H(5,𝔽2)11yescharacteristic
287C23×C132−1+411yescharacteristic
288C23×C132−1+411yescharacteristic
289C23×C132−1+411yescharacteristic
290Q8×C13—232no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—24no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—24no—
302C2×C4×C13—24no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—416no—
312C2×C4×C13C2×C22⋊C418yes—
313C2×C4×C13C2×C22⋊C414yes—
314C2×C4×C13C4×D414yes—
315C2×C4×C13C4×D414yes—
316C2×C4×C13#12014yes—
317C2×C4×C13#12114yes—
318C2×C4×C13#12114yes—
319C2×C4×C13#12314yes—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—24no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—42no—
341C2×Dic13—41no—
342C2×Dic13—42no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—42no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—42no—
361C2×Dic13C22⋊Q814yescomplemented
362C23×Q8C2×D1311yescharacteristic
363C24×C4C2×D1311yescharacteristic
364C2×C22⋊Q8—24no—
365C2×C22⋊Q8—24no—
366C2×C22⋊Q8Dic1318yescomplemented
367C2×C4×Q8—264no—
368C2×C4×Q8—264no—
369C2×C4×Q8—264no—
370C22×C4⋊C4—131no—
371C22×C4⋊C4—132no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4C2×D1311yescharacteristic
374C22×C4⋊C4C2×D1312yes—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—132no—
378C22×C22⋊C4C2×D1312yes—
379C22×C42—131no—
380C22×C42—132no—
381C22×C42—131no—
382#391—264no—
383#380—264no—
384C4×C22⋊C4—264no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—131no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—132no—
391C2×#95—131no—
392C2×#95—132no—
393C2×#95—132no—
394C22×C13—24no—
395C22×C13—24no—
396C22×C13—24no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—42no—
400C22×C13—42no—
401C22×C13—42no—
402C22×C13—42no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—42no—
407C22×C13—42no—
408C22×C13—42no—
409C22×C13C22×C22⋊C411yescharacteristic
410C22×C13C2×C4×D411yescharacteristic
411C22×C13C2×C4×D411yescharacteristic
412C22×C13C2×C4×Q811yescharacteristic
413C22×C13C4×#4111yescharacteristic
414C22×C13#51911yescharacteristic
415C22×C13#52011yescharacteristic
416C22×C13C2×#12011yescharacteristic
417C22×C13C2×#12111yescharacteristic
418C22×C13C2×#12111yescharacteristic
419C22×C13C2×C22⋊Q811yescharacteristic
420C22×C13C2×#12311yescharacteristic
421C22×C13#52511yescharacteristic
422C22×C13#52911yescharacteristic
423C22×C13#53311yescharacteristic
424C22×C13#53611yescharacteristic
425C22×C13#53711yescharacteristic
426C22×C13#54111yescharacteristic
427C22×C13#54211yescharacteristic
428C22×C13#54611yescharacteristic
429C22×C13#54711yescharacteristic
430C22×C13#54811yescharacteristic
431C22×C13#54811yescharacteristic
432C22×C13#54811yescharacteristic
433C22×C13#54811yescharacteristic
434C22×C13#54811yescharacteristic
435C22×C13D4×Q811yescharacteristic
436C22×C13D4×Q811yescharacteristic
437C22×C13D4×Q811yescharacteristic
438C22×C13#55011yescharacteristic
439C22×C13#55011yescharacteristic
440C22×C13#55211yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55411yescharacteristic
443C22×C13#55611yescharacteristic
444C4×C13—28no—
445C4×C13—44no—
446C4×C13—42no—
447C4×C13#38618yes—
448Dic13—24no—
449Dic13—42no—
450Dic13—44no—
451Dic13—42no—
452Dic13—42no—
453Dic13—82no—
454C25C22×D1311yescharacteristic
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8C2×Dic1314yes—
460C22×Q8C22⋊D1314yes—
461C22×Q8C22⋊D1314yes—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—131no—
469C23×C4—131no—
470C23×C4—132no—
471C23×C4—131no—
472C23×C4—131no—
473C23×C4—132no—
474C23×C4C2×Dic1314yes—
475C23×C4C22×D1312yes—
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1312yes—
478C23×C4C22×D1311yescharacteristic
479C22⋊Q8—232no—
480C4×Q8—2632no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4C2×Dic1314yes—
495C2×C4⋊C4C2×Dic1318yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—134no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—522no—
507C2×C22⋊C4C2×Dic1318yes—
508C2×C42—134no—
509C2×C42—264no—
510C2×C42—264no—
511C2×C42—262no—
512C2×C42—264no—
513C2×C42—262no—
514C2×C42—262no—
515C2×C42—262no—
516C2×C42—262no—
517#95—264no—
518#95—264no—
519#95—262no—
520#95—262no—
521#95—264no—
522#95—264no—
523#95—264no—
524#95—522no—
525#95—522no—
526C2×C13—44no—
527C2×C13C2×#38611yescharacteristic
528C2×C13C4×C22⋊Q811yescharacteristic
529C2×C13#232311yescharacteristic
530C2×C13Q8×C22⋊C411yescharacteristic
531C2×C13#234111yescharacteristic
532C2×C13#236011yescharacteristic
533C2×C13#236211yescharacteristic
534C2×C13#240711yescharacteristic
535C2×C13#240911yescharacteristic
536C2×C13#242111yescharacteristic
537C2×C13#242311yescharacteristic
538C2×C13#242611yescharacteristic
539C2×C13#242911yescharacteristic
540C2×C13#253611yescharacteristic
541C2×C13#253811yescharacteristic
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24Q8×D1312yes—
555C24#613112yes—
556C24C22×Dic1312yes—
557C24C23×D1311yescharacteristic
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8C22⋊Dic13116yescomplemented
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—134no—
593C22×C4—132no—
594C22×C4—132no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—262no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—261no—
612C22×C4—262no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—262no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—262no—
622C22×C4—261no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—262no—
630C22×C4D4×D1312yes—
631C22×C4D4×D1312yes—
632C22×C4#612912yes—
633C22×C4#612912yes—
634C22×C4C22×Dic1314yes—
635C22×C4C22×Dic1312yes—
636C22×C4C22×Dic1314yes—
637C22×C4C22×Dic1312yes—
638C22×C4C2×C22⋊D1314yes—
639C22×C4C2×C22⋊D1314yes—
640C22×C4C2×C22⋊D1312yes—
641C22×C4C2×C22⋊D1312yes—
642C4⋊C4—28no—
643C4⋊C4—216no—
644C4⋊C4—2616no—
645C4⋊C4—268no—
646C4⋊C4—524no—
647C22⋊C4—216no—
648C22⋊C4—268no—
649C22⋊C4—268no—
650C22⋊C4—528no—
651C42—2616no—
652C42—268no—
653C42—524no—
654C13#1396911yescharacteristic, complemented, Sylow
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23Q8×Dic1314yescomplemented
690C23C2×D4×D1311yescharacteristic
691C23C2×D4×D1311yescharacteristic
692C23C2×#612911yescharacteristic
693C23C2×#612911yescharacteristic
694C23C2×Q8×D1311yescharacteristic
695C23C2×#613111yescharacteristic
696C23#8825411yescharacteristic
697C23#8825411yescharacteristic
698C23#41×D1311yescharacteristic
699C23#41×D1311yescharacteristic
700C23#8825611yescharacteristic
701C23#8825711yescharacteristic
702C23C23×Dic1311yescharacteristic
703C23C22×C22⋊D1311yescharacteristic
704C23C22×C22⋊D1311yescharacteristic
705Q8—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—416no—
727C2×C4—134no—
728C2×C4—262no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—264no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—264no—
743C2×C4—264no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—522no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—522no—
753C2×C4—521no—
754C2×C4—522no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—522no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—522no—
768C2×C4—522no—
769C2×C4D4×Dic1314yes—
770C2×C4D4×Dic1314yes—
771C2×C4#8818914yes—
772C2×C4#8819114yes—
773C2×C4#8819314yes—
774C2×C4#8819314yes—
775C2×C4C2×C22⋊Dic1318yes—
776C2×C4C2×C22⋊Dic1314yes—
777C22—24no—
778C22—24no—
779C22—24no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22#1171932711yescharacteristic
793C22#1171932911yescharacteristic
794C22#1171933011yescharacteristic
795C22D13×C22⋊Q811yescharacteristic
796C22#1171933211yescharacteristic
797C22#1171933311yescharacteristic
798C22#1171933411yescharacteristic
799C22#1171933511yescharacteristic
800C22#1171933611yescharacteristic
801C22#1171933711yescharacteristic
802C22#1171933811yescharacteristic
803C22#1171934011yescharacteristic
804C22#1171934411yescharacteristic
805C22#1171934611yescharacteristic
806C22#1171934711yescharacteristic
807C22#1171934811yescharacteristic
808C22C2×D4×Dic1311yescharacteristic
809C22C2×D4×Dic1311yescharacteristic
810C22C2×#8818911yescharacteristic
811C22C2×#8819111yescharacteristic
812C22C2×#8819311yescharacteristic
813C22C2×#8819311yescharacteristic
814C22C2×Q8×Dic1311yescharacteristic
815C22#1171951711yescharacteristic
816C22Q8×C22⋊D1311yescharacteristic
817C22Q8×C22⋊D1311yescharacteristic
818C22#1171952211yescharacteristic
819C22#1171952211yescharacteristic
820C22#41×Dic1311yescharacteristic
821C22#1171953211yescharacteristic
822C22#1171953611yescharacteristic
823C22#1171953611yescharacteristic
824C22#1171953911yescharacteristic
825C22#1171953911yescharacteristic
826C22C22×C22⋊Dic1311yescharacteristic
827C4—28no—
828C4—42no—
829C4—44no—
830C4—264no—
831C4—522no—
832C4—522no—
833C4—524no—
834C4—522no—
835C4—1042no—
836C4#1171888118yes—
837C2—44no—
838C2C2×#1171888111yescharacteristic
839C2C22⋊Q8×Dic1311yescharacteristic
840C2#1311752011yescharacteristic
841C2Q8×C22⋊Dic1311yescharacteristic
842C2#1311767711yescharacteristic
843C2#1311784511yescharacteristic
844C2#1311786711yescharacteristic
845C2#1311818311yescharacteristic
846C2#1311819711yescharacteristic
847C2#1311833511yescharacteristic
848C2#1311835711yescharacteristic
849C2#1311840411yescharacteristic
850C2#1311843711yescharacteristic
851C2#1311974311yescharacteristic
852C2#1311975511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×C22⋊Q8C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22×C22⋊Q8D13
hypocenterC13#13969
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×Dic13C2semidirect
2. C2×#11718891C2semidirect
5. #13113089C2semidirect
8. #13113068C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
16. C2×C13×C22⋊Q8C4semidirect
87. C2×C22⋊Dic13Q8semidirect
139. C2×Q8×C13C22⋊C4semidirect
274. C23×C13C4×Q8semidirect
361. C2×Dic13C22⋊Q8semidirect
366. C2×C22⋊Q8Dic13semidirect
564. C2×Q8C22⋊Dic13semidirect
654. C13#13969semidirect
689. C23Q8×Dic13semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic132
C2×#117188912
C2×#117188732
C2×C4×C22⋊Dic132
#131130892
#131130812
#131130732
#131130682
#131130652
C22×C13×C22⋊Q82
#1396913