Finite Group Databasebeta

← #15786732

Subgroups — #15786732

Order 3328.

1838 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88198C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic
3C2×#11718633C211yesmaximal, characteristic
4C2×C4×#6101C211yesmaximal, characteristic
5#13113107C211yesmaximal, characteristic
6#13113106C211yesmaximal, characteristic
7#13113087C211yesmaximal, characteristic
8#13113086C211yesmaximal, characteristic
9#13113069C211yesmaximal, characteristic
10#13113067C211yesmaximal, characteristic
11#13113064C211yesmaximal, characteristic
12#13113064C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic
15C2×C13×#391C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C42×C13C2211yescharacteristic
20C2×#88198—24no—
21C2×#88198—24no—
22C2×#88198C418yescomplemented
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C13×#391—24no—
35C2×C13×#95C2211yescharacteristic
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
54C2×#88071C2211yescharacteristic
55#11718633—24no—
56C4×#6101—24no—
57#11718307—24no—
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—41no—
63C22×Q8×C13—41no—
64C22×Q8×C13C2×C414yes—
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
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—41no—
90C2×C42×C13—22no—
91C2×C42×C13—22no—
92C2×C42×C13—41no—
93#88198—232no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101—22no—
103C2×#6101—22no—
104C2×#6101—22no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—41no—
108C2×#6101C2×C414yes—
109C2×#6101C2×C414yes—
110C2×#6101C2×C414yes—
111C2×#6101C2×C414yes—
112C2×#6101D414yes—
113C2×#6101D414yes—
114C2×#6101Q814yescomplemented
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—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13C2×C414yes—
126C2×C4×Dic13Q814yescomplemented
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95D414yes—
131#88071—22no—
132#88071—22no—
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—41no—
143#88071—41no—
144#88071—41no—
145#88071—41no—
146#88071Q814yescomplemented
147#14053—131nomaximal, Sylow
148C24×C13C2411yescharacteristic
149C2×Q8×C13—28no—
150C2×Q8×C13—28no—
151C2×Q8×C13—44no—
152C2×Q8×C13—44no—
153C2×Q8×C13—44no—
154C2×Q8×C13—44no—
155C2×Q8×C13—44no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
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—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×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×Q812yes—
202C22×C4×C13C2×Q812yes—
203C22×C4×C13C2×Q812yes—
204C22×C4×C13#4112yes—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
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×Dic13C22×C412yes—
245C22×Dic13C22×C412yes—
246C22×Dic13C22×C412yes—
247C22×Dic13C22×C412yes—
248C22×Dic13C2×D412yes—
249C22×Dic13C2×D412yes—
250C22×Dic13C2×D412yes—
251C22×Dic13C2×D412yes—
252C22×Dic13C2×Q812yes—
253C22×Dic13C2×Q812yes—
254C22×Dic13C2×Q812yes—
255C22×Dic13C2×Q812yes—
256C22×Dic13C2×Q812yes—
257C22×Dic13C2×Q812yes—
258C22×Dic13#4112yes—
259C22×Dic13#4112yes—
260C22×Dic13#4112yes—
261C2×Dic26—28no—
262C2×Dic26—28no—
263C2×Dic26—44no—
264C2×Dic26—44no—
265C2×Dic26—44no—
266C2×Dic26—44no—
267C2×Dic26—44no—
268C13×C4⋊C4—44no—
269C42×C13—44no—
270#6101—28no—
271#6101—28no—
272#6101—28no—
273#6101—28no—
274#6101—44no—
275#6101—44no—
276#6101C22⋊C4116yes—
277C4×Dic13—28no—
278C4×Dic13—28no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C22×C4⋊Q8—131no—
282C2×#391—131no—
283C2×#391D1311yescharacteristic
284C2×#389—131no—
285C2×C4×C4⋊C4—131no—
286#1446—131no—
287#1446—131no—
288#1441—131no—
289#1441—131no—
290#1436—131no—
291#1436—131no—
292C4⋊#95—131no—
293C4⋊#95—131no—
294C4⋊#95—131no—
295C4×#95—131no—
296C23×C13C23×C411yescharacteristic
297C23×C13C22×D411yescharacteristic
298C23×C13C22×D411yescharacteristic
299C23×C13C22×D411yescharacteristic
300C23×C13C22×Q811yescharacteristic
301C23×C13C22×Q811yescharacteristic
302C23×C13C22×Q811yescharacteristic
303C23×C13C2×#4111yescharacteristic
304C23×C13C2×#4111yescharacteristic
305C23×C13C2×#4111yescharacteristic
306C23×C13C2×#4111yescharacteristic
307C23×C13H(5,𝔽2)11yescharacteristic
308C23×C13H(5,𝔽2)11yescharacteristic
309C23×C132−1+411yescharacteristic
310C23×C132−1+411yescharacteristic
311Q8×C13—416no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
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—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—41no—
340C2×C4×C13—41no—
341C2×C4×C13—41no—
342C2×C4×C13—41no—
343C2×C4×C13—41no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13C2×C22⋊C414yes—
359C2×C4×C13C4×D414yes—
360C2×C4×C13C4⋊Q814yescomplemented
361C2×Dic13—22no—
362C2×Dic13—22no—
363C2×Dic13—22no—
364C2×Dic13—22no—
365C2×Dic13—22no—
366C2×Dic13—22no—
367C2×Dic13—22no—
368C2×Dic13—22no—
369C2×Dic13—22no—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13C2×C22⋊C414yes—
409C2×Dic13C2×C22⋊C414yes—
410C2×Dic13C4×Q814yes—
411C2×Dic13C4×Q814yes—
412C2×Dic13C4×Q814yes—
413C2×Dic13C22⋊Q814yes—
414C2×Dic13C22⋊Q814yes—
415C2×Dic13#12414yes—
416C2×Dic13C4⋊Q814yes—
417Dic26—416no—
418C23×Q8—131no—
419C23×Q8C2×D1311yescharacteristic
420C2×C4⋊Q8—138no—
421C2×C4⋊Q8—264no—
422C2×C4⋊Q8—264no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4—131no—
426C22×C4⋊C4—131no—
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—131no—
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C42—131no—
432C22×C42—131no—
433C22×C42—131no—
434C22×C42—131no—
435C22×C42C2×D1311yescharacteristic
436#391—24no—
437#391—264no—
438#389—264no—
439C4×C4⋊C4—264no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95C2×D1311yescharacteristic
457C2×#95C2×D1311yescharacteristic
458C2×#95C2×D1311yescharacteristic
459C2×#95C2×D1311yescharacteristic
460C22×C13C22×C22⋊C411yescharacteristic
461C22×C13C2×C4×D411yescharacteristic
462C22×C13C2×C4×Q811yescharacteristic
463C22×C13C2×C4×Q811yescharacteristic
464C22×C13C2×C4×Q811yescharacteristic
465C22×C13#51811yescharacteristic
466C22×C13#51911yescharacteristic
467C22×C13C2×C22⋊Q811yescharacteristic
468C22×C13C2×C22⋊Q811yescharacteristic
469C22×C13C2×#12411yescharacteristic
470C22×C13C2×C4⋊Q811yescharacteristic
471C22×C13C2×C4⋊Q811yescharacteristic
472C22×C13#53211yescharacteristic
473C22×C13#53311yescharacteristic
474C22×C13#53311yescharacteristic
475C22×C13#54211yescharacteristic
476C22×C13#54211yescharacteristic
477C22×C13#54411yescharacteristic
478C22×C13#54411yescharacteristic
479C22×C13D4211yescharacteristic
480C22×C13D4211yescharacteristic
481C22×C13#54611yescharacteristic
482C22×C13#54611yescharacteristic
483C22×C13#54711yescharacteristic
484C22×C13#54811yescharacteristic
485C22×C13#54811yescharacteristic
486C22×C13D4×Q811yescharacteristic
487C22×C13D4×Q811yescharacteristic
488C22×C13D4×Q811yescharacteristic
489C22×C13#55411yescharacteristic
490C22×C13#55411yescharacteristic
491C22×C13#55511yescharacteristic
492C22×C13#55611yescharacteristic
493C22×C13#55711yescharacteristic
494C22×C13Q8211yescharacteristic
495C4×C13—24no—
496C4×C13—24no—
497C4×C13—24no—
498C4×C13—42no—
499C4×C13—42no—
500C4×C13—42no—
501C4×C13—81no—
502Dic13—24no—
503Dic13—24no—
504Dic13—42no—
505Dic13—42no—
506Dic13—42no—
507Dic13—42no—
508Dic13—81no—
509Dic13#39118yescomplemented
510C22×Q8—22no—
511C22×Q8—22no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—134no—
517C22×Q8—262no—
518C22×Q8—262no—
519C22×Q8—262no—
520C22×Q8—262no—
521C22×Q8—521no—
522C22×Q8—521no—
523C22×Q8C4×D1314yes—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4—131no—
528C23×C4—131no—
529C23×C4—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C23×C4C22×D1311yescharacteristic
535C23×C4C22×D1311yescharacteristic
536C23×C4C22×D1311yescharacteristic
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C4⋊Q8—2632no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—134no—
544C2×C4⋊C4—134no—
545C2×C4⋊C4—134no—
546C2×C4⋊C4—134no—
547C2×C4⋊C4—134no—
548C2×C4⋊C4—134no—
549C2×C4⋊C4—134no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4—262no—
552C2×C4⋊C4—262no—
553C2×C4⋊C4—262no—
554C2×C4⋊C4—262no—
555C2×C4⋊C4—262no—
556C2×C4⋊C4—262no—
557C2×C4⋊C4—262no—
558C2×C4⋊C4—262no—
559C2×C4⋊C4—262no—
560C2×C4⋊C4—262no—
561C2×C4⋊C4—262no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—521no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—41no—
567C2×C42—134no—
568C2×C42—134no—
569C2×C42—262no—
570C2×C42—262no—
571C2×C42—262no—
572C2×C42—262no—
573C2×C42—262no—
574C2×C42—262no—
575C2×C42—262no—
576C2×C42—262no—
577C2×C42—262no—
578C2×C42—521no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—134no—
583#95—262no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—262no—
589#95—262no—
590#95—262no—
591#95—262no—
592#95—262no—
593#95—262no—
594#95—521no—
595#95—521no—
596#95—521no—
597#95—521no—
598#95C22⋊D1314yes—
599C2×C13C2×#39111yescharacteristic
600C2×C13C4×C4⋊Q811yescharacteristic
601C2×C13#233111yescharacteristic
602C2×C13D4×C22⋊C411yescharacteristic
603C2×C13Q8×C22⋊C411yescharacteristic
604C2×C13#236511yescharacteristic
605C2×C13#236911yescharacteristic
606C2×C13#243911yescharacteristic
607C2×C13#244011yescharacteristic
608C2×C13#245111yescharacteristic
609C2×C13#245211yescharacteristic
610C2×C13#249111yescharacteristic
611C2×C13#249211yescharacteristic
612C2×C13#255011yescharacteristic
613C2×C13#255111yescharacteristic
614C24C23×D1311yescharacteristic
615C2×Q8—28no—
616C2×Q8—28no—
617C2×Q8—44no—
618C2×Q8—44no—
619C2×Q8—44no—
620C2×Q8—44no—
621C2×Q8—44no—
622C2×Q8—268no—
623C2×Q8—268no—
624C2×Q8—524no—
625C2×Q8—524no—
626C2×Q8—524no—
627C2×Q8—524no—
628C2×Q8—524no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—132no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—132no—
671C22×C4—132no—
672C22×C4—132no—
673C22×C4—132no—
674C22×C4—132no—
675C22×C4—132no—
676C22×C4—132no—
677C22×C4—132no—
678C22×C4—132no—
679C22×C4—132no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4C2×C4×D1312yes—
723C22×C4C2×C4×D1312yes—
724C22×C4C2×C4×D1312yes—
725C22×C4#612712yes—
726C22×C4D4×D1312yes—
727C22×C4D4×D1312yes—
728C22×C4Q8×D1312yes—
729C22×C4Q8×D1312yes—
730C22×C4Q8×D1312yes—
731C22×C4C2×C22⋊D1312yes—
732C22×C4C2×C22⋊D1312yes—
733C22×C4C2×C22⋊D1312yes—
734C4⋊C4—44no—
735C4⋊C4—1316no—
736C4⋊C4—268no—
737C4⋊C4—268no—
738C4⋊C4—268no—
739C4⋊C4—268no—
740C4⋊C4—524no—
741C4⋊C4—524no—
742C42—44no—
743C42—268no—
744C42—268no—
745C42—524no—
746C42—524no—
747C13#1405311yescharacteristic, complemented, Sylow
748C23C22×C4×D1311yescharacteristic
749C23C2×#612711yescharacteristic
750C23C2×D4×D1311yescharacteristic
751C23C2×D4×D1311yescharacteristic
752C23#8825111yescharacteristic
753C23#8825111yescharacteristic
754C23C2×Q8×D1311yescharacteristic
755C23C2×Q8×D1311yescharacteristic
756C23C2×Q8×D1311yescharacteristic
757C23#8825411yescharacteristic
758C23#41×D1311yescharacteristic
759C23#41×D1311yescharacteristic
760C23#41×D1311yescharacteristic
761C23#8825711yescharacteristic
762C23C22×C22⋊D1311yescharacteristic
763Q8—416no—
764Q8—5216no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—134no—
812C2×C4—134no—
813C2×C4—134no—
814C2×C4—134no—
815C2×C4—134no—
816C2×C4—134no—
817C2×C4—134no—
818C2×C4—134no—
819C2×C4—134no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—262no—
823C2×C4—262no—
824C2×C4—262no—
825C2×C4—262no—
826C2×C4—262no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—262no—
830C2×C4—262no—
831C2×C4—262no—
832C2×C4—262no—
833C2×C4—262no—
834C2×C4—262no—
835C2×C4—262no—
836C2×C4—262no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—521no—
845C2×C4—521no—
846C2×C4—521no—
847C2×C4—521no—
848C2×C4—521no—
849C2×C4—521no—
850C2×C4—521no—
851C2×C4—521no—
852C2×C4—521no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4C22⋊C4×D1314yes—
868C2×C4C4×C22⋊D1314yes—
869C2×C4#8819814yescomplemented
870C22C2×C22⋊C4×D1311yescharacteristic
871C22#1171919111yescharacteristic
872C22#1171919511yescharacteristic
873C22#1171919511yescharacteristic
874C22#1171927211yescharacteristic
875C22#1171927311yescharacteristic
876C22C4×Q8×D1311yescharacteristic
877C22C4×Q8×D1311yescharacteristic
878C22C4×Q8×D1311yescharacteristic
879C22#1171927711yescharacteristic
880C22#1171928311yescharacteristic
881C22#1171928311yescharacteristic
882C22#1171932811yescharacteristic
883C22D13×C22⋊Q811yescharacteristic
884C22D13×C22⋊Q811yescharacteristic
885C22#1171933711yescharacteristic
886C22#1171933811yescharacteristic
887C22#1171934111yescharacteristic
888C22#1171934111yescharacteristic
889C22#1171934511yescharacteristic
890C22#1171937411yescharacteristic
891C22#1171937511yescharacteristic
892C22D13×#12411yescharacteristic
893C22#1171938211yescharacteristic
894C22#1171942711yescharacteristic
895C22D13×C4⋊Q811yescharacteristic
896C22#1171943211yescharacteristic
897C22#1171943411yescharacteristic
898C22C2×C4×C22⋊D1311yescharacteristic
899C22D4×C22⋊D1311yescharacteristic
900C22D4×C22⋊D1311yescharacteristic
901C22C2×#8819811yescharacteristic
902C22Q8×C22⋊D1311yescharacteristic
903C22#1171952911yescharacteristic
904C22#1171953711yescharacteristic
905C4—24no—
906C4—24no—
907C4—24no—
908C4—42no—
909C4—42no—
910C4—42no—
911C4—81no—
912C4—138no—
913C4—264no—
914C4—264no—
915C4—522no—
916C4—522no—
917C4—522no—
918C4—522no—
919C4—1041no—
920C2D13×#39111yescharacteristic
921C2C4×#8819811yescharacteristic
922C2#1311757911yescharacteristic
923C2C22⋊C4×C22⋊D1311yescharacteristic
924C2#1311767011yescharacteristic
925C2#1311789011yescharacteristic
926C2#1311792411yescharacteristic
927C2#1311852411yescharacteristic
928C2#1311853511yescharacteristic
929C2#1311867211yescharacteristic
930C2#1311868511yescharacteristic
931C2#1311919611yescharacteristic
932C2#1311920911yescharacteristic
933C2#1311985411yescharacteristic
934C2#1311986311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, prime radical, cosocleC24×C13C24
hypercenterC2×#391D13
hypocenterC13#14053
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
22. C2×#88198C4semidirect
114. C2×#6101Q8semidirect
126. C2×C4×Dic13Q8semidirect
146. #88071Q8semidirect
360. C2×C4×C13C4⋊Q8semidirect
509. Dic13#391semidirect
747. C13#14053semidirect
869. C2×C4#88198semidirect

Maximal subgroups

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

subgroupindex
C22×#881982
C2×#117183072
C2×#117186332
C2×C4×#61012
#131131072
#131131062
#131130872
#131130862
#131130692
#131130672
#131130642
#95×Dic132
C2×C13×#3912
#1405313