Finite Group Databasebeta

← #15785787

Subgroups — #15785787

Order 3328.

1838 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88141C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic
3C2×#11718307C211yesmaximal, characteristic
4C2×#11718633C211yesmaximal, characteristic
5C2×#11718637C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic
7#13113099C211yesmaximal, characteristic
8#13113099C211yesmaximal, characteristic
9#13113071C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic
11#13113068C211yesmaximal, characteristic
12#13113067C211yesmaximal, characteristic
13#13113064C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic
15C13×#1444C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×#88141—24no—
34C2×#88141—24no—
35C2×#88141—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
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
54#11718637—24no—
55#11718633—24no—
56#11718307—24no—
57#11718307C418yescomplemented
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×Dic26—22no—
74C22×Dic26—22no—
75C22×Dic26—22no—
76C22×Dic26—22no—
77C22×Dic26C2×C414yes—
78C22×Dic26D414yes—
79C22×Dic26Q814yes—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4—41no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—41no—
92C2×#6101—22no—
93C2×#6101—22no—
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×#6101—41no—
109C2×#6101—41no—
110C2×#6101—41no—
111C2×#6101C2×C414yes—
112C2×#6101D414yes—
113C2×C4×Dic13—22no—
114C2×C4×Dic13—22no—
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—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13C2×C414yes—
127C2×C4×Dic13D414yes—
128#88141—232no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—41no—
132C13×#95C2×C414yes—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yes—
143#88071C2×C414yes—
144#88071C2×C414yes—
145#88071Q814yescomplemented
146#88071Q814yescomplemented
147#13976—131nomaximal, Sylow
148C24×C13C2411yescharacteristic
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
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×C13C22×C412yes—
189C22×C4×C13C22×C412yes—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C2×D412yes—
192C22×C4×C13C2×D412yes—
193C22×C4×C13C2×D412yes—
194C22×C4×C13C2×Q812yes—
195C22×C4×C13C2×Q812yes—
196C22×C4×C13C2×Q812yes—
197C22×C4×C13#4112yes—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
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×Dic13C22×C412yes—
236C22×Dic13C22×C412yes—
237C22×Dic13C22×C412yes—
238C22×Dic13C22×C412yes—
239C22×Dic13C2×D412yes—
240C22×Dic13C2×D412yes—
241C22×Dic13C2×D412yes—
242C22×Dic13C2×D412yes—
243C22×Dic13C2×D412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13C2×Q812yes—
246C22×Dic13C2×Q812yes—
247C22×Dic13C2×Q812yes—
248C22×Dic13C2×Q812yes—
249C22×Dic13C2×Q812yes—
250C22×Dic13C2×Q812yes—
251C22×Dic13#4112yes—
252C22×Dic13#4112yes—
253C22×Dic13#4112yes—
254C2×Dic26—28no—
255C2×Dic26—28no—
256C2×Dic26—28no—
257C2×Dic26—28no—
258C2×Dic26—28no—
259C2×Dic26—28no—
260C2×Dic26C4⋊C4116yescomplemented
261C13×C4⋊C4—28no—
262C13×C4⋊C4—44no—
263C13×C4⋊C4—44no—
264C4⋊Dic13—44no—
265#6101—28no—
266#6101—28no—
267#6101—28no—
268#6101—44no—
269#6101—44no—
270#6101—44no—
271#6101—44no—
272C4×Dic13—28no—
273C4×Dic13—28no—
274C4×Dic13—28no—
275C4×Dic13—28no—
276C4×Dic13—44no—
277C22×C4×Q8—131no—
278C2×#391—131no—
279C2×#391—131no—
280C2×#389—131no—
281C2×#384—131no—
282#1444—131no—
283#1444—131no—
284#1444—131no—
285#1444D1311yescharacteristic
286#1436—131no—
287#1436—131no—
288#1436—131no—
289#1436—131no—
290C4⋊#95—131no—
291C4×#95—131no—
292C23×C13C23×C411yescharacteristic
293C23×C13C22×D411yescharacteristic
294C23×C13C22×D411yescharacteristic
295C23×C13C22×D411yescharacteristic
296C23×C13C22×Q811yescharacteristic
297C23×C13C22×Q811yescharacteristic
298C23×C13C22×Q811yescharacteristic
299C23×C13C2×#4111yescharacteristic
300C23×C13C2×#4111yescharacteristic
301C23×C13C2×#4111yescharacteristic
302C23×C13C2×#4111yescharacteristic
303C23×C13H(5,𝔽2)11yescharacteristic
304C23×C13H(5,𝔽2)11yescharacteristic
305C23×C132−1+411yescharacteristic
306C23×C132−1+411yescharacteristic
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—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—41no—
332C2×C4×C13—41no—
333C2×C4×C13—41no—
334C2×C4×C13—41no—
335C2×C4×C13—41no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
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×C13C2×C4⋊C414yes—
355C2×C4×C13C4×Q814yescomplemented
356C2×Dic13—22no—
357C2×Dic13—22no—
358C2×Dic13—22no—
359C2×Dic13—22no—
360C2×Dic13—22no—
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—41no—
384C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
403C2×Dic13C2×C4⋊C414yes—
404C2×Dic13C4×D414yes—
405C2×Dic13C4×D414yes—
406C2×Dic13C4×Q814yescomplemented
407C2×Dic13#12014yes—
408C2×Dic13C22⋊Q814yes—
409C2×Dic13C22⋊Q814yes—
410C2×Dic13#12314yes—
411C2×Dic13C4⋊Q814yes—
412Dic26—232no—
413C23×Q8—131no—
414C2×C4×Q8—264no—
415C2×C4×Q8—264no—
416C2×C4×Q8—264no—
417C22×C4⋊C4—131no—
418C22×C4⋊C4—131no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—131no—
423C22×C4⋊C4—131no—
424C22×C4⋊C4—131no—
425C22×C4⋊C4C2×D1311yescharacteristic
426C22×C4⋊C4C2×D1311yescharacteristic
427C22×C4⋊C4C2×D1311yescharacteristic
428C22×C42—131no—
429C22×C42—131no—
430C22×C42—131no—
431C22×C42—131no—
432C22×C42—131no—
433#391—138no—
434#391—264no—
435#389—264no—
436#384—264no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
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×#95C2×D1311yescharacteristic
452C2×#95C2×D1311yescharacteristic
453C2×#95C2×D1311yescharacteristic
454C2×#95C2×D1311yescharacteristic
455C22×C13C22×C4⋊C411yescharacteristic
456C22×C13C2×C4×D411yescharacteristic
457C22×C13C2×C4×D411yescharacteristic
458C22×C13C2×C4×Q811yescharacteristic
459C22×C13C2×C4×Q811yescharacteristic
460C22×C13#52011yescharacteristic
461C22×C13#52011yescharacteristic
462C22×C13C2×#12011yescharacteristic
463C22×C13C2×C22⋊Q811yescharacteristic
464C22×C13C2×C22⋊Q811yescharacteristic
465C22×C13C2×#12311yescharacteristic
466C22×C13C2×C4⋊Q811yescharacteristic
467C22×C13#53211yescharacteristic
468C22×C13#53311yescharacteristic
469C22×C13#53311yescharacteristic
470C22×C13#53511yescharacteristic
471C22×C13#53611yescharacteristic
472C22×C13#54211yescharacteristic
473C22×C13#54211yescharacteristic
474C22×C13#54611yescharacteristic
475C22×C13#54611yescharacteristic
476C22×C13D4×Q811yescharacteristic
477C22×C13D4×Q811yescharacteristic
478C22×C13D4×Q811yescharacteristic
479C22×C13D4×Q811yescharacteristic
480C22×C13#55011yescharacteristic
481C22×C13#55011yescharacteristic
482C22×C13#55211yescharacteristic
483C22×C13#55211yescharacteristic
484C22×C13#55411yescharacteristic
485C22×C13#55411yescharacteristic
486C22×C13#55711yescharacteristic
487C22×C13#55711yescharacteristic
488C22×C13Q8211yescharacteristic
489C22×C13Q8211yescharacteristic
490C4×C13—24no—
491C4×C13—24no—
492C4×C13—42no—
493C4×C13—42no—
494C4×C13—42no—
495C4×C13—42no—
496C4×C13—81no—
497Dic13—24no—
498Dic13—24no—
499Dic13—24no—
500Dic13—42no—
501Dic13—42no—
502Dic13—42no—
503Dic13—81no—
504Dic13#38518yes—
505C22×Q8—134no—
506C22×Q8—134no—
507C22×Q8—134no—
508C22×Q8—262no—
509C22×Q8—262no—
510C22×Q8—262no—
511C22×Q8—262no—
512C23×C4—131no—
513C23×C4—131no—
514C23×C4—131no—
515C23×C4—131no—
516C23×C4—131no—
517C23×C4—131no—
518C23×C4—131no—
519C23×C4—131no—
520C23×C4C22×D1311yescharacteristic
521C23×C4C22×D1311yescharacteristic
522C23×C4C22×D1311yescharacteristic
523C23×C4C22×D1311yescharacteristic
524C23×C4C22×D1311yescharacteristic
525C23×C4C22×D1311yescharacteristic
526C23×C4C22×D1311yescharacteristic
527C4×Q8—2632no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—134no—
538C2×C4⋊C4—134no—
539C2×C4⋊C4—262no—
540C2×C4⋊C4—262no—
541C2×C4⋊C4—262no—
542C2×C4⋊C4—262no—
543C2×C4⋊C4—262no—
544C2×C4⋊C4—262no—
545C2×C4⋊C4—262no—
546C2×C4⋊C4—262no—
547C2×C4⋊C4—262no—
548C2×C4⋊C4—262no—
549C2×C4⋊C4—262no—
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—521no—
557C2×C4⋊C4—521no—
558C2×C4⋊C4—521no—
559C2×C4⋊C4—521no—
560C2×C4⋊C4—521no—
561C2×C42—134no—
562C2×C42—134no—
563C2×C42—262no—
564C2×C42—262no—
565C2×C42—262no—
566C2×C42—262no—
567C2×C42—262no—
568C2×C42—262no—
569C2×C42—262no—
570C2×C42—262no—
571C2×C42—262no—
572C2×C42—262no—
573C2×C42—262no—
574C2×C42—262no—
575C2×C42—262no—
576#95—22no—
577#95—22no—
578#95—41no—
579#95—134no—
580#95—134no—
581#95—134no—
582#95—134no—
583#95—134no—
584#95—262no—
585#95—262no—
586#95—262no—
587#95—262no—
588#95—262no—
589#95—262no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95C4×D1314yes—
594C2×C13C2×#38511yescharacteristic
595C2×C13C4×C4⋊Q811yescharacteristic
596C2×C13#232611yescharacteristic
597C2×C13Q8×C4⋊C411yescharacteristic
598C2×C13Q8×C4⋊C411yescharacteristic
599C2×C13#236011yescharacteristic
600C2×C13#236011yescharacteristic
601C2×C13#242311yescharacteristic
602C2×C13#242311yescharacteristic
603C2×C13#243111yescharacteristic
604C2×C13#243411yescharacteristic
605C2×C13#245111yescharacteristic
606C2×C13#245111yescharacteristic
607C2×C13#256511yescharacteristic
608C2×C13#256711yescharacteristic
609C24C23×D1311yescharacteristic
610C2×Q8—1316no—
611C2×Q8—268no—
612C2×Q8—268no—
613C2×Q8—268no—
614C2×Q8—268no—
615C2×Q8—268no—
616C2×Q8—268no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
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—132no—
657C22×C4—132no—
658C22×C4—132no—
659C22×C4—132no—
660C22×C4—132no—
661C22×C4—132no—
662C22×C4—132no—
663C22×C4—132no—
664C22×C4—132no—
665C22×C4—132no—
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—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
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×C4C2×C4×D1312yes—
713C22×C4C2×C4×D1312yes—
714C22×C4C2×C4×D1312yes—
715C22×C4D4×D1312yes—
716C22×C4D4×D1312yes—
717C22×C4D4×D1312yes—
718C22×C4#612912yes—
719C22×C4Q8×D1312yes—
720C22×C4Q8×D1312yes—
721C22×C4Q8×D1312yes—
722C4⋊C4—28no—
723C4⋊C4—44no—
724C4⋊C4—44no—
725C4⋊C4—268no—
726C4⋊C4—268no—
727C4⋊C4—268no—
728C4⋊C4—524no—
729C4⋊C4—524no—
730C4⋊C4—524no—
731C4⋊C4—524no—
732C4⋊C4—524no—
733C42—268no—
734C42—268no—
735C42—268no—
736C42—268no—
737C42—524no—
738C13#1397611yescharacteristic, complemented, Sylow
739C23C22×C4×D1311yescharacteristic
740C23C2×D4×D1311yescharacteristic
741C23C2×D4×D1311yescharacteristic
742C23C2×D4×D1311yescharacteristic
743C23C2×#612911yescharacteristic
744C23#8825111yescharacteristic
745C23#8825111yescharacteristic
746C23C2×Q8×D1311yescharacteristic
747C23C2×Q8×D1311yescharacteristic
748C23C2×Q8×D1311yescharacteristic
749C23#8825411yescharacteristic
750C23#41×D1311yescharacteristic
751C23#41×D1311yescharacteristic
752C23#41×D1311yescharacteristic
753C23#8825711yescharacteristic
754Q8—2632no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
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—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
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—134no—
803C2×C4—134no—
804C2×C4—134no—
805C2×C4—134no—
806C2×C4—134no—
807C2×C4—134no—
808C2×C4—134no—
809C2×C4—134no—
810C2×C4—134no—
811C2×C4—134no—
812C2×C4—262no—
813C2×C4—262no—
814C2×C4—262no—
815C2×C4—262no—
816C2×C4—262no—
817C2×C4—262no—
818C2×C4—262no—
819C2×C4—262no—
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—521no—
840C2×C4—521no—
841C2×C4—521no—
842C2×C4—521no—
843C2×C4—521no—
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#8814114yescomplemented
859C2×C4C4⋊C4×D1314yes—
860C22C2×#8814111yescharacteristic
861C22C2×C4⋊C4×D1311yescharacteristic
862C22#1171920911yescharacteristic
863C22C4×D4×D1311yescharacteristic
864C22C4×D4×D1311yescharacteristic
865C22#1171925111yescharacteristic
866C22C4×Q8×D1311yescharacteristic
867C22D13×#12011yescharacteristic
868C22#1171929611yescharacteristic
869C22#1171929711yescharacteristic
870C22#1171930111yescharacteristic
871C22#1171930411yescharacteristic
872C22#1171931511yescharacteristic
873C22#1171932711yescharacteristic
874C22D13×C22⋊Q811yescharacteristic
875C22D13×C22⋊Q811yescharacteristic
876C22#1171933311yescharacteristic
877C22#1171933711yescharacteristic
878C22#1171933711yescharacteristic
879C22#1171934111yescharacteristic
880C22#1171934111yescharacteristic
881C22#1171934511yescharacteristic
882C22#1171935511yescharacteristic
883C22D13×#12311yescharacteristic
884C22#1171936711yescharacteristic
885C22#1171939011yescharacteristic
886C22#1171939311yescharacteristic
887C22#1171939811yescharacteristic
888C22#1171942311yescharacteristic
889C22#1171942611yescharacteristic
890C22#1171942711yescharacteristic
891C22#1171942711yescharacteristic
892C22D13×C4⋊Q811yescharacteristic
893C22#1171943211yescharacteristic
894C22#1171943211yescharacteristic
895C4—24no—
896C4—24no—
897C4—42no—
898C4—42no—
899C4—42no—
900C4—42no—
901C4—81no—
902C4—138no—
903C4—264no—
904C4—264no—
905C4—264no—
906C4—522no—
907C4—522no—
908C4—522no—
909C4—1041no—
910C2D13×#38511yescharacteristic
911C2#1311740711yescharacteristic
912C2#1311754211yescharacteristic
913C2#1311774811yescharacteristic
914C2#1311775011yescharacteristic
915C2#1311783611yescharacteristic
916C2#1311783811yescharacteristic
917C2#1311835411yescharacteristic
918C2#1311835611yescharacteristic
919C2#1311845011yescharacteristic
920C2#1311847511yescharacteristic
921C2#1311866811yescharacteristic
922C2#1311867011yescharacteristic
923C2#1312002211yescharacteristic
924C2#1312004011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1444C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1444D13
hypocenterC13#13976
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
57. #11718307C4semidirect
145. #88071Q8semidirect
146. #88071Q8semidirect
260. C2×Dic26C4⋊C4semidirect
355. C2×C4×C13C4×Q8semidirect
406. C2×Dic13C4×Q8semidirect
738. C13#13976semidirect
858. C2×C4#88141semidirect

Maximal subgroups

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

subgroupindex
C22×#881412
C2×#117183072
C2×#117186332
C2×#117186372
#131131002
#131130992
#131130712
#131130702
#131130682
#131130672
#131130642
#95×Dic132
C13×#14442
#1397613