Finite Group Databasebeta

← #15791410

Subgroups — #15791410

Order 3328.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88132C211yesmaximal, characteristic
2C2×#11718316C211yesmaximal, characteristic, complemented
3C2×#11718594C211yesmaximal, characteristic, complemented
4#13113106C211yesmaximal, characteristic, complemented
5#13113106C211yesmaximal, characteristic, complemented
6#13113105C211yesmaximal, characteristic, complemented
7#13113102C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic
9#13113079C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113066C211yesmaximal, characteristic, complemented
12#13113064C211yesmaximal, characteristic, complemented
13#13113058C211yesmaximal, characteristic
14#13113058C211yesmaximal, characteristic
15C13×#1437C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88132—24no—
32C2×#88132—24no—
33C2×#88132C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×#88071C2211yescharacteristic
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
54#11718594—24no—
55#11718316—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×Dic13—22no—
64C23×Dic13—22no—
65C23×Dic13—41no—
66C23×Dic13—41no—
67C23×Dic13—41no—
68C23×Dic13—41no—
69C23×Dic13C2×C414yes—
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C22×Dic26—22no—
79C22×Dic26—22no—
80C22×Dic26—41no—
81C22×Dic26—41no—
82C22×Dic26—41no—
83C22×Dic26—41no—
84C22×Dic26C2×C414yes—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—41no—
90C2×C13×C22⋊C4—41no—
91C2×C13×C22⋊C4—41no—
92C2×C13×C22⋊C4C2×C414yes—
93C2×C13×C22⋊C4Q814yescomplemented
94C2×C42×C13—22no—
95C2×C42×C13—22no—
96C2×C42×C13—41no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13—41no—
104C2×C22⋊Dic13—41no—
105C2×C22⋊Dic13C2×C414yes—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—41no—
111C2×C4⋊Dic13C2×C414yes—
112C2×#6101—22no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—41no—
117C2×#6101C2×C414yes—
118C2×#6101C2×C414yes—
119C2×#6101D414yes—
120C2×#6101D414yes—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—41no—
124#88132—232no—
125C13×#95—22no—
126C13×#95—41no—
127C13×#95—41no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071—41no—
143#88071—41no—
144#88071—41no—
145#14448—131nomaximal, Sylow
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13C22×C412yes—
159C24×C13C2×Q812yes—
160C24×C13#4112yes—
161C24×C13C2411yescharacteristic
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×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13C2×D412yes—
201C22×C4×C13C2×Q812yes—
202C22×C4×C13C2×Q812yes—
203C22×C4×C13#4112yes—
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—28no—
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—44no—
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×Dic13#4112yes—
267C2×Dic26—28no—
268C2×Dic26—44no—
269C2×Dic26—44no—
270C2×Dic26—44no—
271C2×Dic26—44no—
272C2×Dic26—44no—
273C2×Dic26—44no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4—44no—
276C13×C22⋊C4—44no—
277C42×C13—44no—
278C22⋊Dic13—28no—
279C22⋊Dic13—44no—
280C22⋊Dic13—44no—
281C4⋊Dic13—28no—
282C4⋊Dic13—44no—
283#6101—28no—
284#6101—44no—
285#6101C22⋊C4116yescomplemented
286C4×Dic13—44no—
287C22×C22⋊Q8—131no—
288C2×#387—131no—
289C2×#387—131no—
290#1446—131no—
291#1446—131no—
292#1445—131no—
293#1445—131no—
294#1439—131no—
295#1439—131no—
296#1437—131no—
297#1437D1311yescharacteristic
298C4⋊#95—131no—
299C4⋊#95—131no—
300C22⋊#95—131no—
301C22⋊#95—131no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
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—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
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×C13C4×Q814yes—
337C23×C13C23×C411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C22×D411yescharacteristic
340C23×C13C22×Q811yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C132−1+411yescharacteristic
350C23×C132−1+411yescharacteristic
351C23×C132−1+411yescharacteristic
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
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—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
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×C13C2×C22⋊C414yes—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
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—416no—
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×Dic13C2×C22⋊C414yes—
450C2×Dic13C2×C22⋊C414yes—
451Dic26—416no—
452C23×Q8—131no—
453C24×C4—131no—
454C2×C22⋊Q8—138no—
455C2×C22⋊Q8—264no—
456C2×C22⋊Q8—264no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4—131no—
464C22×C22⋊C4—131no—
465C22×C22⋊C4C2×D1311yescharacteristic
466C22×C22⋊C4C2×D1311yescharacteristic
467C22×C22⋊C4C2×D1311yescharacteristic
468C22×C42—131no—
469C22×C42C2×D1311yescharacteristic
470#387—264no—
471#387—264no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95C2×D1311yescharacteristic
490C2×#95C2×D1311yescharacteristic
491C2×#95C2×D1311yescharacteristic
492C22×C13—24no—
493C22×C13—24no—
494C22×C13—24no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13C22×C22⋊C411yescharacteristic
508C22×C13C2×C4×Q811yescharacteristic
509C22×C13C4×#4111yescharacteristic
510C22×C13#51811yescharacteristic
511C22×C13#51811yescharacteristic
512C22×C13#51911yescharacteristic
513C22×C13#52011yescharacteristic
514C22×C13#53511yescharacteristic
515C22×C13#53511yescharacteristic
516C22×C13#53511yescharacteristic
517C22×C13#53511yescharacteristic
518C22×C13#53811yescharacteristic
519C22×C13#53911yescharacteristic
520C22×C13#53911yescharacteristic
521C22×C13#53911yescharacteristic
522C22×C13#54211yescharacteristic
523C22×C13#54211yescharacteristic
524C22×C13#54311yescharacteristic
525C22×C13#54411yescharacteristic
526C22×C13#54611yescharacteristic
527C22×C13#54611yescharacteristic
528C22×C13#54711yescharacteristic
529C22×C13#54711yescharacteristic
530C22×C13#54811yescharacteristic
531C22×C13#54811yescharacteristic
532C22×C13D4×Q811yescharacteristic
533C22×C13D4×Q811yescharacteristic
534C22×C13#55111yescharacteristic
535C22×C13#55111yescharacteristic
536C22×C13#55411yescharacteristic
537C22×C13#55411yescharacteristic
538C22×C13#56211yescharacteristic
539C22×C13#56211yescharacteristic
540C22×C13#56311yescharacteristic
541C22×C13#56311yescharacteristic
542C4×C13—24no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—81no—
548Dic13—24no—
549Dic13—24no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—81no—
554Dic13—81no—
555Dic13—81no—
556C25C22×D1311yescharacteristic
557C22×Q8—134no—
558C22×Q8—262no—
559C22×Q8—262no—
560C22×Q8—521no—
561C22×Q8—521no—
562C22×Q8—521no—
563C22×Q8—521no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—134no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—262no—
574C23×C4—262no—
575C23×C4—521no—
576C23×C4—521no—
577C23×C4—521no—
578C23×C4—521no—
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583C23×C4C22×D1311yescharacteristic
584C23×C4C22×D1311yescharacteristic
585C22⋊Q8—2632no—
586C2×C4⋊C4—134no—
587C2×C4⋊C4—134no—
588C2×C4⋊C4—134no—
589C2×C4⋊C4—134no—
590C2×C4⋊C4—134no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—521no—
600C2×C4⋊C4—521no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—134no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—262no—
612C2×C22⋊C4—262no—
613C2×C22⋊C4—262no—
614C2×C22⋊C4—521no—
615C2×C22⋊C4—521no—
616C2×C22⋊C4—521no—
617C2×C22⋊C4Dic2614yescomplemented
618C2×C22⋊C4C4×D1314yes—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—41no—
622C2×C42—262no—
623C2×C42—262no—
624C2×C42—521no—
625#95—22no—
626#95—41no—
627#95—41no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—521no—
636#95—521no—
637#95—521no—
638#95—521no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95—521no—
643#95—521no—
644#95—521no—
645C2×C13—44no—
646C2×C13#230911yescharacteristic
647C2×C13#232911yescharacteristic
648C2×C13#233211yescharacteristic
649C2×C13#233911yescharacteristic
650C2×C13Q8×C22⋊C411yescharacteristic
651C2×C13#236811yescharacteristic
652C2×C13#237811yescharacteristic
653C2×C13#269211yescharacteristic
654C2×C13#269211yescharacteristic
655C2×C13#269611yescharacteristic
656C2×C13#269611yescharacteristic
657C2×C13#272011yescharacteristic
658C2×C13#272011yescharacteristic
659C2×C13#272311yescharacteristic
660C2×C13#272311yescharacteristic
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C2×Dic2612yes—
674C24C2×C4×D1312yes—
675C24#612712yes—
676C24C23×D1311yescharacteristic
677C2×Q8—268no—
678C2×Q8—524no—
679C2×Q8—524no—
680C2×Q8—524no—
681C2×Q8—524no—
682C2×Q8—524no—
683C2×Q8—524no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
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—132no—
720C22×C4—132no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—268no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
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—524no—
777C22×C4—524no—
778C22×C4—524no—
779C22×C4—524no—
780C22×C4—524no—
781C22×C4—524no—
782C22×C4C2×Dic2612yes—
783C22×C4C2×Dic2612yes—
784C22×C4C2×C4×D1312yes—
785C22×C4C2×C4×D1312yes—
786C22×C4D4×D1312yes—
787C22×C4D4×D1312yes—
788C22×C4#612912yes—
789C4⋊C4—1316no—
790C4⋊C4—268no—
791C4⋊C4—268no—
792C4⋊C4—524no—
793C4⋊C4—524no—
794C22⋊C4—28no—
795C22⋊C4—44no—
796C22⋊C4—44no—
797C22⋊C4—268no—
798C22⋊C4—524no—
799C22⋊C4—524no—
800C42—44no—
801C42—524no—
802C13#1444811yescharacteristic, complemented, Sylow
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23C4×Dic2614yes—
838C23C22×Dic2611yescharacteristic
839C23C22×C4×D1311yescharacteristic
840C23C2×#612711yescharacteristic
841C23C2×D4×D1311yescharacteristic
842C23C2×D4×D1311yescharacteristic
843C23C2×#612911yescharacteristic
844C23#8825111yescharacteristic
845C23#8825111yescharacteristic
846C23#8825111yescharacteristic
847C23#41×D1311yescharacteristic
848C23#8825611yescharacteristic
849C23#8825611yescharacteristic
850C23#8825711yescharacteristic
851C23#8825711yescharacteristic
852C23#8825711yescharacteristic
853Q8—5216no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—134no—
896C2×C4—134no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—262no—
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—5216no—
919C2×C4—521no—
920C2×C4—521no—
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×C4C22⋊C4×D1314yes—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22C2×C4×Dic2611yescharacteristic
969C22#1171918811yescharacteristic
970C22C2×C22⋊C4×D1311yescharacteristic
971C22#1171920011yescharacteristic
972C22#1171922111yescharacteristic
973C22#1171922411yescharacteristic
974C22#1171923211yescharacteristic
975C22C4×#612911yescharacteristic
976C22D4×Dic2611yescharacteristic
977C22D4×Dic2611yescharacteristic
978C22#1171924411yescharacteristic
979C22#1171924811yescharacteristic
980C22#1171925011yescharacteristic
981C22#1171925011yescharacteristic
982C22#1171925111yescharacteristic
983C22#1171925711yescharacteristic
984C22#1171925711yescharacteristic
985C22#1171926511yescharacteristic
986C22#1171926911yescharacteristic
987C22#1171929611yescharacteristic
988C22#1171930811yescharacteristic
989C22#1171931211yescharacteristic
990C22#1171931211yescharacteristic
991C22#1171931511yescharacteristic
992C22#1171931611yescharacteristic
993C22#1171932611yescharacteristic
994C22#1171936011yescharacteristic
995C22#1171937011yescharacteristic
996C22#1171937211yescharacteristic
997C22#1171937411yescharacteristic
998C22#1171937711yescharacteristic
999C22#1171937911yescharacteristic
1000C22#1171941211yescharacteristic
1001C22#1171941711yescharacteristic
1002C22#1171942011yescharacteristic
1003C4—24no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—81no—
1009C4—264no—
1010C4—264no—
1011C4—522no—
1012C4—522no—
1013C4—522no—
1014C4—1041no—
1015C4—1041no—
1016C4—1041no—
1017C2—44no—
1018C2#1311741511yescharacteristic
1019C2#1311756411yescharacteristic
1020C2#1311759311yescharacteristic
1021C2#1311766211yescharacteristic
1022C2C22⋊C4×Dic2611yescharacteristic
1023C2#1311791411yescharacteristic
1024C2#1311799611yescharacteristic
1025C2#1312132911yescharacteristic
1026C2#1312133611yescharacteristic
1027C2#1312138311yescharacteristic
1028C2#1312139011yescharacteristic
1029C2#1312171311yescharacteristic
1030C2#1312172011yescharacteristic
1031C2#1312175211yescharacteristic
1032C2#1312175911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1437C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenter#1437D13
hypocenterC13#14448
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#11718316C2semidirect
3. C2×#11718594C2semidirect
4. #13113106C2semidirect
5. #13113106C2semidirect
6. #13113105C2semidirect
7. #13113102C2semidirect
11. #13113066C2semidirect
12. #13113064C2semidirect
33. C2×#88132C4semidirect
93. C2×C13×C22⋊C4Q8semidirect
285. #6101C22⋊C4semidirect
617. C2×C22⋊C4Dic26semidirect
802. C13#14448semidirect

Maximal subgroups

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

subgroupindex
C22×#881322
C2×#117183162
C2×#117185942
#131131062
#131131052
#131131022
#131130812
#131130792
#131130732
#131130662
#131130642
#131130582
C13×#14372
#1444813