Finite Group Databasebeta

← #15784269

Subgroups — #15784269

Order 3328.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718606C211yesmaximal, characteristic
2C2×#11718605C211yesmaximal, characteristic
3C2×#11718871C211yesmaximal, characteristic
4C2×#11718310C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic13C211yesmaximal, characteristic
6#13113073C211yesmaximal, characteristic
7#13113073C211yesmaximal, characteristic
8#13113071C211yesmaximal, characteristic, complemented
9#13113067C211yesmaximal, characteristic, complemented
10#13113067C211yesmaximal, characteristic, complemented
11#13113067C211yesmaximal, characteristic, complemented
12#13113064C211yesmaximal, characteristic, complemented
13#13113062C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C22⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic13C2211yescharacteristic
20C22×C22⋊Dic13C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37#11718871C418yescomplemented
38C4×C22⋊Dic13—24no—
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
53#11718606C418yescomplemented
54#11718605C418yescomplemented
55#11718310—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
61C23×C4×C13—41no—
62C23×C4×C13—41no—
63C23×C4×C13C2×C414yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C22⋊C4—41no—
79C2×C13×C22⋊C4—41no—
80C2×C13×C22⋊C4—41no—
81C2×C13×C22⋊C4—41no—
82C2×C13×C22⋊C4C2×C414yes—
83C2×C13×C22⋊C4C2×C414yes—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—41no—
89C2×C22⋊Dic13—41no—
90C2×C22⋊Dic13C2×C414yes—
91C2×C22⋊Dic13C2×C414yes—
92C2×C22⋊Dic13C2×C414yes—
93C2×C22⋊Dic13C2×C414yes—
94C2×C22⋊Dic13C2×C414yes—
95C2×C22⋊Dic13C2×C414yes—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—22no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×#6101—41no—
104C2×#6101C2×C414yes—
105C2×#6101C2×C414yes—
106C2×#6101C2×C414yescomplemented
107C2×#6101C2×C414yescomplemented
108C2×C4×Dic13—22no—
109C2×C4×Dic13—22no—
110C2×C4×Dic13—22no—
111C2×C4×Dic13—22no—
112C2×C4×Dic13—22no—
113C2×C4×Dic13—41no—
114C2×C4×Dic13—41no—
115C2×C4×Dic13—41no—
116C2×C4×Dic13—41no—
117C2×C4×Dic13—41no—
118C2×C4×Dic13—41no—
119C2×C4×Dic13—41no—
120C2×C4×Dic13—41no—
121C2×C4×Dic13—41no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13C2×C414yescomplemented
124C2×C4×Dic13C2×C414yescomplemented
125C2×C4×Dic13D414yes—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—41no—
129C13×#95—41no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071C2×C414yes—
139#88071C2×C414yes—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071C2×C414yescomplemented
144#13789—131nomaximal, Sylow
145C24×C13—21no—
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×C13C22×C412yes—
158C24×C13C22×C412yes—
159C24×C13C22×C412yes—
160C24×C13C2411yescharacteristic
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×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—28no—
196C22×C4×C13—44no—
197C22×C4×C13—44no—
198C22×C4×C13—44no—
199C22×C4×C13—44no—
200C22×C4×C13—44no—
201C22×C4×C13—44no—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C22×C412yes—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13#4112yes—
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×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13C22×C412yes—
251C22×Dic13C22×C412yes—
252C22×Dic13C22×C412yes—
253C22×Dic13C22×C412yes—
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C22×C412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13#4112yes—
265C22×Dic13#4112yes—
266C13×C22⋊C4—44no—
267C13×C22⋊C4—44no—
268C22⋊Dic13—28no—
269C22⋊Dic13—28no—
270C22⋊Dic13—44no—
271C22⋊Dic13C42116yescomplemented
272#6101—28no—
273#6101—28no—
274#6101—44no—
275#6101—44no—
276C4×Dic13—28no—
277C4×Dic13—44no—
278C4×Dic13—44no—
279C4×Dic13—44no—
280C4×Dic13—44no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#385—131no—
285C2×C4×C4⋊C4—131no—
286C2×C4×C22⋊C4—131no—
287#1437—131no—
288#1437—131no—
289#1436—131no—
290#1436—131no—
291#1436—131no—
292#1436—131no—
293C4⋊#95—131no—
294#1434—131no—
295C22⋊#95D1311yescharacteristic
296C4×#95—131no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
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—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
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×C13C2×C4214yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C23×C411yescharacteristic
334C23×C13C23×C411yescharacteristic
335C23×C13C22×D411yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C13H(5,𝔽2)11yescharacteristic
342C23×C13H(5,𝔽2)11yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C132−1+411yescharacteristic
345C23×C132−1+411yescharacteristic
346C23×C132−1+411yescharacteristic
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
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—416no—
369C2×C4×C13—41no—
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×C13C4×D414yes—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
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—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
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×Dic13C2×C4214yes—
443C2×Dic13C2×C4214yes—
444C2×Dic13C4×D414yes—
445C2×Dic13C4×D414yes—
446C24×C4C2×D1311yescharacteristic
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C22⋊C4—131no—
452C22×C22⋊C4—131no—
453C22×C22⋊C4—131no—
454C22×C22⋊C4—131no—
455C22×C22⋊C4C2×D1311yescharacteristic
456C22×C22⋊C4C2×D1311yescharacteristic
457C22×C42—131no—
458C22×C42—131no—
459C22×C42—131no—
460C22×C42—131no—
461C22×C42—131no—
462C22×C42—131no—
463#388—138no—
464#388—138no—
465#385—138no—
466C4×C4⋊C4—264no—
467C4×C22⋊C4—264no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
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×#95C2×D1311yescharacteristic
483C2×#95C2×D1311yescharacteristic
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C22×C4211yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C2×C4×D411yescharacteristic
504C22×C13C2×C4×D411yescharacteristic
505C22×C13C4×#4111yescharacteristic
506C22×C13C4×#4111yescharacteristic
507C22×C13C4×#4111yescharacteristic
508C22×C13#51811yescharacteristic
509C22×C13#51811yescharacteristic
510C22×C13#51811yescharacteristic
511C22×C13#51811yescharacteristic
512C22×C13#51911yescharacteristic
513C22×C13#52011yescharacteristic
514C22×C13#52011yescharacteristic
515C22×C13#52011yescharacteristic
516C22×C13#52011yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#52011yescharacteristic
519C22×C13#52011yescharacteristic
520C22×C13#53411yescharacteristic
521C22×C13#53511yescharacteristic
522C22×C13#53611yescharacteristic
523C22×C13#53711yescharacteristic
524C22×C13#53811yescharacteristic
525C22×C13#53811yescharacteristic
526C22×C13#53811yescharacteristic
527C22×C13#53911yescharacteristic
528C22×C13#53911yescharacteristic
529C22×C13#53911yescharacteristic
530C22×C13#54011yescharacteristic
531C22×C13#54111yescharacteristic
532C22×C13#54211yescharacteristic
533C22×C13#54211yescharacteristic
534C22×C13#54211yescharacteristic
535C22×C13#54211yescharacteristic
536C4×C13—24no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542Dic13—24no—
543Dic13—24no—
544Dic13—24no—
545Dic13—24no—
546Dic13—42no—
547Dic13—42no—
548Dic13—42no—
549Dic13—42no—
550C25C22×D1311yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—41no—
554C23×C4—41no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—131no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4C4×D1314yes—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—134no—
573C2×C4⋊C4—134no—
574C2×C4⋊C4—134no—
575C2×C4⋊C4—134no—
576C2×C4⋊C4—262no—
577C2×C4⋊C4—262no—
578C2×C4⋊C4—262no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—521no—
581C2×C4⋊C4—521no—
582C2×C4⋊C4—521no—
583C2×C4⋊C4—521no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—134no—
589C2×C22⋊C4—134no—
590C2×C22⋊C4—134no—
591C2×C22⋊C4—134no—
592C2×C22⋊C4—134no—
593C2×C22⋊C4—134no—
594C2×C22⋊C4—262no—
595C2×C22⋊C4—262no—
596C2×C22⋊C4—262no—
597C2×C22⋊C4—262no—
598C2×C22⋊C4—521no—
599C2×C22⋊C4—521no—
600C2×C22⋊C4C4×D1314yes—
601C2×C22⋊C4C4×D1314yes—
602C2×C42—134no—
603C2×C42—134no—
604C2×C42—134no—
605C2×C42—262no—
606C2×C42—262no—
607C2×C42—262no—
608C2×C42—262no—
609C2×C42—262no—
610C2×C42—521no—
611C2×C42—521no—
612C2×C42—521no—
613C2×C42—521no—
614C2×C42—521no—
615C2×C42—521no—
616C2×C42—521no—
617C2×C42—521no—
618C2×C42—521no—
619C2×C42—521no—
620#95—22no—
621#95—22no—
622#95—41no—
623#95—41no—
624#95—134no—
625#95—134no—
626#95—134no—
627#95—134no—
628#95—134no—
629#95—134no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95—521no—
638C2×C13—44no—
639C2×C13C42×D411yescharacteristic
640C2×C13#227411yescharacteristic
641C2×C13#227511yescharacteristic
642C2×C13#232111yescharacteristic
643C2×C13#232211yescharacteristic
644C2×C13#232311yescharacteristic
645C2×C13#232411yescharacteristic
646C2×C13#232511yescharacteristic
647C2×C13#232611yescharacteristic
648C2×C13#233211yescharacteristic
649C2×C13#233411yescharacteristic
650C2×C13#233411yescharacteristic
651C2×C13#233511yescharacteristic
652C2×C13#233511yescharacteristic
653C2×C13#233711yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×C4×D1312yes—
667C24C2×C4×D1312yes—
668C24C2×C4×D1312yes—
669C24C23×D1311yescharacteristic
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
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—28no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—132no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
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—261no—
728C22×C4—261no—
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×C4C2×C4×D1312yes—
768C22×C4C2×C4×D1312yes—
769C22×C4C2×C4×D1312yes—
770C22×C4C2×C4×D1312yes—
771C22×C4C2×C4×D1312yes—
772C22×C4C2×C4×D1312yes—
773C22×C4D4×D1312yes—
774C22×C4#612912yes—
775C4⋊C4—268no—
776C4⋊C4—268no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C22⋊C4—1316no—
782C22⋊C4—268no—
783C22⋊C4—268no—
784C22⋊C4—524no—
785C42—268no—
786C42—524no—
787C42—524no—
788C42—524no—
789C42—524no—
790C42—524no—
791C13#1378911yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C42×D1314yes—
827C23C22×C4×D1311yescharacteristic
828C23C22×C4×D1311yescharacteristic
829C23C22×C4×D1311yescharacteristic
830C23C2×D4×D1311yescharacteristic
831C23C2×#612911yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23#8825111yescharacteristic
835C23#8825111yescharacteristic
836C23#8825111yescharacteristic
837C23#8825411yescharacteristic
838C23#41×D1311yescharacteristic
839C23#41×D1311yescharacteristic
840C23#8825711yescharacteristic
841C23#8825711yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
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—416no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
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—134no—
885C2×C4—134no—
886C2×C4—134no—
887C2×C4—134no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
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—262no—
919C2×C4—262no—
920C2×C4—262no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
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#8813514yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C42×D1311yescharacteristic
957C22C2×#8813511yescharacteristic
958C22#1171919111yescharacteristic
959C22#1171919111yescharacteristic
960C22#1171919111yescharacteristic
961C22#1171919111yescharacteristic
962C22#1171920911yescharacteristic
963C22#1171920911yescharacteristic
964C22#1171920911yescharacteristic
965C22#1171922111yescharacteristic
966C22#1171922711yescharacteristic
967C22C4×#612911yescharacteristic
968C22C4×#612911yescharacteristic
969C22C4×D4×D1311yescharacteristic
970C22C4×D4×D1311yescharacteristic
971C22#1171925111yescharacteristic
972C22#1171925111yescharacteristic
973C22#1171925111yescharacteristic
974C22#1171925111yescharacteristic
975C22#1171929411yescharacteristic
976C22#1171929711yescharacteristic
977C22#1171929811yescharacteristic
978C22#1171929811yescharacteristic
979C22#1171930811yescharacteristic
980C22#1171931311yescharacteristic
981C22#1171931811yescharacteristic
982C22#1171932011yescharacteristic
983C22#1171933011yescharacteristic
984C22#1171933311yescharacteristic
985C22#1171934311yescharacteristic
986C22#1171934511yescharacteristic
987C22#1171936511yescharacteristic
988C22#1171936511yescharacteristic
989C22#1171936711yescharacteristic
990C22#1171936711yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—264no—
998C4—264no—
999C4—264no—
1000C4—264no—
1001C4—522no—
1002C4—522no—
1003C4—522no—
1004C4—522no—
1005C2—44no—
1006C2C4×#8813511yescharacteristic
1007C2#1311719111yescharacteristic
1008C2#1311719411yescharacteristic
1009C2#1311749111yescharacteristic
1010C2#1311750311yescharacteristic
1011C2#1311751411yescharacteristic
1012C2#1311752611yescharacteristic
1013C2#1311753811yescharacteristic
1014C2#1311754211yescharacteristic
1015C2#1311758911yescharacteristic
1016C2#1311760611yescharacteristic
1017C2#1311761211yescharacteristic
1018C2#1311762211yescharacteristic
1019C2#1311762711yescharacteristic
1020C2#1311764511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×C22⋊#95C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC22⋊#95D13
hypocenterC13#13789
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#11718310C2semidirect
8. #13113071C2semidirect
9. #13113067C2semidirect
10. #13113067C2semidirect
11. #13113067C2semidirect
12. #13113064C2semidirect
13. #13113062C2semidirect
14. #95×Dic13C2semidirect
37. #11718871C4semidirect
53. #11718606C4semidirect
54. #11718605C4semidirect
106. C2×#6101C2×C4semidirect
107. C2×#6101C2×C4semidirect
123. C2×C4×Dic13C2×C4semidirect
124. C2×C4×Dic13C2×C4semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
143. #88071C2×C4semidirect
271. C22⋊Dic13C42semidirect
791. C13#13789semidirect

Maximal subgroups

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

subgroupindex
C2×#117186062
C2×#117186052
C2×#117188712
C2×#117183102
C2×C4×C22⋊Dic132
#131130732
#131130712
#131130672
#131130642
#131130622
#95×Dic132
C13×C22⋊#952
#1378913