Finite Group Databasebeta

← #15784343

Subgroups — #15784343

Order 3328.

2182 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88146C211yesmaximal, characteristic
2C2×#11718648C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic
6#13113072C212yesmaximal
7#13113072C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113062C212yesmaximal, complemented
10#95×Dic13C212yesmaximal, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×#88146—24no—
27C2×#88146—24no—
28C2×#88146C418yescomplemented
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38#11718648C418yescomplemented
39C4⋊C4×Dic13—24no—
40C4×#6103C418yescomplemented
41C4×C4⋊Dic13—24no—
42C24×D13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13C2×C414yes—
58C22×C4×D13C2×C414yes—
59C22×C4×D13C2×C414yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4C2×C414yes—
65C2×C13×C4⋊C4C2×C414yes—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13C2×C414yes—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—42no—
76C2×#6103—42no—
77C2×#6103C2×C418yes—
78C2×#6103C2×C414yes—
79C2×#6103C2×C414yes—
80C2×#6103C2×C418yes—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13C2×C414yes—
84C2×C4⋊Dic13C2×C414yes—
85C2×C4⋊Dic13D414yes—
86C2×C4⋊Dic13D414yes—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—24no—
90C2×C4×Dic13—24no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—42no—
96C2×C4×Dic13—42no—
97C2×C4×Dic13C2×C418yes—
98C2×C4×Dic13C2×C414yes—
99#88146—232no—
100C13×#95—24no—
101C13×#95—42no—
102#88071—24no—
103#88071—24no—
104#88071—24no—
105#88071—42no—
106#88071C2×C414yes—
107#88071C2×C414yes—
108#88071C2×C418yes—
109#13801—131nomaximal, Sylow
110C24×C13C2411yescharacteristic
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13C22×C412yes—
124C23×D13C22×C412yes—
125C23×D13C22×C412yes—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—21no—
147C22×C4×C13—22no—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C22×C414yes—
150C22×C4×C13C22×C414yes—
151C22×C4×C13C22×C412yes—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13C22×C412yes—
186C22×Dic13C22×C414yes—
187C22×Dic13C22×C412yes—
188C22×Dic13C22×C412yes—
189C22×Dic13C22×C412yes—
190C22×Dic13C22×C414yes—
191C22×Dic13C22×C412yes—
192C22×Dic13C2×D414yes—
193C22×Dic13C2×D414yes—
194C22×Dic13#4112yes—
195C22×Dic13#4112yes—
196C2×C4×D13—28no—
197C2×C4×D13—28no—
198C2×C4×D13—28no—
199C2×C4×D13—28no—
200C2×C4×D13—28no—
201C2×C4×D13—28no—
202C2×C4×D13C42116yescomplemented
203C13×C4⋊C4—28no—
204C13×C4⋊C4—28no—
205C42×C13—28no—
206#6103—28no—
207#6103—216no—
208#6103—28no—
209#6103—48no—
210C4⋊Dic13—28no—
211C4⋊Dic13C22⋊C4116yescomplemented
212C4×Dic13—28no—
213C4×Dic13—216no—
214C4×Dic13—48no—
215C4×Dic13—48no—
216C22×#117—131no—
217C2×#380—131no—
218C2×C4×C4⋊C4—131no—
219C2×C4×C4⋊C4—131no—
220C2×C4×C22⋊C4—131no—
221#1437—132no—
222#1437—132no—
223C4⋊#95—131no—
224C4⋊#95D1311yescharacteristic, complemented
225#1434—132no—
226C4×#95—132no—
227C23×C13C23×C411yescharacteristic
228C23×C13C23×C411yescharacteristic
229C23×C13C23×C411yescharacteristic
230C23×C13C22×D411yescharacteristic
231C23×C13C22×D411yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C132−1+411yescharacteristic
241C23×C132−1+411yescharacteristic
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—41no—
261C22×D13—41no—
262C22×D13—41no—
263C22×D13—41no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13—41no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13C2×C4214yes—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—24no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—42no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—41no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—41no—
304C2×C4×C13C2×C4214yes—
305C2×C4×C13C2×C22⋊C414yes—
306C2×C4×C13#11714yes—
307C2×C4×C13#11714yescomplemented
308C2×C4×C13C4×D414yes—
309C2×C4×C13C4×D414yes—
310C2×C4×C13C4×D414yes—
311C2×C4×C13C4×D414yes—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—24no—
324C2×Dic13—24no—
325C2×Dic13—24no—
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—24no—
335C2×Dic13—22no—
336C2×Dic13—42no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—41no—
342C2×Dic13—42no—
343C2×Dic13—41no—
344C2×Dic13C2×C4214yes—
345C2×Dic13C2×C22⋊C418yes—
346C2×Dic13#11714yescomplemented
347C4×D13—232no—
348C24×C4—131no—
349C2×#117—138no—
350C2×#117—264no—
351C2×#117—264no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4C2×D1311yescharacteristic
355C22×C4⋊C4C2×D1311yescharacteristic
356C22×C22⋊C4—132no—
357C22×C22⋊C4—131no—
358C22×C22⋊C4—131no—
359C22×C22⋊C4—132no—
360C22×C42—132no—
361C22×C42—131no—
362C22×C42—132no—
363C22×C42—132no—
364C22×C42C2×D1311yescharacteristic
365#380—138no—
366C4×C4⋊C4—264no—
367C4×C4⋊C4—264no—
368C4×C22⋊C4—138no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95—131no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—132no—
375C2×#95—132no—
376C2×#95C2×D1312yes—
377C2×#95C2×D1312yes—
378C22×C13C22×C4211yescharacteristic
379C22×C13C22×C22⋊C411yescharacteristic
380C22×C13C2×#11711yescharacteristic
381C22×C13C2×#11711yescharacteristic
382C22×C13C2×#11711yescharacteristic
383C22×C13C2×C4×D411yescharacteristic
384C22×C13C2×C4×D411yescharacteristic
385C22×C13C2×C4×D411yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13C4×#4111yescharacteristic
388C22×C13C4×#4111yescharacteristic
389C22×C13C4×#4111yescharacteristic
390C22×C13C4×#4111yescharacteristic
391C22×C13#51811yescharacteristic
392C22×C13#51911yescharacteristic
393C22×C13#52011yescharacteristic
394C22×C13#52011yescharacteristic
395C22×C13#52011yescharacteristic
396C22×C13#52011yescharacteristic
397C22×C13#54611yescharacteristic
398C22×C13#54611yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#54711yescharacteristic
401C22×C13#54811yescharacteristic
402C22×C13#54811yescharacteristic
403C22×C13#55011yescharacteristic
404C22×C13#55011yescharacteristic
405C22×C13#55211yescharacteristic
406C22×C13#55211yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55511yescharacteristic
410C22×C13#55511yescharacteristic
411C22×C13#55611yescharacteristic
412C22×C13#55611yescharacteristic
413C2×D13—24no—
414C2×D13—24no—
415C2×D13—24no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C4×C13—24no—
429C4×C13—44no—
430C4×C13—42no—
431C4×C13—44no—
432C4×C13C4×C22⋊C418yes—
433Dic13—28no—
434Dic13—24no—
435Dic13—24no—
436Dic13—42no—
437Dic13—44no—
438C25—131no—
439C23×C4—132no—
440C23×C4—131no—
441C23×C4—131no—
442C23×C4—134no—
443C23×C4—134no—
444C23×C4—134no—
445C23×C4—132no—
446C23×C4—131no—
447C23×C4—262no—
448C23×C4—262no—
449C23×C4—262no—
450C23×C4—262no—
451C23×C4C22×D1312yes—
452C23×C4C22×D1312yes—
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456#117—2632no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4C4×D1314yes—
468C2×C4⋊C4C4×D1314yes—
469C2×C22⋊C4—138no—
470C2×C22⋊C4—134no—
471C2×C22⋊C4—134no—
472C2×C22⋊C4—138no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—262no—
476C2×C22⋊C4—262no—
477C2×C22⋊C4—262no—
478C2×C22⋊C4—262no—
479C2×C22⋊C4—522no—
480C2×C22⋊C4—522no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—138no—
484C2×C42—134no—
485C2×C42—264no—
486C2×C42—264no—
487C2×C42—262no—
488C2×C42—262no—
489C2×C42—264no—
490C2×C42—264no—
491C2×C42—264no—
492C2×C42—264no—
493C2×C42—522no—
494C2×C42—522no—
495C2×C42C4×D1314yes—
496#95—24no—
497#95—42no—
498#95—134no—
499#95—134no—
500#95—138no—
501#95—264no—
502#95—264no—
503#95—264no—
504#95—522no—
505C2×C13C2×C4×C22⋊C411yescharacteristic
506C2×C13C4×#11711yescharacteristic
507C2×C13#227411yescharacteristic
508C2×C13#233911yescharacteristic
509C2×C13#234111yescharacteristic
510C2×C13#234611yescharacteristic
511C2×C13#234711yescharacteristic
512C2×C13#235211yescharacteristic
513C2×C13#235211yescharacteristic
514C2×C13#235411yescharacteristic
515C2×C13#235411yescharacteristic
516C2×C13#236211yescharacteristic
517C2×C13#236211yescharacteristic
518C2×C13#236311yescharacteristic
519C2×C13#236311yescharacteristic
520D13—44no—
521C24—132no—
522C24—132no—
523C24—132no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24C23×D1311yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—134no—
564C22×C4—134no—
565C22×C4—134no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—1316no—
569C22×C4—132no—
570C22×C4—134no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—262no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—262no—
582C22×C4—261no—
583C22×C4—268no—
584C22×C4—268no—
585C22×C4—268no—
586C22×C4—268no—
587C22×C4—268no—
588C22×C4—268no—
589C22×C4—261no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—262no—
594C22×C4—261no—
595C22×C4—262no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—261no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4C2×C4×D1312yes—
602C22×C4C2×C4×D1314yes—
603C22×C4C2×C4×D1314yes—
604C22×C4C2×C4×D1312yes—
605C22×C4C2×C4×D1312yes—
606C22×C4C2×C4×D1312yes—
607C22×C4C2×C4×D1312yes—
608C22×C4D4×D1312yes—
609C22×C4D4×D1312yes—
610C22×C4#612912yes—
611C22×C4#612912yes—
612C22×C4#613112yes—
613C22×C4#613112yes—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—1316no—
617C4⋊C4—268no—
618C22⋊C4—2616no—
619C22⋊C4—268no—
620C22⋊C4—268no—
621C22⋊C4—528no—
622C42—28no—
623C42—2616no—
624C42—268no—
625C42—528no—
626C42—528no—
627C13#1380111yescharacteristic, complemented, Sylow
628C23—134no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—262no—
644C23—262no—
645C23—262no—
646C23—262no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—521no—
663C23C22×C4×D1311yescharacteristic
664C23C22×C4×D1311yescharacteristic
665C23C22×C4×D1311yescharacteristic
666C23C2×D4×D1311yescharacteristic
667C23C2×D4×D1311yescharacteristic
668C23C2×#612911yescharacteristic
669C23C2×#612911yescharacteristic
670C23#8825111yescharacteristic
671C23C2×#613111yescharacteristic
672C23C2×#613111yescharacteristic
673C23#8825411yescharacteristic
674C23#41×D1311yescharacteristic
675C23#41×D1311yescharacteristic
676C23#8825611yescharacteristic
677C23#8825711yescharacteristic
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—134no—
706C2×C4—138no—
707C2×C4—134no—
708C2×C4—264no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—264no—
718C2×C4—264no—
719C2×C4—264no—
720C2×C4—264no—
721C2×C4—262no—
722C2×C4—264no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—2632no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—264no—
730C2×C4—262no—
731C2×C4—264no—
732C2×C4—264no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—521no—
741C2×C4C42×D1314yes—
742C2×C4C22⋊C4×D1314yes—
743C2×C4#8813514yes—
744C2×C4#8813514yes—
745C2×C4#8814614yes—
746C2×C4#8814614yescomplemented
747C2×C4#8814714yes—
748C2×C4#8814714yes—
749C22—264no—
750C22—264no—
751C22—264no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22C2×C42×D1311yescharacteristic
765C22C2×C22⋊C4×D1311yescharacteristic
766C22C2×#8813511yescharacteristic
767C22C2×#8813511yescharacteristic
768C22C2×#8814611yescharacteristic
769C22C2×#8814611yescharacteristic
770C22C2×#8814711yescharacteristic
771C22C2×#8814711yescharacteristic
772C22#1171920911yescharacteristic
773C22D13×#11711yescharacteristic
774C22#1171922811yescharacteristic
775C22C4×#612911yescharacteristic
776C22C4×#612911yescharacteristic
777C22#1171925011yescharacteristic
778C22#1171925111yescharacteristic
779C22#1171927711yescharacteristic
780C22C4×#613111yescharacteristic
781C22C4×#613111yescharacteristic
782C22#1171927911yescharacteristic
783C22#1171930311yescharacteristic
784C22#1171930411yescharacteristic
785C22#1171932111yescharacteristic
786C22#1171932311yescharacteristic
787C22#1171933511yescharacteristic
788C22#1171933611yescharacteristic
789C22#1171934611yescharacteristic
790C22#1171934711yescharacteristic
791C22#1171938111yescharacteristic
792C22#1171938211yescharacteristic
793C22#1171939911yescharacteristic
794C22#1171940011yescharacteristic
795C22#1171942311yescharacteristic
796C22#1171943111yescharacteristic
797C22#1171943711yescharacteristic
798C22#1171943911yescharacteristic
799C4—24no—
800C4—42no—
801C4—44no—
802C4—44no—
803C4—264no—
804C4—268no—
805C4—264no—
806C4—522no—
807C4—524no—
808C4#1171832718yes—
809C2—524no—
810C2C2×#1171832711yescharacteristic
811C2C4×#8814611yescharacteristic
812C2#1311719011yescharacteristic
813C2#1311766511yescharacteristic
814C2#1311767511yescharacteristic
815C2#1311772011yescharacteristic
816C2#1311772811yescharacteristic
817C2#1311776211yescharacteristic
818C2#1311776711yescharacteristic
819C2#1311778011yescharacteristic
820C2#1311778711yescharacteristic
821C2#1311786211yescharacteristic
822C2#1311786811yescharacteristic
823C2#1311787311yescharacteristic
824C2#1311787911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13801
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic13C2semidirect
4. C2×C4×C4⋊Dic13C2semidirect
8. #13113065C2semidirect
9. #13113062C2semidirect
10. #95×Dic13C2semidirect
11. C13×C4⋊#95C2semidirect
28. C2×#88146C4semidirect
38. #11718648C4semidirect
40. C4×#6103C4semidirect
202. C2×C4×D13C42semidirect
211. C4⋊Dic13C22⋊C4semidirect
224. C4⋊#95D13semidirect
307. C2×C4×C13#117semidirect
346. C2×Dic13#117semidirect
627. C13#13801semidirect
746. C2×C4#88146semidirect

Maximal subgroups

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

subgroupindex
C22×#881462
C2×#117186482
C2×C4⋊C4×Dic132
C2×C4×C4⋊Dic132
C2×C4×#61032
#131130722
#131130652
#131130622
#95×Dic132
C13×C4⋊#952
#1380113