Finite Group Databasebeta

← #15785753

Subgroups — #15785753

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718634C211yesmaximal, characteristic, complemented
2C2×#11718873C211yesmaximal, characteristic
3C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113091C212yesmaximal, complemented
6#13113079C212yesmaximal
7#13113073C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113060C212yesmaximal, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2211yescharacteristic
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C13×#380—24no—
26C2×C13×#95C2212yes—
27#11718873C418yescomplemented
28C4×C22⋊Dic13—24no—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C4⋊C4×Dic13—24no—
39#11718634—24no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13C2×C414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2312yes—
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4D414yes—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—42no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—42no—
74C2×C22⋊Dic13C2×C418yes—
75C2×C22⋊Dic13Q814yes—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13C2×C414yes—
81C2×C4⋊Dic13C2×C414yes—
82C2×#6101—24no—
83C2×#6101—42no—
84C2×#6101—42no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—24no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—42no—
93C2×C4×Dic13D414yes—
94C13×#95—24no—
95#88071—24no—
96#88071—22no—
97#88071—22no—
98#88071—24no—
99#88071—24no—
100#88071—42no—
101#88071—42no—
102#88071—42no—
103#88071C2×C418yes—
104#13973—131nomaximal, Sylow
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13C22×C412yes—
118C24×C13C2×Q812yes—
119C24×C13#4112yes—
120C24×C13C2411yescharacteristic
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
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—28no—
134C22×C4×C13—28no—
135C22×C4×C13—28no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—44no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13—44no—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D414yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—21no—
190C22×Dic13C22×C414yes—
191C22×Dic13C22×C414yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×D412yes—
194C22×Dic13C2×Q812yes—
195C22×Dic13C2×Q812yes—
196C22×Dic13#4112yes—
197C22×Dic13#4112yes—
198C13×C4⋊C4—28no—
199C13×C4⋊C4—44no—
200C13×C22⋊C4—48no—
201C22⋊Dic13—28no—
202C22⋊Dic13—28no—
203C22⋊Dic13—48no—
204C4⋊Dic13—28no—
205C4⋊Dic13—28no—
206#6101—48no—
207C4×Dic13—28no—
208C4×Dic13—48no—
209C4×Dic13—44no—
210C2×#389—131no—
211C2×#380—131no—
212C2×#380D1311yescharacteristic
213C2×C4×C4⋊C4—131no—
214C2×C4×C22⋊C4—131no—
215#1442—132no—
216#1439—132no—
217#1437—132no—
218C4⋊#95—131no—
219C4⋊#95—131no—
220#1434—132no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13C4×Q814yes—
256C23×C13C23×C411yescharacteristic
257C23×C13C22×D411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×Q811yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13H(5,𝔽2)11yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C13H(5,𝔽2)11yescharacteristic
270C23×C132−1+411yescharacteristic
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—24no—
275C2×C4×C13—24no—
276C2×C4×C13—24no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—416no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13#11714yes—
294C2×C4×C13C4×D414yes—
295C2×C4×C13C4×D414yes—
296C2×C4×C13#12114yes—
297C2×C4×C13#12314yes—
298C2×C4×C13#12414yes—
299C2×C4×C13#12614yes—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—24no—
307C2×Dic13—24no—
308C2×Dic13—24no—
309C2×Dic13—24no—
310C2×Dic13—24no—
311C2×Dic13—24no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—42no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—41no—
331C2×Dic13—42no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—42no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—41no—
341C2×Dic13C22⋊Q814yes—
342C24×C4C2×D1311yescharacteristic
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—132no—
346C22×C4⋊C4C2×D1311yescharacteristic
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4—131no—
349C22×C22⋊C4—132no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4C2×D1312yes—
352C22×C42—131no—
353C22×C42—131no—
354C22×C42—132no—
355#389—264no—
356#380—24no—
357#380—138no—
358C4×C4⋊C4—264no—
359C4×C22⋊C4—264no—
360C2×#95—132no—
361C2×#95—131no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—131no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95C2×D1312yes—
370C22×C13—24no—
371C22×C13—24no—
372C22×C13—24no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13C2×#11711yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13C2×C4×D411yescharacteristic
388C22×C13C2×C4×Q811yescharacteristic
389C22×C13C4×#4111yescharacteristic
390C22×C13#51811yescharacteristic
391C22×C13#52011yescharacteristic
392C22×C13C2×#12111yescharacteristic
393C22×C13C2×C22⋊Q811yescharacteristic
394C22×C13C2×#12311yescharacteristic
395C22×C13#52511yescharacteristic
396C22×C13C2×#12411yescharacteristic
397C22×C13C2×#12611yescharacteristic
398C22×C13#52911yescharacteristic
399C22×C13#53311yescharacteristic
400C22×C13#53511yescharacteristic
401C22×C13#53711yescharacteristic
402C22×C13#54011yescharacteristic
403C22×C13#54211yescharacteristic
404C22×C13#54611yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13D4×Q811yescharacteristic
407C22×C13#55011yescharacteristic
408C22×C13#55211yescharacteristic
409C22×C13#55211yescharacteristic
410C22×C13#55211yescharacteristic
411C22×C13#55311yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55311yescharacteristic
414C22×C13#55411yescharacteristic
415C22×C13#55411yescharacteristic
416C22×C13#55411yescharacteristic
417C22×C13#55511yescharacteristic
418C22×C13#55511yescharacteristic
419C22×C13#55511yescharacteristic
420C4×C13—44no—
421C4×C13—42no—
422C4×C13—82no—
423C4×C13#38818yes—
424Dic13—24no—
425Dic13—42no—
426Dic13—42no—
427Dic13—44no—
428Dic13—44no—
429Dic13—42no—
430C25C22×D1311yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—131no—
438C23×C4—132no—
439C23×C4—131no—
440C23×C4—132no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4C4×D1314yes—
444C23×C4C22×D1312yes—
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1312yes—
447C23×C4C22×D1311yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—134no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—522no—
461C2×C4⋊C4—522no—
462C2×C4⋊C4C22⋊D1314yes—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—138no—
468C2×C22⋊C4—262no—
469C2×C22⋊C4—262no—
470C2×C22⋊C4—262no—
471C2×C22⋊C4—262no—
472C2×C22⋊C4—262no—
473C2×C22⋊C4—522no—
474C2×C22⋊C4—522no—
475C2×C42—134no—
476C2×C42—262no—
477C2×C42—262no—
478C2×C42—264no—
479C2×C42—262no—
480C2×C42—262no—
481C2×C42—262no—
482C2×C42—264no—
483C2×C42—522no—
484#95—24no—
485#95—138no—
486#95—264no—
487#95—262no—
488#95—262no—
489#95—264no—
490#95—264no—
491#95—522no—
492#95—522no—
493#95—522no—
494C2×C13—44no—
495C2×C13C2×#38811yescharacteristic
496C2×C13C4×C22⋊Q811yescharacteristic
497C2×C13#232411yescharacteristic
498C2×C13#234511yescharacteristic
499C2×C13#234611yescharacteristic
500C2×C13#236011yescharacteristic
501C2×C13#236311yescharacteristic
502C2×C13#241411yescharacteristic
503C2×C13#241711yescharacteristic
504C2×C13#242011yescharacteristic
505C2×C13#242311yescharacteristic
506C2×C13#249511yescharacteristic
507C2×C13#249711yescharacteristic
508C2×C13#256211yescharacteristic
509C2×C13#256311yescharacteristic
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24C2×C4×D1312yes—
523C24#612912yes—
524C24Q8×D1312yes—
525C24C23×D1311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—134no—
556C22×C4—134no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—262no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—262no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—262no—
576C22×C4—261no—
577C22×C4—262no—
578C22×C4—261no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—262no—
594C22×C4C2×C4×D1312yes—
595C22×C4C2×C4×D1312yes—
596C22×C4#612712yes—
597C22×C4D4×D1312yes—
598C22×C4#612912yes—
599C22×C4#612912yes—
600C22×C4#612912yes—
601C22×C4C2×C22⋊D1314yes—
602C22×C4C2×C22⋊D1312yes—
603C4⋊C4—28no—
604C4⋊C4—44no—
605C4⋊C4—268no—
606C4⋊C4—268no—
607C4⋊C4—528no—
608C22⋊C4—48no—
609C22⋊C4—268no—
610C22⋊C4—268no—
611C22⋊C4—528no—
612C42—268no—
613C42—528no—
614C42—524no—
615C13#1397311yescharacteristic, complemented, Sylow
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23#8814114yes—
651C23C22×C4×D1311yescharacteristic
652C23C2×#612711yescharacteristic
653C23C2×D4×D1311yescharacteristic
654C23C2×#612911yescharacteristic
655C23C2×#612911yescharacteristic
656C23C2×#612911yescharacteristic
657C23C2×#612911yescharacteristic
658C23#8825111yescharacteristic
659C23C2×Q8×D1311yescharacteristic
660C23#8825411yescharacteristic
661C23#41×D1311yescharacteristic
662C23#41×D1311yescharacteristic
663C23#8825611yescharacteristic
664C23#8825611yescharacteristic
665C23C22×C22⋊D1311yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—416no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—134no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—264no—
696C2×C4—264no—
697C2×C4—262no—
698C2×C4—264no—
699C2×C4—264no—
700C2×C4—264no—
701C2×C4—262no—
702C2×C4—264no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—521no—
711C2×C4—521no—
712C2×C4—521no—
713C2×C4—522no—
714C2×C4—521no—
715C2×C4—522no—
716C2×C4—521no—
717C2×C4—522no—
718C2×C4—521no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—521no—
729C2×C4—522no—
730C2×C4#8813114yes—
731C2×C4#8813314yes—
732C2×C4#8813514yes—
733C2×C4#8813914yes—
734C2×C4C4×C22⋊D1314yes—
735C2×C4#8818914yes—
736C2×C4#8819214yes—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22C2×#8813111yescharacteristic
753C22C2×#8813311yescharacteristic
754C22C2×#8813511yescharacteristic
755C22C2×#8813911yescharacteristic
756C22C2×#8814111yescharacteristic
757C22#1171920911yescharacteristic
758C22#1171921611yescharacteristic
759C22#1171921811yescharacteristic
760C22#1171922611yescharacteristic
761C22#1171922711yescharacteristic
762C22#1171923511yescharacteristic
763C22#1171923711yescharacteristic
764C22#1171930511yescharacteristic
765C22#1171931111yescharacteristic
766C22#1171931211yescharacteristic
767C22#1171932111yescharacteristic
768C22#1171932111yescharacteristic
769C22#1171932311yescharacteristic
770C22#1171932311yescharacteristic
771C22#1171932411yescharacteristic
772C22#1171932711yescharacteristic
773C22D13×C22⋊Q811yescharacteristic
774C22#1171933411yescharacteristic
775C22#1171934011yescharacteristic
776C22#1171934011yescharacteristic
777C22#1171934411yescharacteristic
778C22#1171934411yescharacteristic
779C22#1171934811yescharacteristic
780C22C2×C4×C22⋊D1311yescharacteristic
781C22C2×#8818911yescharacteristic
782C22C2×#8819211yescharacteristic
783C22#1171951111yescharacteristic
784C22Q8×C22⋊D1311yescharacteristic
785C22#1171953411yescharacteristic
786C22#1171953911yescharacteristic
787C4—42no—
788C4—44no—
789C4—82no—
790C4—264no—
791C4—522no—
792C4—522no—
793C4—524no—
794C4—524no—
795C4—522no—
796C4#1171860518yes—
797C2—44no—
798C2C2×#1171860511yescharacteristic
799C2#1311736411yescharacteristic
800C2#1311752511yescharacteristic
801C2#1311771511yescharacteristic
802C2#1311772311yescharacteristic
803C2#1311784111yescharacteristic
804C2#1311787411yescharacteristic
805C2#1311825011yescharacteristic
806C2#1311828311yescharacteristic
807C2#1311832411yescharacteristic
808C2#1311835711yescharacteristic
809C2#1311924911yescharacteristic
810C2#1311927111yescharacteristic
811C2#1311999911yescharacteristic
812C2#1312000611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13973
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11718634C2semidirect
3. C2×C4⋊C4×Dic13C2semidirect
5. #13113091C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113060C2semidirect
27. #11718873C4semidirect
615. C13#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130912
#131130792
#131130732
#131130652
#131130602
C2×C13×#3802
#1397313