Finite Group Databasebeta

← #15786020

Subgroups — #15786020

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718589C211yesmaximal, characteristic, complemented
2C2×#11718605C212yesmaximal
3C2×#11718873C211yesmaximal, characteristic
4C2×#11718873C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6#13113091C212yesmaximal, complemented
7#13113083C212yesmaximal
8#13113066C211yesmaximal, characteristic, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113060C212yesmaximal, complemented
11C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C22⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2212yes—
25C4×C13×C22⋊C4—24no—
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28#11718873—24no—
29#11718873C418yescomplemented
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718605—28no—
39C4×C4⋊Dic13—24no—
40#11718589—24no—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13C2×C414yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×Dic13C2312yes—
56C23×Dic13C2312yes—
57C23×Dic13C2312yes—
58C23×Dic13C2312yes—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4D414yes—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×C42×C13D414yes—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—42no—
76C2×C22⋊Dic13C2×C418yes—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13C2×C414yes—
87C2×C4⋊Dic13C2×C414yes—
88C2×C4⋊Dic13D414yes—
89C2×#6101—24no—
90C2×#6101—24no—
91C2×#6101—42no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C13×#95—22no—
96C13×#95—22no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—42no—
104#88071C2×C418yes—
105#13994—131nomaximal, Sylow
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×C13—21no—
118C24×C13C22×C412yes—
119C24×C13C2×D412yes—
120C24×C13#4112yes—
121C24×C13C2411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—28no—
151C22×C4×C13—28no—
152C22×C4×C13—28no—
153C22×C4×C13—44no—
154C22×C4×C13—44no—
155C22×C4×C13—44no—
156C22×C4×C13—44no—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C22×C412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×D412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×C4×C13#4112yes—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13C22×C414yes—
197C22×Dic13C22×C414yes—
198C22×Dic13C2×D414yes—
199C13×C22⋊C4—28no—
200C13×C22⋊C4—28no—
201C42×C13—28no—
202C42×C13—44no—
203C22⋊Dic13—216no—
204C22⋊Dic13—48no—
205C4⋊Dic13—28no—
206C4⋊Dic13—28no—
207C4⋊Dic13—28no—
208C4⋊Dic13—44no—
209#6101—48no—
210C4×Dic13—48no—
211C2×#389—131no—
212C2×#388—132no—
213C2×#380—131no—
214C2×#380—131no—
215C2×C4×C4⋊C4—131no—
216C2×C4×C22⋊C4D1311yescharacteristic
217#1442—132no—
218#1440—132no—
219C4⋊#95—131no—
220C4⋊#95—131no—
221#1434—132no—
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—22no—
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×C13—41no—
256C23×C13C4×D414yes—
257C23×C13C23×C411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×D411yescharacteristic
260C23×C13C22×D411yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C132−1+411yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
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—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—416no—
307C2×C4×C13#11714yes—
308C2×C4×C13C4×D414yes—
309C2×C4×C13C4×D414yes—
310C2×C4×C13#12114yes—
311C2×C4×C13#12114yes—
312C2×C4×C13#12314yes—
313C2×C4×C13#12414yes—
314C2×C4×C13#12614yes—
315C2×Dic13—24no—
316C2×Dic13—24no—
317C2×Dic13—24no—
318C2×Dic13—24no—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C24×C4C2×D1311yescharacteristic
344C22×C4⋊C4—131no—
345C22×C4⋊C4—131no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—132no—
349C22×C22⋊C4—132no—
350C22×C22⋊C4—132no—
351C22×C22⋊C4C2×D1311yescharacteristic
352C22×C22⋊C4C2×D1311yescharacteristic
353C22×C42—132no—
354C22×C42C2×D1311yescharacteristic
355C22×C42C2×D1311yescharacteristic
356#389—264no—
357#388—268no—
358#380—138no—
359#380—264no—
360C4×C4⋊C4—264no—
361C4×C22⋊C4—24no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95C2×D1311yescharacteristic
371C2×#95C2×D1311yescharacteristic
372C22×C13—24no—
373C22×C13—24no—
374C22×C13—24no—
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×C13—42no—
386C22×C13—42no—
387C22×C13C2×#11711yescharacteristic
388C22×C13C2×C4×D411yescharacteristic
389C22×C13C2×C4×D411yescharacteristic
390C22×C13C2×C4×D411yescharacteristic
391C22×C13C4×#4111yescharacteristic
392C22×C13#51911yescharacteristic
393C22×C13#52011yescharacteristic
394C22×C13C2×#12111yescharacteristic
395C22×C13C2×#12111yescharacteristic
396C22×C13C2×#12311yescharacteristic
397C22×C13#52511yescharacteristic
398C22×C13C2×#12411yescharacteristic
399C22×C13C2×#12611yescharacteristic
400C22×C13#52911yescharacteristic
401C22×C13#53211yescharacteristic
402C22×C13#53611yescharacteristic
403C22×C13#53711yescharacteristic
404C22×C13#54111yescharacteristic
405C22×C13#54211yescharacteristic
406C22×C13D4211yescharacteristic
407C22×C13#54711yescharacteristic
408C22×C13#54711yescharacteristic
409C22×C13#54711yescharacteristic
410C22×C13#54711yescharacteristic
411C22×C13#54811yescharacteristic
412C22×C13#54811yescharacteristic
413C22×C13#55211yescharacteristic
414C22×C13#55211yescharacteristic
415C22×C13#55211yescharacteristic
416C22×C13#55211yescharacteristic
417C22×C13#55211yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55511yescharacteristic
420C22×C13#55511yescharacteristic
421C22×C13#55611yescharacteristic
422C4×C13—24no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—42no—
426C4×C13—42no—
427C4×C13#38818yescomplemented
428Dic13—44no—
429Dic13—44no—
430Dic13—44no—
431Dic13—82no—
432C25C22×D1311yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—132no—
440C23×C4—132no—
441C23×C4—132no—
442C23×C4—132no—
443C23×C4C4×D1314yes—
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C2×C4⋊C4—134no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—264no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—522no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—138no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—522no—
476C2×C22⋊C4D5214yes—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—22no—
481C2×C42—22no—
482C2×C42—264no—
483C2×C42—264no—
484C2×C42—264no—
485C2×C42C22⋊D1314yes—
486#95—22no—
487#95—22no—
488#95—138no—
489#95—264no—
490#95—264no—
491#95—264no—
492#95—264no—
493#95—264no—
494#95—264no—
495#95—522no—
496C2×C13—44no—
497C2×C13C2×#38811yescharacteristic
498C2×C13C4×#12111yescharacteristic
499C2×C13#232311yescharacteristic
500C2×C13#234411yescharacteristic
501C2×C13#234611yescharacteristic
502C2×C13#236111yescharacteristic
503C2×C13#236211yescharacteristic
504C2×C13#248511yescharacteristic
505C2×C13#248611yescharacteristic
506C2×C13#248911yescharacteristic
507C2×C13#249111yescharacteristic
508C2×C13#249511yescharacteristic
509C2×C13#249611yescharacteristic
510C2×C13#253611yescharacteristic
511C2×C13#253711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24C2×C4×D1312yes—
525C24C2×D5212yes—
526C24#612712yes—
527C24C23×D1311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—134no—
564C22×C4—134no—
565C22×C4—134no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4C2×C4×D1312yes—
592C22×C4C2×C4×D1312yes—
593C22×C4C2×D5212yes—
594C22×C4C2×D5212yes—
595C22×C4#612712yes—
596C22×C4#612712yes—
597C22×C4#612712yes—
598C22×C4D4×D1312yes—
599C22×C4#612912yes—
600C22×C4#612912yes—
601C22×C4#612912yes—
602C22×C4C2×C22⋊D1312yes—
603C22×C4C2×C22⋊D1312yes—
604C22×C4C2×C22⋊D1312yes—
605C4⋊C4—268no—
606C4⋊C4—268no—
607C4⋊C4—268no—
608C4⋊C4—528no—
609C4⋊C4—524no—
610C22⋊C4—28no—
611C22⋊C4—28no—
612C22⋊C4—2616no—
613C22⋊C4—528no—
614C42—28no—
615C42—44no—
616C42—528no—
617C13#1399411yescharacteristic, complemented, Sylow
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—22no—
635C23—22no—
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—41no—
651C23—41no—
652C23C4×D5214yes—
653C23C22×C4×D1311yescharacteristic
654C23C22×D5211yescharacteristic
655C23C2×#612711yescharacteristic
656C23C2×#612711yescharacteristic
657C23C2×#612711yescharacteristic
658C23C2×#612711yescharacteristic
659C23C2×D4×D1311yescharacteristic
660C23C2×#612911yescharacteristic
661C23C2×#612911yescharacteristic
662C23C2×#612911yescharacteristic
663C23#8825611yescharacteristic
664C23#8825711yescharacteristic
665C23#8825711yescharacteristic
666C23#8825711yescharacteristic
667C23C22×C22⋊D1311yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—416no—
703C2×C4—264no—
704C2×C4—264no—
705C2×C4—264no—
706C2×C4—264no—
707C2×C4—264no—
708C2×C4—264no—
709C2×C4—264no—
710C2×C4—264no—
711C2×C4—264no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4#8813114yes—
732C2×C4#8813314yes—
733C2×C4#8813514yes—
734C2×C4#8813914yes—
735C2×C4C4×C22⋊D1314yes—
736C2×C4#8818414yes—
737C2×C4#8818914yes—
738C2×C4#8819214yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×C4×D5211yescharacteristic
755C22C4×#612711yescharacteristic
756C22#1171918211yescharacteristic
757C22#1171918411yescharacteristic
758C22C2×#8813111yescharacteristic
759C22C2×#8813311yescharacteristic
760C22C2×#8813511yescharacteristic
761C22C2×#8813911yescharacteristic
762C22#1171922111yescharacteristic
763C22#1171922311yescharacteristic
764C22#1171922811yescharacteristic
765C22#1171923911yescharacteristic
766C22#1171924611yescharacteristic
767C22#1171924611yescharacteristic
768C22#1171924611yescharacteristic
769C22#1171924611yescharacteristic
770C22#1171924611yescharacteristic
771C22#1171924711yescharacteristic
772C22D4×D5211yescharacteristic
773C22#1171925611yescharacteristic
774C22#1171925711yescharacteristic
775C22#1171925711yescharacteristic
776C22#1171926011yescharacteristic
777C22#1171926011yescharacteristic
778C22#1171926011yescharacteristic
779C22#1171926811yescharacteristic
780C22#1171926811yescharacteristic
781C22#1171927011yescharacteristic
782C22C2×C4×C22⋊D1311yescharacteristic
783C22C2×#8818411yescharacteristic
784C22#1171949611yescharacteristic
785C22C2×#8818911yescharacteristic
786C22C2×#8819211yescharacteristic
787C22#1171953011yescharacteristic
788C22#1171953811yescharacteristic
789C4—24no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—524no—
795C4—524no—
796C4—524no—
797C4—1042no—
798C4#1171860518yescomplemented
799C2—44no—
800C2C2×#1171860511yescharacteristic
801C2C4×#8818411yescharacteristic
802C2#1311751811yescharacteristic
803C2#1311770311yescharacteristic
804C2#1311771911yescharacteristic
805C2#1311785011yescharacteristic
806C2#1311786111yescharacteristic
807C2#1311913311yescharacteristic
808C2#1311914411yescharacteristic
809C2#1311917711yescharacteristic
810C2#1311919911yescharacteristic
811C2#1311924711yescharacteristic
812C2#1311925811yescharacteristic
813C2#1311974511yescharacteristic
814C2#1311974911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13994
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718589C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
6. #13113091C2semidirect
8. #13113066C2semidirect
9. #13113066C2semidirect
10. #13113060C2semidirect
29. #11718873C4semidirect
427. C4×C13#388semidirect
617. C13#13994semidirect
798. C4#11718605semidirect

Maximal subgroups

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

subgroupindex
C2×#117185892
C2×#117186052
C2×#117188732
C2×C4×C4⋊Dic132
#131130912
#131130832
#131130662
#131130602
C2×C4×C13×C22⋊C42
#1399413