Finite Group Databasebeta

← #15785757

Subgroups — #15785757

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×#11718589C211yesmaximal, characteristic, complemented
2C2×#11718873C211yesmaximal, characteristic
3C2×#11718873C211yesmaximal, characteristic
4C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
5#13113094C212yesmaximal, complemented
6#13113079C212yesmaximal
7#13113073C212yesmaximal
8#13113066C211yesmaximal, characteristic, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113062C212yesmaximal, 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—
38C4×C4⋊Dic13—24no—
39#11718589—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×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13C2312yes—
55C23×Dic13C2312yes—
56C23×Dic13C2312yes—
57C23×Dic13C2312yes—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4—22no—
60C2×C13×C22⋊C4—22no—
61C2×C13×C22⋊C4—22no—
62C2×C13×C22⋊C4—22no—
63C2×C13×C22⋊C4Q814yes—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13D414yes—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—42no—
73C2×C22⋊Dic13—42no—
74C2×C22⋊Dic13—42no—
75C2×C22⋊Dic13C2×C418yes—
76C2×C4⋊Dic13—22no—
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⋊Dic13C2×C414yes—
86C2×C4⋊Dic13C2×C414yes—
87C2×C4⋊Dic13D414yes—
88C2×#6101—24no—
89C2×#6101—42no—
90C2×#6101—42no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—42no—
94C13×#95—22no—
95C13×#95—22no—
96#88071—24no—
97#88071—24no—
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—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—28no—
150C22×C4×C13—28no—
151C22×C4×C13—28no—
152C22×C4×C13—44no—
153C22×C4×C13—44no—
154C22×C4×C13—44no—
155C22×C4×C13—44no—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C22×C412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×Q812yes—
163C22×C4×C13C2×Q812yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×C4×C13#4112yes—
168C22×C4×C13#4112yes—
169C22×C4×C13#4112yes—
170C22×Dic13—22no—
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×Dic13C22×C414yes—
196C22×Dic13C22×C414yes—
197C22×Dic13C2×D414yes—
198C13×C22⋊C4—28no—
199C13×C22⋊C4—28no—
200C42×C13—28no—
201C42×C13—44no—
202C22⋊Dic13—48no—
203C22⋊Dic13—48no—
204C4⋊Dic13—28no—
205C4⋊Dic13—28no—
206C4⋊Dic13—28no—
207C4⋊Dic13—44no—
208#6101—48no—
209C4×Dic13—48no—
210C2×#389—131no—
211C2×#380—131no—
212C2×#380—131no—
213C2×C4×C4⋊C4—131no—
214C2×C4×C22⋊C4D1311yescharacteristic
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—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—41no—
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—416no—
306C2×C4×C13#11714yes—
307C2×C4×C13C4×D414yes—
308C2×C4×C13C4×D414yes—
309C2×C4×C13#12114yes—
310C2×C4×C13C22⋊Q814yes—
311C2×C4×C13#12314yes—
312C2×C4×C13#12414yes—
313C2×C4×C13#12614yes—
314C2×Dic13—24no—
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—42no—
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—
342C24×C4C2×D1311yescharacteristic
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—131no—
346C22×C4⋊C4—131no—
347C22×C4⋊C4—132no—
348C22×C22⋊C4—132no—
349C22×C22⋊C4—132no—
350C22×C22⋊C4C2×D1311yescharacteristic
351C22×C22⋊C4C2×D1311yescharacteristic
352C22×C42—132no—
353C22×C42C2×D1311yescharacteristic
354C22×C42C2×D1311yescharacteristic
355#389—264no—
356#380—138no—
357#380—264no—
358C4×C4⋊C4—264no—
359C4×C22⋊C4—24no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95C2×D1311yescharacteristic
369C2×#95C2×D1311yescharacteristic
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—24no—
421C4×C13—42no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13#38818yes—
426Dic13—44no—
427Dic13—44no—
428Dic13—44no—
429Dic13—82no—
430C25C22×D1311yescharacteristic
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—132no—
438C23×C4—132no—
439C23×C4—132no—
440C23×C4—132no—
441C23×C4C4×D1314yes—
442C23×C4C22×D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C2×C4⋊C4—134no—
449C2×C4⋊C4—134no—
450C2×C4⋊C4—134no—
451C2×C4⋊C4—262no—
452C2×C4⋊C4—262no—
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—262no—
461C2×C4⋊C4—522no—
462C2×C4⋊C4—522no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—138no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—522no—
472C2×C22⋊C4—522no—
473C2×C22⋊C4—522no—
474C2×C22⋊C4Dic2614yes—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—264no—
481C2×C42—264no—
482C2×C42—522no—
483C2×C42C22⋊D1314yes—
484#95—22no—
485#95—22no—
486#95—138no—
487#95—264no—
488#95—264no—
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×Dic2612yes—
523C24C2×C4×D1312yes—
524C24#612712yes—
525C24C23×D1311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
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—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—134no—
562C22×C4—134no—
563C22×C4—134no—
564C22×C4—262no—
565C22×C4—262no—
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×C4C2×Dic2612yes—
590C22×C4C2×Dic2612yes—
591C22×C4C2×C4×D1312yes—
592C22×C4C2×C4×D1312yes—
593C22×C4#612712yes—
594C22×C4#612712yes—
595C22×C4#612712yes—
596C22×C4D4×D1312yes—
597C22×C4#612912yes—
598C22×C4#612912yes—
599C22×C4#612912yes—
600C22×C4C2×C22⋊D1312yes—
601C22×C4C2×C22⋊D1312yes—
602C22×C4C2×C22⋊D1312yes—
603C4⋊C4—268no—
604C4⋊C4—268no—
605C4⋊C4—268no—
606C4⋊C4—528no—
607C4⋊C4—524no—
608C22⋊C4—28no—
609C22⋊C4—28no—
610C22⋊C4—528no—
611C22⋊C4—528no—
612C42—28no—
613C42—44no—
614C42—528no—
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—
650C23C4×Dic2614yes—
651C23C22×Dic2611yescharacteristic
652C23C22×C4×D1311yescharacteristic
653C23C2×#612711yescharacteristic
654C23C2×#612711yescharacteristic
655C23C2×#612711yescharacteristic
656C23C2×#612711yescharacteristic
657C23C2×D4×D1311yescharacteristic
658C23C2×#612911yescharacteristic
659C23C2×#612911yescharacteristic
660C23C2×#612911yescharacteristic
661C23#8825611yescharacteristic
662C23#8825611yescharacteristic
663C23#8825611yescharacteristic
664C23#8825711yescharacteristic
665C23C22×C22⋊D1311yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
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—41no—
685C2×C4—41no—
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—416no—
701C2×C4—264no—
702C2×C4—264no—
703C2×C4—264no—
704C2×C4—264no—
705C2×C4—264no—
706C2×C4—264no—
707C2×C4—264no—
708C2×C4—264no—
709C2×C4—264no—
710C2×C4—522no—
711C2×C4—522no—
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#8813114yes—
730C2×C4#8813314yes—
731C2×C4#8813514yes—
732C2×C4#8813714yes—
733C2×C4#8817814yes—
734C2×C4C4×C22⋊D1314yes—
735C2×C4#8819014yes—
736C2×C4#8819314yes—
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×C4×Dic2611yescharacteristic
753C22#1171917511yescharacteristic
754C22C4×#612711yescharacteristic
755C22#1171918411yescharacteristic
756C22C2×#8813111yescharacteristic
757C22C2×#8813311yescharacteristic
758C22C2×#8813511yescharacteristic
759C22C2×#8813711yescharacteristic
760C22#1171922611yescharacteristic
761C22#1171922811yescharacteristic
762C22#1171923911yescharacteristic
763C22#1171924011yescharacteristic
764C22D4×Dic2611yescharacteristic
765C22#1171924611yescharacteristic
766C22#1171924611yescharacteristic
767C22#1171924611yescharacteristic
768C22#1171924811yescharacteristic
769C22#1171924811yescharacteristic
770C22#1171924811yescharacteristic
771C22#1171925511yescharacteristic
772C22#1171925511yescharacteristic
773C22#1171925811yescharacteristic
774C22#1171926811yescharacteristic
775C22#1171926811yescharacteristic
776C22#1171926811yescharacteristic
777C22#1171927011yescharacteristic
778C22#1171927011yescharacteristic
779C22#1171927011yescharacteristic
780C22C2×#8817811yescharacteristic
781C22C2×C4×C22⋊D1311yescharacteristic
782C22#1171949611yescharacteristic
783C22C2×#8819011yescharacteristic
784C22C2×#8819311yescharacteristic
785C22#1171953511yescharacteristic
786C22#1171953811yescharacteristic
787C4—24no—
788C4—42no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—524no—
793C4—524no—
794C4—524no—
795C4—1042no—
796C4#1171860618yes—
797C2—44no—
798C2C2×#1171860611yescharacteristic
799C2C4×#8817811yescharacteristic
800C2#1311752911yescharacteristic
801C2#1311771111yescharacteristic
802C2#1311771911yescharacteristic
803C2#1311783911yescharacteristic
804C2#1311787211yescharacteristic
805C2#1311825411yescharacteristic
806C2#1311828711yescharacteristic
807C2#1311832811yescharacteristic
808C2#1311836111yescharacteristic
809C2#1311924711yescharacteristic
810C2#1311926911yescharacteristic
811C2#1312000211yescharacteristic
812C2#1312000911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13973
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
4. C2×C4×C4⋊Dic13C2semidirect
5. #13113094C2semidirect
8. #13113066C2semidirect
9. #13113066C2semidirect
10. #13113062C2semidirect
29. #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×#117185892
C2×#117188732
C2×C4×C4⋊Dic132
#131130942
#131130792
#131130732
#131130662
#131130622
C2×C4×C13×C22⋊C42
#1397313