Finite Group Databasebeta

← #15830196

Subgroups — #15830196

Order 3328.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718868C211yesmaximal, characteristic, complemented
3#13113377C214yesmaximal, complemented
4#13113368C212yesmaximal, complemented
5#13113364C212yesmaximal, complemented
6#13113325C214yesmaximal, complemented
7C13×#2280C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C2×C13×#117—21no—
11C2×#88207—21no—
12#11719496—21no—
13#11719496—21no—
14#11719496—21no—
15#11719496—21no—
16#11719496C412yescomplemented
17#11719496C412yescomplemented
18#11719496C2212yes—
19#11719496C2212yes—
20C2×#88184C411yescharacteristic, complemented
21C2×#88184C2211yescharacteristic
22C2×#88183—21no—
23C2×C4×C22⋊D13—21no—
24C2×C4×C22⋊D13—21no—
25C2×#88180C411yescharacteristic, complemented
26C2×#88178C411yescharacteristic, complemented
27C2×#88178C2211yescharacteristic
28C22×#6099—21no—
29C13×#381C2212yes—
30C13×#380—21no—
31C13×#380C2212yescomplemented
32C13×#379—21no—
33C4×C13×C22⋊C4—21no—
34C4×C13×C22⋊C4C2212yescomplemented
35#11718868—21no—
36#11718868—21no—
37#11718868C2212yes—
38#11718868C2212yescomplemented
39C2×C22⋊#1055—21no—
40C2×C22⋊#1055C2212yescomplemented
41#11718044C2218yescomplemented
42#11718043C2218yescomplemented
43C25×C13D411yescharacteristic
44C23×C4×C13—44no—
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—21no—
60C22×C22⋊D13—21no—
61C22×C22⋊D13—21no—
62C2×#6127—21no—
63C2×#6127—21no—
64C2×#6127—44no—
65C2×#6127C2×C412yes—
66C2×#6127C2×C412yes—
67C22×D52C2×C411yescharacteristic
68C22×C4×D13—21no—
69C22×Dic26C2×C411yescharacteristic
70C13×#117—44no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C42×C13—22no—
76#88207—22no—
77#88207—22no—
78#88207—22no—
79#88207—22no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83#88184—21no—
84#88184—21no—
85#88184—21no—
86#88184—21no—
87#88184C2×C412yes—
88#88184C2×C412yes—
89#88184C2×C412yes—
90#88184C2312yes—
91#88183—22no—
92#88183—22no—
93#88183—22no—
94#88183—22no—
95C4×C22⋊D13—22no—
96C4×C22⋊D13—22no—
97C4×C22⋊D13—22no—
98C4×C22⋊D13—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C2×#6103—21no—
104C2×#6103—21no—
105#88180—21no—
106#88180—21no—
107#88180C2×C412yes—
108#88180C2×C412yes—
109C2×C4⋊Dic13C2×C411yescharacteristic
110C2×C4⋊Dic13C2×C411yescharacteristic
111#88178—21no—
112#88178—21no—
113#88178—21no—
114#88178—21no—
115#88178C2×C412yes—
116#88178C2×C412yes—
117#88178C2×C412yes—
118#88178C2312yes—
119C2×#6101—21no—
120C2×#6101—21no—
121C2×C4×Dic13—21no—
122C2×#6099—22no—
123C2×#6099—22no—
124C2×#6099—44no—
125C22×#1055—22no—
126C13×#95—22no—
127C13×#95C2314yes—
128C22⋊#1055—22no—
129C22⋊#1055—22no—
130C22⋊#1055—22no—
131C22⋊#1055C2314yes—
132#17559—131nomaximal, Sylow
133C24×C13—42no—
134C24×C13—42no—
135C24×C13—42no—
136C24×C13C22⋊C411yescharacteristic
137C24×C13C22⋊C411yescharacteristic
138C24×C13C22⋊C411yescharacteristic
139C24×C13C22⋊C411yescharacteristic
140C24×C13C2×D411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C23×D13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13—42no—
159C22×C4×C13C22⋊C411yescharacteristic
160C22×C4×C13C22⋊C411yescharacteristic
161C22×C4×C13C22⋊C411yescharacteristic
162C22×C4×C13C22⋊C411yescharacteristic
163C22×C4×C13C22⋊C411yescharacteristic
164C22×C4×C13C22⋊C411yescharacteristic
165C22×C4×C13C22⋊C411yescharacteristic
166C22×C4×C13C22⋊C411yescharacteristic
167C22×C4×C13C22⋊C411yescharacteristic
168C22×C4×C13C22⋊C411yescharacteristic
169C22×C4×C13C22⋊C411yescharacteristic
170C22×C4×C13C22⋊C411yescharacteristic
171C22×C4×C13C22×C411yescharacteristic
172C22×C4×C13C22×C411yescharacteristic
173C22×C4×C13C22×C411yescharacteristic
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C22×C411yescharacteristic
176C22×C4×C13C22×C411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2411yescharacteristic
187C2×C22⋊D13—22no—
188C2×C22⋊D13—22no—
189C2×C22⋊D13—22no—
190C2×C22⋊D13—22no—
191C2×C22⋊D13—22no—
192C2×C22⋊D13—22no—
193C2×C22⋊D13—44no—
194C2×C22⋊D13—44no—
195C2×C22⋊D13—44no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199#6127—44no—
200#6127—44no—
201#6127—44no—
202#6127—44no—
203C2×D52—21no—
204C2×D52—42no—
205C2×D52C22×C412yes—
206C2×C4×D13—22no—
207C2×C4×D13—22no—
208C2×C4×D13—44no—
209C2×Dic26—21no—
210C2×Dic26—42no—
211C2×Dic26C22×C412yes—
212C13×C4⋊C4—44no—
213C13×C22⋊C4—44no—
214C13×C22⋊C4—44no—
215C13×C22⋊C4—44no—
216C42×C13—44no—
217C22⋊Dic13—22no—
218C22⋊Dic13—22no—
219C22⋊Dic13—22no—
220C22⋊Dic13—22no—
221C22⋊Dic13—22no—
222C22⋊Dic13—22no—
223#6103—22no—
224#6103—22no—
225#6103—22no—
226#6103—22no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13C22×C412yes—
230C4⋊Dic13C22×C412yes—
231#6101—22no—
232#6101—22no—
233#6101—22no—
234#6101—22no—
235C4×Dic13—22no—
236C4×Dic13—22no—
237#6099—44no—
238#6099—44no—
239C2×#1055—24no—
240C2×#1055—44no—
241C2×#525—131no—
242C2×#407—131no—
243#2280D1311yescharacteristic, complemented
244#1513—134no—
245#1511—132no—
246#1510—132no—
247#1501—134no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—41no—
258C23×C13—41no—
259C23×C13—41no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—416no—
270C23×C13C2×C22⋊C411yescharacteristic
271C23×C13C2×C22⋊C411yescharacteristic
272C23×C13C2×C22⋊C411yescharacteristic
273C23×C13C2×C22⋊C411yescharacteristic
274C23×C13C2×C22⋊C411yescharacteristic
275C23×C13C2×C22⋊C411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C22×D13—22no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
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—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
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—41no—
307C2×C4×C13—41no—
308C2×C4×C13—44no—
309C2×C4×C13—44no—
310C2×C4×C13—44no—
311C2×C4×C13#9914yes—
312C2×C4×C13C2×C22⋊C411yescharacteristic
313C2×C4×C13C2×C22⋊C411yescharacteristic
314C2×C4×C13C2×C22⋊C411yescharacteristic
315C2×C4×C13C2×C22⋊C411yescharacteristic
316C2×C4×C13C2×C22⋊C411yescharacteristic
317C2×C4×C13C2×C22⋊C411yescharacteristic
318C2×C4×C13C23×C411yescharacteristic
319C2×C4×C13C22×D411yescharacteristic
320C22⋊D13—44no—
321C22⋊D13—44no—
322C22⋊D13—44no—
323C22⋊D13—44no—
324C22⋊D13—44no—
325C22⋊D13—44no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332D52—42no—
333D52—42no—
334C4×D13—44no—
335C4×D13—44no—
336Dic26—42no—
337Dic26—42no—
338#1055—44no—
339C22×#41—131no—
340C24×C4C2×D1311yescharacteristic
341C22×M16—261no—
342#525—132no—
343#525—132no—
344#525—132no—
345#525—132no—
346#525—261no—
347#525—261no—
348#525—261no—
349#525—261no—
350C2×#123—261no—
351C2×C22⋊Q8—131no—
352C2×C22⋊Q8—131no—
353C2×#121—131no—
354C2×#121—131no—
355C2×#120—261no—
356C2×C4×D4—261no—
357C2×C4×D4—261no—
358C2×#117—21no—
359C2×#117—131no—
360#407—132no—
361#407—132no—
362#407—261no—
363#407—261no—
364C2×C22⋊C8—132no—
365C2×C22⋊C8—261no—
366#381C2×D1312yes—
367#380—21no—
368#380C2×D1312yescomplemented
369#379—21no—
370C4×C22⋊C4—21no—
371C4×C22⋊C4C2×D1312yescomplemented
372#328—138no—
373#327—138no—
374C22×C13—21no—
375C22×C13—21no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13—21no—
379C22×C13—21no—
380C22×C13—21no—
381C22×C13—21no—
382C22×C13—21no—
383C22×C13—21no—
384C22×C13—21no—
385C22×C13—21no—
386C22×C13—21no—
387C22×C13—21no—
388C22×C13—21no—
389C22×C13—21no—
390C22×C13—21no—
391C22×C13—21no—
392C22×C13—44no—
393C22×C13—44no—
394C22×C13—44no—
395C22×C13—44no—
396C22×C13—44no—
397C22×C13—44no—
398C22×C13—44no—
399C22×C13C2×#9912yes—
400C22×C13#42112yes—
401C22×C13C22×C22⋊C411yescharacteristic
402C22×C13#57512yes—
403C2×D13—42no—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—84no—
407C4×C13—21no—
408C4×C13—21no—
409C4×C13—21no—
410C4×C13—21no—
411C4×C13—21no—
412C4×C13—21no—
413C4×C13—84no—
414C4×C13C2×#9912yes—
415C4×C13C2×#9912yes—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419C25C22⋊D1311yescharacteristic
420C2×#41—132no—
421C2×#41—132no—
422C2×#41—261no—
423C2×#41—261no—
424C2×#41—524no—
425C22×Q8—131no—
426C22×D4—131no—
427C22×D4—261no—
428C22×D4—261no—
429C22×D4—261no—
430C23×C4—44no—
431C23×C4—261no—
432C23×C4C4×D1311yescharacteristic
433C23×C4C4×D1311yescharacteristic
434C23×C4C4×D1311yescharacteristic
435C23×C4C4×D1311yescharacteristic
436C23×C4D5211yescharacteristic
437C23×C4D5211yescharacteristic
438C23×C4D5211yescharacteristic
439C23×C4D5211yescharacteristic
440C23×C4C22⋊D1311yescharacteristic
441C23×C4C22⋊D1311yescharacteristic
442C23×C4C22⋊D1311yescharacteristic
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C2×M16—262no—
447C2×M16—262no—
448C2×M16—524no—
449C22×C8—262no—
450#123—262no—
451#123—262no—
452#123—262no—
453#123—262no—
454C22⋊Q8—132no—
455C22⋊Q8—132no—
456C22⋊Q8—132no—
457C22⋊Q8—132no—
458C22⋊Q8—261no—
459C22⋊Q8—261no—
460C22⋊Q8—261no—
461C22⋊Q8—261no—
462#121—132no—
463#121—132no—
464#121—132no—
465#121—132no—
466#121—261no—
467#121—261no—
468#121—261no—
469#121—261no—
470#120—262no—
471#120—262no—
472#120—262no—
473#120—262no—
474C4×D4—262no—
475C4×D4—262no—
476C4×D4—262no—
477C4×D4—262no—
478C4×D4—262no—
479C4×D4—262no—
480C4×D4—262no—
481C4×D4—262no—
482#117—44no—
483#117—132no—
484#117—132no—
485#117—261no—
486#117—261no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—261no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4—261no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4—261no—
500C2×C42—22no—
501C2×C42—261no—
502C22⋊C8—134no—
503C22⋊C8—262no—
504C22⋊C8—262no—
505C22⋊C8—262no—
506#95—22no—
507#95C22×D1314yes—
508C2×C13—22no—
509C2×C13—22no—
510C2×C13—22no—
511C2×C13—41no—
512C2×C13—41no—
513C2×C13—41no—
514C2×C13—41no—
515C2×C13C22×#9911yescharacteristic
516C2×C13#289611yescharacteristic
517C2×C13C2×#42111yescharacteristic
518D13—82no—
519C24—42no—
520C24—42no—
521C24—42no—
522C24—261no—
523C24#610311yescharacteristic
524C24#610311yescharacteristic
525C24#610311yescharacteristic
526C24#610311yescharacteristic
527C24C2×C22⋊D1311yescharacteristic
528C24C2×C22⋊D1311yescharacteristic
529C24C2×C22⋊D1311yescharacteristic
530#41—524no—
531#41—524no—
532#41—524no—
533#41—524no—
534C2×Q8—132no—
535C2×Q8—261no—
536C2×Q8—522no—
537C2×D4—132no—
538C2×D4—262no—
539C2×D4—262no—
540C2×D4—262no—
541C2×D4—262no—
542C2×D4—262no—
543C2×D4—262no—
544C2×D4—261no—
545C2×D4—522no—
546C2×D4—524no—
547C2×D4—524no—
548C2×D4—524no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—524no—
570C22×C4#610311yescharacteristic
571C22×C4#610311yescharacteristic
572C22×C4#610311yescharacteristic
573C22×C4#610311yescharacteristic
574C22×C4#610311yescharacteristic
575C22×C4#610311yescharacteristic
576C22×C4#610311yescharacteristic
577C22×C4#610311yescharacteristic
578C22×C4#610311yescharacteristic
579C22×C4#610311yescharacteristic
580C22×C4#610311yescharacteristic
581C22×C4#610311yescharacteristic
582C22×C4C2×C4×D1311yescharacteristic
583C22×C4C2×C4×D1311yescharacteristic
584C22×C4C2×C4×D1311yescharacteristic
585C22×C4C2×C4×D1311yescharacteristic
586C22×C4C2×C4×D1311yescharacteristic
587C22×C4C2×C4×D1311yescharacteristic
588C22×C4C2×D5211yescharacteristic
589C22×C4C2×D5211yescharacteristic
590C22×C4C2×D5211yescharacteristic
591C22×C4C2×D5211yescharacteristic
592C22×C4C2×D5211yescharacteristic
593C22×C4C2×D5211yescharacteristic
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C23×D1311yescharacteristic
598M16—524no—
599M16—524no—
600C2×C8—264no—
601C2×C8—524no—
602C4⋊C4—44no—
603C4⋊C4—132no—
604C4⋊C4—132no—
605C4⋊C4—261no—
606C4⋊C4—261no—
607C4⋊C4—262no—
608C4⋊C4—262no—
609C4⋊C4—262no—
610C4⋊C4—262no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—262no—
615C22⋊C4—262no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—262no—
620C22⋊C4—262no—
621C22⋊C4—262no—
622C22⋊C4—262no—
623C22⋊C4—262no—
624C42—44no—
625C42—262no—
626C42—262no—
627C13#1755911yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
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—416no—
650C23—262no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23C2×#610311yescharacteristic
655C23C2×#610311yescharacteristic
656C23C2×#610311yescharacteristic
657C23C2×#610311yescharacteristic
658C23C2×#610311yescharacteristic
659C23C2×#610311yescharacteristic
660C23C22×C22⋊D1311yescharacteristic
661Q8—522no—
662Q8—522no—
663D4—522no—
664D4—522no—
665D4—524no—
666D4—524no—
667D4—524no—
668D4—524no—
669D4—524no—
670D4—524no—
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—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—522no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—524no—
708C2×C4—524no—
709C2×C4#8804614yes—
710C2×C4C2×#610311yescharacteristic
711C2×C4C2×#610311yescharacteristic
712C2×C4C2×#610311yescharacteristic
713C2×C4C2×#610311yescharacteristic
714C2×C4C2×#610311yescharacteristic
715C2×C4C2×#610311yescharacteristic
716C2×C4C22×C4×D1311yescharacteristic
717C2×C4C22×D5211yescharacteristic
718C8—524no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—522no—
745C22—522no—
746C22—522no—
747C22—1044no—
748C22C2×#8804612yes—
749C22#1171866612yes—
750C22C22×#610311yescharacteristic
751C22#1171952712yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—522no—
760C4—522no—
761C4—522no—
762C4C2×#8804612yes—
763C4C2×#8804612yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—1042no—
772C2C22×#8804611yescharacteristic
773C2#1312335311yescharacteristic
774C2C2×#1171866611yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2280C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenter#2280D13
hypocenterC13#17559
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#11718868C2semidirect
3. #13113377C2semidirect
4. #13113368C2semidirect
5. #13113364C2semidirect
6. #13113325C2semidirect
7. C13×#2280C2semidirect
9. C22×#6127C4semidirect
16. #11719496C4semidirect
17. #11719496C4semidirect
20. C2×#88184C4semidirect
25. C2×#88180C4semidirect
26. C2×#88178C4semidirect
31. C13×#380C22semidirect
34. C4×C13×C22⋊C4C22semidirect
38. #11718868C22semidirect
40. C2×C22⋊#1055C22semidirect
41. #11718044C22semidirect
42. #11718043C22semidirect
243. #2280D13semidirect
368. #380C2×D13semidirect
371. C4×C22⋊C4C2×D13semidirect
627. C13#17559semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188682
#131133772
#131133682
#131133642
#131133252
C13×#22802
#1755913