Finite Group Databasebeta

← #15830275

Subgroups — #15830275

Order 3328.

1470 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
2C22×C22⋊#1055C211yesmaximal, characteristic, complemented
3#13113407C212yesmaximal, complemented
4#13113403C212yesmaximal, complemented
5#13113390C214yesmaximal, 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
28C23×#1055—21no—
29C13×#381C2212yescomplemented
30C13×#380—21no—
31C13×#380C2212yes—
32C13×#379—21no—
33C4×C13×C22⋊C4—21no—
34C4×C13×C22⋊C4C2212yescomplemented
35C2×C22⋊#1055—21no—
36C2×C22⋊#1055—21no—
37C2×C22⋊#1055—21no—
38C2×C22⋊#1055C2212yes—
39C2×C22⋊#1055C2212yescomplemented
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—
122C22×#1055—22no—
123C22×#1055—22no—
124C22×#1055—22no—
125C22×#1055—44no—
126C13×#95—22no—
127C13×#95C2314yes—
128C22⋊#1055—22no—
129C22⋊#1055—22no—
130C22⋊#1055—22no—
131C22⋊#1055C2314yes—
132#17572—131nomaximal, Sylow
133C24×C13—24no—
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—
237C2×#1055—24no—
238C2×#1055—44no—
239C2×#1055—44no—
240C2×#1055—44no—
241C2×#525—131no—
242C22×C22⋊C8—131no—
243#2280D1311yescharacteristic, complemented
244#1520—132no—
245#1519—132no—
246#1516—134no—
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—22no—
258C23×C13—22no—
259C23×C13—22no—
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—416no—
269C23×C13C2×C22⋊C411yescharacteristic
270C23×C13C2×C22⋊C411yescharacteristic
271C23×C13C2×C22⋊C411yescharacteristic
272C23×C13C2×C22⋊C411yescharacteristic
273C23×C13C2×C22⋊C411yescharacteristic
274C23×C13C2×C22⋊C411yescharacteristic
275C23×C13#13514yes—
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
341C23×C8—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—
360C2×C22⋊C8—132no—
361C2×C22⋊C8—132no—
362C2×C22⋊C8—132no—
363C2×C22⋊C8—261no—
364C2×C22⋊C8—261no—
365C2×C22⋊C8—261no—
366#381C2×D1312yescomplemented
367#380—21no—
368#380C2×D1312yes—
369#379—21no—
370C4×C22⋊C4—21no—
371C4×C22⋊C4C2×D1312yescomplemented
372#328—138no—
373#327—138no—
374C22×C13—28no—
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—44no—
392C22×C13—44no—
393C22×C13—44no—
394C22×C13—44no—
395C22×C13—44no—
396C22×C13—44no—
397C22×C13C2×#9912yes—
398C22×C13#41612yes—
399C22×C13#41612yes—
400C22×C13#42112yes—
401C22×C13C22×C22⋊C411yescharacteristic
402C22×C13C2×#13512yes—
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
446C22×C8—262no—
447C22×C8—262no—
448C22×C8—262no—
449C22×C8—524no—
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—22no—
512C2×C13—22no—
513C2×C13—41no—
514C2×C13—41no—
515C2×C13C22×#9911yescharacteristic
516C2×C13C2×#41611yescharacteristic
517C2×C13C2×#42111yescharacteristic
518D13—82no—
519C24—24no—
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
598C2×C8—264no—
599C2×C8—524no—
600C2×C8—524no—
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#1757211yescharacteristic, complemented, Sylow
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—416no—
649C23—262no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23C2×#610311yescharacteristic
654C23C2×#610311yescharacteristic
655C23C2×#610311yescharacteristic
656C23C2×#610311yescharacteristic
657C23C2×#610311yescharacteristic
658C23C2×#610311yescharacteristic
659C23#8820414yes—
660C23C22×C22⋊D1311yescharacteristic
661Q8—522no—
662Q8—522no—
663D4—522no—
664D4—524no—
665D4—524no—
666D4—524no—
667D4—524no—
668D4—524no—
669D4—524no—
670D4—522no—
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—524no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
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—28no—
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—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22—1044no—
746C22C2×#8804612yes—
747C22#1171866312yes—
748C22#1171866312yes—
749C22#1171866612yes—
750C22C22×#610311yescharacteristic
751C22C2×#8820412yes—
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—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—1042no—
772C2C22×#8804611yescharacteristic
773C2C2×#1171866311yescharacteristic
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#17572
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. C22×C22⋊#1055C2semidirect
3. #13113407C2semidirect
4. #13113403C2semidirect
5. #13113390C2semidirect
6. #13113325C2semidirect
7. C13×#2280C2semidirect
9. C22×#6127C4semidirect
16. #11719496C4semidirect
17. #11719496C4semidirect
20. C2×#88184C4semidirect
25. C2×#88180C4semidirect
26. C2×#88178C4semidirect
29. C13×#381C22semidirect
34. C4×C13×C22⋊C4C22semidirect
39. C2×C22⋊#1055C22semidirect
40. C2×C22⋊#1055C22semidirect
41. #11718044C22semidirect
42. #11718043C22semidirect
243. #2280D13semidirect
366. #381C2×D13semidirect
371. C4×C22⋊C4C2×D13semidirect
627. C13#17572semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C22×C22⋊#10552
#131134072
#131134032
#131133902
#131133252
C13×#22802
#1757213