Finite Group Databasebeta

← #15872721

Subgroups — #15872721

Order 3328.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic, complemented
3#13115821C212yesmaximal, complemented
4#13115672C212yesmaximal, complemented
5#13115287C214yesmaximal, complemented
6#13114821C214yesmaximal, complemented
7C13×#2280C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C2×C13×#117—21no—
11C2×#88207C2212yes—
12C22×C22⋊Dic13C2212yes—
13#11719496—21no—
14#11719496—21no—
15#11719496—21no—
16#11719496—21no—
17#11719496—21no—
18#11719496—21no—
19#11719496—21no—
20#11719496—21no—
21C2×#88184C411yescharacteristic, complemented
22C2×#88184C2211yescharacteristic
23C2×#88183C412yescomplemented
24C2×C4×C22⋊D13C412yescomplemented
25C2×C4×C22⋊D13C2212yes—
26C2×#88180C411yescharacteristic, complemented
27C22×C4⋊Dic13—21no—
28C2×#88178C411yescharacteristic, complemented
29C2×#88178C2211yescharacteristic
30C13×#381—21no—
31C13×#380—21no—
32C13×#380C2212yes—
33C13×#379C2212yes—
34C4×C13×C22⋊C4—21no—
35C4×C13×C22⋊C4C2212yes—
36#11718873—21no—
37#11718873—21no—
38#11718873C2212yes—
39#11718873C2212yes—
40C2×#88071—21no—
41C2×#88046C2218yes—
42#11718119C2218yes—
43C25×C13C2311yescharacteristic
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×C13D411yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13C2×C412yes—
60C22×C22⋊D13C2×C412yes—
61C22×C22⋊D13C2312yes—
62C23×Dic13—22no—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—21no—
66C2×#6127—21no—
67C2×#6127—44no—
68C22×D52C2×C411yescharacteristic, complemented
69C22×C4×D13C2×C412yescomplemented
70C22×Dic26C2×C411yescharacteristic, complemented
71C13×#117—44no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C13×C22⋊C4—22no—
75C2×C13×C22⋊C4C2314yes—
76C2×C42×C13—22no—
77#88207—22no—
78#88207—22no—
79#88207—22no—
80#88207—22no—
81C2×C22⋊Dic13—22no—
82C2×C22⋊Dic13—44no—
83C2×C22⋊Dic13C2×C412yes—
84C2×C22⋊Dic13C2×C412yes—
85C2×C22⋊Dic13C2314yes—
86C2×C22⋊Dic13C2312yes—
87#88184—21no—
88#88184—21no—
89#88184—21no—
90#88184—21no—
91#88184—21no—
92#88184—21no—
93#88184—21no—
94#88184—21no—
95#88183—22no—
96#88183—22no—
97#88183—22no—
98#88183—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C4×C22⋊D13—22no—
104C4×C22⋊D13—22no—
105C4×C22⋊D13—22no—
106C4×C22⋊D13—22no—
107C2×#6103C2×C412yescomplemented
108C2×#6103C2×C412yescomplemented
109#88180—21no—
110#88180—21no—
111#88180—21no—
112#88180—21no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13—44no—
116C2×C4⋊Dic13C2×C411yescharacteristic, complemented
117C2×C4⋊Dic13C2×C411yescharacteristic, complemented
118#88178—21no—
119#88178—21no—
120#88178—21no—
121#88178—21no—
122#88178—21no—
123#88178—21no—
124#88178—21no—
125#88178—21no—
126C2×#6101C2×C412yescomplemented
127C2×#6101C2×C412yescomplemented
128C2×C4×Dic13C2×C412yescomplemented
129C13×#95—22no—
130C13×#95—22no—
131#88071—22no—
132#88071—22no—
133#88046—48no—
134#21874—131nomaximal, Sylow
135C24×C13—22no—
136C24×C13—22no—
137C24×C13—42no—
138C24×C13—42no—
139C24×C13C22×C411yescharacteristic
140C24×C13C22×C411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C24×C13C2×D411yescharacteristic
145C24×C13C2411yescharacteristic
146C23×D13C22×C412yes—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
149C22×C4×C13—24no—
150C22×C4×C13—24no—
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×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
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×C13C22⋊C411yescharacteristic
178C22×C4×C13C22×C411yescharacteristic
179C22×C4×C13C22×C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C22×C411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C2×C22⋊D13—22no—
191C2×C22⋊D13—22no—
192C2×C22⋊D13—22no—
193C2×C22⋊D13—22no—
194C2×C22⋊D13—22no—
195C2×C22⋊D13—22no—
196C2×C22⋊D13—24no—
197C2×C22⋊D13—24no—
198C2×C22⋊D13—44no—
199C2×C22⋊D13—44no—
200C22×Dic13—24no—
201C22×Dic13—44no—
202C22×Dic13—44no—
203C22×Dic13—44no—
204C22×Dic13C22×C412yes—
205C22×Dic13C22×C412yes—
206C22×Dic13C22×C412yes—
207#6127—44no—
208#6127—44no—
209#6127—44no—
210#6127—44no—
211C2×D52—21no—
212C2×D52—21no—
213C2×D52—42no—
214C2×C4×D13—22no—
215C2×C4×D13—22no—
216C2×C4×D13—44no—
217C2×Dic26—21no—
218C2×Dic26—21no—
219C2×Dic26—42no—
220C13×C4⋊C4—44no—
221C13×C22⋊C4—24no—
222C13×C22⋊C4—24no—
223C13×C22⋊C4—44no—
224C13×C22⋊C4—44no—
225C42×C13—44no—
226C22⋊Dic13—22no—
227C22⋊Dic13—22no—
228C22⋊Dic13—22no—
229C22⋊Dic13—22no—
230C22⋊Dic13—22no—
231C22⋊Dic13—22no—
232C22⋊Dic13—28no—
233C22⋊Dic13—44no—
234#6103—22no—
235#6103—22no—
236#6103—22no—
237#6103—22no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13—21no—
241C4⋊Dic13—21no—
242C4⋊Dic13—44no—
243C4⋊Dic13—44no—
244#6101—22no—
245#6101—22no—
246#6101—22no—
247#6101—22no—
248C4×Dic13—22no—
249C4×Dic13—22no—
250C2×#525—131no—
251#2280D1311yescharacteristic, complemented
252C2×#380—131no—
253#1996—132no—
254#1964—132no—
255#1898—134no—
256#1799—134no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—22no—
268C23×C13—22no—
269C23×C13—22no—
270C23×C13—22no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13—41no—
279C23×C13—48no—
280C23×C13—48no—
281C23×C13C2×C22⋊C411yescharacteristic
282C23×C13C2×C22⋊C411yescharacteristic
283C23×C13C2×C22⋊C411yescharacteristic
284C23×C13C2×C22⋊C411yescharacteristic
285C23×C13C23×C411yescharacteristic
286C23×C13C22×D411yescharacteristic
287C23×C13C22×D411yescharacteristic
288C23×C13H(5,𝔽2)12yes—
289C23×C132−1+412yes—
290C22×D13—22no—
291C22×D13—24no—
292C22×D13—42no—
293C22×D13—42no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—44no—
322C2×C4×C13—44no—
323C2×C4×C13—44no—
324C2×C4×C13#9914yescomplemented
325C2×C4×C13C2×C22⋊C411yescharacteristic
326C2×C4×C13C2×C22⋊C411yescharacteristic
327C2×C4×C13C2×C22⋊C411yescharacteristic
328C2×C4×C13C2×C22⋊C411yescharacteristic
329C2×C4×C13C2×C22⋊C411yescharacteristic
330C2×C4×C13C2×C22⋊C411yescharacteristic
331C2×C4×C13C2×C22⋊C411yescharacteristic
332C2×C4×C13C2×C22⋊C411yescharacteristic
333C22⋊D13—44no—
334C22⋊D13—44no—
335C22⋊D13—42no—
336C22⋊D13—42no—
337C22⋊D13—44no—
338C22⋊D13—44no—
339C22⋊D13—44no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—24no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—44no—
347C2×Dic13—44no—
348C2×Dic13—44no—
349C2×Dic13—88no—
350D52—42no—
351D52—42no—
352C4×D13—44no—
353C4×D13—44no—
354Dic26—42no—
355Dic26—42no—
356C22×#41—131no—
357C24×C4C2×D1311yescharacteristic
358#525—261no—
359#525—261no—
360#525—261no—
361#525—261no—
362#525—261no—
363#525—261no—
364#525—261no—
365#525—261no—
366C2×#123—132no—
367C2×C22⋊Q8—131no—
368C2×C22⋊Q8—131no—
369C2×#121—131no—
370C2×#121—131no—
371C2×#120—132no—
372C2×C4×D4—132no—
373C2×C4×D4—132no—
374C2×#117—21no—
375C2×#117—131no—
376C22×C4⋊C4—261no—
377C22×C22⋊C4—132no—
378C2×#99—138no—
379#381—21no—
380#380—21no—
381#380—132no—
382#380—132no—
383#380—261no—
384#380—261no—
385#380C2×D1312yes—
386#379C2×D1312yes—
387C4×C22⋊C4—21no—
388C4×C22⋊C4C2×D1312yes—
389C2×#95—261no—
390#342—138no—
391C22×C13—24no—
392C22×C13—24no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13—21no—
396C22×C13—21no—
397C22×C13—21no—
398C22×C13—21no—
399C22×C13—21no—
400C22×C13—21no—
401C22×C13—21no—
402C22×C13—21no—
403C22×C13—21no—
404C22×C13—21no—
405C22×C13—21no—
406C22×C13—21no—
407C22×C13—21no—
408C22×C13—21no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13—44no—
412C22×C13—44no—
413C22×C13—44no—
414C22×C13—44no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13C2×#9912yes—
418C22×C13#41012yes—
419C22×C13C22×C22⋊C411yescharacteristic
420C22×C13#52012yes—
421C22×C13#53511yescharacteristic
422C22×C13#53611yescharacteristic
423C22×C13#53712yes—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—84no—
428C4×C13—21no—
429C4×C13—21no—
430C4×C13—21no—
431C4×C13—21no—
432C4×C13—21no—
433C4×C13—21no—
434C4×C13—84no—
435C4×C13C2×#9912yes—
436C4×C13C2×#9912yes—
437Dic13—42no—
438Dic13—42no—
439Dic13—42no—
440Dic13—84no—
441C25C22×D1311yescharacteristic
442C2×#41—261no—
443C2×#41—261no—
444C2×#41—261no—
445C2×#41—261no—
446C2×#41—524no—
447C22×Q8—131no—
448C22×D4—132no—
449C22×D4—132no—
450C22×D4—132no—
451C22×D4—131no—
452C23×C4—44no—
453C23×C4—132no—
454C23×C4—262no—
455C23×C4C4×D1311yescharacteristic
456C23×C4C4×D1311yescharacteristic
457C23×C4C4×D1311yescharacteristic
458C23×C4C4×D1311yescharacteristic
459C23×C4D5211yescharacteristic
460C23×C4D5211yescharacteristic
461C23×C4D5211yescharacteristic
462C23×C4D5211yescharacteristic
463C23×C4C22⋊D1311yescharacteristic
464C23×C4C22⋊D1311yescharacteristic
465C23×C4C22⋊D1311yescharacteristic
466C23×C4C22⋊D1311yescharacteristic
467C23×C4C22×D1311yescharacteristic
468C23×C4C22×D1311yescharacteristic
469#123—262no—
470#123—262no—
471#123—262no—
472#123—262no—
473C22⋊Q8—261no—
474C22⋊Q8—261no—
475C22⋊Q8—261no—
476C22⋊Q8—261no—
477C22⋊Q8—261no—
478C22⋊Q8—261no—
479C22⋊Q8—261no—
480C22⋊Q8—261no—
481#121—261no—
482#121—261no—
483#121—261no—
484#121—261no—
485#121—261no—
486#121—261no—
487#121—261no—
488#121—261no—
489#120—262no—
490#120—262no—
491#120—262no—
492#120—262no—
493C4×D4—262no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4—262no—
497C4×D4—262no—
498C4×D4—262no—
499C4×D4—262no—
500C4×D4—262no—
501#117—44no—
502#117—261no—
503#117—261no—
504#117—261no—
505#117—261no—
506C2×C4⋊C4—22no—
507C2×C4⋊C4—131no—
508C2×C4⋊C4—131no—
509C2×C4⋊C4—132no—
510C2×C4⋊C4—132no—
511C2×C4⋊C4—262no—
512C2×C4⋊C4—262no—
513C2×C4⋊C4—524no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—132no—
517C2×C22⋊C4—132no—
518C2×C22⋊C4—132no—
519C2×C22⋊C4—132no—
520C2×C22⋊C4—132no—
521C2×C22⋊C4—134no—
522C2×C22⋊C4—262no—
523C2×C22⋊C4—524no—
524C2×C22⋊C4C22×D1314yes—
525C2×C42—22no—
526C2×C42—132no—
527#99—528no—
528#95—22no—
529#95—22no—
530#95—262no—
531#95—262no—
532C2×C13—21no—
533C2×C13—22no—
534C2×C13—22no—
535C2×C13—21no—
536C2×C13—22no—
537C2×C13—22no—
538C2×C13—41no—
539C2×C13—41no—
540C2×C13#231111yescharacteristic
541C2×C13C22×#9911yescharacteristic
542C2×C13C2×#41011yescharacteristic
543D13—82no—
544C24—22no—
545C24—22no—
546C24—42no—
547C24—42no—
548C24—132no—
549C24C2×C4×D1311yescharacteristic
550C24C2×C4×D1311yescharacteristic
551C24C2×D5211yescharacteristic
552C24C2×D5211yescharacteristic
553C24C2×C22⋊D1311yescharacteristic
554C24C2×C22⋊D1311yescharacteristic
555C24C23×D1311yescharacteristic
556#41—524no—
557#41—524no—
558#41—524no—
559#41—524no—
560C2×Q8—261no—
561C2×Q8—261no—
562C2×Q8—522no—
563C2×D4—262no—
564C2×D4—262no—
565C2×D4—262no—
566C2×D4—262no—
567C2×D4—262no—
568C2×D4—264no—
569C2×D4—264no—
570C2×D4—262no—
571C2×D4—261no—
572C2×D4—261no—
573C2×D4—522no—
574C2×D4—524no—
575C2×D4—524no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—264no—
597C22×C4—524no—
598C22×C4—524no—
599C22×C4—524no—
600C22×C4—524no—
601C22×C4#610311yescharacteristic
602C22×C4#610311yescharacteristic
603C22×C4#610311yescharacteristic
604C22×C4#610311yescharacteristic
605C22×C4#610311yescharacteristic
606C22×C4#610311yescharacteristic
607C22×C4#610311yescharacteristic
608C22×C4#610311yescharacteristic
609C22×C4#610311yescharacteristic
610C22×C4#610311yescharacteristic
611C22×C4#610311yescharacteristic
612C22×C4#610311yescharacteristic
613C22×C4#610311yescharacteristic
614C22×C4#610311yescharacteristic
615C22×C4#610311yescharacteristic
616C22×C4#610311yescharacteristic
617C22×C4C2×C4×D1311yescharacteristic
618C22×C4C2×C4×D1311yescharacteristic
619C22×C4C2×C4×D1311yescharacteristic
620C22×C4C2×C4×D1311yescharacteristic
621C22×C4C2×D5211yescharacteristic
622C22×C4C2×D5211yescharacteristic
623C22×C4C2×D5211yescharacteristic
624C22×C4C2×D5211yescharacteristic
625C22×C4C2×C22⋊D1311yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C22×C4C2×C22⋊D1311yescharacteristic
628C22×C4C2×C22⋊D1311yescharacteristic
629C4⋊C4—44no—
630C4⋊C4—261no—
631C4⋊C4—261no—
632C4⋊C4—261no—
633C4⋊C4—261no—
634C4⋊C4—262no—
635C4⋊C4—262no—
636C4⋊C4—262no—
637C4⋊C4—262no—
638C4⋊C4—524no—
639C4⋊C4—524no—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—262no—
645C22⋊C4—262no—
646C22⋊C4—262no—
647C22⋊C4—262no—
648C22⋊C4—262no—
649C22⋊C4—262no—
650C22⋊C4—262no—
651C22⋊C4—262no—
652C22⋊C4—262no—
653C22⋊C4—262no—
654C22⋊C4—268no—
655C22⋊C4—524no—
656C42—44no—
657C42—262no—
658C42—262no—
659C13#2187411yescharacteristic, complemented, Sylow
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—21no—
669C23—21no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—48no—
683C23—48no—
684C23—262no—
685C23—264no—
686C23—522no—
687C23—522no—
688C23C2×#610311yescharacteristic
689C23C2×#610311yescharacteristic
690C23C2×#610311yescharacteristic
691C23C2×#610311yescharacteristic
692C23C22×C4×D1311yescharacteristic
693C23C22×D5211yescharacteristic
694C23#8825612yes—
695C23#8825712yes—
696C23C22×C22⋊D1311yescharacteristic
697Q8—522no—
698Q8—522no—
699D4—522no—
700D4—524no—
701D4—524no—
702D4—524no—
703D4—522no—
704D4—522no—
705D4—524no—
706D4—524no—
707D4—522no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—264no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—524no—
743C2×C4—524no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—524no—
747C2×C4—524no—
748C2×C4—524no—
749C2×C4—1048no—
750C2×C4#8804614yescomplemented
751C2×C4C2×#610311yescharacteristic
752C2×C4C2×#610311yescharacteristic
753C2×C4C2×#610311yescharacteristic
754C2×C4C2×#610311yescharacteristic
755C2×C4C2×#610311yescharacteristic
756C2×C4C2×#610311yescharacteristic
757C2×C4C2×#610311yescharacteristic
758C2×C4C2×#610311yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—1044no—
789C22C2×#8804612yes—
790C22#1171866712yes—
791C22#1171922812yes—
792C22#1171923011yescharacteristic
793C22#1171923111yescharacteristic
794C22C22×#610311yescharacteristic
795C22#1171953812yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—84no—
803C4—522no—
804C4—522no—
805C4—522no—
806C4—1044no—
807C4C2×#8804612yes—
808C4C2×#8804612yes—
809C2—22no—
810C2—21no—
811C2—22no—
812C2—21no—
813C2—22no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—1042no—
818C2#1311742411yescharacteristic
819C2C22×#8804611yescharacteristic
820C2C2×#1171866711yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC23×C13C23×C4
FrattiniC24C23×D13
FittingC13×#2280C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719496C2
cosocleC24×C13C24
hypercenter#2280D13
hypocenterC13#21874
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C2×#11718873C2semidirect
3. #13115821C2semidirect
4. #13115672C2semidirect
5. #13115287C2semidirect
6. #13114821C2semidirect
7. C13×#2280C2semidirect
9. C22×#6127C4semidirect
21. C2×#88184C4semidirect
23. C2×#88183C4semidirect
24. C2×C4×C22⋊D13C4semidirect
26. C2×#88180C4semidirect
28. C2×#88178C4semidirect
68. C22×D52C2×C4semidirect
69. C22×C4×D13C2×C4semidirect
70. C22×Dic26C2×C4semidirect
107. C2×#6103C2×C4semidirect
108. C2×#6103C2×C4semidirect
116. C2×C4⋊Dic13C2×C4semidirect
117. C2×C4⋊Dic13C2×C4semidirect
126. C2×#6101C2×C4semidirect
127. C2×#6101C2×C4semidirect
128. C2×C4×Dic13C2×C4semidirect
251. #2280D13semidirect
324. C2×C4×C13#99semidirect
659. C13#21874semidirect
750. C2×C4#88046semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188732
#131158212
#131156722
#131152872
#131148212
C13×#22802
#2187413