Finite Group Databasebeta

← #15868713

Subgroups — #15868713

Order 3328.

1344 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718889C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic, complemented
3C2×C4×#6107C211yesmaximal, characteristic, complemented
4#13117518C211yesmaximal, characteristic
5#13115177C211yesmaximal, characteristic, complemented
6#13115177C211yesmaximal, characteristic, complemented
7#13115148C211yesmaximal, characteristic
8#13115104C211yesmaximal, characteristic, complemented
9#13115090C211yesmaximal, characteristic, complemented
10#13115035C211yesmaximal, characteristic
11#13114771C211yesmaximal, characteristic
12#13114666C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic
15C2×C13×#519C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C13×#519—24no—
18C13×#519—24no—
19C2×C4×Q8×C13—21no—
20C2×C4×Q8×C13—21no—
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×Q8×C13C2211yescharacteristic
24C2×C4×Q8×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117—21no—
27C2×C13×#117C2211yescharacteristic
28C2×C13×#117C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C22×#6107C2211yescharacteristic
31C2×#88178C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33#11718889C418yescomplemented
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88075C2211yescharacteristic
40#11718873C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718691—24no—
44C4×#6107—24no—
45#11718639—21no—
46#11718633—21no—
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88047C2211yescharacteristic
51#11718606—21no—
52#11718605—21no—
53C4×C4⋊Dic13C2211yescharacteristic
54#11718590C2211yescharacteristic
55#11718589C2211yescharacteristic
56C2×#88043C2211yescharacteristic
57C2×C4×#1055C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718116C2211yescharacteristic
63#11718116C2211yescharacteristic
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—21no—
69C22×Q8×C13—22no—
70C22×Q8×C13C2×C414yes—
71C22×Q8×C13C2311yescharacteristic
72C22×Q8×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13C2311yescharacteristic
75C22×Dic26C2311yescharacteristic
76C4×Q8×C13—28no—
77C4×Q8×C13—28no—
78C4×Q8×C13—22no—
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13—22no—
83C4×Q8×C13—22no—
84C4×Q8×C13D414yes—
85C4×Q8×C13D414yes—
86C13×#117—28no—
87C13×#117—28no—
88C13×#117—22no—
89C13×#117—22no—
90C13×#117—22no—
91C13×#117—22no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4D411yescharacteristic
97C2×C13×C4⋊C4D411yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C4⋊C4C2311yescharacteristic
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C13×C22⋊C4D411yescharacteristic
103C2×C42×C13—21no—
104C2×C42×C13—21no—
105C2×C42×C13—21no—
106C2×C42×C13—21no—
107C2×C42×C13—21no—
108C2×C42×C13C2311yescharacteristic
109C2×C42×C13C2311yescharacteristic
110C2×C22⋊Dic13—21no—
111C2×C22⋊Dic13—21no—
112C2×#6107—22no—
113C2×#6107—22no—
114C2×#6107—22no—
115C2×#6107—22no—
116C2×#6107C2×C414yes—
117C2×#6107C2×C414yes—
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121#88178—22no—
122#88178C2×C414yes—
123C2×#6101—21no—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C2×C4×Dic13—21no—
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C4×Dic26—22no—
133C4×Dic26—22no—
134#88075—22no—
135#88075—22no—
136#88075—22no—
137#88075—22no—
138#88075C2×C414yes—
139#88075C2×C414yes—
140#88071—21no—
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88071—21no—
145C22⋊#1055—22no—
146C22⋊#1055C2×C414yes—
147#88050—22no—
148#88050—22no—
149#88048—22no—
150#88047—22no—
151#88043—22no—
152C4×#1055—22no—
153#21463—131nomaximal, Sylow
154C24×C13C2×D411yescharacteristic
155C2×Q8×C13—24no—
156C2×Q8×C13—28no—
157C2×Q8×C13—28no—
158C2×Q8×C13—24no—
159C2×Q8×C13—28no—
160C2×Q8×C13—28no—
161C2×Q8×C13—24no—
162C2×Q8×C13—21no—
163C2×Q8×C13—21no—
164C2×Q8×C13—21no—
165C2×Q8×C13—21no—
166C2×Q8×C13—21no—
167C2×Q8×C13—21no—
168C2×Q8×C13C22×C412yes—
169C2×Q8×C13C22×C412yes—
170C2×Q8×C13C2×D412yes—
171C2×Q8×C13C2×D412yes—
172C2×Q8×C13#4112yes—
173C2×Q8×C13#4112yes—
174C22×C4×C13—24no—
175C22×C4×C13—24no—
176C22×C4×C13—24no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13#4112yes—
192C22×C4×C13C2411yescharacteristic
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C2×Dic26—21no—
198C2×Dic26—21no—
199C2×Dic26—21no—
200C2×Dic26—21no—
201C2×Dic26—21no—
202C2×Dic26C22×C412yes—
203C13×C4⋊C4—24no—
204C13×C4⋊C4—24no—
205C13×C4⋊C4—24no—
206C13×C4⋊C4—24no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—22no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C4⋊C4C2×D412yes—
212C13×C4⋊C4C2×D412yes—
213C13×C22⋊C4—24no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C42×C13—24no—
217C42×C13—24no—
218C42×C13—24no—
219C42×C13—24no—
220C42×C13—24no—
221C42×C13—21no—
222C42×C13—21no—
223C42×C13C2×D412yes—
224C42×C13C2×D412yes—
225C22⋊Dic13—24no—
226C22⋊Dic13—81no—
227#6107—28no—
228#6107—28no—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13—21no—
233C4⋊Dic13—21no—
234C4⋊Dic13C22×C412yes—
235#6101—24no—
236#6101—42no—
237#6101—81no—
238C4×Dic13—42no—
239C4×Dic13—81no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055—21no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055C22×C412yes—
251C2×#1055C22×C412yes—
252C2×#519D1311yescharacteristic
253C2×#451—131no—
254C2×#441—131no—
255C2×C4×Q16—131no—
256#2323—131no—
257#1878—131no—
258#1878—131no—
259#1873—131no—
260#1865—131no—
261#1863—131no—
262#1854—131no—
263#1787—131no—
264#1763—131no—
265C4×#103—131no—
266#1750—131no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—21no—
272C23×C13—21no—
273C23×C13C4×D412yes—
274C23×C13C22×D411yescharacteristic
275Q8×C13—216no—
276Q8×C13—22no—
277Q8×C13—22no—
278Q8×C13—22no—
279Q8×C13—22no—
280Q8×C13—22no—
281Q8×C13—22no—
282Q8×C13C4×D414yes—
283Q8×C13C4×D414yes—
284C2×C4×C13—216no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—21no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—21no—
302C2×C4×C13—21no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13C4×D412yes—
314C2×C4×C13#12012yes—
315C2×C4×C13#12012yes—
316C2×C4×C13C23×C411yescharacteristic
317C2×C4×C13C22×D411yescharacteristic
318C2×C4×C13C22×D411yescharacteristic
319C2×C4×C13C2×#4111yescharacteristic
320C2×C4×C13C2×#4111yescharacteristic
321C2×C4×C13C2×#4111yescharacteristic
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334Dic26—22no—
335Dic26—22no—
336Dic26—41no—
337Dic26—41no—
338#1055—22no—
339#1055—22no—
340#1055—41no—
341#1055—41no—
342C23×Q8C2×D1311yescharacteristic
343C22×Q16—131no—
344C22×Q16—131no—
345C2×C22⋊Q8—131no—
346#519—24no—
347#519—24no—
348C2×C4×Q8—21no—
349C2×C4×Q8—21no—
350C2×C4×Q8—131no—
351C2×C4×Q8C2×D1311yescharacteristic
352C2×C4×Q8C2×D1311yescharacteristic
353C2×C4×Q8C2×D1311yescharacteristic
354C2×C4×Q8C2×D1311yescharacteristic
355C2×#117—21no—
356C2×#117—21no—
357C2×#117C2×D1311yescharacteristic
358C2×#117C2×D1311yescharacteristic
359#451—138no—
360#441—264no—
361C4×Q16—264no—
362C2×#107—131no—
363C2×#106—131no—
364C2×#103—131no—
365C2×#103—131no—
366C2×#103—131no—
367C2×#103—131no—
368C2×#103—131no—
369C2×#103—131no—
370C2×#103—131no—
371C2×#103—131no—
372C2×C22⋊C8—131no—
373C2×C22⋊C8—131no—
374C2×#97—131no—
375C2×C4×C8—131no—
376#391—131no—
377#389—131no—
378#389—261no—
379#388—261no—
380#388—261no—
381#387—261no—
382#380—131no—
383C4×C4⋊C4—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#340—131no—
388#336—131no—
389#336—131no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—41no—
394C22×C13—41no—
395C22×C13—41no—
396C22×C13—41no—
397C22×C13C2×C4×D411yescharacteristic
398C22×C13C2×#12011yescharacteristic
399C22×C13#52511yescharacteristic
400C22×C13#57711yescharacteristic
401C22×C13#57811yescharacteristic
402C22×C13#57811yescharacteristic
403C22×C13#57811yescharacteristic
404C4×C13—22no—
405C4×C13—22no—
406C4×C13—24no—
407C4×C13—24no—
408C4×C13—22no—
409C4×C13—41no—
410C4×C13—42no—
411C4×C13—41no—
412C4×C13—42no—
413C4×C13C2×C4×D411yescharacteristic
414C4×C13C2×C4×D411yescharacteristic
415C4×C13#52511yescharacteristic
416C4×C13#52511yescharacteristic
417Dic13—42no—
418Dic13—42no—
419Dic13—81no—
420Dic13—81no—
421C22×Q8—22no—
422C22×Q8—22no—
423C22×Q8—22no—
424C22×Q8—22no—
425C22×Q8—22no—
426C22×Q8—21no—
427C22×Q8—131no—
428C22×Q8C4×D1314yes—
429C22×Q8C22×D1311yescharacteristic
430C22×Q8C22×D1311yescharacteristic
431C23×C4—21no—
432C23×C4C22×D1311yescharacteristic
433C2×Q16—134no—
434C2×Q16—134no—
435C2×Q16—262no—
436C2×Q16—262no—
437C2×Q16—262no—
438C2×Q16—262no—
439C22×C8—131no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—131no—
443C22⋊Q8—134no—
444C22⋊Q8—262no—
445C4×Q8—28no—
446C4×Q8—28no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8—22no—
450C4×Q8—22no—
451C4×Q8—22no—
452C4×Q8—22no—
453C4×Q8—262no—
454C4×Q8—262no—
455C4×Q8C22⋊D1314yes—
456C4×Q8C22⋊D1314yes—
457#117—28no—
458#117—28no—
459#117—22no—
460#117—22no—
461#117—22no—
462#117—22no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—131no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4—261no—
472C2×C4⋊C4—261no—
473C2×C4⋊C4C22⋊D1311yescharacteristic
474C2×C4⋊C4C22⋊D1311yescharacteristic
475C2×C4⋊C4C22×D1311yescharacteristic
476C2×C4⋊C4C22×D1311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4—261no—
480C2×C22⋊C4C22⋊D1311yescharacteristic
481C2×C22⋊C4C22⋊D1311yescharacteristic
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—261no—
488C2×C42—261no—
489C2×C42C22×D1311yescharacteristic
490C2×C42C22×D1311yescharacteristic
491#107—262no—
492#106—262no—
493#103—134no—
494#103—134no—
495#103—262no—
496#103—262no—
497#103—262no—
498#103—262no—
499#103—262no—
500#103—262no—
501C22⋊C8—134no—
502C22⋊C8—262no—
503#97—262no—
504C4×C8—262no—
505#95—261no—
506#95—261no—
507#95—261no—
508#95—261no—
509#95—261no—
510C2×C13—42no—
511C2×C13C4×#12011yescharacteristic
512C2×C13#294711yescharacteristic
513C2×C13#295011yescharacteristic
514C2×C13#301111yescharacteristic
515C2×C13#301311yescharacteristic
516C2×C13#312111yescharacteristic
517C2×C13#312711yescharacteristic
518C24C2×C22⋊D1311yescharacteristic
519C2×Q8—24no—
520C2×Q8—28no—
521C2×Q8—28no—
522C2×Q8—24no—
523C2×Q8—28no—
524C2×Q8—28no—
525C2×Q8—24no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—132no—
533C2×Q8—261no—
534C2×Q8—261no—
535C2×Q8—261no—
536C2×Q8—261no—
537C2×Q8—261no—
538C2×Q8C2×C4×D1312yes—
539C2×Q8C2×C4×D1312yes—
540C2×Q8#612712yes—
541C2×Q8#612712yes—
542C2×Q8C2×C22⋊D1312yes—
543C2×Q8C2×C22⋊D1312yes—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
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—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4C2×C4×D1312yes—
560C22×C4#612712yes—
561C22×C4C2×C22⋊D1311yescharacteristic
562C22×C4C2×C22⋊D1311yescharacteristic
563C22×C4C2×C22⋊D1311yescharacteristic
564C22×C4C2×C22⋊D1311yescharacteristic
565C22×C4C2×C22⋊D1311yescharacteristic
566C22×C4C23×D1311yescharacteristic
567Q16—268no—
568Q16—268no—
569C2×C8—132no—
570C2×C8—132no—
571C2×C8—261no—
572C2×C8—261no—
573C2×C8—261no—
574C2×C8—261no—
575C2×C8—261no—
576C2×C8—261no—
577C2×C8—261no—
578C2×C8—261no—
579C2×C8—261no—
580C2×C8—261no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—132no—
590C4⋊C4—264no—
591C4⋊C4—261no—
592C4⋊C4—261no—
593C4⋊C4—261no—
594C4⋊C4—261no—
595C4⋊C4—261no—
596C4⋊C4—522no—
597C4⋊C4—1041no—
598C4⋊C4C2×C22⋊D1312yes—
599C4⋊C4C2×C22⋊D1312yes—
600C22⋊C4—24no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—264no—
604C22⋊C4—1041no—
605C42—24no—
606C42—24no—
607C42—24no—
608C42—24no—
609C42—24no—
610C42—21no—
611C42—21no—
612C42—522no—
613C42—1041no—
614C42C2×C22⋊D1312yes—
615C42C2×C22⋊D1312yes—
616C13#2146311yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C4×C22⋊D1312yes—
624C23C22×C22⋊D1311yescharacteristic
625Q8—216no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—262no—
633Q8—262no—
634Q8—521no—
635Q8—521no—
636Q8C4×C22⋊D1314yes—
637Q8C4×C22⋊D1314yes—
638C2×C4—216no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—262no—
668C2×C4—262no—
669C2×C4—521no—
670C2×C4—521no—
671C2×C4—521no—
672C2×C4—521no—
673C2×C4—521no—
674C2×C4—521no—
675C2×C4—521no—
676C2×C4—521no—
677C2×C4—521no—
678C2×C4—521no—
679C2×C4C4×C22⋊D1312yes—
680C2×C4#8820712yes—
681C2×C4#8820712yes—
682C2×C4C22×C4×D1311yescharacteristic
683C2×C4C2×#612711yescharacteristic
684C2×C4C2×#612711yescharacteristic
685C2×C4C2×#612711yescharacteristic
686C2×C4C22×C22⋊D1311yescharacteristic
687C2×C4C22×C22⋊D1311yescharacteristic
688C8—262no—
689C8—262no—
690C8—521no—
691C8—521no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22C2×C4×C22⋊D1311yescharacteristic
700C22#1171949611yescharacteristic
701C22#1171954211yescharacteristic
702C22#1171954311yescharacteristic
703C22#1171954311yescharacteristic
704C22#1171954311yescharacteristic
705C22C2×#8820711yescharacteristic
706C4—22no—
707C4—22no—
708C4—24no—
709C4—24no—
710C4—22no—
711C4—41no—
712C4—42no—
713C4—41no—
714C4—42no—
715C4—522no—
716C4—522no—
717C4—1041no—
718C4—1041no—
719C4C2×C4×C22⋊D1311yescharacteristic
720C4C2×C4×C22⋊D1311yescharacteristic
721C4#1171949611yescharacteristic
722C4#1171949611yescharacteristic
723C2—42no—
724C2C4×#8820711yescharacteristic
725C2#1312367911yescharacteristic
726C2#1312370211yescharacteristic
727C2#1312413111yescharacteristic
728C2#1312415111yescharacteristic
729C2#1312506511yescharacteristic
730C2#1312513611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#519C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC2×#519D13
hypocenterC13#21463
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
2. C2×#11718691C2semidirect
3. C2×C4×#6107C2semidirect
5. #13115177C2semidirect
6. #13115177C2semidirect
8. #13115104C2semidirect
9. #13115090C2semidirect
12. #13114666C2semidirect
13. C4×#88075C2semidirect
33. #11718889C4semidirect
616. C13#21463semidirect

Maximal subgroups

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

subgroupindex
C2×#117188892
C2×#117186912
C2×C4×#61072
#131175182
#131151772
#131151482
#131151042
#131150902
#131150352
#131147712
#131146662
C4×#880752
#131146022
C2×C13×#5192
#2146313