Finite Group Databasebeta

← #15868683

Subgroups — #15868683

Order 3328.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718900C211yesmaximal, characteristic
2C2×#11718691C211yesmaximal, characteristic, complemented
3C2×C4×#6105C211yesmaximal, characteristic, complemented
4#13117518C211yesmaximal, characteristic, complemented
5#13115177C211yesmaximal, characteristic, complemented
6#13115170C211yesmaximal, characteristic, complemented
7#13115143C211yesmaximal, characteristic, complemented
8#13115104C211yesmaximal, characteristic, complemented
9#13115097C211yesmaximal, characteristic, complemented
10#13115029C211yesmaximal, characteristic, complemented
11#13114776C211yesmaximal, characteristic
12#13114661C211yesmaximal, characteristic, complemented
13C4×#88075C211yesmaximal, characteristic, complemented
14#13114602C211yesmaximal, characteristic, complemented
15C2×C13×#520C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C13×#520—24no—
18C13×#520—24no—
19C2×C4×Q8×C13C2211yescharacteristic
20C2×C4×Q8×C13C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13C2211yescharacteristic
24C2×C4×D4×C13C2211yescharacteristic
25C2×C13×#117—21no—
26C2×C13×#117C2211yescharacteristic
27C22×C13×C4⋊C4—21no—
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×#6107C2211yescharacteristic
30C22×#6105C2211yescharacteristic
31C2×#88178C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33#11718900C418yescomplemented
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40#11718873C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718691—24no—
44C4×#6105—24no—
45#11718639—21no—
46#11718633—21no—
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88048C2211yescharacteristic
50C2×#88048C2211yescharacteristic
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
64C2×C13×#41—22no—
65C2×C13×#41—22no—
66C2×C13×#41—22no—
67C2×C13×#41—22no—
68C2×C13×#41—22no—
69C2×C13×#41C2×C414yes—
70C22×Q8×C13C2311yescharacteristic
71C22×D4×C13—21no—
72C22×D4×C13C2311yescharacteristic
73C23×C4×C13—21no—
74C23×C4×C13—21no—
75C23×C4×C13—21no—
76C23×C4×C13—21no—
77C23×C4×C13C2311yescharacteristic
78C22×Dic26C2311yescharacteristic
79C4×Q8×C13—22no—
80C4×Q8×C13—22no—
81C4×Q8×C13—22no—
82C4×Q8×C13D414yes—
83C4×D4×C13—28no—
84C4×D4×C13—28no—
85C4×D4×C13—22no—
86C4×D4×C13—22no—
87C4×D4×C13—22no—
88C4×D4×C13D414yes—
89C13×#117—28no—
90C13×#117—22no—
91C13×#117—22no—
92C2×C13×C4⋊C4—28no—
93C2×C13×C4⋊C4—21no—
94C2×C13×C4⋊C4—21no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4D411yescharacteristic
99C2×C13×C4⋊C4D411yescharacteristic
100C2×C13×C4⋊C4C2311yescharacteristic
101C2×C13×C4⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—21no—
104C2×C13×C22⋊C4D411yescharacteristic
105C2×C13×C22⋊C4D411yescharacteristic
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×#6107C2×C414yescomplemented
115C2×#6105—22no—
116C2×#6105—22no—
117C2×#6105C2×C414yescomplemented
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4⋊Dic13C2311yescharacteristic
121#88178—22no—
122#88178C2×C414yescomplemented
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#88075C2×C414yescomplemented
137#88072—22no—
138#88072—22no—
139#88072C2×C414yescomplemented
140#88071—21no—
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88071—21no—
145C22⋊#1055—22no—
146C22⋊#1055C2×C414yescomplemented
147#88050—22no—
148#88050—22no—
149#88048—22no—
150#88048—22no—
151#88043—22no—
152C4×#1055—22no—
153#21461—131nomaximal, Sylow
154C24×C13—21no—
155C24×C13C2×D411yescharacteristic
156C13×#41—28no—
157C13×#41—28no—
158C13×#41—28no—
159C13×#41—28no—
160C2×Q8×C13—21no—
161C2×Q8×C13—21no—
162C2×Q8×C13—21no—
163C2×Q8×C13C22×C412yes—
164C2×Q8×C13C2×D412yes—
165C2×Q8×C13#4112yes—
166C2×D4×C13—24no—
167C2×D4×C13—24no—
168C2×D4×C13—24no—
169C2×D4×C13—21no—
170C2×D4×C13—21no—
171C2×D4×C13—21no—
172C2×D4×C13C22×C412yes—
173C2×D4×C13C2×D412yes—
174C2×D4×C13#4112yes—
175C22×C4×C13—24no—
176C22×C4×C13—24no—
177C22×C4×C13—21no—
178C22×C4×C13—24no—
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×C13—24no—
186C22×C4×C13—24no—
187C22×C4×C13—24no—
188C22×C4×C13—81no—
189C22×C4×C13—81no—
190C22×C4×C13—81no—
191C22×C4×C13—81no—
192C22×C4×C13—81no—
193C22×C4×C13—81no—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C2×D411yescharacteristic
196C22×C4×C13C2×D411yescharacteristic
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13#4112yes—
201C22×C4×C13C2411yescharacteristic
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C2×Dic26—21no—
207C2×Dic26—21no—
208C2×Dic26—21no—
209C2×Dic26—21no—
210C2×Dic26—21no—
211C2×Dic26C22×C412yes—
212C13×C4⋊C4—24no—
213C13×C4⋊C4—24no—
214C13×C4⋊C4—22no—
215C13×C4⋊C4—24no—
216C13×C4⋊C4—22no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4C2×D412yes—
220C13×C4⋊C4C2×D412yes—
221C13×C22⋊C4—24no—
222C13×C22⋊C4—24no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—22no—
225C42×C13—24no—
226C42×C13—24no—
227C42×C13—21no—
228C42×C13—21no—
229C42×C13C2×D412yes—
230C42×C13C2×D412yes—
231C22⋊Dic13—24no—
232C22⋊Dic13—81no—
233#6107—28no—
234#6105—28no—
235C4⋊Dic13—21no—
236C4⋊Dic13—21no—
237C4⋊Dic13—21no—
238C4⋊Dic13—21no—
239C4⋊Dic13—21no—
240C4⋊Dic13C22×C412yes—
241#6101—24no—
242#6101—42no—
243#6101—81no—
244C4×Dic13—42no—
245C4×Dic13—81no—
246C2×#1055—21no—
247C2×#1055—21no—
248C2×#1055—21no—
249C2×#1055—21no—
250C2×#1055—21no—
251C2×#1055—21no—
252C2×#1055—21no—
253C2×#1055—21no—
254C2×#1055—21no—
255C2×#1055—21no—
256C2×#1055C22×C412yes—
257C2×#1055C22×C412yes—
258C2×#520D1311yescharacteristic
259C2×#452—131no—
260C2×#441—131no—
261C2×C4×SD16—131no—
262#2323—131no—
263#1878—131no—
264#1877—131no—
265#1872—131no—
266#1865—131no—
267#1864—131no—
268#1853—131no—
269#1788—131no—
270#1762—131no—
271C4×#103—131no—
272#1750—131no—
273C23×C13—22no—
274C23×C13—21no—
275C23×C13—22no—
276C23×C13—21no—
277C23×C13—22no—
278C23×C13—21no—
279C23×C13—21no—
280C23×C13—21no—
281C23×C13—21no—
282C23×C13—41no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13C4×D412yes—
287C23×C13C22×D411yescharacteristic
288Q8×C13—22no—
289Q8×C13—22no—
290Q8×C13—22no—
291Q8×C13C4×D414yes—
292D4×C13—216no—
293D4×C13—22no—
294D4×C13—22no—
295D4×C13—22no—
296D4×C13C4×D414yes—
297C2×C4×C13—216no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—21no—
301C2×C4×C13—21no—
302C2×C4×C13—22no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—84no—
324C2×C4×C13—84no—
325C2×C4×C13—84no—
326C2×C4×C13C4×D412yes—
327C2×C4×C13#12012yes—
328C2×C4×C13#12012yes—
329C2×C4×C13C23×C411yescharacteristic
330C2×C4×C13C22×D411yescharacteristic
331C2×C4×C13C22×D411yescharacteristic
332C2×C4×C13C2×#4111yescharacteristic
333C2×C4×C13C2×#4111yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347Dic26—22no—
348Dic26—22no—
349Dic26—41no—
350Dic26—41no—
351#1055—22no—
352#1055—22no—
353#1055—41no—
354#1055—41no—
355C22×#41C2×D1311yescharacteristic
356C22×Q16—131no—
357C22×SD16—131no—
358C2×C22⋊Q8—131no—
359#520—24no—
360#520—24no—
361C2×C4×Q8—131no—
362C2×C4×Q8C2×D1311yescharacteristic
363C2×C4×Q8C2×D1311yescharacteristic
364C2×C4×D4—21no—
365C2×C4×D4—21no—
366C2×C4×D4C2×D1311yescharacteristic
367C2×C4×D4C2×D1311yescharacteristic
368C2×#117—21no—
369C2×#117C2×D1311yescharacteristic
370C22×C4⋊C4—21no—
371C22×C4⋊C4C2×D1311yescharacteristic
372#452—138no—
373#441—264no—
374C4×SD16—264no—
375C2×#106—131no—
376C2×#106—131no—
377C2×#103—131no—
378C2×#103—131no—
379C2×#103—131no—
380C2×#103—131no—
381C2×#103—131no—
382C2×#102—131no—
383C2×#102—131no—
384C2×#102—131no—
385C2×C22⋊C8—131no—
386C2×C22⋊C8—131no—
387C2×#97—131no—
388C2×C4×C8—131no—
389#391—131no—
390#389—131no—
391#389—261no—
392#388—261no—
393#388—261no—
394#387—261no—
395#380—131no—
396C4×C4⋊C4—131no—
397#340—131no—
398#340—131no—
399#340—131no—
400#340—131no—
401#336—131no—
402#336—131no—
403C22×C13—22no—
404C22×C13—22no—
405C22×C13—22no—
406C22×C13—24no—
407C22×C13—41no—
408C22×C13—42no—
409C22×C13—41no—
410C22×C13—42no—
411C22×C13—42no—
412C22×C13—42no—
413C22×C13—41no—
414C22×C13—42no—
415C22×C13—41no—
416C22×C13—42no—
417C22×C13C2×C4×D411yescharacteristic
418C22×C13C2×#12011yescharacteristic
419C22×C13#52511yescharacteristic
420C22×C13#57711yescharacteristic
421C22×C13#57711yescharacteristic
422C22×C13#57711yescharacteristic
423C22×C13#57811yescharacteristic
424C4×C13—22no—
425C4×C13—22no—
426C4×C13—22no—
427C4×C13—24no—
428C4×C13—41no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13—41no—
432C4×C13C2×C4×D411yescharacteristic
433C4×C13C2×C4×D411yescharacteristic
434C4×C13#52511yescharacteristic
435C4×C13#52511yescharacteristic
436Dic13—42no—
437Dic13—42no—
438Dic13—81no—
439Dic13—81no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41—22no—
443C2×#41—22no—
444C2×#41—22no—
445C2×#41C4×D1314yes—
446C22×Q8—131no—
447C22×Q8C22×D1311yescharacteristic
448C22×D4—21no—
449C22×D4C22×D1311yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—21no—
453C23×C4—21no—
454C23×C4C22×D1311yescharacteristic
455C2×Q16—134no—
456C2×Q16—262no—
457C2×Q16—262no—
458C2×SD16—134no—
459C2×SD16—262no—
460C2×SD16—262no—
461C22×C8—131no—
462C22×C8—131no—
463C22×C8—131no—
464C22×C8—131no—
465C22⋊Q8—134no—
466C22⋊Q8—262no—
467C4×Q8—22no—
468C4×Q8—22no—
469C4×Q8—22no—
470C4×Q8—262no—
471C4×Q8—262no—
472C4×Q8C22⋊D1314yes—
473C4×D4—28no—
474C4×D4—28no—
475C4×D4—22no—
476C4×D4—22no—
477C4×D4—22no—
478C4×D4C22⋊D1314yes—
479#117—28no—
480#117—22no—
481#117—22no—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—131no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4C22⋊D1311yescharacteristic
495C2×C4⋊C4C22⋊D1311yescharacteristic
496C2×C4⋊C4C22×D1311yescharacteristic
497C2×C4⋊C4C22×D1311yescharacteristic
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4C22⋊D1311yescharacteristic
503C2×C22⋊C4C22⋊D1311yescharacteristic
504C2×C42—21no—
505C2×C42—21no—
506C2×C42—261no—
507C2×C42—261no—
508C2×C42C22×D1311yescharacteristic
509C2×C42C22×D1311yescharacteristic
510#106—262no—
511#106—262no—
512#103—134no—
513#103—262no—
514#103—262no—
515#103—262no—
516#103—262no—
517#102—134no—
518#102—262no—
519#102—262no—
520C22⋊C8—134no—
521C22⋊C8—262no—
522#97—262no—
523C4×C8—262no—
524#95—261no—
525#95—261no—
526#95—261no—
527#95—261no—
528#95—261no—
529C2×C13—42no—
530C2×C13—44no—
531C2×C13C4×#12011yescharacteristic
532C2×C13#294711yescharacteristic
533C2×C13#295211yescharacteristic
534C2×C13#300911yescharacteristic
535C2×C13#301311yescharacteristic
536C2×C13#312011yescharacteristic
537C2×C13#312511yescharacteristic
538C24—21no—
539C24C2×C22⋊D1311yescharacteristic
540#41—28no—
541#41—28no—
542#41—28no—
543#41—28no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—132no—
548C2×Q8—261no—
549C2×Q8—261no—
550C2×Q8—261no—
551C2×Q8—261no—
552C2×Q8—261no—
553C2×Q8C2×C4×D1312yes—
554C2×Q8#612712yes—
555C2×Q8C2×C22⋊D1312yes—
556C2×D4—24no—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4C2×C4×D1312yes—
563C2×D4#612712yes—
564C2×D4C2×C22⋊D1312yes—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—24no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—81no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4C2×C4×D1312yes—
589C22×C4#612712yes—
590C22×C4C2×C22⋊D1311yescharacteristic
591C22×C4C2×C22⋊D1311yescharacteristic
592C22×C4C2×C22⋊D1311yescharacteristic
593C22×C4C2×C22⋊D1311yescharacteristic
594C22×C4C2×C22⋊D1311yescharacteristic
595C22×C4C23×D1311yescharacteristic
596Q16—268no—
597SD16—268no—
598C2×C8—132no—
599C2×C8—132no—
600C2×C8—261no—
601C2×C8—261no—
602C2×C8—261no—
603C2×C8—261no—
604C2×C8—261no—
605C2×C8—261no—
606C2×C8—261no—
607C2×C8—261no—
608C2×C8—261no—
609C2×C8—261no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4—22no—
613C4⋊C4—24no—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—132no—
618C4⋊C4—264no—
619C4⋊C4—261no—
620C4⋊C4—261no—
621C4⋊C4—261no—
622C4⋊C4—261no—
623C4⋊C4—261no—
624C4⋊C4—522no—
625C4⋊C4—1041no—
626C4⋊C4C2×C22⋊D1312yes—
627C4⋊C4C2×C22⋊D1312yes—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—264no—
633C22⋊C4—1041no—
634C42—24no—
635C42—24no—
636C42—21no—
637C42—21no—
638C42—522no—
639C42—1041no—
640C42C2×C22⋊D1312yes—
641C42C2×C22⋊D1312yes—
642C13#2146111yescharacteristic, complemented, Sylow
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—22no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C4×C22⋊D1312yes—
657C23C22×C22⋊D1311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—262no—
662Q8—262no—
663Q8—521no—
664Q8—521no—
665Q8C4×C22⋊D1314yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4C4×C22⋊D1314yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—521no—
712C2×C4C4×C22⋊D1312yes—
713C2×C4#8820712yes—
714C2×C4#8820712yes—
715C2×C4C22×C4×D1311yescharacteristic
716C2×C4C2×#612711yescharacteristic
717C2×C4C2×#612711yescharacteristic
718C2×C4C2×#612711yescharacteristic
719C2×C4C22×C22⋊D1311yescharacteristic
720C2×C4C22×C22⋊D1311yescharacteristic
721C8—262no—
722C8—262no—
723C8—521no—
724C8—521no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—41no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×C4×C22⋊D1311yescharacteristic
740C22#1171949611yescharacteristic
741C22#1171954111yescharacteristic
742C22#1171954111yescharacteristic
743C22#1171954211yescharacteristic
744C22#1171954311yescharacteristic
745C22C2×#8820711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—24no—
750C4—41no—
751C4—42no—
752C4—42no—
753C4—41no—
754C4—522no—
755C4—522no—
756C4—1041no—
757C4—1041no—
758C4C2×C4×C22⋊D1311yescharacteristic
759C4C2×C4×C22⋊D1311yescharacteristic
760C4#1171949611yescharacteristic
761C4#1171949611yescharacteristic
762C2—42no—
763C2—44no—
764C2C4×#8820711yescharacteristic
765C2#1312367511yescharacteristic
766C2#1312371711yescharacteristic
767C2#1312411311yescharacteristic
768C2#1312415111yescharacteristic
769C2#1312505011yescharacteristic
770C2#1312511311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#520C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
cosocleC22×C4×C13C24
hypercenterC2×#520D13
hypocenterC13#21461
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#11718691C2semidirect
3. C2×C4×#6105C2semidirect
4. #13117518C2semidirect
5. #13115177C2semidirect
6. #13115170C2semidirect
7. #13115143C2semidirect
8. #13115104C2semidirect
9. #13115097C2semidirect
10. #13115029C2semidirect
12. #13114661C2semidirect
13. C4×#88075C2semidirect
14. #13114602C2semidirect
33. #11718900C4semidirect
114. C2×#6107C2×C4semidirect
117. C2×#6105C2×C4semidirect
122. #88178C2×C4semidirect
136. #88075C2×C4semidirect
139. #88072C2×C4semidirect
146. C22⋊#1055C2×C4semidirect
642. C13#21461semidirect

Maximal subgroups

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

subgroupindex
C2×#117189002
C2×#117186912
C2×C4×#61052
#131175182
#131151772
#131151702
#131151432
#131151042
#131150972
#131150292
#131147762
#131146612
C4×#880752
#131146022
C2×C13×#5202
#2146113