Finite Group Databasebeta

← #15883172

Subgroups — #15883172

Order 3328.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718879C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic, complemented
3C22×#88072C211yesmaximal, characteristic
4#13117839C211yesmaximal, characteristic, complemented
5#13115716C211yesmaximal, characteristic, complemented
6#13115536C211yesmaximal, characteristic, complemented
7#13115453C211yesmaximal, characteristic, complemented
8#13115257C211yesmaximal, characteristic, complemented
9#13115194C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic, complemented
11#13115083C211yesmaximal, characteristic, complemented
12#13115023C211yesmaximal, characteristic, complemented
13#13114661C211yesmaximal, characteristic, complemented
14#13114614C211yesmaximal, characteristic, complemented
15D4×C13×C22⋊C4C211yesmaximal, characteristic
16C23×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C22⋊C4—21no—
20C22×#6105C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C23×#1055C2211yescharacteristic
25C2×C4×Dic26C2211yescharacteristic, complemented
26C13×#390C2211yescharacteristic
27C13×#390C2211yescharacteristic
28C13×#386—21no—
29C13×#386—21no—
30C13×#380C2211yescharacteristic
31C13×#379—21no—
32C4×C13×C22⋊C4C2211yescharacteristic
33#11718879C418yescomplemented
34C2×#88072—24no—
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39C2×#88072C2211yescharacteristic
40C2×#88072C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718679—24no—
43C2×#88050C2211yescharacteristic, complemented
44C2×#88050C2211yescharacteristic, complemented
45C2×#88047C2211yescharacteristic, complemented
46C2×#88047C2211yescharacteristic, complemented
47#11718607—21no—
48C22⋊C4×Dic13—21no—
49C4×C4⋊Dic13C2211yescharacteristic, complemented
50#11718590C2211yescharacteristic, complemented
51#11718589C2211yescharacteristic, complemented
52C2×#88043C2211yescharacteristic, complemented
53C2×#88043C2211yescharacteristic, complemented
54#11718316—21no—
55#11718308—21no—
56#11718121C2211yescharacteristic, complemented
57#11718121C2211yescharacteristic, complemented
58#11718121C2211yescharacteristic, complemented
59#11718121C2211yescharacteristic, complemented
60#11718116C2211yescharacteristic, complemented
61#11718116C2211yescharacteristic, complemented
62C25×C13—21no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—21no—
66C22×D4×C13—22no—
67C22×D4×C13—41no—
68C22×D4×C13—41no—
69C22×D4×C13C2×C414yes—
70C22×D4×C13C2311yescharacteristic
71C22×D4×C13C2311yescharacteristic
72C23×C4×C13—21no—
73C23×C4×C13—21no—
74C23×C4×C13C2311yescharacteristic
75C23×Dic13—21no—
76C22×Dic26C2311yescharacteristic
77C4×D4×C13—22no—
78C4×D4×C13—22no—
79C4×D4×C13—41no—
80C4×D4×C13—41no—
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—44no—
91C2×C13×C22⋊C4D411yescharacteristic
92C2×C13×C22⋊C4D411yescharacteristic
93C2×C42×C13C2311yescharacteristic
94C2×C42×C13C2311yescharacteristic
95C2×C22⋊Dic13—21no—
96C2×#6105—22no—
97C2×#6105—22no—
98C2×#6105—41no—
99C2×#6105—41no—
100C2×#6105C2×C414yescomplemented
101C2×#6105C2×C414yescomplemented
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—41no—
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4⋊Dic13C2311yescharacteristic
107C2×C4⋊Dic13C2311yescharacteristic
108#88178—22no—
109#88178C2×C414yescomplemented
110C2×#6101—21no—
111C2×#6101—21no—
112C2×#6101—21no—
113C2×C4×Dic13—21no—
114C2×C4×Dic13—21no—
115C22×#1055—22no—
116C22×#1055—22no—
117C22×#1055—41no—
118C22×#1055C2311yescharacteristic
119C22×#1055C2311yescharacteristic
120C22×#1055C2311yescharacteristic
121C22×#1055C2311yescharacteristic
122C4×Dic26—22no—
123C4×Dic26—41no—
124C13×#95—21no—
125C13×#95D411yescharacteristic
126C13×#95D411yescharacteristic
127#88072—22no—
128#88072—22no—
129#88072—22no—
130#88072C2×C414yescomplemented
131#88072C2×C414yescomplemented
132#88072D414yes—
133#88071—21no—
134#88071—21no—
135#88071—21no—
136#88071—21no—
137C22⋊#1055C2×C414yescomplemented
138#88050—22no—
139#88050—41no—
140#88047—22no—
141#88047—41no—
142#88043—22no—
143#88043—41no—
144#22854—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—24no—
148C24×C13—42no—
149C24×C13—42no—
150C24×C13—42no—
151C24×C13—42no—
152C24×C13—81no—
153C24×C13—81no—
154C24×C13C2×D411yescharacteristic
155C2×D4×C13—28no—
156C2×D4×C13—24no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13—21no—
163C2×D4×C13—21no—
164C2×D4×C13—21no—
165C2×D4×C13—44no—
166C2×D4×C13—44no—
167C2×D4×C13—44no—
168C2×D4×C13—42no—
169C2×D4×C13—42no—
170C2×D4×C13C22×C412yes—
171C2×D4×C13C22×C412yes—
172C2×D4×C13C2×D412yes—
173C2×D4×C13#4112yes—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—42no—
181C22×C4×C13—42no—
182C22×C4×C13—42no—
183C22×C4×C13—42no—
184C22×C4×C13—81no—
185C22×C4×C13—81no—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2×D411yescharacteristic
192C22×C4×C13#4112yes—
193C22×C4×C13C2411yescharacteristic
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—42no—
199C22×Dic13—42no—
200C22×Dic13—81no—
201C2×Dic26—21no—
202C2×Dic26—21no—
203C2×Dic26—21no—
204C2×Dic26—21no—
205C2×Dic26—21no—
206C2×Dic26C22×C412yes—
207C13×C4⋊C4—21no—
208C13×C4⋊C4—21no—
209C13×C4⋊C4—21no—
210C13×C4⋊C4—21no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—42no—
214C13×C22⋊C4—42no—
215C13×C22⋊C4—42no—
216C13×C22⋊C4—42no—
217C13×C22⋊C4—42no—
218C13×C22⋊C4—81no—
219C13×C22⋊C4—81no—
220C42×C13—21no—
221C42×C13—21no—
222C42×C13—21no—
223C42×C13—21no—
224C22⋊Dic13—24no—
225#6105—28no—
226#6105—44no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229C4⋊Dic13—21no—
230C4⋊Dic13—21no—
231C4⋊Dic13—42no—
232C4⋊Dic13C22×C412yes—
233C4⋊Dic13C2×D412yes—
234#6101—24no—
235#6101—42no—
236#6101—81no—
237C4×Dic13—42no—
238C4×Dic13—81no—
239C2×#1055—21no—
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—44no—
249C2×#1055C22×C412yes—
250C2×#1055C22×C412yes—
251C2×#1055C2×D412yes—
252C2×#450—131no—
253C2×#440—131no—
254C22×#102—131no—
255#2360—131no—
256D4×C22⋊C4D1311yescharacteristic
257#1973—131no—
258#1936—131no—
259#1925—131no—
260#1892—131no—
261#1880—131no—
262#1877—131no—
263#1862—131no—
264#1852—131no—
265#1762—131no—
266#1752—131no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—48no—
276C23×C13—41no—
277C23×C13—41no—
278C23×C13—41no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13—41no—
284C23×C13—41no—
285C23×C13—41no—
286C23×C13—48no—
287C23×C13—84no—
288C23×C13—84no—
289C23×C13—84no—
290C23×C13—84no—
291C23×C13—84no—
292C23×C13C4×D412yes—
293C23×C13AGL(1,ℤ/8)12yes—
294C23×C13#13712yes—
295C23×C13C22×D411yescharacteristic
296D4×C13—22no—
297D4×C13—22no—
298D4×C13—22no—
299D4×C13—22no—
300D4×C13—22no—
301D4×C13—48no—
302D4×C13—41no—
303D4×C13—41no—
304D4×C13C4×D414yes—
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—21no—
314C2×C4×C13—21no—
315C2×C4×C13—21no—
316C2×C4×C13—21no—
317C2×C4×C13—21no—
318C2×C4×C13—21no—
319C2×C4×C13—21no—
320C2×C4×C13—21no—
321C2×C4×C13—21no—
322C2×C4×C13—21no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—84no—
330C2×C4×C13—84no—
331C2×C4×C13C4×D412yes—
332C2×C4×C13C23×C411yescharacteristic
333C2×C4×C13C22×D411yescharacteristic
334C2×C4×C13C2×#4111yescharacteristic
335C2×C4×C13C2×#4111yescharacteristic
336C2×C4×C13H(5,𝔽2)11yescharacteristic
337C2×C4×C13H(5,𝔽2)11yescharacteristic
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—84no—
351Dic26—22no—
352Dic26—22no—
353Dic26—41no—
354Dic26—41no—
355#1055—22no—
356#1055—22no—
357#1055—22no—
358#1055—41no—
359C23×D4C2×D1311yescharacteristic
360C22×SD16—131no—
361C22×SD16—131no—
362C23×C8—131no—
363C2×C22⋊Q8—131no—
364C2×C4×Q8—131no—
365C2×C4×D4C2×D1311yescharacteristic
366C2×C4×D4C2×D1311yescharacteristic
367C22×C4⋊C4—131no—
368C22×C22⋊C4—21no—
369#450—138no—
370#440—264no—
371C2×#107—131no—
372C2×#107—131no—
373C2×#103—131no—
374C2×#103—131no—
375C2×#102—131no—
376C2×#102—131no—
377C2×#102—131no—
378C2×#102—131no—
379C2×#102—131no—
380C2×#102—131no—
381C2×#102—264no—
382C2×C22⋊C8—131no—
383C2×#97—131no—
384C2×#97—131no—
385#391—131no—
386#390C2×D1311yescharacteristic
387#390C2×D1311yescharacteristic
388#389—131no—
389#389—261no—
390#387—261no—
391#386—21no—
392#386—21no—
393#385—261no—
394#380C2×D1311yescharacteristic
395#379—21no—
396C4×C4⋊C4—131no—
397C4×C22⋊C4—261no—
398C4×C22⋊C4C2×D1311yescharacteristic
399#340—131no—
400#340—131no—
401#340—131no—
402#340—131no—
403#336—131no—
404#336—131no—
405C22×C13—22no—
406C22×C13—22no—
407C22×C13—22no—
408C22×C13—22no—
409C22×C13—22no—
410C22×C13—22no—
411C22×C13—24no—
412C22×C13—42no—
413C22×C13—42no—
414C22×C13—42no—
415C22×C13—42no—
416C22×C13—42no—
417C22×C13—42no—
418C22×C13—42no—
419C22×C13—42no—
420C22×C13—42no—
421C22×C13—816no—
422C22×C13—81no—
423C22×C13—81no—
424C22×C13—81no—
425C22×C13—81no—
426C22×C13#44014yescomplemented
427C22×C13C2×C4×D411yescharacteristic
428C22×C13D4211yescharacteristic
429C22×C13#54611yescharacteristic
430C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
431C22×C13C2×#13711yescharacteristic
432C22×C13#57611yescharacteristic
433C22×C13#57711yescharacteristic
434C4×C13—22no—
435C4×C13—41no—
436C4×C13—41no—
437C4×C13—41no—
438C4×C13—41no—
439C4×C13—81no—
440C4×C13—81no—
441C4×C13C2×C4×D411yescharacteristic
442C4×C13#51811yescharacteristic
443C4×C13#54611yescharacteristic
444C4×C13#55111yescharacteristic
445Dic13—42no—
446Dic13—42no—
447Dic13—42no—
448Dic13—81no—
449C25—21no—
450C22×Q8—131no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—21no—
455C22×D4—41no—
456C22×D4—41no—
457C22×D4C4×D1314yes—
458C22×D4C22×D1311yescharacteristic
459C22×D4C22×D1311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—261no—
463C23×C4C22×D1311yescharacteristic
464C2×SD16—134no—
465C2×SD16—134no—
466C2×SD16—262no—
467C2×SD16—262no—
468C2×SD16—521no—
469C2×SD16—521no—
470C22×C8—131no—
471C22×C8—131no—
472C22×C8—131no—
473C22×C8—131no—
474C22×C8—262no—
475C22×C8—262no—
476C22×C8—521no—
477C22⋊Q8—134no—
478C22⋊Q8—262no—
479C4×Q8—262no—
480C4×Q8—521no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—41no—
484C4×D4—41no—
485C2×C4⋊C4—131no—
486C2×C4⋊C4—131no—
487C2×C4⋊C4—131no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—521no—
494C2×C4⋊C4C22×D1311yescharacteristic
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—44no—
504C2×C22⋊C4—261no—
505C2×C22⋊C4C22⋊D1311yescharacteristic
506C2×C22⋊C4C22⋊D1311yescharacteristic
507C2×C42—261no—
508C2×C42—261no—
509C2×C42C22×D1311yescharacteristic
510C2×C42C22×D1311yescharacteristic
511#107—262no—
512#107—521no—
513#103—262no—
514#103—521no—
515#102—134no—
516#102—134no—
517#102—134no—
518#102—262no—
519#102—262no—
520#102—262no—
521C22⋊C8—134no—
522#97—262no—
523#97—521no—
524#95—21no—
525#95—261no—
526#95—261no—
527#95—261no—
528#95—261no—
529#95C22⋊D1311yescharacteristic
530#95C22⋊D1311yescharacteristic
531C2×C13—24no—
532C2×C13—44no—
533C2×C13—82no—
534C2×C13#235811yescharacteristic
535C2×C13C2×#44011yescharacteristic
536C2×C13#294611yescharacteristic
537C2×C13#326411yescharacteristic
538C2×C13#326611yescharacteristic
539C2×C13#331011yescharacteristic
540C2×C13#331411yescharacteristic
541C24—21no—
542C24—21no—
543C24—24no—
544C24—42no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—81no—
549C24—81no—
550C24C2×C22⋊D1311yescharacteristic
551C2×Q8—132no—
552C2×Q8—261no—
553C2×Q8—261no—
554C2×Q8—261no—
555C2×Q8—261no—
556C2×Q8—261no—
557C2×D4—28no—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4C2×C4×D1312yes—
573C2×D4C2×C4×D1312yes—
574C2×D4D4×D1312yes—
575C2×D4#612912yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—81no—
587C22×C4—81no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—522no—
593C22×C4—522no—
594C22×C4—1041no—
595C22×C4C2×C4×D1312yes—
596C22×C4#612712yes—
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C2×C22⋊D1311yescharacteristic
602C22×C4C23×D1311yescharacteristic
603SD16—268no—
604SD16—524no—
605C2×C8—132no—
606C2×C8—132no—
607C2×C8—132no—
608C2×C8—261no—
609C2×C8—261no—
610C2×C8—261no—
611C2×C8—261no—
612C2×C8—261no—
613C2×C8—261no—
614C2×C8—261no—
615C2×C8—261no—
616C2×C8—261no—
617C2×C8—524no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—132no—
623C4⋊C4—132no—
624C4⋊C4—264no—
625C4⋊C4—261no—
626C4⋊C4—261no—
627C4⋊C4—261no—
628C4⋊C4—261no—
629C4⋊C4—522no—
630C4⋊C4—522no—
631C4⋊C4—1041no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—264no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—522no—
647C42—1041no—
648C13#2285411yescharacteristic, complemented, Sylow
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×C22⋊D1312yes—
675C23#8818612yes—
676C23#8820512yes—
677C23C22×C22⋊D1311yescharacteristic
678Q8—262no—
679Q8—262no—
680Q8—521no—
681Q8—521no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4#8813514yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—84no—
716C2×C4—84no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—1044no—
730C2×C4C4×C22⋊D1312yes—
731C2×C4C22×C4×D1311yescharacteristic
732C2×C4C2×#612711yescharacteristic
733C2×C4C2×D4×D1311yescharacteristic
734C2×C4C2×#612911yescharacteristic
735C2×C4#8825111yescharacteristic
736C2×C4#8825111yescharacteristic
737C8—262no—
738C8—262no—
739C8—262no—
740C8—521no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22#1171867914yescomplemented
763C22C2×C4×C22⋊D1311yescharacteristic
764C22C2×#8818611yescharacteristic
765C22D4×C22⋊D1311yescharacteristic
766C22#1171951111yescharacteristic
767C22C2×#8820511yescharacteristic
768C22#1171954011yescharacteristic
769C22#1171954111yescharacteristic
770C4—22no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—522no—
778C4—522no—
779C4—522no—
780C4—1041no—
781C4C2×#8813511yescharacteristic
782C4#1171919111yescharacteristic
783C4#1171919511yescharacteristic
784C4#1171920011yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#1311781511yescharacteristic
789C2C2×#1171867911yescharacteristic
790C2#1312366811yescharacteristic
791C2#1312631211yescharacteristic
792C2#1312634211yescharacteristic
793C2#1312685711yescharacteristic
794C2#1312691711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC23×D4×C13C22
cosocleC22×C4×C13C24
hypercenterD4×C22⋊C4D13
hypocenterC13#22854
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718679C2semidirect
4. #13117839C2semidirect
5. #13115716C2semidirect
6. #13115536C2semidirect
7. #13115453C2semidirect
8. #13115257C2semidirect
9. #13115194C2semidirect
10. #13115170C2semidirect
11. #13115083C2semidirect
12. #13115023C2semidirect
13. #13114661C2semidirect
14. #13114614C2semidirect
25. C2×C4×Dic26C22semidirect
33. #11718879C4semidirect
43. C2×#88050C22semidirect
44. C2×#88050C22semidirect
45. C2×#88047C22semidirect
46. C2×#88047C22semidirect
49. C4×C4⋊Dic13C22semidirect
50. #11718590C22semidirect
51. #11718589C22semidirect
52. C2×#88043C22semidirect
53. C2×#88043C22semidirect
56. #11718121C22semidirect
57. #11718121C22semidirect
58. #11718121C22semidirect
59. #11718121C22semidirect
60. #11718116C22semidirect
61. #11718116C22semidirect
100. C2×#6105C2×C4semidirect
101. C2×#6105C2×C4semidirect
109. #88178C2×C4semidirect
130. #88072C2×C4semidirect
131. #88072C2×C4semidirect
137. C22⋊#1055C2×C4semidirect
426. C22×C13#440semidirect
648. C13#22854semidirect
762. C22#11718679semidirect

Maximal subgroups

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

subgroupindex
C2×#117188792
C2×#117186792
C22×#880722
#131178392
#131157162
#131155362
#131154532
#131152572
#131151942
#131151702
#131150832
#131150232
#131146612
#131146142
D4×C13×C22⋊C42
#2285413