Finite Group Databasebeta

← #15883192

Subgroups — #15883192

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718701C211yesmaximal, characteristic
2C2×#11718679C211yesmaximal, characteristic, complemented
3C22×#88050C211yesmaximal, characteristic, complemented
4C22⋊C4×Dic26C211yesmaximal, characteristic, complemented
5#13115716C211yesmaximal, characteristic, complemented
6#13115525C211yesmaximal, characteristic, complemented
7#13115477C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic
9#13115194C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic, complemented
11#13115089C211yesmaximal, characteristic, complemented
12#13115024C211yesmaximal, characteristic, complemented
13#13114669C211yesmaximal, characteristic, complemented
14#13114614C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C2×C4×D4×C13—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×#6105C2211yescharacteristic
22C22×#6105C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24C2×C4×Dic26C2211yescharacteristic
25C2×C4×Dic26C2211yescharacteristic
26C13×#390C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#388—21no—
29C13×#386—21no—
30C13×#385—21no—
31C4×C13×C4⋊C4C2211yescharacteristic
32C4×C13×C22⋊C4C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718873C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718701C418yescomplemented
38#11718679—24no—
39C2×#88050—24no—
40C2×#88050C2211yescharacteristic
41C2×#88050C2211yescharacteristic
42C2×#88050C2211yescharacteristic
43C2×#88050C2211yescharacteristic
44C2×#88050C2211yescharacteristic
45C2×#88050C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718603—21no—
49C22⋊C4×Dic13—21no—
50#11718590C2211yescharacteristic
51#11718590C2211yescharacteristic
52C2×#88043C2211yescharacteristic
53C2×#88043C2211yescharacteristic
54#11718307—21no—
55#11718307—21no—
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718116C2211yescharacteristic
61#11718116C2211yescharacteristic
62C22×D4×C13—21no—
63C22×D4×C13C2311yescharacteristic
64C23×C4×C13—21no—
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C23×Dic13—21no—
68C22×Dic26—22no—
69C22×Dic26—22no—
70C22×Dic26—21no—
71C22×Dic26—22no—
72C22×Dic26—41no—
73C22×Dic26—41no—
74C22×Dic26C2×C414yescomplemented
75C22×Dic26C2311yescharacteristic
76C22×Dic26C2311yescharacteristic
77C13×#121—22no—
78C13×#121C2×C414yes—
79C4×D4×C13—22no—
80C4×D4×C13—41no—
81C4×D4×C13—44no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4C2311yescharacteristic
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4D411yescharacteristic
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C42×C13—21no—
96C2×C42×C13C2311yescharacteristic
97C2×C42×C13C2311yescharacteristic
98C2×C22⋊Dic13—21no—
99C2×#6105—22no—
100C2×#6105—22no—
101C2×#6105—41no—
102C2×#6105—41no—
103C2×#6105C2×C414yescomplemented
104C2×#6105C2×C414yescomplemented
105C2×C4⋊Dic13C2311yescharacteristic
106C2×C4⋊Dic13C2311yescharacteristic
107C2×#6101—21no—
108C2×#6101—21no—
109C2×C4×Dic13—21no—
110C2×C4×Dic13—21no—
111C22×#1055—22no—
112C22×#1055—22no—
113C22×#1055—41no—
114C22×#1055C2311yescharacteristic
115C22×#1055C2311yescharacteristic
116C22×#1055C2311yescharacteristic
117C22×#1055C2311yescharacteristic
118C4×Dic26—22no—
119C4×Dic26—22no—
120C4×Dic26—41no—
121C4×Dic26—41no—
122C13×#95—21no—
123C13×#95—21no—
124C13×#95D411yescharacteristic
125C13×#95D411yescharacteristic
126#88072—22no—
127#88072—41no—
128#88071—21no—
129#88071—21no—
130#88071—21no—
131#88071—21no—
132#88071—21no—
133C22⋊#1055C2×C414yescomplemented
134#88050—22no—
135#88050—22no—
136#88050—22no—
137#88050C2×C414yescomplemented
138#88050C2×C414yescomplemented
139#88050D414yescomplemented
140#88047—22no—
141#88047—41no—
142#88043—22no—
143#88043—41no—
144#22855—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13C2×D411yescharacteristic
147C2×D4×C13—24no—
148C2×D4×C13—21no—
149C2×D4×C13—21no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—42no—
154C2×D4×C13—42no—
155C2×D4×C13C22×C412yes—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—42no—
164C22×C4×C13—42no—
165C22×C4×C13—42no—
166C22×C4×C13—42no—
167C22×C4×C13—81no—
168C22×C4×C13—81no—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13#4112yes—
176C22×C4×C13C2411yescharacteristic
177C22×Dic13—21no—
178C22×Dic13—24no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—42no—
183C22×Dic13—42no—
184C2×Dic26—21no—
185C2×Dic26—21no—
186C2×Dic26—21no—
187C2×Dic26—21no—
188C2×Dic26—21no—
189C2×Dic26—21no—
190C2×Dic26—21no—
191C2×Dic26—28no—
192C2×Dic26—24no—
193C2×Dic26—21no—
194C2×Dic26—44no—
195C2×Dic26—44no—
196C2×Dic26—44no—
197C2×Dic26—42no—
198C2×Dic26—42no—
199C2×Dic26C22×C412yes—
200C2×Dic26C22×C412yes—
201C2×Dic26C2×D412yes—
202C2×Dic26#4112yes—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—42no—
208C13×C4⋊C4—42no—
209C13×C4⋊C4C22×C412yes—
210C13×C4⋊C4C2×D412yes—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—24no—
214C13×C22⋊C4—42no—
215C13×C22⋊C4—42no—
216C13×C22⋊C4—81no—
217C42×C13—21no—
218C42×C13—21no—
219C42×C13—21no—
220C42×C13—21no—
221C42×C13—42no—
222C22⋊Dic13—42no—
223#6105—28no—
224#6105—44no—
225C4⋊Dic13—21no—
226C4⋊Dic13—21no—
227C4⋊Dic13—21no—
228C4⋊Dic13—21no—
229#6101—42no—
230#6101—42no—
231C4×Dic13—42no—
232C4×Dic13—42no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—44no—
243C2×#1055C22×C412yes—
244C2×#1055C22×C412yes—
245C2×#1055C2×D412yes—
246C2×#448—131no—
247C2×#440—131no—
248C22×#103—131no—
249#2361D1311yescharacteristic
250Q8×C22⋊C4—131no—
251#1973—131no—
252#1935—131no—
253#1928—131no—
254#1893—131no—
255#1880—131no—
256#1877—131no—
257#1863—131no—
258#1852—131no—
259#1763—131no—
260#1752—131no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—22no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13C4×D412yes—
273C23×C13AGL(1,ℤ/8)12yes—
274C23×C13#13712yes—
275C23×C13C22×D411yescharacteristic
276D4×C13—22no—
277D4×C13—22no—
278D4×C13—48no—
279D4×C13—41no—
280D4×C13—41no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—21no—
289C2×C4×C13—21no—
290C2×C4×C13—22no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—21no—
298C2×C4×C13—21no—
299C2×C4×C13—21no—
300C2×C4×C13—21no—
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—84no—
309C2×C4×C13—84no—
310C2×C4×C13C4×D412yes—
311C2×C4×C13C23×C411yescharacteristic
312C2×C4×C13C22×D411yescharacteristic
313C2×C4×C13C2×#4111yescharacteristic
314C2×C4×C13C2×#4111yescharacteristic
315C2×C4×C13H(5,𝔽2)11yescharacteristic
316C2×C4×C13H(5,𝔽2)11yescharacteristic
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—48no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330Dic26—22no—
331Dic26—22no—
332Dic26—22no—
333Dic26—22no—
334Dic26—22no—
335Dic26—48no—
336Dic26—41no—
337Dic26—41no—
338Dic26C4×D414yescomplemented
339#1055—22no—
340#1055—22no—
341#1055—22no—
342#1055—41no—
343C23×Q8—131no—
344C22×SD16—131no—
345C22×SD16—131no—
346C23×C8—131no—
347C2×#121C2×D1311yescharacteristic
348C2×C4×Q8—131no—
349C2×C4×Q8—131no—
350C2×C4×D4—21no—
351C2×C4×D4C2×D1311yescharacteristic
352C22×C4⋊C4C2×D1311yescharacteristic
353#448—138no—
354#440—264no—
355C2×#107—131no—
356C2×#107—131no—
357C2×#103—131no—
358C2×#103—131no—
359C2×#103—131no—
360C2×#103—131no—
361C2×#103—131no—
362C2×#103—131no—
363C2×#103—264no—
364C2×#102—131no—
365C2×#102—131no—
366C2×C22⋊C8—131no—
367C2×#97—131no—
368C2×#97—131no—
369#391—131no—
370#391—131no—
371#391—261no—
372#391—261no—
373#390C2×D1311yescharacteristic
374#389C2×D1311yescharacteristic
375#388—21no—
376#386—21no—
377#385—21no—
378#380—131no—
379#380—261no—
380C4×C4⋊C4C2×D1311yescharacteristic
381C4×C22⋊C4—261no—
382C4×C22⋊C4C2×D1311yescharacteristic
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#336—131no—
388#336—131no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—42no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—81no—
399C22×C13—81no—
400C22×C13—81no—
401C22×C13—81no—
402C22×C13#44014yescomplemented
403C22×C13C2×C4×D411yescharacteristic
404C22×C13D4211yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C13C2×#13711yescharacteristic
408C22×C13#57711yescharacteristic
409C22×C13#57811yescharacteristic
410C4×C13—22no—
411C4×C13—42no—
412C4×C13—41no—
413C4×C13—42no—
414C4×C13—41no—
415C4×C13—41no—
416C4×C13—41no—
417C4×C13—81no—
418C4×C13C2×C4×D411yescharacteristic
419C4×C13#51811yescharacteristic
420C4×C13#54611yescharacteristic
421C4×C13#55111yescharacteristic
422Dic13—24no—
423Dic13—42no—
424Dic13—81no—
425Dic13—81no—
426C22×Q8—134no—
427C22×Q8—131no—
428C22×Q8—131no—
429C22×Q8—262no—
430C22×Q8—262no—
431C22×Q8—262no—
432C22×Q8—261no—
433C22×Q8—521no—
434C22×Q8—521no—
435C22×D4—21no—
436C22×D4C22×D1311yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—261no—
440C23×C4C22×D1311yescharacteristic
441C2×SD16—134no—
442C2×SD16—134no—
443C2×SD16—262no—
444C2×SD16—262no—
445C2×SD16—521no—
446C2×SD16—521no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—131no—
450C22×C8—131no—
451C22×C8—262no—
452C22×C8—262no—
453C22×C8—521no—
454#121—22no—
455#121C4×D1314yes—
456C4×Q8—262no—
457C4×Q8—262no—
458C4×Q8—521no—
459C4×Q8—521no—
460C4×D4—22no—
461C4×D4—41no—
462C4×D4—44no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—131no—
468C2×C4⋊C4—131no—
469C2×C4⋊C4—261no—
470C2×C4⋊C4—261no—
471C2×C4⋊C4C22×D1311yescharacteristic
472C2×C4⋊C4C22×D1311yescharacteristic
473C2×C4⋊C4C22×D1311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—261no—
479C2×C22⋊C4C22⋊D1311yescharacteristic
480C2×C22⋊C4C22⋊D1311yescharacteristic
481C2×C42—21no—
482C2×C42—261no—
483C2×C42—261no—
484C2×C42C22×D1311yescharacteristic
485C2×C42C22×D1311yescharacteristic
486#107—262no—
487#107—521no—
488#103—134no—
489#103—134no—
490#103—134no—
491#103—262no—
492#103—262no—
493#103—262no—
494#102—262no—
495#102—521no—
496C22⋊C8—134no—
497#97—262no—
498#97—521no—
499#95—21no—
500#95—21no—
501#95—261no—
502#95—261no—
503#95—261no—
504#95—261no—
505#95—261no—
506#95C22⋊D1311yescharacteristic
507#95C22⋊D1311yescharacteristic
508C2×C13—24no—
509C2×C13—82no—
510C2×C13#235811yescharacteristic
511C2×C13C2×#44011yescharacteristic
512C2×C13#294711yescharacteristic
513C2×C13#326511yescharacteristic
514C2×C13#327011yescharacteristic
515C2×C13#330811yescharacteristic
516C2×C13#332011yescharacteristic
517C24—21no—
518C24C2×C22⋊D1311yescharacteristic
519C2×Q8—132no—
520C2×Q8—132no—
521C2×Q8—132no—
522C2×Q8—132no—
523C2×Q8—268no—
524C2×Q8—264no—
525C2×Q8—261no—
526C2×Q8—261no—
527C2×Q8—261no—
528C2×Q8—261no—
529C2×Q8—261no—
530C2×Q8—261no—
531C2×Q8—261no—
532C2×Q8—261no—
533C2×Q8—522no—
534C2×Q8—522no—
535C2×Q8—524no—
536C2×Q8—524no—
537C2×Q8—524no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4C2×C4×D1312yes—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—81no—
559C22×C4—81no—
560C22×C4—261no—
561C22×C4—264no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—522no—
566C22×C4—522no—
567C22×C4C2×C4×D1312yes—
568C22×C4#612712yes—
569C22×C4C2×C22⋊D1311yescharacteristic
570C22×C4C2×C22⋊D1311yescharacteristic
571C22×C4C2×C22⋊D1311yescharacteristic
572C22×C4C2×C22⋊D1311yescharacteristic
573C22×C4C2×C22⋊D1311yescharacteristic
574C22×C4C23×D1311yescharacteristic
575SD16—268no—
576SD16—524no—
577C2×C8—132no—
578C2×C8—132no—
579C2×C8—132no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—524no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—261no—
597C4⋊C4—261no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—522no—
601C4⋊C4—522no—
602C4⋊C4C2×C4×D1312yes—
603C4⋊C4D4×D1312yes—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—24no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—81no—
610C22⋊C4—522no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C42—522no—
617C42—522no—
618C13#2285511yescharacteristic, complemented, Sylow
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23C4×C22⋊D1312yes—
631C23#8818612yes—
632C23#8820512yes—
633C23C22×C22⋊D1311yescharacteristic
634Q8—134no—
635Q8—262no—
636Q8—262no—
637Q8—262no—
638Q8—262no—
639Q8—262no—
640Q8—528no—
641Q8—521no—
642Q8—521no—
643D4—22no—
644D4—22no—
645D4—48no—
646D4—41no—
647D4—41no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
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—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—262no—
678C2×C4—262no—
679C2×C4—262no—
680C2×C4—262no—
681C2×C4—528no—
682C2×C4—521no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4—521no—
690C2×C4C4×C22⋊D1312yes—
691C2×C4C22×C4×D1311yescharacteristic
692C2×C4C2×#612711yescharacteristic
693C2×C4C2×D4×D1311yescharacteristic
694C2×C4#8825111yescharacteristic
695C2×C4#41×D1311yescharacteristic
696C2×C4#8825611yescharacteristic
697C8—262no—
698C8—262no—
699C8—262no—
700C8—521no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—22no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22#1171867914yescomplemented
715C22C2×C4×C22⋊D1311yescharacteristic
716C22C2×#8818611yescharacteristic
717C22D4×C22⋊D1311yescharacteristic
718C22C2×#8820511yescharacteristic
719C22#1171953411yescharacteristic
720C22#1171954111yescharacteristic
721C22#1171954311yescharacteristic
722C4—22no—
723C4—41no—
724C4—42no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—264no—
731C4—522no—
732C4—1041no—
733C4—1041no—
734C4C4×D4×D1311yescharacteristic
735C4#1171925011yescharacteristic
736C4#1171925511yescharacteristic
737C4#1171926111yescharacteristic
738C2—24no—
739C2—82no—
740C2#1311781311yescharacteristic
741C2C2×#1171867911yescharacteristic
742C2#1312367511yescharacteristic
743C2#1312632711yescharacteristic
744C2#1312640211yescharacteristic
745C2#1312682111yescharacteristic
746C2#1312700111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
cosocleC22×C4×C13C24
hypercenter#2361D13
hypocenterC13#22855
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
2. C2×#11718679C2semidirect
3. C22×#88050C2semidirect
4. C22⋊C4×Dic26C2semidirect
5. #13115716C2semidirect
6. #13115525C2semidirect
7. #13115477C2semidirect
9. #13115194C2semidirect
10. #13115170C2semidirect
11. #13115089C2semidirect
12. #13115024C2semidirect
13. #13114669C2semidirect
14. #13114614C2semidirect
37. #11718701C4semidirect
74. C22×Dic26C2×C4semidirect
103. C2×#6105C2×C4semidirect
104. C2×#6105C2×C4semidirect
133. C22⋊#1055C2×C4semidirect
137. #88050C2×C4semidirect
138. #88050C2×C4semidirect
139. #88050D4semidirect
338. Dic26C4×D4semidirect
402. C22×C13#440semidirect
618. C13#22855semidirect
714. C22#11718679semidirect

Maximal subgroups

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

subgroupindex
C2×#117187012
C2×#117186792
C22×#880502
C22⋊C4×Dic262
#131157162
#131155252
#131154772
#131152652
#131151942
#131151702
#131150892
#131150242
#131146692
#131146142
C13×#23612
#2285513