Finite Group Databasebeta

← #15785331

Subgroups — #15785331

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic26C211yesmaximal, characteristic
2C2×#11718307C212yesmaximal
3C2×#11718637C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic
5#13113088C212yesmaximal
6#13113087C212yesmaximal
7#13113066C211yesmaximal, characteristic
8#13113065C211yesmaximal, characteristic
9#13113065C211yesmaximal, characteristic
10#13113064C212yesmaximal
11C13×C4⋊#95C211yesmaximal, characteristic
12C23×Dic26C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×C4⋊Dic13C2211yescharacteristic
17C22×C4⋊Dic13C2211yescharacteristic
18C22×C4⋊Dic13C2211yescharacteristic
19C22×#6101C2212yes—
20C22×#6101C2211yescharacteristic
21C22×#6101C2211yescharacteristic
22C22×#6101C2212yes—
23C22×C4×Dic13C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C2×C4×Dic26—24no—
27C2×C4×Dic26—24no—
28C2×C4×Dic26C418yescomplemented
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718637—24no—
39C4⋊C4×Dic13—24no—
40#11718307—28no—
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×Dic26—22no—
53C22×Dic26—22no—
54C22×Dic26—22no—
55C22×Dic26—22no—
56C22×Dic26C2×C414yes—
57C22×Dic26D414yes—
58C22×Dic26Q814yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4Q814yescomplemented
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13C2×C414yes—
68C2×C4⋊Dic13—22no—
69C2×C4⋊Dic13—22no—
70C2×C4⋊Dic13—22no—
71C2×C4⋊Dic13—22no—
72C2×C4⋊Dic13—22no—
73C2×C4⋊Dic13—22no—
74C2×C4⋊Dic13—22no—
75C2×C4⋊Dic13C2×C414yes—
76C2×C4⋊Dic13Q814yescomplemented
77C2×#6101—22no—
78C2×#6101—22no—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×#6101—24no—
82C2×#6101—24no—
83C2×#6101—24no—
84C2×#6101—24no—
85C2×#6101—42no—
86C2×#6101—42no—
87C2×#6101C2×C414yes—
88C2×#6101C2×C414yes—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13C2×C414yes—
95C2×C4×Dic13C2×C414yes—
96C2×C4×Dic13D414yes—
97C2×C4×Dic13D414yes—
98C4×Dic26—232no—
99C13×#95—24no—
100C13×#95—42no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—24no—
105#88071—42no—
106#88071—42no—
107#88071—42no—
108#13926—131nomaximal, Sylow
109C24×C13C2411yescharacteristic
110C22×C4×C13—21no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—22no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—22no—
119C22×C4×C13—22no—
120C22×C4×C13—21no—
121C22×C4×C13—22no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C22×C412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D412yes—
139C22×C4×C13C2×Q814yes—
140C22×C4×C13C2×Q812yes—
141C22×C4×C13C2×Q812yes—
142C22×C4×C13C2×Q812yes—
143C22×C4×C13#4112yes—
144C22×C4×C13#4112yes—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—22no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—22no—
165C22×Dic13—22no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13C22×C412yes—
173C22×Dic13C22×C412yes—
174C22×Dic13C22×C412yes—
175C22×Dic13C22×C412yes—
176C22×Dic13C2×D412yes—
177C22×Dic13C2×D412yes—
178C22×Dic13C2×D412yes—
179C22×Dic13C2×D412yes—
180C22×Dic13C2×D412yes—
181C22×Dic13C2×D412yes—
182C22×Dic13C2×Q814yes—
183C22×Dic13C2×Q812yes—
184C22×Dic13C2×Q812yes—
185C22×Dic13#4112yes—
186C22×Dic13#4112yes—
187C2×Dic26—28no—
188C2×Dic26—28no—
189C2×Dic26—28no—
190C2×Dic26—28no—
191C2×Dic26—28no—
192C2×Dic26—28no—
193C2×Dic26C4⋊C4116yescomplemented
194C13×C4⋊C4—28no—
195C13×C4⋊C4—44no—
196C42×C13—28no—
197C4⋊Dic13—28no—
198C4⋊Dic13—28no—
199C4⋊Dic13—44no—
200#6101—28no—
201#6101—28no—
202#6101—48no—
203#6101—48no—
204C4×Dic13—28no—
205C4×Dic13—48no—
206C4×Dic13C22⋊C4116yes—
207C22×C4×Q8—131no—
208C2×#391—132no—
209C2×#384—131no—
210C2×C4×C4⋊C4—131no—
211#1441—132no—
212#1441—132no—
213C4⋊#95—131no—
214C4⋊#95—132no—
215C4⋊#95—131no—
216C4⋊#95—131no—
217C4⋊#95D1311yescharacteristic
218C23×C13C23×C411yescharacteristic
219C23×C13C22×D411yescharacteristic
220C23×C13C22×D411yescharacteristic
221C23×C13C22×D411yescharacteristic
222C23×C13C22×Q811yescharacteristic
223C23×C13C22×Q811yescharacteristic
224C23×C13C22×Q811yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13H(5,𝔽2)11yescharacteristic
230C23×C13H(5,𝔽2)11yescharacteristic
231C23×C132−1+411yescharacteristic
232C23×C132−1+411yescharacteristic
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—24no—
244C2×C4×C13—24no—
245C2×C4×C13—42no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13C2×C22⋊C414yes—
261C2×C4×C13C2×C4⋊C414yes—
262C2×C4×C13C4×Q814yes—
263C2×C4×C13C4×Q814yes—
264C2×C4×C13C22⋊Q814yes—
265C2×C4×C13C22⋊Q814yes—
266C2×C4×C13#12414yes—
267C2×C4×C13C4⋊Q814yes—
268C2×Dic13—22no—
269C2×Dic13—22no—
270C2×Dic13—22no—
271C2×Dic13—22no—
272C2×Dic13—22no—
273C2×Dic13—22no—
274C2×Dic13—22no—
275C2×Dic13—22no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—22no—
282C2×Dic13—22no—
283C2×Dic13—24no—
284C2×Dic13—24no—
285C2×Dic13—24no—
286C2×Dic13—42no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—42no—
292C2×Dic13—42no—
293C2×Dic13—42no—
294C2×Dic13—42no—
295C2×Dic13—42no—
296C2×Dic13—42no—
297C2×Dic13—42no—
298C2×Dic13—42no—
299C2×Dic13—42no—
300C2×Dic13—42no—
301C2×Dic13C2×C22⋊C414yes—
302C2×Dic13C2×C22⋊C414yes—
303C2×Dic13C2×C4⋊C414yes—
304C2×Dic13C2×C4⋊C414yes—
305C2×Dic13#11714yes—
306C2×Dic13#12114yes—
307C2×Dic13#12114yes—
308C2×Dic13C22⋊Q814yes—
309C2×Dic13C22⋊Q814yes—
310Dic26—232no—
311C23×Q8—131no—
312C2×C4×Q8—138no—
313C2×C4×Q8—264no—
314C2×C4×Q8—264no—
315C22×C4⋊C4—131no—
316C22×C4⋊C4—131no—
317C22×C4⋊C4—131no—
318C22×C4⋊C4—131no—
319C22×C4⋊C4—132no—
320C22×C4⋊C4—131no—
321C22×C4⋊C4—132no—
322C22×C4⋊C4C2×D1311yescharacteristic
323C22×C4⋊C4C2×D1311yescharacteristic
324C22×C42—131no—
325C22×C42—131no—
326C22×C42—132no—
327C22×C42C2×D1311yescharacteristic
328#391—268no—
329#384—264no—
330C4×C4⋊C4—264no—
331C2×#95—132no—
332C2×#95—132no—
333C2×#95—132no—
334C2×#95—132no—
335C2×#95—132no—
336C2×#95—132no—
337C2×#95—132no—
338C2×#95C2×D1312yes—
339C2×#95C2×D1312yes—
340C22×C13C22×C22⋊C411yescharacteristic
341C22×C13C22×C4⋊C411yescharacteristic
342C22×C13C2×#11711yescharacteristic
343C22×C13C2×C4×Q811yescharacteristic
344C22×C13C2×C4×Q811yescharacteristic
345C22×C13#52011yescharacteristic
346C22×C13#52011yescharacteristic
347C22×C13C2×#12111yescharacteristic
348C22×C13C2×#12111yescharacteristic
349C22×C13C2×C22⋊Q811yescharacteristic
350C22×C13C2×C22⋊Q811yescharacteristic
351C22×C13C2×C22⋊Q811yescharacteristic
352C22×C13C2×C22⋊Q811yescharacteristic
353C22×C13C2×#12411yescharacteristic
354C22×C13C2×C4⋊Q811yescharacteristic
355C22×C13#53511yescharacteristic
356C22×C13#53611yescharacteristic
357C22×C13#53711yescharacteristic
358C22×C13#53711yescharacteristic
359C22×C13D4×Q811yescharacteristic
360C22×C13D4×Q811yescharacteristic
361C22×C13#55011yescharacteristic
362C22×C13#55011yescharacteristic
363C22×C13#55411yescharacteristic
364C22×C13#55411yescharacteristic
365C22×C13#55611yescharacteristic
366C22×C13#55611yescharacteristic
367C22×C13#55711yescharacteristic
368C22×C13#55711yescharacteristic
369C22×C13#55711yescharacteristic
370C22×C13#55711yescharacteristic
371C22×C13Q8211yescharacteristic
372C22×C13Q8211yescharacteristic
373C22×C13#55911yescharacteristic
374C22×C13#55911yescharacteristic
375C4×C13—24no—
376C4×C13—42no—
377C4×C13—44no—
378C4×C13—82no—
379C4×C13#39118yescomplemented
380Dic13—24no—
381Dic13—24no—
382Dic13—42no—
383Dic13—44no—
384Dic13—82no—
385Dic13#38018yes—
386C22×Q8—134no—
387C22×Q8—134no—
388C22×Q8—134no—
389C22×Q8—262no—
390C22×Q8—262no—
391C22×Q8—262no—
392C22×Q8—262no—
393C23×C4—131no—
394C23×C4—131no—
395C23×C4—131no—
396C23×C4—131no—
397C23×C4—132no—
398C23×C4—132no—
399C23×C4C22×D1312yes—
400C23×C4C22×D1312yes—
401C23×C4C22×D1311yescharacteristic
402C23×C4C22×D1311yescharacteristic
403C23×C4C22×D1311yescharacteristic
404C4×Q8—2632no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—134no—
411C2×C4⋊C4—134no—
412C2×C4⋊C4—134no—
413C2×C4⋊C4—134no—
414C2×C4⋊C4—262no—
415C2×C4⋊C4—262no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—262no—
418C2×C4⋊C4—262no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—262no—
421C2×C4⋊C4—262no—
422C2×C4⋊C4—264no—
423C2×C4⋊C4—264no—
424C2×C4⋊C4—264no—
425C2×C4⋊C4—264no—
426C2×C4⋊C4—262no—
427C2×C4⋊C4—262no—
428C2×C4⋊C4—262no—
429C2×C4⋊C4—522no—
430C2×C4⋊C4—522no—
431C2×C4⋊C4Dic2614yescomplemented
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—134no—
435C2×C42—134no—
436C2×C42—134no—
437C2×C42—134no—
438C2×C42—262no—
439C2×C42—262no—
440C2×C42—264no—
441C2×C42—264no—
442C2×C42—264no—
443C2×C42C4×D1314yes—
444#95—24no—
445#95—42no—
446#95—264no—
447#95—264no—
448#95—264no—
449#95—264no—
450#95—522no—
451#95—522no—
452#95—522no—
453C2×C13C2×#38011yescharacteristic
454C2×C13C2×#39111yescharacteristic
455C2×C13#231111yescharacteristic
456C2×C13Q8×C4⋊C411yescharacteristic
457C2×C13Q8×C4⋊C411yescharacteristic
458C2×C13#235511yescharacteristic
459C2×C13#235511yescharacteristic
460C2×C13#253811yescharacteristic
461C2×C13#253811yescharacteristic
462C2×C13#254611yescharacteristic
463C2×C13#254811yescharacteristic
464C2×C13#256711yescharacteristic
465C2×C13#256811yescharacteristic
466C2×C13#258211yescharacteristic
467C2×C13#258211yescharacteristic
468C24C23×D1311yescharacteristic
469C2×Q8—1316no—
470C2×Q8—268no—
471C2×Q8—268no—
472C2×Q8—268no—
473C2×Q8—268no—
474C2×Q8—268no—
475C2×Q8—268no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—132no—
500C22×C4—132no—
501C22×C4—132no—
502C22×C4—132no—
503C22×C4—132no—
504C22×C4—132no—
505C22×C4—132no—
506C22×C4—132no—
507C22×C4—132no—
508C22×C4—132no—
509C22×C4—132no—
510C22×C4—132no—
511C22×C4—132no—
512C22×C4—132no—
513C22×C4—134no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—261no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—261no—
521C22×C4—261no—
522C22×C4—262no—
523C22×C4—262no—
524C22×C4—262no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4—262no—
529C22×C4—261no—
530C22×C4—262no—
531C22×C4—261no—
532C22×C4—262no—
533C22×C4—261no—
534C22×C4—262no—
535C22×C4—262no—
536C22×C4—262no—
537C22×C4—262no—
538C22×C4—262no—
539C22×C4—262no—
540C22×C4—262no—
541C22×C4C2×Dic2614yes—
542C22×C4C2×Dic2612yes—
543C22×C4C2×C4×D1312yes—
544C22×C4C2×C4×D1312yes—
545C22×C4C2×C4×D1312yes—
546C22×C4#612712yes—
547C22×C4D4×D1312yes—
548C22×C4D4×D1312yes—
549C22×C4D4×D1312yes—
550C22×C4#612912yes—
551C22×C4Q8×D1312yes—
552C22×C4Q8×D1312yes—
553C4⋊C4—28no—
554C4⋊C4—44no—
555C4⋊C4—268no—
556C4⋊C4—268no—
557C4⋊C4—268no—
558C4⋊C4—268no—
559C4⋊C4—528no—
560C4⋊C4—528no—
561C4⋊C4—524no—
562C42—28no—
563C42—1316no—
564C42—268no—
565C42—528no—
566C13#1392611yescharacteristic, complemented, Sylow
567C23C22×Dic2611yescharacteristic
568C23C22×C4×D1311yescharacteristic
569C23C2×#612711yescharacteristic
570C23C2×D4×D1311yescharacteristic
571C23C2×D4×D1311yescharacteristic
572C23C2×D4×D1311yescharacteristic
573C23C2×#612911yescharacteristic
574C23#8825111yescharacteristic
575C23C2×Q8×D1311yescharacteristic
576C23C2×Q8×D1311yescharacteristic
577C23#8825411yescharacteristic
578C23#41×D1311yescharacteristic
579C23#41×D1311yescharacteristic
580C23#8825611yescharacteristic
581C23#8825711yescharacteristic
582Q8—2632no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—134no—
611C2×C4—134no—
612C2×C4—134no—
613C2×C4—134no—
614C2×C4—134no—
615C2×C4—134no—
616C2×C4—134no—
617C2×C4—134no—
618C2×C4—134no—
619C2×C4—262no—
620C2×C4—262no—
621C2×C4—262no—
622C2×C4—262no—
623C2×C4—262no—
624C2×C4—262no—
625C2×C4—262no—
626C2×C4—262no—
627C2×C4—262no—
628C2×C4—262no—
629C2×C4—262no—
630C2×C4—262no—
631C2×C4—264no—
632C2×C4—262no—
633C2×C4—262no—
634C2×C4—264no—
635C2×C4—262no—
636C2×C4—264no—
637C2×C4—522no—
638C2×C4—522no—
639C2×C4—522no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—522no—
644C2×C4—521no—
645C2×C4—522no—
646C2×C4—522no—
647C2×C4—522no—
648C2×C4—522no—
649C2×C4—522no—
650C2×C4—522no—
651C2×C4—522no—
652C2×C4C4×Dic2614yes—
653C2×C4#8813214yes—
654C2×C4C22⋊C4×D1314yes—
655C2×C4#8813914yes—
656C2×C4#8814114yes—
657C2×C4#8814214yes—
658C2×C4C4⋊C4×D1314yes—
659C2×C4#8815014yes—
660C22C2×C4×Dic2611yescharacteristic
661C22C2×#8813211yescharacteristic
662C22C2×C22⋊C4×D1311yescharacteristic
663C22C2×#8813911yescharacteristic
664C22C2×#8814111yescharacteristic
665C22C2×#8814211yescharacteristic
666C22C2×C4⋊C4×D1311yescharacteristic
667C22#1171920911yescharacteristic
668C22C2×#8815011yescharacteristic
669C22D13×#11711yescharacteristic
670C22#1171922811yescharacteristic
671C22D4×Dic2611yescharacteristic
672C22#1171924411yescharacteristic
673C22#1171925811yescharacteristic
674C22#1171926411yescharacteristic
675C22Q8×Dic2611yescharacteristic
676C22#1171927211yescharacteristic
677C22#1171927311yescharacteristic
678C22#1171927411yescharacteristic
679C22D13×#12111yescharacteristic
680C22D13×#12111yescharacteristic
681C22#1171931211yescharacteristic
682C22#1171931311yescharacteristic
683C22D13×C22⋊Q811yescharacteristic
684C22D13×C22⋊Q811yescharacteristic
685C22#1171933311yescharacteristic
686C22#1171933411yescharacteristic
687C22#1171937611yescharacteristic
688C22#1171938611yescharacteristic
689C22#1171939011yescharacteristic
690C22#1171939511yescharacteristic
691C22#1171942311yescharacteristic
692C22#1171942611yescharacteristic
693C22#1171942711yescharacteristic
694C22#1171943211yescharacteristic
695C4—24no—
696C4—44no—
697C4—42no—
698C4—82no—
699C4—138no—
700C4—264no—
701C4—264no—
702C4—524no—
703C4—522no—
704C4—1042no—
705C4#1171830718yescomplemented
706C2D13×#38011yescharacteristic
707C2C2×#1171830711yescharacteristic
708C2#1311742511yescharacteristic
709C2#1311774811yescharacteristic
710C2C4⋊C4×Dic2611yescharacteristic
711C2#1311778811yescharacteristic
712C2#1311779411yescharacteristic
713C2#1311975611yescharacteristic
714C2#1311975711yescharacteristic
715C2#1311982311yescharacteristic
716C2#1311983711yescharacteristic
717C2#1312004311yescharacteristic
718C2#1312005011yescharacteristic
719C2#1312020711yescharacteristic
720C2#1312020811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, prime radical, cosocleC24×C13C24
hypercenterC4⋊#95D13
hypocenterC13#13926
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
28. C2×C4×Dic26C4semidirect
64. C2×C13×C4⋊C4Q8semidirect
76. C2×C4⋊Dic13Q8semidirect
193. C2×Dic26C4⋊C4semidirect
379. C4×C13#391semidirect
431. C2×C4⋊C4Dic26semidirect
566. C13#13926semidirect
705. C4#11718307semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic262
C2×#117183072
C2×#117186372
C2×C4⋊C4×Dic132
#131130882
#131130872
#131130662
#131130652
#131130642
C13×C4⋊#952
#1392613