Finite Group Databasebeta

← #15768199

Subgroups — #15768199

Order 3328.

1518 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88146C211yesmaximal, characteristic
2C22×#88060C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718143C211yesmaximal, characteristic, complemented
5C2×#11718121C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6103—21no—
13C22×#6103—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×C4×Dic13—21no—
17C23×#1055C2211yescharacteristic
18C2×#88146—22no—
19C2×#88146—22no—
20C2×#88146—22no—
21C2×#88146—22no—
22C2×#88146—22no—
23C2×#88146C414yescomplemented
24C2×#88071—21no—
25C2×#88060—22no—
26C2×#88060—22no—
27C2×#88060C414yescomplemented
28#11718648—22no—
29#11718648C414yescomplemented
30C13×#340—22no—
31#11718143—22no—
32#11718121—22no—
33#11718121—22no—
34C24×D13D411yescharacteristic
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13C2311yescharacteristic
38C23×Dic13—21no—
39C23×Dic13—21no—
40C23×Dic13D411yescharacteristic
41C22×C4×D13—21no—
42C22×C4×D13—21no—
43C22×C4×D13—21no—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13—21no—
47C22×C4×D13—21no—
48C22×C4×D13—21no—
49C22×C4×D13C2×C412yes—
50C22×C4×D13C2×C412yes—
51C22×C4×D13C2×C412yes—
52C22×C4×D13D412yes—
53C22×C4×D13D412yes—
54C22×C4×D13Q812yes—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13—21no—
58C22×C8×C13—21no—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13C2×C412yes—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2×C412yes—
71C2×C13×C4⋊C4C2×C412yes—
72C2×C13×C4⋊C4D412yes—
73C2×C13×C4⋊C4D412yes—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2×C412yes—
89C2×C4⋊Dic13C2×C412yes—
90C2×C4⋊Dic13D412yes—
91C2×C4⋊Dic13D412yes—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C22×#1055—21no—
101C22×#1055C2×C412yes—
102#88146—28no—
103#88146—28no—
104#88146—28no—
105#88146—28no—
106#88071—24no—
107#88060—28no—
108#10731—131nomaximal, Sylow
109C24×C13C2×D411yescharacteristic
110C23×D13—21no—
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13C22⋊C412yes—
123C23×D13C22⋊C412yes—
124C23×D13C4⋊C412yes—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—41no—
130C22×C4×C13—41no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—41no—
134C22×C4×C13—41no—
135C22×C4×C13—41no—
136C22×C4×C13—41no—
137C22×C4×C13—41no—
138C22×C4×C13—41no—
139C22×C4×C13C22×C411yescharacteristic
140C22×C4×C13C22×C411yescharacteristic
141C22×C4×C13C22×C411yescharacteristic
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×Q811yescharacteristic
149C22×C4×C13#4111yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C22×C4×C13#4111yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—22no—
158C22×Dic13—22no—
159C22×Dic13—22no—
160C22×Dic13—22no—
161C22×Dic13—41no—
162C22×Dic13—41no—
163C22×Dic13—41no—
164C22×Dic13—41no—
165C22×Dic13—41no—
166C22×Dic13—41no—
167C22×Dic13—41no—
168C22×Dic13—41no—
169C22×Dic13—41no—
170C22×Dic13—41no—
171C22×Dic13C22⋊C412yes—
172C22×Dic13C22⋊C412yes—
173C22×Dic13C4⋊C412yes—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—22no—
177C2×C4×D13—22no—
178C2×C4×D13—22no—
179C2×C4×D13—22no—
180C2×C4×D13—22no—
181C2×C4×D13—22no—
182C2×C4×D13—22no—
183C2×C4×D13—22no—
184C2×C4×D13—22no—
185C2×C4×D13—22no—
186C2×C4×D13—22no—
187C2×C4×D13—22no—
188C2×C4×D13—22no—
189C2×C4×D13—22no—
190C2×C4×D13—22no—
191C2×C4×D13—22no—
192C2×C4×D13—22no—
193C2×C4×D13—22no—
194C2×C4×D13—22no—
195C2×C4×D13—22no—
196C2×C4×D13—22no—
197C2×C4×D13—22no—
198C2×C4×D13C4214yes—
199C2×C4×D13C22⋊C414yes—
200C2×C4×D13C4⋊C414yes—
201C2×C4×D13C4⋊C414yes—
202C2×C8×C13—22no—
203C2×C8×C13—22no—
204C2×C8×C13—22no—
205C2×C8×C13—41no—
206C2×C8×C13—41no—
207C2×C8×C13—41no—
208C2×C8×C13—41no—
209C13×C4⋊C4—22no—
210C13×C4⋊C4—22no—
211C13×C4⋊C4—22no—
212C13×C4⋊C4—22no—
213C13×C4⋊C4—22no—
214C13×C4⋊C4—41no—
215C13×C4⋊C4—41no—
216C13×C4⋊C4C22⋊C414yescomplemented
217#6103—216no—
218#6103—48no—
219C4⋊Dic13—22no—
220C4⋊Dic13—22no—
221C4⋊Dic13—22no—
222C4⋊Dic13—22no—
223C4⋊Dic13—22no—
224C4⋊Dic13—41no—
225C4⋊Dic13—41no—
226C4⋊Dic13C22⋊C414yescomplemented
227C4×Dic13—216no—
228C2×#1055—22no—
229C2×#1055—22no—
230C2×#1055—22no—
231C2×#1055—41no—
232C2×#1055—41no—
233C2×#1055—41no—
234C2×#1055—41no—
235C22×#117—131no—
236C22×C22⋊C8—131no—
237C2×#380—131no—
238C2×#340—131no—
239C2×#340—131no—
240C2×#340—131no—
241C2×#340D1311yescharacteristic, complemented
242C23×C13C2×C22⋊C411yescharacteristic
243C23×C13C2×C22⋊C411yescharacteristic
244C23×C13C2×C4⋊C411yescharacteristic
245C23×C13#12011yescharacteristic
246C23×C13#12011yescharacteristic
247C23×C13#12311yescharacteristic
248C23×C13#12311yescharacteristic
249C23×C13#13511yescharacteristic
250C23×C13#13511yescharacteristic
251C23×C13#13511yescharacteristic
252C23×C13#13511yescharacteristic
253C23×C13AGL(1,ℤ/8)11yescharacteristic
254C23×C13AGL(1,ℤ/8)11yescharacteristic
255C23×C13#13711yescharacteristic
256C23×C13#13711yescharacteristic
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288C22×D13—41no—
289C22×D13—41no—
290C22×D13—41no—
291C22×D13#9514yes—
292C2×C4×C13—24no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—81no—
303C2×C4×C13—81no—
304C2×C4×C13—81no—
305C2×C4×C13—81no—
306C2×C4×C13C2×C4211yescharacteristic
307C2×C4×C13C2×C22⋊C411yescharacteristic
308C2×C4×C13C2×C22⋊C411yescharacteristic
309C2×C4×C13C2×C22⋊C411yescharacteristic
310C2×C4×C13C2×C4⋊C411yescharacteristic
311C2×C4×C13C2×C4⋊C411yescharacteristic
312C2×C4×C13#11711yescharacteristic
313C2×C4×C13#11711yescharacteristic
314C2×C4×C13C4×D411yescharacteristic
315C2×C4×C13C4×D411yescharacteristic
316C2×C4×C13C4×D411yescharacteristic
317C2×C4×C13C4×D411yescharacteristic
318C2×C4×C13C4×D411yescharacteristic
319C2×C4×C13C4×D411yescharacteristic
320C2×C4×C13C4×D411yescharacteristic
321C2×C4×C13C4×D411yescharacteristic
322C2×C4×C13#12011yescharacteristic
323C2×C4×C13#12011yescharacteristic
324C2×C4×C13#12111yescharacteristic
325C2×C4×C13#12111yescharacteristic
326C2×C4×C13#12111yescharacteristic
327C2×C4×C13#12111yescharacteristic
328C2×C4×C13C22⋊Q811yescharacteristic
329C2×C4×C13C22⋊Q811yescharacteristic
330C2×C4×C13C22⋊Q811yescharacteristic
331C2×C4×C13C22⋊Q811yescharacteristic
332C2×C4×C13#12311yescharacteristic
333C2×C4×C13#12311yescharacteristic
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—24no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—81no—
351C2×Dic13—81no—
352C2×Dic13—81no—
353C2×Dic13—81no—
354C2×Dic13#9514yes—
355C4×D13—24no—
356C4×D13—24no—
357C4×D13—24no—
358C4×D13—24no—
359C4×D13—24no—
360C4×D13—24no—
361C4×D13—24no—
362C4×D13—24no—
363C8×C13—42no—
364#1055—42no—
365C24×C4—131no—
366C23×C8—131no—
367C23×C8C2×D1311yescharacteristic
368C2×#117—134no—
369C2×#117—262no—
370C2×#117—262no—
371C2×#117—262no—
372C2×#117—262no—
373C2×#117—262no—
374C22×C4⋊C4—131no—
375C22×C4⋊C4—131no—
376C22×C4⋊C4C2×D1311yescharacteristic
377C22×C4⋊C4C2×D1311yescharacteristic
378C22×C22⋊C4—261no—
379C22×C22⋊C4—261no—
380C22×C42—261no—
381C2×C22⋊C8—134no—
382C2×C22⋊C8—262no—
383C2×C22⋊C8—262no—
384#380—134no—
385#380—262no—
386C2×#95—261no—
387#340—22no—
388#340—262no—
389#340—262no—
390#340—262no—
391C22×C13C2×#9511yescharacteristic
392C22×C13#37911yescharacteristic
393C22×C13#38111yescharacteristic
394C22×C13#38511yescharacteristic
395C22×C13#38511yescharacteristic
396C22×C13#38611yescharacteristic
397C22×C13#38611yescharacteristic
398C22×C13#41611yescharacteristic
399C22×C13#41611yescharacteristic
400C22×C13#41611yescharacteristic
401C22×C13#41611yescharacteristic
402C22×C13#41711yescharacteristic
403C22×C13#41711yescharacteristic
404C22×C13#41811yescharacteristic
405C22×C13#41911yescharacteristic
406C22×C13#42711yescharacteristic
407C22×C13#42711yescharacteristic
408C22×C13#42811yescharacteristic
409C22×C13#42811yescharacteristic
410C22×C13#44911yescharacteristic
411C22×C13#44911yescharacteristic
412C22×C13#44911yescharacteristic
413C22×C13#44911yescharacteristic
414C22×C13#45211yescharacteristic
415C22×C13#45211yescharacteristic
416C22×C13#45211yescharacteristic
417C22×C13#45211yescharacteristic
418C22×C13#48211yescharacteristic
419C22×C13#48211yescharacteristic
420C22×C13#48211yescharacteristic
421C22×C13#48211yescharacteristic
422C22×C13#48511yescharacteristic
423C22×C13#48511yescharacteristic
424C22×C13#48511yescharacteristic
425C22×C13#48511yescharacteristic
426C2×D13—24no—
427C2×D13—24no—
428C2×D13—24no—
429C2×D13—42no—
430C2×D13—42no—
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C4×C13—44no—
442C4×C13—82no—
443C4×C13C4×C22⋊C411yescharacteristic
444C4×C13C4×C22⋊C411yescharacteristic
445C4×C13#38011yescharacteristic
446C4×C13#38011yescharacteristic
447C4×C13#38511yescharacteristic
448C4×C13#38511yescharacteristic
449C4×C13#38611yescharacteristic
450C4×C13#38611yescharacteristic
451Dic13—24no—
452Dic13—44no—
453Dic13—82no—
454C25—131no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—131no—
458C23×C4—132no—
459C23×C4—132no—
460C23×C4—132no—
461C23×C4—132no—
462C23×C4—132no—
463C23×C4—132no—
464C23×C4—261no—
465C23×C4—261no—
466C23×C4—261no—
467C23×C4—261no—
468C23×C4—261no—
469C23×C4—261no—
470C23×C4—261no—
471C23×C4—261no—
472C23×C4—261no—
473C23×C4—261no—
474C23×C4C22×D1311yescharacteristic
475C22×C8—21no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—132no—
482C22×C8—261no—
483C22×C8—261no—
484C22×C8—261no—
485C22×C8—261no—
486C22×C8—261no—
487C22×C8—261no—
488C22×C8C4×D1312yes—
489#117—268no—
490#117—268no—
491#117—268no—
492#117—268no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—132no—
502C2×C4⋊C4—132no—
503C2×C4⋊C4—132no—
504C2×C4⋊C4—132no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—261no—
507C2×C4⋊C4—261no—
508C2×C4⋊C4—261no—
509C2×C4⋊C4—261no—
510C2×C4⋊C4—261no—
511C2×C4⋊C4—261no—
512C2×C4⋊C4—261no—
513C2×C4⋊C4C4×D1312yes—
514C2×C4⋊C4C4×D1312yes—
515C2×C4⋊C4D5212yes—
516C2×C4⋊C4C22⋊D1312yes—
517C2×C22⋊C4—264no—
518C2×C22⋊C4—264no—
519C2×C22⋊C4—264no—
520C2×C22⋊C4—264no—
521C2×C22⋊C4—522no—
522C2×C22⋊C4—522no—
523C2×C42—264no—
524C2×C42—264no—
525C2×C42—264no—
526C22⋊C8—268no—
527#95—264no—
528C2×C13C22⋊#9511yescharacteristic
529C2×C13#173511yescharacteristic
530C2×C13#173611yescharacteristic
531C2×C13#178811yescharacteristic
532C2×C13#178811yescharacteristic
533C2×C13#182511yescharacteristic
534C2×C13#182511yescharacteristic
535C2×C13#185411yescharacteristic
536C2×C13#185411yescharacteristic
537C2×C13#185411yescharacteristic
538C2×C13#185411yescharacteristic
539C2×C13#187311yescharacteristic
540C2×C13#187311yescharacteristic
541C2×C13#187511yescharacteristic
542C2×C13#187511yescharacteristic
543D13—44no—
544C24—132no—
545C24—132no—
546C24—132no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24—261no—
555C24—261no—
556C24—261no—
557C24—261no—
558C24—261no—
559C24D4×D1311yescharacteristic
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—132no—
575C22×C4—132no—
576C22×C4—132no—
577C22×C4—134no—
578C22×C4—134no—
579C22×C4—134no—
580C22×C4—134no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—521no—
614C22×C4—521no—
615C22×C4—521no—
616C22×C4—521no—
617C22×C4—521no—
618C22×C4—521no—
619C22×C4—521no—
620C22×C4—521no—
621C22×C4—521no—
622C22×C4—521no—
623C22×C4C2×C4×D1311yescharacteristic
624C22×C4C2×C4×D1311yescharacteristic
625C22×C4C2×C4×D1311yescharacteristic
626C22×C4C2×D5211yescharacteristic
627C22×C4#612711yescharacteristic
628C22×C4#612711yescharacteristic
629C22×C4D4×D1311yescharacteristic
630C22×C4D4×D1311yescharacteristic
631C22×C4D4×D1311yescharacteristic
632C22×C4D4×D1311yescharacteristic
633C22×C4#612911yescharacteristic
634C22×C4Q8×D1311yescharacteristic
635C22×C4#613111yescharacteristic
636C22×C4C2×C22⋊D1311yescharacteristic
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8—41no—
643C2×C8—41no—
644C2×C8—262no—
645C2×C8—262no—
646C2×C8—262no—
647C2×C8—521no—
648C2×C8—521no—
649C2×C8—521no—
650C2×C8—521no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—22no—
655C4⋊C4—22no—
656C4⋊C4—41no—
657C4⋊C4—41no—
658C4⋊C4—134no—
659C4⋊C4—262no—
660C4⋊C4—262no—
661C4⋊C4—262no—
662C4⋊C4—262no—
663C4⋊C4—262no—
664C4⋊C4—521no—
665C4⋊C4—521no—
666C4⋊C4#610314yescomplemented
667C22⋊C4—2616no—
668C22⋊C4—528no—
669C42—2616no—
670C13#1073111yescharacteristic, complemented, Sylow
671C23—134no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—262no—
678C23—262no—
679C23—262no—
680C23—262no—
681C23—262no—
682C23—262no—
683C23—262no—
684C23—262no—
685C23—262no—
686C23—262no—
687C23—262no—
688C23—262no—
689C23—262no—
690C23—521no—
691C23—521no—
692C23—521no—
693C23—521no—
694C23—521no—
695C23—521no—
696C23—521no—
697C23—521no—
698C23—521no—
699C23—521no—
700C23—521no—
701C23—521no—
702C23—521no—
703C23—521no—
704C23—521no—
705C23—521no—
706C23C22⋊C4×D1311yescharacteristic
707C23C22⋊C4×D1311yescharacteristic
708C23#8813611yescharacteristic
709C23#8813711yescharacteristic
710C23C4⋊C4×D1311yescharacteristic
711C23#8814811yescharacteristic
712C23#8816511yescharacteristic
713C23#8816611yescharacteristic
714C23#8816811yescharacteristic
715C23#8816911yescharacteristic
716C23#8817011yescharacteristic
717C23#8817011yescharacteristic
718C23#8817211yescharacteristic
719C23#8817311yescharacteristic
720C23#8819111yescharacteristic
721C2×C4—24no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—134no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—264no—
743C2×C4—264no—
744C2×C4—264no—
745C2×C4—264no—
746C2×C4—264no—
747C2×C4—264no—
748C2×C4—264no—
749C2×C4—264no—
750C2×C4—264no—
751C2×C4—522no—
752C2×C4—522no—
753C2×C4—522no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—522no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—1041no—
761C2×C4—1041no—
762C2×C4—1041no—
763C2×C4—1041no—
764C2×C4C42×D1311yescharacteristic
765C2×C4#8812611yescharacteristic
766C2×C4C4×D5211yescharacteristic
767C2×C4C4×D5211yescharacteristic
768C2×C4C22⋊C4×D1311yescharacteristic
769C2×C4C22⋊C4×D1311yescharacteristic
770C2×C4#8813511yescharacteristic
771C2×C4#8813511yescharacteristic
772C2×C4#8813611yescharacteristic
773C2×C4#8813711yescharacteristic
774C2×C4#8813811yescharacteristic
775C2×C4#8813811yescharacteristic
776C2×C4C4⋊C4×D1311yescharacteristic
777C2×C4C4⋊C4×D1311yescharacteristic
778C2×C4#8814611yescharacteristic
779C2×C4#8814711yescharacteristic
780C2×C4#8814711yescharacteristic
781C2×C4#8814811yescharacteristic
782C2×C4#8814911yescharacteristic
783C2×C4#8815011yescharacteristic
784C2×C4#8815011yescharacteristic
785C2×C4#8815111yescharacteristic
786C2×C4C2×#610311yescharacteristic
787C2×C4C4×C22⋊D1311yescharacteristic
788C2×C4C4×C22⋊D1311yescharacteristic
789C2×C4#8819111yescharacteristic
790C2×C4#8819211yescharacteristic
791C2×C4#8820011yescharacteristic
792C8—42no—
793C8—522no—
794C22—264no—
795C22—264no—
796C22—264no—
797C22—522no—
798C22—522no—
799C22—522no—
800C22—522no—
801C22—522no—
802C22—522no—
803C22—522no—
804C22—522no—
805C22—522no—
806C22—522no—
807C22—522no—
808C22—522no—
809C22D13×#9511yescharacteristic
810C22#1171832511yescharacteristic
811C22#1171832611yescharacteristic
812C22#1171832911yescharacteristic
813C22#1171843111yescharacteristic
814C22#1171843211yescharacteristic
815C22#1171843311yescharacteristic
816C22#1171843311yescharacteristic
817C22#1171844011yescharacteristic
818C22#1171844211yescharacteristic
819C22#1171844411yescharacteristic
820C22#1171844511yescharacteristic
821C22#1171846311yescharacteristic
822C22#1171846411yescharacteristic
823C22#1171846511yescharacteristic
824C22#1171846511yescharacteristic
825C22#1171847111yescharacteristic
826C22#1171847211yescharacteristic
827C22#1171847511yescharacteristic
828C22#1171847611yescharacteristic
829C22#1171852111yescharacteristic
830C22#1171852211yescharacteristic
831C22#1171852711yescharacteristic
832C22#1171852811yescharacteristic
833C22#1171854111yescharacteristic
834C22#1171854211yescharacteristic
835C22#1171854611yescharacteristic
836C22#1171854911yescharacteristic
837C22#1171861611yescharacteristic
838C22#1171861711yescharacteristic
839C22#1171865011yescharacteristic
840C22#1171881911yescharacteristic
841C22#1171883311yescharacteristic
842C22#1171883411yescharacteristic
843C22#1171884811yescharacteristic
844C4—44no—
845C4—82no—
846C4—264no—
847C4—524no—
848C4—1042no—
849C4#1171832611yescharacteristic
850C4#1171832711yescharacteristic
851C4#1171832811yescharacteristic
852C4#1171832911yescharacteristic
853C4C4×#610311yescharacteristic
854C4#1171861711yescharacteristic
855C4#1171864811yescharacteristic
856C4#1171865011yescharacteristic
857C2—524no—
858C2#1311305711yescharacteristic
859C2#1311455111yescharacteristic
860C2#1311455411yescharacteristic
861C2#1311477311yescharacteristic
862C2#1311477511yescharacteristic
863C2#1311492911yescharacteristic
864C2#1311493011yescharacteristic
865C2#1311503211yescharacteristic
866C2#1311503411yescharacteristic
867C2#1311503611yescharacteristic
868C2#1311503811yescharacteristic
869C2#1311514511yescharacteristic
870C2#1311514711yescharacteristic
871C2#1311515511yescharacteristic
872C2#1311515711yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC2×C4×C13C2×C42
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#10731
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#11718143C2semidirect
5. C2×#11718121C2semidirect
6. C2×#11718121C2semidirect
7. C2×C13×#340C2semidirect
23. C2×#88146C4semidirect
27. C2×#88060C4semidirect
29. #11718648C4semidirect
216. C13×C4⋊C4C22⋊C4semidirect
226. C4⋊Dic13C22⋊C4semidirect
241. C2×#340D13semidirect
666. C4⋊C4#6103semidirect
670. C13#10731semidirect

Maximal subgroups

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

subgroupindex
C22×#881462
C22×#880602
C2×#117186482
C2×#117181432
C2×#117181212
C2×C13×#3402
#1073113