Finite Group Databasebeta

← #15768195

Subgroups — #15768195

Order 3328.

1822 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, 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×D13—21no—
9C23×C4×D13C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×#6103—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4⋊Dic13C2211yescharacteristic
16C22×#6101—21no—
17C23×#1055C2211yescharacteristic
18C2×C4⋊C4×D13—22no—
19C2×C4⋊C4×D13—22no—
20C2×C4⋊C4×D13—22no—
21C2×C4⋊C4×D13—22no—
22C2×C4⋊C4×D13—22no—
23C2×C4⋊C4×D13C414yescomplemented
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×D13—24no—
50C22×C4×D13—24no—
51C22×C4×D13—24no—
52C22×C4×D13—42no—
53C22×C4×D13—42no—
54C22×C4×D13—42no—
55C22×C4×D13—42no—
56C22×C4×D13C2×C412yes—
57C22×C4×D13C2×C412yes—
58C22×C4×D13C2×C412yes—
59C22×C4×D13D412yes—
60C22×C4×D13D412yes—
61C22×C4×D13Q812yes—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C22×C8×C13—21no—
68C22×C8×C13C2×C412yescomplemented
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4C2×C412yes—
78C2×C13×C4⋊C4C2×C412yescomplemented
79C2×C13×C4⋊C4D412yes—
80C2×C13×C4⋊C4D412yes—
81C2×#6103—24no—
82C2×#6103—42no—
83C2×#6103—42no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13C2×C412yes—
93C2×C4⋊Dic13C2×C412yescomplemented
94C2×C4⋊Dic13D412yes—
95C2×C4⋊Dic13D412yes—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—24no—
99C22×#1055—21no—
100C22×#1055—21no—
101C22×#1055—21no—
102C22×#1055—21no—
103C22×#1055—21no—
104C22×#1055—21no—
105C22×#1055C2×C412yescomplemented
106C4⋊C4×D13—28no—
107C4⋊C4×D13—28no—
108C4⋊C4×D13—28no—
109C4⋊C4×D13—28no—
110#88071—24no—
111#88060—28no—
112#10730—131nomaximal, Sylow
113C24×C13C2×D411yescharacteristic
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—
125C23×D13D812yes—
126C23×D13SD1612yes—
127C23×D13SD1612yes—
128C23×D13Q1612yes—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
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×C13—41no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13C22×C411yescharacteristic
144C22×C4×C13C22×C411yescharacteristic
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×Q811yescharacteristic
153C22×C4×C13#4111yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C22×C4×C13#4111yescharacteristic
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—41no—
166C22×Dic13—41no—
167C22×Dic13—41no—
168C22×Dic13—41no—
169C22×Dic13—41no—
170C22×Dic13—41no—
171C22×Dic13—41no—
172C22×Dic13—41no—
173C22×Dic13—41no—
174C22×Dic13—41no—
175C22×Dic13C22⋊C412yes—
176C22×Dic13C22⋊C412yes—
177C22×Dic13C4⋊C412yes—
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×D13—22no—
199C2×C4×D13—22no—
200C2×C4×D13—22no—
201C2×C4×D13—22no—
202C2×C4×D13—216no—
203C2×C4×D13—48no—
204C2×C4×D13—48no—
205C2×C4×D13—48no—
206C2×C4×D13—48no—
207C2×C4×D13—48no—
208C2×C4×D13—48no—
209C2×C4×D13C4214yes—
210C2×C4×D13C22⋊C414yes—
211C2×C4×D13C4⋊C414yes—
212C2×C4×D13C4⋊C414yes—
213C2×C8×C13—22no—
214C2×C8×C13—22no—
215C2×C8×C13—22no—
216C2×C8×C13—41no—
217C2×C8×C13—41no—
218C2×C8×C13—41no—
219C2×C8×C13—41no—
220C13×C4⋊C4—22no—
221C13×C4⋊C4—22no—
222C13×C4⋊C4—22no—
223C13×C4⋊C4—22no—
224C13×C4⋊C4—22no—
225C13×C4⋊C4—41no—
226C13×C4⋊C4—41no—
227C13×C4⋊C4C22⋊C414yescomplemented
228#6103—48no—
229C4⋊Dic13—22no—
230C4⋊Dic13—22no—
231C4⋊Dic13—22no—
232C4⋊Dic13—22no—
233C4⋊Dic13—22no—
234C4⋊Dic13—41no—
235C4⋊Dic13—41no—
236C4⋊Dic13C22⋊C414yescomplemented
237#6101—216no—
238C2×#1055—22no—
239C2×#1055—22no—
240C2×#1055—22no—
241C2×#1055—41no—
242C2×#1055—41no—
243C2×#1055—41no—
244C2×#1055—41no—
245C23×C4⋊C4—131no—
246C22×C22⋊C8—131no—
247C2×#380—131no—
248C2×#340—131no—
249C2×#340—131no—
250C2×#340—131no—
251C2×#340D1311yescharacteristic, complemented
252C23×C13C2×C22⋊C411yescharacteristic
253C23×C13C2×C22⋊C411yescharacteristic
254C23×C13C2×C4⋊C411yescharacteristic
255C23×C13#12011yescharacteristic
256C23×C13#12011yescharacteristic
257C23×C13#12311yescharacteristic
258C23×C13#12311yescharacteristic
259C23×C13C2×D811yescharacteristic
260C23×C13C2×SD1611yescharacteristic
261C23×C13C2×SD1611yescharacteristic
262C23×C13C2×Q1611yescharacteristic
263C23×C13AGL(1,ℤ/8)11yescharacteristic
264C23×C13AGL(1,ℤ/8)11yescharacteristic
265C23×C13#13711yescharacteristic
266C23×C13#13711yescharacteristic
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—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—22no—
281C22×D13—22no—
282C22×D13—22no—
283C22×D13—22no—
284C22×D13—22no—
285C22×D13—22no—
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—22no—
294C22×D13—22no—
295C22×D13#9514yes—
296C22×D13#10214yes—
297C22×D13#10214yes—
298C22×D13#10314yes—
299C22×D13#10314yes—
300C22×D13#10614yes—
301C22×D13#10714yes—
302C2×C4×C13—24no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—81no—
313C2×C4×C13—81no—
314C2×C4×C13—81no—
315C2×C4×C13—81no—
316C2×C4×C13C2×C4211yescharacteristic
317C2×C4×C13C2×C22⋊C411yescharacteristic
318C2×C4×C13C2×C22⋊C411yescharacteristic
319C2×C4×C13C2×C22⋊C411yescharacteristic
320C2×C4×C13C2×C4⋊C411yescharacteristic
321C2×C4×C13C2×C4⋊C411yescharacteristic
322C2×C4×C13#11711yescharacteristic
323C2×C4×C13#11711yescharacteristic
324C2×C4×C13C4×D411yescharacteristic
325C2×C4×C13C4×D411yescharacteristic
326C2×C4×C13C4×D411yescharacteristic
327C2×C4×C13C4×D411yescharacteristic
328C2×C4×C13C4×D411yescharacteristic
329C2×C4×C13C4×D411yescharacteristic
330C2×C4×C13C4×D411yescharacteristic
331C2×C4×C13C4×D411yescharacteristic
332C2×C4×C13#12011yescharacteristic
333C2×C4×C13#12011yescharacteristic
334C2×C4×C13#12111yescharacteristic
335C2×C4×C13#12111yescharacteristic
336C2×C4×C13#12111yescharacteristic
337C2×C4×C13#12111yescharacteristic
338C2×C4×C13C22⋊Q811yescharacteristic
339C2×C4×C13C22⋊Q811yescharacteristic
340C2×C4×C13C22⋊Q811yescharacteristic
341C2×C4×C13C22⋊Q811yescharacteristic
342C2×C4×C13#12311yescharacteristic
343C2×C4×C13#12311yescharacteristic
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—24no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—42no—
360C2×Dic13—81no—
361C2×Dic13—81no—
362C2×Dic13—81no—
363C2×Dic13—81no—
364C2×Dic13#9514yes—
365C4×D13—24no—
366C4×D13—24no—
367C4×D13—24no—
368C4×D13—24no—
369C4×D13—24no—
370C4×D13—24no—
371C4×D13—24no—
372C4×D13—24no—
373C4×D13—432no—
374C8×C13—42no—
375#1055—42no—
376C24×C4—131no—
377C24×C4—261no—
378C23×C8—131no—
379C23×C8C2×D1311yescharacteristic
380C22×C4⋊C4—131no—
381C22×C4⋊C4—131no—
382C22×C4⋊C4—134no—
383C22×C4⋊C4—262no—
384C22×C4⋊C4—262no—
385C22×C4⋊C4—262no—
386C22×C4⋊C4—261no—
387C22×C4⋊C4—262no—
388C22×C4⋊C4—262no—
389C22×C4⋊C4C2×D1311yescharacteristic
390C22×C4⋊C4C2×D1311yescharacteristic
391C22×C22⋊C4—261no—
392C2×C22⋊C8—134no—
393C2×C22⋊C8—262no—
394C2×C22⋊C8—262no—
395#380—134no—
396#380—262no—
397C2×#95—261no—
398#340—22no—
399#340—262no—
400#340—262no—
401#340—262no—
402C22×C13C2×#9511yescharacteristic
403C22×C13#37911yescharacteristic
404C22×C13#38111yescharacteristic
405C22×C13#38511yescharacteristic
406C22×C13#38511yescharacteristic
407C22×C13#38611yescharacteristic
408C22×C13#38611yescharacteristic
409C22×C13C2×#10211yescharacteristic
410C22×C13C2×#10211yescharacteristic
411C22×C13C2×#10311yescharacteristic
412C22×C13C2×#10311yescharacteristic
413C22×C13#41711yescharacteristic
414C22×C13#41711yescharacteristic
415C22×C13#41811yescharacteristic
416C22×C13#41911yescharacteristic
417C22×C13C2×#10611yescharacteristic
418C22×C13C2×#10711yescharacteristic
419C22×C13#42811yescharacteristic
420C22×C13#42811yescharacteristic
421C22×C13#44711yescharacteristic
422C22×C13#44711yescharacteristic
423C22×C13#44811yescharacteristic
424C22×C13#44811yescharacteristic
425C22×C13#45011yescharacteristic
426C22×C13#45011yescharacteristic
427C22×C13#45111yescharacteristic
428C22×C13#45111yescharacteristic
429C22×C13#48011yescharacteristic
430C22×C13#48011yescharacteristic
431C22×C13#48111yescharacteristic
432C22×C13#48111yescharacteristic
433C22×C13#48311yescharacteristic
434C22×C13#48311yescharacteristic
435C22×C13#48411yescharacteristic
436C22×C13#48411yescharacteristic
437C2×D13—24no—
438C2×D13—24no—
439C2×D13—24no—
440C2×D13—24no—
441C2×D13—24no—
442C2×D13—24no—
443C2×D13—24no—
444C2×D13—24no—
445C2×D13—24no—
446C2×D13—24no—
447C2×D13—24no—
448C2×D13—24no—
449C2×D13—24no—
450C2×D13—24no—
451C2×D13#34018yescomplemented
452C4×C13—44no—
453C4×C13—82no—
454C4×C13C4×C22⋊C411yescharacteristic
455C4×C13C4×C22⋊C411yescharacteristic
456C4×C13#38011yescharacteristic
457C4×C13#38011yescharacteristic
458C4×C13#38511yescharacteristic
459C4×C13#38511yescharacteristic
460C4×C13#38611yescharacteristic
461C4×C13#38611yescharacteristic
462Dic13—24no—
463Dic13—44no—
464Dic13—82no—
465C25—131no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—131no—
469C23×C4—132no—
470C23×C4—132no—
471C23×C4—132no—
472C23×C4—132no—
473C23×C4—132no—
474C23×C4—132no—
475C23×C4—264no—
476C23×C4—264no—
477C23×C4—264no—
478C23×C4—261no—
479C23×C4—261no—
480C23×C4—261no—
481C23×C4—261no—
482C23×C4—261no—
483C23×C4—261no—
484C23×C4—261no—
485C23×C4—261no—
486C23×C4—261no—
487C23×C4—261no—
488C23×C4—522no—
489C23×C4—522no—
490C23×C4—522no—
491C23×C4—522no—
492C23×C4C22×D1311yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8—21no—
496C22×C8—21no—
497C22×C8—21no—
498C22×C8—21no—
499C22×C8—132no—
500C22×C8—261no—
501C22×C8—261no—
502C22×C8—261no—
503C22×C8—261no—
504C22×C8—261no—
505C22×C8—261no—
506C22×C8C4×D1312yescomplemented
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—132no—
516C2×C4⋊C4—132no—
517C2×C4⋊C4—132no—
518C2×C4⋊C4—132no—
519C2×C4⋊C4—268no—
520C2×C4⋊C4—268no—
521C2×C4⋊C4—268no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—264no—
524C2×C4⋊C4—264no—
525C2×C4⋊C4—261no—
526C2×C4⋊C4—261no—
527C2×C4⋊C4—261no—
528C2×C4⋊C4—268no—
529C2×C4⋊C4—261no—
530C2×C4⋊C4—261no—
531C2×C4⋊C4—261no—
532C2×C4⋊C4—261no—
533C2×C4⋊C4—261no—
534C2×C4⋊C4C4×D1312yes—
535C2×C4⋊C4C4×D1312yescomplemented
536C2×C4⋊C4D5212yes—
537C2×C4⋊C4C22⋊D1312yes—
538C2×C22⋊C4—264no—
539C2×C22⋊C4—522no—
540C2×C22⋊C4—522no—
541C22⋊C8—268no—
542#95—264no—
543C2×C13C22⋊#9511yescharacteristic
544C2×C13C2×#34011yescharacteristic
545C2×C13#173611yescharacteristic
546C2×C13#178611yescharacteristic
547C2×C13#178711yescharacteristic
548C2×C13#182311yescharacteristic
549C2×C13#182411yescharacteristic
550C2×C13#185211yescharacteristic
551C2×C13#185211yescharacteristic
552C2×C13#185311yescharacteristic
553C2×C13#185311yescharacteristic
554C2×C13#187211yescharacteristic
555C2×C13#187211yescharacteristic
556C2×C13#187411yescharacteristic
557C2×C13#187411yescharacteristic
558D13—28no—
559C24—132no—
560C24—132no—
561C24—132no—
562C24—132no—
563C24—132no—
564C24—132no—
565C24—132no—
566C24—261no—
567C24—261no—
568C24—261no—
569C24—261no—
570C24—261no—
571C24—261no—
572C24—261no—
573C24—261no—
574C24D4×D1311yescharacteristic
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—134no—
593C22×C4—134no—
594C22×C4—134no—
595C22×C4—134no—
596C22×C4—2616no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
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—262no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—262no—
623C22×C4—262no—
624C22×C4—262no—
625C22×C4—262no—
626C22×C4—262no—
627C22×C4—262no—
628C22×C4—262no—
629C22×C4—528no—
630C22×C4—528no—
631C22×C4—528no—
632C22×C4—528no—
633C22×C4—528no—
634C22×C4—528no—
635C22×C4—521no—
636C22×C4—521no—
637C22×C4—521no—
638C22×C4—521no—
639C22×C4—521no—
640C22×C4—521no—
641C22×C4—521no—
642C22×C4—521no—
643C22×C4—521no—
644C22×C4—521no—
645C22×C4C2×C4×D1311yescharacteristic
646C22×C4C2×C4×D1311yescharacteristic
647C22×C4C2×C4×D1311yescharacteristic
648C22×C4C2×D5211yescharacteristic
649C22×C4#612711yescharacteristic
650C22×C4#612711yescharacteristic
651C22×C4D4×D1311yescharacteristic
652C22×C4D4×D1311yescharacteristic
653C22×C4D4×D1311yescharacteristic
654C22×C4D4×D1311yescharacteristic
655C22×C4#612911yescharacteristic
656C22×C4Q8×D1311yescharacteristic
657C22×C4#613111yescharacteristic
658C22×C4C2×C22⋊D1311yescharacteristic
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—41no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—262no—
667C2×C8—262no—
668C2×C8—262no—
669C2×C8—521no—
670C2×C8—521no—
671C2×C8—521no—
672C2×C8—521no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—41no—
679C4⋊C4—41no—
680C4⋊C4—134no—
681C4⋊C4—2616no—
682C4⋊C4—262no—
683C4⋊C4—262no—
684C4⋊C4—262no—
685C4⋊C4—262no—
686C4⋊C4—262no—
687C4⋊C4—521no—
688C4⋊C4—521no—
689C4⋊C4#610314yescomplemented
690C22⋊C4—528no—
691C13#1073011yescharacteristic, complemented, Sylow
692C23—134no—
693C23—134no—
694C23—134no—
695C23—134no—
696C23—134no—
697C23—134no—
698C23—134no—
699C23—262no—
700C23—262no—
701C23—262no—
702C23—262no—
703C23—262no—
704C23—262no—
705C23—262no—
706C23—262no—
707C23—262no—
708C23—262no—
709C23—262no—
710C23—262no—
711C23—262no—
712C23—262no—
713C23—262no—
714C23—262no—
715C23—262no—
716C23—262no—
717C23—262no—
718C23—262no—
719C23—262no—
720C23—262no—
721C23—262no—
722C23—262no—
723C23—262no—
724C23—262no—
725C23—262no—
726C23—262no—
727C23C22⋊C4×D1311yescharacteristic
728C23C22⋊C4×D1311yescharacteristic
729C23#8813611yescharacteristic
730C23#8813711yescharacteristic
731C23C4⋊C4×D1311yescharacteristic
732C23#8814811yescharacteristic
733C23D8×D1311yescharacteristic
734C23#8816511yescharacteristic
735C23SD16×D1311yescharacteristic
736C23SD16×D1311yescharacteristic
737C23#8816811yescharacteristic
738C23#8816911yescharacteristic
739C23Q16×D1311yescharacteristic
740C23#8817211yescharacteristic
741C23#8819111yescharacteristic
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—81no—
753C2×C4—81no—
754C2×C4—81no—
755C2×C4—81no—
756C2×C4—134no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—262no—
761C2×C4—262no—
762C2×C4—262no—
763C2×C4—264no—
764C2×C4—264no—
765C2×C4—264no—
766C2×C4—264no—
767C2×C4—264no—
768C2×C4—264no—
769C2×C4—264no—
770C2×C4—264no—
771C2×C4—264no—
772C2×C4—5232no—
773C2×C4—522no—
774C2×C4—522no—
775C2×C4—522no—
776C2×C4—522no—
777C2×C4—522no—
778C2×C4—522no—
779C2×C4—522no—
780C2×C4—522no—
781C2×C4—522no—
782C2×C4—1041no—
783C2×C4—1041no—
784C2×C4—1041no—
785C2×C4—1041no—
786C2×C4C42×D1311yescharacteristic
787C2×C4#8812611yescharacteristic
788C2×C4C4×D5211yescharacteristic
789C2×C4C4×D5211yescharacteristic
790C2×C4C22⋊C4×D1311yescharacteristic
791C2×C4C22⋊C4×D1311yescharacteristic
792C2×C4#8813511yescharacteristic
793C2×C4#8813511yescharacteristic
794C2×C4#8813611yescharacteristic
795C2×C4#8813711yescharacteristic
796C2×C4#8813811yescharacteristic
797C2×C4#8813811yescharacteristic
798C2×C4C4⋊C4×D1311yescharacteristic
799C2×C4C4⋊C4×D1311yescharacteristic
800C2×C4#8814611yescharacteristic
801C2×C4#8814711yescharacteristic
802C2×C4#8814711yescharacteristic
803C2×C4#8814811yescharacteristic
804C2×C4#8814911yescharacteristic
805C2×C4#8815011yescharacteristic
806C2×C4#8815011yescharacteristic
807C2×C4#8815111yescharacteristic
808C2×C4C2×#610311yescharacteristic
809C2×C4C4×C22⋊D1311yescharacteristic
810C2×C4C4×C22⋊D1311yescharacteristic
811C2×C4#8819111yescharacteristic
812C2×C4#8819211yescharacteristic
813C2×C4#8820011yescharacteristic
814C8—42no—
815C8—522no—
816C22—138no—
817C22—264no—
818C22—264no—
819C22—264no—
820C22—264no—
821C22—264no—
822C22—264no—
823C22—264no—
824C22—264no—
825C22—264no—
826C22—264no—
827C22—264no—
828C22—264no—
829C22—264no—
830C22—264no—
831C22D13×#9511yescharacteristic
832C22#1171832511yescharacteristic
833C22#1171832611yescharacteristic
834C22#1171832911yescharacteristic
835C22D13×#10211yescharacteristic
836C22D13×#10211yescharacteristic
837C22#1171843111yescharacteristic
838C22#1171843211yescharacteristic
839C22#1171843411yescharacteristic
840C22#1171843511yescharacteristic
841C22#1171843711yescharacteristic
842C22#1171843811yescharacteristic
843C22D13×#10311yescharacteristic
844C22D13×#10311yescharacteristic
845C22#1171846311yescharacteristic
846C22#1171846411yescharacteristic
847C22#1171846611yescharacteristic
848C22#1171846711yescharacteristic
849C22#1171846911yescharacteristic
850C22#1171847011yescharacteristic
851C22D13×#10611yescharacteristic
852C22#1171852211yescharacteristic
853C22#1171852311yescharacteristic
854C22#1171852411yescharacteristic
855C22D13×#10711yescharacteristic
856C22#1171854211yescharacteristic
857C22#1171854311yescharacteristic
858C22#1171854511yescharacteristic
859C22#1171861611yescharacteristic
860C22#1171861711yescharacteristic
861C22#1171865011yescharacteristic
862C22#1171881711yescharacteristic
863C22#1171883011yescharacteristic
864C22#1171883111yescharacteristic
865C22#1171884711yescharacteristic
866C4—44no—
867C4—82no—
868C4—264no—
869C4—524no—
870C4—1042no—
871C4#1171832611yescharacteristic
872C4#1171832711yescharacteristic
873C4#1171832811yescharacteristic
874C4#1171832911yescharacteristic
875C4C4×#610311yescharacteristic
876C4#1171861711yescharacteristic
877C4#1171864811yescharacteristic
878C4#1171865011yescharacteristic
879C2—268no—
880C2#1311305711yescharacteristic
881C2D13×#34011yescharacteristic
882C2#1311455411yescharacteristic
883C2#1311476511yescharacteristic
884C2#1311476911yescharacteristic
885C2#1311492111yescharacteristic
886C2#1311492511yescharacteristic
887C2#1311502211yescharacteristic
888C2#1311502511yescharacteristic
889C2#1311502711yescharacteristic
890C2#1311503011yescharacteristic
891C2#1311514011yescharacteristic
892C2#1311514211yescharacteristic
893C2#1311515011yescharacteristic
894C2#1311515211yescharacteristic
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#10730
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×C4⋊C4×D13C4semidirect
27. C2×#88060C4semidirect
29. #11718648C4semidirect
68. C22×C8×C13C2×C4semidirect
78. C2×C13×C4⋊C4C2×C4semidirect
93. C2×C4⋊Dic13C2×C4semidirect
105. C22×#1055C2×C4semidirect
227. C13×C4⋊C4C22⋊C4semidirect
236. C4⋊Dic13C22⋊C4semidirect
251. C2×#340D13semidirect
451. C2×D13#340semidirect
506. C22×C8C4×D13semidirect
535. C2×C4⋊C4C4×D13semidirect
689. C4⋊C4#6103semidirect
691. C13#10730semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C22×#880602
C2×#117186482
C2×#117181432
C2×#117181212
C2×C13×#3402
#1073013