Finite Group Databasebeta

← #27289368

Subgroups — #27289368

Order 13568.

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×D53C211yesmaximal, characteristic
2C22×#13133129C211yesmaximal, characteristic
3C2×#16810480C211yesmaximal, characteristic
4C2×#16810386C211yesmaximal, characteristic, complemented
5C2×#16810385C211yesmaximal, characteristic, complemented
6C2×#16810385C211yesmaximal, characteristic, complemented
7C2×C53×#340C211yesmaximal, characteristic, complemented
8C23×C4×D53—21no—
9C23×C4×D53C2211yescharacteristic
10C23×#88322C2211yescharacteristic
11C22×C4⋊Dic53C2211yescharacteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×#11719919—21no—
14C2×C4⋊C4×D53—22no—
15C2×C4⋊C4×D53—22no—
16C2×C4⋊C4×D53—22no—
17C2×C4⋊C4×D53—22no—
18C2×C4⋊C4×D53—22no—
19C2×C4⋊C4×D53C414yescomplemented
20C22×#11719921—21no—
21C2×#13133129—22no—
22C2×#13133129—22no—
23C2×#13133129C414yescomplemented
24#16810480—22no—
25#16810480C414yescomplemented
26C2×#13133124—21no—
27#16810386—22no—
28#16810385—22no—
29#16810385—22no—
30C23×C8×C53C2211yescharacteristic
31C22×C4⋊C4×C53C2211yescharacteristic
32C22×C4⋊C4×C53C2211yescharacteristic
33C53×#340—22no—
34C24×D53D411yescharacteristic
35C23×Dic53—21no—
36C23×Dic53—21no—
37C23×Dic53D411yescharacteristic
38C22×C4×D53—21no—
39C22×C4×D53—21no—
40C22×C4×D53—21no—
41C22×C4×D53—21no—
42C22×C4×D53—21no—
43C22×C4×D53—21no—
44C22×C4×D53—21no—
45C22×C4×D53—21no—
46C22×C4×D53—24no—
47C22×C4×D53—24no—
48C22×C4×D53—24no—
49C22×C4×D53—42no—
50C22×C4×D53—42no—
51C22×C4×D53—42no—
52C22×C4×D53—42no—
53C22×C4×D53C2×C412yes—
54C22×C4×D53C2×C412yes—
55C22×C4×D53C2×C412yes—
56C22×C4×D53D412yes—
57C22×C4×D53D412yes—
58C22×C4×D53Q812yes—
59C22×#88322—21no—
60C22×#88322—21no—
61C22×#88322—21no—
62C22×#88322—21no—
63C22×#88322—21no—
64C22×#88322—21no—
65C22×#88322C2×C412yescomplemented
66C2×C4⋊Dic53—21no—
67C2×C4⋊Dic53—21no—
68C2×C4⋊Dic53—21no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53—21no—
71C2×C4⋊Dic53—21no—
72C2×C4⋊Dic53—21no—
73C2×C4⋊Dic53—21no—
74C2×C4⋊Dic53C2×C412yes—
75C2×C4⋊Dic53C2×C412yescomplemented
76C2×C4⋊Dic53D412yes—
77C2×C4⋊Dic53D412yes—
78C2×#11719919—24no—
79C2×#11719919—24no—
80C2×#11719919—24no—
81C4⋊C4×D53—28no—
82C4⋊C4×D53—28no—
83C4⋊C4×D53—28no—
84C4⋊C4×D53—28no—
85C2×#11719921—24no—
86C2×#11719921—42no—
87C2×#11719921—42no—
88#13133129—28no—
89#13133124—24no—
90C23×C4×C53—21no—
91C23×C4×C53—21no—
92C23×C4×C53C2311yescharacteristic
93C22×C8×C53—21no—
94C22×C8×C53—21no—
95C22×C8×C53—21no—
96C22×C8×C53—21no—
97C22×C8×C53—21no—
98C22×C8×C53—21no—
99C22×C8×C53C2×C412yescomplemented
100C2×C4⋊C4×C53—21no—
101C2×C4⋊C4×C53—21no—
102C2×C4⋊C4×C53—21no—
103C2×C4⋊C4×C53—21no—
104C2×C4⋊C4×C53—21no—
105C2×C4⋊C4×C53—21no—
106C2×C4⋊C4×C53—21no—
107C2×C4⋊C4×C53—21no—
108C2×C4⋊C4×C53C2×C412yes—
109C2×C4⋊C4×C53C2×C412yescomplemented
110C2×C4⋊C4×C53D412yes—
111C2×C4⋊C4×C53D412yes—
112C24×C53C2×D411yescharacteristic
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53C22⋊C412yes—
122C23×D53C22⋊C412yes—
123C23×D53C4⋊C412yes—
124C23×D53D812yes—
125C23×D53SD1612yes—
126C23×D53SD1612yes—
127C23×D53Q1612yes—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—41no—
133C22×C4×C53—41no—
134C22×C4×C53—41no—
135C22×C4×C53—41no—
136C22×C4×C53—41no—
137C22×C4×C53—41no—
138C22×C4×C53—41no—
139C22×C4×C53—41no—
140C22×C4×C53—41no—
141C22×C4×C53—41no—
142C22×C4×C53C22×C411yescharacteristic
143C22×C4×C53C22×C411yescharacteristic
144C22×C4×C53C22×C411yescharacteristic
145C22×C4×C53C2×D411yescharacteristic
146C22×C4×C53C2×D411yescharacteristic
147C22×C4×C53C2×D411yescharacteristic
148C22×C4×C53C2×D411yescharacteristic
149C22×C4×C53C2×D411yescharacteristic
150C22×C4×C53C2×D411yescharacteristic
151C22×C4×C53C2×Q811yescharacteristic
152C22×C4×C53#4111yescharacteristic
153C22×C4×C53#4111yescharacteristic
154C22×C4×C53#4111yescharacteristic
155C22×C4×C53#4111yescharacteristic
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—41no—
165C22×Dic53—41no—
166C22×Dic53—41no—
167C22×Dic53—41no—
168C22×Dic53—41no—
169C22×Dic53—41no—
170C22×Dic53—41no—
171C22×Dic53—41no—
172C22×Dic53—41no—
173C22×Dic53—41no—
174C22×Dic53C22⋊C412yes—
175C22×Dic53C22⋊C412yes—
176C22×Dic53C4⋊C412yes—
177C2×C4×D53—22no—
178C2×C4×D53—22no—
179C2×C4×D53—22no—
180C2×C4×D53—22no—
181C2×C4×D53—22no—
182C2×C4×D53—22no—
183C2×C4×D53—22no—
184C2×C4×D53—22no—
185C2×C4×D53—22no—
186C2×C4×D53—22no—
187C2×C4×D53—22no—
188C2×C4×D53—22no—
189C2×C4×D53—22no—
190C2×C4×D53—22no—
191C2×C4×D53—22no—
192C2×C4×D53—22no—
193C2×C4×D53—22no—
194C2×C4×D53—22no—
195C2×C4×D53—22no—
196C2×C4×D53—22no—
197C2×C4×D53—22no—
198C2×C4×D53—22no—
199C2×C4×D53—22no—
200C2×C4×D53—22no—
201C2×C4×D53—216no—
202C2×C4×D53—48no—
203C2×C4×D53—48no—
204C2×C4×D53—48no—
205C2×C4×D53—48no—
206C2×C4×D53—48no—
207C2×C4×D53—48no—
208C2×C4×D53C4214yes—
209C2×C4×D53C22⋊C414yes—
210C2×C4×D53C4⋊C414yes—
211C2×C4×D53C4⋊C414yes—
212C2×C8×C53—22no—
213C2×C8×C53—22no—
214C2×C8×C53—22no—
215C2×C8×C53—41no—
216C2×C8×C53—41no—
217C2×C8×C53—41no—
218C2×C8×C53—41no—
219C4⋊C4×C53—22no—
220C4⋊C4×C53—22no—
221C4⋊C4×C53—22no—
222C4⋊C4×C53—22no—
223C4⋊C4×C53—22no—
224C4⋊C4×C53—41no—
225C4⋊C4×C53—41no—
226C4⋊C4×C53C22⋊C414yescomplemented
227#11719921—48no—
228C4⋊Dic53—22no—
229C4⋊Dic53—22no—
230C4⋊Dic53—22no—
231C4⋊Dic53—22no—
232C4⋊Dic53—22no—
233C4⋊Dic53—41no—
234C4⋊Dic53—41no—
235C4⋊Dic53C22⋊C414yescomplemented
236#11719919—216no—
237C2×#88322—22no—
238C2×#88322—22no—
239C2×#88322—22no—
240C2×#88322—41no—
241C2×#88322—41no—
242C2×#88322—41no—
243C2×#88322—41no—
244C23×C53C2×C22⋊C411yescharacteristic
245C23×C53C2×C22⋊C411yescharacteristic
246C23×C53C2×C4⋊C411yescharacteristic
247C23×C53#12011yescharacteristic
248C23×C53#12011yescharacteristic
249C23×C53#12311yescharacteristic
250C23×C53#12311yescharacteristic
251C23×C53C2×D811yescharacteristic
252C23×C53C2×SD1611yescharacteristic
253C23×C53C2×SD1611yescharacteristic
254C23×C53C2×Q1611yescharacteristic
255C23×C53AGL(1,ℤ/8)11yescharacteristic
256C23×C53AGL(1,ℤ/8)11yescharacteristic
257C23×C53#13711yescharacteristic
258C23×C53#13711yescharacteristic
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—22no—
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53#9514yes—
288C22×D53#10214yes—
289C22×D53#10214yes—
290C22×D53#10314yes—
291C22×D53#10314yes—
292C22×D53#10614yes—
293C22×D53#10714yes—
294C2×C4×C53—24no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—81no—
305C2×C4×C53—81no—
306C2×C4×C53—81no—
307C2×C4×C53—81no—
308C2×C4×C53C2×C4211yescharacteristic
309C2×C4×C53C2×C22⋊C411yescharacteristic
310C2×C4×C53C2×C22⋊C411yescharacteristic
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C2×C4⋊C411yescharacteristic
313C2×C4×C53C2×C4⋊C411yescharacteristic
314C2×C4×C53#11711yescharacteristic
315C2×C4×C53#11711yescharacteristic
316C2×C4×C53C4×D411yescharacteristic
317C2×C4×C53C4×D411yescharacteristic
318C2×C4×C53C4×D411yescharacteristic
319C2×C4×C53C4×D411yescharacteristic
320C2×C4×C53C4×D411yescharacteristic
321C2×C4×C53C4×D411yescharacteristic
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53#12011yescharacteristic
325C2×C4×C53#12011yescharacteristic
326C2×C4×C53#12111yescharacteristic
327C2×C4×C53#12111yescharacteristic
328C2×C4×C53#12111yescharacteristic
329C2×C4×C53#12111yescharacteristic
330C2×C4×C53C22⋊Q811yescharacteristic
331C2×C4×C53C22⋊Q811yescharacteristic
332C2×C4×C53C22⋊Q811yescharacteristic
333C2×C4×C53C22⋊Q811yescharacteristic
334C2×C4×C53#12311yescharacteristic
335C2×C4×C53#12311yescharacteristic
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—24no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—42no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—42no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—81no—
353C2×Dic53—81no—
354C2×Dic53—81no—
355C2×Dic53—81no—
356C2×Dic53#9514yes—
357C4×D53—24no—
358C4×D53—24no—
359C4×D53—24no—
360C4×D53—24no—
361C4×D53—24no—
362C4×D53—24no—
363C4×D53—24no—
364C4×D53—24no—
365C4×D53—432no—
366C8×C53—42no—
367#88322—42no—
368#10730—531nomaximal, Sylow
369C22×C53C2×#9511yescharacteristic
370C22×C53#37911yescharacteristic
371C22×C53#38111yescharacteristic
372C22×C53#38511yescharacteristic
373C22×C53#38511yescharacteristic
374C22×C53#38611yescharacteristic
375C22×C53#38611yescharacteristic
376C22×C53C2×#10211yescharacteristic
377C22×C53C2×#10211yescharacteristic
378C22×C53C2×#10311yescharacteristic
379C22×C53C2×#10311yescharacteristic
380C22×C53#41711yescharacteristic
381C22×C53#41711yescharacteristic
382C22×C53#41811yescharacteristic
383C22×C53#41911yescharacteristic
384C22×C53C2×#10611yescharacteristic
385C22×C53C2×#10711yescharacteristic
386C22×C53#42811yescharacteristic
387C22×C53#42811yescharacteristic
388C22×C53#44711yescharacteristic
389C22×C53#44711yescharacteristic
390C22×C53#44811yescharacteristic
391C22×C53#44811yescharacteristic
392C22×C53#45011yescharacteristic
393C22×C53#45011yescharacteristic
394C22×C53#45111yescharacteristic
395C22×C53#45111yescharacteristic
396C22×C53#48011yescharacteristic
397C22×C53#48011yescharacteristic
398C22×C53#48111yescharacteristic
399C22×C53#48111yescharacteristic
400C22×C53#48311yescharacteristic
401C22×C53#48311yescharacteristic
402C22×C53#48411yescharacteristic
403C22×C53#48411yescharacteristic
404C2×D53—24no—
405C2×D53—24no—
406C2×D53—24no—
407C2×D53—24no—
408C2×D53—24no—
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—24no—
413C2×D53—24no—
414C2×D53—24no—
415C2×D53—24no—
416C2×D53—24no—
417C2×D53—24no—
418C2×D53#34018yescomplemented
419C4×C53—44no—
420C4×C53—82no—
421C4×C53C4×C22⋊C411yescharacteristic
422C4×C53C4×C22⋊C411yescharacteristic
423C4×C53#38011yescharacteristic
424C4×C53#38011yescharacteristic
425C4×C53#38511yescharacteristic
426C4×C53#38511yescharacteristic
427C4×C53#38611yescharacteristic
428C4×C53#38611yescharacteristic
429Dic53—24no—
430Dic53—44no—
431Dic53—82no—
432C23×C4⋊C4—531no—
433C22×C22⋊C8—531no—
434C2×#380—531no—
435C2×#340—531no—
436C2×#340—531no—
437C2×#340—531no—
438C2×#340D5311yescharacteristic, complemented
439C2×C53C22⋊#9511yescharacteristic
440C2×C53C2×#34011yescharacteristic
441C2×C53#173611yescharacteristic
442C2×C53#178611yescharacteristic
443C2×C53#178711yescharacteristic
444C2×C53#182311yescharacteristic
445C2×C53#182411yescharacteristic
446C2×C53#185211yescharacteristic
447C2×C53#185211yescharacteristic
448C2×C53#185311yescharacteristic
449C2×C53#185311yescharacteristic
450C2×C53#187211yescharacteristic
451C2×C53#187211yescharacteristic
452C2×C53#187411yescharacteristic
453C2×C53#187411yescharacteristic
454D53—28no—
455C24×C4—531no—
456C24×C4—1061no—
457C23×C8—531no—
458C23×C8C2×D5311yescharacteristic
459C22×C4⋊C4—531no—
460C22×C4⋊C4—531no—
461C22×C4⋊C4—534no—
462C22×C4⋊C4—1062no—
463C22×C4⋊C4—1062no—
464C22×C4⋊C4—1062no—
465C22×C4⋊C4—1061no—
466C22×C4⋊C4—1062no—
467C22×C4⋊C4—1062no—
468C22×C4⋊C4C2×D5311yescharacteristic
469C22×C4⋊C4C2×D5311yescharacteristic
470C22×C22⋊C4—1061no—
471C2×C22⋊C8—534no—
472C2×C22⋊C8—1062no—
473C2×C22⋊C8—1062no—
474#380—534no—
475#380—1062no—
476C2×#95—1061no—
477#340—22no—
478#340—1062no—
479#340—1062no—
480#340—1062no—
481C53#1073011yescharacteristic, complemented, Sylow
482C25—531no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—531no—
486C23×C4—532no—
487C23×C4—532no—
488C23×C4—532no—
489C23×C4—532no—
490C23×C4—532no—
491C23×C4—532no—
492C23×C4—1064no—
493C23×C4—1064no—
494C23×C4—1064no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4—1061no—
498C23×C4—1061no—
499C23×C4—1061no—
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4—2122no—
506C23×C4—2122no—
507C23×C4—2122no—
508C23×C4—2122no—
509C23×C4C22×D5311yescharacteristic
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8—21no—
514C22×C8—21no—
515C22×C8—21no—
516C22×C8—532no—
517C22×C8—1061no—
518C22×C8—1061no—
519C22×C8—1061no—
520C22×C8—1061no—
521C22×C8—1061no—
522C22×C8—1061no—
523C22×C8C4×D5312yescomplemented
524C2×C4⋊C4—21no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—532no—
533C2×C4⋊C4—532no—
534C2×C4⋊C4—532no—
535C2×C4⋊C4—532no—
536C2×C4⋊C4—1068no—
537C2×C4⋊C4—1068no—
538C2×C4⋊C4—1068no—
539C2×C4⋊C4—1064no—
540C2×C4⋊C4—1064no—
541C2×C4⋊C4—1064no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1068no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4C4×D5312yes—
552C2×C4⋊C4C4×D5312yescomplemented
553C2×C4⋊C4D21212yes—
554C2×C4⋊C4C22⋊D5312yes—
555C2×C22⋊C4—1064no—
556C2×C22⋊C4—2122no—
557C2×C22⋊C4—2122no—
558C22⋊C8—1068no—
559#95—1064no—
560C24—532no—
561C24—532no—
562C24—532no—
563C24—532no—
564C24—532no—
565C24—532no—
566C24—532no—
567C24—1061no—
568C24—1061no—
569C24—1061no—
570C24—1061no—
571C24—1061no—
572C24—1061no—
573C24—1061no—
574C24—1061no—
575C24D4×D5311yescharacteristic
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
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—41no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—534no—
594C22×C4—534no—
595C22×C4—534no—
596C22×C4—534no—
597C22×C4—10616no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1062no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1062no—
630C22×C4—2128no—
631C22×C4—2128no—
632C22×C4—2128no—
633C22×C4—2128no—
634C22×C4—2128no—
635C22×C4—2128no—
636C22×C4—2121no—
637C22×C4—2121no—
638C22×C4—2121no—
639C22×C4—2121no—
640C22×C4—2121no—
641C22×C4—2121no—
642C22×C4—2121no—
643C22×C4—2121no—
644C22×C4—2121no—
645C22×C4—2121no—
646C22×C4C2×C4×D5311yescharacteristic
647C22×C4C2×C4×D5311yescharacteristic
648C22×C4C2×C4×D5311yescharacteristic
649C22×C4C2×D21211yescharacteristic
650C22×C4#1171994511yescharacteristic
651C22×C4#1171994511yescharacteristic
652C22×C4D4×D5311yescharacteristic
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4D4×D5311yescharacteristic
656C22×C4#1171994711yescharacteristic
657C22×C4Q8×D5311yescharacteristic
658C22×C4#1171994911yescharacteristic
659C22×C4C2×C22⋊D5311yescharacteristic
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—41no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—41no—
667C2×C8—1062no—
668C2×C8—1062no—
669C2×C8—1062no—
670C2×C8—2121no—
671C2×C8—2121no—
672C2×C8—2121no—
673C2×C8—2121no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—41no—
680C4⋊C4—41no—
681C4⋊C4—534no—
682C4⋊C4—10616no—
683C4⋊C4—1062no—
684C4⋊C4—1062no—
685C4⋊C4—1062no—
686C4⋊C4—1062no—
687C4⋊C4—1062no—
688C4⋊C4—2121no—
689C4⋊C4—2121no—
690C4⋊C4#1171992114yescomplemented
691C22⋊C4—2128no—
692C23—534no—
693C23—534no—
694C23—534no—
695C23—534no—
696C23—534no—
697C23—534no—
698C23—534no—
699C23—1062no—
700C23—1062no—
701C23—1062no—
702C23—1062no—
703C23—1062no—
704C23—1062no—
705C23—1062no—
706C23—1062no—
707C23—1062no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—1062no—
719C23—1062no—
720C23—1062no—
721C23—1062no—
722C23—1062no—
723C23—1062no—
724C23—1062no—
725C23—1062no—
726C23—1062no—
727C23C22⋊C4×D5311yescharacteristic
728C23C22⋊C4×D5311yescharacteristic
729C23C4⋊C4×D5311yescharacteristic
730C23#1313318511yescharacteristic
731C23#1313318711yescharacteristic
732C23#1313319911yescharacteristic
733C23#1313320211yescharacteristic
734C23D8×D5311yescharacteristic
735C23SD16×D5311yescharacteristic
736C23SD16×D5311yescharacteristic
737C23Q16×D5311yescharacteristic
738C23#1313324111yescharacteristic
739C23#1313324411yescharacteristic
740C23#1313324611yescharacteristic
741C23#1313324911yescharacteristic
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—534no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1064no—
764C2×C4—1064no—
765C2×C4—1064no—
766C2×C4—1064no—
767C2×C4—1064no—
768C2×C4—1064no—
769C2×C4—1064no—
770C2×C4—1064no—
771C2×C4—1064no—
772C2×C4—4241no—
773C2×C4—4241no—
774C2×C4—4241no—
775C2×C4—4241no—
776C2×C4—21232no—
777C2×C4—2122no—
778C2×C4—2122no—
779C2×C4—2122no—
780C2×C4—2122no—
781C2×C4—2122no—
782C2×C4—2122no—
783C2×C4—2122no—
784C2×C4—2122no—
785C2×C4—2122no—
786C2×C4C42×D5311yescharacteristic
787C2×C4C22⋊C4×D5311yescharacteristic
788C2×C4C22⋊C4×D5311yescharacteristic
789C2×C4C2×#1171992111yescharacteristic
790C2×C4C4⋊C4×D5311yescharacteristic
791C2×C4C4⋊C4×D5311yescharacteristic
792C2×C4#1313317411yescharacteristic
793C2×C4#1313317511yescharacteristic
794C2×C4#1313317711yescharacteristic
795C2×C4#1313317711yescharacteristic
796C2×C4C4×C22⋊D5311yescharacteristic
797C2×C4C4×C22⋊D5311yescharacteristic
798C2×C4#1313317911yescharacteristic
799C2×C4#1313317911yescharacteristic
800C2×C4C4×D21211yescharacteristic
801C2×C4C4×D21211yescharacteristic
802C2×C4#1313318511yescharacteristic
803C2×C4#1313318711yescharacteristic
804C2×C4#1313318811yescharacteristic
805C2×C4#1313319011yescharacteristic
806C2×C4#1313319011yescharacteristic
807C2×C4#1313319211yescharacteristic
808C2×C4#1313319311yescharacteristic
809C2×C4#1313319511yescharacteristic
810C2×C4#1313319511yescharacteristic
811C2×C4#1313319711yescharacteristic
812C2×C4#1313319911yescharacteristic
813C2×C4#1313320211yescharacteristic
814C8—42no—
815C8—2122no—
816C22—538no—
817C22—1064no—
818C22—1064no—
819C22—1064no—
820C22—1064no—
821C22—1064no—
822C22—1064no—
823C22—1064no—
824C22—1064no—
825C22—1064no—
826C22—1064no—
827C22—1064no—
828C22—1064no—
829C22—1064no—
830C22—1064no—
831C22#95×D5311yescharacteristic
832C22#1681047811yescharacteristic
833C22#1681048511yescharacteristic
834C22#1681049411yescharacteristic
835C22#1681049711yescharacteristic
836C22#1681049911yescharacteristic
837C22#1681050111yescharacteristic
838C22#102×D5311yescharacteristic
839C22#102×D5311yescharacteristic
840C22#103×D5311yescharacteristic
841C22#103×D5311yescharacteristic
842C22#1681062111yescharacteristic
843C22#1681062311yescharacteristic
844C22#1681062611yescharacteristic
845C22#1681063011yescharacteristic
846C22#106×D5311yescharacteristic
847C22#107×D5311yescharacteristic
848C22#1681066211yescharacteristic
849C22#1681066411yescharacteristic
850C22#1681075511yescharacteristic
851C22#1681075811yescharacteristic
852C22#1681076011yescharacteristic
853C22#1681076311yescharacteristic
854C22#1681077211yescharacteristic
855C22#1681077511yescharacteristic
856C22#1681077711yescharacteristic
857C22#1681078011yescharacteristic
858C22#1681093511yescharacteristic
859C22#1681093811yescharacteristic
860C22#1681094011yescharacteristic
861C22#1681094311yescharacteristic
862C22#1681095211yescharacteristic
863C22#1681095511yescharacteristic
864C22#1681095711yescharacteristic
865C22#1681096011yescharacteristic
866C4—44no—
867C4—82no—
868C4—1064no—
869C4—4242no—
870C4—2124no—
871C4#1681047011yescharacteristic
872C4C4×#1171992111yescharacteristic
873C4#1681048011yescharacteristic
874C4#1681048211yescharacteristic
875C4#1681049411yescharacteristic
876C4#1681049711yescharacteristic
877C4#1681049911yescharacteristic
878C4#1681050111yescharacteristic
879C2—1068no—
880C2#2027293611yescharacteristic
881C2#340×D5311yescharacteristic
882C2#2027443311yescharacteristic
883C2#2027464411yescharacteristic
884C2#2027464811yescharacteristic
885C2#2027480011yescharacteristic
886C2#2027480411yescharacteristic
887C2#2027490111yescharacteristic
888C2#2027490411yescharacteristic
889C2#2027490611yescharacteristic
890C2#2027490911yescharacteristic
891C2#2027501911yescharacteristic
892C2#2027502111yescharacteristic
893C2#2027502911yescharacteristic
894C2#2027503111yescharacteristic
subgroupG/H
centerC24D4×D53
commutatorC2×C4×C53C2×C42
FrattiniC23×C4C22×D53
FittingC2×C53×#340C2
socleC24×C53C2×D4
prime radicalC24×D53D4
cosocleC23×C4×C53C23
hypercenterC2×#340D53
hypocenterC53#10730
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. C2×#16810386C2semidirect
5. C2×#16810385C2semidirect
6. C2×#16810385C2semidirect
7. C2×C53×#340C2semidirect
19. C2×C4⋊C4×D53C4semidirect
23. C2×#13133129C4semidirect
25. #16810480C4semidirect
65. C22×#88322C2×C4semidirect
75. C2×C4⋊Dic53C2×C4semidirect
99. C22×C8×C53C2×C4semidirect
109. C2×C4⋊C4×C53C2×C4semidirect
226. C4⋊C4×C53C22⋊C4semidirect
235. C4⋊Dic53C22⋊C4semidirect
418. C2×D53#340semidirect
438. C2×#340D53semidirect
481. C53#10730semidirect
523. C22×C8C4×D53semidirect
552. C2×C4⋊C4C4×D53semidirect
690. C4⋊C4#11719921semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D532
C22×#131331292
C2×#168104802
C2×#168103862
C2×#168103852
C2×C53×#3402
#1073053