Finite Group Databasebeta

← C2×#20291449 #28329456

Subgroups — C2×#20291449 #28329456

Order 13568.

2926 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133304C211yesmaximal, characteristic, complemented
2C22×D53⋊M16C211yesmaximal, characteristic, complemented
3#20291449C2116yesmaximal, direct product factor
4C2×#16811657C211yesmaximal, characteristic, complemented
5C2×#16811656C211yesmaximal, characteristic, complemented
6C2×#16811655C211yesmaximal, characteristic, complemented
7C2×#16811653C211yesmaximal, characteristic, complemented
8C2×#16811653C211yesmaximal, characteristic, complemented
9C2×#16811652C211yesmaximal, characteristic, complemented
10C2×#16811651C211yesmaximal, characteristic, complemented
11C2×#16811650C211yesmaximal, characteristic, complemented
12C2×#16811629C211yesmaximal, characteristic, complemented
13C2×#16811596C211yesmaximal, characteristic, complemented
14C22×#13133274C211yesmaximal, characteristic, complemented
15C2×#16811587C211yesmaximal, characteristic, complemented
16C2×#16811131C211yesmaximal, characteristic
17C2×#13133304—28no—
18C2×#13133304C2218yescomplemented
19C22×#11719936C2211yescharacteristic
20C22×#11719936C2211yescharacteristic
21C22×#11719936C2211yescharacteristic, complemented
22C2×D53⋊M16—28no—
23C2×D53⋊M16C2218yescomplemented
24C22×#11719940C2211yescharacteristic
25C22×#11719940C2211yescharacteristic
26C22×#11719940C2211yescharacteristic, complemented
27C22×D53⋊C8C2211yescharacteristic
28C22×D53⋊C8C2211yescharacteristic
29C22×D53⋊C8C2211yescharacteristic, complemented
30C23×#88324C2211yescharacteristic
31C23×#88324C2211yescharacteristic
32C23×#88324C2211yescharacteristic, complemented
33#16811657C2218yescomplemented
34#16811656C2218yescomplemented
35#16811655C2218yescomplemented
36#16811653C2218yescomplemented
37#16811653C2218yescomplemented
38#16811652C2218yescomplemented
39#16811651C2218yescomplemented
40#16811650C2218yescomplemented
41#16811629C2218yescomplemented
42C2×#13133284C2211yescharacteristic, complemented
43C2×#13133284C2211yescharacteristic, complemented
44C2×C4⋊#88324C2211yescharacteristic, complemented
45C2×C4⋊#88324C2211yescharacteristic, complemented
46#16811596C2218yescomplemented
47C2×#13133274C2211yescharacteristic
48C2×#13133274C2211yescharacteristic
49C2×#13133274C2211yescharacteristic
50C2×#13133274C2211yescharacteristic
51C2×#13133274C2218yescomplemented
52C2×#13133274C2211yescharacteristic, complemented
53C2×#13133274C2211yescharacteristic, complemented
54C2×C22⋊#88324C2211yescharacteristic, complemented
55C2×C22⋊#88324C2211yescharacteristic, complemented
56#16811587C2218yescomplemented
57C2×#13133272C2211yescharacteristic, complemented
58C2×#13133272C2211yescharacteristic, complemented
59C2×C4×#88324C2211yescharacteristic, complemented
60C2×C4×#88324C2211yescharacteristic, complemented
61C22×#11719947C2211yescharacteristic
62C23×C4×D53C2211yescharacteristic
63#16811131C418yes—
64#16811131C2218yes—
65C2×#13133200C411yescharacteristic
66C2×#13133195C411yescharacteristic
67C2×#13133195C411yescharacteristic
68C2×#13133190C411yescharacteristic
69C2×#13133190C411yescharacteristic
70C2×#13133187C411yescharacteristic
71C2×#13133185C411yescharacteristic
72C2×#13133179C2211yescharacteristic
73C2×#13133179C2211yescharacteristic
74C2×#13133177C2211yescharacteristic
75C2×#13133177C2211yescharacteristic
76C2×#13133173C2211yescharacteristic
77C2×#123×C53C411yescharacteristic
78#13133304—232no—
79C2×#11719936—24no—
80C2×#11719936—24no—
81C2×#11719936—24no—
82C2×#11719936C2314yes—
83C2×#11719936C2314yes—
84C2×#11719936C2314yescomplemented
85D53⋊M16—232no—
86C2×#11719940—24no—
87C2×#11719940—24no—
88C2×#11719940D418yescomplemented
89C2×#11719940C2314yes—
90C2×#11719940C2314yes—
91C2×#11719940C2314yescomplemented
92C2×D53⋊C8—24no—
93C2×D53⋊C8—24no—
94C2×D53⋊C8—24no—
95C2×D53⋊C8C2314yes—
96C2×D53⋊C8C2314yes—
97C2×D53⋊C8C2314yescomplemented
98C22×#88324—24no—
99C22×#88324—24no—
100C22×#88324—24no—
101C22×#88324C2311yescharacteristic
102C22×#88324C2311yescharacteristic
103C22×#88324C2314yes—
104C22×#88324C2311yescharacteristic
105C22×#88324C2311yescharacteristic
106C22×#88324C2311yescharacteristic
107C22×#88324C2311yescharacteristic
108C22×#88324C2314yes—
109C22×#88324C2311yescharacteristic
110C22×#88324C2311yescharacteristic
111C22×#88324C2314yescomplemented
112#13133284C2314yescomplemented
113#13133284C2314yescomplemented
114C4⋊#88324C2314yescomplemented
115C4⋊#88324C2314yescomplemented
116#13133274C2314yes—
117#13133274C2314yes—
118#13133274C2314yes—
119#13133274C2314yes—
120#13133274C2314yescomplemented
121#13133274C2314yescomplemented
122C22⋊#88324C2314yescomplemented
123C22⋊#88324C2314yescomplemented
124#13133272C2314yescomplemented
125#13133272C2314yescomplemented
126C4×#88324C2314yescomplemented
127C4×#88324C2314yescomplemented
128C24×D53C2×C411yescharacteristic
129C2×#11719947—24no—
130C2×#11719947—24no—
131C2×#11719947C2×C414yes—
132C2×#11719947C2314yes—
133C22×Dic106C2×C411yescharacteristic
134C22×D212C2×C411yescharacteristic
135C22×D212C2×C411yescharacteristic
136C22×C22⋊D53C2×C411yescharacteristic
137C22×C22⋊D53C2×C411yescharacteristic
138C22×C22⋊D53C2×C411yescharacteristic
139C22×C22⋊D53C2×C411yescharacteristic
140C23×Dic53C2311yescharacteristic
141C23×Dic53C2311yescharacteristic
142C22×C4×D53—24no—
143C22×C4×D53—24no—
144C22×C4×D53C2×C411yescharacteristic
145C22×C4×D53C2×C411yescharacteristic
146C22×C4×D53C2×C414yes—
147C22×C4×D53C2311yescharacteristic
148C22×C4×D53C2311yescharacteristic
149C22×C4×D53C2311yescharacteristic
150C22×C4×D53C2314yes—
151#13133200C2×C418yes—
152#13133195C2×C418yes—
153#13133195C2×C418yes—
154#13133190C2×C418yes—
155#13133190C2×C418yes—
156#13133187C2×C418yes—
157#13133185C2×C418yes—
158#13133179C2×C414yes—
159#13133179C2×C414yes—
160#13133179C2314yes—
161#13133179C2314yes—
162#13133177C2×C414yes—
163#13133177C2×C414yes—
164#13133177C2314yes—
165#13133177C2314yes—
166#13133173C2×C414yes—
167#13133173C2314yes—
168C2×#11719919C2×C411yescharacteristic
169C2×#11719919C2×C411yescharacteristic
170C2×#11719919C2×C411yescharacteristic
171C2×#11719919C2×C411yescharacteristic
172C2×C22⋊Dic53C2×C411yescharacteristic
173C2×#11719921C2×C411yescharacteristic
174C2×#11719921C2×C411yescharacteristic
175C2×#11719921C2×C411yescharacteristic
176C2×#11719921C2×C411yescharacteristic
177C2×#11719921C2×C411yescharacteristic
178C2×#11719921C2×C411yescharacteristic
179C2×C4×Dic53C2311yescharacteristic
180C2×C4×Dic53C2311yescharacteristic
181C22×D4×C53C2×C411yescharacteristic
182C23×C4×C53C2×C411yescharacteristic
183#123×C53C2×C418yes—
184C2×C4⋊C4×C53C2×C411yescharacteristic
185C2×C4⋊C4×C53C2×C411yescharacteristic
186C2×C22⋊C4×C53C2×C411yescharacteristic
187C2×C22⋊C4×C53C2×C411yescharacteristic
188C2×C22⋊C4×C53C2×C411yescharacteristic
189C24×C53C22×C411yescharacteristic
190C24×C53C22×C411yescharacteristic
191C23×D53—24no—
192C23×D53—24no—
193C23×D53—42no—
194C23×D53C22×C411yescharacteristic
195C23×D53C22×C411yescharacteristic
196C23×D53C22×C414yes—
197C23×D53C22×C411yescharacteristic
198C2×D4×C53—24no—
199C2×D4×C53C22×C414yes—
200C22×C4×C53—24no—
201C22×C4×C53C22×C411yescharacteristic
202C22×C4×C53C22×C411yescharacteristic
203C22×C4×C53C22×C411yescharacteristic
204C22×C4×C53C22×C411yescharacteristic
205C22×C4×C53C22×C411yescharacteristic
206C22×C4×C53C22×C414yes—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—24no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—42no—
211C2×C22⋊D53C22×C414yes—
212C2×C22⋊D53C22×C414yes—
213C2×C22⋊D53C22×C414yes—
214C2×C22⋊D53C22×C414yes—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53C22×C411yescharacteristic
218C22×Dic53C22×C411yescharacteristic
219C22×Dic53C22×C411yescharacteristic
220C22×Dic53C22×C412yes—
221C22×Dic53C22×C411yescharacteristic
222C22×Dic53C22×C412yes—
223C22×Dic53C2×D414yes—
224C22×Dic53#4114yes—
225C22×Dic53C2412yes—
226C22×Dic53C2411yescharacteristic
227C22×Dic53C2412yes—
228#11719947—216no—
229#11719947—28no—
230#11719947—28no—
231C2×D212—24no—
232C2×D212—42no—
233C2×D212C22×C414yes—
234C2×D212C22×C414yes—
235C2×C4×D53—24no—
236C2×C4×D53—24no—
237C2×C4×D53—216no—
238C2×C4×D53—22no—
239C2×C4×D53—28no—
240C2×C4×D53—22no—
241C2×C4×D53—22no—
242C2×C4×D53—22no—
243C2×C4×D53—22no—
244C2×C4×D53—28no—
245C2×C4×D53—22no—
246C2×C4×D53C22×C412yes—
247C2×C4×D53C22×C412yes—
248C2×C4×D53C22×C412yes—
249C2×C4×D53C22×C414yes—
250C2×C4×D53C22×C414yes—
251C2×C4×D53C2412yes—
252C2×C4×D53C2412yes—
253C2×C4×D53C2412yes—
254C2×Dic106—24no—
255C2×Dic106C22×C414yes—
256#11719940—28no—
257#11719940—28no—
258#11719940C2×D4116yescomplemented
259C2×#88324—22no—
260C2×#88324—22no—
261C2×#88324—28no—
262C2×#88324—22no—
263C2×#88324—22no—
264C2×#88324—22no—
265C2×#88324—22no—
266C2×#88324—28no—
267C2×#88324—28no—
268C2×#88324C2×D414yes—
269C2×#88324C2×D414yes—
270C2×#88324C2412yes—
271C2×#88324C2412yes—
272C2×#88324C2412yes—
273C2×#88324C2412yes—
274C2×#88324C2412yes—
275C2×#88324C2412yes—
276C2×#88324C2412yes—
277C2×#88324C2412yes—
278#11719936—28no—
279#11719936—28no—
280#11719936—28no—
281D53⋊C8—28no—
282D53⋊C8—28no—
283D53⋊C8—28no—
284C4⋊C4×C53C22×C414yes—
285C4⋊C4×C53C22×C414yes—
286C22⋊C4×C53C22×C414yes—
287C22⋊C4×C53C22×C414yes—
288C22⋊C4×C53C22×C414yes—
289C22⋊Dic53C22×C414yes—
290#11719921C22×C414yes—
291#11719921C22×C414yes—
292#11719921C22×C414yes—
293#11719921C22×C414yes—
294#11719921C22×C414yes—
295#11719921C22×C414yes—
296#11719919C22×C414yes—
297#11719919C22×C414yes—
298#11719919C22×C414yes—
299#11719919C22×C414yes—
300C4×Dic53C22×C412yes—
301C4×Dic53C22×C412yes—
302C4×Dic53C2412yes—
303C4×Dic53C2412yes—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53C4×D414yes—
310C23×C53C23×C412yes—
311C23×C53C23×C412yes—
312C23×C53C23×C411yescharacteristic
313C22×D53—22no—
314C22×D53—22no—
315C22×D53—28no—
316C22×D53—22no—
317C22×D53—22no—
318C22×D53—22no—
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—28no—
323C22×D53—44no—
324C22×D53—416no—
325C22×D53#13114yescomplemented
326C22×D53C23×C412yes—
327C22×D53C23×C412yes—
328C22×D53C23×C412yes—
329D4×C53—28no—
330C2×C4×C53—22no—
331C2×C4×C53—28no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53C23×C412yes—
337C2×C4×C53C23×C412yes—
338C2×C4×C53C23×C412yes—
339C2×C4×C53C23×C412yes—
340C2×C4×C53C23×C412yes—
341C22⋊D53—28no—
342C22⋊D53—28no—
343C22⋊D53—28no—
344C22⋊D53—44no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—24no—
349C2×Dic53—22no—
350C2×Dic53—22no—
351C2×Dic53C4×D414yes—
352C2×Dic53C4×D418yes—
353C2×Dic53C23×C412yes—
354C2×Dic53C23×C412yes—
355C2×Dic53C23×C412yes—
356C2×Dic53C23×C412yes—
357C2×Dic53C23×C411yescharacteristic
358C2×Dic53C22×D412yes—
359C2×Dic53C22×D414yes—
360C2×Dic53C2×#4112yes—
361C2×Dic53C2×#4114yes—
362C2×Dic53C2511yescharacteristic
363D212—28no—
364D212—44no—
365C4×D53—28no—
366C4×D53—28no—
367C4×D53—24no—
368C4×D53—24no—
369C4×D53—24no—
370C4×D53—22no—
371C4×D53—22no—
372C4×D53—22no—
373C4×D53—22no—
374C4×D53—22no—
375C4×D53—22no—
376Dic106—28no—
377#88324—22no—
378#88324—22no—
379#88324—22no—
380#88324—22no—
381#88324—22no—
382#88324—22no—
383#88324C22×D414yes—
384#88324C22×D414yes—
385C2×#2933—531nomaximal, Sylow
386C22×C53—28no—
387C22×C53—22no—
388C22×C53—22no—
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—22no—
392C22×C53—44no—
393C22×C53C2×C4×D414yes—
394C22×C53C2×C4×D412yes—
395C22×C53C2×#13112yes—
396C22×C53#56812yes—
397C22×C53C24×C411yescharacteristic
398C2×D53—22no—
399C2×D53—28no—
400C2×D53—22no—
401C2×D53—22no—
402C2×D53—22no—
403C2×D53—22no—
404C2×D53—22no—
405C2×D53—22no—
406C2×D53—22no—
407C2×D53—416no—
408C2×D53—44no—
409C2×D53—44no—
410C2×D53C2×#13114yescomplemented
411C4×C53—22no—
412C4×C53—22no—
413C4×C53—22no—
414C4×C53—22no—
415C4×C53—22no—
416Dic53—22no—
417Dic53—22no—
418Dic53—22no—
419Dic53C2×C4×D414yes—
420Dic53C2×C4×D412yes—
421Dic53C23×D411yescharacteristic
422Dic53C22×#4111yescharacteristic
423C22×#131—531no—
424C23×M16—531no—
425C2×#525—531no—
426#2933—5316no—
427C2×#436—531no—
428C2×#436—531no—
429C2×#435—531no—
430C2×#435—531no—
431C2×#435—531no—
432C2×#435—531no—
433C2×C8×D4—531no—
434C2×C8×D4—531no—
435C2×#424—531no—
436C2×#408—531no—
437C22×C22⋊C8—531no—
438C2×#405—531no—
439C2×C53—24no—
440C2×C53—42no—
441C2×C53#293314yescomplemented
442C2×C53C22×C4×D411yescharacteristic
443C2×C53C22×#13111yescharacteristic
444C2×C53C2×#56811yescharacteristic
445D53—24no—
446D53—42no—
447D53—42no—
448C22×#41—531no—
449C24×C4—531no—
450C2×#131—538no—
451C2×#131—1068no—
452C22×M16—531no—
453C22×M16—531no—
454C22×M16—531no—
455C22×M16—531no—
456C22×M16—531no—
457C22×M16—531no—
458C22×M16—538no—
459C22×M16—1068no—
460C23×C8—531no—
461C23×C8—531no—
462C23×C8—531no—
463C23×C8—531no—
464C23×C8—531no—
465C23×C8—531no—
466#525—538no—
467#525—538no—
468C2×#123—531no—
469C2×#123#615711yescharacteristic
470C2×C22⋊Q8—531no—
471C2×C22⋊Q8—531no—
472C2×#121—531no—
473C2×#121—531no—
474C2×#120—531no—
475C2×#120—531no—
476C2×C4×D4—531no—
477C2×C4×D4—531no—
478C2×C4×D4—531no—
479C2×C4×D4—531no—
480C2×#117—531no—
481#436—538no—
482#436—538no—
483#435—538no—
484#435—538no—
485#435—538no—
486#435—538no—
487C8×D4—538no—
488C8×D4—538no—
489#424—538no—
490C2×C4⋊C8—531no—
491C2×C4⋊C8—531no—
492C2×C4⋊C8—531no—
493C2×C4⋊C8—531no—
494#408—538no—
495C2×C22⋊C8—531no—
496C2×C22⋊C8—531no—
497C2×C22⋊C8—531no—
498C2×C22⋊C8—531no—
499C2×C22⋊C8—538no—
500C2×C22⋊C8—531no—
501C2×C22⋊C8—531no—
502C2×C22⋊C8—531no—
503C2×C22⋊C8—531no—
504#405—538no—
505C2×#97—531no—
506C2×#97—531no—
507C2×C4×C8—531no—
508C2×C4×C8—531no—
509C53C2×#293311yescharacteristic, complemented, Sylow
510C25—531no—
511C2×#41—534no—
512C2×#41—534no—
513C2×#41—1064no—
514C2×#41—1064no—
515C22×Q8—531no—
516C22×D4—531no—
517C22×D4—531no—
518C22×D4—531no—
519C22×D4—531no—
520C22×D4—531no—
521C22×D4—531no—
522C22×D4C2×#615711yescharacteristic
523C23×C4—531no—
524C23×C4—531no—
525C23×C4—531no—
526C23×C4—531no—
527C23×C4—531no—
528C23×C4—531no—
529C23×C4—531no—
530C23×C4—534no—
531C23×C4—534no—
532C23×C4—1064no—
533C23×C4—1064no—
534C23×C4C2×#615711yescharacteristic
535#131—10632no—
536C2×M16—534no—
537C2×M16—538no—
538C2×M16—534no—
539C2×M16—534no—
540C2×M16—534no—
541C2×M16—534no—
542C2×M16—534no—
543C2×M16—1064no—
544C2×M16—1064no—
545C2×M16—1064no—
546C2×M16—1064no—
547C2×M16—10632no—
548C2×M16—1064no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—531no—
554C22×C8—531no—
555C22×C8—534no—
556C22×C8—534no—
557C22×C8—534no—
558C22×C8—534no—
559C22×C8—534no—
560C22×C8—531no—
561C22×C8—531no—
562C22×C8—534no—
563C22×C8—1064no—
564C22×C8—1064no—
565C22×C8—1064no—
566C22×C8—1064no—
567C22×C8—1064no—
568C22×C8—1064no—
569#123—538no—
570#123C2×#615718yes—
571C22⋊Q8—538no—
572C22⋊Q8—538no—
573#121—538no—
574#121—538no—
575#120—538no—
576#120—538no—
577C4×D4—534no—
578C4×D4—534no—
579C4×D4—534no—
580C4×D4—534no—
581C4×D4—534no—
582C4×D4—534no—
583C4×D4—534no—
584C4×D4—534no—
585#117—534no—
586#117—534no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—531no—
589C2×C4⋊C4—531no—
590C2×C4⋊C4—531no—
591C2×C4⋊C4C2×#615711yescharacteristic
592C2×C4⋊C4C2×#615711yescharacteristic
593C2×C22⋊C4—531no—
594C2×C22⋊C4—531no—
595C2×C22⋊C4—531no—
596C2×C22⋊C4—531no—
597C2×C22⋊C4—531no—
598C2×C22⋊C4—531no—
599C2×C22⋊C4—531no—
600C2×C22⋊C4C2×#615711yescharacteristic
601C2×C22⋊C4C2×#615711yescharacteristic
602C2×C22⋊C4C2×#615711yescharacteristic
603C2×C42—531no—
604C2×C42—531no—
605C4⋊C8—534no—
606C4⋊C8—534no—
607C4⋊C8—534no—
608C4⋊C8—534no—
609C22⋊C8—534no—
610C22⋊C8—534no—
611C22⋊C8—534no—
612C22⋊C8—534no—
613C22⋊C8—534no—
614C22⋊C8—534no—
615C22⋊C8—534no—
616C22⋊C8—534no—
617#97—534no—
618#97—534no—
619C4×C8—534no—
620C4×C8—534no—
621C24—531no—
622C24—531no—
623C24—531no—
624C24—534no—
625C24—1064no—
626C24—1064no—
627C24—2122no—
628C24C22×#615711yescharacteristic
629C24C22×#615711yescharacteristic
630#41—1068no—
631#41—10616no—
632#41—1068no—
633C2×Q8—534no—
634C2×Q8—1064no—
635C2×D4—24no—
636C2×D4—534no—
637C2×D4—534no—
638C2×D4—534no—
639C2×D4—534no—
640C2×D4—534no—
641C2×D4—534no—
642C2×D4—1064no—
643C2×D4—1064no—
644C2×D4—1064no—
645C2×D4—1064no—
646C2×D4—2122no—
647C2×D4—2122no—
648C2×D4C22×#615714yes—
649C22×C4—24no—
650C22×C4—534no—
651C22×C4—534no—
652C22×C4—532no—
653C22×C4—532no—
654C22×C4—531no—
655C22×C4—531no—
656C22×C4—532no—
657C22×C4—532no—
658C22×C4—531no—
659C22×C4—531no—
660C22×C4—531no—
661C22×C4—532no—
662C22×C4—532no—
663C22×C4—532no—
664C22×C4—534no—
665C22×C4—534no—
666C22×C4—532no—
667C22×C4—532no—
668C22×C4—532no—
669C22×C4—1062no—
670C22×C4—1062no—
671C22×C4—1062no—
672C22×C4—1068no—
673C22×C4—1064no—
674C22×C4—1064no—
675C22×C4—10616no—
676C22×C4—1062no—
677C22×C4—1062no—
678C22×C4—1068no—
679C22×C4—1062no—
680C22×C4—1062no—
681C22×C4—1062no—
682C22×C4C22×#615714yes—
683C22×C4C22×#615711yescharacteristic
684C22×C4C22×#615711yescharacteristic
685C22×C4C22×#615711yescharacteristic
686C22×C4C22×#615711yescharacteristic
687C22×C4C22×#615711yescharacteristic
688M16—5316no—
689M16—1068no—
690M16—1068no—
691M16—1068no—
692M16—1068no—
693M16—1068no—
694C2×C8—534no—
695C2×C8—534no—
696C2×C8—532no—
697C2×C8—532no—
698C2×C8—532no—
699C2×C8—532no—
700C2×C8—532no—
701C2×C8—532no—
702C2×C8—532no—
703C2×C8—532no—
704C2×C8—1068no—
705C2×C8—1068no—
706C2×C8—1068no—
707C2×C8—1068no—
708C2×C8—1062no—
709C2×C8—1062no—
710C2×C8—1068no—
711C2×C8—1062no—
712C2×C8—1062no—
713C2×C8—1062no—
714C2×C8—1062no—
715C2×C8—1068no—
716C4⋊C4—534no—
717C4⋊C4—534no—
718C4⋊C4—534no—
719C4⋊C4—534no—
720C4⋊C4C22×#615714yes—
721C4⋊C4C22×#615714yes—
722C22⋊C4—534no—
723C22⋊C4—534no—
724C22⋊C4—534no—
725C22⋊C4—534no—
726C22⋊C4—534no—
727C22⋊C4—534no—
728C22⋊C4—534no—
729C22⋊C4C22×#615714yes—
730C22⋊C4C22×#615714yes—
731C22⋊C4C22×#615714yes—
732C42—532no—
733C42—532no—
734C42—532no—
735C42—532no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—534no—
742C23—532no—
743C23—532no—
744C23—532no—
745C23—1068no—
746C23—1062no—
747C23—1062no—
748C23—1068no—
749C23—1062no—
750C23—1062no—
751C23—1062no—
752C23—1062no—
753C23—1062no—
754C23—1062no—
755C23—2124no—
756C23—21216no—
757C23D4×#615714yes—
758C23C23×#615712yes—
759C23C23×#615712yes—
760C23C23×#615711yescharacteristic
761Q8—1068no—
762D4—28no—
763D4—1068no—
764D4—1068no—
765D4—1068no—
766D4—1068no—
767D4—2124no—
768D4—2124no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—534no—
776C2×C4—538no—
777C2×C4—532no—
778C2×C4—534no—
779C2×C4—532no—
780C2×C4—534no—
781C2×C4—531no—
782C2×C4—532no—
783C2×C4—531no—
784C2×C4—532no—
785C2×C4—532no—
786C2×C4—532no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1062no—
791C2×C4—1062no—
792C2×C4—1064no—
793C2×C4—1064no—
794C2×C4—1068no—
795C2×C4—1068no—
796C2×C4—1062no—
797C2×C4—1064no—
798C2×C4—1062no—
799C2×C4—1062no—
800C2×C4—1064no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—1062no—
804C2×C4C23×#615712yes—
805C2×C4C23×#615712yes—
806C2×C4C23×#615712yes—
807C2×C4C23×#615712yes—
808C2×C4C23×#615712yes—
809C8—534no—
810C8—534no—
811C8—1062no—
812C8—1062no—
813C8—1062no—
814C8—1062no—
815C8—1062no—
816C8—1062no—
817C22—22no—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—22no—
822C22—22no—
823C22—44no—
824C22—534no—
825C22—1062no—
826C22—1068no—
827C22—1062no—
828C22—1062no—
829C22—1062no—
830C22—1062no—
831C22—1062no—
832C22—1062no—
833C22—1062no—
834C22—21216no—
835C22—2124no—
836C22—2124no—
837C22C2×D4×#615714yes—
838C22C2×D4×#615712yes—
839C22D53⋊#13112yes—
840C22#1681170212yes—
841C22C24×#615711yescharacteristic
842C4—22no—
843C4—22no—
844C4—22no—
845C4—22no—
846C4—22no—
847C4—531no—
848C4—531no—
849C4—532no—
850C4—534no—
851C4—1062no—
852C4—1062no—
853C4—1062no—
854C2—24no—
855C2—42no—
856C2—1064no—
857C2—2122no—
858C2—2122no—
859C2#2029144914yesdirect product factor
860C2C22×D4×#615711yescharacteristic
861C2C2×D53⋊#13111yescharacteristic
862C2C2×#1681170211yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#123×C53C4
socleC23×C53C23×C4
prime radicalC2×#16811131C2
cosocleC2×Dic53C25
hypercenterC2×#123#6157
hypocenterC53C2×#2933
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×#13133304C2semidirect
2. C22×D53⋊M16C2semidirect
3. #20291449C2direct (N × H)
4. C2×#16811657C2semidirect
5. C2×#16811656C2semidirect
6. C2×#16811655C2semidirect
7. C2×#16811653C2semidirect
8. C2×#16811653C2semidirect
9. C2×#16811652C2semidirect
10. C2×#16811651C2semidirect
11. C2×#16811650C2semidirect
12. C2×#16811629C2semidirect
13. C2×#16811596C2semidirect
14. C22×#13133274C2semidirect
15. C2×#16811587C2semidirect
18. C2×#13133304C22semidirect
21. C22×#11719936C22semidirect
23. C2×D53⋊M16C22semidirect
26. C22×#11719940C22semidirect
29. C22×D53⋊C8C22semidirect
32. C23×#88324C22semidirect
33. #16811657C22semidirect
34. #16811656C22semidirect
35. #16811655C22semidirect
36. #16811653C22semidirect
37. #16811653C22semidirect
38. #16811652C22semidirect
39. #16811651C22semidirect
40. #16811650C22semidirect
41. #16811629C22semidirect
42. C2×#13133284C22semidirect
43. C2×#13133284C22semidirect
44. C2×C4⋊#88324C22semidirect
45. C2×C4⋊#88324C22semidirect
46. #16811596C22semidirect
51. C2×#13133274C22semidirect
52. C2×#13133274C22semidirect
53. C2×#13133274C22semidirect
54. C2×C22⋊#88324C22semidirect
55. C2×C22⋊#88324C22semidirect
56. #16811587C22semidirect
57. C2×#13133272C22semidirect
58. C2×#13133272C22semidirect
59. C2×C4×#88324C22semidirect
60. C2×C4×#88324C22semidirect
84. C2×#11719936C23semidirect
88. C2×#11719940D4semidirect
91. C2×#11719940C23semidirect
97. C2×D53⋊C8C23semidirect
111. C22×#88324C23semidirect
112. #13133284C23semidirect
113. #13133284C23semidirect
114. C4⋊#88324C23semidirect
115. C4⋊#88324C23semidirect
120. #13133274C23semidirect
121. #13133274C23semidirect
122. C22⋊#88324C23semidirect
123. C22⋊#88324C23semidirect
124. #13133272C23semidirect
125. #13133272C23semidirect
126. C4×#88324C23semidirect
127. C4×#88324C23semidirect
258. #11719940C2×D4semidirect
325. C22×D53#131semidirect
410. C2×D53C2×#131semidirect
441. C2×C53#2933semidirect
509. C53C2×#2933semidirect
859. C2#20291449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131333042
C22×D53⋊M162
#202914492
C2×#168116572
C2×#168116562
C2×#168116552
C2×#168116532
C2×#168116522
C2×#168116512
C2×#168116502
C2×#168116292
C2×#168115962
C22×#131332742
C2×#168115872
C2×#168111312
C2×#293353