Finite Group Databasebeta

← C2×#20290700 #28319675

Subgroups — C2×#20290700 #28319675

Order 13568.

2270 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊#6157C211yesmaximal, characteristic
2C22×#13133280C212yesmaximal, complemented
3C2×D53⋊(C22⋊C8)C211yesmaximal, characteristic
4#20290700C218yesmaximal, direct product factor
5C2×#16811496C212yesmaximal, complemented
6C2×C22⋊Q8×D53C211yesmaximal, characteristic
7C24×#6157—21no—
8C22×D53⋊C8C2212yes—
9C22×C4⋊#6157—28no—
10C22×C4⋊#6157—21no—
11C22×C4⋊#6157—22no—
12C22×C4⋊#6157C2214yes—
13C22×C4⋊#6157C2212yes—
14C2×#13133280—28no—
15C2×#13133280C2218yescomplemented
16C2×#13133274—21no—
17D53⋊(C22⋊C8)—22no—
18D53⋊(C22⋊C8)C2214yes—
19C2×C22⋊#88324—21no—
20#16811496C2218yescomplemented
21C22×Q8×D53C2211yescharacteristic
22C23×C4×D53C2211yescharacteristic
23C2×#13133197C411yescharacteristic, complemented
24C2×#13133196C411yescharacteristic, complemented
25C2×#13133195—21no—
26C2×#13133194—21no—
27C2×#13133193C411yescharacteristic, complemented
28C22⋊Q8×D53—22no—
29C22⋊Q8×D53—22no—
30C22⋊Q8×D53C414yescomplemented
31C22⋊Q8×D53C2214yes—
32C2×C4⋊C4×D53—21no—
33C2×C4⋊C4×D53C2211yescharacteristic
34C2×C22⋊C4×D53—21no—
35C2×C22⋊Q8×C53C411yescharacteristic, complemented
36C23×#6157—28no—
37C23×#6157—24no—
38C23×#6157—22no—
39C23×#6157—44no—
40C23×#6157—44no—
41C2×D53⋊C8—22no—
42C2×D53⋊C8—24no—
43C2×D53⋊C8—24no—
44C2×D53⋊C8C2314yes—
45C22×#88324—22no—
46C2×C4⋊#6157—28no—
47C2×C4⋊#6157—216no—
48C2×C4⋊#6157—24no—
49C2×C4⋊#6157—22no—
50C2×C4⋊#6157—24no—
51C2×C4⋊#6157—216no—
52C2×C4⋊#6157D418yes—
53C2×C4⋊#6157C2314yes—
54#13133280—216no—
55#13133274—24no—
56C22⋊#88324—24no—
57C24×D53D411yescharacteristic
58C22×Dic106—21no—
59C22×Dic106C2×C411yescharacteristic, complemented
60C2×Q8×D53—21no—
61C2×Q8×D53—21no—
62C2×Q8×D53—24no—
63C2×Q8×D53—24no—
64C2×Q8×D53C2×C412yescomplemented
65C2×Q8×D53C2312yes—
66C23×Dic53D411yescharacteristic
67C22×C4×D53—24no—
68C22×C4×D53—24no—
69C22×C4×D53—21no—
70C22×C4×D53—21no—
71C22×C4×D53C2×C412yes—
72C22×C4×D53C2×C411yescharacteristic
73C22×C4×D53D411yescharacteristic
74C22×C4×D53D412yes—
75C22×C4×D53D412yes—
76C22×C4×D53D411yescharacteristic
77C22×C4×D53C2312yes—
78C22×C4×D53C2311yescharacteristic
79#13133197—22no—
80#13133197C2×C414yescomplemented
81#13133196—22no—
82#13133196C2×C414yescomplemented
83#13133195—24no—
84#13133195—24no—
85#13133194—24no—
86#13133194—24no—
87#13133193—22no—
88#13133193C2×C414yescomplemented
89C2×C4⋊Dic53—21no—
90C2×C4⋊Dic53C2×C411yescharacteristic, complemented
91C2×#11719919—21no—
92C2×#11719919—21no—
93C2×#11719919—21no—
94C4⋊C4×D53—24no—
95C4⋊C4×D53—24no—
96C4⋊C4×D53—21no—
97C4⋊C4×D53—21no—
98C4⋊C4×D53C2×C412yescomplemented
99C4⋊C4×D53C2312yes—
100C2×C22⋊Dic53—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C22⋊C4×D53—24no—
104C22⋊C4×D53—24no—
105C22×Q8×C53C2×C411yescharacteristic, complemented
106C23×C4×C53C2×C411yescharacteristic
107C22⋊Q8×C53—22no—
108C22⋊Q8×C53C2×C414yescomplemented
109C2×C4⋊C4×C53—21no—
110C2×C4⋊C4×C53C2×C411yescharacteristic, complemented
111C2×C22⋊C4×C53—21no—
112C24×C53C22⋊C411yescharacteristic
113C23×D53—22no—
114C23×D53—22no—
115C23×D53—22no—
116C23×D53—22no—
117C23×D53C22⋊C412yes—
118C23×D53C22⋊C411yescharacteristic
119C23×D53SD1614yes—
120C23×D53Q1614yes—
121C23×D53C2×D412yes—
122C23×D53C2×D411yescharacteristic
123C22×#6157—216no—
124C22×#6157—28no—
125C22×#6157—24no—
126C22×#6157—48no—
127C22×#6157—432no—
128C22×#6157—48no—
129C22×#6157—44no—
130C22×#6157—44no—
131C2×Q8×C53—21no—
132C2×Q8×C53—24no—
133C2×Q8×C53C22×C412yescomplemented
134C22×C4×C53—24no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53C22⋊C411yescharacteristic
138C22×C4×C53C22⋊C412yes—
139C22×C4×C53C22×C412yes—
140C22×C4×C53C22×C411yescharacteristic
141C22×Dic53—24no—
142C22×Dic53—21no—
143C22×Dic53—21no—
144C22×Dic53C22⋊C411yescharacteristic
145C22×Dic53C22⋊C412yes—
146C22×Dic53C2×D412yes—
147C22×Dic53C2×D411yescharacteristic
148Q8×D53—28no—
149Q8×D53—24no—
150Q8×D53—24no—
151Q8×D53—42no—
152Q8×D53—44no—
153Q8×D53—42no—
154C2×C4×D53—22no—
155C2×C4×D53—22no—
156C2×C4×D53—24no—
157C2×C4×D53—24no—
158C2×C4×D53—28no—
159C2×C4×D53—24no—
160C2×C4×D53—28no—
161C2×C4×D53—24no—
162C2×C4×D53—24no—
163C2×C4×D53—24no—
164C2×C4×D53—22no—
165C2×C4×D53—22no—
166C2×C4×D53—22no—
167C2×C4×D53—22no—
168C2×C4×D53—42no—
169C2×C4×D53—42no—
170C2×C4×D53—42no—
171C2×C4×D53—42no—
172C2×C4×D53C22⋊C412yes—
173C2×C4×D53C22⋊C412yes—
174C2×C4×D53C22⋊C412yes—
175C2×C4×D53C22×C412yes—
176C2×C4×D53C22×C411yescharacteristic
177C2×C4×D53C2×D412yes—
178C2×C4×D53C2×D412yes—
179C2×C4×D53C2×D414yes—
180C2×C4×D53C2×D411yescharacteristic
181C2×C4×D53C2×D411yescharacteristic
182C2×C4×D53#4114yes—
183C2×C4×D53C2411yescharacteristic
184C2×Dic106—24no—
185C2×Dic106—21no—
186C2×Dic106—22no—
187C2×Dic106—22no—
188C2×Dic106—44no—
189C2×Dic106C22×C412yescomplemented
190C2×#88324—24no—
191C2×#88324—44no—
192C4⋊#6157—216no—
193C4⋊#6157—28no—
194C4⋊#6157—24no—
195C4⋊#6157C2×D418yes—
196D53⋊C8—24no—
197D53⋊C8—24no—
198D53⋊C8—44no—
199C4⋊C4×C53—24no—
200C4⋊C4×C53—21no—
201C4⋊C4×C53C22×C412yescomplemented
202C22⋊C4×C53—24no—
203C22⋊Dic53—24no—
204#11719921—24no—
205#11719921—24no—
206C4⋊Dic53—21no—
207C4⋊Dic53—24no—
208C4⋊Dic53C22×C412yescomplemented
209#11719919—24no—
210#11719919—24no—
211#11719919—22no—
212#11719919—22no—
213C23×C53—22no—
214C23×C53—22no—
215C23×C53#10314yescomplemented
216C23×C53C2×C22⋊C412yes—
217C23×C53C2×C22⋊C411yescharacteristic
218C22×D53—22no—
219C22×D53—22no—
220C22×D53—22no—
221C22×D53—22no—
222C22×D53—22no—
223C22×D53—22no—
224C22×D53—24no—
225C22×D53—24no—
226C22×D53—28no—
227C22×D53—28no—
228C22×D53—28no—
229C22×D53—28no—
230C22×D53#10318yescomplemented
231C22×D53#10314yescomplemented
232C22×D53C2×C22⋊C412yes—
233C22×D53C2×C22⋊C411yescharacteristic
234C22×D53#12012yes—
235C22×D53#12312yes—
236C22×D53C2×SD1614yes—
237C22×D53C2×SD1612yes—
238C22×D53C2×Q1614yes—
239C22×D53C2×Q1612yes—
240C22×D53AGL(1,ℤ/8)12yes—
241C22×D53#13712yes—
242C22×D53C22×D411yescharacteristic
243C2×#6157—28no—
244C2×#6157—432no—
245C2×#6157—44no—
246C2×#6157—44no—
247C2×#6157—416no—
248Q8×C53—24no—
249Q8×C53—42no—
250C2×C4×C53—22no—
251C2×C4×C53—24no—
252C2×C4×C53—24no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—42no—
256C2×C4×C53—42no—
257C2×C4×C53C2×C22⋊C412yes—
258C2×C4×C53C2×C22⋊C411yescharacteristic
259C2×C4×C53C4×D414yes—
260C2×C4×C53C23×C411yescharacteristic
261C2×Dic53—22no—
262C2×Dic53—24no—
263C2×Dic53—24no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—42no—
267C2×Dic53—42no—
268C2×Dic53C2×C22⋊C412yes—
269C2×Dic53C2×C22⋊C411yescharacteristic
270C2×Dic53#12114yes—
271C2×Dic53C22×D411yescharacteristic
272C4×D53—22no—
273C4×D53—22no—
274C4×D53—24no—
275C4×D53—24no—
276C4×D53—24no—
277C4×D53—24no—
278C4×D53—24no—
279C4×D53—42no—
280C4×D53—42no—
281C4×D53—42no—
282C4×D53—42no—
283C4×D53—44no—
284C4×D53—44no—
285C4×D53C4×D414yes—
286C4×D53#12012yes—
287C4×D53#12114yes—
288C4×D53#12312yes—
289C4×D53C22×D412yes—
290C4×D53C2×#4112yes—
291Dic106—24no—
292Dic106—42no—
293Dic106—44no—
294Dic106—44no—
295#88324—44no—
296C2×#1872—531nomaximal, Sylow
297C22×C53—22no—
298C22×C53—28no—
299C22×C53—22no—
300C22×C53#38612yes—
301C22×C53C2×#10312yes—
302C22×C53C2×#10314yescomplemented
303C22×C53#41712yes—
304C22×C53C22×C22⋊C411yescharacteristic
305C2×D53—22no—
306C2×D53—28no—
307C2×D53—22no—
308C2×D53—24no—
309C2×D53—24no—
310C2×D53—216no—
311C2×D53—24no—
312C2×D53—24no—
313C2×D53#38612yes—
314C2×D53C2×#10312yes—
315C2×D53C2×#10314yescomplemented
316C2×D53#41712yes—
317C2×D53#45014yes—
318C2×D53#45114yes—
319C2×D53#48314yes—
320C2×D53#48414yes—
321C2×D53C2×#12011yescharacteristic
322C2×D53C2×#12311yescharacteristic
323C2×D53C22×SD1611yescharacteristic
324C2×D53C22×Q1611yescharacteristic
325C2×D53C2×AGL(1,ℤ/8)11yescharacteristic
326C2×D53C2×#13711yescharacteristic
327#6157—48no—
328C4×C53—22no—
329C4×C53—42no—
330C4×C53—42no—
331C4×C53#38612yes—
332C4×C53C2×C4×D412yes—
333Dic53—22no—
334Dic53—42no—
335Dic53—42no—
336Dic53#38612yes—
337Dic53C2×#12112yes—
338C22×C22⋊Q8—531no—
339C23×C4⋊C4—531no—
340C22×#103—532no—
341C22×C22⋊C8—531no—
342#1872—538no—
343C2×#340—532no—
344C2×C53—24no—
345C2×C53#187214yescomplemented
346C2×C53C2×#38611yescharacteristic
347C2×C53C22×#10311yescharacteristic
348C2×C53C2×#41711yescharacteristic
349D53—24no—
350D53#187214yescomplemented
351D53C2×#45011yescharacteristic
352D53C2×#45111yescharacteristic
353D53C2×#48311yescharacteristic
354D53C2×#48411yescharacteristic
355C23×Q8—531no—
356C24×C4—531no—
357C24×C4—1061no—
358C23×C8—532no—
359C2×C22⋊Q8—531no—
360C2×C22⋊Q8—531no—
361C2×C22⋊Q8—534no—
362C2×C22⋊Q8—534no—
363C2×C22⋊Q8—531no—
364C2×C22⋊Q8—1061no—
365C2×C22⋊Q8—1061no—
366C2×C22⋊Q8—1062no—
367C2×C22⋊Q8—1062no—
368C2×C22⋊Q8#615711yescharacteristic, complemented
369C22×C4⋊C4—532no—
370C22×C4⋊C4—531no—
371C22×C4⋊C4—534no—
372C22×C4⋊C4—1061no—
373C22×C4⋊C4—1068no—
374C22×C4⋊C4—1061no—
375C22×C4⋊C4—1062no—
376C22×C22⋊C4—1061no—
377C2×#103—538no—
378C2×#103—1068no—
379C2×C22⋊C8—534no—
380C2×C22⋊C8—1061no—
381C2×C22⋊C8—1062no—
382C2×C22⋊C8—1061no—
383#340—538no—
384C53C2×#187211yescharacteristic, complemented, Sylow
385C25—531no—
386C22×Q8—532no—
387C22×Q8—532no—
388C22×Q8—531no—
389C22×Q8—1061no—
390C22×Q8—1061no—
391C22×Q8—1061no—
392C22×Q8—1064no—
393C22×Q8—1064no—
394C22×Q8C2×#615711yescharacteristic, complemented
395C23×C4—531no—
396C23×C4—531no—
397C23×C4—531no—
398C23×C4—532no—
399C23×C4—531no—
400C23×C4—532no—
401C23×C4—532no—
402C23×C4—532no—
403C23×C4—531no—
404C23×C4—1064no—
405C23×C4—1064no—
406C23×C4—1061no—
407C23×C4—1061no—
408C23×C4—1062no—
409C23×C4—1064no—
410C23×C4—1068no—
411C23×C4—2124no—
412C23×C4—2124no—
413C23×C4C2×#615711yescharacteristic
414C22×C8—534no—
415C22×C8—1062no—
416C22×C8—1062no—
417C22×C8—1064no—
418C22×C8—1064no—
419C22⋊Q8—22no—
420C22⋊Q8—534no—
421C22⋊Q8—534no—
422C22⋊Q8—534no—
423C22⋊Q8—1064no—
424C22⋊Q8—1064no—
425C22⋊Q8—1064no—
426C22⋊Q8—1064no—
427C22⋊Q8—1062no—
428C22⋊Q8—1062no—
429C22⋊Q8—1062no—
430C22⋊Q8C2×#615714yescomplemented
431C2×C4⋊C4—21no—
432C2×C4⋊C4—534no—
433C2×C4⋊C4—538no—
434C2×C4⋊C4—531no—
435C2×C4⋊C4—532no—
436C2×C4⋊C4—532no—
437C2×C4⋊C4—1061no—
438C2×C4⋊C4—1061no—
439C2×C4⋊C4—1064no—
440C2×C4⋊C4—1064no—
441C2×C4⋊C4—10616no—
442C2×C4⋊C4—1061no—
443C2×C4⋊C4—1061no—
444C2×C4⋊C4—1061no—
445C2×C4⋊C4—1062no—
446C2×C4⋊C4—1064no—
447C2×C4⋊C4—1064no—
448C2×C4⋊C4—10616no—
449C2×C4⋊C4—1068no—
450C2×C4⋊C4—1061no—
451C2×C4⋊C4C2×#615711yescharacteristic, complemented
452C2×C22⋊C4—21no—
453C2×C22⋊C4—1064no—
454C2×C22⋊C4—1064no—
455C2×C22⋊C4—1061no—
456C2×C22⋊C4—1061no—
457C2×C22⋊C4—1061no—
458#103—10616no—
459C22⋊C8—1064no—
460C22⋊C8—1064no—
461C24—531no—
462C24—534no—
463C24—534no—
464C24—532no—
465C24—532no—
466C24—531no—
467C24—1062no—
468C24—1062no—
469C24—1062no—
470C24—1062no—
471C24C22⋊#615711yescharacteristic
472C2×Q8—21no—
473C2×Q8—24no—
474C2×Q8—532no—
475C2×Q8—1062no—
476C2×Q8—1062no—
477C2×Q8—1064no—
478C2×Q8—1068no—
479C2×Q8—1064no—
480C2×Q8—1061no—
481C2×Q8—1064no—
482C2×Q8—2124no—
483C2×Q8—2122no—
484C2×Q8—2124no—
485C2×Q8—2122no—
486C2×Q8C22×#615712yescomplemented
487C22×C4—24no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—531no—
491C22×C4—531no—
492C22×C4—531no—
493C22×C4—534no—
494C22×C4—534no—
495C22×C4—531no—
496C22×C4—531no—
497C22×C4—532no—
498C22×C4—532no—
499C22×C4—531no—
500C22×C4—532no—
501C22×C4—532no—
502C22×C4—532no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—532no—
506C22×C4—1064no—
507C22×C4—1064no—
508C22×C4—1064no—
509C22×C4—1068no—
510C22×C4—1064no—
511C22×C4—1068no—
512C22×C4—1064no—
513C22×C4—1062no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1064no—
520C22×C4—1064no—
521C22×C4—1068no—
522C22×C4—1064no—
523C22×C4—10616no—
524C22×C4—1061no—
525C22×C4—1061no—
526C22×C4—2122no—
527C22×C4—2122no—
528C22×C4—2122no—
529C22×C4—2122no—
530C22×C4—2124no—
531C22×C4—2124no—
532C22×C4—2128no—
533C22×C4—2128no—
534C22×C4—21232no—
535C22×C4C22⋊#615712yes—
536C22×C4C22⋊#615711yescharacteristic
537C22×C4C22×#615712yes—
538C22×C4C22×#615711yescharacteristic
539C2×C8—1064no—
540C2×C8—1064no—
541C2×C8—1064no—
542C2×C8—2124no—
543C2×C8—2124no—
544C4⋊C4—24no—
545C4⋊C4—21no—
546C4⋊C4—538no—
547C4⋊C4—532no—
548C4⋊C4—1062no—
549C4⋊C4—1062no—
550C4⋊C4—1064no—
551C4⋊C4—1064no—
552C4⋊C4—1068no—
553C4⋊C4—1064no—
554C4⋊C4—10616no—
555C4⋊C4—1061no—
556C4⋊C4—1064no—
557C4⋊C4C22×#615712yescomplemented
558C22⋊C4—24no—
559C22⋊C4—1064no—
560C22⋊C4—1064no—
561C22⋊C4—1064no—
562C23—22no—
563C23—22no—
564C23—532no—
565C23—532no—
566C23—532no—
567C23—532no—
568C23—532no—
569C23—532no—
570C23—531no—
571C23—531no—
572C23—534no—
573C23—538no—
574C23—534no—
575C23—534no—
576C23—532no—
577C23—1062no—
578C23—1062no—
579C23—1064no—
580C23—1062no—
581C23—1068no—
582C23—1062no—
583C23—1064no—
584C23—1068no—
585C23—1068no—
586C23—1068no—
587C23—1062no—
588C23—1062no—
589C23#1313328014yescomplemented
590C23C2×C22⋊#615712yes—
591C23C2×C22⋊#615711yescharacteristic
592Q8—24no—
593Q8—42no—
594Q8—1064no—
595Q8—2124no—
596Q8—2124no—
597Q8—2122no—
598C2×C4—22no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—534no—
606C2×C4—531no—
607C2×C4—531no—
608C2×C4—532no—
609C2×C4—534no—
610C2×C4—532no—
611C2×C4—534no—
612C2×C4—532no—
613C2×C4—532no—
614C2×C4—532no—
615C2×C4—1064no—
616C2×C4—1064no—
617C2×C4—1062no—
618C2×C4—1062no—
619C2×C4—1064no—
620C2×C4—1064no—
621C2×C4—1064no—
622C2×C4—1062no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1068no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—2122no—
629C2×C4—2122no—
630C2×C4—2124no—
631C2×C4—2122no—
632C2×C4—2122no—
633C2×C4—2124no—
634C2×C4—2124no—
635C2×C4—2124no—
636C2×C4—21216no—
637C2×C4—21232no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4C2×C22⋊#615712yes—
641C2×C4C2×C22⋊#615711yescharacteristic
642C2×C4D4×#615714yes—
643C2×C4C23×#615711yescharacteristic
644C8—2124no—
645C22—22no—
646C22—22no—
647C22—28no—
648C22—531no—
649C22—531no—
650C22—532no—
651C22—531no—
652C22—531no—
653C22—532no—
654C22—531no—
655C22—531no—
656C22—532no—
657C22—534no—
658C22—534no—
659C22—534no—
660C22—534no—
661C22—534no—
662C22—1064no—
663C22—1064no—
664C22—1064no—
665C22—10616no—
666C22—1064no—
667C22—1062no—
668C22—1062no—
669C22—1068no—
670C22#1681157112yes—
671C22C2×#1313328012yes—
672C22C2×#1313328014yescomplemented
673C22#1681161412yes—
674C22C22×C22⋊#615711yescharacteristic
675C4—22no—
676C4—42no—
677C4—42no—
678C4—532no—
679C4—532no—
680C4—1062no—
681C4—2128no—
682C4—2122no—
683C4—2122no—
684C4#1681157112yes—
685C4C2×D4×#615712yes—
686C2—24no—
687C2—531no—
688C2—531no—
689C2—531no—
690C2—534no—
691C2—531no—
692C2—1064no—
693C2#2029070014yesdirect product factor
694C2C2×#1681157111yescharacteristic
695C2C22×#1313328011yescharacteristic
696C2C2×#1681161411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6157
commutatorC2×C4×C53C23×C4
FrattiniC2×C4C23×#6157
FittingC2×C22⋊Q8×C53C4
socleC23×C53C2×C22⋊C4
prime radicalC24×D53D4
cosocleC2×C4×D53C24
hypercenterC2×C22⋊Q8#6157
hypocenterC53C2×#1872
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C22×#13133280C2semidirect
4. #20290700C2direct (N × H)
5. C2×#16811496C2semidirect
15. C2×#13133280C22semidirect
20. #16811496C22semidirect
23. C2×#13133197C4semidirect
24. C2×#13133196C4semidirect
27. C2×#13133193C4semidirect
30. C22⋊Q8×D53C4semidirect
35. C2×C22⋊Q8×C53C4semidirect
59. C22×Dic106C2×C4semidirect
64. C2×Q8×D53C2×C4semidirect
80. #13133197C2×C4semidirect
82. #13133196C2×C4semidirect
88. #13133193C2×C4semidirect
90. C2×C4⋊Dic53C2×C4semidirect
98. C4⋊C4×D53C2×C4semidirect
105. C22×Q8×C53C2×C4semidirect
108. C22⋊Q8×C53C2×C4semidirect
110. C2×C4⋊C4×C53C2×C4semidirect
133. C2×Q8×C53C22×C4semidirect
189. C2×Dic106C22×C4semidirect
201. C4⋊C4×C53C22×C4semidirect
208. C4⋊Dic53C22×C4semidirect
215. C23×C53#103semidirect
230. C22×D53#103semidirect
231. C22×D53#103semidirect
302. C22×C53C2×#103semidirect
315. C2×D53C2×#103semidirect
345. C2×C53#1872semidirect
350. D53#1872semidirect
368. C2×C22⋊Q8#6157semidirect
384. C53C2×#1872semidirect
394. C22×Q8C2×#6157semidirect
430. C22⋊Q8C2×#6157semidirect
451. C2×C4⋊C4C2×#6157semidirect
486. C2×Q8C22×#6157semidirect
557. C4⋊C4C22×#6157semidirect
589. C23#13133280semidirect
672. C22C2×#13133280semidirect
693. C2#20290700direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C4⋊#61572
C22×#131332802
C2×D53⋊(C22⋊C8)2
#202907002
C2×#168114962
C2×C22⋊Q8×D532
C2×#187253