Finite Group Databasebeta

← C22⋊C4×#11719919 #27305510

Subgroups — C22⋊C4×#11719919 #27305510

Order 13568.

2574 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719919C211yesmaximal, characteristic
2C2×#16810481C211yesmaximal, characteristic
3C2×C4×#11719919C212yesmaximal, complemented
4C2×C22⋊C4×Dic53C211yesmaximal, characteristic
5C2×C22⋊C4×Dic53C211yesmaximal, characteristic
6#20272948C212yesmaximal, complemented
7#20272946C212yesmaximal, complemented
8#20272943C212yesmaximal, complemented
9#20272938C211yesmaximal, characteristic
10#20272937C211yesmaximal, characteristic
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic
12C24×Dic53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C22×#11719919—28no—
15C22×#11719919C418yescomplemented
16C22×#11719919C2211yescharacteristic
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C22⋊Dic53C2211yescharacteristic
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2212yes—
25#16810481C418yescomplemented
26C4×#11719919—28no—
27C22⋊C4×Dic53—24no—
28C22⋊C4×Dic53C418yescomplemented
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2211yescharacteristic
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2212yes—
40C4×C22⋊C4×C53—24no—
41C2×#95×C53C2212yes—
42C23×Dic53—24no—
43C23×Dic53—24no—
44C23×Dic53—22no—
45C23×Dic53—22no—
46C23×Dic53—24no—
47C23×Dic53—42no—
48C23×Dic53C2×C414yes—
49C23×Dic53C2×C414yes—
50C23×Dic53C2×C414yes—
51C23×Dic53C2×C414yes—
52C23×Dic53C2312yes—
53C23×Dic53C2312yes—
54C23×Dic53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C2×#11719919—232no—
59C2×#11719919—24no—
60C2×#11719919—24no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919C2×C414yes—
65C2×#11719919C2×C414yes—
66C2×#11719919C2×C414yes—
67C2×#11719919C2×C414yes—
68C2×#11719919C2×C418yescomplemented
69C2×#11719919D418yes—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—22no—
73C2×C22⋊Dic53—22no—
74C2×C22⋊Dic53C2×C414yes—
75C2×C22⋊Dic53C2×C414yes—
76C2×C4×Dic53—24no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—24no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—42no—
81C2×C4×Dic53C2×C418yescomplemented
82#13133124—24no—
83#13133124—24no—
84#13133124—24no—
85#13133124—42no—
86#13133124—42no—
87#13133124C2×C418yescomplemented
88#13133124C2×C418yescomplemented
89C25×C53C2311yescharacteristic
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—24no—
93C23×C4×C53—42no—
94C23×C4×C53C2×C414yes—
95C23×C4×C53C2312yes—
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2312yes—
99C2×C22⋊C4×C53—22no—
100C2×C22⋊C4×C53—22no—
101C2×C22⋊C4×C53C2×C414yes—
102C2×C22⋊C4×C53C2×C414yes—
103C2×C22⋊C4×C53D414yes—
104C2×C22⋊C4×C53Q814yes—
105C2×C42×C53—24no—
106C2×C42×C53—24no—
107C2×C42×C53—42no—
108#95×C53—24no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53—22no—
113C24×C53C22×C412yes—
114C24×C53C22×C412yes—
115C24×C53C22×C412yes—
116C24×C53C2×D412yes—
117C24×C53C2×Q812yes—
118C24×C53#4112yes—
119C24×C53#4112yes—
120C24×C53C2411yescharacteristic
121C22×C4×C53—21no—
122C22×C4×C53—22no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—28no—
129C22×C4×C53—21no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—28no—
140C22×C4×C53—44no—
141C22×C4×C53—48no—
142C22×C4×C53—48no—
143C22×C4×C53C22×C414yes—
144C22×C4×C53C22×C412yes—
145C22×C4×C53C22×C412yes—
146C22×C4×C53C22×C414yes—
147C22×C4×C53C2×D414yes—
148C22×C4×C53C2×D414yes—
149C22×C4×C53C2×Q814yes—
150C22×Dic53—21no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—21no—
154C22×Dic53—22no—
155C22×Dic53—28no—
156C22×Dic53—28no—
157C22×Dic53—216no—
158C22×Dic53—216no—
159C22×Dic53—28no—
160C22×Dic53—22no—
161C22×Dic53—21no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—28no—
177C22×Dic53—44no—
178C22×Dic53—48no—
179C22×Dic53—48no—
180C22×Dic53C42116yescomplemented
181C22×Dic53C22×C414yes—
182C22×Dic53C22×C414yes—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C412yes—
185C22×Dic53C22×C412yes—
186C22×Dic53C22×C412yes—
187C22×Dic53C22×C412yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C22×C412yes—
190C22×Dic53C22×C412yes—
191C22×Dic53C2×D414yes—
192C22×Dic53C2×D414yes—
193C22×Dic53#4114yes—
194C22⋊C4×C53—28no—
195C22⋊C4×C53C4⋊C4116yescomplemented
196C42×C53—48no—
197C22⋊Dic53—28no—
198C22⋊Dic53—28no—
199#11719919—28no—
200#11719919—28no—
201#11719919—28no—
202#11719919—216no—
203#11719919C22⋊C4116yesdirect product factor
204C4×Dic53—216no—
205C4×Dic53—48no—
206C23×C53—22no—
207C23×C53—22no—
208C23×C53—24no—
209C23×C53—24no—
210C23×C53—22no—
211C23×C53—22no—
212C23×C53—24no—
213C23×C53—24no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53C2×C4214yes—
223C23×C53C2×C4⋊C414yes—
224C23×C53#11714yes—
225C23×C53C4×D414yes—
226C23×C53C4×D414yes—
227C23×C53C4×Q814yes—
228C23×C53C4×Q814yes—
229C23×C53C23×C411yescharacteristic
230C23×C53C23×C411yescharacteristic
231C23×C53C23×C411yescharacteristic
232C23×C53C22×D412yes—
233C23×C53C22×D411yescharacteristic
234C23×C53C22×Q811yescharacteristic
235C23×C53C2×#4112yes—
236C23×C53C2×#4111yescharacteristic
237C23×C53C2×#4111yescharacteristic
238C23×C53H(5,𝔽2)12yes—
239C23×C532−1+412yes—
240C2×C4×C53—22no—
241C2×C4×C53—24no—
242C2×C4×C53—22no—
243C2×C4×C53—24no—
244C2×C4×C53—24no—
245C2×C4×C53—24no—
246C2×C4×C53—24no—
247C2×C4×C53—24no—
248C2×C4×C53—24no—
249C2×C4×C53—24no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—24no—
253C2×C4×C53—24no—
254C2×C4×C53—22no—
255C2×C4×C53—24no—
256C2×C4×C53—416no—
257C2×C4×C53—42no—
258C2×C4×C53—42no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53C2×C22⋊C414yes—
264C2×C4×C53C2×C4⋊C418yescomplemented
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—24no—
268C2×Dic53—24no—
269C2×Dic53—22no—
270C2×Dic53—22no—
271C2×Dic53—24no—
272C2×Dic53—24no—
273C2×Dic53—232no—
274C2×Dic53—22no—
275C2×Dic53—24no—
276C2×Dic53—22no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—22no—
281C2×Dic53—24no—
282C2×Dic53—24no—
283C2×Dic53—416no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53C2×C4214yes—
295C2×Dic53C2×C4214yes—
296C2×Dic53C2×C22⋊C414yes—
297C2×Dic53C2×C22⋊C414yes—
298C2×Dic53#11714yes—
299C2×Dic53C4×D418yes—
300C2×Dic53C4×D418yes—
301C22⋊C4×C4⋊C4—531nomaximal, Sylow
302C22×C53—24no—
303C22×C53—24no—
304C22×C53—24no—
305C22×C53—24no—
306C22×C53—28no—
307C22×C53—28no—
308C22×C53—28no—
309C22×C53—28no—
310C22×C53—24no—
311C22×C53—24no—
312C22×C53C4×C4⋊C418yescomplemented
313C22×C53C22×C4211yescharacteristic
314C22×C53C22×C22⋊C411yescharacteristic
315C22×C53C22×C4⋊C411yescharacteristic
316C22×C53C2×#11711yescharacteristic
317C22×C53C2×#11711yescharacteristic
318C22×C53C2×C4×D412yes—
319C22×C53C2×C4×D412yes—
320C22×C53C2×C4×D411yescharacteristic
321C22×C53C2×C4×D411yescharacteristic
322C22×C53C2×C4×Q811yescharacteristic
323C22×C53C2×C4×Q811yescharacteristic
324C22×C53#51811yescharacteristic
325C22×C53#51911yescharacteristic
326C22×C53#52012yes—
327C22×C53#52012yes—
328C22×C53D4212yes—
329C22×C53#54612yes—
330C22×C53#54712yes—
331C22×C53#54812yes—
332C22×C53D4×Q812yes—
333C22×C53#55212yes—
334C22×C53#55312yes—
335C22×C53#55412yes—
336C4×C53—24no—
337C4×C53—28no—
338C4×C53—42no—
339C4×C53—44no—
340Dic53—24no—
341Dic53—24no—
342Dic53—42no—
343Dic53—44no—
344Dic53—44no—
345Dic53C4×C22⋊C418yescomplemented
346C23×C4⋊C4—531no—
347C2×#380—531no—
348C2×C4×C4⋊C4—532no—
349C2×C4×C22⋊C4—531no—
350C2×C4×C22⋊C4—531no—
351C2×C4×C22⋊C4D5311yescharacteristic
352#1436—532no—
353#1436—532no—
354C4⋊#95—532no—
355C22⋊#95—531no—
356C22⋊#95—531no—
357C2×C53—28no—
358C2×C53C2×C4×C22⋊C411yescharacteristic
359C2×C53C2×C4×C4⋊C411yescharacteristic
360C2×C53#227411yescharacteristic
361C2×C53D4×C22⋊C411yescharacteristic
362C2×C53Q8×C22⋊C411yescharacteristic
363C2×C53#234411yescharacteristic
364C2×C53#234511yescharacteristic
365C2×C53D4×C4⋊C412yes—
366C2×C53#235212yes—
367C2×C53#236012yes—
368C2×C53#236112yes—
369C24×C4—531no—
370C24×C4—531no—
371C24×C4C2×D5311yescharacteristic
372C22×C4⋊C4—531no—
373C22×C4⋊C4—538no—
374C22×C4⋊C4—531no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—531no—
377C22×C4⋊C4—532no—
378C22×C4⋊C4—1068no—
379C22×C22⋊C4—531no—
380C22×C22⋊C4—531no—
381C22×C22⋊C4C2×D5311yescharacteristic
382C22×C22⋊C4C2×D5311yescharacteristic
383C22×C42—532no—
384C22×C42—532no—
385C22×C42C2×D5312yes—
386#380—538no—
387C4×C4⋊C4—1068no—
388C4×C22⋊C4—24no—
389C4×C22⋊C4—538no—
390C4×C22⋊C4—1064no—
391C2×#95—532no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—532no—
395C2×#95—532no—
396C2×#95—532no—
397C2×#95—532no—
398C2×#95C2×D5312yes—
399C53C22⋊C4×C4⋊C411yescharacteristic, complemented, Sylow
400C25C22×D5311yescharacteristic
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—531no—
406C23×C4—534no—
407C23×C4—534no—
408C23×C4—534no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—532no—
412C23×C4—532no—
413C23×C4—531no—
414C23×C4—534no—
415C23×C4—1064no—
416C23×C4—1064no—
417C23×C4—1064no—
418C23×C4—1062no—
419C23×C4—1062no—
420C23×C4—2122no—
421C23×C4C4×D5314yes—
422C23×C4C22×D5312yes—
423C23×C4C22×D5311yescharacteristic
424C23×C4C22×D5312yes—
425C23×C4C22×D5311yescharacteristic
426C2×C4⋊C4—534no—
427C2×C4⋊C4—538no—
428C2×C4⋊C4—534no—
429C2×C4⋊C4—534no—
430C2×C4⋊C4—534no—
431C2×C4⋊C4—538no—
432C2×C4⋊C4—10632no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1064no—
435C2×C4⋊C4—1064no—
436C2×C4⋊C4—1064no—
437C2×C4⋊C4—1064no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—534no—
441C2×C22⋊C4—534no—
442C2×C22⋊C4—1062no—
443C2×C22⋊C4—1062no—
444C2×C22⋊C4—1062no—
445C2×C22⋊C4—1062no—
446C2×C22⋊C4Dic10614yes—
447C2×C22⋊C4C4×D5314yes—
448C2×C22⋊C4C4×D5314yes—
449C2×C22⋊C4C22⋊D5314yes—
450C2×C42—24no—
451C2×C42—24no—
452C2×C42—42no—
453C2×C42—538no—
454C2×C42—1064no—
455C2×C42—1064no—
456C2×C42—1064no—
457C2×C42—1064no—
458C2×C42—2122no—
459#95—24no—
460#95—538no—
461#95—538no—
462#95—1064no—
463#95—1064no—
464#95—1064no—
465#95—2122no—
466#95—2122no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24C2×Dic10612yes—
472C24C2×C4×D5312yes—
473C24C2×C4×D5312yes—
474C24C2×C4×D5312yes—
475C24#1171994512yes—
476C24#1171994512yes—
477C24C2×C22⋊D5312yes—
478C24C23×D5311yescharacteristic
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—44no—
499C22×C4—48no—
500C22×C4—48no—
501C22×C4—532no—
502C22×C4—532no—
503C22×C4—532no—
504C22×C4—534no—
505C22×C4—534no—
506C22×C4—5316no—
507C22×C4—532no—
508C22×C4—532no—
509C22×C4—532no—
510C22×C4—532no—
511C22×C4—534no—
512C22×C4—534no—
513C22×C4—534no—
514C22×C4—532no—
515C22×C4—1068no—
516C22×C4—1068no—
517C22×C4—10616no—
518C22×C4—10616no—
519C22×C4—1068no—
520C22×C4—1062no—
521C22×C4—1061no—
522C22×C4—1062no—
523C22×C4—1061no—
524C22×C4—1062no—
525C22×C4—1068no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1061no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4—1062no—
536C22×C4—1061no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—2124no—
543C22×C4—2128no—
544C22×C4—2128no—
545C22×C4C2×Dic10614yes—
546C22×C4C2×C4×D5314yes—
547C22×C4C2×C4×D5312yes—
548C22×C4C2×C4×D5312yes—
549C22×C4C2×C4×D5314yes—
550C22×C4D4×D5314yes—
551C22×C4C2×C22⋊D5314yes—
552C4⋊C4—5316no—
553C4⋊C4—1068no—
554C4⋊C4—1068no—
555C4⋊C4—10616no—
556C4⋊C4—1068no—
557C22⋊C4—28no—
558C22⋊C4—1068no—
559C22⋊C4—1068no—
560C22⋊C4#11719919116yesdirect product factor
561C42—48no—
562C42—10616no—
563C42—2128no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—22no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—24no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23C42×D5314yes—
581C23C2×#1171991914yes—
582C23#1313317414yes—
583C23C4×C22⋊D5314yes—
584C23C4×C22⋊D5314yes—
585C23C4×Dic10614yes—
586C23C4×Dic10614yes—
587C23C22×C4×D5311yescharacteristic
588C23C22×C4×D5311yescharacteristic
589C23C22×C4×D5311yescharacteristic
590C23C2×D4×D5312yes—
591C23C22×C22⋊D5311yescharacteristic
592C23C22×Dic10611yescharacteristic
593C23#41×D5312yes—
594C23C2×#1171994511yescharacteristic
595C23C2×#1171994511yescharacteristic
596C23#1313326212yes—
597C23#1313326412yes—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—416no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—534no—
622C2×C4—534no—
623C2×C4—534no—
624C2×C4—538no—
625C2×C4—538no—
626C2×C4—534no—
627C2×C4—534no—
628C2×C4—10632no—
629C2×C4—1062no—
630C2×C4—1062no—
631C2×C4—1064no—
632C2×C4—1064no—
633C2×C4—1062no—
634C2×C4—1062no—
635C2×C4—1064no—
636C2×C4—1064no—
637C2×C4—1062no—
638C2×C4—1064no—
639C2×C4—1064no—
640C2×C4—1064no—
641C2×C4—1064no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1064no—
645C2×C4—1064no—
646C2×C4—21216no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4—2122no—
650C2×C4—2122no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4—2122no—
656C2×C4—2122no—
657C2×C4C22⋊C4×D5314yes—
658C2×C4C2×#1171991918yescomplemented
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22—28no—
668C22—28no—
669C22C4×#1171991918yescomplemented
670C22C2×C42×D5311yescharacteristic
671C22C2×C22⋊C4×D5311yescharacteristic
672C22C22×#1171991911yescharacteristic
673C22#117×D5311yescharacteristic
674C22C2×#1313317411yescharacteristic
675C22C4×D4×D5312yes—
676C22C4×D4×D5312yes—
677C22C2×C4×C22⋊D5311yescharacteristic
678C22C2×C4×C22⋊D5311yescharacteristic
679C22C2×C4×Dic10611yescharacteristic
680C22C2×C4×Dic10611yescharacteristic
681C22#1681109611yescharacteristic
682C22#1681110011yescharacteristic
683C22#1681110212yes—
684C22#1681110212yes—
685C22D4×C22⋊D5312yes—
686C22#1681126312yes—
687C22#1681127212yes—
688C22#1681128212yes—
689C22D4×Dic10612yes—
690C22#1681130612yes—
691C22#1681132212yes—
692C22#1681133212yes—
693C4—24no—
694C4—28no—
695C4—42no—
696C4—44no—
697C4—538no—
698C4—1064no—
699C4—1064no—
700C4—2122no—
701C4—2124no—
702C4—2124no—
703C2—28no—
704C2C4×C22⋊C4×D5311yescharacteristic
705C2C2×C4×#1171991911yescharacteristic
706C2#2027707011yescharacteristic
707C2C22⋊C4×C22⋊D5311yescharacteristic
708C2C22⋊C4×Dic10611yescharacteristic
709C2#2027758511yescharacteristic
710C2#2027759311yescharacteristic
711C2D4×#1171991912yes—
712C2#2027763812yes—
713C2#2027772112yes—
714C2#2027773212yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C22⋊C4×C4⋊C4
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×#11719919C2semidirect
6. #20272948C2semidirect
7. #20272946C2semidirect
8. #20272943C2semidirect
15. C22×#11719919C4semidirect
25. #16810481C4semidirect
28. C22⋊C4×Dic53C4semidirect
68. C2×#11719919C2×C4semidirect
81. C2×C4×Dic53C2×C4semidirect
87. #13133124C2×C4semidirect
88. #13133124C2×C4semidirect
180. C22×Dic53C42semidirect
195. C22⋊C4×C53C4⋊C4semidirect
203. #11719919C22⋊C4direct (N × H)
264. C2×C4×C53C2×C4⋊C4semidirect
312. C22×C53C4×C4⋊C4semidirect
345. Dic53C4×C22⋊C4semidirect
399. C53C22⋊C4×C4⋊C4semidirect
560. C22⋊C4#11719919direct (N × H)
658. C2×C4C2×#11719919semidirect
669. C22C4×#11719919semidirect

Maximal subgroups

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

subgroupindex
C23×#117199192
C2×#168104812
C2×C4×#117199192
C2×C22⋊C4×Dic532
#202729482
#202729462
#202729432
#202729382
#202729372
C2×C4×C22⋊C4×C532
C22⋊C4×C4⋊C453