Finite Group Databasebeta

← #28328926

Subgroups — #28328926

Order 13568.

2912 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811691C211yesmaximal, characteristic, complemented
2C22×Q8×#6157C211yesmaximal, characteristic, complemented
3#20291244C213yesmaximal, complemented
4#20291241C213yesmaximal, complemented
5#20291239C213yesmaximal, complemented
6#20291231C213yesmaximal
7#20291230C211yesmaximal, characteristic, complemented
8Q8×C22⋊#6157C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6157C211yesmaximal, characteristic, complemented
10#20291206C213yesmaximal, complemented
11#20291202C213yesmaximal, complemented
12C22⋊Q8×#6157C213yesmaximal, complemented
13#20291169C213yesmaximal
14#20291155C211yesmaximal, characteristic, complemented
15D4×Q8×D53C211yesmaximal, characteristic
16#16811691—28no—
17C2×Q8×#6157—28no—
18C2×Q8×#6157C2211yescharacteristic
19C2×Q8×#6157C2213yes—
20C2×Q8×#6157C2211yescharacteristic
21C2×Q8×#6157C2213yes—
22C2×Q8×#6157C2213yes—
23C2×Q8×#6157C2211yescharacteristic
24C2×Q8×#6157C2213yes—
25C2×Q8×#6157C2211yescharacteristic
26C2×#13133296C2213yes—
27C2×#13133296C2213yes—
28C22×C4⋊#6157C2213yes—
29C22×C4×#6157C2213yes—
30(C2×#6157)⋊Q8C2213yes—
31(C2×#6157)⋊Q8C2213yes—
32(C2×#6157)⋊Q8C2213yes—
33(C2×#6157)⋊Q8C2213yes—
34#16811574C2213yes—
35#16811574C2213yes—
36#16811574C2216yes—
37#16811573C2213yes—
38#16811573C2213yes—
39#16811573C2216yes—
40#16811572C2213yes—
41#16811572C2213yes—
42#16811572C2216yes—
43#16811572C2216yes—
44#16811572C2216yes—
45#16811571C2211yescharacteristic
46#16811571C2213yes—
47#16811570C2213yes—
48#16811570C2213yes—
49#16811567C2213yes—
50#16811565C2213yes—
51#16811565C2213yes—
52C4⋊C4×#6157C2213yes—
53C4⋊C4×#6157C2213yes—
54C4⋊C4×#6157C2216yes—
55C4×C4⋊#6157C2213yes—
56C4×C4⋊#6157C2213yes—
57C22⋊C4×#6157C2216yes—
58C4×C22⋊#6157C2213yes—
59C4×C22⋊#6157C2213yes—
60#16811559C2213yes—
61C22×Q8×D53C2211yescharacteristic
62C22×Q8×D53C2211yescharacteristic
63Q8×D212C411yescharacteristic, complemented
64D4×Dic106C413yescomplemented
65#16811288C413yescomplemented
66Q8×C22⋊D53C411yescharacteristic, complemented
67Q8×C22⋊D53C411yescharacteristic, complemented
68#16811286C413yescomplemented
69#16811286C413yescomplemented
70C4⋊Q8×D53C2213yes—
71C22⋊Q8×D53C2213yes—
72C22⋊Q8×D53C2213yes—
73C4×Q8×D53C2211yescharacteristic
74C4×D4×D53C2213yes—
75D4×Q8×C53C411yescharacteristic, complemented
76C23×#6157C2311yescharacteristic
77C23×#6157C2313yes—
78Q8×#6157—24no—
79Q8×#6157—24no—
80Q8×#6157—24no—
81Q8×#6157—212no—
82Q8×#6157—212no—
83Q8×#6157—212no—
84Q8×#6157—212no—
85Q8×#6157D418yescomplemented
86#13133296—212no—
87#13133296—212no—
88C2×C4⋊#6157—212no—
89C2×C4⋊#6157C2313yes—
90C2×C4⋊#6157C2313yes—
91C2×C4⋊#6157C2313yes—
92C2×C4⋊#6157C2313yes—
93C2×C4⋊#6157C2313yes—
94C2×C4⋊#6157C2313yes—
95C2×C4⋊#6157C2316yes—
96C2×C4⋊#6157C2313yes—
97C2×C4⋊#6157C2313yes—
98C2×C22⋊#6157C2311yescharacteristic
99C2×C22⋊#6157C2311yescharacteristic
100C2×C22⋊#6157C2313yes—
101C2×C22⋊#6157C2313yes—
102C2×C22⋊#6157C2311yescharacteristic
103C2×C22⋊#6157C2313yes—
104C2×C4×#6157—212no—
105C2×C4×#6157C2313yes—
106C2×C4×#6157C2313yes—
107C2×C4×#6157C2313yes—
108C2×C4×#6157C2316yes—
109C2×C4×#6157C2313yes—
110C2×C4×#6157C2313yes—
111C2×C4×#6157C2316yes—
112C2×C4×#6157C2313yes—
113(C2×#6157)⋊C4C2311yescharacteristic
114(C2×#6157)⋊C4C2313yes—
115(C2×#6157)⋊C4C2313yes—
116(C2×#6157)⋊C4C2313yes—
117(C2×#6157)⋊C4C2313yes—
118(C2×#6157)⋊C4C2313yes—
119(C2×#6157)⋊C4C2313yes—
120(C2×#6157)⋊C4C2313yes—
121(C2×#6157)⋊C4C2316yes—
122(C2×#6157)⋊C4C2316yes—
123(C2×#6157)⋊C4C2311yescharacteristic
124(C2×#6157)⋊C4C2313yes—
125(C2×#6157)⋊C4C2316yes—
126C22×Dic106C2×C413yes—
127C22×Dic106C2×C413yescomplemented
128C2×Q8×D53—24no—
129C2×Q8×D53—24no—
130C2×Q8×D53—24no—
131C2×Q8×D53—24no—
132C2×Q8×D53C2×C413yes—
133C2×Q8×D53C2×C411yescharacteristic
134C2×Q8×D53C2×C413yescomplemented
135C2×Q8×D53C2×C411yescharacteristic, complemented
136C2×Q8×D53C2313yes—
137C2×Q8×D53C2313yes—
138C2×Q8×D53C2311yescharacteristic
139C2×D4×D53C2311yescharacteristic
140C22×C4×D53C2313yes—
141C22×C4×D53C2313yes—
142#13133217C2×C413yescomplemented
143#13133216C2×C416yescomplemented
144#13133216C2×C416yescomplemented
145#13133215C2×C413yescomplemented
146#13133215C2×C413yescomplemented
147#13133197C2×C413yes—
148#13133197C2×C413yescomplemented
149#13133196C2×C413yes—
150#13133196C2×C413yescomplemented
151#13133195C2×C416yes—
152#13133195C2×C416yescomplemented
153#13133194C2×C416yes—
154#13133194C2×C416yescomplemented
155#13133193C2×C413yes—
156#13133193C2×C413yescomplemented
157Q8×Dic53C2×C411yescharacteristic, complemented
158C4×Dic106C2×C413yescomplemented
159#13133182C2×C413yescomplemented
160C4×D212C2×C413yes—
161D4×Dic53C2×C413yes—
162#13133179C2×C413yes—
163C4×C22⋊D53C2×C413yes—
164C4×C22⋊D53C2×C413yes—
165#13133177C2×C413yes—
166#13133177C2×C413yes—
167C4⋊C4×D53C2313yes—
168C4⋊C4×D53C2316yes—
169C4⋊C4×D53C2313yes—
170C22⋊C4×D53C2313yes—
171C22⋊C4×D53C2313yes—
172C42×D53C2313yes—
173C22×Q8×C53C2×C411yescharacteristic
174C22×Q8×C53C2×C411yescharacteristic, complemented
175C4⋊Q8×C53C2×C413yescomplemented
176C22⋊Q8×C53C2×C413yes—
177C22⋊Q8×C53C2×C413yescomplemented
178C4×Q8×C53C2×C411yescharacteristic, complemented
179C4×D4×C53C2×C413yes—
180C23×D53C2411yescharacteristic
181C23×D53C2411yescharacteristic
182C22×#6157—22no—
183C22×#6157—22no—
184C22×#6157—22no—
185C22×#6157—26no—
186C22×#6157—26no—
187C22×#6157—43no—
188C22×#6157C2411yescharacteristic
189C22×#6157C2413yes—
190C22×#6157C2413yes—
191C22×#6157C2413yes—
192C22×#6157C2411yescharacteristic
193C22×#6157C2411yescharacteristic
194C22×#6157C2413yes—
195C22×#6157C2411yescharacteristic
196C2×Q8×C53—24no—
197C2×Q8×C53—24no—
198C2×Q8×C53C22×C413yes—
199C2×Q8×C53C22×C413yes—
200C2×Q8×C53C22×C411yescharacteristic
201C2×D4×C53C22×C411yescharacteristic
202C22×C4×C53C22×C413yes—
203C22×C4×C53C22×C413yes—
204C2×C22⋊D53C22×C411yescharacteristic
205C2×C22⋊D53C22×C411yescharacteristic
206C22×Dic53C22×C413yes—
207C22×Dic53C22×C413yes—
208Q8×D53—24no—
209Q8×D53—24no—
210Q8×D53—26no—
211Q8×D53—26no—
212Q8×D53—26no—
213Q8×D53—26no—
214Q8×D53—212no—
215Q8×D53—212no—
216Q8×D53C2×D414yes—
217Q8×D53#4114yes—
218D4×D53—22no—
219D4×D53—22no—
220C2×D212C22×C411yescharacteristic
221C2×C4×D53—26no—
222C2×C4×D53—26no—
223C2×C4×D53—26no—
224C2×C4×D53—26no—
225C2×C4×D53C22×C413yes—
226C2×C4×D53C22×C413yes—
227C2×C4×D53C22×C413yes—
228C2×C4×D53C22×C413yes—
229C2×C4×D53C2411yescharacteristic
230C2×C4×D53C2413yes—
231C2×C4×D53C2413yes—
232C2×C4×D53C2413yes—
233C2×C4×D53C2413yes—
234C2×Dic106—212no—
235C2×Dic106—212no—
236C2×Dic106C22×C416yes—
237C2×Dic106C22×C416yes—
238C2×Dic106C22×C413yes—
239C2×Dic106C22×C413yes—
240C2×Dic106C22×C413yes—
241C22⋊#6157—26no—
242C22⋊#6157—22no—
243C22⋊#6157—22no—
244C22⋊#6157—26no—
245C22⋊#6157—22no—
246C22⋊#6157—43no—
247C4⋊#6157—212no—
248C4⋊#6157—26no—
249C4⋊#6157—26no—
250C4⋊#6157—26no—
251C4⋊#6157—26no—
252C4⋊#6157—26no—
253C4⋊#6157—26no—
254C4⋊#6157—43no—
255C4⋊#6157C2×D4112yes—
256C4×#6157—26no—
257C4×#6157—26no—
258C4×#6157—212no—
259C4×#6157—26no—
260C4×#6157—26no—
261C4×#6157—26no—
262C4×#6157—46no—
263C4×#6157C2×D4112yes—
264C4⋊C4×C53C22×C413yes—
265C4⋊C4×C53C22×C413yes—
266C4⋊C4×C53C22×C416yes—
267C22⋊C4×C53C22×C413yes—
268C22⋊C4×C53C22×C413yes—
269C42×C53C22×C413yes—
270C22⋊Dic53C22×C413yes—
271C22⋊Dic53C22×C413yes—
272#11719921C22×C413yes—
273#11719921C22×C413yes—
274#11719921C22×C413yes—
275#11719921C22×C413yes—
276C4⋊Dic53C22×C413yes—
277C4⋊Dic53C22×C413yes—
278C4⋊Dic53C22×C416yes—
279#11719919C22×C413yes—
280#11719919C22×C413yes—
281#11719919C22×C416yes—
282#11719919C22×C416yes—
283#11719919C22×C416yes—
284C4×Dic53C22×C413yes—
285C4×Dic53C22×C413yes—
286C4×Dic53C22×C413yes—
287C23×C53C23×C411yescharacteristic
288C23×C53C23×C411yescharacteristic
289C22×D53—21no—
290C22×D53—21no—
291C22×D53—21no—
292C22×D53—21no—
293C22×D53—21no—
294C22×D53—21no—
295C22×D53—21no—
296C22×D53—21no—
297C22×D53—21no—
298C22×D53—21no—
299C22×D53C23×C411yescharacteristic
300C22×D53C23×C411yescharacteristic
301C22×D532−1+412yes—
302C22×D532−1+412yes—
303C22×D53C2511yescharacteristic
304C2×#6157—28no—
305C2×#6157—21no—
306C2×#6157—21no—
307C2×#6157—21no—
308C2×#6157—21no—
309C2×#6157—23no—
310C2×#6157—23no—
311C2×#6157—23no—
312C2×#6157—21no—
313C2×#6157—23no—
314C2×#6157—21no—
315C2×#6157—23no—
316C2×#6157—23no—
317C2×#6157—23no—
318C2×#6157—21no—
319C2×#6157—23no—
320C2×#6157—21no—
321C2×#6157—21no—
322C2×#6157—23no—
323C2×#6157—23no—
324C2×#6157—21no—
325C2×#6157—23no—
326C2×#6157—412no—
327C2×#6157C22×D412yes—
328C2×#6157C22×D416yes—
329C2×#61572−1+412yes—
330Q8×C53—26no—
331Q8×C53—26no—
332Q8×C53C4×D414yes—
333D4×C53—22no—
334C2×C4×C53—26no—
335C2×C4×C53—26no—
336C2×C4×C53C23×C413yes—
337C2×C4×C53C23×C413yes—
338C2×C4×C53C23×C411yescharacteristic
339C2×C4×C53C23×C413yes—
340C2×C4×C53C23×C413yes—
341C22⋊D53—22no—
342C22⋊D53—22no—
343C2×Dic53—26no—
344C2×Dic53—26no—
345C2×Dic53C23×C413yes—
346C2×Dic53C23×C413yes—
347C2×Dic53C23×C411yescharacteristic
348C2×Dic53C23×C413yes—
349C2×Dic53C23×C413yes—
350D212—22no—
351C4×D53—23no—
352C4×D53—23no—
353C4×D53—23no—
354C4×D53—23no—
355C4×D53—23no—
356C4×D53—21no—
357C4×D53—21no—
358C4×D53—23no—
359C4×D53—26no—
360C4×D53—26no—
361C4×D53—26no—
362C4×D53—26no—
363C4×D53C22×D416yes—
364C4×D53C2×#4116yes—
365Dic106—26no—
366Dic106—26no—
367Dic106—212no—
368Dic106—212no—
369Dic106C4×D4112yes—
370#34291—531nomaximal, Sylow
371C22×C53—21no—
372C22×C53—21no—
373C22×C53—21no—
374C22×C53—21no—
375C22×C53—21no—
376C22×C53#51912yescomplemented
377C22×C53C24×C411yescharacteristic
378C2×D53—21no—
379C2×D53—21no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—21no—
385C2×D53—21no—
386C2×D53—21no—
387C2×D53—41no—
388C2×D53—41no—
389C2×D53—41no—
390C2×D53—41no—
391C2×D53#51912yescomplemented
392C2×D53C23×D411yescharacteristic
393C2×D53C22×#4111yescharacteristic
394C2×D53C2×2−1+411yescharacteristic
395C2×D53C2×2−1+411yescharacteristic
396C2×D53C2×2−1+411yescharacteristic
397C2×D53#58511yescharacteristic
398#6157—22no—
399#6157—22no—
400#6157—26no—
401#6157—43no—
402#6157—41no—
403#6157—43no—
404#6157—43no—
405#6157—41no—
406C4×C53—23no—
407C4×C53—23no—
408C4×C53—21no—
409C4×C53—23no—
410C4×C53C2×C4×D416yes—
411Dic53—23no—
412Dic53—23no—
413Dic53—21no—
414Dic53—23no—
415Dic53C2×C4×D416yes—
416C2×D4×Q8—531no—
417C2×#519—531no—
418C22×C4×Q8—531no—
419#2365—533no—
420#2362—533no—
421#2360—533no—
422#2352—533no—
423#2351—531no—
424Q8×C22⋊C4—531no—
425Q8×C22⋊C4—531no—
426#2327—533no—
427#2323—533no—
428C4×C22⋊Q8—533no—
429#2290—533no—
430#2276—531no—
431C2×C53—22no—
432C2×C53—41no—
433C2×C53C22×C4×D411yescharacteristic
434C2×C53C2×#51911yescharacteristic
435C2×C53C4×2−1+411yescharacteristic
436D53—22no—
437D53—41no—
438D53#348611yescharacteristic
439D53#348911yescharacteristic
440D53#351611yescharacteristic
441D53#352311yescharacteristic
442C23×Q8—531no—
443C23×Q8—531no—
444D4×Q8—531no—
445D4×Q8—531no—
446D4×Q8—533no—
447D4×Q8—533no—
448D4×Q8—533no—
449D4×Q8—531no—
450D4×Q8—533no—
451D4×Q8#615711yescharacteristic, complemented
452C2×C4⋊Q8—533no—
453C2×C22⋊Q8—533no—
454C2×C22⋊Q8—533no—
455#519—1068no—
456C2×C4×Q8—531no—
457C2×C4×Q8—531no—
458C2×C4×Q8—533no—
459C2×C4×Q8—533no—
460C2×C4×Q8—531no—
461C2×C4×Q8—531no—
462C2×C4×Q8—531no—
463C2×C4×Q8—533no—
464C2×C4×Q8—533no—
465C2×C4×Q8—1068no—
466C2×C4×D4—533no—
467C2×#117—533no—
468C2×#117—533no—
469C22×C4⋊C4—533no—
470C22×C42—533no—
471#391—533no—
472#391—533no—
473#391—533no—
474#391—533no—
475#389—533no—
476#389—536no—
477#389—533no—
478#388—533no—
479#388—536no—
480#388—533no—
481#387—536no—
482#387—533no—
483#387—536no—
484#387—536no—
485#387—533no—
486#386—533no—
487#386—531no—
488#385—533no—
489#385—533no—
490#382—533no—
491#380—533no—
492#380—533no—
493C4×C4⋊C4—533no—
494C4×C4⋊C4—533no—
495C4×C4⋊C4—533no—
496C4×C4⋊C4—533no—
497C4×C4⋊C4—536no—
498C4×C22⋊C4—533no—
499C4×C22⋊C4—533no—
500C4×C22⋊C4—536no—
501#376—533no—
502C53#3429111yescharacteristic, complemented, Sylow
503C22×Q8—531no—
504C22×Q8—533no—
505C22×Q8—533no—
506C22×Q8—533no—
507C22×Q8—531no—
508C22×Q8—533no—
509C22×Q8—531no—
510C22×Q8—533no—
511C22×Q8—533no—
512C22×Q8—1064no—
513C22×Q8—1064no—
514C22×Q8—1064no—
515C22×Q8—1064no—
516C22×Q8C2×#615711yescharacteristic
517C22×Q8C2×#615711yescharacteristic, complemented
518C22×D4—531no—
519C23×C4—533no—
520C23×C4—533no—
521C23×C4—531no—
522C23×C4—533no—
523C4⋊Q8—533no—
524C4⋊Q8—533no—
525C4⋊Q8—536no—
526C4⋊Q8—536no—
527C4⋊Q8—533no—
528C4⋊Q8C2×#615713yescomplemented
529C22⋊Q8—533no—
530C22⋊Q8—533no—
531C22⋊Q8—533no—
532C22⋊Q8—533no—
533C22⋊Q8—536no—
534C22⋊Q8—536no—
535C22⋊Q8—533no—
536C22⋊Q8—533no—
537C22⋊Q8—536no—
538C22⋊Q8—536no—
539C22⋊Q8C2×#615713yes—
540C22⋊Q8C2×#615713yescomplemented
541C4×Q8—538no—
542C4×Q8—531no—
543C4×Q8—533no—
544C4×Q8—533no—
545C4×Q8—10612no—
546C4×Q8—10612no—
547C4×Q8—10612no—
548C4×Q8—10612no—
549C4×Q8—1064no—
550C4×Q8—1064no—
551C4×Q8—1064no—
552C4×Q8C2×#615711yescharacteristic, complemented
553C4×D4—533no—
554C4×D4—533no—
555C4×D4—533no—
556C4×D4—533no—
557C4×D4—533no—
558C4×D4—533no—
559C4×D4—533no—
560C4×D4C2×#615713yes—
561#117—10612no—
562#117—10612no—
563C2×C4⋊C4—533no—
564C2×C4⋊C4—533no—
565C2×C4⋊C4—533no—
566C2×C4⋊C4—536no—
567C2×C4⋊C4—533no—
568C2×C4⋊C4—536no—
569C2×C4⋊C4—533no—
570C2×C4⋊C4—533no—
571C2×C4⋊C4—533no—
572C2×C4⋊C4—533no—
573C2×C4⋊C4—533no—
574C2×C4⋊C4—533no—
575C2×C4⋊C4—10612no—
576C2×C22⋊C4—533no—
577C2×C22⋊C4—533no—
578C2×C22⋊C4—531no—
579C2×C22⋊C4—533no—
580C2×C22⋊C4—533no—
581C2×C22⋊C4—531no—
582C2×C22⋊C4—531no—
583C2×C22⋊C4—533no—
584C2×C42—533no—
585C2×C42—533no—
586C2×C42—536no—
587C2×C42—533no—
588C2×C42—533no—
589C2×C42—533no—
590C2×C42—533no—
591C2×C42—533no—
592C2×C42—536no—
593C2×C42—10612no—
594#95—531no—
595#95—533no—
596#95—533no—
597#95—533no—
598#95—533no—
599#95—536no—
600#95—536no—
601#95—533no—
602#95—533no—
603#95—533no—
604#95—531no—
605#95—536no—
606#95—533no—
607C24—531no—
608C24—531no—
609C2×Q8—24no—
610C2×Q8—24no—
611C2×Q8—534no—
612C2×Q8—534no—
613C2×Q8—533no—
614C2×Q8—536no—
615C2×Q8—536no—
616C2×Q8—533no—
617C2×Q8—533no—
618C2×Q8—10612no—
619C2×Q8—10612no—
620C2×Q8—1066no—
621C2×Q8—1066no—
622C2×Q8—1066no—
623C2×Q8—1066no—
624C2×Q8—10612no—
625C2×Q8—10612no—
626C2×Q8—1064no—
627C2×Q8—1064no—
628C2×Q8C22×#615713yes—
629C2×Q8C22×#615713yes—
630C2×Q8C22×#615711yescharacteristic
631C2×D4—531no—
632C2×D4—531no—
633C2×D4—531no—
634C2×D4—1062no—
635C2×D4—1062no—
636C2×D4C22×#615711yescharacteristic
637C22×C4—533no—
638C22×C4—531no—
639C22×C4—531no—
640C22×C4—533no—
641C22×C4—533no—
642C22×C4—533no—
643C22×C4—533no—
644C22×C4—533no—
645C22×C4—533no—
646C22×C4—533no—
647C22×C4—531no—
648C22×C4—533no—
649C22×C4—533no—
650C22×C4—533no—
651C22×C4—531no—
652C22×C4—533no—
653C22×C4—533no—
654C22×C4—533no—
655C22×C4—531no—
656C22×C4—1066no—
657C22×C4—1066no—
658C22×C4—1066no—
659C22×C4—1066no—
660C22×C4—1062no—
661C22×C4—1062no—
662C22×C4—1066no—
663C22×C4—1062no—
664C22×C4—1066no—
665C22×C4—2123no—
666C22×C4C22×#615713yes—
667C22×C4C22×#615713yes—
668C4⋊C4—5312no—
669C4⋊C4—533no—
670C4⋊C4—533no—
671C4⋊C4—533no—
672C4⋊C4—536no—
673C4⋊C4—533no—
674C4⋊C4—536no—
675C4⋊C4—536no—
676C4⋊C4—536no—
677C4⋊C4—1066no—
678C4⋊C4—1066no—
679C4⋊C4—10612no—
680C4⋊C4—1066no—
681C4⋊C4—1066no—
682C4⋊C4—1066no—
683C4⋊C4—1066no—
684C4⋊C4—2123no—
685C4⋊C4C22×#615713yes—
686C4⋊C4C22×#615713yes—
687C4⋊C4C22×#615716yes—
688C22⋊C4—533no—
689C22⋊C4—533no—
690C22⋊C4—533no—
691C22⋊C4—533no—
692C22⋊C4—533no—
693C22⋊C4—533no—
694C22⋊C4—1062no—
695C22⋊C4—1062no—
696C22⋊C4—1066no—
697C22⋊C4—1066no—
698C22⋊C4—1062no—
699C22⋊C4—2123no—
700C22⋊C4C22×#615713yes—
701C22⋊C4C22×#615713yes—
702C42—5312no—
703C42—533no—
704C42—533no—
705C42—533no—
706C42—1066no—
707C42—1066no—
708C42—1066no—
709C42—1066no—
710C42—10612no—
711C42—1066no—
712C42—2126no—
713C42C22×#615713yes—
714C23—531no—
715C23—532no—
716C23—532no—
717C23—531no—
718C23—531no—
719C23—1061no—
720C23—1061no—
721C23—1061no—
722C23—1061no—
723C23—1061no—
724C23—1061no—
725C23—1061no—
726C23—1061no—
727C23—1061no—
728C23—1061no—
729C23C23×#615711yescharacteristic
730C23C23×#615711yescharacteristic
731Q8—26no—
732Q8—26no—
733Q8—5312no—
734Q8—10612no—
735Q8—10612no—
736Q8—1066no—
737Q8—1066no—
738Q8D4×#615714yes—
739D4—22no—
740D4—1062no—
741D4—1062no—
742D4—1062no—
743C2×C4—26no—
744C2×C4—26no—
745C2×C4—533no—
746C2×C4—536no—
747C2×C4—536no—
748C2×C4—532no—
749C2×C4—536no—
750C2×C4—532no—
751C2×C4—531no—
752C2×C4—533no—
753C2×C4—533no—
754C2×C4—533no—
755C2×C4—1066no—
756C2×C4—1066no—
757C2×C4—1063no—
758C2×C4—1063no—
759C2×C4—1063no—
760C2×C4—1063no—
761C2×C4—1063no—
762C2×C4—1063no—
763C2×C4—1061no—
764C2×C4—1061no—
765C2×C4—1066no—
766C2×C4—1066no—
767C2×C4—1061no—
768C2×C4—1063no—
769C2×C4—1061no—
770C2×C4—1061no—
771C2×C4—1061no—
772C2×C4—1063no—
773C2×C4—1068no—
774C2×C4—1066no—
775C2×C4—1066no—
776C2×C4—1063no—
777C2×C4—1061no—
778C2×C4—1061no—
779C2×C4—1063no—
780C2×C4—1063no—
781C2×C4—1063no—
782C2×C4—1061no—
783C2×C4—1063no—
784C2×C4—1063no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1063no—
788C2×C4—1063no—
789C2×C4—1061no—
790C2×C4—1063no—
791C2×C4—21212no—
792C2×C4C23×#615711yescharacteristic
793C2×C4C23×#615713yes—
794C2×C4C23×#615713yes—
795C2×C4C23×#615713yes—
796C2×C4C23×#615713yes—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—531no—
803C22—531no—
804C22—531no—
805C22—531no—
806C22—531no—
807C22—531no—
808C22—532no—
809C22—1062no—
810C22—1062no—
811C22—1062no—
812C22—1062no—
813C22—1061no—
814C22—1061no—
815C22—1061no—
816C22—1061no—
817C22—1061no—
818C22—2121no—
819C22—2121no—
820C22—2121no—
821C22—2121no—
822C22#1681169112yescomplemented
823C22C24×#615711yescharacteristic
824C4—23no—
825C4—23no—
826C4—21no—
827C4—23no—
828C4—536no—
829C4—1062no—
830C4—1062no—
831C4—1066no—
832C4—1063no—
833C4—1063no—
834C4—1061no—
835C4—1063no—
836C4—2123no—
837C4—2121no—
838C4—2123no—
839C4—2123no—
840C4—2121no—
841C4C2×D4×#615716yes—
842C2—22no—
843C2—41no—
844C2—531no—
845C2—531no—
846C2—531no—
847C2—531no—
848C2—1062no—
849C2—2121no—
850C2C22×D4×#615711yescharacteristic
851C2C2×#1681169111yescharacteristic
852C22−1+4×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingD4×Q8×C53C4
prime radicalC2×D4×D53C23
cosocleC22×D53C25
hypercenterD4×Q8#6157
hypocenterC53#34291
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16811691C2semidirect
2. C22×Q8×#6157C2semidirect
3. #20291244C2semidirect
4. #20291241C2semidirect
5. #20291239C2semidirect
7. #20291230C2semidirect
8. Q8×C22⋊#6157C2semidirect
9. Q8×C22⋊#6157C2semidirect
10. #20291206C2semidirect
11. #20291202C2semidirect
12. C22⋊Q8×#6157C2semidirect
14. #20291155C2semidirect
63. Q8×D212C4semidirect
64. D4×Dic106C4semidirect
65. #16811288C4semidirect
66. Q8×C22⋊D53C4semidirect
67. Q8×C22⋊D53C4semidirect
68. #16811286C4semidirect
69. #16811286C4semidirect
75. D4×Q8×C53C4semidirect
85. Q8×#6157D4semidirect
127. C22×Dic106C2×C4semidirect
134. C2×Q8×D53C2×C4semidirect
135. C2×Q8×D53C2×C4semidirect
142. #13133217C2×C4semidirect
143. #13133216C2×C4semidirect
144. #13133216C2×C4semidirect
145. #13133215C2×C4semidirect
146. #13133215C2×C4semidirect
148. #13133197C2×C4semidirect
150. #13133196C2×C4semidirect
152. #13133195C2×C4semidirect
154. #13133194C2×C4semidirect
156. #13133193C2×C4semidirect
157. Q8×Dic53C2×C4semidirect
158. C4×Dic106C2×C4semidirect
159. #13133182C2×C4semidirect
174. C22×Q8×C53C2×C4semidirect
175. C4⋊Q8×C53C2×C4semidirect
177. C22⋊Q8×C53C2×C4semidirect
178. C4×Q8×C53C2×C4semidirect
376. C22×C53#519semidirect
391. C2×D53#519semidirect
451. D4×Q8#6157semidirect
502. C53#34291semidirect
517. C22×Q8C2×#6157semidirect
528. C4⋊Q8C2×#6157semidirect
540. C22⋊Q8C2×#6157semidirect
552. C4×Q8C2×#6157semidirect
822. C22#16811691semidirect

Maximal subgroups

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

subgroupindex
C2×#168116912
C22×Q8×#61572
#202912442
#202912412
#202912392
#202912312
#202912302
Q8×C22⋊#61572
#202912062
#202912022
C22⋊Q8×#61572
#202911692
#202911552
D4×Q8×D532
#3429153