Finite Group Databasebeta

← #30617918

Subgroups — #30617918

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462500C211yesmaximal, characteristic
2#21462281C211yesmaximal, characteristic
3#21462007C211yesmaximal, characteristic, complemented
4#21462006C211yesmaximal, characteristic, complemented
5#21462005C211yesmaximal, characteristic, complemented
6#21462004C211yesmaximal, characteristic, complemented
7#21461996C211yesmaximal, characteristic, complemented
8#21461996C211yesmaximal, characteristic, complemented
9#21461995C211yesmaximal, characteristic, complemented
10#21461994C211yesmaximal, characteristic, complemented
11#21461727C211yesmaximal, characteristic
12#21461727C211yesmaximal, characteristic
13#21461726C211yesmaximal, characteristic
14#21461725C211yesmaximal, characteristic
15#21459223C211yesmaximal, characteristic
16#16840787—21no—
17#16840787—21no—
18#16840786—21no—
19#16840786—21no—
20#16840767C2211yescharacteristic
21#16840766C2211yescharacteristic
22#16840733C2211yescharacteristic
23#16840733C2211yescharacteristic
24C4×#11758213C2211yescharacteristic
25C4×#11758213C2211yescharacteristic
26#16840712—21no—
27#16840712—21no—
28#16840711—21no—
29#16840711—21no—
30C4×C4⋊#6923C2211yescharacteristic
31C4×C4⋊#6923C2211yescharacteristic
32C4×C22⋊#6923C2211yescharacteristic
33C4×C22⋊#6923C2211yescharacteristic
34#16840698C2211yescharacteristic
35C42×#6923C2211yescharacteristic
36#16840632C2211yescharacteristic
37#16840632C2211yescharacteristic
38#16840632C2211yescharacteristic
39#16840632C2211yescharacteristic
40#16840632C2211yescharacteristic
41#16840632C2211yescharacteristic
42#16840632C2211yescharacteristic
43#16840632C2211yescharacteristic
44#16840632C2211yescharacteristic
45#16840632C2211yescharacteristic
46#16840632C2211yescharacteristic
47#16840632C2211yescharacteristic
48#16840632C2211yescharacteristic
49#16840632C2211yescharacteristic
50#16840632C2211yescharacteristic
51#16840632C2211yescharacteristic
52#16840393C411yescharacteristic, complemented
53#16840392—21no—
54#16840392C411yescharacteristic, complemented
55#16840392C411yescharacteristic, complemented
56#16840390C411yescharacteristic, complemented
57#16840390C411yescharacteristic, complemented
58#16840389—21no—
59#16840389C411yescharacteristic, complemented
60#16840389C411yescharacteristic, complemented
61#16840387—21no—
62#16840387—21no—
63#16840318—21no—
64#16840318C2211yescharacteristic
65#16840318C2211yescharacteristic
66#16840317—21no—
67#16840317C2211yescharacteristic
68#16840317C2211yescharacteristic
69#16840314—21no—
70#16840314—21no—
71C2×#14519735C2211yescharacteristic
72#117×D61C2211yescharacteristic
73#117×D61C2211yescharacteristic
74C61×#544C411yescharacteristic, complemented
75C2×#11758213C2311yescharacteristic
76C2×#11758213C2311yescharacteristic
77C2×#11758213C2311yescharacteristic
78C2×#11758213C2311yescharacteristic
79C2×C4⋊#6923—21no—
80C2×C4⋊#6923—21no—
81C2×C22⋊#6923—21no—
82C2×C22⋊#6923—21no—
83C2×C4×#6923—21no—
84C2×C4×#6923—21no—
85C2×C4×#6923C2311yescharacteristic
86C2×C4×#6923C2311yescharacteristic
87C2×C4×#6923C2311yescharacteristic
88C2×C4×#6923C2311yescharacteristic
89#14519844—21no—
90#14519844—21no—
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93#14519834—21no—
94#14519834—21no—
95C22⋊#92420—21no—
96C22⋊#92420—21no—
97#14519832—21no—
98#14519832—21no—
99C4×#92420—21no—
100C4×#92420—21no—
101(C2×#6923)⋊C4—21no—
102(C2×#6923)⋊C4—21no—
103(C2×#6923)⋊C4—21no—
104(C2×#6923)⋊C4—21no—
105(C2×#6923)⋊C4—21no—
106(C2×#6923)⋊C4—21no—
107C22×C4×D61C2311yescharacteristic
108#14519777—21no—
109#14519777C2×C411yescharacteristic
110#14519777C2×C411yescharacteristic
111#14519776—21no—
112#14519776—21no—
113#14519776—21no—
114#14519776—21no—
115#14519776C2×C411yescharacteristic
116#14519776C2×C411yescharacteristic
117#14519776C2×C411yescharacteristic
118#14519776C2×C411yescharacteristic
119#14519775—21no—
120#14519775—21no—
121#14519769—21no—
122#14519769C2×C411yescharacteristic
123#14519769C2×C411yescharacteristic
124#14519768—21no—
125#14519768—21no—
126#14519768C2×C411yescharacteristic
127#14519768C2×C411yescharacteristic
128#14519768C2×C411yescharacteristic
129#14519768C2×C411yescharacteristic
130#14519767—21no—
131#14519767—21no—
132#14519767—21no—
133#14519767—21no—
134#14519757—21no—
135#14519757—21no—
136#14519757—21no—
137#14519757—21no—
138#14519756—21no—
139#14519756—21no—
140#14519755—21no—
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519755—21no—
145#14519755—21no—
146#14519755—21no—
147#14519755—21no—
148#14519754—21no—
149#14519754—21no—
150#14519754—21no—
151#14519754—21no—
152#14519753—21no—
153#14519753—21no—
154#14519753—21no—
155#14519753—21no—
156Q8×Dic61—21no—
157Q8×Dic61—21no—
158#14519742—21no—
159#14519742—21no—
160#14519742—21no—
161#14519742—21no—
162#14519742—21no—
163#14519742—21no—
164#14519736C2×C411yescharacteristic
165#14519736C2×C411yescharacteristic
166#14519735—21no—
167#14519735—21no—
168#14519735C2×C411yescharacteristic
169#14519735C2×C411yescharacteristic
170#14519735D411yescharacteristic
171#14519735D411yescharacteristic
172#14519735C2311yescharacteristic
173#14519735C2311yescharacteristic
174#14519735C2311yescharacteristic
175#14519735C2311yescharacteristic
176#14519734—21no—
177#14519734C2×C411yescharacteristic
178#14519734C2×C411yescharacteristic
179#14519733—21no—
180#14519733D411yescharacteristic
181#14519733D411yescharacteristic
182C2×C4⋊Dic61C2×C411yescharacteristic
183C4⋊C4×D61C2×C411yescharacteristic
184C4⋊C4×D61C2×C411yescharacteristic
185C4⋊C4×D61D411yescharacteristic
186C4⋊C4×D61D411yescharacteristic
187C2×#11758198—21no—
188C22⋊C4×D61—21no—
189C22⋊C4×D61D411yescharacteristic
190C22⋊C4×D61D411yescharacteristic
191C2×C4×Dic61—21no—
192C42×D61—21no—
193C42×D61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C4⋊Q8×C61—21no—
196C4⋊Q8×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#125×C61—21no—
199#125×C61C2×C411yescharacteristic
200#125×C61C2×C411yescharacteristic
201C22⋊Q8×C61—21no—
202C22⋊Q8×C61—21no—
203#117×C61C2×C411yescharacteristic
204#117×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61C2×C411yescharacteristic
206C23×D61C2×D411yescharacteristic
207C22×#6923—21no—
208C22×#6923—21no—
209C22×#6923—21no—
210C22×#6923—21no—
211C2×Q8×C61—21no—
212C2×Q8×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61C22×C411yescharacteristic
215C22×Dic61—21no—
216C22×Dic61C2×D411yescharacteristic
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61C22×C411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C22⋊#6923—42no—
238C22⋊#6923—42no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—21no—
242C2×#92420—21no—
243C4⋊#6923—42no—
244C4⋊#6923—42no—
245C4×#6923—21no—
246C4×#6923—21no—
247C4×#6923—21no—
248C4×#6923—21no—
249C4×#6923—21no—
250C4×#6923—21no—
251C4×#6923—21no—
252C4×#6923—21no—
253C4×#6923—42no—
254C4×#6923—42no—
255#11758213—21no—
256#11758213—21no—
257#11758213—21no—
258#11758213—21no—
259#11758213—21no—
260#11758213—21no—
261#11758213—21no—
262#11758213—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C22⋊C411yescharacteristic
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C4⋊C4×C61C22×C411yescharacteristic
274C4⋊C4×C61C22×C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61C22⋊C411yescharacteristic
278C22⋊C4×C61C22⋊C411yescharacteristic
279C42×C61—21no—
280C42×C61C22×C411yescharacteristic
281C42×C61C22×C411yescharacteristic
282C22⋊Dic61—21no—
283C22⋊Dic61C22⋊C411yescharacteristic
284C22⋊Dic61C22⋊C411yescharacteristic
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22⋊C411yescharacteristic
304C4⋊Dic61C22×C411yescharacteristic
305C4⋊Dic61C22×C411yescharacteristic
306C4⋊Dic61C22×C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196—21no—
318#11758196—21no—
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196C22⋊C411yescharacteristic
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326C4×Dic61—21no—
327C4×Dic61—21no—
328C4×Dic61—21no—
329C4×Dic61—21no—
330C4×Dic61—21no—
331C4×Dic61—21no—
332C4×Dic61—21no—
333C4×Dic61C22×C411yescharacteristic
334C4×Dic61C22×C411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338C4×Dic61C2×D411yescharacteristic
339C23×C61C2×C22⋊C411yescharacteristic
340C22×D61—21no—
341C22×D61—21no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61C2×C22⋊C411yescharacteristic
345C22×D61C22×D411yescharacteristic
346C2×#6923—22no—
347C2×#6923—22no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358Q8×C61—81no—
359Q8×C61—81no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—21no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—21no—
366C2×C4×C61—81no—
367C2×C4×C61C2×C22⋊C411yescharacteristic
368C2×C4×C61C2×C22⋊C411yescharacteristic
369C2×C4×C61C2×C22⋊C411yescharacteristic
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C23×C411yescharacteristic
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—21no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—81no—
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C22×D411yescharacteristic
386C4×D61—21no—
387C4×D61—21no—
388C4×D61—21no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—41no—
393C4×D61—41no—
394C4×D61—41no—
395C4×D61—41no—
396C4×D61—81no—
397C4×D61—81no—
398C4×D612−1+411yescharacteristic
399C4×D612−1+411yescharacteristic
400C4×D612−1+411yescharacteristic
401C4×D612−1+411yescharacteristic
402Dic122—81no—
403Dic122—81no—
404Dic122—81no—
405Dic122—81no—
406Dic122—81no—
407Dic122—81no—
408#92420—41no—
409#92420—41no—
410#92420—41no—
411#92420—41no—
412#21846—611nomaximal, Sylow
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61C22×C22⋊C411yescharacteristic
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—21no—
421C2×D61—21no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61#53611yescharacteristic
425C2×D61#53611yescharacteristic
426#6923—42no—
427#6923—42no—
428#6923—81no—
429#6923—81no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—21no—
434C4×C61—21no—
435C4×C61—41no—
436C4×C61—41no—
437C4×C61—41no—
438C4×C61—41no—
439C4×C61#51911yescharacteristic
440C4×C61#51911yescharacteristic
441Dic61—21no—
442Dic61—21no—
443Dic61—21no—
444Dic61—21no—
445Dic61—21no—
446Dic61—41no—
447Dic61—41no—
448Dic61—41no—
449Dic61—41no—
450Dic61#53611yescharacteristic
451Dic61#53611yescharacteristic
452#3458—611no—
453#2921—611no—
454#2298—611no—
455#1995—611no—
456#1995—611no—
457#1994—611no—
458#1994—611no—
459#1986—611no—
460#1986—611no—
461#1986—611no—
462#1986—611no—
463#1826—611no—
464#1826—611no—
465#1826—611no—
466#1826—611no—
467C2×C61—41no—
468C2×C61#231011yescharacteristic
469C2×C61#290111yescharacteristic
470C2×C61#290111yescharacteristic
471D61—21no—
472D61—21no—
473D61—41no—
474#544—611no—
475#544—611no—
476#544—611no—
477#544—611no—
478#544—611no—
479#544—611no—
480#544—611no—
481#544—1221no—
482#544—1221no—
483#544#692311yescharacteristic, complemented
484#543—1221no—
485#543—1221no—
486#533—611no—
487#533—611no—
488#533—611no—
489#533—611no—
490#533—1221no—
491#533—1221no—
492#533—1221no—
493#533—1221no—
494C2×#117—611no—
495C2×#117—611no—
496C2×#117—611no—
497#433—1221no—
498#433—1221no—
499#433—1221no—
500#433—1221no—
501#423—611no—
502#423—611no—
503#407—611no—
504#407—611no—
505C4×M16—611no—
506C4×M16—611no—
507#388—1221no—
508#388—1221no—
509#387—1221no—
510#387—1221no—
511C4×C4⋊C4—611no—
512C4×C4⋊C4—611no—
513C4×C22⋊C4—611no—
514C4×C22⋊C4—611no—
515#376—611no—
516C43—611no—
517#339—611no—
518#339—611no—
519#339—611no—
520#339—611no—
521#339—611no—
522#339—611no—
523#339—611no—
524#339—611no—
525#339—611no—
526#339—611no—
527#339—611no—
528#339—611no—
529#339—611no—
530#339—611no—
531#339—611no—
532#339—611no—
533C61#2184611yescharacteristic, complemented, Sylow
534C23×C4—611no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—611no—
539C4⋊Q8—21no—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—611no—
543C4⋊Q8—611no—
544C4⋊Q8—611no—
545C4⋊Q8—611no—
546C4⋊Q8—1221no—
547C4⋊Q8—1221no—
548C4⋊Q8—1221no—
549C4⋊Q8—1221no—
550C4⋊Q8—1221no—
551C4⋊Q8—1221no—
552C4⋊Q8—1221no—
553C4⋊Q8C2×#692311yescharacteristic
554C4⋊Q8C2×#692311yescharacteristic
555#125—21no—
556#125—611no—
557#125—611no—
558#125—611no—
559#125—611no—
560#125—611no—
561#125—611no—
562#125—1221no—
563#125—1221no—
564#125—1221no—
565#125—1221no—
566#125—1221no—
567#125—1221no—
568#125—1221no—
569#125C2×#692311yescharacteristic
570#125C2×#692311yescharacteristic
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8—1221no—
577C22⋊Q8—1221no—
578C22⋊Q8—1221no—
579C22⋊Q8—1221no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586C22⋊Q8—1221no—
587C22⋊Q8—1221no—
588C22⋊Q8—1221no—
589C22⋊Q8—1221no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C4×Q8—1221no—
596C4×Q8—1221no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×Q8—1221no—
600C4×Q8—1221no—
601C4×Q8—1221no—
602C4×Q8—1221no—
603#117—611no—
604#117—611no—
605#117—611no—
606#117—611no—
607#117—611no—
608#117—611no—
609#117—611no—
610#117—611no—
611#117—611no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—1221no—
618#117—1221no—
619#117—1221no—
620#117—1221no—
621#117C2×#692311yescharacteristic
622#117C2×#692311yescharacteristic
623C2×C4⋊C4—611no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—1221no—
629C2×C4⋊C4—1221no—
630C2×C4⋊C4C2×#692311yescharacteristic
631C2×C22⋊C4—611no—
632C2×C22⋊C4—611no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C2×C42—611no—
641C2×C42—611no—
642C2×C42—611no—
643C2×C42—1221no—
644C2×C42—1221no—
645C2×C42—1221no—
646C2×C42—1221no—
647C4⋊C8—1221no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C22⋊C8—1221no—
652C22⋊C8—1221no—
653C22⋊C8—1221no—
654C22⋊C8—1221no—
655#97—1221no—
656#97—1221no—
657C4×C8—1221no—
658C4×C8—1221no—
659#95—1221no—
660#95—1221no—
661#95—1221no—
662#95—1221no—
663#95—1221no—
664#95—1221no—
665C24—611no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—1221no—
672C2×Q8—1221no—
673C2×Q8—1221no—
674C22×C4—21no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—611no—
683C22×C4—611no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4C22×#692311yescharacteristic
696M16—1221no—
697M16—1221no—
698M16—1221no—
699M16—1221no—
700M16—1221no—
701M16—1221no—
702M16—1221no—
703M16—1221no—
704C2×C8—1221no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—611no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—2442no—
747C4⋊C4—2442no—
748C4⋊C4C22⋊#692311yescharacteristic
749C4⋊C4C22⋊#692311yescharacteristic
750C4⋊C4C22×#692311yescharacteristic
751C4⋊C4C22×#692311yescharacteristic
752C4⋊C4C22×#692311yescharacteristic
753C4⋊C4C22×#692311yescharacteristic
754C22⋊C4—21no—
755C22⋊C4—611no—
756C22⋊C4—611no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—2442no—
769C22⋊C4—2442no—
770C22⋊C4C22⋊#692311yescharacteristic
771C22⋊C4C22⋊#692311yescharacteristic
772C42—21no—
773C42—611no—
774C42—611no—
775C42—611no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—1221no—
780C42—1221no—
781C42—1221no—
782C42—1221no—
783C42—1221no—
784C42—1221no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42—1221no—
789C42—1221no—
790C42—1221no—
791C42—1221no—
792C42—1221no—
793C42—1221no—
794C42—2442no—
795C42—2442no—
796C42C22×#692311yescharacteristic
797C42C22×#692311yescharacteristic
798C23—611no—
799C23—611no—
800C23—1221no—
801C23—1221no—
802C23—2441no—
803C23—2441no—
804C23C2×C22⋊#692311yescharacteristic
805Q8—81no—
806Q8—81no—
807Q8—4881no—
808Q8—4881no—
809Q8—4881no—
810Q8—4881no—
811Q8—4881no—
812Q8—4881no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—81no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—611no—
824C2×C4—611no—
825C2×C4—611no—
826C2×C4—611no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1222no—
839C2×C4—1222no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—4881no—
845C2×C4—4881no—
846C2×C4—4881no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4—2441no—
855C2×C4—2441no—
856C2×C4—2441no—
857C2×C4—2441no—
858C2×C4—2441no—
859C2×C4—2441no—
860C2×C4—2441no—
861C2×C4C2×C22⋊#692311yescharacteristic
862C2×C4C2×C22⋊#692311yescharacteristic
863C2×C4C2×C22⋊#692311yescharacteristic
864C2×C4C2×C22⋊#692311yescharacteristic
865C2×C4C2×C22⋊#692311yescharacteristic
866C2×C4C23×#692311yescharacteristic
867C8—2441no—
868C8—2441no—
869C8—2441no—
870C8—2441no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—611no—
875C22—611no—
876C22—1221no—
877C22—1221no—
878C22—1221no—
879C22—1221no—
880C22—1221no—
881C22—4881no—
882C22—4881no—
883C22C22×C22⋊#692311yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—611no—
894C4—611no—
895C4—1221no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—4881no—
901C4—4881no—
902C4—2442no—
903C4—2442no—
904C4—2441no—
905C4—2441no—
906C4—2441no—
907C4—2441no—
908C4#1684083011yescharacteristic
909C4#1684083011yescharacteristic
910C2—41no—
911C2—1221no—
912C2—1221no—
913C2—2441no—
914C2#2146229311yescharacteristic
915C2#2146244911yescharacteristic
916C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#544#6923
hypocenterC61#21846
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #21462007C2semidirect
4. #21462006C2semidirect
5. #21462005C2semidirect
6. #21462004C2semidirect
7. #21461996C2semidirect
8. #21461996C2semidirect
9. #21461995C2semidirect
10. #21461994C2semidirect
52. #16840393C4semidirect
54. #16840392C4semidirect
55. #16840392C4semidirect
56. #16840390C4semidirect
57. #16840390C4semidirect
59. #16840389C4semidirect
60. #16840389C4semidirect
74. C61×#544C4semidirect
483. #544#6923semidirect
533. C61#21846semidirect

Maximal subgroups

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

subgroupindex
#214625002
#214622812
#214620072
#214620062
#214620052
#214620042
#214619962
#214619952
#214619942
#214617272
#214617262
#214617252
#214592232
#2184661