Finite Group Databasebeta

← #30620317

Subgroups — #30620317

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462325C212yesmaximal, complemented
2#21462010C212yesmaximal, complemented
3#21461843C212yesmaximal, complemented
4#21461841C212yesmaximal
5#21461716C211yesmaximal, characteristic, complemented
6#21461714C211yesmaximal, characteristic, complemented
7#21461680C211yesmaximal, characteristic, complemented
8C4×#14519836C211yesmaximal, characteristic, complemented
9#21461518C211yesmaximal, characteristic, complemented
10C2×#16840640C211yesmaximal, characteristic, complemented
11C2×#16840436C211yesmaximal, characteristic
12C2×#14519856C2212yes—
13C22×C22⋊#6923C2212yes—
14C2×#14519836C2212yes—
15C2×#14519836C2212yes—
16#16840712—22no—
17#16840712—22no—
18#16840709—22no—
19#16840705C2212yes—
20#16840704C2212yes—
21#16840703C2212yes—
22C22⋊C4×#6923—22no—
23C4×C22⋊#6923C2212yes—
24#16840640C2211yescharacteristic
25#16840640C2212yes—
26#16840640C2211yescharacteristic
27#16840640C2212yes—
28#16840640C2211yescharacteristic
29#16840640C2211yescharacteristic
30#16840640C2212yes—
31#16840640C2212yes—
32#16840436—22no—
33#16840436—22no—
34#16840436—22no—
35#16840436—22no—
36C2×#14519772C411yescharacteristic, complemented
37C2×#14519771C411yescharacteristic, complemented
38C2×#14519765C411yescharacteristic, complemented
39C2×#14519762C411yescharacteristic, complemented
40C2×#14519762C2211yescharacteristic
41C2×#14519760C411yescharacteristic, complemented
42C2×#14519755C2211yescharacteristic
43C2×#14519754C411yescharacteristic, complemented
44C2×#14519747C2211yescharacteristic
45C2×C4×D244C2211yescharacteristic
46C2×#14519737C411yescharacteristic, complemented
47C2×#14519734C2211yescharacteristic
48C22×#11758198C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×#117×C61C411yescharacteristic, complemented
51C23×#6923—22no—
52#14519856—24no—
53#14519856—42no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923—22no—
56C2×C22⋊#6923—24no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—22no—
59C2×C22⋊#6923—22no—
60C2×C22⋊#6923—42no—
61C2×C22⋊#6923C2312yes—
62C2×C22⋊#6923C2312yes—
63C2×C22⋊#6923C2312yes—
64C2×C22⋊#6923C2312yes—
65C2×C4×#6923—22no—
66C2×C4×#6923—22no—
67#14519836—24no—
68#14519836—42no—
69(C2×#6923)⋊C4—22no—
70(C2×#6923)⋊C4—22no—
71(C2×#6923)⋊C4—22no—
72(C2×#6923)⋊C4—22no—
73C24×D61C2311yescharacteristic
74C22×Dic122C2×C411yescharacteristic, complemented
75C22×D244C2×C411yescharacteristic
76C22×D244C2311yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic, complemented
80C22×C4×D61C2311yescharacteristic
81C22×C4×D61C2311yescharacteristic
82#14519772—22no—
83#14519772—22no—
84#14519771—22no—
85#14519771—22no—
86#14519765—22no—
87#14519765—22no—
88#14519762—22no—
89#14519762—22no—
90#14519762—22no—
91#14519762—22no—
92#14519760—22no—
93#14519760—22no—
94#14519755—22no—
95#14519755—22no—
96#14519754—22no—
97#14519754—22no—
98#14519747—22no—
99#14519747—22no—
100C4×D244—22no—
101C4×D244—22no—
102#14519737—21no—
103#14519737—21no—
104#14519737—21no—
105#14519737—21no—
106#14519734—22no—
107#14519734—22no—
108C2×C4⋊Dic61C2×C411yescharacteristic, complemented
109C2×#11758196C2×C411yescharacteristic, complemented
110C2×#11758196C2×C411yescharacteristic, complemented
111C2×#11758196C2×C411yescharacteristic, complemented
112C2×#11758196C2×C411yescharacteristic, complemented
113C2×#11758196C2×C411yescharacteristic, complemented
114C2×C22⋊Dic61C2×C411yescharacteristic
115C2×#11758198—22no—
116C2×#11758198—22no—
117C2×#11758198C2×C411yescharacteristic
118C2×#11758198C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic, complemented
123C2×#11758198C2×C411yescharacteristic, complemented
124C2×#11758198C2×C411yescharacteristic, complemented
125C2×#11758198C2311yescharacteristic
126C2×#11758198C2311yescharacteristic
127C2×#11758198C2311yescharacteristic
128C22⋊C4×D61D412yes—
129C22⋊C4×D61D412yes—
130C22⋊C4×D61D412yes—
131C22⋊C4×D61D412yes—
132C2×C4×Dic61C2×C411yescharacteristic, complemented
133C23×C4×C61C2×C411yescharacteristic
134#117×C61—21no—
135#117×C61—21no—
136#117×C61—21no—
137#117×C61—21no—
138C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C42×C61C2×C411yescharacteristic, complemented
143C2×C42×C61C2×C411yescharacteristic, complemented
144C24×C61C22×C411yescharacteristic
145C23×D61—22no—
146C23×D61—21no—
147C23×D61—21no—
148C23×D61—42no—
149C23×D61—81no—
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C411yescharacteristic
152C23×D61C2×D412yes—
153C23×D61C2×D412yes—
154C23×D61C2411yescharacteristic
155C22×#6923—22no—
156C22×#6923—22no—
157C22×#6923—22no—
158C22×#6923—22no—
159C22×#6923—44no—
160C22×#6923—44no—
161C22×#6923—82no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—42no—
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C2×C22⋊D61—21no—
172C2×C22⋊D61—21no—
173C2×C22⋊D61—42no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—81no—
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—21no—
185C2×D244—21no—
186C2×D244—22no—
187C2×D244—81no—
188C2×C4×D61—22no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—81no—
194C2×C4×D61—81no—
195C2×C4×D61C2×D412yes—
196C2×C4×D61C2×D412yes—
197C2×C4×D61C2×D412yes—
198C2×C4×D61C2×D412yes—
199C2×Dic122—22no—
200C2×Dic122—81no—
201C22⋊#6923—22no—
202C22⋊#6923—22no—
203C22⋊#6923—22no—
204C22⋊#6923—22no—
205C22⋊#6923—22no—
206C22⋊#6923—22no—
207C22⋊#6923—22no—
208C22⋊#6923—44no—
209C22⋊#6923—44no—
210C22⋊#6923—82no—
211C22⋊#6923#4114yes—
212C4⋊#6923—44no—
213C4⋊#6923—82no—
214C4×#6923—44no—
215C4×#6923—82no—
216C4⋊C4×C61—21no—
217C4⋊C4×C61—21no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61—21no—
222C22⋊C4×C61C22⋊C411yescharacteristic
223C22⋊C4×C61C22⋊C411yescharacteristic
224C22⋊C4×C61C22⋊C411yescharacteristic
225C22⋊C4×C61C22⋊C411yescharacteristic
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61—21no—
230C22⋊Dic61C22⋊C412yes—
231C22⋊Dic61C22⋊C412yes—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—22no—
236#11758198—22no—
237#11758198—22no—
238#11758198—21no—
239#11758198—21no—
240#11758198—22no—
241#11758198—22no—
242#11758198C22⋊C412yes—
243#11758198C22⋊C412yes—
244#11758198C22⋊C412yes—
245#11758198C22⋊C412yes—
246C4⋊Dic61—22no—
247#11758196—21no—
248#11758196—21no—
249#11758196—22no—
250#11758196—22no—
251#11758196—22no—
252#11758196—22no—
253C4×Dic61—21no—
254C4×Dic61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—22no—
258C23×C61—41no—
259C23×C61C2×C22⋊C411yescharacteristic
260C23×C61C2×C22⋊C411yescharacteristic
261C23×C61C23×C411yescharacteristic
262C22×D61—24no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—21no—
270C22×D61—21no—
271C22×D61—21no—
272C22×D61—41no—
273C22×D61—42no—
274C22×D61—41no—
275C22×D61—42no—
276C22×D61—41no—
277C22×D61—41no—
278C22×D61—42no—
279C22×D61—41no—
280C22×D61—41no—
281C22×D61—84no—
282C22×D61—82no—
283C22×D61—82no—
284C22×D61C2×C22⋊C412yes—
285C22×D61C22×D412yes—
286C22×D61C2×#4112yes—
287C22×D61H(5,𝔽2)11yescharacteristic
288C22×D612−1+411yescharacteristic
289C2×#6923—24no—
290C2×#6923—42no—
291C2×#6923—42no—
292C2×#6923—42no—
293C2×#6923—42no—
294C2×#6923—42no—
295C2×#6923—42no—
296C2×#6923—42no—
297C2×#6923—42no—
298C2×#6923—42no—
299C2×#6923—42no—
300C2×#6923—42no—
301C2×#6923—88no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—41no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—41no—
316C2×C4×C61C2×C22⋊C411yescharacteristic
317C2×C4×C61C2×C22⋊C411yescharacteristic
318C2×C4×C61C2×C22⋊C411yescharacteristic
319C2×C4×C61C2×C22⋊C411yescharacteristic
320C22⋊D61—42no—
321C22⋊D61—42no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—81no—
332C2×Dic61—81no—
333C2×Dic61C2×C22⋊C412yes—
334C2×Dic61C2×C22⋊C412yes—
335D244—42no—
336D244—42no—
337D244—82no—
338C4×D61—22no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—42no—
343C4×D61—42no—
344C4×D61—81no—
345C4×D61—81no—
346Dic122—82no—
347#22477—611nomaximal, Sylow
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—21no—
351C22×C61—21no—
352C22×C61—21no—
353C22×C61—21no—
354C22×C61—21no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61#41012yes—
358C22×C61C22×C22⋊C411yescharacteristic
359C22×C61C4×#4111yescharacteristic
360C22×C61#52011yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—42no—
367C2×D61—41no—
368C2×D61—41no—
369C2×D61—44no—
370C2×D61—44no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—82no—
375C2×D61—82no—
376C2×D61—81no—
377C2×D61—81no—
378C2×D61—81no—
379C2×D61—81no—
380C2×D61#54612yes—
381C2×D61#54712yes—
382#6923—44no—
383#6923—82no—
384#6923—82no—
385#6923—82no—
386C4×C61—21no—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—41no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394Dic61—22no—
395Dic61—22no—
396Dic61—41no—
397Dic61—41no—
398Dic61—41no—
399C2×#551—611no—
400#2342—612no—
401#1996—612no—
402#1899—612no—
403#1898—612no—
404#1820—611no—
405#1819—611no—
406#1799—611no—
407C4×#99—611no—
408#1740—611no—
409C2×#342—611no—
410C2×C61—22no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—41no—
414C2×C61#233911yescharacteristic
415C2×C61C2×#41011yescharacteristic
416C2×C61#288311yescharacteristic
417D61—22no—
418D61—22no—
419D61—42no—
420D61—81no—
421#551—1222no—
422#551—1222no—
423#551—1222no—
424#551—1222no—
425C2×#126—611no—
426C2×#126—611no—
427C2×#124—611no—
428C2×#123—611no—
429C2×#123—611no—
430C2×#123—611no—
431C2×C22⋊Q8—611no—
432C2×C22⋊Q8—611no—
433C2×#120—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×#117—611no—
437C2×#117—612no—
438C2×#117#692311yescharacteristic, complemented
439C22×C22⋊C4—611no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—612no—
442C2×#99—612no—
443C2×#99—612no—
444#388—1222no—
445#388—1222no—
446#385—1222no—
447#381—612no—
448#380—612no—
449#379—612no—
450C4×C22⋊C4—612no—
451C4×C22⋊C4—1222no—
452#342—611no—
453#342—611no—
454#342—611no—
455#342—612no—
456#342—612no—
457#342—612no—
458#342—612no—
459#342—611no—
460C61#2247711yescharacteristic, complemented, Sylow
461C25—611no—
462C22×Q8—611no—
463C22×D4—611no—
464C22×D4—611no—
465C22×D4—611no—
466C23×C4—611no—
467C23×C4—611no—
468C23×C4—611no—
469C23×C4—611no—
470C23×C4—1222no—
471C23×C4C2×#692311yescharacteristic
472#126—1222no—
473#126—1222no—
474#126—1222no—
475#126—1222no—
476#124—1222no—
477#124—1222no—
478#123—1222no—
479#123—1222no—
480#123—1222no—
481#123—1222no—
482#123—1222no—
483#123—1222no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#120—1222no—
489#120—1222no—
490C4×D4—1222no—
491C4×D4—1222no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1221no—
495C4×D4—1221no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117—1222no—
501#117—1222no—
502#117—1224no—
503#117—2442no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—611no—
506C2×C4⋊C4—611no—
507C2×C4⋊C4—611no—
508C2×C4⋊C4—611no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4C2×#692311yescharacteristic, complemented
513C2×C4⋊C4C2×#692311yescharacteristic, complemented
514C2×C22⋊C4—611no—
515C2×C22⋊C4—611no—
516C2×C22⋊C4—611no—
517C2×C22⋊C4—612no—
518C2×C22⋊C4—612no—
519C2×C22⋊C4—612no—
520C2×C22⋊C4—612no—
521C2×C22⋊C4—612no—
522C2×C22⋊C4—611no—
523C2×C22⋊C4—611no—
524C2×C22⋊C4—611no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—611no—
528C2×C22⋊C4—611no—
529C2×C22⋊C4—611no—
530C2×C22⋊C4—611no—
531C2×C22⋊C4—612no—
532C2×C22⋊C4—612no—
533C2×C22⋊C4—612no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1222no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1222no—
539C2×C22⋊C4—1222no—
540C2×C22⋊C4—2442no—
541C2×C22⋊C4C2×#692311yescharacteristic
542C2×C22⋊C4C2×#692311yescharacteristic
543C2×C42—611no—
544C2×C42—1222no—
545C2×C42—1222no—
546C2×C42C2×#692311yescharacteristic, complemented
547C2×C42C2×#692311yescharacteristic, complemented
548#99—1224no—
549#99—2442no—
550#95—1222no—
551#95—1222no—
552#95—1222no—
553#95—1222no—
554C24—611no—
555C24—612no—
556C24—612no—
557C24—611no—
558C24—611no—
559C24—1222no—
560C24—1221no—
561C24—1221no—
562C24—4881no—
563C24—2442no—
564C24C22×#692311yescharacteristic
565C2×Q8—1222no—
566C2×Q8—4881no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1222no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—4881no—
575C2×D4—2442no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—611no—
580C22×C4—611no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—612no—
584C22×C4—612no—
585C22×C4—611no—
586C22×C4—611no—
587C22×C4—611no—
588C22×C4—1222no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1221no—
592C22×C4—1221no—
593C22×C4—1222no—
594C22×C4—1221no—
595C22×C4—1221no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—4881no—
600C22×C4—4881no—
601C22×C4—4882no—
602C22×C4—4881no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4C22×#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609C22×C4C22×#692311yescharacteristic
610C22×C4C22×#692311yescharacteristic
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—1222no—
616C4⋊C4—1222no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C4⋊C4—1222no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—4882no—
623C4⋊C4—2444no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—612no—
627C22⋊C4—612no—
628C22⋊C4—612no—
629C22⋊C4—612no—
630C22⋊C4—612no—
631C22⋊C4—612no—
632C22⋊C4—614no—
633C22⋊C4—1222no—
634C22⋊C4—1222no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1221no—
643C22⋊C4—1221no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—4882no—
651C22⋊C4—2444no—
652C22⋊C4—2444no—
653C22⋊C4C22⋊#692311yescharacteristic
654C22⋊C4C22⋊#692311yescharacteristic
655C22⋊C4C22⋊#692311yescharacteristic
656C22⋊C4C22⋊#692311yescharacteristic
657C42—21no—
658C42—21no—
659C42—21no—
660C42—21no—
661C42—1221no—
662C42—1221no—
663C42—4882no—
664C42—2444no—
665C23—22no—
666C23—21no—
667C23—21no—
668C23—41no—
669C23—612no—
670C23—612no—
671C23—611no—
672C23—611no—
673C23—612no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1221no—
679C23—1221no—
680C23—1224no—
681C23—1221no—
682C23—1221no—
683C23—1221no—
684C23—4882no—
685C23—4884no—
686C23—4882no—
687C23—2442no—
688C23—2441no—
689C23—2441no—
690C23—2442no—
691C23—2441no—
692C23—2442no—
693C23—2441no—
694C23—2441no—
695C23—2441no—
696C23C2×C22⋊#692311yescharacteristic
697C23C2×C22⋊#692311yescharacteristic
698C23C23×#692311yescharacteristic
699Q8—4882no—
700D4—4882no—
701D4—2442no—
702D4—2442no—
703D4—2442no—
704D4—2442no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—612no—
720C2×C4—612no—
721C2×C4—1222no—
722C2×C4—1222no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1221no—
726C2×C4—1221no—
727C2×C4—1224no—
728C2×C4—1221no—
729C2×C4—1221no—
730C2×C4—1221no—
731C2×C4—4881no—
732C2×C4—4881no—
733C2×C4—4888no—
734C2×C4—4881no—
735C2×C4—4881no—
736C2×C4—2442no—
737C2×C4—2442no—
738C2×C4—2441no—
739C2×C4—2442no—
740C2×C4—2442no—
741C2×C4—2442no—
742C2×C4—2442no—
743C2×C4—2442no—
744C2×C4—2442no—
745C2×C4—2442no—
746C2×C4—2442no—
747C2×C4—2442no—
748C2×C4—2442no—
749C2×C4—2442no—
750C2×C4—2441no—
751C2×C4—2441no—
752C2×C4—2441no—
753C2×C4C2×C22⋊#692311yescharacteristic
754C2×C4C2×C22⋊#692311yescharacteristic
755C2×C4C2×C22⋊#692311yescharacteristic
756C2×C4C2×C22⋊#692311yescharacteristic
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—612no—
767C22—612no—
768C22—1222no—
769C22—1222no—
770C22—1222no—
771C22—1222no—
772C22—1222no—
773C22—4881no—
774C22—4881no—
775C22—4881no—
776C22—4881no—
777C22—4882no—
778C22—4882no—
779C22—2442no—
780C22—2441no—
781C22—2441no—
782C22—2444no—
783C22—2444no—
784C22—2441no—
785C22—2441no—
786C22—2441no—
787C22#1684074112yes—
788C22C22×C22⋊#692311yescharacteristic
789C22#41×#692311yescharacteristic
790C22#1684083111yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—21no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—41no—
799C4—1222no—
800C4—1222no—
801C4—4882no—
802C4—4882no—
803C4—4882no—
804C4—2444no—
805C4—2441no—
806C4—2441no—
807C4—2441no—
808C2—21no—
809C2—21no—
810C2—22no—
811C2—41no—
812C2—1222no—
813C2—1222no—
814C2—4881no—
815C2—2442no—
816C2#2146232211yescharacteristic
817C2C2×#1684074111yescharacteristic
818C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C22
cosocleC23×D61C24
hypercenterC2×#117#6923
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462325C2semidirect
2. #21462010C2semidirect
3. #21461843C2semidirect
5. #21461716C2semidirect
6. #21461714C2semidirect
7. #21461680C2semidirect
8. C4×#14519836C2semidirect
9. #21461518C2semidirect
10. C2×#16840640C2semidirect
36. C2×#14519772C4semidirect
37. C2×#14519771C4semidirect
38. C2×#14519765C4semidirect
39. C2×#14519762C4semidirect
41. C2×#14519760C4semidirect
43. C2×#14519754C4semidirect
46. C2×#14519737C4semidirect
50. C2×#117×C61C4semidirect
74. C22×Dic122C2×C4semidirect
79. C22×C4×D61C2×C4semidirect
108. C2×C4⋊Dic61C2×C4semidirect
109. C2×#11758196C2×C4semidirect
110. C2×#11758196C2×C4semidirect
111. C2×#11758196C2×C4semidirect
112. C2×#11758196C2×C4semidirect
113. C2×#11758196C2×C4semidirect
122. C2×#11758198C2×C4semidirect
123. C2×#11758198C2×C4semidirect
124. C2×#11758198C2×C4semidirect
132. C2×C4×Dic61C2×C4semidirect
138. C2×C4⋊C4×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
142. C2×C42×C61C2×C4semidirect
143. C2×C42×C61C2×C4semidirect
438. C2×#117#6923semidirect
460. C61#22477semidirect
512. C2×C4⋊C4C2×#6923semidirect
513. C2×C4⋊C4C2×#6923semidirect
546. C2×C42C2×#6923semidirect
547. C2×C42C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623252
#214620102
#214618432
#214618412
#214617162
#214617142
#214616802
C4×#145198362
#214615182
C2×#168406402
C2×#168404362
#2247761