Finite Group Databasebeta

← #30620323

Subgroups — #30620323

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#21462008C212yesmaximal, complemented
3#21461843C212yesmaximal, complemented
4#21461841C212yesmaximal
5#21461717C211yesmaximal, characteristic, complemented
6#21461714C211yesmaximal, characteristic, complemented
7#21461682C211yesmaximal, characteristic, complemented
8#21461564C211yesmaximal, characteristic, complemented
9#21461519C211yesmaximal, characteristic, complemented
10C2×#16840640C211yesmaximal, characteristic, complemented
11C2×#16840439C211yesmaximal, 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#16840439—22no—
33#16840439—22no—
34#16840439—22no—
35#16840439—22no—
36C2×#14519772C411yescharacteristic, complemented
37C2×#14519772C411yescharacteristic, complemented
38C2×#14519766C411yescharacteristic, complemented
39C2×#14519762C411yescharacteristic, complemented
40C2×#14519762C2211yescharacteristic
41C2×#14519761C411yescharacteristic, complemented
42C2×#14519753C2211yescharacteristic
43C2×#14519747C2211yescharacteristic
44C2×#14519739C2211yescharacteristic
45C2×C4×C22⋊D61C411yescharacteristic, complemented
46C2×#14519735C2211yescharacteristic
47C2×#14519733C411yescharacteristic, complemented
48C22×#11758198C2211yescharacteristic
49C2×C22⋊C4×D61C2211yescharacteristic
50C2×C22⋊Q8×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×D244C2×C411yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C23×Dic61C2×C411yescharacteristic
78C22×C4×D61C2×C411yescharacteristic, complemented
79C22×C4×D61C2311yescharacteristic
80C22×C4×D61C2311yescharacteristic
81#14519772—22no—
82#14519772—22no—
83#14519772—22no—
84#14519772—22no—
85#14519766—22no—
86#14519766—22no—
87#14519762—22no—
88#14519762—22no—
89#14519762—22no—
90#14519762—22no—
91#14519761—22no—
92#14519761—22no—
93#14519753—22no—
94#14519753—22no—
95#14519747—22no—
96#14519747—22no—
97#14519739—22no—
98#14519739—22no—
99C4×C22⋊D61—21no—
100C4×C22⋊D61—21no—
101C4×C22⋊D61—21no—
102C4×C22⋊D61—21no—
103#14519735—22no—
104#14519735—22no—
105#14519733—21no—
106#14519733—21no—
107#14519733—21no—
108#14519733—21no—
109C2×C4⋊Dic61C2×C411yescharacteristic, complemented
110C2×C4⋊Dic61C2×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
133C2×C4×Dic61C2×C411yescharacteristic, complemented
134C2×C4×Dic61C2×C411yescharacteristic, complemented
135C22×Q8×C61C2×C411yescharacteristic, complemented
136C23×C4×C61C2×C411yescharacteristic
137C22⋊Q8×C61—22no—
138C22⋊Q8×C61—22no—
139C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
140C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
141C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
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—
162C2×Q8×C61—22no—
163C2×Q8×C61—81no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—81no—
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C2×C22⋊D61—21no—
174C2×C22⋊D61—21no—
175C2×C22⋊D61—42no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—42no—
179C22×Dic61C22×C411yescharacteristic
180C22×Dic61C22×C411yescharacteristic
181C22×Dic61C22×C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C411yescharacteristic
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—21no—
187C2×D244—21no—
188C2×D244—22no—
189C2×D244—81no—
190C2×C4×D61—22no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61C2×D412yes—
198C2×C4×D61C2×D412yes—
199C2×C4×D61C2×D412yes—
200C2×C4×D61C2×D412yes—
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—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—22no—
219C22⋊C4×C61—21no—
220C22⋊C4×C61—21no—
221C22⋊C4×C61C22⋊C412yes—
222C22⋊C4×C61C22⋊C412yes—
223C22⋊Dic61C22⋊C411yescharacteristic
224C22⋊Dic61C22⋊C411yescharacteristic
225C22⋊Dic61C22⋊C411yescharacteristic
226C22⋊Dic61C22⋊C411yescharacteristic
227#11758198—22no—
228#11758198—22no—
229#11758198—22no—
230#11758198—22no—
231#11758198—22no—
232#11758198—22no—
233#11758198—22no—
234#11758198—22no—
235#11758198—21no—
236#11758198—21no—
237#11758198C22⋊C412yes—
238#11758198C22⋊C412yes—
239#11758198C22⋊C412yes—
240#11758198C22⋊C412yes—
241C4⋊Dic61—22no—
242C4⋊Dic61—22no—
243#11758196—21no—
244#11758196—21no—
245#11758196—21no—
246#11758196—21no—
247#11758196—21no—
248#11758196—21no—
249C4×Dic61—21no—
250C4×Dic61—21no—
251C4×Dic61—21no—
252C4×Dic61—21no—
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—
302Q8×C61—82no—
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—21no—
311C2×C4×C61—41no—
312C2×C4×C61—41no—
313C2×C4×C61—41no—
314C2×C4×C61—41no—
315C2×C4×C61—81no—
316C2×C4×C61—81no—
317C2×C4×C61C2×C22⋊C412yes—
318C2×C4×C61C2×C22⋊C412yes—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—41no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61C2×C22⋊C411yescharacteristic
333C2×Dic61C2×C22⋊C411yescharacteristic
334C2×Dic61C2×C22⋊C411yescharacteristic
335C2×Dic61C2×C22⋊C411yescharacteristic
336D244—42no—
337D244—42no—
338D244—82no—
339C4×D61—22no—
340C4×D61—22no—
341C4×D61—22no—
342C4×D61—22no—
343C4×D61—42no—
344C4×D61—42no—
345C4×D61—81no—
346C4×D61—81no—
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—22no—
387C4×C61—22no—
388C4×C61—41no—
389C4×C61—41no—
390C4×C61—41no—
391C4×C61—41no—
392Dic61—21no—
393Dic61—21no—
394Dic61—21no—
395Dic61—21no—
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#692311yescharacteristic, complemented
433C2×#120—611no—
434C2×C4×D4—611no—
435C2×C4×D4—611no—
436C2×#117—611no—
437C2×#117—611no—
438C2×#117—612no—
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×Q8C2×#692311yescharacteristic, complemented
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—22no—
485C22⋊Q8—22no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#120—1222no—
489#120—1222no—
490C4×D4—1221no—
491C4×D4—1221no—
492C4×D4—1221no—
493C4×D4—1221no—
494C4×D4—1222no—
495C4×D4—1222no—
496#117—1221no—
497#117—1221no—
498#117—1221no—
499#117—1221no—
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—1222no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4C2×#692311yescharacteristic, complemented
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—611no—
545C2×C42—611no—
546C2×C42—1222no—
547C2×C42—1222no—
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—22no—
566C2×Q8—81no—
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—81no—
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—1221no—
589C22×C4—1221no—
590C22×C4—1222no—
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—2444no—
603C22×C4—2444no—
604C22×C4—2442no—
605C22×C4C22×#692311yescharacteristic
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692311yescharacteristic
608C22×C4C22×#692311yescharacteristic
609C22×C4C22×#692311yescharacteristic
610C22×C4C22×#692311yescharacteristic
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1222no—
621C4⋊C4—1222no—
622C4⋊C4—4882no—
623C4⋊C4—2444no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—611no—
627C22⋊C4—611no—
628C22⋊C4—611no—
629C22⋊C4—611no—
630C22⋊C4—612no—
631C22⋊C4—612no—
632C22⋊C4—612no—
633C22⋊C4—612no—
634C22⋊C4—614no—
635C22⋊C4—1221no—
636C22⋊C4—1221no—
637C22⋊C4—1222no—
638C22⋊C4—1222no—
639C22⋊C4—1222no—
640C22⋊C4—1222no—
641C22⋊C4—1222no—
642C22⋊C4—1222no—
643C22⋊C4—1222no—
644C22⋊C4—1222no—
645C22⋊C4—1222no—
646C22⋊C4—1222no—
647C22⋊C4—1222no—
648C22⋊C4—1222no—
649C22⋊C4—1222no—
650C22⋊C4—1222no—
651C22⋊C4—1222no—
652C22⋊C4—4882no—
653C22⋊C4—2444no—
654C22⋊C4—2444no—
655C22⋊C4C22⋊#692312yes—
656C22⋊C4C22⋊#692312yes—
657C42—1221no—
658C42—1221no—
659C42—1221no—
660C42—1221no—
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—82no—
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—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—611no—
720C2×C4—611no—
721C2×C4—611no—
722C2×C4—611no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1221no—
728C2×C4—1221no—
729C2×C4—1224no—
730C2×C4—1221no—
731C2×C4—1221no—
732C2×C4—1221no—
733C2×C4—4881no—
734C2×C4—4881no—
735C2×C4—4888no—
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—2442no—
751C2×C4—2442no—
752C2×C4—2441no—
753C2×C4—2441no—
754C2×C4—2441no—
755C2×C4C2×C22⋊#692312yes—
756C2×C4C2×C22⋊#692312yes—
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#1684074312yes—
788C22C22×C22⋊#692311yescharacteristic
789C22#41×#692311yescharacteristic
790C22#1684083111yescharacteristic
791C4—22no—
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—1221no—
798C4—1221no—
799C4—1221no—
800C4—1221no—
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×#1684074311yescharacteristic
818C2#2146241811yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C22
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #21462325C2semidirect
2. #21462008C2semidirect
3. #21461843C2semidirect
5. #21461717C2semidirect
6. #21461714C2semidirect
7. #21461682C2semidirect
8. #21461564C2semidirect
9. #21461519C2semidirect
10. C2×#16840640C2semidirect
36. C2×#14519772C4semidirect
37. C2×#14519772C4semidirect
38. C2×#14519766C4semidirect
39. C2×#14519762C4semidirect
41. C2×#14519761C4semidirect
45. C2×C4×C22⋊D61C4semidirect
47. C2×#14519733C4semidirect
50. C2×C22⋊Q8×C61C4semidirect
78. C22×C4×D61C2×C4semidirect
109. C2×C4⋊Dic61C2×C4semidirect
110. C2×C4⋊Dic61C2×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
133. C2×C4×Dic61C2×C4semidirect
134. C2×C4×Dic61C2×C4semidirect
135. C22×Q8×C61C2×C4semidirect
139. C2×C4⋊C4×C61C2×C4semidirect
140. C2×C4⋊C4×C61C2×C4semidirect
141. C2×C4⋊C4×C61C2×C4semidirect
432. C2×C22⋊Q8#6923semidirect
460. C61#22477semidirect
462. C22×Q8C2×#6923semidirect
511. C2×C4⋊C4C2×#6923semidirect
512. C2×C4⋊C4C2×#6923semidirect
513. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623252
#214620082
#214618432
#214618412
#214617172
#214617142
#214616822
#214615642
#214615192
C2×#168406402
C2×#168404392
#2247761