Finite Group Databasebeta

← #29695619

Subgroups — #29695619

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840403C211yesmaximal, characteristic
2C2×#16839838C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839768C211yesmaximal, characteristic, complemented
5#21448741C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446627C211yesmaximal, characteristic, complemented
8#21446256C211yesmaximal, characteristic, complemented
9#21446135C211yesmaximal, characteristic, complemented
10#21446132C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445749C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1894C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758189C2211yescharacteristic, complemented
19#16840403—24no—
20#16840403C418yescomplemented
21C2×#14519766C2211yescharacteristic
22C2×#14519762—21no—
23C2×#14519752—21no—
24C2×#14519752C2211yescharacteristic
25C2×#14519747—21no—
26C2×#14519739C2211yescharacteristic
27C2×C4×C22⋊D61C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29C2×C4⋊C4×D61C2211yescharacteristic, complemented
30C2×C22⋊C4×D61—21no—
31#16839838—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839768—24no—
34#16839762—24no—
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×C22⋊#92418C2211yescharacteristic
46C2×#14519689C2211yescharacteristic, complemented
47C2×C8×Dic61C2211yescharacteristic, complemented
48#16839650—21no—
49#16839644—21no—
50#16839638—21no—
51#16839627C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic, complemented
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54#16839609—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C22×M16×C61C2211yescharacteristic
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yes—
71C22×D244—22no—
72C22×D244—22no—
73C22×D244—21no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—21no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244C2×C414yescomplemented
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519766—22no—
93#14519766C2×C414yescomplemented
94#14519762—28no—
95#14519752—22no—
96#14519752—28no—
97#14519752C2×C414yes—
98#14519747—28no—
99#14519739—22no—
100#14519739C2×C414yescomplemented
101C4×C22⋊D61C2×C414yes—
102C4×C22⋊D61D414yes—
103#14519736—22no—
104#14519736—41no—
105C2×C4⋊Dic61C2311yescharacteristic
106C2×C4⋊Dic61C2311yescharacteristic
107C2×#11758196—21no—
108C2×#11758196D411yescharacteristic
109C4⋊C4×D61—22no—
110C4⋊C4×D61—41no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61D411yescharacteristic
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519701—22no—
125#14519701—41no—
126#14519699—22no—
127#14519699—22no—
128#14519699—22no—
129#14519699D414yescomplemented
130#14519697—22no—
131#14519697—22no—
132#14519697—41no—
133#14519697—41no—
134C22⋊#92418—22no—
135#14519689—22no—
136C8×Dic61—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C2×M16×C61—22no—
144C2×M16×C61—22no—
145C2×M16×C61—41no—
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22⋊Q8×C61—22no—
149C22⋊Q8×C61C2×C414yescomplemented
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156#103×C61—22no—
157#103×C61—41no—
158#95×C61—21no—
159C24×C61C2×D411yescharacteristic
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D412yes—
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—41no—
189C2×C22⋊D61—41no—
190C2×C22⋊D61C22⋊C414yes—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61C2×D411yescharacteristic
194C22×Dic61C2×D411yescharacteristic
195C22×Dic61C2×D411yescharacteristic
196#11758226—28no—
197#11758226—44no—
198#11758226—44no—
199#11758226—44no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—28no—
208C2×D244—24no—
209C2×D244—24no—
210C2×D244—21no—
211C2×D244—24no—
212C2×D244—44no—
213C2×D244—44no—
214C2×D244—44no—
215C2×D244—42no—
216C2×D244—42no—
217C2×D244—42no—
218C2×D244—42no—
219C2×D244—81no—
220C2×D244—81no—
221C2×D244C22×C412yes—
222C2×D244C22×C412yes—
223C2×D244C2×D412yes—
224C2×D244#4112yes—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—24no—
230C2×C4×D61—24no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—42no—
234C2×C4×D61—42no—
235C2×C4×D61—81no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C2×D412yes—
240M16×C61—44no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61C2×D412yes—
247C4⋊C4×C61—24no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C22×C412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—81no—
256C22⋊Dic61—42no—
257C22⋊Dic61C22⋊C414yes—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—24no—
262#11758198—42no—
263#11758198C22⋊C414yes—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61C2×D412yes—
268#11758196—42no—
269#11758196C22⋊C414yes—
270C4×Dic61—42no—
271C4×Dic61—81no—
272C4×Dic61C22×C412yes—
273C4×Dic61C2×D412yes—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280#11758189—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61C2×C22⋊C412yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—22no—
292C22×D61—21no—
293C22×D61—22no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—48no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—48no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61C2×C22⋊C412yes—
340C2×C4×C61C23×C411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C22⋊D61—44no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61C2×C22⋊C412yes—
360C2×Dic61C2×C22⋊C412yes—
361C2×Dic61C2×C22⋊C412yes—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—48no—
368D244—48no—
369D244—41no—
370D244—41no—
371D244—84no—
372D244C4×D414yes—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—48no—
378C4×D61—84no—
379C4×D61—84no—
380C8×C61—22no—
381C8×C61—41no—
382#92418—41no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61C22×C22⋊C411yescharacteristic
393C22×C61D4211yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61#57511yescharacteristic
396C22×C61#57511yescharacteristic
397C22×C61#57611yescharacteristic
398C22×C61#57711yescharacteristic
399C2×D61—22no—
400C2×D61—24no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—41no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—41no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61—81no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—22no—
433Dic61—42no—
434Dic61—81no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894D6111yescharacteristic, complemented
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—42no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61#289611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#327311yescharacteristic
455C2×C61#327511yescharacteristic
456C2×C61#332211yescharacteristic
457C2×C61#332311yescharacteristic
458D61—42no—
459D61—44no—
460D61—82no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16C2×D6111yescharacteristic
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8C2×D6111yescharacteristic
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4—611no—
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#103C2×D6111yescharacteristic, complemented
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8—611no—
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380C2×D6111yescharacteristic
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340C2×D6111yescharacteristic, complemented
508#340C2×D6111yescharacteristic, complemented
509C61#2242711yescharacteristic, complemented, Sylow
510C25—1221no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—611no—
519C22×D4—614no—
520C22×D4—611no—
521C22×D4—611no—
522C22×D4—1222no—
523C22×D4—1222no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—1222no—
528C22×D4—2441no—
529C22×D4—2441no—
530C23×C4—611no—
531C23×C4—1221no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—41no—
538C2×M16—1222no—
539C2×M16—1222no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—22no—
549C22⋊Q8C4×D6114yescomplemented
550#121—614no—
551#121—1228no—
552#121—1222no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1222no—
565C2×C4⋊C4—1221no—
566C2×C4⋊C4—2441no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—611no—
574C2×C22⋊C4—1228no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—22no—
586#103—41no—
587#103—1222no—
588#103—2441no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—1222no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—21no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—611no—
606C24—1221no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24D4×D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D6112yes—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4—1228no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1224no—
643C2×D4—4881no—
644C2×D4—4881no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2444no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2441no—
653C2×D4—2441no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—611no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—612no—
666C22×C4—612no—
667C22×C4—1224no—
668C22×C4—1224no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—4881no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4—2442no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—44no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8D4×D6112yes—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—614no—
707C4⋊C4—612no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—2442no—
712C4⋊C4C2×C4×D6112yes—
713C22⋊C4—24no—
714C22⋊C4—81no—
715C22⋊C4—614no—
716C22⋊C4—614no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—2442no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—612no—
734C23—1222no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1222no—
741C23—1221no—
742C23—1222no—
743C23—1222no—
744C23—4884no—
745C23—4884no—
746C23—4884no—
747C23—4884no—
748C23—4884no—
749C23—2448no—
750C23—2448no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23C22⋊C4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—614no—
768D4—1222no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—4884no—
774D4—2448no—
775D4—2448no—
776D4—2444no—
777D4—2441no—
778D4—2441no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—612no—
798C2×C4—612no—
799C2×C4—612no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—4884no—
812C2×C4—4884no—
813C2×C4—2448no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4#41×D6111yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—22no—
827C8—41no—
828C8—2441no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—1222no—
838C22—1222no—
839C22—1222no—
840C22—1224no—
841C22—48816no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—4881no—
846C22—2442no—
847C22—2442no—
848C22—2442no—
849C22—2442no—
850C22—2442no—
851C22—2441no—
852C22—2442no—
853C22—2441no—
854C22—2442no—
855C22—2441no—
856C22—2442no—
857C22—2441no—
858C22—2442no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039611yescharacteristic
861C22#1684040111yescharacteristic
862C22#1684056111yescharacteristic
863C22#1684056111yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—1222no—
872C4—1222no—
873C4—1222no—
874C4—4881no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4#1684039411yescharacteristic
879C4#1684040411yescharacteristic
880C2—42no—
881C2—4882no—
882C2—2442no—
883C2—2444no—
884C2#2144863711yescharacteristic
885C2#2145433711yescharacteristic
886C2#2145434311yescharacteristic
887C2#2145742711yescharacteristic
888C2#2145744711yescharacteristic
889C2#2145802611yescharacteristic
890C2#2145804111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1894C2
socleC23×C61C22×D4
prime radicalC2×#16840403C2
cosocleC22×C4×C61C24
hypercenter#1894D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#16839838C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839768C2semidirect
5. #21448741C2semidirect
6. #21446748C2semidirect
7. #21446627C2semidirect
8. #21446256C2semidirect
9. #21446135C2semidirect
10. #21446132C2semidirect
11. #21445828C2semidirect
12. #21445758C2semidirect
13. #21445749C2semidirect
14. #21445633C2semidirect
15. C61×#1894C2semidirect
18. C22×#11758189C22semidirect
20. #16840403C4semidirect
29. C2×C4⋊C4×D61C22semidirect
32. C2×#14519706C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
46. C2×#14519689C22semidirect
47. C2×C8×Dic61C22semidirect
51. #16839627C22semidirect
52. #16839619C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
79. C22×D244C2×C4semidirect
93. #14519766C2×C4semidirect
100. #14519739C2×C4semidirect
129. #14519699D4semidirect
149. C22⋊Q8×C61C2×C4semidirect
443. #1894D61semidirect
484. C2×#103C2×D61semidirect
485. C2×#103C2×D61semidirect
507. #340C2×D61semidirect
508. #340C2×D61semidirect
509. C61#22427semidirect
549. C22⋊Q8C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404032
C2×#168398382
C2×#168397622
C2×#168397682
#214487412
#214467482
#214466272
#214462562
#214461352
#214461322
#214458282
#214457582
#214457492
#214456332
C61×#18942
#2242761