Finite Group Databasebeta

← #29695620

Subgroups — #29695620

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×#16840405C211yesmaximal, characteristic
2C2×#16839839C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448751C211yesmaximal, characteristic, complemented
6#21446631C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446249C211yesmaximal, characteristic, complemented
9#21446133C211yesmaximal, characteristic, complemented
10#21446128C211yesmaximal, characteristic, complemented
11#21445830C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14C4×#14519697C211yesmaximal, characteristic, complemented
15C61×#1983C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×#11758189C2211yescharacteristic, complemented
20#16840405—24no—
21#16840405C418yescomplemented
22C2×#14519759—21no—
23C2×#14519753C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519748C2211yescharacteristic
26C2×#14519747—21no—
27C2×C4×D244C2211yescharacteristic
28C2×C4×D244C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C2×C22⋊C4×D61—21no—
32#16839839—24no—
33#16839765—24no—
34#16839762—24no—
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519701C2211yescharacteristic, complemented
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519698C2211yescharacteristic
40C2×#14519698C2211yescharacteristic
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic, complemented
45C2×C4×#92418C2211yescharacteristic, complemented
46#16839653—21no—
47#16839647—21no—
48#16839640—21no—
49#16839628C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic, complemented
52C4×#11758198—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#124×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic, complemented
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C4×C4⋊C4×C61C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yes—
71C22×D244—21no—
72C22×D244D411yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61C2×C414yescomplemented
82C22×C4×D61—21no—
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758189—22no—
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—22no—
91C2×#11758189—41no—
92C2×#11758189—41no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95#14519759—28no—
96#14519753—22no—
97#14519753C2×C414yescomplemented
98#14519750—28no—
99#14519748—22no—
100#14519748C2×C414yes—
101#14519747—28no—
102C4×D244—22no—
103C4×D244C2×C414yes—
104C4×D244C2×C414yescomplemented
105C4×D244D414yes—
106#14519735—22no—
107#14519735—41no—
108C2×C4⋊Dic61D411yescharacteristic
109C2×C4⋊Dic61C2311yescharacteristic
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196—21no—
114C4⋊C4×D61—22no—
115C4⋊C4×D61—41no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C22⋊C4×D61—28no—
125C2×C4×Dic61—21no—
126#14519701—22no—
127#14519701—41no—
128#14519699—22no—
129#14519699—22no—
130#14519698—22no—
131#14519698—41no—
132#14519697—22no—
133#14519697D414yescomplemented
134#14519689—22no—
135#14519689—22no—
136C4×#92418—22no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C22×D4×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145#124×C61—22no—
146#124×C61C2×C414yescomplemented
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61C2311yescharacteristic
149C2×C22⋊C4×C61—21no—
150C2×C22⋊C4×C61—21no—
151C2×C42×C61—21no—
152C2×C42×C61C2311yescharacteristic
153C4⋊C8×C61—22no—
154#103×C61—22no—
155#103×C61—41no—
156#102×C61—22no—
157#102×C61—41no—
158#95×C61—21no—
159C24×C61—21no—
160C23×D61—21no—
161C23×D61—24no—
162C23×D61—42no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—81no—
167C23×D61—81no—
168C23×D61C2×D411yescharacteristic
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—
176C2×D4×C61—21no—
177C2×D4×C61—21no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61C22×C412yes—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2411yescharacteristic
188C2×C22⋊D61—24no—
189C2×C22⋊D61—24no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C2×C22⋊D61—81no—
193C2×C22⋊D61—81no—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61—21no—
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758226—28no—
200#11758226—44no—
201#11758226—44no—
202#11758226—44no—
203D4×D61—28no—
204D4×D61—44no—
205D4×D61—44no—
206D4×D61—44no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—24no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244—42no—
214C2×D244—42no—
215C2×D244C22⋊C414yes—
216C2×D244C22×C412yes—
217C2×D244C2×D412yes—
218C2×D244#4112yes—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—24no—
228C2×C4×D61—24no—
229C2×C4×D61—42no—
230C2×C4×D61—42no—
231C2×C4×D61—42no—
232C2×C4×D61—42no—
233C2×C4×D61—81no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2×D412yes—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61C2×D412yes—
250C22⋊C4×C61—24no—
251C22⋊C4×C61—24no—
252C42×C61—81no—
253C42×C61C22×C412yes—
254C42×C61C2×D412yes—
255C22⋊Dic61—24no—
256#11758198—24no—
257#11758198—24no—
258#11758198—42no—
259#11758198—42no—
260#11758198—81no—
261#11758198C22⋊C414yes—
262#11758198C22⋊C414yes—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C22⋊C414yes—
269C4⋊Dic61C22×C412yes—
270#11758196—24no—
271#11758196—42no—
272C4×Dic61—42no—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418C2×D412yes—
279#11758189—44no—
280#11758189—44no—
281C23×C61—22no—
282C23×C61—41no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61—41no—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—21no—
292C22×D61—22no—
293C22×D61—21no—
294C22×D61—21no—
295C22×D61—22no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—48no—
305C22×D61—48no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C2×C22⋊C412yes—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321D4×C61—22no—
322D4×C61—22no—
323D4×C61—41no—
324D4×C61—41no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—22no—
330C2×C4×C61—22no—
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×C61C2×C22⋊C412yes—
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—48no—
347C22⋊D61—84no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—22no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—44no—
367D244—48no—
368D244C4×D414yes—
369C4×D61—22no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—48no—
378C4×D61—84no—
379C4×D61—84no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#22427—611nomaximal, Sylow
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
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—22no—
401C2×D61—24no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—22no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—41no—
409C2×D61—41no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—42no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—42no—
420C2×D61—816no—
421C4×C61—22no—
422C4×C61—22no—
423C4×C61—42no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—42no—
433Dic61—81no—
434Dic61—81no—
435C2×#546—611no—
436C2×#436—611no—
437C2×#417—611no—
438C2×#418—611no—
439#2352—611no—
440#1983D6111yescharacteristic, complemented
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874—611no—
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—82no—
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—42no—
460D61—44no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16—611no—
465#546—618no—
466#546—1224no—
467C2×#124C2×D6111yescharacteristic
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
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⋊C8C2×D6111yescharacteristic, complemented
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×#102C2×D6111yescharacteristic
493C2×#102C2×D6111yescharacteristic
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#380—611no—
503C4×C4⋊C4C2×D6111yescharacteristic, complemented
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340—611no—
508#340—611no—
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—614no—
519C22×D4—611no—
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1222no—
523C22×D4—1221no—
524C22×D4—1222no—
525C22×D4—1222no—
526C22×D4—1221no—
527C22×D4—2441no—
528C22×D4—2441no—
529C22×D4C22×D6111yescharacteristic
530C23×C4—611no—
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4—1221no—
535C2×M16—1222no—
536C2×M16—1222no—
537C2×M16—1222no—
538C2×M16—1222no—
539C2×M16—2441no—
540C2×M16—2441no—
541C22×C8—611no—
542C22×C8—611no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—22no—
546#124C4×D6114yescomplemented
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
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—611no—
561C2×C4⋊C4—611no—
562C2×C4⋊C4—611no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—1221no—
565C2×C4⋊C4—1222no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4—2441no—
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—21no—
582C2×C42—1221no—
583C2×C42C22×D6111yescharacteristic
584C4⋊C8—22no—
585#103—22no—
586#103—41no—
587#103—1222no—
588#103—2441no—
589#102—22no—
590#102—41no—
591#102—614no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—1222no—
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—21no—
606C24—611no—
607C24—611no—
608C24—1224no—
609C24—1221no—
610C24—4881no—
611C24—4881no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24—2442no—
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—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—612no—
632C2×D4—612no—
633C2×D4—612no—
634C2×D4—614no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1228no—
638C2×D4—1224no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—4881no—
643C2×D4—4881no—
644C2×D4—2441no—
645C2×D4—2441no—
646C2×D4—2442no—
647C2×D4—2442no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4—2444no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4C2×C4×D6112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—1224no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—1221no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—4881no—
677C22×C4—4881no—
678C22×C4—4881no—
679C22×C4—2442no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4—2442no—
683C22×C4D4×D6111yescharacteristic
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686M16—2444no—
687M16—2444no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—612no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—614no—
704C4⋊C4—612no—
705C4⋊C4—1224no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—2442no—
712C4⋊C4D4×D6112yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—614no—
716C22⋊C4—614no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—4881no—
721C22⋊C4—2442no—
722C22⋊C4—2442no—
723C42—81no—
724C42—2442no—
725C42C2×C4×D6112yes—
726C42D4×D6112yes—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—612no—
735C23—612no—
736C23—1222no—
737C23—1221no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—1221no—
749C23—1221no—
750C23—1222no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—4884no—
756C23—2448no—
757C23—2448no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23—2441no—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—614no—
772D4—1222no—
773D4—1222no—
774D4—1222no—
775D4—4884no—
776D4—2444no—
777D4—2448no—
778D4—2448no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—612no—
793C2×C4—612no—
794C2×C4—1221no—
795C2×C4—1221no—
796C2×C4—1221no—
797C2×C4—1221no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—4884no—
808C2×C4—4884no—
809C2×C4—2448no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4C22⋊C4×D6112yes—
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—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—1222no—
838C22—1222no—
839C22—1222no—
840C22—1222no—
841C22—1224no—
842C22—1222no—
843C22—1222no—
844C22—48816no—
845C22—2442no—
846C22—2441no—
847C22—2441no—
848C22—2442no—
849C22—2441no—
850C22—2441no—
851C22—2442no—
852C22—2441no—
853C22—2441no—
854C22—2442no—
855C22—2441no—
856C22—2441no—
857C22—2442no—
858C22—2442no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039611yescharacteristic
861C22#1684040911yescharacteristic
862C22#1684055911yescharacteristic
863C22#1684055911yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057111yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—1222no—
872C4—1222no—
873C4—4881no—
874C4—4881no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4#1684039711yescharacteristic
879C4#1684040511yescharacteristic
880C2—82no—
881C2—2442no—
882C2—2442no—
883C2—2444no—
884C2#2144864011yescharacteristic
885C2#2145433411yescharacteristic
886C2#2145434311yescharacteristic
887C2#2145742511yescharacteristic
888C2#2145744511yescharacteristic
889C2#2145802711yescharacteristic
890C2#2145804211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC2×#16840405C2
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16839839C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839765C2semidirect
5. #21448751C2semidirect
6. #21446631C2semidirect
7. #21446254C2semidirect
8. #21446249C2semidirect
9. #21446133C2semidirect
10. #21446128C2semidirect
11. #21445830C2semidirect
12. #21445758C2semidirect
13. #21445748C2semidirect
14. C4×#14519697C2semidirect
15. C61×#1983C2semidirect
19. C22×#11758189C22semidirect
21. #16840405C4semidirect
30. C2×C4⋊C4×D61C22semidirect
35. C2×#14519701C22semidirect
36. C2×#14519701C22semidirect
44. C2×#14519689C22semidirect
45. C2×C4×#92418C22semidirect
49. #16839628C22semidirect
51. #16839619C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×C4⋊C8×C61C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
63. C4×C4⋊C4×C61C22semidirect
81. C2×D4×D61C2×C4semidirect
97. #14519753C2×C4semidirect
104. C4×D244C2×C4semidirect
133. #14519697D4semidirect
146. #124×C61C2×C4semidirect
440. #1983D61semidirect
479. C2×C4⋊C8C2×D61semidirect
484. C2×#103C2×D61semidirect
485. C2×#103C2×D61semidirect
503. C4×C4⋊C4C2×D61semidirect
509. C61#22427semidirect
546. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404052
C2×#168398392
C2×#168397622
C2×#168397652
#214487512
#214466312
#214462542
#214462492
#214461332
#214461282
#214458302
#214457582
#214457482
C4×#145196972
C61×#19832
#2242761