Finite Group Databasebeta

← #29695616

Subgroups — #29695616

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×#16840409C211yesmaximal, characteristic
2C2×#16839837C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5#21448744C211yesmaximal, characteristic, complemented
6#21446750C211yesmaximal, characteristic, complemented
7#21446629C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446251C211yesmaximal, characteristic, complemented
10#21446130C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445760C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19C22×#11758189C2211yescharacteristic
20#16840409—24no—
21#16840409C418yescomplemented
22C2×#14519764C2211yescharacteristic
23C2×#14519759—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519748—21no—
26C2×#14519745—21no—
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30C2×C22⋊C4×D61—21no—
31#16839837—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839765—24no—
34#16839761—24no—
35C2×#14519702C2211yescharacteristic, complemented
36C2×#14519702C2211yescharacteristic, complemented
37C2×#14519700C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519699C2211yescharacteristic
40C2×#14519699C2211yescharacteristic
41C2×#14519698C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic, complemented
47#16839652—21no—
48#16839643—21no—
49#16839641—21no—
50#16839627C2211yescharacteristic, complemented
51#16839622C2211yescharacteristic, complemented
52#16839619C2211yescharacteristic
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C4×C22⋊Dic61—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#121×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—41no—
69C2×#11758222—41no—
70C2×#11758222C2×C414yes—
71C22×Dic122C2311yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61D411yescharacteristic
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×D61C2311yescharacteristic
85C2×#11758194—22no—
86C2×#11758194—22no—
87C2×#11758194—41no—
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—41no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93#14519764—22no—
94#14519764C2×C414yescomplemented
95#14519759—28no—
96#14519757—22no—
97#14519757C2×C414yescomplemented
98#14519748—28no—
99#14519745—28no—
100#14519739—22no—
101#14519739C2×C414yescomplemented
102C4×C22⋊D61C2×C414yes—
103C4×C22⋊D61D414yes—
104#14519735—22no—
105#14519735—41no—
106C2×C4⋊Dic61—21no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196D411yescharacteristic
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61—21no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61D411yescharacteristic
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#14519702—41no—
125#14519702—41no—
126#14519700—22no—
127#14519700—22no—
128#14519699—22no—
129#14519699—22no—
130#14519698—22no—
131#14519698—41no—
132#14519697—22no—
133#14519697D414yescomplemented
134#14519689—22no—
135C8×Dic61—22no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×D4×C61—21no—
142C22×D4×C61C2311yescharacteristic
143C23×C4×C61—21no—
144C23×C4×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147#121×C61—22no—
148#121×C61C2×C414yes—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—41no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156#102×C61—22no—
157#102×C61—41no—
158C22⋊C8×C61—22no—
159C24×C61—21no—
160C24×C61C2×D411yescharacteristic
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×D4×C61—24no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—81no—
177C2×D4×C61—81no—
178C2×D4×C61C22×C412yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—42no—
187C22×C4×C61—42no—
188C22×C4×C61—81no—
189C22×C4×C61C22×C412yes—
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D412yes—
192C22×C4×C61C2411yescharacteristic
193C2×C22⋊D61—24no—
194C2×C22⋊D61—24no—
195C2×C22⋊D61—41no—
196C2×C22⋊D61—41no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—42no—
200C2×C22⋊D61—42no—
201C2×C22⋊D61C22⋊C414yes—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208D4×D61—28no—
209D4×D61—44no—
210D4×D61—44no—
211D4×D61—44no—
212#11758222—28no—
213#11758222—44no—
214#11758222—44no—
215#11758222—44no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244C22×C412yes—
220C2×D244C2×D412yes—
221C2×D244#4112yes—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61—24no—
227C2×C4×D61—24no—
228C2×C4×D61—42no—
229C2×C4×D61—42no—
230C2×C4×D61—81no—
231C2×C4×D61—81no—
232C2×C4×D61C22×C412yes—
233C2×C4×D61C2×D412yes—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122C22×C412yes—
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×C61—21no—
250C4⋊C4×C61—42no—
251C4⋊C4×C61C22×C412yes—
252C4⋊C4×C61C2×D412yes—
253C22⋊C4×C61—24no—
254C22⋊Dic61—24no—
255C22⋊Dic61—24no—
256C22⋊Dic61—42no—
257C22⋊Dic61C22⋊C414yes—
258#11758198—24no—
259#11758198—24no—
260#11758198—42no—
261#11758198—81no—
262#11758198C22⋊C414yes—
263C4⋊Dic61—24no—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273#11758194—44no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418C2×D412yes—
280#11758189—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—22no—
288C23×C61—41no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61C2×C22⋊C412yes—
295C23×C61C22×D411yescharacteristic
296C22×D61—22no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—21no—
300C22×D61—22no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—48no—
306C22×D61—48no—
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—
317D4×C61—22no—
318D4×C61—22no—
319D4×C61—41no—
320D4×C61—41no—
321D4×C61—84no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
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—84no—
338C2×C4×C61C2×C22⋊C412yes—
339C2×C4×C61C23×C411yescharacteristic
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C2×#4111yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344C2×C4×C61H(5,𝔽2)11yescharacteristic
345C22⋊D61—44no—
346C22⋊D61—48no—
347C22⋊D61—48no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—22no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61C2×C22⋊C412yes—
364C2×Dic61C2×C22⋊C412yes—
365C2×Dic61C2×C22⋊C412yes—
366D244—22no—
367D244—22no—
368D244—22no—
369D244C4×D414yes—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—22no—
373C4×D61—22no—
374C4×D61—48no—
375C4×D61—84no—
376Dic122—22no—
377Dic122—22no—
378Dic122—41no—
379Dic122—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
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×C61—42no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—81no—
396C22×C61—81no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61C22×C22⋊C411yescharacteristic
400C22×C61D4211yescharacteristic
401C22×C61#54611yescharacteristic
402C22×C61#57511yescharacteristic
403C22×C61#57511yescharacteristic
404C22×C61#57611yescharacteristic
405C22×C61#57711yescharacteristic
406C2×D61—22no—
407C2×D61—24no—
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—41no—
413C2×D61—42no—
414C2×D61—41no—
415C2×D61—42no—
416C2×D61—41no—
417C2×D61—42no—
418C2×D61—41no—
419C2×D61—42no—
420C2×D61—816no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61—81no—
425C4×C61C2×C4×D411yescharacteristic
426C4×C61#51811yescharacteristic
427C4×C61D4211yescharacteristic
428C4×C61#54611yescharacteristic
429Dic61—22no—
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#1983—611no—
441#1958—611no—
442#1895—611no—
443#1894—611no—
444#1874D6111yescharacteristic, complemented
445#1873—611no—
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—42no—
451C2×C61—82no—
452C2×C61D4×C22⋊C411yescharacteristic
453C2×C61#289611yescharacteristic
454C2×C61#289711yescharacteristic
455C2×C61#327311yescharacteristic
456C2×C61#327511yescharacteristic
457C2×C61#332211yescharacteristic
458C2×C61#332311yescharacteristic
459D61—42no—
460D61—44no—
461C22×#41—611no—
462C23×D4—611no—
463C22×M16—611no—
464C22×M16—611no—
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8—611no—
470C2×#121—1221no—
471C2×#121C2×D6111yescharacteristic
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4C2×D6111yescharacteristic, complemented
477C22×C22⋊C4—1221no—
478#436—1224no—
479C2×C4⋊C8—611no—
480#418—1224no—
481#417—1224no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—611no—
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⋊C8C2×D6111yescharacteristic, complemented
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380—611no—
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×Q8—611no—
518C22×D4—21no—
519C22×D4—611no—
520C22×D4—614no—
521C22×D4—611no—
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—21no—
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
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—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—614no—
549C22⋊Q8—1222no—
550#121—22no—
551#121—1228no—
552#121C4×D6114yes—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—1221no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
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—1222no—
586#103—1222no—
587#103—2441no—
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—22no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—21no—
606C24—611no—
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—612no—
621C2×Q8—1221no—
622C2×Q8—1221no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—614no—
635C2×D4—612no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—1224no—
639C2×D4—1228no—
640C2×D4—1224no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—2444no—
645C2×D4—2444no—
646C2×D4—2444no—
647C2×D4—2441no—
648C2×D4—2441no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4C2×C4×D6112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—611no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—612no—
668C22×C4—612no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1224no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—4881no—
679C22×C4—4881no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
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—21no—
704C4⋊C4—42no—
705C4⋊C4—614no—
706C4⋊C4—1224no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4C2×C4×D6112yes—
712C4⋊C4D4×D6112yes—
713C22⋊C4—24no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—4881no—
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—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—612no—
741C23—1222no—
742C23—1221no—
743C23—1221no—
744C23—1221no—
745C23—1221no—
746C23—1221no—
747C23—1222no—
748C23—1221no—
749C23—1222no—
750C23—4884no—
751C23—4884no—
752C23—4884no—
753C23—4884no—
754C23—4884no—
755C23—2448no—
756C23—2448no—
757C23—2441no—
758C23—2441no—
759C23—2441no—
760C23—2441no—
761C23C22⋊C4×D6112yes—
762C23C2×D4×D6111yescharacteristic
763Q8—1222no—
764Q8—1222no—
765Q8—2441no—
766Q8—2441no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—84no—
772D4—614no—
773D4—1222no—
774D4—1222no—
775D4—1222no—
776D4—2444no—
777D4—2448no—
778D4—2448no—
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—84no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—612no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1221no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—4884no—
810C2×C4—2448no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4—2441no—
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—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—1222no—
845C22—1222no—
846C22—1224no—
847C22—1222no—
848C22—48816no—
849C22—2442no—
850C22—2441no—
851C22—2442no—
852C22—2441no—
853C22—2442no—
854C22—2441no—
855C22—2442no—
856C22—2441no—
857C22—2442no—
858C22—2442no—
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039411yescharacteristic
861C22#1684040411yescharacteristic
862C22#1684055811yescharacteristic
863C22#1684056111yescharacteristic
864C22#1684056311yescharacteristic
865C22#1684056811yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—1222no—
871C4—1222no—
872C4—1222no—
873C4—4881no—
874C4—4881no—
875C4—2442no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4#1684039611yescharacteristic
879C4#1684040111yescharacteristic
880C2—42no—
881C2—82no—
882C2—2442no—
883C2—2444no—
884C2#2144863711yescharacteristic
885C2#2145433511yescharacteristic
886C2#2145434011yescharacteristic
887C2#2145743011yescharacteristic
888C2#2145745311yescharacteristic
889C2#2145802311yescharacteristic
890C2#2145803811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840409C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#22427
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16839837C2semidirect
3. C2×#16839761C2semidirect
4. C2×#16839765C2semidirect
5. #21448744C2semidirect
6. #21446750C2semidirect
7. #21446629C2semidirect
8. #21446258C2semidirect
9. #21446251C2semidirect
10. #21446130C2semidirect
11. #21445828C2semidirect
12. #21445760C2semidirect
13. #21445748C2semidirect
14. #21445633C2semidirect
15. C61×#1874C2semidirect
18. C22×#11758194C22semidirect
21. #16840409C4semidirect
32. C2×#14519706C22semidirect
35. C2×#14519702C22semidirect
36. C2×#14519702C22semidirect
37. C2×#14519700C22semidirect
38. C2×#14519700C22semidirect
46. C2×C8×Dic61C22semidirect
50. #16839627C22semidirect
51. #16839622C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C22×C4⋊C4×C61C22semidirect
61. C2×C22⋊C8×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
81. C2×D4×D61C2×C4semidirect
94. #14519764C2×C4semidirect
97. #14519757C2×C4semidirect
101. #14519739C2×C4semidirect
133. #14519697D4semidirect
444. #1874D61semidirect
476. C22×C4⋊C4C2×D61semidirect
495. C2×C22⋊C8C2×D61semidirect
507. #340C2×D61semidirect
508. #340C2×D61semidirect
509. C61#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404092
C2×#168398372
C2×#168397612
C2×#168397652
#214487442
#214467502
#214466292
#214462582
#214462512
#214461302
#214458282
#214457602
#214457482
#214456332
C61×#18742
#2242761