Finite Group Databasebeta

← #29707491

Subgroups — #29707491

Order 15616.

1610 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840272C211yesmaximal, characteristic
2C2×#16839797C211yesmaximal, characteristic, complemented
3C2×#16839755C211yesmaximal, characteristic, complemented
4C2×#16839755C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×D61C211yesmaximal, characteristic, complemented
6#21448201C211yesmaximal, characteristic, complemented
7#21447025C211yesmaximal, characteristic, complemented
8#21447022C211yesmaximal, characteristic, complemented
9#21447017C211yesmaximal, characteristic, complemented
10#21447016C211yesmaximal, characteristic, complemented
11#21447007C211yesmaximal, characteristic, complemented
12#21446999C211yesmaximal, characteristic, complemented
13#21446998C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#2034C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C23×C4×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840272—24no—
21#16840272—24no—
22C2×#14519759—21no—
23C2×#14519757C2211yescharacteristic
24C2×#14519756C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519745—21no—
27C2×D4×Dic61—21no—
28C2×#14519737—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519735C2211yescharacteristic
31C2×#14519735C2211yescharacteristic
32#16839797—24no—
33C2×#14519710C2211yescharacteristic, complemented
34C2×#14519710C2211yescharacteristic, complemented
35C2×#14519709C2211yescharacteristic, complemented
36#16839755—24no—
37#16839755—24no—
38C2×#14519702C2211yescharacteristic, complemented
39C2×#14519702C2211yescharacteristic, complemented
40C2×#14519700C2211yescharacteristic, complemented
41C2×#14519700C2211yescharacteristic, complemented
42C2×#14519698C2211yescharacteristic, complemented
43C2×#14519698C2211yescharacteristic, complemented
44C2×C22⋊#92418C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519689C2211yescharacteristic
47C22⋊C8×D61—24no—
48#16839624—21no—
49#16839622C2211yescharacteristic
50#16839619C2211yescharacteristic
51#16839619C2211yescharacteristic
52#16839617—21no—
53C22⋊C4×Dic61—21no—
54#16839609—21no—
55#16839525C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#106×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×C22⋊C8×C61C2211yescharacteristic
63C61×#380C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C24×D61D411yescharacteristic
66C2×#11758224—22no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224D414yes—
72C22×Dic122C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C23×Dic61—21no—
76C23×Dic61D411yescharacteristic
77C22×C4×D61—22no—
78C22×C4×D61—22no—
79C22×C4×D61—22no—
80C22×C4×D61—22no—
81C22×C4×D61—22no—
82C22×C4×D61—22no—
83C22×C4×D61D411yescharacteristic
84C22×C4×D61D411yescharacteristic
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88C22×#92418C2311yescharacteristic
89C2×C8×D61—22no—
90C2×C8×D61—22no—
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—22no—
94C2×C8×D61D414yescomplemented
95#14519759—28no—
96#14519757—22no—
97#14519757—22no—
98#14519756—22no—
99#14519756—22no—
100#14519748—22no—
101#14519748—22no—
102#14519745—28no—
103D4×Dic61—28no—
104#14519737—28no—
105#14519735—22no—
106#14519735—22no—
107#14519735—22no—
108#14519735—22no—
109#14519735—22no—
110#14519735D414yes—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C2×C22⋊Dic61—21no—
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C2×C4×Dic61—21no—
128#14519710—22no—
129#14519710—22no—
130#14519709—22no—
131#14519702—22no—
132#14519702—22no—
133#14519700—22no—
134#14519700—22no—
135#14519698—22no—
136#14519698—22no—
137C22⋊#92418—22no—
138#14519689—22no—
139#14519689—22no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61—21no—
144C22×D4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148#121×C61—22no—
149#121×C61—22no—
150C2×C4⋊C4×C61C2311yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C22⋊C4×C61—21no—
154C2×C22⋊C4×C61—21no—
155#106×C61—22no—
156#102×C61—22no—
157#102×C61—22no—
158C22⋊C8×C61—22no—
159#95×C61—21no—
160C24×C61—21no—
161C24×C61C2×D411yescharacteristic
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—41no—
168C23×D61—41no—
169C23×D61C2×D411yescharacteristic
170C23×D61C2×D411yescharacteristic
171C2×D4×C61—24no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C2×D4×C61—21no—
176C2×D4×C61—21no—
177C2×D4×C61—42no—
178C2×D4×C61—42no—
179C2×D4×C61C2×D412yes—
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—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—24no—
192C2×C22⋊D61—24no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—42no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—22no—
200C22×Dic61—24no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61—42no—
206C22×Dic61—42no—
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209#11758224—28no—
210#11758224—28no—
211#11758224—44no—
212#11758224—44no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—22no—
223C2×C4×D61—22no—
224C2×C4×D61—22no—
225C2×C4×D61—44no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61—44no—
229C2×C4×D61C2×D412yes—
230C2×C4×D61C2×D412yes—
231C2×C4×D61C2×D412yes—
232C2×C4×D61#4112yes—
233C2×C4×D61#4112yes—
234C2×C4×D61#4112yes—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—21no—
238C2×Dic122—21no—
239C2×Dic122—21no—
240C2×Dic122C2×D412yes—
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—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61C2×D412yes—
253C22⋊C4×C61—24no—
254C22⋊C4×C61—42no—
255C22⋊Dic61—24no—
256C22⋊Dic61—24no—
257C22⋊Dic61—42no—
258#11758198—24no—
259#11758198—24no—
260#11758198—42no—
261#11758198—42no—
262#11758198—42no—
263#11758198—42no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61C2×D412yes—
271#11758196—24no—
272C4×Dic61—24no—
273C4×Dic61—42no—
274C4×Dic61—42no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418C2×D412yes—
281C8×D61—28no—
282C8×D61—44no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—21no—
289C23×C61—22no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61#13512yes—
297C23×C61C22×D411yescharacteristic
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—28no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—44no—
310C22×D61—44no—
311C22×D61—44no—
312C22×D61—44no—
313C22×D61—44no—
314C22×D61—44no—
315C22×D61#12012yes—
316C22×D61#12112yes—
317C22×D61#12312yes—
318C22×D61#13512yes—
319D4×C61—22no—
320D4×C61—22no—
321D4×C61—48no—
322D4×C61—41no—
323D4×C61—41no—
324C2×C4×C61—22no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—41no—
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×C61—41no—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C22×D411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C2×#4111yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C22⋊D61—48no—
347C22⋊D61—48no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—41no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—44no—
358C2×Dic61—48no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61#12012yes—
366C2×Dic61#12112yes—
367C2×Dic61#12312yes—
368C4×D61—44no—
369C4×D61—41no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—44no—
374C4×D61#12114yes—
375C4×D61#12114yes—
376C4×D61#12314yes—
377C4×D61#12414yes—
378Dic122—22no—
379Dic122—22no—
380Dic122—41no—
381Dic122—41no—
382C8×C61—22no—
383C8×C61—41no—
384#92418—22no—
385#92418—41no—
386#23479—611nomaximal, Sylow
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—81no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61C2×#12011yescharacteristic
402C22×C61C2×#12111yescharacteristic
403C22×C61C2×#12311yescharacteristic
404C22×C61C2×#13511yescharacteristic
405C22×C61C2×#13511yescharacteristic
406C22×C61#57511yescharacteristic
407C22×C61#57511yescharacteristic
408C2×D61—22no—
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—416no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61#39414yes—
423C4×C61—41no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61—81no—
427C4×C61C2×#12111yescharacteristic
428C4×C61C2×#12111yescharacteristic
429C4×C61C2×#12311yescharacteristic
430C4×C61C2×#12411yescharacteristic
431Dic61—42no—
432Dic61—41no—
433Dic61—42no—
434Dic61—81no—
435Dic61—81no—
436Dic61#39414yes—
437C2×#525—611no—
438C2×#427—611no—
439C2×#416—611no—
440C2×#416—611no—
441C22×C22⋊C8—611no—
442#2280—611no—
443#2036—611no—
444#2036—611no—
445#2035—611no—
446#2035—611no—
447#2034—611no—
448#2034D6111yescharacteristic, complemented
449#2033—611no—
450#2033—611no—
451#1735—611no—
452C2×C61—42no—
453C2×C61—82no—
454C2×C61C2×#39411yescharacteristic
455C2×C61#300211yescharacteristic
456C2×C61#300211yescharacteristic
457C2×C61#305011yescharacteristic
458C2×C61#305411yescharacteristic
459C2×C61#309111yescharacteristic
460C2×C61#309111yescharacteristic
461D61—24no—
462D61—42no—
463C22×#41—611no—
464C24×C4—611no—
465C23×C8—611no—
466C23×C8—611no—
467#525—1224no—
468#525—1224no—
469C2×#123—1221no—
470C2×C22⋊Q8—611no—
471C2×C22⋊Q8—611no—
472C2×#121—611no—
473C2×#121C2×D6111yescharacteristic
474C2×#120—1221no—
475C2×C4×D4—1221no—
476C2×C4×D4—1221no—
477C2×#117—611no—
478C2×#117—611no—
479C2×#117—611no—
480#427—1224no—
481C2×#107—611no—
482C2×#107—611no—
483C2×#106—611no—
484C2×#106C2×D6111yescharacteristic, complemented
485#416—1224no—
486#416—1224no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102C2×D6111yescharacteristic, complemented
494C2×#102C2×D6111yescharacteristic, complemented
495C2×C22⋊C8—611no—
496C2×C22⋊C8—611no—
497C2×C22⋊C8—611no—
498C2×C22⋊C8—1224no—
499C2×C22⋊C8C2×D6111yescharacteristic
500#381—1221no—
501#380—611no—
502#380—611no—
503#380—611no—
504#380C2×D6111yescharacteristic
505#379—1221no—
506C4×C22⋊C4—1221no—
507C4×C22⋊C4—1221no—
508#340—611no—
509#340—611no—
510#340—611no—
511#340C2×D6111yescharacteristic, complemented
512C61#2347911yescharacteristic, complemented, Sylow
513C25—611no—
514C2×#41—614no—
515C2×#41—1222no—
516C2×#41—1222no—
517C2×#41—1222no—
518C2×#41—1222no—
519C2×#41—1222no—
520C22×Q8—611no—
521C22×D4—21no—
522C22×D4—1221no—
523C22×D4—1221no—
524C22×D4C22×D6111yescharacteristic
525C23×C4—611no—
526C23×C4—611no—
527C23×C4—611no—
528C23×C4—611no—
529C23×C4—611no—
530C23×C4—1222no—
531C23×C4—1222no—
532C23×C4—1222no—
533C23×C4—1222no—
534C23×C4—1222no—
535C23×C4—1222no—
536C23×C4—1221no—
537C23×C4C22×D6111yescharacteristic
538C22×C8—611no—
539C22×C8—614no—
540C22×C8—611no—
541C22×C8—1222no—
542C22×C8—1222no—
543C22×C8—1222no—
544C22×C8—1222no—
545C22×C8—1222no—
546C22×C8C22×D6111yescharacteristic
547C22×C8C22×D6111yescharacteristic
548#123—1228no—
549C22⋊Q8—1222no—
550C22⋊Q8—1222no—
551C22⋊Q8—1222no—
552C22⋊Q8—1222no—
553#121—22no—
554#121—22no—
555#121—1222no—
556#121—1222no—
557#120—1228no—
558C4×D4—1228no—
559C4×D4—1228no—
560#117—614no—
561#117—1222no—
562#117—1222no—
563#117—1222no—
564#117—1222no—
565#117—1222no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—611no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4C22×D6111yescharacteristic
572C2×C4⋊C4C22×D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C42—1221no—
586C2×C42—1221no—
587C2×C42—1221no—
588#107—1222no—
589#107—1222no—
590#106—22no—
591#106—1222no—
592#103—1222no—
593#103—1222no—
594#103—1222no—
595#103—1222no—
596#102—22no—
597#102—22no—
598#102—1222no—
599#102—1222no—
600C22⋊C8—22no—
601C22⋊C8—1222no—
602C22⋊C8—1222no—
603C22⋊C8—1222no—
604#95—21no—
605#95—1221no—
606#95—1221no—
607#95—1221no—
608C24—21no—
609C24—611no—
610C24—611no—
611C24—1222no—
612C24—1222no—
613C24—1222no—
614C24—1222no—
615C24—1222no—
616C24—2441no—
617C24—2441no—
618C24D4×D6111yescharacteristic
619#41—1228no—
620#41—1228no—
621#41—2444no—
622#41—2444no—
623C2×Q8—612no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1221no—
628C2×Q8—1221no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—1224no—
638C2×D4—1224no—
639C2×D4—2442no—
640C2×D4—2442no—
641C2×D4—2442no—
642C2×D4—2442no—
643C2×D4D4×D6112yes—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—611no—
654C22×C4—612no—
655C22×C4—612no—
656C22×C4—612no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—611no—
661C22×C4—1222no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1222no—
665C22×C4—1222no—
666C22×C4—1222no—
667C22×C4—1222no—
668C22×C4—1224no—
669C22×C4—1222no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—2444no—
682C22×C4—2444no—
683C22×C4—2444no—
684C22×C4—2444no—
685C22×C4—2442no—
686C22×C4—2442no—
687C22×C4D4×D6111yescharacteristic
688C22×C4C23×D6111yescharacteristic
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—612no—
695C2×C8—1228no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—2444no—
702C2×C8D4×D6112yes—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—612no—
709C4⋊C4—1224no—
710C4⋊C4—1224no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4—1221no—
714C4⋊C4—1221no—
715C4⋊C4—1221no—
716C4⋊C4D4×D6112yes—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—2442no—
724C22⋊C4—2442no—
725C22⋊C4—2442no—
726C22⋊C4—2442no—
727C22⋊C4—2442no—
728C42—1224no—
729C42—2442no—
730C42—2442no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—612no—
745C23—612no—
746C23—612no—
747C23—612no—
748C23—1228no—
749C23—1221no—
750C23—1221no—
751C23—1221no—
752C23—1221no—
753C23—1221no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—2444no—
760C23—2444no—
761C23—2444no—
762C23—2444no—
763C23—2444no—
764C23—2444no—
765C23#1451979812yes—
766C23C2×D4×D6111yescharacteristic
767Q8—1222no—
768Q8—1222no—
769Q8—2441no—
770Q8—2441no—
771D4—22no—
772D4—22no—
773D4—48no—
774D4—41no—
775D4—41no—
776D4—2448no—
777D4—2448no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—612no—
795C2×C4—612no—
796C2×C4—612no—
797C2×C4—614no—
798C2×C4—614no—
799C2×C4—614no—
800C2×C4—614no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1222no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—2444no—
807C2×C4—2444no—
808C2×C4—2444no—
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×C4—2441no—
819C2×C4—2441no—
820C2×C4—2441no—
821C2×C4—2441no—
822C2×C4—2441no—
823C2×C4—2441no—
824C2×C4C2×D4×D6111yescharacteristic
825C2×C4C2×D4×D6111yescharacteristic
826C2×C4C2×D4×D6111yescharacteristic
827C2×C4#41×D6111yescharacteristic
828C2×C4#41×D6111yescharacteristic
829C2×C4#41×D6111yescharacteristic
830C8—22no—
831C8—41no—
832C8—1222no—
833C8—2441no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—614no—
849C22—1222no—
850C22—1222no—
851C22—1222no—
852C22—1222no—
853C22—1222no—
854C22—1222no—
855C22—1222no—
856C22—1222no—
857C22—1222no—
858C22—24416no—
859C22—2441no—
860C22—2441no—
861C22—2441no—
862C22—2441no—
863C22#120×D6111yescharacteristic
864C22#121×D6111yescharacteristic
865C22#123×D6111yescharacteristic
866C22#135×D6111yescharacteristic
867C22C2×#1451979811yescharacteristic
868C22#1684055811yescharacteristic
869C22#1684055811yescharacteristic
870C4—41no—
871C4—42no—
872C4—81no—
873C4—81no—
874C4—614no—
875C4—4881no—
876C4—4881no—
877C4—2441no—
878C4—2442no—
879C4—2442no—
880C4#121×D6111yescharacteristic
881C4#121×D6111yescharacteristic
882C4#123×D6111yescharacteristic
883C4#124×D6111yescharacteristic
884C2—42no—
885C2—82no—
886C2—1224no—
887C2—2442no—
888C2#394×D6111yescharacteristic
889C2#2145503411yescharacteristic
890C2#2145503811yescharacteristic
891C2#2145539511yescharacteristic
892C2#2145542611yescharacteristic
893C2#2145572911yescharacteristic
894C2#2145573111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2034C2
socleC23×C61C22×D4
prime radicalC2×#16840272C2
hypercenter#2034D61
hypocenterC61#23479
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#16839797C2semidirect
3. C2×#16839755C2semidirect
4. C2×#16839755C2semidirect
5. C2×C22⋊C8×D61C2semidirect
6. #21448201C2semidirect
7. #21447025C2semidirect
8. #21447022C2semidirect
9. #21447017C2semidirect
10. #21447016C2semidirect
11. #21447007C2semidirect
12. #21446999C2semidirect
13. #21446998C2semidirect
14. #21445534C2semidirect
15. C61×#2034C2semidirect
33. C2×#14519710C22semidirect
34. C2×#14519710C22semidirect
35. C2×#14519709C22semidirect
38. C2×#14519702C22semidirect
39. C2×#14519702C22semidirect
40. C2×#14519700C22semidirect
41. C2×#14519700C22semidirect
42. C2×#14519698C22semidirect
43. C2×#14519698C22semidirect
55. #16839525C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
59. C2×#106×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
64. C61×#340C22semidirect
94. C2×C8×D61D4semidirect
448. #2034D61semidirect
484. C2×#106C2×D61semidirect
493. C2×#102C2×D61semidirect
494. C2×#102C2×D61semidirect
511. #340C2×D61semidirect
512. C61#23479semidirect

Maximal subgroups

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

subgroupindex
C2×#168402722
C2×#168397972
C2×#168397552
C2×C22⋊C8×D612
#214482012
#214470252
#214470222
#214470172
#214470162
#214470072
#214469992
#214469982
#214455342
C61×#20342
#2347961