Finite Group Databasebeta

← #29586816

Subgroups — #29586816

Order 15616.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11758190C211yesmaximal, characteristic
2C22×#14519700C211yesmaximal, characteristic, complemented
3C22×#14519697C211yesmaximal, characteristic
4C2×#16839667C211yesmaximal, characteristic, complemented
5C2×#16839663C211yesmaximal, characteristic
6C2×#16839516C211yesmaximal, characteristic, complemented
7C2×C61×#340C211yesmaximal, characteristic, complemented
8C23×Dic122C2211yescharacteristic
9C23×D244C2211yescharacteristic
10C22×#11758190—22no—
11C22×#11758190—22no—
12C22×#11758190—22no—
13C22×#11758190—22no—
14C22×#11758190—22no—
15C22×#11758190—22no—
16C22×#11758190C414yescomplemented
17C23×#92418C2211yescharacteristic
18C22×#11758198—22no—
19C22×C4×Dic61C2211yescharacteristic
20C2×#14519700—22no—
21C2×#14519700—22no—
22C2×#14519700—22no—
23C2×#14519697—22no—
24C2×#14519697—22no—
25C2×#14519697—22no—
26#16839667—22no—
27#16839667—22no—
28#16839663—22no—
29#16839663—22no—
30C2×#14519684—22no—
31#16839516—22no—
32C23×C8×C61C2211yescharacteristic
33C22×C4⋊C4×C61C2211yescharacteristic
34C22×C4⋊C4×C61C2211yescharacteristic
35C61×#340—22no—
36C24×D61—21no—
37C22×Dic122—21no—
38C22×Dic122—21no—
39C22×Dic122—21no—
40C22×Dic122—21no—
41C22×Dic122—21no—
42C22×Dic122—21no—
43C22×Dic122—21no—
44C22×Dic122—21no—
45C22×Dic122—21no—
46C22×Dic122—21no—
47C22×Dic122—21no—
48C22×Dic122C2×C412yes—
49C22×Dic122D412yes—
50C22×Dic122D412yes—
51C22×D244—21no—
52C22×D244—21no—
53C22×D244—21no—
54C22×D244—21no—
55C22×D244—21no—
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244C2×C412yes—
63C22×D244D412yes—
64C22×D244D412yes—
65C23×Dic61—21no—
66C23×Dic61D412yes—
67C2×#11758190—28no—
68C2×#11758190—28no—
69C2×#11758190—28no—
70C2×#11758190—28no—
71C2×#11758190—28no—
72C2×#11758190—28no—
73C2×#11758190—28no—
74C22×#92418—21no—
75C22×#92418—21no—
76C22×#92418—21no—
77C22×#92418—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80C22×#92418D412yes—
81C2×#11758198—28no—
82C2×#11758198—44no—
83C2×#11758198—44no—
84C2×C4×Dic61—21no—
85C2×C4×Dic61—21no—
86C2×C4×Dic61—21no—
87C2×C4×Dic61—21no—
88C2×C4×Dic61—21no—
89C2×C4×Dic61—21no—
90#14519700—28no—
91#14519697—28no—
92#14519684—28no—
93C23×C4×C61—21no—
94C23×C4×C61—21no—
95C23×C4×C61C2311yescharacteristic
96C22×C8×C61—21no—
97C22×C8×C61—21no—
98C22×C8×C61—21no—
99C22×C8×C61—21no—
100C22×C8×C61C2×C412yes—
101C22×C8×C61D412yes—
102C22×C8×C61D412yes—
103C2×C4⋊C4×C61—21no—
104C2×C4⋊C4×C61—21no—
105C2×C4⋊C4×C61—21no—
106C2×C4⋊C4×C61—21no—
107C2×C4⋊C4×C61—21no—
108C2×C4⋊C4×C61—21no—
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61—21no—
111C2×C4⋊C4×C61—21no—
112C2×C4⋊C4×C61—21no—
113C2×C4⋊C4×C61D412yes—
114C2×C4⋊C4×C61D412yes—
115C24×C61C2×D411yescharacteristic
116C23×D61—22no—
117C23×D61—22no—
118C23×D61—22no—
119C23×D61—41no—
120C23×D61—41no—
121C23×D61—41no—
122C23×D61—41no—
123C23×D61—42no—
124C23×D61—42no—
125C23×D61—42no—
126C23×D61—42no—
127C22×C4×C61—22no—
128C22×C4×C61—22no—
129C22×C4×C61—41no—
130C22×C4×C61—41no—
131C22×C4×C61—41no—
132C22×C4×C61—41no—
133C22×C4×C61—42no—
134C22×C4×C61—42no—
135C22×C4×C61—42no—
136C22×C4×C61—42no—
137C22×C4×C61C22×C411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61#4111yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—22no—
159C22×Dic61—22no—
160C22×Dic61—41no—
161C22×Dic61—41no—
162C22×Dic61—41no—
163C22×Dic61—41no—
164C22×Dic61SD1614yescomplemented
165C2×D244—22no—
166C2×D244—22no—
167C2×D244—22no—
168C2×D244—22no—
169C2×D244—22no—
170C2×D244—22no—
171C2×D244—22no—
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—22no—
177C2×D244—22no—
178C2×D244—22no—
179C2×D244—22no—
180C2×D244—41no—
181C2×D244—41no—
182C2×D244—41no—
183C2×D244—41no—
184C2×D244—41no—
185C2×D244—41no—
186C2×D244—41no—
187C2×D244—41no—
188C2×D244—41no—
189C2×D244—41no—
190C2×D244—41no—
191C2×D244—41no—
192C2×D244C22⋊C414yes—
193C2×Dic122—22no—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122—22no—
199C2×Dic122—22no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—22no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—22no—
208C2×Dic122—41no—
209C2×Dic122—41no—
210C2×Dic122—41no—
211C2×Dic122—41no—
212C2×Dic122—41no—
213C2×Dic122—41no—
214C2×Dic122—41no—
215C2×Dic122—41no—
216C2×Dic122—41no—
217C2×Dic122—41no—
218C2×Dic122—41no—
219C2×Dic122—41no—
220C2×Dic122C22⋊C414yescomplemented
221C2×C8×C61—22no—
222C2×C8×C61—22no—
223C2×C8×C61—22no—
224C2×C8×C61—22no—
225C2×C8×C61—22no—
226C2×C8×C61—22no—
227C2×C8×C61C22⋊C414yescomplemented
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—22no—
232C4⋊C4×C61—41no—
233C4⋊C4×C61—41no—
234C4⋊C4×C61—41no—
235C4⋊C4×C61—41no—
236#11758198—416no—
237C4×Dic61—41no—
238C4×Dic61—41no—
239C4×Dic61—41no—
240C4×Dic61—41no—
241C2×#92418—22no—
242C2×#92418—22no—
243C2×#92418—22no—
244C2×#92418—41no—
245C2×#92418—41no—
246C2×#92418—41no—
247C2×#92418—41no—
248#11758190—232no—
249C23×C61C4×D411yescharacteristic
250C23×C61#12011yescharacteristic
251C23×C61#12011yescharacteristic
252C23×C61#12111yescharacteristic
253C23×C61#12111yescharacteristic
254C23×C61#12111yescharacteristic
255C23×C61#12711yescharacteristic
256C23×C61C2×SD1612yes—
257C23×C61#13512yes—
258C23×C61AGL(1,ℤ/8)12yes—
259C23×C61#13712yes—
260C22×D61—24no—
261C22×D61—42no—
262C22×D61—42no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—44no—
268C22×D61—44no—
269C22×D61—44no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—82no—
274C22×D61—82no—
275C22×D61—82no—
276C22×D61—82no—
277C22×D61—82no—
278C22×D61—82no—
279C22×D61—81no—
280C22×D61—81no—
281C22×D61—81no—
282C22×D61—81no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—44no—
286C2×C4×C61—44no—
287C2×C4×C61—82no—
288C2×C4×C61—82no—
289C2×C4×C61—81no—
290C2×C4×C61—81no—
291C2×C4×C61—81no—
292C2×C4×C61—81no—
293C2×C4×C61C2×C22⋊C411yescharacteristic
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61#12011yescharacteristic
300C2×C4×C61#12011yescharacteristic
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61#12311yescharacteristic
317C2×C4×C61#12311yescharacteristic
318C2×C4×C61#12411yescharacteristic
319C2×C4×C61#12411yescharacteristic
320C2×C4×C61#12711yescharacteristic
321C2×Dic61—24no—
322C2×Dic61—24no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—42no—
328C2×Dic61—42no—
329C2×Dic61—42no—
330C2×Dic61—42no—
331C2×Dic61—42no—
332C2×Dic61—42no—
333C2×Dic61—42no—
334C2×Dic61—42no—
335D244—24no—
336D244—24no—
337D244—42no—
338D244—42no—
339D244—42no—
340D244—42no—
341D244—42no—
342D244—42no—
343Dic122—24no—
344Dic122—24no—
345Dic122—42no—
346Dic122—42no—
347Dic122—42no—
348Dic122—42no—
349Dic122—42no—
350Dic122—42no—
351C8×C61—24no—
352#92418—42no—
353#11023—611nomaximal, Sylow
354C22×C61#38611yescharacteristic
355C22×C61#38611yescharacteristic
356C22×C61#39011yescharacteristic
357C22×C61#39211yescharacteristic
358C22×C61#39211yescharacteristic
359C22×C61#39211yescharacteristic
360C22×C61#39411yescharacteristic
361C22×C61C4×SD1612yes—
362C22×C61#44012yes—
363C22×C61#44812yes—
364C22×C61#44912yes—
365C22×C61#45012yes—
366C22×C61#45212yes—
367C22×C61#46012yes—
368C22×C61#46112yes—
369C22×C61#46312yes—
370C22×C61#46412yes—
371C22×C61#46512yes—
372C22×C61#46812yes—
373C22×C61#49211yescharacteristic
374C22×C61#49511yescharacteristic
375C22×C61#49611yescharacteristic
376C22×C61#49711yescharacteristic
377C2×D61—48no—
378C2×D61—44no—
379C2×D61—84no—
380C2×D61—84no—
381C2×D61—82no—
382C2×D61—82no—
383C2×D61—84no—
384C2×D61—82no—
385C2×D61—82no—
386C2×D61—82no—
387C2×D61—82no—
388C4×C61—82no—
389C4×C61—82no—
390C4×C61#37911yescharacteristic
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#39011yescharacteristic
394C4×C61#39211yescharacteristic
395C4×C61#39411yescharacteristic
396C4×C61#39411yescharacteristic
397C4×C61#39411yescharacteristic
398Dic61—44no—
399Dic61—44no—
400C23×SD16—611no—
401C22×#103—611no—
402C22×#102—611no—
403C2×#391—611no—
404C2×#390—611no—
405C2×#340D6111yescharacteristic, complemented
406C2×#336—611no—
407C2×C61#143811yescharacteristic
408C2×C61#187712yes—
409C2×C61#188012yes—
410C2×C61#196811yescharacteristic
411C2×C61#197311yescharacteristic
412C2×C61#200012yes—
413C2×C61#201211yescharacteristic
414C2×C61#201311yescharacteristic
415C2×C61#201411yescharacteristic
416C2×C61#201511yescharacteristic
417C2×C61#205512yes—
418D61—84no—
419C23×Q8—611no—
420C23×D4—611no—
421C22×SD16—614no—
422C22×SD16—1222no—
423C22×SD16—1222no—
424C22×SD16—1222no—
425C22×SD16—1222no—
426C22×SD16—1222no—
427C22×SD16—1222no—
428C23×C8—611no—
429C23×C8C2×D6111yescharacteristic
430C22×C4⋊C4C2×D6111yescharacteristic
431C22×C4⋊C4C2×D6111yescharacteristic
432C22×C22⋊C4—1222no—
433C22×C42—611no—
434C2×#103—1222no—
435C2×#103—1222no—
436C2×#103—1222no—
437C2×#102—1222no—
438C2×#102—1222no—
439C2×#102—1222no—
440#391—1222no—
441#391—1222no—
442#390—1222no—
443#390—1222no—
444C2×#95—1222no—
445#340—22no—
446#336—1222no—
447C61#1102311yescharacteristic, complemented, Sylow
448C25—1221no—
449C22×Q8—612no—
450C22×Q8—612no—
451C22×Q8—612no—
452C22×Q8—1221no—
453C22×Q8—1221no—
454C22×Q8—1221no—
455C22×Q8—1221no—
456C22×Q8—1221no—
457C22×Q8—1221no—
458C22×Q8—1221no—
459C22×Q8—1221no—
460C22×Q8—1221no—
461C22×Q8—1221no—
462C22×Q8—1221no—
463C22×D4—612no—
464C22×D4—612no—
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—612no—
480C23×C4—1221no—
481C23×C4C22×D6111yescharacteristic
482C2×SD16—1228no—
483C2×SD16—1228no—
484C2×SD16—1228no—
485C2×SD16—1228no—
486C2×SD16—1228no—
487C2×SD16—1228no—
488C2×SD16—1228no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—612no—
494C22×C8—1221no—
495C22×C8—1221no—
496C22×C8—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499C22×C8—1221no—
500C22×C8C4×D6112yes—
501C22×C8D24412yes—
502C22×C8C22⋊D6112yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D24412yes—
514C2×C4⋊C4D24412yes—
515C2×C22⋊C4—1228no—
516C2×C22⋊C4—2444no—
517C2×C22⋊C4—2444no—
518C2×C42—1221no—
519C2×C42—1221no—
520C2×C42—1221no—
521C2×C42—1221no—
522C2×C42—1221no—
523C2×C42—1221no—
524#103—1228no—
525#102—1228no—
526#95—1228no—
527C24—1222no—
528C24—1222no—
529C24—1222no—
530C24—2442no—
531C24—2441no—
532C24—2441no—
533C24—2441no—
534C24—2441no—
535C24—2442no—
536C24—2442no—
537C24—2442no—
538C24D4×D6111yescharacteristic
539C2×Q8—614no—
540C2×Q8—1222no—
541C2×Q8—1222no—
542C2×Q8—1222no—
543C2×Q8—1222no—
544C2×Q8—1222no—
545C2×Q8—1222no—
546C2×Q8—1222no—
547C2×Q8—1222no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×Q8—1222no—
551C2×Q8—1222no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×Q8—1222no—
555C2×Q8—2441no—
556C2×Q8—2441no—
557C2×Q8—2441no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×Q8—2441no—
561C2×Q8—2441no—
562C2×Q8—2441no—
563C2×Q8—2441no—
564C2×Q8—2441no—
565C2×Q8—2441no—
566C2×Q8—2441no—
567C2×D4—614no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1222no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—2441no—
584C2×D4—2441no—
585C2×D4—2441no—
586C2×D4—2441no—
587C2×D4—2441no—
588C2×D4—2441no—
589C2×D4—2441no—
590C2×D4—2441no—
591C2×D4—2441no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—614no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—2441no—
616C22×C4—2441no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4C2×C4×D6111yescharacteristic
620C22×C4C2×D24411yescharacteristic
621C22×C4C2×D24411yescharacteristic
622C22×C4C2×D24411yescharacteristic
623C22×C4#1175822211yescharacteristic
624C22×C4#1175822211yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4#1175822611yescharacteristic
631C22×C4#1175822611yescharacteristic
632C22×C4C2×C22⋊D6111yescharacteristic
633SD16—12232no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—1222no—
641C2×C8—1222no—
642C2×C8—1222no—
643C2×C8—2441no—
644C2×C8—2441no—
645C2×C8—2441no—
646C2×C8—2441no—
647C2×C8#1175819814yescomplemented
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C22⋊C4—24416no—
657C42—2441no—
658C42—2441no—
659C42—2441no—
660C42—2441no—
661C23—1224no—
662C23—4882no—
663C23—4882no—
664C23—4882no—
665C23—4882no—
666C23—4881no—
667C23—4881no—
668C23—4881no—
669C23—4881no—
670C23—4882no—
671C23—4882no—
672C23—2442no—
673C23—2444no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2442no—
678C23—2444no—
679C23—2442no—
680C23—2442no—
681C23—2442no—
682C23—2444no—
683C23—2442no—
684C23#1451973911yescharacteristic
685C23#1451974711yescharacteristic
686C23#1451974711yescharacteristic
687C23#1451975011yescharacteristic
688C23#1451975011yescharacteristic
689C23#1451975211yescharacteristic
690C23#1451977311yescharacteristic
691C23SD16×D6112yes—
692C23#1451979812yes—
693C23#1451980112yes—
694C23#1451980912yes—
695Q8—1224no—
696Q8—1224no—
697Q8—2442no—
698Q8—2442no—
699Q8—2442no—
700Q8—2442no—
701Q8—2442no—
702Q8—2442no—
703D4—1224no—
704D4—1224no—
705D4—2442no—
706D4—2442no—
707D4—2442no—
708D4—2442no—
709D4—2442no—
710D4—2442no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—82no—
716C2×C4—82no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—1224no—
722C2×C4—1224no—
723C2×C4—1224no—
724C2×C4—1224no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4—2442no—
730C2×C4—2442no—
731C2×C4—2442no—
732C2×C4—2442no—
733C2×C4—2442no—
734C2×C4—2442no—
735C2×C4C22⋊C4×D6111yescharacteristic
736C2×C4C22⋊C4×D6111yescharacteristic
737C2×C4C2×#1175819811yescharacteristic
738C2×C4#1451973911yescharacteristic
739C2×C4C4×D24411yescharacteristic
740C2×C4C4×D24411yescharacteristic
741C2×C4#1451974511yescharacteristic
742C2×C4#1451974511yescharacteristic
743C2×C4#1451974711yescharacteristic
744C2×C4#1451974711yescharacteristic
745C2×C4#1451974711yescharacteristic
746C2×C4#1451974711yescharacteristic
747C2×C4#1451975011yescharacteristic
748C2×C4#1451975011yescharacteristic
749C2×C4#1451975111yescharacteristic
750C2×C4#1451975111yescharacteristic
751C2×C4#1451975211yescharacteristic
752C2×C4#1451975211yescharacteristic
753C2×C4#1451975211yescharacteristic
754C2×C4#1451975211yescharacteristic
755C2×C4#1451975211yescharacteristic
756C2×C4#1451976211yescharacteristic
757C2×C4#1451976211yescharacteristic
758C2×C4#1451976211yescharacteristic
759C2×C4#1451976211yescharacteristic
760C2×C4#1451976511yescharacteristic
761C2×C4#1451976611yescharacteristic
762C2×C4#1451977411yescharacteristic
763C8—24no—
764C8—2442no—
765C22—4882no—
766C22—4882no—
767C22—4884no—
768C22—4882no—
769C22—4884no—
770C22—4884no—
771C22—4882no—
772C22—4882no—
773C22—4882no—
774C22—2448no—
775C22—2444no—
776C22#1683964011yescharacteristic
777C22#1683964011yescharacteristic
778C22#1683966311yescharacteristic
779C22#1683967111yescharacteristic
780C22#1683967111yescharacteristic
781C22#1683967211yescharacteristic
782C22#1683968011yescharacteristic
783C22#1683984912yes—
784C22#1683986112yes—
785C22#1683990212yes—
786C22#1683990812yes—
787C22#1683991412yes—
788C22#1683992712yes—
789C22#1683996112yes—
790C22#1683996612yes—
791C22#1683997612yes—
792C22#1683998712yes—
793C22#1683999212yes—
794C22#1684000912yes—
795C22#1684013311yescharacteristic
796C22#1684014311yescharacteristic
797C22#1684015011yescharacteristic
798C22#1684015511yescharacteristic
799C4—82no—
800C4—82no—
801C4—2444no—
802C4—2444no—
803C4#1683961711yescharacteristic
804C4#1683964011yescharacteristic
805C4#1683964011yescharacteristic
806C4#1683966411yescharacteristic
807C4#1683967211yescharacteristic
808C4#1683967911yescharacteristic
809C4#1683967911yescharacteristic
810C4#1683968011yescharacteristic
811C2—4884no—
812C2#2144405911yescharacteristic
813C2#2144615412yes—
814C2#2144617512yes—
815C2#2144667111yescharacteristic
816C2#2144669811yescharacteristic
817C2#2144682512yes—
818C2#2144689811yescharacteristic
819C2#2144690311yescharacteristic
820C2#2144690811yescharacteristic
821C2#2144691411yescharacteristic
822C2#2144713812yes—
subgroupG/H
centerC24D4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#340C2
socleC24×C61C2×D4
prime radicalC23×D244C22
cosocleC23×C4×C61C23
hypercenterC2×#340D61
hypocenterC61#11023
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14519700C2semidirect
4. C2×#16839667C2semidirect
6. C2×#16839516C2semidirect
7. C2×C61×#340C2semidirect
16. C22×#11758190C4semidirect
164. C22×Dic61SD16semidirect
220. C2×Dic122C22⋊C4semidirect
227. C2×C8×C61C22⋊C4semidirect
405. C2×#340D61semidirect
447. C61#11023semidirect
647. C2×C8#11758198semidirect

Maximal subgroups

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

subgroupindex
C23×#117581902
C22×#145197002
C22×#145196972
C2×#168396672
C2×#168396632
C2×#168395162
C2×C61×#3402
#1102361