Finite Group Databasebeta

← #29586776

Subgroups — #29586776

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic
2C22×#14519705C211yesmaximal, characteristic
3C2×#16839770C211yesmaximal, characteristic, complemented
4#21448407C211yesmaximal, characteristic
5C2×#16839668C211yesmaximal, characteristic, complemented
6C2×#16839530C211yesmaximal, characteristic, complemented
7C2×C61×#339C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9C23×Dic122C2211yescharacteristic
10C2×#14519810—22no—
11C2×#14519810—22no—
12C2×#14519810—22no—
13C2×#14519810—22no—
14C2×#14519810—22no—
15C2×#14519810C414yescomplemented
16C22×Dic244—21no—
17C22×#11758190—21no—
18C22×#11758194C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C2×#14519705—22no—
21C2×#14519705—22no—
22C2×#14519705—22no—
23#16839770—22no—
24#16839770—22no—
25C2×#14519700—22no—
26#16839668—22no—
27#16839668—22no—
28#16839668—21no—
29#16839664—21no—
30#16839639—22no—
31#16839619—22no—
32C2×#14519684—22no—
33#16839530—22no—
34C22×M16×C61C2211yescharacteristic
35C2×#117×C61C2211yescharacteristic
36C22×C42×C61C2211yescharacteristic
37C61×#339—22no—
38C2×#11758222—21no—
39C2×#11758222—21no—
40C2×#11758222—21no—
41C2×#11758222—21no—
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222C2×C412yes—
49C2×#11758222D412yes—
50C22×Dic122—21no—
51C22×Dic122—21no—
52C22×Dic122—21no—
53C22×Dic122—21no—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122C2×C412yes—
62C22×Dic122D411yescharacteristic
63C22×Dic122D412yes—
64C22×Dic122D412yes—
65C22×D244D411yescharacteristic
66C22×C22⋊D61—21no—
67C23×Dic61—21no—
68C23×Dic61D412yes—
69C22×C4×D61—21no—
70#14519810—28no—
71#14519810—28no—
72#14519810—28no—
73#14519810—28no—
74C2×Dic244—24no—
75C2×Dic244—24no—
76C2×Dic244—24no—
77C2×#11758190—24no—
78C2×#11758190—24no—
79C2×#11758190—24no—
80C2×#11758194—21no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194D412yes—
86C22×#92418—21no—
87C2×C4⋊Dic61—21no—
88C2×C4⋊Dic61—21no—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C4⋊Dic61—21no—
93C2×#11758198—24no—
94#14519705—28no—
95#14519700—28no—
96#14519684—28no—
97#14519684—24no—
98C23×C4×C61—21no—
99C23×C4×C61C2311yescharacteristic
100C2×M16×C61—21no—
101C2×M16×C61—21no—
102C2×M16×C61—21no—
103C2×M16×C61C2×C412yes—
104C2×M16×C61D412yes—
105C2×M16×C61D412yes—
106C22×C8×C61—21no—
107#117×C61—21no—
108#117×C61—21no—
109#117×C61—21no—
110#117×C61—21no—
111C2×C4⋊C4×C61D412yes—
112C2×C22⋊C4×C61—21no—
113C2×C42×C61—21no—
114C2×C42×C61—21no—
115C2×C42×C61—21no—
116C2×C42×C61—21no—
117C2×C42×C61—21no—
118C2×C42×C61—21no—
119C2×C42×C61D412yes—
120C24×C61C2×D411yescharacteristic
121C23×D61—21no—
122C22×C4×C61—24no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—42no—
126C22×C4×C61—41no—
127C22×C4×C61—41no—
128C22×C4×C61C22×C411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61C2×D411yescharacteristic
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61#4111yescharacteristic
139C22×C4×C61#4111yescharacteristic
140C22×C4×C61#4111yescharacteristic
141C22×C4×C61#4111yescharacteristic
142C2×C22⋊D61—22no—
143C2×C22⋊D61—22no—
144C2×C22⋊D61—41no—
145C2×C22⋊D61—41no—
146C2×C22⋊D61—41no—
147C2×C22⋊D61—41no—
148C22×Dic61—22no—
149C22×Dic61—21no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61—22no—
155C22×Dic61—41no—
156C22×Dic61—41no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C22×Dic61—44no—
160#11758222—22no—
161#11758222—22no—
162#11758222—22no—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—41no—
169#11758222—41no—
170#11758222—41no—
171#11758222—41no—
172#11758222—41no—
173#11758222—41no—
174#11758222—41no—
175#11758222—41no—
176C2×D244—21no—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244C22⋊C412yes—
182C2×C4×D61—22no—
183C2×C4×D61—22no—
184C2×C4×D61—41no—
185C2×C4×D61—41no—
186C2×C4×D61—41no—
187C2×C4×D61—41no—
188C2×Dic122—22no—
189C2×Dic122—22no—
190C2×Dic122—22no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—22no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—21no—
198C2×Dic122—21no—
199C2×Dic122—22no—
200C2×Dic122—22no—
201C2×Dic122—21no—
202C2×Dic122—21no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—21no—
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⋊C412yes—
221C2×Dic122C22⋊C414yescomplemented
222M16×C61—22no—
223M16×C61—22no—
224M16×C61—22no—
225M16×C61C22⋊C414yescomplemented
226C2×C8×C61—22no—
227C2×C8×C61—22no—
228C2×C8×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C22⋊C4×C61—41no—
232C22⋊C4×C61—41no—
233C42×C61—22no—
234C42×C61—22no—
235C42×C61—41no—
236C42×C61—41no—
237C42×C61—41no—
238C42×C61—41no—
239#11758198—84no—
240C4⋊Dic61—41no—
241C4⋊Dic61—41no—
242C4⋊Dic61—41no—
243C4⋊Dic61—41no—
244#11758194—22no—
245#11758194—22no—
246#11758194—41no—
247#11758194—41no—
248C2×#92418—22no—
249C2×#92418—41no—
250C2×#92418—41no—
251Dic244—216no—
252#11758190—216no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61C4×D411yescharacteristic
256C23×C61#12011yescharacteristic
257C23×C61#12011yescharacteristic
258C23×C61#12111yescharacteristic
259C23×C61#12111yescharacteristic
260C23×C61#12111yescharacteristic
261C23×C61#12711yescharacteristic
262C22×D61—22no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—42no—
266C22×D61—42no—
267C2×C4×C61—24no—
268C2×C4×C61—44no—
269C2×C4×C61—42no—
270C2×C4×C61—44no—
271C2×C4×C61—42no—
272C2×C4×C61—42no—
273C2×C4×C61—42no—
274C2×C4×C61—42no—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C4×D411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C4×D411yescharacteristic
281C2×C4×C61#12011yescharacteristic
282C2×C4×C61#12011yescharacteristic
283C2×C4×C61#12011yescharacteristic
284C2×C4×C61#12011yescharacteristic
285C2×C4×C61#12011yescharacteristic
286C2×C4×C61#12011yescharacteristic
287C2×C4×C61#12111yescharacteristic
288C2×C4×C61#12111yescharacteristic
289C2×C4×C61#12111yescharacteristic
290C2×C4×C61#12111yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12111yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61#12311yescharacteristic
298C2×C4×C61#12311yescharacteristic
299C2×C4×C61#12311yescharacteristic
300C2×C4×C61#12411yescharacteristic
301C2×C4×C61#12411yescharacteristic
302C2×C4×C61#12711yescharacteristic
303C22⋊D61—42no—
304C22⋊D61—42no—
305C22⋊D61—42no—
306C22⋊D61—42no—
307C2×Dic61—24no—
308C2×Dic61—22no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61—42no—
317C2×Dic61—44no—
318C2×Dic61—42no—
319C2×Dic61—44no—
320C2×Dic61—82no—
321D244—22no—
322D244—22no—
323D244—41no—
324D244—41no—
325C4×D61—42no—
326C4×D61—42no—
327C4×D61—42no—
328C4×D61—42no—
329Dic122—24no—
330Dic122—22no—
331Dic122—24no—
332Dic122—22no—
333Dic122—42no—
334Dic122—42no—
335Dic122—42no—
336Dic122—42no—
337Dic122—42no—
338Dic122—42no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—24no—
342#92418—42no—
343#11017—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—21no—
347C22×C61—21no—
348C22×C61—21no—
349C22×C61—21no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61#38611yescharacteristic
353C22×C61#38611yescharacteristic
354C22×C61#39011yescharacteristic
355C22×C61#39211yescharacteristic
356C22×C61#39211yescharacteristic
357C22×C61#39211yescharacteristic
358C22×C61#39411yescharacteristic
359C22×C61#45512yes—
360C22×C61#45612yes—
361C2×D61—44no—
362C2×D61—42no—
363C2×D61—81no—
364C2×D61—81no—
365C2×D61—82no—
366C4×C61—44no—
367C4×C61—82no—
368C4×C61#37911yescharacteristic
369C4×C61#38611yescharacteristic
370C4×C61#38611yescharacteristic
371C4×C61#39011yescharacteristic
372C4×C61#39211yescharacteristic
373C4×C61#39411yescharacteristic
374C4×C61#39411yescharacteristic
375C4×C61#39411yescharacteristic
376Dic61—44no—
377Dic61—42no—
378Dic61—82no—
379C22×#137—611no—
380C22×#104—611no—
381C2×#419—611no—
382#2311—611no—
383C2×#391—611no—
384C2×#343—611no—
385C2×#339D6111yescharacteristic, complemented
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61#143811yescharacteristic
391C2×C61#188212yes—
392C2×C61#200411yescharacteristic
393C2×C61#200511yescharacteristic
394C2×C61#200712yes—
395D61—82no—
396C22×#41—611no—
397C23×Q8—611no—
398C2×#137—614no—
399C2×#137—1222no—
400C2×#137—1222no—
401C2×#137—1222no—
402C2×#137—1222no—
403C2×#137—1222no—
404C22×Q16—1221no—
405C22×SD16—1221no—
406C22×M16—611no—
407C22×M16C2×D6111yescharacteristic
408C2×#117C2×D6111yescharacteristic
409C22×C4⋊C4—611no—
410C22×C42C2×D6111yescharacteristic
411C2×#104—1222no—
412C2×#104—1222no—
413C2×#104—1222no—
414#419—1222no—
415#419—1222no—
416C2×#103—1222no—
417#391—1221no—
418#391—1222no—
419#391—1222no—
420#390—1221no—
421#386—1222no—
422#380—1222no—
423C2×#95—1222no—
424#343—1222no—
425#339—22no—
426C61#1101711yescharacteristic, complemented, Sylow
427C2×#41—612no—
428C2×#41—612no—
429C2×#41—1221no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C2×#41—1221no—
439C22×Q8—612no—
440C22×Q8—611no—
441C22×Q8—612no—
442C22×Q8—612no—
443C22×Q8—1221no—
444C22×Q8—1221no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8—1221no—
449C22×Q8—1221no—
450C22×Q8—1221no—
451C22×Q8—1221no—
452C22×Q8—1221no—
453C22×Q8—1221no—
454C22×D4—611no—
455C22×D4—1221no—
456C23×C4—21no—
457C23×C4—612no—
458C23×C4—1221no—
459C23×C4—1221no—
460C23×C4C22×D6111yescharacteristic
461#137—1228no—
462#137—1228no—
463#137—1228no—
464#137—1228no—
465C2×Q16—1224no—
466C2×Q16—1224no—
467C2×Q16—1224no—
468C2×SD16—1224no—
469C2×SD16—1224no—
470C2×SD16—1224no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—612no—
475C2×M16—1221no—
476C2×M16—1221no—
477C2×M16—1221no—
478C2×M16—1221no—
479C2×M16—1221no—
480C2×M16C4×D6112yes—
481C2×M16D24412yes—
482C2×M16C22⋊D6112yes—
483C22×C8—21no—
484C22×C8—1221no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—21no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4—1221no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4D24412yes—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—1224no—
498C2×C42—21no—
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—21no—
502C2×C42—21no—
503C2×C42—21no—
504C2×C42D24412yes—
505#104—1228no—
506#103—1228no—
507#95—1228no—
508#95—1224no—
509C24—1221no—
510C24D4×D6111yescharacteristic
511#41—1222no—
512#41—1222no—
513#41—1222no—
514#41—1222no—
515#41—1222no—
516#41—1222no—
517#41—1222no—
518#41—1222no—
519#41—2441no—
520#41—2441no—
521#41—2441no—
522#41—2441no—
523#41—2441no—
524#41—2441no—
525#41—2441no—
526#41—2441no—
527C2×Q8—612no—
528C2×Q8—614no—
529C2×Q8—1222no—
530C2×Q8—1222no—
531C2×Q8—1222no—
532C2×Q8—1221no—
533C2×Q8—1222no—
534C2×Q8—1222no—
535C2×Q8—1222no—
536C2×Q8—1222no—
537C2×Q8—1222no—
538C2×Q8—1221no—
539C2×Q8—1222no—
540C2×Q8—1222no—
541C2×Q8—1222no—
542C2×Q8—1221no—
543C2×Q8—1222no—
544C2×Q8—1222no—
545C2×Q8—1221no—
546C2×Q8—1222no—
547C2×Q8—1221no—
548C2×Q8—1222no—
549C2×Q8—2441no—
550C2×Q8—2441no—
551C2×Q8—2441no—
552C2×Q8—2441no—
553C2×Q8—2441no—
554C2×Q8—2441no—
555C2×Q8—2441no—
556C2×Q8—2441no—
557C2×Q8—2441no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×Q8—2441no—
561C2×D4—612no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—1221no—
565C2×D4—1221no—
566C2×D4—1221no—
567C2×D4—1221no—
568C2×D4—1221no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—42no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1221no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—2444no—
589C22×C4—2441no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4—2441no—
596C22×C4—2441no—
597C22×C4C2×C4×D6111yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4C2×D24411yescharacteristic
600C22×C4C2×D24411yescharacteristic
601C22×C4#1175822211yescharacteristic
602C22×C4#1175822211yescharacteristic
603C22×C4D4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4D4×D6111yescharacteristic
608C22×C4#1175822611yescharacteristic
609C22×C4#1175822611yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611Q16—12216no—
612SD16—12216no—
613M16—22no—
614M16—22no—
615M16—22no—
616M16—1222no—
617M16—1222no—
618M16—2441no—
619M16—2441no—
620M16#1175819814yescomplemented
621C2×C8—22no—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—1222no—
625C2×C8—2441no—
626C2×C8—2441no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—2441no—
630C4⋊C4—2441no—
631C4⋊C4—2441no—
632C4⋊C4—2441no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C22⋊C4—4884no—
636C42—22no—
637C42—22no—
638C42—41no—
639C42—41no—
640C42—41no—
641C42—41no—
642C23—22no—
643C23—22no—
644C23—1222no—
645C23—2442no—
646C23—2442no—
647C23—2441no—
648C23—2441no—
649C23#1451973911yescharacteristic
650C23#1451974711yescharacteristic
651C23#1451974711yescharacteristic
652C23#1451975011yescharacteristic
653C23#1451975011yescharacteristic
654C23#1451975211yescharacteristic
655C23#1451977311yescharacteristic
656Q8—1224no—
657Q8—1222no—
658Q8—1224no—
659Q8—1222no—
660Q8—2442no—
661Q8—2441no—
662Q8—2442no—
663Q8—2442no—
664Q8—2442no—
665Q8—2442no—
666Q8—2442no—
667Q8—2441no—
668D4—1222no—
669D4—1222no—
670D4—2442no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674D4—2441no—
675D4—2441no—
676C2×C4—24no—
677C2×C4—44no—
678C2×C4—42no—
679C2×C4—44no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—4882no—
687C2×C4—2444no—
688C2×C4—2444no—
689C2×C4—2442no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2441no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2441no—
697C2×C4—2442no—
698C2×C4—2442no—
699C2×C4—2442no—
700C2×C4—2442no—
701C2×C4—2442no—
702C2×C4C22⋊C4×D6111yescharacteristic
703C2×C4C22⋊C4×D6111yescharacteristic
704C2×C4C2×#1175819811yescharacteristic
705C2×C4#1451973911yescharacteristic
706C2×C4C4×D24411yescharacteristic
707C2×C4C4×D24411yescharacteristic
708C2×C4#1451974511yescharacteristic
709C2×C4#1451974511yescharacteristic
710C2×C4#1451974711yescharacteristic
711C2×C4#1451974711yescharacteristic
712C2×C4#1451974711yescharacteristic
713C2×C4#1451974711yescharacteristic
714C2×C4#1451975011yescharacteristic
715C2×C4#1451975011yescharacteristic
716C2×C4#1451975111yescharacteristic
717C2×C4#1451975111yescharacteristic
718C2×C4#1451975211yescharacteristic
719C2×C4#1451975211yescharacteristic
720C2×C4#1451975211yescharacteristic
721C2×C4#1451975211yescharacteristic
722C2×C4#1451975211yescharacteristic
723C2×C4#1451976211yescharacteristic
724C2×C4#1451976211yescharacteristic
725C2×C4#1451976211yescharacteristic
726C2×C4#1451976211yescharacteristic
727C2×C4#1451976511yescharacteristic
728C2×C4#1451976611yescharacteristic
729C2×C4#1451977411yescharacteristic
730C8—24no—
731C8—2442no—
732C22—22no—
733C22—22no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—22no—
740C22—4881no—
741C22—4881no—
742C22—4882no—
743C22—2444no—
744C22—2442no—
745C22#1683964011yescharacteristic
746C22#1683964011yescharacteristic
747C22#1683966311yescharacteristic
748C22#1683967111yescharacteristic
749C22#1683967111yescharacteristic
750C22#1683967211yescharacteristic
751C22#1683968011yescharacteristic
752C22#1683994112yes—
753C22#1683994612yes—
754C4—44no—
755C4—82no—
756C4—4882no—
757C4—2442no—
758C4—2444no—
759C4#1683961711yescharacteristic
760C4#1683964011yescharacteristic
761C4#1683964011yescharacteristic
762C4#1683966411yescharacteristic
763C4#1683967211yescharacteristic
764C4#1683967911yescharacteristic
765C4#1683967911yescharacteristic
766C4#1683968011yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—4882no—
772C2#2144405911yescharacteristic
773C2#2144618912yes—
774C2#2144685111yescharacteristic
775C2#2144685811yescharacteristic
776C2#2144686712yes—
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#339C2
socleC23×C61#120
prime radicalC22×#11758222C22
cosocleC23×C4×C61C23
hypercenterC2×#339D61
hypocenterC61#11017
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
3. C2×#16839770C2semidirect
5. C2×#16839668C2semidirect
6. C2×#16839530C2semidirect
7. C2×C61×#339C2semidirect
15. C2×#14519810C4semidirect
221. C2×Dic122C22⋊C4semidirect
225. M16×C61C22⋊C4semidirect
385. C2×#339D61semidirect
426. C61#11017semidirect
620. M16#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198102
C22×#145197052
C2×#168397702
#214484072
C2×#168396682
C2×#168395302
C2×C61×#3392
#1101761