Finite Group Databasebeta

← #29707523

Subgroups — #29707523

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839802C211yesmaximal, characteristic, complemented
3C2×#16839761C211yesmaximal, characteristic, complemented
4C2×#16839761C211yesmaximal, characteristic, complemented
5C2×#16839726C211yesmaximal, characteristic, complemented
6#21447022C212yesmaximal, complemented
7#21447015C212yesmaximal, complemented
8#21447008C212yesmaximal, complemented
9#21447001C212yesmaximal, complemented
10#21445538C211yesmaximal, characteristic, complemented
11C2×C61×#380C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C22×#11758194C2211yescharacteristic
14C22×#11758194C2211yescharacteristic
15#16840273—24no—
16#16840273—24no—
17C2×#14519760—21no—
18C2×#14519756C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519751C2211yescharacteristic
21C2×#14519751C2211yescharacteristic
22C2×#14519746—21no—
23C2×C4×C22⋊D61—21no—
24C2×C4×C22⋊D61—21no—
25C2×#14519736C2211yescharacteristic
26#16839802—24no—
27C2×#14519710C2212yescomplemented
28C2×#14519708C2212yescomplemented
29#16839761—24no—
30#16839761—24no—
31C2×#14519700C2212yescomplemented
32C2×#14519700C2212yescomplemented
33C2×#14519697C2212yescomplemented
34C2×#14519697C2212yescomplemented
35#16839726—24no—
36C2×C22⋊#92418C2212yes—
37C2×C22⋊#92418C2212yes—
38#16839524C2212yescomplemented
39#16839524C2212yescomplemented
40C24×C4×C61C2211yescharacteristic
41C22×C4⋊C4×C61C2211yescharacteristic
42C22×C4⋊C4×C61C2211yescharacteristic
43C22×C22⋊C4×C61—21no—
44C61×#380—21no—
45C61×#380—21no—
46C61×#380C2212yes—
47C61×#380C2212yes—
48C2×#95×C61—21no—
49C2×#11758222—22no—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—22no—
54C2×#11758222D414yes—
55C22×Dic122C2311yescharacteristic
56C22×D244C2311yescharacteristic
57C22×C22⋊D61—21no—
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C4×D61—21no—
61C2×#11758194—22no—
62C2×#11758194—22no—
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194D414yescomplemented
67C22×#92418C2312yes—
68C22×#92418C2312yes—
69#14519760—28no—
70#14519756—22no—
71#14519756—22no—
72#14519756—22no—
73#14519756—22no—
74#14519751—22no—
75#14519751—22no—
76#14519751—22no—
77#14519751—22no—
78#14519746—28no—
79C4×C22⋊D61—28no—
80C4×C22⋊D61—28no—
81#14519736—22no—
82#14519736D414yes—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×#11758198—21no—
91C2×#11758198—21no—
92C2×C4×Dic61—21no—
93#14519710—24no—
94#14519708—24no—
95#14519700—24no—
96#14519700—24no—
97#14519697—24no—
98#14519697—24no—
99C22⋊#92418—24no—
100C22⋊#92418—24no—
101C25×C61D411yescharacteristic
102C23×C4×C61—22no—
103C23×C4×C61—22no—
104C23×C4×C61—22no—
105C23×C4×C61—22no—
106C23×C4×C61—22no—
107C23×C4×C61—22no—
108C23×C4×C61—21no—
109C23×C4×C61—21no—
110C23×C4×C61D411yescharacteristic
111C23×C4×C61D411yescharacteristic
112C23×C4×C61D411yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C23×C4×C61C2311yescharacteristic
115C23×C4×C61C2311yescharacteristic
116C2×C4⋊C4×C61—22no—
117C2×C4⋊C4×C61—22no—
118C2×C4⋊C4×C61—22no—
119C2×C4⋊C4×C61—22no—
120C2×C4⋊C4×C61—21no—
121C2×C4⋊C4×C61—21no—
122C2×C4⋊C4×C61C2312yes—
123C2×C4⋊C4×C61C2312yes—
124C2×C22⋊C4×C61—22no—
125C2×C22⋊C4×C61—22no—
126C2×C22⋊C4×C61—44no—
127#95×C61—22no—
128#95×C61—22no—
129C24×C61—22no—
130C24×C61—22no—
131C24×C61—22no—
132C24×C61—22no—
133C24×C61—22no—
134C24×C61—41no—
135C24×C61—41no—
136C24×C61C2×D411yescharacteristic
137C24×C61C2×D411yescharacteristic
138C24×C61C2×D411yescharacteristic
139C23×D61—21no—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61—22no—
143C22×C4×C61—22no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—44no—
164C22×C4×C61—44no—
165C22×C4×C61—44no—
166C22×C4×C61—44no—
167C22×C4×C61—42no—
168C22×C4×C61—42no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—42no—
172C22×C4×C61—42no—
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D412yes—
177C22×C4×C61C2×D412yes—
178C22×C4×C61C2×D412yes—
179C22×C4×C61#4112yes—
180C22×C4×C61#4112yes—
181C22×C4×C61#4112yes—
182C22×C4×C61C2411yescharacteristic
183C2×C22⋊D61—24no—
184C2×C22⋊D61—24no—
185C2×C22⋊D61—24no—
186C2×C22⋊D61—42no—
187C2×C22⋊D61—42no—
188C2×C22⋊D61—42no—
189C2×C22⋊D61—42no—
190C2×C22⋊D61—42no—
191C2×C22⋊D61—42no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195#11758222—28no—
196#11758222—28no—
197#11758222—44no—
198#11758222—44no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244—21no—
204C2×D244C2×D412yes—
205C2×C4×D61—24no—
206C2×C4×D61—42no—
207C2×C4×D61—42no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122C2×D412yes—
214C4⋊C4×C61—22no—
215C4⋊C4×C61—22no—
216C4⋊C4×C61—22no—
217C4⋊C4×C61—22no—
218C4⋊C4×C61—42no—
219C4⋊C4×C61—42no—
220C22⋊C4×C61—44no—
221C22⋊C4×C61—44no—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224C22⋊Dic61—24no—
225#11758198—24no—
226#11758198—24no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61C2×D412yes—
230C4⋊Dic61C2×D412yes—
231#11758196—24no—
232#11758196—24no—
233C4×Dic61—24no—
234#11758194—28no—
235#11758194—44no—
236C2×#92418—22no—
237C2×#92418—22no—
238C2×#92418—22no—
239C2×#92418—22no—
240C2×#92418—22no—
241C2×#92418C2×D414yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—28no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—44no—
260C23×C61—44no—
261C23×C61—44no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61#12012yes—
266C23×C61#12112yes—
267C23×C61#12312yes—
268C23×C61AGL(1,ℤ/8)12yes—
269C23×C61#13712yes—
270C23×C61C22×D411yescharacteristic
271C22×D61—22no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61—41no—
277C22×D61—41no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—44no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—41no—
291C2×C4×C61—41no—
292C2×C4×C61—41no—
293C2×C4×C61—44no—
294C2×C4×C61—44no—
295C2×C4×C61—42no—
296C2×C4×C61—42no—
297C2×C4×C61—42no—
298C2×C4×C61—42no—
299C2×C4×C61—42no—
300C2×C4×C61—42no—
301C2×C4×C61—84no—
302C2×C4×C61—84no—
303C2×C4×C61#12012yes—
304C2×C4×C61#12114yes—
305C2×C4×C61#12114yes—
306C2×C4×C61#12112yes—
307C2×C4×C61#12314yes—
308C2×C4×C61#12312yes—
309C2×C4×C61#12414yes—
310C2×C4×C61C22×D411yescharacteristic
311C2×C4×C61C22×D411yescharacteristic
312C2×C4×C61C22×D411yescharacteristic
313C2×C4×C61C2×#4111yescharacteristic
314C2×C4×C61C2×#4111yescharacteristic
315C2×C4×C61C2×#4111yescharacteristic
316C22⋊D61—48no—
317C22⋊D61—48no—
318C22⋊D61—48no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328D244—22no—
329D244—22no—
330D244—41no—
331D244—41no—
332C4×D61—48no—
333Dic122—22no—
334Dic122—22no—
335Dic122—41no—
336Dic122—41no—
337#92418—24no—
338#92418—42no—
339#23482—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—416no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61#39414yes—
362C22×C61C2×#12011yescharacteristic
363C22×C61C2×#12111yescharacteristic
364C22×C61C2×#12311yescharacteristic
365C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
366C22×C61C2×#13711yescharacteristic
367C22×C61#57511yescharacteristic
368C22×C61#57511yescharacteristic
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—81no—
373C2×D61—81no—
374C2×D61—81no—
375C2×D61—81no—
376C4×C61—41no—
377C4×C61—41no—
378C4×C61—82no—
379C4×C61—82no—
380C4×C61#39414yes—
381C4×C61C2×#12111yescharacteristic
382C4×C61C2×#12111yescharacteristic
383C4×C61C2×#12311yescharacteristic
384C4×C61C2×#12411yescharacteristic
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C2×#525—611no—
389C2×#428—611no—
390C2×#417—611no—
391C2×#417—611no—
392C2×#407—611no—
393C2×#380D6111yescharacteristic, complemented
394#2036—612no—
395#2035—612no—
396#2034—612no—
397#2033—612no—
398#1736—611no—
399C2×C61—24no—
400C2×C61—42no—
401C2×C61—42no—
402C2×C61C2×#39411yescharacteristic
403C2×C61#300611yescharacteristic
404C2×C61#300711yescharacteristic
405C2×C61#305511yescharacteristic
406C2×C61#305611yescharacteristic
407C2×C61#309211yescharacteristic
408C2×C61#309311yescharacteristic
409D61—82no—
410C22×#41—611no—
411C24×C4C2×D6111yescharacteristic
412C22×M16—611no—
413C22×M16—611no—
414#525—1224no—
415#525—1224no—
416C2×#123—1221no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—1221no—
422C2×C4×D4—1221no—
423C2×C4×D4—1221no—
424C2×#117—611no—
425C22×C4⋊C4C2×D6111yescharacteristic
426C22×C4⋊C4C2×D6111yescharacteristic
427C22×C22⋊C4—21no—
428#428—1224no—
429C2×#107—612no—
430C2×#106—612no—
431#417—1224no—
432#417—1224no—
433C2×#103—612no—
434C2×#103—612no—
435C2×#102—612no—
436C2×#102—612no—
437#407—1224no—
438C2×C22⋊C8—612no—
439C2×C22⋊C8—612no—
440#380—21no—
441#380—21no—
442#380C2×D6112yes—
443#380C2×D6112yes—
444C2×#95—21no—
445#340—612no—
446#340—612no—
447C61#2348211yescharacteristic, complemented, Sylow
448C25C22⋊D6111yescharacteristic
449C2×#41—614no—
450C2×#41—1222no—
451C2×#41—1222no—
452C2×#41—1222no—
453C2×#41—1222no—
454C2×#41—1222no—
455C22×Q8—611no—
456C22×D4—611no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4—1221no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—21no—
467C23×C4—21no—
468C23×C4—1221no—
469C23×C4C22⋊D6111yescharacteristic
470C23×C4C22⋊D6111yescharacteristic
471C23×C4C22⋊D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C2×M16—614no—
476C2×M16—1222no—
477C2×M16—1222no—
478C2×M16—1222no—
479C2×M16—1222no—
480C2×M16—1222no—
481C22×C8—612no—
482C22×C8—612no—
483#123—1228no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492#120—1228no—
493C4×D4—1228no—
494C4×D4—1228no—
495#117—614no—
496#117—1222no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1221no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4C22×D6112yes—
508C2×C4⋊C4C22×D6112yes—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—44no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1221no—
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C42—1221no—
518#107—1224no—
519#106—1224no—
520#103—1224no—
521#103—1224no—
522#102—1224no—
523#102—1224no—
524C22⋊C8—1224no—
525C22⋊C8—1224no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—41no—
534C24—41no—
535C24—1221no—
536C24C2×C22⋊D6111yescharacteristic
537C24C2×C22⋊D6111yescharacteristic
538C24C2×C22⋊D6111yescharacteristic
539#41—1228no—
540#41—1228no—
541#41—2444no—
542#41—2444no—
543C2×Q8—612no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×D4—612no—
550C2×D4—1224no—
551C2×D4—1224no—
552C2×D4—1224no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4—1221no—
556C2×D4—1221no—
557C2×D4—1221no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4—2442no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1224no—
601C22×C4—2442no—
602C22×C4—2442no—
603C22×C4#1175822212yes—
604C22×C4#1175822212yes—
605C22×C4D4×D6112yes—
606C22×C4D4×D6112yes—
607C22×C4D4×D6112yes—
608C22×C4#1175822412yes—
609C22×C4C2×C22⋊D6111yescharacteristic
610C22×C4C2×C22⋊D6111yescharacteristic
611C22×C4C2×C22⋊D6111yescharacteristic
612C22×C4C23×D6111yescharacteristic
613M16—1228no—
614M16—2444no—
615C2×C8—614no—
616C2×C8—1222no—
617C2×C8—1222no—
618C2×C8—1222no—
619C2×C8—1222no—
620C2×C8—1222no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—612no—
628C4⋊C4—612no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1221no—
632C4⋊C4—1221no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—1224no—
639C22⋊C4—1224no—
640C42—1224no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—1222no—
665C23—2441no—
666C23—2441no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23#1451974512yes—
672C23#1451974912yes—
673C23#1451976012yes—
674C23#1451980312yes—
675C23#1451980812yes—
676C23C22×C22⋊D6111yescharacteristic
677Q8—1222no—
678Q8—1222no—
679Q8—2441no—
680Q8—2441no—
681D4—1222no—
682D4—1222no—
683D4—2448no—
684D4—2448no—
685D4—2448no—
686D4—2441no—
687D4—2441no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—84no—
712C2×C4—84no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2448no—
723C2×C4#1451974512yes—
724C2×C4#1451974912yes—
725C2×C4#1451975014yes—
726C2×C4#1451975014yes—
727C2×C4#1451975914yes—
728C2×C4#1451976012yes—
729C2×C4#1451976314yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C2×D4×D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822211yescharacteristic
735C2×C4C2×#1175822211yescharacteristic
736C8—1224no—
737C8—2442no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—4881no—
760C22—4881no—
761C22—4881no—
762C22—4881no—
763C22—2442no—
764C22—2442no—
765C22—2442no—
766C22#1683967714yes—
767C22C2×#1451974511yescharacteristic
768C22C2×#1451974911yescharacteristic
769C22C2×#1451976011yescharacteristic
770C22C2×#1451980311yescharacteristic
771C22C2×#1451980811yescharacteristic
772C22#1684056011yescharacteristic
773C22#1684056011yescharacteristic
774C4—41no—
775C4—41no—
776C4—82no—
777C4—82no—
778C4—2442no—
779C4—2442no—
780C4—2442no—
781C4#1683967714yes—
782C4C2×#1451975011yescharacteristic
783C4C2×#1451975011yescharacteristic
784C4C2×#1451975911yescharacteristic
785C4C2×#1451976311yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—4882no—
790C2C2×#1683967711yescharacteristic
791C2#2145506911yescharacteristic
792C2#2145507711yescharacteristic
793C2#2145543411yescharacteristic
794C2#2145544511yescharacteristic
795C2#2145574211yescharacteristic
796C2#2145575011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#380C2
socleC23×C61C22×D4
prime radicalC2×#16840273C2
hypercenterC2×#380D61
hypocenterC61#23482
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#16839802C2semidirect
3. C2×#16839761C2semidirect
4. C2×#16839761C2semidirect
5. C2×#16839726C2semidirect
6. #21447022C2semidirect
7. #21447015C2semidirect
8. #21447008C2semidirect
9. #21447001C2semidirect
10. #21445538C2semidirect
11. C2×C61×#380C2semidirect
27. C2×#14519710C22semidirect
28. C2×#14519708C22semidirect
31. C2×#14519700C22semidirect
32. C2×#14519700C22semidirect
33. C2×#14519697C22semidirect
34. C2×#14519697C22semidirect
38. #16839524C22semidirect
39. #16839524C22semidirect
66. C2×#11758194D4semidirect
393. C2×#380D61semidirect
447. C61#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168398022
C2×#168397612
C2×#168397262
#214470222
#214470152
#214470082
#214470012
#214455382
C2×C61×#3802
#2348261