Finite Group Databasebeta

← #29586743

Subgroups — #29586743

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C2×#16839768C211yesmaximal, characteristic, complemented
3C2×#16839736C211yesmaximal, characteristic, complemented
4#21448399C211yesmaximal, characteristic, complemented
5C2×#16839534C211yesmaximal, characteristic, complemented
6C2×#16839518C211yesmaximal, characteristic, complemented
7C2×C61×#421C211yesmaximal, characteristic, complemented
8C23×D244C2211yescharacteristic
9C2×#14519802—22no—
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802—22no—
15C22×#11758201C412yescomplemented
16C22×#11758199C412yescomplemented
17C22×#11758194C2211yescharacteristic
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20#16839768—22no—
21#16839768—22no—
22C2×#14519699—22no—
23#16839736—22no—
24#16839736—22no—
25C2×#14519692—22no—
26#16839664—22no—
27#16839663—22no—
28#16839617—22no—
29#16839534—22no—
30#16839518—22no—
31C22×#41×C61C2211yescharacteristic
32C22×M16×C61C2211yescharacteristic
33C2×#117×C61C2211yescharacteristic
34C61×#421—22no—
35C61×#421—22no—
36C2×#104×C61—22no—
37C24×D61—21no—
38C22×D244—21no—
39C22×D244—21no—
40C22×D244—21no—
41C22×D244—21no—
42C22×D244—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244C2×C412yes—
50C22×D244D412yes—
51C22×D244D412yes—
52#14519802—28no—
53#14519802—28no—
54#14519802—28no—
55#14519802—28no—
56C2×#11758201—24no—
57C2×#11758201—24no—
58C2×#11758201—24no—
59C2×#11758199—24no—
60C2×#11758199—24no—
61C2×#11758199—24no—
62C2×#11758194—21no—
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194D412yes—
67C2×#11758194D412yes—
68C22×#92418C2×C412yes—
69#14519736—21no—
70#14519736—21no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75#14519736—21no—
76#14519736D412yes—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C22⋊Dic61—21no—
80C2×C22⋊Dic61D412yes—
81C2×#11758198—28no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84#14519699—28no—
85#14519692—28no—
86C2×#41×C61—21no—
87C2×#41×C61—21no—
88C2×#41×C61—21no—
89C2×#41×C61—21no—
90C2×#41×C61—21no—
91C2×#41×C61—21no—
92C2×#41×C61—21no—
93C2×#41×C61—21no—
94C2×#41×C61—21no—
95C2×#41×C61—21no—
96C2×#41×C61D412yes—
97C2×#41×C61D412yes—
98C22×Q8×C61C2×C411yescharacteristic
99C22×D4×C61—21no—
100C22×D4×C61C2×C411yescharacteristic
101C23×C4×C61—21no—
102C23×C4×C61C2311yescharacteristic
103C2×M16×C61—21no—
104C2×M16×C61—21no—
105C2×M16×C61—21no—
106C2×M16×C61—21no—
107C2×M16×C61—21no—
108C2×M16×C61D412yes—
109C22×C8×C61—21no—
110#117×C61—21no—
111#117×C61—21no—
112#117×C61—21no—
113#117×C61—21no—
114C2×C4⋊C4×C61—21no—
115C2×C22⋊C4×C61—21no—
116C2×C42×C61D412yes—
117#104×C61—28no—
118C24×C61—21no—
119C24×C61C2×D411yescharacteristic
120C23×D61—22no—
121C23×D61—22no—
122C23×D61—22no—
123C23×D61—41no—
124C23×D61—41no—
125C23×D61—41no—
126C23×D61—41no—
127C23×D61—84no—
128#41×C61—22no—
129#41×C61—22no—
130#41×C61—22no—
131#41×C61—22no—
132#41×C61—22no—
133#41×C61—22no—
134#41×C61—22no—
135#41×C61—22no—
136#41×C61—41no—
137#41×C61—41no—
138#41×C61—41no—
139#41×C61—41no—
140#41×C61—41no—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C22⋊C412yescomplemented
150C2×D4×C61—22no—
151C2×D4×C61—22no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—21no—
157C2×D4×C61—41no—
158C2×D4×C61—41no—
159C2×D4×C61—41no—
160C2×D4×C61—41no—
161C2×D4×C61C22⋊C412yescomplemented
162C22×C4×C61—21no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D411yescharacteristic
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61C2×D411yescharacteristic
178C22×C4×C61C2×D411yescharacteristic
179C22×C4×C61C2×D411yescharacteristic
180C22×C4×C61#4111yescharacteristic
181C22×C4×C61#4111yescharacteristic
182C22×C4×C61#4111yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×Dic61—22no—
185C22×Dic61—41no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—41no—
202C2×D244—41no—
203C2×D244—41no—
204C2×D244—41no—
205C2×D244—41no—
206C2×D244—41no—
207C2×D244—41no—
208C2×D244—41no—
209C2×D244—41no—
210C2×D244—41no—
211C2×D244—41no—
212C2×D244—41no—
213C2×D244C22⋊C414yes—
214M16×C61—22no—
215M16×C61—22no—
216M16×C61—41no—
217M16×C61—41no—
218C2×C8×C61—22no—
219C2×C8×C61—41no—
220C2×C8×C61—41no—
221C4⋊C4×C61—41no—
222C4⋊C4×C61—41no—
223C22⋊C4×C61—41no—
224C22⋊C4×C61—41no—
225C42×C61—22no—
226C42×C61—22no—
227C22⋊Dic61—22no—
228C22⋊Dic61—22no—
229C22⋊Dic61—22no—
230C22⋊Dic61—41no—
231#11758201—216no—
232#11758199—216no—
233#11758198—88no—
234C4⋊Dic61—22no—
235C4⋊Dic61—41no—
236C4⋊Dic61—41no—
237C4⋊Dic61—41no—
238C4×Dic61—22no—
239C4×Dic61—41no—
240C4×Dic61—41no—
241C4×Dic61—41no—
242#11758194—22no—
243#11758194—22no—
244#11758194—22no—
245#11758194—22no—
246C2×#92418—22no—
247C2×#92418—22no—
248C2×#92418C22⋊C414yescomplemented
249C23×C61—22no—
250C23×C61—42no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61—82no—
254C23×C61C4×D411yescharacteristic
255C23×C61#12011yescharacteristic
256C23×C61#12011yescharacteristic
257C23×C61#12111yescharacteristic
258C23×C61#12111yescharacteristic
259C23×C61#12111yescharacteristic
260C23×C61#12711yescharacteristic
261C22×D61—24no—
262C22×D61—48no—
263C22×D61—42no—
264C22×D61—42no—
265C22×D61—42no—
266C22×D61—42no—
267C22×D61—42no—
268C22×D61—42no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272C22×D61—84no—
273C22×D61—84no—
274C22×D61—84no—
275Q8×C61—22no—
276Q8×C61—22no—
277Q8×C61—41no—
278Q8×C61—41no—
279D4×C61—22no—
280D4×C61—22no—
281D4×C61—42no—
282D4×C61—42no—
283D4×C61—42no—
284D4×C61—42no—
285D4×C61—41no—
286D4×C61—41no—
287C2×C4×C61—22no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—42no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—44no—
295C2×C4×C61—42no—
296C2×C4×C61C2×C22⋊C411yescharacteristic
297C2×C4×C61C2×C22⋊C411yescharacteristic
298C2×C4×C61C2×C22⋊C411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12011yescharacteristic
307C2×C4×C61#12011yescharacteristic
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#12111yescharacteristic
315C2×C4×C61#12111yescharacteristic
316C2×C4×C61#12111yescharacteristic
317C2×C4×C61#12311yescharacteristic
318C2×C4×C61#12311yescharacteristic
319C2×C4×C61#12311yescharacteristic
320C2×C4×C61#12311yescharacteristic
321C2×C4×C61#12411yescharacteristic
322C2×C4×C61#12411yescharacteristic
323C2×C4×C61#12711yescharacteristic
324C2×Dic61—44no—
325C2×Dic61—42no—
326C2×Dic61—42no—
327C2×Dic61—82no—
328D244—24no—
329D244—24no—
330D244—42no—
331D244—42no—
332D244—42no—
333D244—42no—
334D244—42no—
335D244—42no—
336C8×C61—42no—
337#92418—24no—
338#11012—611nomaximal, Sylow
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—41no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—42no—
347C22×C61—82no—
348C22×C61—82no—
349C22×C61—82no—
350C22×C61#38611yescharacteristic
351C22×C61#38611yescharacteristic
352C22×C61#39011yescharacteristic
353C22×C61#39211yescharacteristic
354C22×C61#39211yescharacteristic
355C22×C61#39211yescharacteristic
356C22×C61#39411yescharacteristic
357C2×D61—48no—
358C2×D61—44no—
359C2×D61—84no—
360C2×D61—84no—
361C2×D61—84no—
362C2×D61—84no—
363C2×D61—84no—
364C2×D61—84no—
365C4×C61—42no—
366C4×C61—82no—
367C4×C61#37911yescharacteristic
368C4×C61#38611yescharacteristic
369C4×C61#38611yescharacteristic
370C4×C61#39011yescharacteristic
371C4×C61#39211yescharacteristic
372C4×C61#39411yescharacteristic
373C4×C61#39411yescharacteristic
374C4×C61#39411yescharacteristic
375Dic61—82no—
376Dic61—82no—
377C22×AGL(1,ℤ/8)—611no—
378C2×#421D6111yescharacteristic, complemented
379C2×#418—611no—
380C2×#410—611no—
381#2309—611no—
382C2×#344—611no—
383C2×H(3,ℤ/4)—611no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61—21no—
390C2×C61—82no—
391C2×C61#143811yescharacteristic
392C2×C61#190412yes—
393D61—84no—
394C22×#41C2×D6111yescharacteristic
395C23×D4—611no—
396C2×AGL(1,ℤ/8)—1222no—
397C2×AGL(1,ℤ/8)—1222no—
398C2×AGL(1,ℤ/8)—1222no—
399C2×AGL(1,ℤ/8)—1222no—
400C2×AGL(1,ℤ/8)—1222no—
401C2×AGL(1,ℤ/8)—1222no—
402C22×SD16—612no—
403C22×D8—612no—
404C22×M16—611no—
405C22×M16C2×D6111yescharacteristic
406C2×#117—611no—
407C2×#117—611no—
408C2×#117C2×D6111yescharacteristic
409#421—22no—
410#421—22no—
411C2×#104—22no—
412#418—1222no—
413#418—1222no—
414C2×#102—1222no—
415#410—1222no—
416#410—1222no—
417C2×#99—1222no—
418#390—1222no—
419#390—1222no—
420#379—1222no—
421#344—1222no—
422H(3,ℤ/4)—1222no—
423C61#1101211yescharacteristic, complemented, Sylow
424C25—1221no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41D24412yes—
436C2×#41C22⋊D6112yes—
437C22×Q8C4×D6111yescharacteristic
438C22×D4—21no—
439C22×D4—612no—
440C22×D4—612no—
441C22×D4—612no—
442C22×D4—1221no—
443C22×D4—1221no—
444C22×D4—1221no—
445C22×D4—1221no—
446C22×D4—1221no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4—1221no—
450C22×D4—1221no—
451C22×D4—1221no—
452C22×D4—1221no—
453C22×D4C4×D6111yescharacteristic
454C23×C4—21no—
455C23×C4C22×D6111yescharacteristic
456AGL(1,ℤ/8)—1228no—
457AGL(1,ℤ/8)—1228no—
458AGL(1,ℤ/8)—1228no—
459AGL(1,ℤ/8)—1228no—
460C2×SD16—1224no—
461C2×SD16—1224no—
462C2×SD16—1224no—
463C2×D8—1224no—
464C2×D8—1224no—
465C2×D8—1224no—
466C2×M16—21no—
467C2×M16—21no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—612no—
472C2×M16—612no—
473C2×M16—1221no—
474C2×M16—1221no—
475C2×M16—1221no—
476C2×M16—1221no—
477C2×M16C22⋊D6112yes—
478C22×C8—21no—
479C22×C8—612no—
480#117—21no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—612no—
485#117—1221no—
486#117—1221no—
487#117—1221no—
488#117—1221no—
489#117—1221no—
490#117—1221no—
491#117—1221no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—612no—
497C2×C22⋊C4—1221no—
498C2×C22⋊C4—1228no—
499C2×C42—1221no—
500C2×C42—1221no—
501C2×C42C22⋊D6112yes—
502#104—28no—
503#102—1228no—
504#99—1228no—
505C24—21no—
506C24—1222no—
507C24—1222no—
508C24—1222no—
509C24—4884no—
510C24—2441no—
511C24—2441no—
512C24—2441no—
513C24—2441no—
514C24D4×D6111yescharacteristic
515#41—22no—
516#41—22no—
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8#1175819812yescomplemented
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—614no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—1222no—
552C2×D4—1222no—
553C2×D4—1222no—
554C2×D4—1222no—
555C2×D4—1222no—
556C2×D4—1222no—
557C2×D4—1222no—
558C2×D4—1222no—
559C2×D4—1222no—
560C2×D4—1222no—
561C2×D4—1222no—
562C2×D4—1222no—
563C2×D4—1222no—
564C2×D4—2441no—
565C2×D4—2441no—
566C2×D4—2441no—
567C2×D4—2441no—
568C2×D4—2441no—
569C2×D4—2441no—
570C2×D4—2441no—
571C2×D4—2441no—
572C2×D4—2441no—
573C2×D4—2441no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4#1175819812yescomplemented
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—1222no—
586C22×C4—2441no—
587C22×C4C2×C4×D6111yescharacteristic
588C22×C4C2×D24411yescharacteristic
589C22×C4#1175822211yescharacteristic
590C22×C4#1175822211yescharacteristic
591C22×C4D4×D6111yescharacteristic
592C22×C4D4×D6111yescharacteristic
593C22×C4D4×D6111yescharacteristic
594C22×C4D4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4#1175822411yescharacteristic
597C22×C4#1175822411yescharacteristic
598C22×C4C2×C22⋊D6111yescharacteristic
599C22×C4C2×C22⋊D6111yescharacteristic
600C22×C4C2×C22⋊D6111yescharacteristic
601SD16—12216no—
602D8—12216no—
603M16—22no—
604M16—22no—
605M16—41no—
606M16—41no—
607M16—1222no—
608M16—1222no—
609M16—1222no—
610M16—1222no—
611C2×C8—22no—
612C2×C8—41no—
613C2×C8—41no—
614C2×C8—614no—
615C2×C8—1222no—
616C2×C8—1222no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4—1222no—
620C4⋊C4—2441no—
621C4⋊C4—2441no—
622C4⋊C4—2441no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—1222no—
626C22⋊C4—1222no—
627C22⋊C4—1222no—
628C22⋊C4—4888no—
629C22⋊C4—2441no—
630C42—22no—
631C42—22no—
632C42—1222no—
633C42—2441no—
634C42—2441no—
635C42—2441no—
636C23—22no—
637C23—42no—
638C23—41no—
639C23—41no—
640C23—82no—
641C23—1224no—
642C23—4884no—
643C23—4884no—
644C23—4884no—
645C23—4884no—
646C23—4884no—
647C23—4884no—
648C23—2448no—
649C23—2442no—
650C23—2442no—
651C23—2442no—
652C23—2442no—
653C23—2442no—
654C23—2442no—
655C23#1451973711yescharacteristic
656C23#1451974511yescharacteristic
657C23#1451974711yescharacteristic
658C23#1451974911yescharacteristic
659C23#1451975011yescharacteristic
660C23#1451975011yescharacteristic
661C23#1451977311yescharacteristic
662Q8—22no—
663Q8—22no—
664Q8—41no—
665Q8—41no—
666D4—22no—
667D4—22no—
668D4—42no—
669D4—42no—
670D4—42no—
671D4—42no—
672D4—41no—
673D4—41no—
674D4—1224no—
675D4—1224no—
676D4—2442no—
677D4—2442no—
678D4—2442no—
679D4—2442no—
680D4—2442no—
681D4—2442no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—44no—
690C2×C4—42no—
691C2×C4—4882no—
692C2×C4—2444no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4C22⋊C4×D6111yescharacteristic
696C2×C4C22⋊C4×D6111yescharacteristic
697C2×C4C2×#1175819811yescharacteristic
698C2×C4#1451973711yescharacteristic
699C2×C4C4×C22⋊D6111yescharacteristic
700C2×C4C4×C22⋊D6111yescharacteristic
701C2×C4#1451974511yescharacteristic
702C2×C4#1451974511yescharacteristic
703C2×C4#1451974511yescharacteristic
704C2×C4#1451974611yescharacteristic
705C2×C4#1451974711yescharacteristic
706C2×C4#1451974711yescharacteristic
707C2×C4#1451974811yescharacteristic
708C2×C4#1451974811yescharacteristic
709C2×C4#1451974911yescharacteristic
710C2×C4#1451974911yescharacteristic
711C2×C4#1451974911yescharacteristic
712C2×C4#1451975011yescharacteristic
713C2×C4#1451975011yescharacteristic
714C2×C4#1451975111yescharacteristic
715C2×C4#1451975111yescharacteristic
716C2×C4#1451975911yescharacteristic
717C2×C4#1451975911yescharacteristic
718C2×C4#1451976011yescharacteristic
719C2×C4#1451976111yescharacteristic
720C2×C4#1451976311yescharacteristic
721C2×C4#1451976311yescharacteristic
722C2×C4#1451977311yescharacteristic
723C8—42no—
724C8—1224no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—82no—
734C22—82no—
735C22—82no—
736C22—4884no—
737C22—4884no—
738C22—4884no—
739C22—4884no—
740C22—4884no—
741C22—4884no—
742C22—2448no—
743C22—2444no—
744C22#1683963811yescharacteristic
745C22#1683963911yescharacteristic
746C22#1683966211yescharacteristic
747C22#1683967011yescharacteristic
748C22#1683967111yescharacteristic
749C22#1683967111yescharacteristic
750C22#1683967711yescharacteristic
751C4—42no—
752C4—82no—
753C4—4882no—
754C4—4882no—
755C4#1683961711yescharacteristic
756C4#1683963811yescharacteristic
757C4#1683964111yescharacteristic
758C4#1683966211yescharacteristic
759C4#1683967011yescharacteristic
760C4#1683967711yescharacteristic
761C4#1683967811yescharacteristic
762C4#1683967811yescharacteristic
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—82no—
770C2—4884no—
771C2#2144405811yescharacteristic
772C2#2144630312yes—
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#421C2
socleC22×C61#386
prime radicalC22×#14519802C2
cosocleC23×C4×C61C23
hypercenterC2×#421D61
hypocenterC61#11012
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839768C2semidirect
3. C2×#16839736C2semidirect
4. #21448399C2semidirect
5. C2×#16839534C2semidirect
6. C2×#16839518C2semidirect
7. C2×C61×#421C2semidirect
15. C22×#11758201C4semidirect
16. C22×#11758199C4semidirect
149. C2×Q8×C61C22⋊C4semidirect
161. C2×D4×C61C22⋊C4semidirect
248. C2×#92418C22⋊C4semidirect
378. C2×#421D61semidirect
423. C61#11012semidirect
536. C2×Q8#11758198semidirect
576. C2×D4#11758198semidirect

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168397682
C2×#168397362
#214483992
C2×#168395342
C2×#168395182
C2×C61×#4212
#1101261