Finite Group Databasebeta

← #29586641

Subgroups — #29586641

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840273C211yesmaximal, characteristic
2C2×#16839778C211yesmaximal, characteristic, complemented
3#21454339C211yesmaximal, characteristic, complemented
4#21448202C211yesmaximal, characteristic, complemented
5#21445530C211yesmaximal, characteristic, complemented
6C2×#16839519C211yesmaximal, characteristic, complemented
7C2×C61×#407C211yesmaximal, characteristic, complemented
8C22×#11758222C2211yescharacteristic
9#16840273—22no—
10#16840273—22no—
11#16840273—22no—
12#16840273C414yescomplemented
13C2×#14519760—21no—
14C2×#14519756—21no—
15C2×#14519751—21no—
16C2×#14519746—21no—
17C2×C4×C22⋊D61—22no—
18C2×#14519736C2211yescharacteristic
19C2×#14519736C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21#16839778—22no—
22#16839778—22no—
23C2×#14519703—22no—
24#16839772—21no—
25#16839768—21no—
26#16839764—22no—
27#16839759—22no—
28#16839625—21no—
29#16839622—22no—
30#16839618—21no—
31C4×C22⋊Dic61—22no—
32#16839523—22no—
33#16839519—22no—
34C24×C4×C61C2211yescharacteristic
35C22×M16×C61C2211yescharacteristic
36C22×M16×C61C2211yescharacteristic
37C61×#407—22no—
38C61×#407—22no—
39C2×C22⋊C8×C61—22no—
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×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222C2×C412yes—
51C2×#11758222D412yes—
52C22×Dic122D411yescharacteristic
53C22×D244D411yescharacteristic
54C22×C22⋊D61—22no—
55C22×C22⋊D61—21no—
56C22×C4×D61—21no—
57#14519760—24no—
58#14519760—24no—
59#14519756—24no—
60#14519756—24no—
61#14519751—24no—
62#14519751—24no—
63#14519746—24no—
64#14519746—24no—
65C4×C22⋊D61—28no—
66C4×C22⋊D61—28no—
67#14519736—21no—
68#14519736—21no—
69#14519736—21no—
70#14519736—21no—
71#14519736—21no—
72#14519736—21no—
73#14519736—21no—
74#14519736—21no—
75#14519736—21no—
76#14519736—21no—
77#14519736C2×C412yes—
78#14519736D412yes—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61D412yescomplemented
82C2×#11758196—22no—
83C2×C22⋊Dic61—22no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—24no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×#11758198—22no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61D412yes—
91C2×C4×Dic61D412yescomplemented
92#14519703—28no—
93#14519702—24no—
94#14519699—24no—
95#14519684—24no—
96C25×C61D411yescharacteristic
97C23×C4×C61—21no—
98C23×C4×C61—21no—
99C23×C4×C61—21no—
100C23×C4×C61—21no—
101C23×C4×C61—21no—
102C23×C4×C61—21no—
103C23×C4×C61—21no—
104C23×C4×C61—21no—
105C23×C4×C61—21no—
106C23×C4×C61—21no—
107C23×C4×C61—21no—
108C23×C4×C61—21no—
109C23×C4×C61C2×C412yes—
110C23×C4×C61D411yescharacteristic
111C23×C4×C61D412yes—
112C23×C4×C61C2311yescharacteristic
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61—21no—
120C2×M16×C61—21no—
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61D412yescomplemented
125C22×C8×C61—21no—
126C22×C8×C61D412yescomplemented
127C22⋊C8×C61—28no—
128C24×C61—21no—
129C24×C61—21no—
130C24×C61—21no—
131C24×C61—21no—
132C24×C61—21no—
133C24×C61—21no—
134C24×C61—44no—
135C24×C61C22⋊C412yes—
136C24×C61C2×D411yescharacteristic
137C23×D61—21no—
138C22×C4×C61—21no—
139C22×C4×C61—21no—
140C22×C4×C61—21no—
141C22×C4×C61—21no—
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—22no—
145C22×C4×C61—22no—
146C22×C4×C61—22no—
147C22×C4×C61—22no—
148C22×C4×C61—22no—
149C22×C4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—22no—
153C22×C4×C61—22no—
154C22×C4×C61—22no—
155C22×C4×C61—22no—
156C22×C4×C61—41no—
157C22×C4×C61—41no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C22×C4×C61—41no—
162C22×C4×C61—41no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61—41no—
169C22×C4×C61—41no—
170C22×C4×C61—41no—
171C22×C4×C61—41no—
172C22×C4×C61C22⋊C412yes—
173C22×C4×C61C22×C411yescharacteristic
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×C61C2×D411yescharacteristic
181C22×C4×C61C2×D411yescharacteristic
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61#4111yescharacteristic
184C22×C4×C61#4111yescharacteristic
185C22×C4×C61#4111yescharacteristic
186C22×C4×C61#4111yescharacteristic
187C2×C22⋊D61—28no—
188C2×C22⋊D61—22no—
189C2×C22⋊D61—22no—
190C2×C22⋊D61—48no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61—41no—
193C2×C22⋊D61—41no—
194C2×C22⋊D61—41no—
195C22×Dic61—21no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199#11758222—22no—
200#11758222—22no—
201#11758222—22no—
202#11758222—22no—
203#11758222—22no—
204#11758222—22no—
205#11758222—22no—
206#11758222—22no—
207#11758222—41no—
208#11758222—41no—
209#11758222—41no—
210#11758222—41no—
211#11758222—41no—
212#11758222—41no—
213#11758222—41no—
214#11758222—41no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244C22⋊C412yescomplemented
221C2×C4×D61—22no—
222C2×C4×D61—22no—
223C2×C4×D61—41no—
224C2×C4×D61—41no—
225C2×C4×D61—41no—
226C2×C4×D61—41no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122C22⋊C412yescomplemented
233M16×C61—22no—
234M16×C61—22no—
235M16×C61—41no—
236M16×C61—41no—
237M16×C61—41no—
238M16×C61—41no—
239M16×C61—41no—
240M16×C61—41no—
241C2×C8×C61—22no—
242C2×C8×C61—22no—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61—41no—
246C2×C8×C61—41no—
247C22⋊Dic61—28no—
248C22⋊Dic61—22no—
249C22⋊Dic61—22no—
250C22⋊Dic61—48no—
251C22⋊Dic61—41no—
252C22⋊Dic61—41no—
253C22⋊Dic61—41no—
254C22⋊Dic61—41no—
255#11758198—28no—
256C4⋊Dic61—22no—
257C4⋊Dic61—22no—
258C4⋊Dic61—22no—
259C4⋊Dic61—22no—
260C4⋊Dic61—41no—
261C4⋊Dic61—41no—
262#11758196—28no—
263C4×Dic61—22no—
264C4×Dic61—22no—
265C4×Dic61—22no—
266C4×Dic61—41no—
267C4×Dic61—41no—
268C4×Dic61C22⋊C414yescomplemented
269C23×C61—24no—
270C23×C61—24no—
271C23×C61—24no—
272C23×C61—22no—
273C23×C61—22no—
274C23×C61—22no—
275C23×C61—44no—
276C23×C61—42no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61—42no—
280C23×C61—44no—
281C23×C61—44no—
282C23×C61—44no—
283C23×C61—41no—
284C23×C61—41no—
285C23×C61—41no—
286C23×C61—41no—
287C23×C61C2×C22⋊C411yescharacteristic
288C23×C61#12011yescharacteristic
289C23×C61#12011yescharacteristic
290C23×C61#12011yescharacteristic
291C23×C61#12111yescharacteristic
292C23×C61#12111yescharacteristic
293C23×C61#12311yescharacteristic
294C22×D61—22no—
295C22×D61—44no—
296C22×D61—41no—
297C22×D61—41no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61—41no—
304C2×C4×C61—41no—
305C2×C4×C61—42no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12111yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12111yescharacteristic
332C2×C4×C61#12111yescharacteristic
333C2×C4×C61#12111yescharacteristic
334C2×C4×C61#12311yescharacteristic
335C2×C4×C61#12311yescharacteristic
336C2×C4×C61#12311yescharacteristic
337C2×C4×C61#12411yescharacteristic
338C2×C4×C61#12411yescharacteristic
339C2×C4×C61#12711yescharacteristic
340C2×C4×C61#12711yescharacteristic
341C22⋊D61—416no—
342C22⋊D61—42no—
343C22⋊D61—42no—
344C22⋊D61—42no—
345C22⋊D61—42no—
346C2×Dic61—24no—
347C2×Dic61—22no—
348C2×Dic61—44no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61—44no—
352C2×Dic61—44no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355D244—22no—
356D244—22no—
357D244—41no—
358D244—41no—
359C4×D61—42no—
360C4×D61—42no—
361C4×D61—42no—
362C4×D61—42no—
363Dic122—22no—
364Dic122—22no—
365Dic122—41no—
366Dic122—41no—
367C8×C61—42no—
368C8×C61—42no—
369#10994—611nomaximal, Sylow
370C22×C61—22no—
371C22×C61—22no—
372C22×C61—22no—
373C22×C61—24no—
374C22×C61—24no—
375C22×C61—24no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—42no—
381C22×C61—44no—
382C22×C61—44no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—44no—
386C22×C61—42no—
387C22×C61—44no—
388C22×C61#37911yescharacteristic
389C22×C61#38611yescharacteristic
390C22×C61#38611yescharacteristic
391C22×C61#39211yescharacteristic
392C22×C61#39211yescharacteristic
393C22×C61#39411yescharacteristic
394C22×C61#39411yescharacteristic
395C2×D61—44no—
396C2×D61—42no—
397C2×D61—82no—
398C2×D61—82no—
399C4×C61—42no—
400C4×C61#38611yescharacteristic
401C4×C61#38611yescharacteristic
402C4×C61#39011yescharacteristic
403C4×C61#39011yescharacteristic
404C4×C61#39211yescharacteristic
405C4×C61#39211yescharacteristic
406C4×C61#39411yescharacteristic
407C4×C61#39411yescharacteristic
408Dic61—44no—
409Dic61—42no—
410Dic61—82no—
411Dic61—82no—
412C2×#525—611no—
413C2×#421—611no—
414#2896—611no—
415C2×#407D6111yescharacteristic, complemented
416#2280—611no—
417#1733—611no—
418C2×H(3,ℤ/4)—611no—
419C2×C61—21no—
420C2×C61—21no—
421C2×C61—21no—
422C2×C61—21no—
423C2×C61—21no—
424C2×C61—21no—
425C2×C61—44no—
426C2×C61#143811yescharacteristic
427C2×C61#201012yes—
428D61—82no—
429C22×#41—611no—
430C24×C4C2×D6111yescharacteristic
431C22×M16C2×D6111yescharacteristic
432C22×M16C2×D6111yescharacteristic
433#525—614no—
434#525—1222no—
435#525—1222no—
436#525—1222no—
437C2×#123—1221no—
438C2×C22⋊Q8—1221no—
439C2×#121—1221no—
440C2×#120—1221no—
441C2×C4×D4—1222no—
442C2×#117—611no—
443C2×#117—611no—
444C2×#117—611no—
445#421—1222no—
446#421—1222no—
447C2×#104—1222no—
448#419—1221no—
449#418—1221no—
450#417—1222no—
451#416—1222no—
452#407—22no—
453#407—22no—
454C2×C22⋊C8—22no—
455#381—1221no—
456#380—1222no—
457#379—1221no—
458C4×C22⋊C4—1222no—
459#339—1222no—
460H(3,ℤ/4)—1222no—
461C61#1099411yescharacteristic, complemented, Sylow
462C25D24411yescharacteristic
463C2×#41—612no—
464C2×#41—612no—
465C2×#41—1221no—
466C2×#41—1221no—
467C2×#41—1221no—
468C2×#41—1221no—
469C2×#41—1221no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C22×Q8—611no—
476C22×D4—611no—
477C22×D4—1222no—
478C22×D4—1221no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—1221no—
492C23×C4C4×D6112yes—
493C23×C4D24411yescharacteristic
494C23×C4C22⋊D6112yes—
495C23×C4C22×D6111yescharacteristic
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16C22⋊D6112yescomplemented
508C22×C8—21no—
509C22×C8C22⋊D6112yescomplemented
510#123—1224no—
511#123—1224no—
512C22⋊Q8—1224no—
513C22⋊Q8—1224no—
514#121—1224no—
515#121—1224no—
516#120—1224no—
517#120—1224no—
518C4×D4—1228no—
519C4×D4—1228no—
520#117—612no—
521#117—612no—
522#117—1221no—
523#117—1221no—
524#117—1221no—
525#117—1221no—
526#117—1221no—
527#117—1221no—
528#117—1221no—
529#117—1221no—
530#117—1221no—
531#117—1221no—
532C2×C4⋊C4—612no—
533C2×C4⋊C4—1222no—
534C2×C4⋊C4—1221no—
535C2×C4⋊C4—1221no—
536C2×C22⋊C4—1222no—
537C2×C22⋊C4—1222no—
538C2×C22⋊C4—1221no—
539C2×C22⋊C4—1224no—
540C2×C22⋊C4—1221no—
541C2×C22⋊C4—1221no—
542C2×C42—612no—
543C2×C42—612no—
544C2×C42—1221no—
545#104—1228no—
546#103—1224no—
547#102—1224no—
548C22⋊C8—28no—
549#95—1224no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—44no—
557C24—1221no—
558C24#1175819812yes—
559C24C2×D24411yescharacteristic
560#41—1222no—
561#41—1222no—
562#41—1222no—
563#41—1222no—
564#41—1222no—
565#41—1222no—
566#41—1222no—
567#41—1222no—
568#41—2441no—
569#41—2441no—
570#41—2441no—
571#41—2441no—
572#41—2441no—
573#41—2441no—
574#41—2441no—
575#41—2441no—
576C2×Q8—612no—
577C2×Q8—1221no—
578C2×Q8—1221no—
579C2×Q8—1221no—
580C2×Q8—1221no—
581C2×Q8—1221no—
582C2×D4—612no—
583C2×D4—1228no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1221no—
587C2×D4—1221no—
588C2×D4—1221no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—2448no—
592C2×D4—2441no—
593C2×D4—2441no—
594C2×D4—2441no—
595C2×D4—2441no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—1222no—
631C22×C4—1221no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—2441no—
637C22×C4—2441no—
638C22×C4—2441no—
639C22×C4—2441no—
640C22×C4#1175819812yes—
641C22×C4C2×C4×D6111yescharacteristic
642C22×C4#1175822211yescharacteristic
643C22×C4#1175822211yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4D4×D6111yescharacteristic
648C22×C4D4×D6111yescharacteristic
649C22×C4D4×D6111yescharacteristic
650C22×C4#1175822411yescharacteristic
651C22×C4#1175822411yescharacteristic
652C22×C4C2×C22⋊D6111yescharacteristic
653C22×C4C2×C22⋊D6111yescharacteristic
654C22×C4C2×C22⋊D6111yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—41no—
660M16—41no—
661M16—41no—
662M16—41no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—1228no—
670C4⋊C4—1222no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—2441no—
675C4⋊C4—2441no—
676C22⋊C4—1228no—
677C22⋊C4—1228no—
678C22⋊C4—1222no—
679C22⋊C4—1222no—
680C22⋊C4—2448no—
681C22⋊C4—2441no—
682C22⋊C4—2441no—
683C22⋊C4—2441no—
684C22⋊C4—2441no—
685C42—614no—
686C42—1222no—
687C42—1222no—
688C42—1222no—
689C42—2441no—
690C42—2441no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—1222no—
710C23—2444no—
711C23—2441no—
712C23—2441no—
713C23C2×#1175819811yescharacteristic
714C23#1451974711yescharacteristic
715C23#1451974711yescharacteristic
716C23#1451974711yescharacteristic
717C23#1451975111yescharacteristic
718C23#1451975111yescharacteristic
719C23#1451976111yescharacteristic
720Q8—1222no—
721Q8—1222no—
722Q8—2441no—
723Q8—2441no—
724D4—1222no—
725D4—1222no—
726D4—24416no—
727D4—2442no—
728D4—2442no—
729D4—2442no—
730D4—2442no—
731D4—2441no—
732D4—2441no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—1224no—
749C2×C4—1222no—
750C2×C4—2444no—
751C2×C4—2444no—
752C2×C4—2442no—
753C2×C4—2442no—
754C2×C4—2444no—
755C2×C4—2441no—
756C2×C4—2441no—
757C2×C4—2442no—
758C2×C4—2442no—
759C2×C4—2442no—
760C2×C4—2442no—
761C2×C4C22⋊C4×D6111yescharacteristic
762C2×C4C22⋊C4×D6111yescharacteristic
763C2×C4#1451973711yescharacteristic
764C2×C4#1451973711yescharacteristic
765C2×C4C4×C22⋊D6111yescharacteristic
766C2×C4C4×C22⋊D6111yescharacteristic
767C2×C4#1451974511yescharacteristic
768C2×C4#1451974511yescharacteristic
769C2×C4#1451974511yescharacteristic
770C2×C4#1451974511yescharacteristic
771C2×C4#1451974611yescharacteristic
772C2×C4#1451974811yescharacteristic
773C2×C4#1451974811yescharacteristic
774C2×C4#1451974911yescharacteristic
775C2×C4#1451974911yescharacteristic
776C2×C4#1451974911yescharacteristic
777C2×C4#1451974911yescharacteristic
778C2×C4#1451975011yescharacteristic
779C2×C4#1451975011yescharacteristic
780C2×C4#1451975011yescharacteristic
781C2×C4#1451975011yescharacteristic
782C2×C4#1451975911yescharacteristic
783C2×C4#1451975911yescharacteristic
784C2×C4#1451976011yescharacteristic
785C2×C4#1451976311yescharacteristic
786C2×C4#1451976311yescharacteristic
787C2×C4#1451977311yescharacteristic
788C2×C4#1451977311yescharacteristic
789C8—42no—
790C8—42no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—42no—
808C22—44no—
809C22—4882no—
810C22—4882no—
811C22—2444no—
812C22—2442no—
813C22#1683961711yescharacteristic
814C22#1683963911yescharacteristic
815C22#1683964111yescharacteristic
816C22#1683967111yescharacteristic
817C22#1683967111yescharacteristic
818C22#1683967811yescharacteristic
819C22#1683967811yescharacteristic
820C4—42no—
821C4—4882no—
822C4—4882no—
823C4—2444no—
824C4—2442no—
825C4#1683963811yescharacteristic
826C4#1683963811yescharacteristic
827C4#1683966211yescharacteristic
828C4#1683966211yescharacteristic
829C4#1683967011yescharacteristic
830C4#1683967011yescharacteristic
831C4#1683967711yescharacteristic
832C4#1683967711yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—4882no—
841C2#2144405811yescharacteristic
842C2#2144688612yes—
subgroupG/H
centerC2×C4#14519773
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#407C2
socleC22×C61#392
prime radicalC2×#16840273C2
cosocleC23×C4×C61C23
hypercenterC2×#407D61
hypocenterC61#10994
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16839778C2semidirect
3. #21454339C2semidirect
4. #21448202C2semidirect
5. #21445530C2semidirect
6. C2×#16839519C2semidirect
7. C2×C61×#407C2semidirect
12. #16840273C4semidirect
81. C2×C4⋊Dic61D4semidirect
91. C2×C4×Dic61D4semidirect
124. C2×M16×C61D4semidirect
126. C22×C8×C61D4semidirect
220. C2×D244C22⋊C4semidirect
232. C2×Dic122C22⋊C4semidirect
268. C4×Dic61C22⋊C4semidirect
415. C2×#407D61semidirect
461. C61#10994semidirect
507. C2×M16C22⋊D61semidirect
509. C22×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168402732
C2×#168397782
#214543392
#214482022
#214455302
C2×#168395192
C2×C61×#4072
#1099461