Finite Group Databasebeta

← C2×#21446291 #29681869

Subgroups — C2×#21446291 #29681869

Order 15616.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519810C211yesmaximal, characteristic
2C2×#16840528C211yesmaximal, characteristic
3C2×#16839780C211yesmaximal, characteristic
4C2×#16839770C211yesmaximal, characteristic, complemented
5C22×#14519695C211yesmaximal, characteristic, complemented
6#21446291C218yesmaximal, direct product factor
7C2×#16839520C211yesmaximal, characteristic, complemented
8C2×C61×#344C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C2×#14519810—22no—
12C2×#14519810—22no—
13C2×#14519810—22no—
14C2×#14519810—22no—
15C2×#14519810C414yescomplemented
16C2×#14519810C2214yes—
17C22×Dic244C412yescomplemented
18C22×#11758190C412yescomplemented
19#16840528—22no—
20#16840528—22no—
21#16840528—22no—
22#16840528C2214yes—
23C2×#14519785—22no—
24C2×#14519783—22no—
25C22×#11758194C2211yescharacteristic
26C22×#11758194C2211yescharacteristic
27C2×M16×D61—22no—
28#16839780—22no—
29#16839780C2214yes—
30C2×#14519705—22no—
31#16839770—22no—
32#16839770C2214yescomplemented
33C2×#14519700—22no—
34C2×#14519695—22no—
35C2×#14519695—22no—
36C2×#14519695C2214yescomplemented
37#16839520C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×#344C2214yescomplemented
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222C2×C412yes—
49C2×#11758222D412yes—
50C2×#11758222D412yes—
51C2×#11758222D412yes—
52C2×#11758222D412yes—
53C2×#11758222C2312yes—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—21no—
62C22×Dic122—21no—
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122C2×C412yes—
66C22×Dic122C2×C412yes—
67C22×Dic122C2×C411yescharacteristic
68C22×Dic122C2312yes—
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73#14519810—28no—
74#14519810—28no—
75#14519810—28no—
76#14519810—28no—
77C2×Dic244—24no—
78C2×Dic244—24no—
79C2×Dic244C2×C418yescomplemented
80C2×#11758190—24no—
81C2×#11758190—24no—
82C2×#11758190C2×C418yescomplemented
83#14519785—28no—
84#14519785—28no—
85#14519783—28no—
86#14519783—28no—
87C2×#11758194—21no—
88C2×#11758194—21no—
89C2×#11758194—21no—
90C2×#11758194—21no—
91C2×#11758194—21no—
92C2×#11758194—21no—
93C2×#11758194—21no—
94C2×#11758194—21no—
95C2×#11758194—21no—
96C2×#11758194D412yes—
97C2×#11758194C2312yes—
98C2×#11758194C2312yes—
99C2×#11758189—24no—
100M16×D61—28no—
101M16×D61—28no—
102C22×#92418—21no—
103C22×#92418D412yes—
104C2×C8×D61—24no—
105#14519705—28no—
106#14519700—28no—
107#14519695—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61—21no—
115C2×M16×C61—21no—
116C2×M16×C61C2×C412yes—
117C2×M16×C61D412yes—
118C2×M16×C61D412yes—
119C2×M16×C61C2312yes—
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
122C22×C8×C61C2×C412yes—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61—21no—
126#117×C61C2312yes—
127C2×C4⋊C4×C61—21no—
128C2×C22⋊C4×C61—21no—
129C2×C42×C61—21no—
130C24×C61#4111yescharacteristic
131C23×D61—21no—
132C22×C4×C61—41no—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×C4×C61C2411yescharacteristic
147C2×C22⋊D61—22no—
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61—22no—
153C22×Dic61—21no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C22×Dic61—41no—
160C22×Dic61—41no—
161#11758222—22no—
162#11758222—22no—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222C22⋊C414yes—
174#11758222C22⋊C414yes—
175#11758222C2×D414yes—
176#11758222C2×D414yes—
177C2×D244—21no—
178C2×D244—21no—
179C2×D244—21no—
180C2×D244C22⋊C412yes—
181C2×D244C22⋊C412yes—
182C2×D244C22×C412yes—
183C2×C4×D61—22no—
184C2×C4×D61—22no—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—21no—
192C2×Dic122—22no—
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—41no—
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×Dic122C22⋊C412yes—
220C2×Dic122C22⋊C412yes—
221C2×Dic122C22×C414yes—
222C2×Dic122C22×C412yes—
223M16×C61—22no—
224M16×C61—22no—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—22no—
229M16×C61—22no—
230M16×C61C2×D414yes—
231C2×C8×C61—22no—
232C2×C8×C61—22no—
233C2×C8×C61—22no—
234C2×C8×C61—22no—
235C2×C8×C61—22no—
236C2×C8×C61C22×C414yes—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—41no—
239C22⋊C4×C61—22no—
240C22⋊C4×C61—41no—
241C42×C61—22no—
242C42×C61—41no—
243#11758194—22no—
244#11758194—22no—
245#11758194—22no—
246#11758194—22no—
247#11758194—22no—
248#11758194—22no—
249#11758194—41no—
250#11758194—41no—
251C2×#92418—22no—
252C2×#92418—22no—
253C2×#92418—22no—
254C2×#92418—41no—
255C2×#92418—41no—
256C2×#92418C2×D414yes—
257Dic244—216no—
258#11758190—216no—
259#11758189—216no—
260C8×D61—216no—
261C23×C61—42no—
262C23×C61C4×D411yescharacteristic
263C23×C61C4×D411yescharacteristic
264C23×C61#12111yescharacteristic
265C23×C61#12111yescharacteristic
266C23×C61#12311yescharacteristic
267C23×C61#12311yescharacteristic
268C23×C61C2×#4111yescharacteristic
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—82no—
273C2×C4×C61—42no—
274C2×C4×C61—82no—
275C2×C4×C61C2×C22⋊C411yescharacteristic
276C2×C4×C61C2×C22⋊C411yescharacteristic
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C4×D411yescharacteristic
281C2×C4×C61C4×D411yescharacteristic
282C2×C4×C61C4×D411yescharacteristic
283C2×C4×C61C4×D411yescharacteristic
284C2×C4×C61C4×D411yescharacteristic
285C2×C4×C61#12011yescharacteristic
286C2×C4×C61#12011yescharacteristic
287C2×C4×C61#12011yescharacteristic
288C2×C4×C61#12011yescharacteristic
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#12311yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61C23×C411yescharacteristic
298C2×C4×C61C22×D411yescharacteristic
299C2×C4×C61C22×D411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C22⋊D61—24no—
304C22⋊D61—24no—
305C22⋊D61—24no—
306C22⋊D61—24no—
307C2×Dic61—22no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—24no—
311C2×Dic61—42no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317D244—22no—
318D244—22no—
319D244—22no—
320D244C2×C22⋊C414yes—
321C4×D61—24no—
322C4×D61—24no—
323C4×D61—24no—
324C4×D61—24no—
325Dic122—22no—
326Dic122—22no—
327Dic122—22no—
328Dic122—24no—
329Dic122—24no—
330Dic122—42no—
331Dic122—42no—
332Dic122—42no—
333Dic122—42no—
334Dic122—42no—
335Dic122—42no—
336Dic122C2×C22⋊C414yes—
337C8×C61—24no—
338C8×C61—24no—
339#92418—24no—
340#92418—42no—
341C2×#1902—611nomaximal, Sylow
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61#38611yescharacteristic
350C22×C61#38611yescharacteristic
351C22×C61#38611yescharacteristic
352C22×C61#38611yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×#12111yescharacteristic
355C22×C61C2×#12311yescharacteristic
356C2×D61—24no—
357C2×D61—44no—
358C2×D61—82no—
359C2×D61—82no—
360C4×C61—82no—
361C4×C61#38611yescharacteristic
362C4×C61#38611yescharacteristic
363C4×C61#38611yescharacteristic
364C4×C61#38611yescharacteristic
365C4×C61C22×C22⋊C411yescharacteristic
366C4×C61C2×C4×D411yescharacteristic
367C4×C61C2×#12011yescharacteristic
368C4×C61C2×#12111yescharacteristic
369Dic61—24no—
370Dic61—44no—
371C22×#137—611no—
372C2×#568—611no—
373C2×#421—611no—
374C2×#419—611no—
375C22×#101—611no—
376#1902—618no—
377C2×#344D6111yescharacteristic, complemented
378C2×#338—611no—
379C2×C61—21no—
380C2×C61—21no—
381C2×C61—21no—
382C2×C61—21no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61#190212yescomplemented
386C2×C61C2×#38611yescharacteristic
387D61—44no—
388C22×#41—611no—
389C23×Q8—611no—
390C2×#137—614no—
391C2×#137—614no—
392C2×#137—1222no—
393C2×#137—1222no—
394C2×#137—1222no—
395C2×#137—1222no—
396C22×Q16—612no—
397C22×SD16—612no—
398#568—614no—
399#568—1222no—
400#568—1222no—
401#568—1222no—
402C2×#131—1222no—
403C2×#131—1222no—
404C22×M16—611no—
405C22×M16—611no—
406C22×M16—1222no—
407C22×M16C2×D6111yescharacteristic
408C22×M16C2×D6111yescharacteristic
409C2×#117C2×D6111yescharacteristic
410#421—614no—
411#421—1222no—
412C2×#104—1222no—
413#419—614no—
414#419—1222no—
415C2×#103—1222no—
416C2×#101—614no—
417C2×#101—1222no—
418C2×#101—1222no—
419#344C2×D6114yescomplemented
420#338—614no—
421C61C2×#190211yescharacteristic, complemented, Sylow
422C2×#41—612no—
423C2×#41—612no—
424C2×#41—612no—
425C2×#41—612no—
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—1221no—
429C2×#41—1221no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C22×Q8—611no—
435C22×Q8—612no—
436C22×Q8—612no—
437C22×Q8—612no—
438C22×Q8—1221no—
439C22×Q8—1221no—
440C22×Q8—1221no—
441C22×Q8—1221no—
442C22×Q8—1221no—
443C22×Q8—1221no—
444C22×Q8—1221no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8—1221no—
449C22×D4—611no—
450C22×D4—1221no—
451C23×C4—1221no—
452C23×C4—1221no—
453C23×C4C22×D6111yescharacteristic
454#137—1228no—
455#137—1228no—
456#137—1228no—
457#137—1228no—
458C2×Q16—618no—
459C2×Q16—1224no—
460C2×Q16—1224no—
461C2×SD16—618no—
462C2×SD16—1224no—
463C2×SD16—1224no—
464#131—1228no—
465#131—1228no—
466#131—1228no—
467#131—1228no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16—21no—
475C2×M16—612no—
476C2×M16—612no—
477C2×M16—612no—
478C2×M16—1224no—
479C2×M16—1228no—
480C2×M16—1221no—
481C2×M16—1221no—
482C2×M16—1221no—
483C2×M16—1221no—
484C2×M16—1228no—
485C2×M16—1221no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16C4×D6112yes—
491C2×M16D24412yes—
492C2×M16D24412yes—
493C2×M16C22×D6112yes—
494C2×M16C22×D6112yes—
495C22×C8—21no—
496C22×C8—612no—
497C22×C8—1224no—
498C22×C8—1221no—
499C22×C8C4×D6112yes—
500#117—21no—
501#117—21no—
502#117—21no—
503#117C22×D6112yes—
504C2×C4⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C42—21no—
507#104—1228no—
508#103—1228no—
509#101—1228no—
510C24—1221no—
511C24#1175822211yescharacteristic
512#41—614no—
513#41—614no—
514#41—614no—
515#41—614no—
516#41—1222no—
517#41—1222no—
518#41—1222no—
519#41—1222no—
520#41—1222no—
521#41—1222no—
522#41—1222no—
523#41—1222no—
524#41—1222no—
525#41—1222no—
526#41—1222no—
527#41—1222no—
528C2×Q8—612no—
529C2×Q8—614no—
530C2×Q8—612no—
531C2×Q8—612no—
532C2×Q8—1222no—
533C2×Q8—1221no—
534C2×Q8—1221no—
535C2×Q8—1221no—
536C2×Q8—1222no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×Q8—1222no—
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—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×Q8—2441no—
562C2×D4—612no—
563C2×D4—612no—
564C2×D4—612no—
565C2×D4—1222no—
566C2×D4—1222no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1222no—
570C2×D4—1222no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C22×C4—41no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—2441no—
586C22×C4—2441no—
587C22×C4—2441no—
588C22×C4—2441no—
589C22×C4C2×C4×D6111yescharacteristic
590C22×C4C2×C4×D6111yescharacteristic
591C22×C4C2×D24411yescharacteristic
592C22×C4C2×D24411yescharacteristic
593C22×C4#1175822211yescharacteristic
594C22×C4D4×D6111yescharacteristic
595C22×C4D4×D6111yescharacteristic
596C22×C4D4×D6111yescharacteristic
597C22×C4D4×D6111yescharacteristic
598C22×C4D4×D6111yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4#1175822611yescharacteristic
601C22×C4#1175822611yescharacteristic
602C22×C4C23×D6111yescharacteristic
603Q16—12216no—
604SD16—12216no—
605M16—22no—
606M16—22no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—22no—
611M16—22no—
612M16—12216no—
613M16—1222no—
614M16—1222no—
615M16—1222no—
616M16—1222no—
617M16—1222no—
618M16—1222no—
619M16—2441no—
620M16—2441no—
621M16C2×D24414yes—
622C2×C8—22no—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—614no—
628C2×C8—12216no—
629C2×C8—1222no—
630C2×C8—1222no—
631C2×C8—1222no—
632C2×C8—2441no—
633C2×C8—2441no—
634C2×C8C2×C4×D6114yes—
635C4⋊C4—22no—
636C4⋊C4—41no—
637C22⋊C4—22no—
638C22⋊C4—41no—
639C42—22no—
640C42—41no—
641C23—42no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—4882no—
646C23C4×D24411yescharacteristic
647C23C4×D24411yescharacteristic
648C23#1451975011yescharacteristic
649C23#1451975011yescharacteristic
650C23#1451976211yescharacteristic
651C23#1451976211yescharacteristic
652C23C2×#1175822211yescharacteristic
653Q8—614no—
654Q8—1222no—
655Q8—1222no—
656Q8—1222no—
657Q8—1224no—
658Q8—1224no—
659Q8—2442no—
660Q8—2442no—
661Q8—2442no—
662Q8—2442no—
663Q8—2442no—
664Q8—2442no—
665D4—614no—
666D4—1224no—
667D4—1224no—
668D4—1224no—
669D4—1224no—
670D4—1222no—
671D4—1222no—
672D4—1222no—
673C2×C4—42no—
674C2×C4—82no—
675C2×C4—1222no—
676C2×C4—1222no—
677C2×C4—1222no—
678C2×C4—1224no—
679C2×C4—1224no—
680C2×C4—1224no—
681C2×C4—1224no—
682C2×C4—1224no—
683C2×C4—2442no—
684C2×C4—2442no—
685C2×C4—2442no—
686C2×C4—2442no—
687C2×C4—2442no—
688C2×C4—2442no—
689C2×C4C22⋊C4×D6111yescharacteristic
690C2×C4C22⋊C4×D6111yescharacteristic
691C2×C4C22⋊C4×D6111yescharacteristic
692C2×C4C22⋊C4×D6111yescharacteristic
693C2×C4#1451973911yescharacteristic
694C2×C4#1451973911yescharacteristic
695C2×C4#1451973911yescharacteristic
696C2×C4#1451973911yescharacteristic
697C2×C4C4×D24411yescharacteristic
698C2×C4C4×D24411yescharacteristic
699C2×C4#1451974711yescharacteristic
700C2×C4#1451974711yescharacteristic
701C2×C4#1451974711yescharacteristic
702C2×C4#1451974711yescharacteristic
703C2×C4#1451975011yescharacteristic
704C2×C4#1451975011yescharacteristic
705C2×C4#1451975211yescharacteristic
706C2×C4#1451975211yescharacteristic
707C2×C4#1451975211yescharacteristic
708C2×C4#1451975211yescharacteristic
709C2×C4#1451976211yescharacteristic
710C2×C4#1451976211yescharacteristic
711C2×C4C22×C4×D6111yescharacteristic
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4C2×D4×D6111yescharacteristic
714C2×C4C2×D4×D6111yescharacteristic
715C2×C4C22×D24411yescharacteristic
716C2×C4C2×#1175822611yescharacteristic
717C8—24no—
718C8—24no—
719C8—1224no—
720C8—2442no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—1224no—
729C22—4882no—
730C22—4882no—
731C22—2444no—
732C22#1683964011yescharacteristic
733C22#1683964011yescharacteristic
734C22#1683964011yescharacteristic
735C22#1683964011yescharacteristic
736C22C2×C4×D24411yescharacteristic
737C22C2×#1451975011yescharacteristic
738C22C2×#1451976211yescharacteristic
739C4—82no—
740C4—1224no—
741C4—2444no—
742C4#1683964011yescharacteristic
743C4#1683964011yescharacteristic
744C4#1683964011yescharacteristic
745C4#1683964011yescharacteristic
746C4C2×C22⋊C4×D6111yescharacteristic
747C4C2×#1451973911yescharacteristic
748C4C2×#1451974711yescharacteristic
749C4C2×#1451975211yescharacteristic
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—2444no—
757C2#2144629112yesdirect product factor
758C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#344C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#344D61
hypocenterC61C2×#1902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
4. C2×#16839770C2semidirect
5. C22×#14519695C2semidirect
6. #21446291C2direct (N × H)
7. C2×#16839520C2semidirect
8. C2×C61×#344C2semidirect
15. C2×#14519810C4semidirect
17. C22×Dic244C4semidirect
18. C22×#11758190C4semidirect
32. #16839770C22semidirect
36. C2×#14519695C22semidirect
37. #16839520C22semidirect
41. C61×#344C22semidirect
79. C2×Dic244C2×C4semidirect
82. C2×#11758190C2×C4semidirect
377. C2×#344D61semidirect
385. C2×C61#1902semidirect
419. #344C2×D61semidirect
421. C61C2×#1902semidirect
757. C2#21446291direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198102
C2×#168405282
C2×#168397802
C2×#168397702
C22×#145196952
#214462912
C2×#168395202
C2×C61×#3442
C2×#190261