Finite Group Databasebeta

← C2×#21446338 #29681983

Subgroups — C2×#21446338 #29681983

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2C2×#16840336C211yesmaximal, characteristic
3C2×#16839771C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic
5#21446338C218yesmaximal, direct product factor
6C2×#16839519C211yesmaximal, characteristic, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#419C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13#16840528C2214yes—
14C2×#14519785—22no—
15C2×#14519783—22no—
16C22×#11758194C2211yescharacteristic
17C2×M16×D61—22no—
18#16840336—22no—
19#16840336—22no—
20#16840336C414yescomplemented
21#16840336C2214yes—
22C2×#14519775C412yescomplemented
23C2×#14519766C412yescomplemented
24C2×#14519760—22no—
25C2×#14519753—22no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28#16839771—22no—
29#16839771C2214yescomplemented
30C2×#14519701—22no—
31#16839735—22no—
32#16839735C2214yes—
33C2×#14519691—22no—
34#16839519C2214yescomplemented
35#16839518C2214yescomplemented
36C23×Q8×C61C2211yescharacteristic
37C22×M16×C61C2211yescharacteristic
38C2×#117×C61C2211yescharacteristic
39C61×#419—22no—
40C61×#419C2214yescomplemented
41C2×#103×C61—22no—
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—
52C2×#11758222D412yes—
53C2×#11758222C2312yes—
54C22×Dic122C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61D412yes—
57C22×C4×D61D412yes—
58#14519785—28no—
59#14519785—28no—
60#14519783—28no—
61#14519783—28no—
62C2×#11758194—21no—
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194D412yes—
67C2×#11758194C2312yes—
68C2×#11758189—24no—
69M16×D61—28no—
70M16×D61—28no—
71C22×#92418D412yes—
72C2×C8×D61—24no—
73#14519775—24no—
74#14519775C2×C418yescomplemented
75#14519766—24no—
76#14519766C2×C418yescomplemented
77#14519760—28no—
78#14519760—28no—
79#14519753—28no—
80#14519753—28no—
81#14519736—21no—
82#14519736—21no—
83#14519736—21no—
84#14519736—21no—
85#14519736—21no—
86#14519736C2×C412yes—
87#14519736C2312yes—
88#14519736C2312yes—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×#11758196—24no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×#11758198—24no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61C2×C412yes—
97#14519701—28no—
98#14519691—28no—
99C22×Q8×C61—21no—
100C22×Q8×C61—21no—
101C22×Q8×C61—21no—
102C22×Q8×C61—21no—
103C22×Q8×C61—21no—
104C22×Q8×C61—21no—
105C22×Q8×C61—21no—
106C22×Q8×C61—21no—
107C22×Q8×C61—21no—
108C22×Q8×C61—21no—
109C22×Q8×C61—21no—
110C22×Q8×C61C2×C412yes—
111C22×Q8×C61C2×C412yes—
112C22×Q8×C61C2312yes—
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C2×M16×C61—21no—
118C2×M16×C61—21no—
119C2×M16×C61D412yes—
120C2×M16×C61C2312yes—
121C22×C8×C61D412yes—
122#117×C61—21no—
123#117×C61—21no—
124#117×C61—21no—
125#117×C61C2312yes—
126C2×C4⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129#103×C61—28no—
130C24×C61C2×D411yescharacteristic
131C23×D61C22⋊C412yes—
132C2×Q8×C61—22no—
133C2×Q8×C61—22no—
134C2×Q8×C61—22no—
135C2×Q8×C61—22no—
136C2×Q8×C61—22no—
137C2×Q8×C61—22no—
138C2×Q8×C61—22no—
139C2×Q8×C61—22no—
140C2×Q8×C61—22no—
141C2×Q8×C61—22no—
142C2×Q8×C61—22no—
143C2×Q8×C61—22no—
144C2×Q8×C61—22no—
145C2×Q8×C61—22no—
146C2×Q8×C61—22no—
147C2×Q8×C61—41no—
148C2×Q8×C61—41no—
149C2×Q8×C61—41no—
150C2×Q8×C61—41no—
151C2×Q8×C61—41no—
152C2×Q8×C61—41no—
153C2×Q8×C61—41no—
154C2×Q8×C61—41no—
155C2×Q8×C61—41no—
156C2×Q8×C61—41no—
157C2×Q8×C61—41no—
158C2×Q8×C61—41no—
159C2×Q8×C61C22×C414yes—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—41no—
164C22×C4×C61—41no—
165C22×C4×C61—41no—
166C22×C4×C61—41no—
167C22×C4×C61—41no—
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C2×D411yescharacteristic
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×C61#4111yescharacteristic
178C22×C4×C61#4111yescharacteristic
179C22×C4×C61#4111yescharacteristic
180C22×C4×C61#4111yescharacteristic
181C22×C4×C61C2411yescharacteristic
182C2×C22⋊D61—22no—
183C2×C22⋊D61—22no—
184C2×C22⋊D61—22no—
185C2×C22⋊D61—22no—
186C2×C22⋊D61C22⋊C414yes—
187C2×C22⋊D61C2×D414yes—
188C22×Dic61—22no—
189C22×Dic61—41no—
190C22×Dic61C22⋊C412yes—
191#11758222—22no—
192#11758222—22no—
193#11758222—22no—
194#11758222—22no—
195#11758222—22no—
196#11758222—22no—
197#11758222—22no—
198#11758222—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—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244C22⋊C412yes—
212C2×D244C22×C412yes—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61C22⋊C414yes—
218C2×C4×D61C2×D414yes—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122C22⋊C412yes—
224C2×Dic122C22×C412yes—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61C2×D414yes—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—41no—
234C22⋊C4×C61—22no—
235C22⋊C4×C61—41no—
236C42×C61—22no—
237C42×C61—41no—
238C22⋊Dic61—22no—
239C22⋊Dic61—22no—
240C22⋊Dic61—22no—
241C22⋊Dic61—41no—
242#11758198—216no—
243C4⋊Dic61—22no—
244C4⋊Dic61—22no—
245C4⋊Dic61—22no—
246C4⋊Dic61—41no—
247#11758196—216no—
248C4×Dic61—22no—
249C4×Dic61—22no—
250C4×Dic61—41no—
251C4×Dic61C22×C414yes—
252#11758194—22no—
253#11758194—22no—
254#11758194—22no—
255#11758194—22no—
256C2×#92418—22no—
257C2×#92418—22no—
258C2×#92418C2×D414yes—
259#11758189—216no—
260C8×D61—216no—
261C23×C61—42no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61#12111yescharacteristic
265C23×C61#12111yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—44no—
272C22×D61C2×C22⋊C414yes—
273Q8×C61—24no—
274Q8×C61—24no—
275Q8×C61—42no—
276Q8×C61—42no—
277Q8×C61—42no—
278Q8×C61—42no—
279Q8×C61—42no—
280Q8×C61—42no—
281C2×C4×C61—24no—
282C2×C4×C61—42no—
283C2×C4×C61—42no—
284C2×C4×C61—42no—
285C2×C4×C61—42no—
286C2×C4×C61—42no—
287C2×C4×C61—42no—
288C2×C4×C61—42no—
289C2×C4×C61—82no—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C4×D411yescharacteristic
293C2×C4×C61C4×D411yescharacteristic
294C2×C4×C61C4×D411yescharacteristic
295C2×C4×C61C4×D411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61#12011yescharacteristic
301C2×C4×C61#12011yescharacteristic
302C2×C4×C61#12011yescharacteristic
303C2×C4×C61#12011yescharacteristic
304C2×C4×C61#12111yescharacteristic
305C2×C4×C61#12111yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12311yescharacteristic
309C2×C4×C61#12311yescharacteristic
310C2×C4×C61#12311yescharacteristic
311C2×C4×C61#12311yescharacteristic
312C2×C4×C61C23×C411yescharacteristic
313C2×C4×C61C22×D411yescharacteristic
314C2×C4×C61C22×D411yescharacteristic
315C2×C4×C61C22×D411yescharacteristic
316C2×C4×C61C2×#4111yescharacteristic
317C2×C4×C61C2×#4111yescharacteristic
318C22⋊D61—24no—
319C22⋊D61—24no—
320C22⋊D61—24no—
321C22⋊D61—24no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—24no—
325C2×Dic61—44no—
326C2×Dic61—42no—
327C2×Dic61—82no—
328C2×Dic61C2×C22⋊C414yes—
329D244—22no—
330D244—22no—
331D244—22no—
332D244—22no—
333C4×D61—24no—
334C4×D61—24no—
335C4×D61—24no—
336C4×D61—24no—
337Dic122—22no—
338Dic122—22no—
339Dic122—22no—
340Dic122—22no—
341C8×C61—24no—
342#92418—24no—
343C2×#1909—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61#38611yescharacteristic
352C22×C61#38611yescharacteristic
353C22×C61#38611yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C2×#12111yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C2×D61—24no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—82no—
362C4×C61—44no—
363C4×C61—82no—
364C4×C61#38611yescharacteristic
365C4×C61#38611yescharacteristic
366C4×C61#38611yescharacteristic
367C4×C61#38611yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×#12011yescharacteristic
371C4×C61C2×#12311yescharacteristic
372Dic61—24no—
373Dic61—44no—
374Dic61—82no—
375C2×#568—611no—
376C2×#536—611no—
377C2×#419—611no—
378C2×#419D6111yescharacteristic, complemented
379C2×#410—611no—
380#1909—618no—
381C2×H(3,ℤ/4)—611no—
382C2×H(3,ℤ/4)—611no—
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61#190912yescomplemented
390C2×C61C2×#38611yescharacteristic
391D61—44no—
392C22×#41—611no—
393C23×Q8C2×D6111yescharacteristic
394#568—614no—
395#568—1222no—
396#568—1222no—
397#568—1222no—
398C2×#131—1222no—
399C2×#131—1222no—
400C22×M16—611no—
401C22×M16—1222no—
402C22×M16C2×D6111yescharacteristic
403#536—614no—
404#536—614no—
405#536—1222no—
406#536—1222no—
407C2×C4⋊Q8—612no—
408C2×#124—612no—
409C2×#123—1222no—
410C2×C22⋊Q8—1222no—
411C2×#117—611no—
412C2×#117—611no—
413C2×#117C2×D6111yescharacteristic
414#419—22no—
415#419—614no—
416#419—1222no—
417#419C2×D6114yescomplemented
418C2×#103—22no—
419C2×#103—1222no—
420#410—614no—
421#410—1222no—
422C2×#99—1222no—
423H(3,ℤ/4)—614no—
424H(3,ℤ/4)—614no—
425C61C2×#190911yescharacteristic, complemented, Sylow
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—612no—
429C2×#41—612no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—611no—
450C22×Q8C4×D6112yes—
451C22×Q8C4×D6112yes—
452C22×Q8C22×D6112yes—
453C22×D4—612no—
454C22×D4—611no—
455C23×C4—21no—
456C23×C4—612no—
457C23×C4C22×D6111yescharacteristic
458#131—1228no—
459#131—1228no—
460#131—1228no—
461#131—1228no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—612no—
467C2×M16—612no—
468C2×M16—1224no—
469C2×M16—1228no—
470C2×M16—1228no—
471C2×M16—1221no—
472C2×M16—1221no—
473C2×M16—1221no—
474C2×M16—1221no—
475C2×M16C22⋊D6112yes—
476C2×M16C22×D6112yes—
477C22×C8—612no—
478C22×C8—1224no—
479C22×C8C22⋊D6112yes—
480C4⋊Q8—618no—
481C4⋊Q8—1224no—
482#124—618no—
483#124—1224no—
484#123—1228no—
485#123—1228no—
486C22⋊Q8—1228no—
487C22⋊Q8—1228no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—612no—
492#117—612no—
493#117—612no—
494#117—1221no—
495#117—1221no—
496#117—1221no—
497#117—1221no—
498#117—1221no—
499#117C22×D6112yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1221no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C42—21no—
509C2×C42—612no—
510C2×C42—1221no—
511#103—28no—
512#103—1228no—
513#99—1228no—
514C24—612no—
515C24D4×D6111yescharacteristic
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—
528#41—1222no—
529#41—1222no—
530#41—1222no—
531#41—1222no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—41no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8—41no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—612no—
560C2×Q8—612no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8C2×C4×D6114yes—
566C2×D4—614no—
567C2×D4—614no—
568C2×D4—612no—
569C2×D4—612no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—612no—
587C22×C4—614no—
588C22×C4—614no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—2441no—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4#1175822211yescharacteristic
598C22×C4#1175822211yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4D4×D6111yescharacteristic
603C22×C4D4×D6111yescharacteristic
604C22×C4#1175822411yescharacteristic
605C22×C4#1175822411yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C23×D6111yescharacteristic
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—12216no—
614M16—1222no—
615M16—1222no—
616M16—1222no—
617M16—1222no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—614no—
621C2×C8—12216no—
622C2×C8—1222no—
623C2×C8—1222no—
624C2×C8C2×C22⋊D6114yes—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—12216no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—2441no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—12216no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C22⋊C4—2441no—
639C42—22no—
640C42—41no—
641C42—614no—
642C42—1222no—
643C42—1222no—
644C42—2441no—
645C23—42no—
646C23—614no—
647C23—1222no—
648C23—1222no—
649C23—2444no—
650C23C22⋊C4×D6111yescharacteristic
651C23C22⋊C4×D6111yescharacteristic
652C23#1451974811yescharacteristic
653C23#1451974811yescharacteristic
654C23#1451975011yescharacteristic
655C23#1451975011yescharacteristic
656C23C2×D4×D6111yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—42no—
660Q8—42no—
661Q8—42no—
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—1222no—
666Q8—1222no—
667Q8—1222no—
668Q8—1222no—
669D4—1224no—
670D4—1224no—
671D4—1224no—
672D4—1224no—
673D4—1222no—
674D4—1222no—
675D4—1222no—
676D4—1222no—
677C2×C4—24no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—614no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1224no—
690C2×C4—1224no—
691C2×C4—1224no—
692C2×C4—1224no—
693C2×C4—1224no—
694C2×C4—4882no—
695C2×C4—2442no—
696C2×C4—2444no—
697C2×C4C22⋊C4×D6111yescharacteristic
698C2×C4C22⋊C4×D6111yescharacteristic
699C2×C4#1451973711yescharacteristic
700C2×C4#1451973711yescharacteristic
701C2×C4#1451973711yescharacteristic
702C2×C4#1451973711yescharacteristic
703C2×C4C4×C22⋊D6111yescharacteristic
704C2×C4C4×C22⋊D6111yescharacteristic
705C2×C4C4×C22⋊D6111yescharacteristic
706C2×C4C4×C22⋊D6111yescharacteristic
707C2×C4#1451974511yescharacteristic
708C2×C4#1451974511yescharacteristic
709C2×C4#1451974511yescharacteristic
710C2×C4#1451974511yescharacteristic
711C2×C4#1451974811yescharacteristic
712C2×C4#1451974811yescharacteristic
713C2×C4#1451975011yescharacteristic
714C2×C4#1451975011yescharacteristic
715C2×C4#1451975911yescharacteristic
716C2×C4#1451975911yescharacteristic
717C2×C4#1451975911yescharacteristic
718C2×C4#1451975911yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C22×C22⋊D6111yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4C2×#1175822211yescharacteristic
725C8—24no—
726C8—1224no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—1224no—
735C22—4882no—
736C22—2444no—
737C22—2444no—
738C22#1683963811yescharacteristic
739C22#1683963811yescharacteristic
740C22#1683963811yescharacteristic
741C22#1683963811yescharacteristic
742C22C2×C22⋊C4×D6111yescharacteristic
743C22C2×#1451974811yescharacteristic
744C22C2×#1451975011yescharacteristic
745C4—44no—
746C4—82no—
747C4—1224no—
748C4—4882no—
749C4—2444no—
750C4#1683963811yescharacteristic
751C4#1683963811yescharacteristic
752C4#1683963811yescharacteristic
753C4#1683963811yescharacteristic
754C4C2×#1451973711yescharacteristic
755C4C2×C4×C22⋊D6111yescharacteristic
756C4C2×#1451974511yescharacteristic
757C4C2×#1451975911yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—2444no—
765C2#2144633812yesdirect product factor
766C2C2×#1683963811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#419C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#419D61
hypocenterC61C2×#1909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#16839771C2semidirect
5. #21446338C2direct (N × H)
6. C2×#16839519C2semidirect
7. C2×#16839518C2semidirect
8. C2×C61×#419C2semidirect
20. #16840336C4semidirect
22. C2×#14519775C4semidirect
23. C2×#14519766C4semidirect
29. #16839771C22semidirect
34. #16839519C22semidirect
35. #16839518C22semidirect
40. C61×#419C22semidirect
74. #14519775C2×C4semidirect
76. #14519766C2×C4semidirect
378. C2×#419D61semidirect
389. C2×C61#1909semidirect
417. #419C2×D61semidirect
425. C61C2×#1909semidirect
765. C2#21446338direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168403362
C2×#168397712
C2×#168397352
#214463382
C2×#168395192
C2×#168395182
C2×C61×#4192
C2×#190961