Finite Group Databasebeta

← C2×#21446311 #29681901

Subgroups — C2×#21446311 #29681901

Order 15616.

1678 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
1C22×#14519808C211yesmaximal, characteristic
2C2×#16840240C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic
4C2×#16839735C211yesmaximal, characteristic
5#21446311C218yesmaximal, direct product factor
6C2×#16839534C211yesmaximal, characteristic, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#419C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C2×#14519808—22no—
11C2×#14519808—22no—
12C2×#14519808—22no—
13C2×#14519808—22no—
14C2×#14519808C414yescomplemented
15C2×#14519808C2214yes—
16C22×#11758202C412yescomplemented
17C22×#11758201C412yescomplemented
18C22×#11758194C2211yescharacteristic
19#16840240—22no—
20#16840240—22no—
21#16840240—22no—
22#16840240C2214yescomplemented
23C2×Q8×Dic61—22no—
24C2×Q8×Dic61—22no—
25C2×#14519736—22no—
26C2×#14519736C2211yescharacteristic
27C2×#14519736C2211yescharacteristic
28#16839778—22no—
29#16839778C2214yes—
30C2×#14519703—22no—
31#16839735—22no—
32#16839735C2214yes—
33C2×#14519691—22no—
34#16839534C2214yescomplemented
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×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222C2×C412yes—
53C2×#11758222C2312yes—
54C22×Dic122C2×C411yescharacteristic
55C22×D244C2×C411yescharacteristic
56C22×C22⋊D61—21no—
57C22×C4×D61—21no—
58#14519808—28no—
59#14519808—28no—
60#14519808—28no—
61#14519808—28no—
62C2×#11758202—24no—
63C2×#11758202—24no—
64C2×#11758202C2×C418yescomplemented
65C2×#11758201—24no—
66C2×#11758201—24no—
67C2×#11758201C2×C418yescomplemented
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194C2×C412yes—
73C2×#11758194C2312yes—
74C22×#92418C2×C412yes—
75Q8×Dic61—28no—
76Q8×Dic61—28no—
77Q8×Dic61—28no—
78Q8×Dic61—28no—
79#14519736—28no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83#14519736—21no—
84#14519736—28no—
85#14519736D412yes—
86#14519736D412yes—
87#14519736C2312yes—
88#14519736C2312yes—
89C2×C4⋊Dic61—24no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61D412yes—
94C2×C4×Dic61—24no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61D412yes—
97#14519703—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×C61C2×C412yes—
107C22×Q8×C61C2×C412yes—
108C22×Q8×C61D412yes—
109C22×Q8×C61D412yes—
110C22×Q8×C61D412yes—
111C22×Q8×C61D412yes—
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×C61—21no—
120C2×M16×C61C2312yes—
121C22×C8×C61—21no—
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×D61—21no—
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—22no—
148C2×Q8×C61—22no—
149C2×Q8×C61—22no—
150C2×Q8×C61—22no—
151C2×Q8×C61—22no—
152C2×Q8×C61—22no—
153C2×Q8×C61C22⋊C414yes—
154C2×Q8×C61C22⋊C414yes—
155C2×Q8×C61C22⋊C414yes—
156C2×Q8×C61C22⋊C414yes—
157C2×Q8×C61C22×C414yes—
158C2×Q8×C61C2×D414yes—
159C2×Q8×C61C2×D414yes—
160C22×C4×C61—22no—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
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—41no—
185C2×C22⋊D61—41no—
186C2×C22⋊D61—41no—
187C2×C22⋊D61—41no—
188C22×Dic61—21no—
189C22×Dic61—22no—
190C22×Dic61—22no—
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—41no—
200#11758222—41no—
201#11758222—41no—
202#11758222—41no—
203#11758222—41no—
204#11758222—41no—
205#11758222—41no—
206#11758222—41no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—21no—
211C2×D244—21no—
212C2×D244C22×C412yes—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—41no—
216C2×C4×D61—41no—
217C2×C4×D61—41no—
218C2×C4×D61—41no—
219C2×Dic122—21no—
220C2×Dic122—21no—
221C2×Dic122—21no—
222C2×Dic122—21no—
223C2×Dic122—21no—
224C2×Dic122C22×C412yes—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—41no—
228M16×C61—41no—
229C2×C8×C61—22no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
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⋊Dic61C2×D414yes—
242#11758202—216no—
243#11758201—216no—
244C4⋊Dic61—216no—
245C4⋊Dic61—22no—
246C4⋊Dic61—22no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249C4×Dic61—216no—
250C4×Dic61—22no—
251C4×Dic61—22no—
252C4×Dic61—22no—
253C4×Dic61C2×D414yes—
254#11758194—22no—
255#11758194—22no—
256#11758194—22no—
257#11758194—22no—
258C2×#92418—22no—
259C2×#92418—22no—
260C2×#92418C22×C414yes—
261C23×C61—42no—
262C23×C61C4×D411yescharacteristic
263C23×C61C4×D411yescharacteristic
264C23×C61#12011yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—82no—
273Q8×C61—24no—
274Q8×C61—24no—
275Q8×C61—24no—
276Q8×C61—24no—
277Q8×C61—24no—
278Q8×C61—24no—
279Q8×C61—24no—
280Q8×C61C2×C22⋊C418yes—
281C2×C4×C61—24no—
282C2×C4×C61—24no—
283C2×C4×C61—24no—
284C2×C4×C61—24no—
285C2×C4×C61—24no—
286C2×C4×C61—24no—
287C2×C4×C61—24no—
288C2×C4×C61—42no—
289C2×C4×C61—82no—
290C2×C4×C61C2×C22⋊C411yescharacteristic
291C2×C4×C61C2×C22⋊C411yescharacteristic
292C2×C4×C61C2×C22⋊C411yescharacteristic
293C2×C4×C61C2×C22⋊C411yescharacteristic
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#12111yescharacteristic
303C2×C4×C61#12111yescharacteristic
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—42no—
319C22⋊D61—42no—
320C22⋊D61—42no—
321C22⋊D61—42no—
322C2×Dic61—22no—
323C2×Dic61—24no—
324C2×Dic61—24no—
325C2×Dic61—44no—
326C2×Dic61—44no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329D244—22no—
330D244—22no—
331D244—41no—
332D244—41no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—42no—
336C4×D61—42no—
337Dic122—22no—
338Dic122—22no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—42no—
342#92418—24no—
343C2×#1905—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×C61C2×C4×D411yescharacteristic
356C22×C61C2×#12011yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C2×D61—42no—
359C2×D61—82no—
360C2×D61—82no—
361C2×D61—82no—
362C4×C61—28no—
363C4×C61—82no—
364C4×C61#38611yescharacteristic
365C4×C61#38611yescharacteristic
366C4×C61#38611yescharacteristic
367C4×C61#38611yescharacteristic
368C4×C61C22×C22⋊C411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×#12111yescharacteristic
371C4×C61C2×#12311yescharacteristic
372Dic61—44no—
373Dic61—44no—
374Dic61—42no—
375C22×#137—611no—
376C2×#519—611no—
377C2×#421—611no—
378C2×#419D6111yescharacteristic, complemented
379C2×#410—611no—
380#1905—618no—
381C2×#344—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#190512yescomplemented
390C2×C61C2×#38611yescharacteristic
391D61—82no—
392C22×#41—611no—
393C23×Q8C2×D6111yescharacteristic
394C2×#137—614no—
395C2×#137—614no—
396C2×#137—1222no—
397C2×#137—1222no—
398C2×#137—1222no—
399C2×#137—1222no—
400C22×Q16—612no—
401C22×SD16—612no—
402C22×M16—611no—
403C22×M16C2×D6111yescharacteristic
404#519—614no—
405#519—1222no—
406#519—1222no—
407#519—1222no—
408C2×C4×Q8—1222no—
409C2×C4×Q8—1222no—
410C2×#117—611no—
411C2×#117—611no—
412C2×#117—1222no—
413C2×#117C2×D6111yescharacteristic
414#421—614no—
415#421—1222no—
416C2×#104—1222no—
417#419—22no—
418#419C2×D6114yescomplemented
419C2×#103—22no—
420#410—614no—
421#410—1222no—
422C2×#99—1222no—
423#344—614no—
424H(3,ℤ/4)—614no—
425C61C2×#190511yescharacteristic, complemented, Sylow
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—1221no—
429C2×#41—1221no—
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—611no—
446C22×Q8C4×D6112yes—
447C22×Q8C4×D6112yes—
448C22×Q8D24412yes—
449C22×Q8D24412yes—
450C22×Q8C22⋊D6112yes—
451C22×Q8C22⋊D6112yes—
452C22×Q8C22×D6112yes—
453C22×D4—611no—
454C22×D4—1221no—
455C23×C4—21no—
456C23×C4—1221no—
457C23×C4C22×D6111yescharacteristic
458#137—1228no—
459#137—1228no—
460#137—1228no—
461#137—1228no—
462C2×Q16—618no—
463C2×Q16—1224no—
464C2×Q16—1224no—
465C2×SD16—618no—
466C2×SD16—1224no—
467C2×SD16—1224no—
468C2×M16—21no—
469C2×M16—21no—
470C2×M16—21no—
471C2×M16—21no—
472C2×M16—21no—
473C2×M16—612no—
474C2×M16—612no—
475C2×M16—1221no—
476C2×M16—1221no—
477C2×M16—1221no—
478C2×M16—1221no—
479C2×M16C22×D6112yes—
480C22×C8—21no—
481C22×C8—612no—
482C4×Q8—1228no—
483C4×Q8—1228no—
484C4×Q8—1228no—
485C4×Q8—1228no—
486#117—21no—
487#117—21no—
488#117—21no—
489#117—612no—
490#117—612no—
491#117—612no—
492#117—612no—
493#117—1228no—
494#117—1228no—
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—612no—
506C2×C22⋊C4—1221no—
507C2×C42—21no—
508C2×C42—612no—
509C2×C42—1224no—
510C2×C42—1221no—
511#104—1228no—
512#103—28no—
513#99—1228no—
514C24—1221no—
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—2441no—
525#41—2441no—
526#41—2441no—
527#41—2441no—
528#41—2441no—
529#41—2441no—
530#41—2441no—
531#41—2441no—
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—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—612no—
554C2×Q8—1221no—
555C2×Q8—1221no—
556C2×Q8—1221no—
557C2×Q8—1221no—
558C2×Q8—1221no—
559C2×Q8#1175819814yes—
560C2×Q8#1175819814yes—
561C2×Q8#1175819814yes—
562C2×Q8#1175819814yes—
563C2×Q8C2×C4×D6114yes—
564C2×Q8C2×D24414yes—
565C2×Q8C2×C22⋊D6114yes—
566C2×D4—612no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—1221no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4D4×D6111yescharacteristic
600C22×C4D4×D6111yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4#1175822411yescharacteristic
603C22×C4#1175822411yescharacteristic
604C22×C4#1175822411yescharacteristic
605C22×C4#1175822411yescharacteristic
606C22×C4C2×C22⋊D6111yescharacteristic
607C22×C4C2×C22⋊D6111yescharacteristic
608C22×C4C23×D6111yescharacteristic
609Q16—12216no—
610SD16—12216no—
611M16—22no—
612M16—22no—
613M16—41no—
614M16—41no—
615M16—1222no—
616M16—1222no—
617M16—1222no—
618M16—1222no—
619C2×C8—22no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—614no—
623C2×C8—1222no—
624C2×C8—1222no—
625C4⋊C4—22no—
626C4⋊C4—41no—
627C4⋊C4—12216no—
628C4⋊C4—1222no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C22⋊C4—22no—
633C22⋊C4—41no—
634C22⋊C4—614no—
635C22⋊C4—1222no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C42—22no—
639C42—41no—
640C42—614no—
641C42—12216no—
642C42—1222no—
643C42—1222no—
644C42—1222no—
645C23—42no—
646C23—1222no—
647C23—4882no—
648C23—2441no—
649C23—2441no—
650C23#1451973711yescharacteristic
651C23#1451973711yescharacteristic
652C23#1451974711yescharacteristic
653C23#1451974711yescharacteristic
654C23#1451974911yescharacteristic
655C23#1451974911yescharacteristic
656C23C2×D4×D6111yescharacteristic
657Q8—24no—
658Q8—24no—
659Q8—24no—
660Q8—24no—
661Q8—24no—
662Q8—24no—
663Q8—24no—
664Q8—1222no—
665Q8—1222no—
666Q8—2441no—
667Q8—2441no—
668Q8C2×#1175819818yes—
669D4—1222no—
670D4—1222no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674D4—2442no—
675D4—2441no—
676D4—2441no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—42no—
685C2×C4—82no—
686C2×C4—1222no—
687C2×C4—1224no—
688C2×C4—1224no—
689C2×C4—2444no—
690C2×C4—2444no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C2×#1175819811yescharacteristic
698C2×C4C2×#1175819811yescharacteristic
699C2×C4C2×#1175819811yescharacteristic
700C2×C4C2×#1175819811yescharacteristic
701C2×C4#1451973711yescharacteristic
702C2×C4#1451973711yescharacteristic
703C2×C4#1451973711yescharacteristic
704C2×C4#1451973711yescharacteristic
705C2×C4#1451973711yescharacteristic
706C2×C4#1451973711yescharacteristic
707C2×C4#1451974711yescharacteristic
708C2×C4#1451974711yescharacteristic
709C2×C4#1451974911yescharacteristic
710C2×C4#1451974911yescharacteristic
711C2×C4#1451974911yescharacteristic
712C2×C4#1451974911yescharacteristic
713C2×C4#1451974911yescharacteristic
714C2×C4#1451974911yescharacteristic
715C2×C4#1451976111yescharacteristic
716C2×C4#1451976111yescharacteristic
717C2×C4#1451976111yescharacteristic
718C2×C4#1451976111yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C22×C22⋊D6111yescharacteristic
722C2×C4C22×D24411yescharacteristic
723C2×C4C2×#1175822411yescharacteristic
724C2×C4C2×#1175822411yescharacteristic
725C8—42no—
726C8—1224no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—4882no—
735C22—4882no—
736C22—4882no—
737C22—2442no—
738C22#1683963911yescharacteristic
739C22#1683963911yescharacteristic
740C22#1683963911yescharacteristic
741C22#1683963911yescharacteristic
742C22C2×#1451973711yescharacteristic
743C22C2×#1451974711yescharacteristic
744C22C2×#1451974911yescharacteristic
745C4—28no—
746C4—82no—
747C4—2444no—
748C4—2444no—
749C4—2442no—
750C4#1683963911yescharacteristic
751C4#1683963911yescharacteristic
752C4#1683963911yescharacteristic
753C4#1683963911yescharacteristic
754C4C22×#1175819811yescharacteristic
755C4C2×#1451973711yescharacteristic
756C4C2×#1451974911yescharacteristic
757C4C2×#1451976111yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—4882no—
765C2#2144631112yesdirect product factor
766C2C2×#1683963911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#419C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×#419D61
hypocenterC61C2×#1905
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
2. C2×#16840240C2semidirect
5. #21446311C2direct (N × H)
6. C2×#16839534C2semidirect
7. C2×#16839518C2semidirect
8. C2×C61×#419C2semidirect
14. C2×#14519808C4semidirect
16. C22×#11758202C4semidirect
17. C22×#11758201C4semidirect
22. #16840240C22semidirect
34. #16839534C22semidirect
35. #16839518C22semidirect
40. C61×#419C22semidirect
64. C2×#11758202C2×C4semidirect
67. C2×#11758201C2×C4semidirect
378. C2×#419D61semidirect
389. C2×C61#1905semidirect
418. #419C2×D61semidirect
425. C61C2×#1905semidirect
765. C2#21446311direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198082
C2×#168402402
C2×#168397782
C2×#168397352
#214463112
C2×#168395342
C2×#168395182
C2×C61×#4192
C2×#190561