Finite Group Databasebeta

← C2×#21446309 #29681898

Subgroups — C2×#21446309 #29681898

Order 15616.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic
2C2×#16840236C211yesmaximal, characteristic, complemented
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5#21446309C218yesmaximal, direct product factor
6C2×#16839532C211yesmaximal, characteristic, complemented
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×#410C211yesmaximal, characteristic, complemented
9C23×D244C2211yescharacteristic
10C2×#14519802—22no—
11C2×#14519802—22no—
12C2×#14519802—22no—
13C2×#14519802—22no—
14C2×#14519802C414yescomplemented
15C2×#14519802C2214yes—
16C22×#11758201C412yescomplemented
17C22×#11758199C412yescomplemented
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20#16840236—22no—
21#16840236—22no—
22#16840236—22no—
23#16840236C2214yescomplemented
24C2×C4×D244—22no—
25C2×#14519739—22no—
26C2×#14519736C2211yescharacteristic
27C2×C22⋊C4×D61—22no—
28#16839779—22no—
29#16839779C2214yescomplemented
30C2×#14519704—22no—
31#16839766—22no—
32#16839766C2214yescomplemented
33C2×#14519697—22no—
34#16839532C2214yescomplemented
35#16839518C2214yescomplemented
36C22×#41×C61C2211yescharacteristic
37C2×#117×C61C2211yescharacteristic
38C2×#117×C61C2211yescharacteristic
39C61×#410—22no—
40C61×#410C2214yescomplemented
41C2×#99×C61—22no—
42C24×D61—21no—
43C22×D244—21no—
44C22×D244—21no—
45C22×D244—21no—
46C22×D244—21no—
47C22×D244—21no—
48C22×D244—21no—
49C22×D244—21no—
50C22×D244C2×C412yes—
51C22×D244C2×C412yes—
52C22×D244D412yes—
53C22×D244D412yes—
54C22×D244D412yes—
55C22×D244D412yes—
56C22×D244C2312yes—
57C22×C4×D61—24no—
58#14519802—28no—
59#14519802—28no—
60#14519802—28no—
61#14519802—28no—
62C2×#11758201—24no—
63C2×#11758201—24no—
64C2×#11758201C2×C418yescomplemented
65C2×#11758199—24no—
66C2×#11758199—24no—
67C2×#11758199C2×C418yescomplemented
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194C2×C412yescomplemented
78C2×#11758194C2312yes—
79C2×#11758194C2312yes—
80C22×#92418—21no—
81C22×#92418C2×C412yescomplemented
82C4×D244—28no—
83C4×D244—28no—
84#14519739—28no—
85#14519739—28no—
86#14519736—21no—
87#14519736—21no—
88#14519736D412yes—
89#14519736C2312yes—
90C2×C4⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—24no—
93C22⋊C4×D61—28no—
94C22⋊C4×D61—28no—
95C2×C4×Dic61D412yes—
96#14519704—28no—
97#14519697—28no—
98C2×#41×C61—21no—
99C2×#41×C61—21no—
100C2×#41×C61—21no—
101C2×#41×C61—21no—
102C2×#41×C61—21no—
103C2×#41×C61—21no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61C2×C412yescomplemented
109C2×#41×C61C2312yes—
110C22×Q8×C61C2×C411yescharacteristic, complemented
111C22×D4×C61—21no—
112C22×D4×C61C2×C411yescharacteristic, complemented
113C23×C4×C61—21no—
114C23×C4×C61C2311yescharacteristic
115#117×C61—21no—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61D412yes—
121#117×C61C2312yes—
122#117×C61C2312yes—
123C2×C4⋊C4×C61—21no—
124C2×C4⋊C4×C61—21no—
125C2×C22⋊C4×C61—21no—
126C2×C22⋊C4×C61D412yes—
127C2×C42×C61—21no—
128C2×C42×C61—21no—
129#99×C61—28no—
130C24×C61—21no—
131C24×C61C2×D411yescharacteristic
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—22no—
137C23×D61—22no—
138C23×D61—22no—
139C23×D61—84no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
147#41×C61—22no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61C22×C412yescomplemented
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C2×D4×C61C22×C412yescomplemented
174C22×C4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—41no—
179C22×C4×C61—41no—
180C22×C4×C61—41no—
181C22×C4×C61—41no—
182C22×C4×C61—41no—
183C22×C4×C61C22×C411yescharacteristic
184C22×C4×C61C22×C411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61#4111yescharacteristic
196C22×C4×C61C2411yescharacteristic
197C22×Dic61—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—22no—
205C2×D244—22no—
206C2×D244—22no—
207C2×D244—22no—
208C2×D244—22no—
209C2×D244—22no—
210C2×D244—22no—
211C2×D244—22no—
212C2×D244—22no—
213C2×D244—22no—
214C2×D244—22no—
215C2×D244—22no—
216C2×D244—22no—
217C2×D244—22no—
218C2×D244—22no—
219C2×D244C22⋊C414yes—
220C2×D244C22⋊C414yes—
221C2×D244C22⋊C414yes—
222C2×D244C22⋊C414yes—
223C2×D244C22×C414yes—
224C2×D244C2×D414yes—
225C2×D244C2×D414yes—
226C2×C4×D61—216no—
227C2×C4×D61—88no—
228C4⋊C4×C61—22no—
229C4⋊C4×C61—22no—
230C4⋊C4×C61—22no—
231C4⋊C4×C61—41no—
232C22⋊C4×C61—22no—
233C22⋊C4×C61—22no—
234C22⋊C4×C61—41no—
235C22⋊C4×C61C2×D414yes—
236C42×C61—22no—
237C42×C61—22no—
238C42×C61—22no—
239C42×C61—41no—
240C22⋊Dic61—22no—
241C22⋊Dic61—22no—
242#11758201—216no—
243#11758199—216no—
244#11758198—216no—
245C4⋊Dic61—22no—
246C4⋊Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61C2×D414yes—
249#11758194—22no—
250#11758194—22no—
251#11758194—22no—
252#11758194—22no—
253#11758194—22no—
254#11758194—22no—
255#11758194—41no—
256#11758194—41no—
257C2×#92418—22no—
258C2×#92418—22no—
259C2×#92418—22no—
260C2×#92418—41no—
261C2×#92418—41no—
262C2×#92418C22×C414yescomplemented
263C23×C61—22no—
264C23×C61—42no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—82no—
268C23×C61C4×D411yescharacteristic
269C23×C61C4×D411yescharacteristic
270C23×C61#12011yescharacteristic
271C23×C61#12011yescharacteristic
272C23×C61#12111yescharacteristic
273C23×C61#12111yescharacteristic
274C23×C61C22×D411yescharacteristic
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—24no—
279C22×D61—24no—
280C22×D61—24no—
281C22×D61—24no—
282C22×D61—48no—
283C22×D61—84no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289Q8×C61—22no—
290Q8×C61—22no—
291Q8×C61—41no—
292Q8×C61—41no—
293D4×C61—22no—
294D4×C61—22no—
295D4×C61—42no—
296D4×C61—42no—
297D4×C61—42no—
298D4×C61—42no—
299D4×C61—41no—
300D4×C61—41no—
301C2×C4×C61—22no—
302C2×C4×C61—24no—
303C2×C4×C61—44no—
304C2×C4×C61—41no—
305C2×C4×C61—41no—
306C2×C4×C61—42no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—82no—
312C2×C4×C61C2×C22⋊C411yescharacteristic
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C2×C22⋊C411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
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#12311yescharacteristic
331C2×C4×C61#12311yescharacteristic
332C2×C4×C61#12311yescharacteristic
333C2×C4×C61#12311yescharacteristic
334C2×C4×C61C23×C411yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C2×#4111yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×Dic61—24no—
341C2×Dic61—44no—
342D244—24no—
343D244—24no—
344D244—24no—
345D244—24no—
346D244—24no—
347D244—24no—
348D244—24no—
349D244C2×C22⋊C418yes—
350C4×D61—816no—
351#92418—24no—
352#92418—42no—
353C2×#1904—611nomaximal, Sylow
354C22×C61—22no—
355C22×C61—22no—
356C22×C61—22no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—42no—
362C22×C61—82no—
363C22×C61—82no—
364C22×C61—82no—
365C22×C61#38611yescharacteristic
366C22×C61#38611yescharacteristic
367C22×C61#38611yescharacteristic
368C22×C61#38611yescharacteristic
369C22×C61C2×C4×D411yescharacteristic
370C22×C61C2×#12011yescharacteristic
371C22×C61C2×#12111yescharacteristic
372C2×D61—28no—
373C2×D61—48no—
374C2×D61—48no—
375C2×D61—48no—
376C2×D61—84no—
377C2×D61—84no—
378C2×D61—84no—
379C2×D61—84no—
380C4×C61—44no—
381C4×C61—42no—
382C4×C61—82no—
383C4×C61#38611yescharacteristic
384C4×C61#38611yescharacteristic
385C4×C61#38611yescharacteristic
386C4×C61#38611yescharacteristic
387C4×C61C22×C22⋊C411yescharacteristic
388C4×C61C2×C4×D411yescharacteristic
389C4×C61C2×#12111yescharacteristic
390C4×C61C2×#12311yescharacteristic
391Dic61—44no—
392C22×AGL(1,ℤ/8)—611no—
393C2×#518—611no—
394C2×#421—611no—
395C2×#418—611no—
396C2×#410D6111yescharacteristic, complemented
397#1904—618no—
398C2×#344—611no—
399C2×H(3,ℤ/4)—611no—
400C2×C61—21no—
401C2×C61—21no—
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—82no—
407C2×C61#190412yescomplemented
408C2×C61C2×#38611yescharacteristic
409D61—48no—
410C22×#41C2×D6111yescharacteristic
411C23×D4—611no—
412C2×AGL(1,ℤ/8)—614no—
413C2×AGL(1,ℤ/8)—614no—
414C2×AGL(1,ℤ/8)—1222no—
415C2×AGL(1,ℤ/8)—1222no—
416C2×AGL(1,ℤ/8)—1222no—
417C2×AGL(1,ℤ/8)—1222no—
418C22×SD16—612no—
419C22×D8—612no—
420C22×M16—611no—
421C22×M16—611no—
422#518—614no—
423#518—1222no—
424#518—1222no—
425#518—1222no—
426C2×C4×D4—1222no—
427C2×C4×D4—1222no—
428C2×#117—611no—
429C2×#117C2×D6111yescharacteristic
430C2×#117C2×D6111yescharacteristic
431C22×C22⋊C4—1222no—
432#421—614no—
433#421—1222no—
434C2×#104—1222no—
435#418—614no—
436#418—1222no—
437C2×#102—1222no—
438#410—22no—
439#410C2×D6114yescomplemented
440C2×#99—22no—
441#344—614no—
442H(3,ℤ/4)—614no—
443C61C2×#190411yescharacteristic, complemented, Sylow
444C25—1221no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41C4×D6112yescomplemented
456C2×#41C22×D6112yes—
457C22×Q8C4×D6111yescharacteristic, complemented
458C22×D4—21no—
459C22×D4—612no—
460C22×D4—612no—
461C22×D4—612no—
462C22×D4—612no—
463C22×D4—612no—
464C22×D4—612no—
465C22×D4—612no—
466C22×D4—1221no—
467C22×D4—1221no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4C4×D6111yescharacteristic, complemented
474C23×C4—21no—
475C23×C4—1224no—
476C23×C4C22×D6111yescharacteristic
477AGL(1,ℤ/8)—1228no—
478AGL(1,ℤ/8)—1228no—
479AGL(1,ℤ/8)—1228no—
480AGL(1,ℤ/8)—1228no—
481C2×SD16—618no—
482C2×SD16—1224no—
483C2×SD16—1224no—
484C2×D8—618no—
485C2×D8—1224no—
486C2×D8—1224no—
487C2×M16—612no—
488C2×M16—612no—
489C2×M16—612no—
490C2×M16—1221no—
491C2×M16—1221no—
492C2×M16—1221no—
493C2×M16—1221no—
494C2×M16—1221no—
495C2×M16—1221no—
496C2×M16—1221no—
497C2×M16—1221no—
498C2×M16—1221no—
499C22×C8—612no—
500C22×C8—1221no—
501C4×D4—1228no—
502C4×D4—1228no—
503C4×D4—1228no—
504C4×D4—1228no—
505#117—21no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—612no—
511#117—612no—
512#117—1221no—
513#117—1221no—
514#117C22⋊D6112yes—
515#117C22×D6112yes—
516#117C22×D6112yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—1221no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—1228no—
522C2×C22⋊C4—1224no—
523C2×C22⋊C4—1221no—
524C2×C22⋊C4—1228no—
525C2×C22⋊C4C22⋊D6112yes—
526C2×C42—21no—
527C2×C42—21no—
528C2×C42—612no—
529#104—1228no—
530#102—1228no—
531#99—28no—
532C24—21no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—4884no—
541C24C2×C22⋊D6111yescharacteristic
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8C2×C4×D6112yescomplemented
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—614no—
576C2×D4—614no—
577C2×D4—614no—
578C2×D4—614no—
579C2×D4—614no—
580C2×D4—614no—
581C2×D4—614no—
582C2×D4—1222no—
583C2×D4—1222no—
584C2×D4—1222no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1222no—
590C2×D4—1222no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4C2×C4×D6112yescomplemented
604C22×C4—21no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—12216no—
614C22×C4—1222no—
615C22×C4—4888no—
616C22×C4C2×C4×D6111yescharacteristic
617C22×C4C2×C4×D6111yescharacteristic
618C22×C4#1175822211yescharacteristic
619C22×C4#1175822211yescharacteristic
620C22×C4D4×D6111yescharacteristic
621C22×C4D4×D6111yescharacteristic
622C22×C4D4×D6111yescharacteristic
623C22×C4D4×D6111yescharacteristic
624C22×C4D4×D6111yescharacteristic
625C22×C4D4×D6111yescharacteristic
626C22×C4#1175822411yescharacteristic
627C22×C4#1175822411yescharacteristic
628C22×C4C2×C22⋊D6111yescharacteristic
629C22×C4C23×D6111yescharacteristic
630SD16—12216no—
631D8—12216no—
632M16—1222no—
633M16—1222no—
634M16—1222no—
635M16—1222no—
636M16—1222no—
637M16—1222no—
638M16—2441no—
639M16—2441no—
640C2×C8—614no—
641C2×C8—1222no—
642C2×C8—1222no—
643C2×C8—1222no—
644C2×C8—2441no—
645C2×C8—2441no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—1222no—
651C4⋊C4—1222no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—41no—
655C22⋊C4—12216no—
656C22⋊C4—1222no—
657C22⋊C4—1222no—
658C22⋊C4C2×C22⋊D6114yes—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—41no—
663C42—614no—
664C42—1222no—
665C23—22no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—82no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1224no—
677C23—4884no—
678C23—4884no—
679C23—4884no—
680C23—4884no—
681C23—4884no—
682C23—4884no—
683C23—2448no—
684C23C4×C22⋊D6111yescharacteristic
685C23C4×C22⋊D6111yescharacteristic
686C23#1451974511yescharacteristic
687C23#1451974511yescharacteristic
688C23#1451974811yescharacteristic
689C23#1451974811yescharacteristic
690C23C22×C22⋊D6111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—22no—
696D4—22no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—41no—
702D4—41no—
703D4—618no—
704D4—1224no—
705D4—1224no—
706D4—1224no—
707D4—1224no—
708D4—1224no—
709D4—1224no—
710D4—1224no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—44no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—82no—
722C2×C4—1224no—
723C2×C4—48816no—
724C2×C4—2444no—
725C2×C4C22⋊C4×D6111yescharacteristic
726C2×C4C22⋊C4×D6111yescharacteristic
727C2×C4C22⋊C4×D6111yescharacteristic
728C2×C4C22⋊C4×D6111yescharacteristic
729C2×C4#1451973711yescharacteristic
730C2×C4#1451973711yescharacteristic
731C2×C4#1451973711yescharacteristic
732C2×C4#1451973711yescharacteristic
733C2×C4C4×C22⋊D6111yescharacteristic
734C2×C4C4×C22⋊D6111yescharacteristic
735C2×C4#1451974511yescharacteristic
736C2×C4#1451974511yescharacteristic
737C2×C4#1451974811yescharacteristic
738C2×C4#1451974811yescharacteristic
739C2×C4#1451975011yescharacteristic
740C2×C4#1451975011yescharacteristic
741C2×C4#1451975011yescharacteristic
742C2×C4#1451975011yescharacteristic
743C2×C4#1451975911yescharacteristic
744C2×C4#1451975911yescharacteristic
745C2×C4#1451975911yescharacteristic
746C2×C4#1451975911yescharacteristic
747C2×C4C22×C4×D6111yescharacteristic
748C2×C4C2×D4×D6111yescharacteristic
749C2×C4C2×D4×D6111yescharacteristic
750C2×C4C2×D4×D6111yescharacteristic
751C2×C4C2×#1175822411yescharacteristic
752C2×C4C2×#1175822211yescharacteristic
753C8—1224no—
754C8—2442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—1228no—
767C22—4884no—
768C22—4884no—
769C22—4884no—
770C22—4884no—
771C22—2448no—
772C22—2448no—
773C22—2448no—
774C22#1683963811yescharacteristic
775C22#1683963811yescharacteristic
776C22#1683963811yescharacteristic
777C22#1683963811yescharacteristic
778C22C2×C4×C22⋊D6111yescharacteristic
779C22C2×#1451974511yescharacteristic
780C22C2×#1451974811yescharacteristic
781C4—44no—
782C4—42no—
783C4—82no—
784C4—2444no—
785C4#1683963811yescharacteristic
786C4#1683963811yescharacteristic
787C4#1683963811yescharacteristic
788C4#1683963811yescharacteristic
789C4C2×C22⋊C4×D6111yescharacteristic
790C4C2×#1451973711yescharacteristic
791C4C2×#1451975011yescharacteristic
792C4C2×#1451975911yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—82no—
800C2—2448no—
801C2#2144630912yesdirect product factor
802C2C2×#1683963811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#410C2
socleC22×C61#386
prime radicalC22×#14519802C2
cosocleC22×C4×C61C24
hypercenterC2×#410D61
hypocenterC61C2×#1904
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#16840236C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839766C2semidirect
5. #21446309C2direct (N × H)
6. C2×#16839532C2semidirect
7. C2×#16839518C2semidirect
8. C2×C61×#410C2semidirect
14. C2×#14519802C4semidirect
16. C22×#11758201C4semidirect
17. C22×#11758199C4semidirect
23. #16840236C22semidirect
29. #16839779C22semidirect
32. #16839766C22semidirect
34. #16839532C22semidirect
35. #16839518C22semidirect
40. C61×#410C22semidirect
64. C2×#11758201C2×C4semidirect
67. C2×#11758199C2×C4semidirect
77. C2×#11758194C2×C4semidirect
81. C22×#92418C2×C4semidirect
108. C2×#41×C61C2×C4semidirect
110. C22×Q8×C61C2×C4semidirect
112. C22×D4×C61C2×C4semidirect
161. C2×Q8×C61C22×C4semidirect
173. C2×D4×C61C22×C4semidirect
262. C2×#92418C22×C4semidirect
396. C2×#410D61semidirect
407. C2×C61#1904semidirect
439. #410C2×D61semidirect
443. C61C2×#1904semidirect
455. C2×#41C4×D61semidirect
457. C22×Q8C4×D61semidirect
473. C22×D4C4×D61semidirect
563. C2×Q8C2×C4×D61semidirect
603. C2×D4C2×C4×D61semidirect
801. C2#21446309direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168402362
C2×#168397792
C2×#168397662
#214463092
C2×#168395322
C2×#168395182
C2×C61×#4102
C2×#190461