Finite Group Databasebeta

← C2×#21445791 #29679351

Subgroups — C2×#21445791 #29679351

Order 15616.

3602 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic
2C2×#16839780C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839771C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6C2×#16839735C211yesmaximal, characteristic, complemented
7#21445791C218yesmaximal, direct product factor
8C2×C61×#419C211yesmaximal, characteristic, complemented
9C2×#14519825—22no—
10C2×#14519825—22no—
11C2×#14519825—22no—
12C2×#14519825—22no—
13C2×#14519825—22no—
14C2×#14519825—22no—
15C2×#14519825—22no—
16C2×#14519825—22no—
17C2×#14519825—22no—
18C2×#14519825—22no—
19C2×#14519825C414yescomplemented
20C2×#14519825C2214yes—
21C22×#11758226—21no—
22C22×#11758226C412yescomplemented
23C22×#11758222—22no—
24C22×#11758222C2211yescharacteristic
25C22×#11758222C2211yescharacteristic
26C22×Q8×D61—21no—
27C22×Q8×D61C412yescomplemented
28C22×#11758194C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839780—22no—
31#16839780C2214yescomplemented
32#16839778—22no—
33#16839778C2214yescomplemented
34C2×#14519705—22no—
35C2×#14519703—22no—
36#16839771—22no—
37#16839771C2214yescomplemented
38C2×#14519701—22no—
39#16839744—22no—
40#16839744C2214yescomplemented
41C2×#14519695—21no—
42C2×#14519693—21no—
43#16839735—22no—
44#16839735C2214yescomplemented
45C2×#14519691—22no—
46C23×Q8×C61C2211yescharacteristic
47C22×M16×C61C2211yescharacteristic
48C2×#117×C61C2211yescharacteristic
49C61×#419—22no—
50C61×#419C2214yescomplemented
51C2×#103×C61—22no—
52#14519825—28no—
53#14519825—28no—
54#14519825—28no—
55#14519825—28no—
56#14519825—28no—
57#14519825—28no—
58#14519825—28no—
59#14519825—28no—
60#14519825—28no—
61#14519825—28no—
62#14519825—28no—
63#14519825—28no—
64#14519825—28no—
65#14519825—28no—
66#14519825—28no—
67#14519825—28no—
68C2×#11758226—24no—
69C2×#11758226—24no—
70C2×#11758226—24no—
71C2×#11758226—24no—
72C2×#11758226—24no—
73C2×#11758226—24no—
74C2×#11758226—24no—
75C2×#11758226—24no—
76C2×#11758226—24no—
77C2×#11758226—24no—
78C2×#11758226—24no—
79C2×#11758226C2×C418yescomplemented
80C2×#11758222—28no—
81C2×#11758222—28no—
82C2×#11758222—28no—
83C2×#11758222—28no—
84C2×#11758222—21no—
85C2×#11758222—21no—
86C2×#11758222—21no—
87C2×#11758222—21no—
88C2×#11758222—21no—
89C2×#11758222—21no—
90C2×#11758222—21no—
91C2×#11758222—21no—
92C2×#11758222—21no—
93C2×#11758222—21no—
94C2×#11758222—21no—
95C2×#11758222—21no—
96C2×#11758222—21no—
97C2×#11758222—21no—
98C2×#11758222—28no—
99C2×#11758222—28no—
100C2×#11758222C2×C412yes—
101C2×#11758222C2×C412yes—
102C2×#11758222D412yes—
103C2×#11758222D412yes—
104C2×#11758222D412yes—
105C2×#11758222D412yes—
106C2×#11758222D412yes—
107C2×#11758222D412yes—
108C2×#11758222C2312yes—
109C2×#11758222C2312yes—
110C22×Dic122—22no—
111C22×Dic122C2×C411yescharacteristic
112C22×Dic122D411yescharacteristic
113C2×Q8×D61—24no—
114C2×Q8×D61—24no—
115C2×Q8×D61—24no—
116C2×Q8×D61—24no—
117C2×Q8×D61—24no—
118C2×Q8×D61—24no—
119C2×Q8×D61—24no—
120C2×Q8×D61—24no—
121C2×Q8×D61—24no—
122C2×Q8×D61—24no—
123C2×Q8×D61—24no—
124C2×Q8×D61C2×C418yescomplemented
125C22×D244—22no—
126C22×D244C2×C411yescharacteristic
127C22×D244D411yescharacteristic
128C22×C22⋊D61—21no—
129C22×C22⋊D61D412yes—
130C22×C4×D61—22no—
131C22×C4×D61—21no—
132C22×C4×D61—22no—
133C22×C4×D61C2×C412yes—
134C2×#11758194—21no—
135C2×#11758194—21no—
136C2×#11758194—21no—
137C2×#11758194—21no—
138C2×#11758194—21no—
139C2×#11758194C2312yes—
140C22×#92418—21no—
141#14519736—21no—
142#14519736—21no—
143#14519736—21no—
144#14519736C2312yes—
145C2×C4⋊Dic61—21no—
146C2×C22⋊Dic61—21no—
147C2×C4×Dic61—21no—
148#14519705—28no—
149#14519703—28no—
150#14519701—28no—
151#14519695—24no—
152#14519693—24no—
153#14519691—28no—
154C22×Q8×C61—21no—
155C22×Q8×C61—21no—
156C22×Q8×C61—21no—
157C22×Q8×C61—21no—
158C22×Q8×C61—21no—
159C22×Q8×C61—21no—
160C22×Q8×C61—21no—
161C22×Q8×C61C2×C412yes—
162C22×Q8×C61C2×C412yes—
163C22×Q8×C61D412yes—
164C22×Q8×C61D412yes—
165C22×Q8×C61D412yes—
166C22×Q8×C61D412yes—
167C22×Q8×C61C2312yes—
168C23×C4×C61—21no—
169C23×C4×C61C2311yescharacteristic
170C2×M16×C61—21no—
171C2×M16×C61—21no—
172C2×M16×C61—21no—
173C2×M16×C61—21no—
174C2×M16×C61—21no—
175C2×M16×C61C2312yes—
176C22×C8×C61—21no—
177#117×C61—21no—
178#117×C61—21no—
179#117×C61—21no—
180#117×C61C2312yes—
181C2×C4⋊C4×C61—21no—
182C2×C22⋊C4×C61—21no—
183C2×C42×C61—21no—
184#103×C61—28no—
185C24×C61C2×D411yescharacteristic
186C23×D61—21no—
187C23×D61C22⋊C412yes—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—22no—
191C2×Q8×C61—22no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—22no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61—22no—
204C2×Q8×C61—22no—
205C2×Q8×C61—22no—
206C2×Q8×C61—22no—
207C2×Q8×C61—22no—
208C2×Q8×C61—22no—
209C2×Q8×C61C22⋊C414yes—
210C2×Q8×C61C22⋊C414yes—
211C2×Q8×C61C22⋊C414yes—
212C2×Q8×C61C22⋊C414yes—
213C2×Q8×C61C22×C414yes—
214C2×Q8×C61C2×D414yes—
215C2×Q8×C61C2×D414yes—
216C22×C4×C61—22no—
217C22×C4×C61—22no—
218C22×C4×C61—22no—
219C22×C4×C61—22no—
220C22×C4×C61—22no—
221C22×C4×C61—22no—
222C22×C4×C61—22no—
223C22×C4×C61—41no—
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2411yescharacteristic
238C2×C22⋊D61—22no—
239C2×C22⋊D61—22no—
240C2×C22⋊D61—22no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—22no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248C2×C22⋊D61C22⋊C414yes—
249C2×C22⋊D61C2×D414yes—
250C22×Dic61—21no—
251C22×Dic61—41no—
252C22×Dic61C22⋊C412yes—
253#11758226—216no—
254#11758226—216no—
255#11758226—216no—
256#11758226—216no—
257#11758226—216no—
258#11758226—216no—
259#11758226—216no—
260#11758226—216no—
261Q8×D61—216no—
262Q8×D61—216no—
263Q8×D61—216no—
264Q8×D61—216no—
265Q8×D61—216no—
266Q8×D61—216no—
267Q8×D61—216no—
268Q8×D61—216no—
269#11758222—232no—
270#11758222—232no—
271#11758222—232no—
272#11758222—232no—
273#11758222—22no—
274#11758222—22no—
275#11758222—22no—
276#11758222—22no—
277#11758222—22no—
278#11758222—22no—
279#11758222—22no—
280#11758222—22no—
281#11758222—22no—
282#11758222—22no—
283#11758222—22no—
284#11758222—22no—
285#11758222—22no—
286#11758222—22no—
287#11758222—22no—
288#11758222—22no—
289#11758222—22no—
290#11758222—22no—
291#11758222—22no—
292#11758222—22no—
293#11758222—22no—
294#11758222—22no—
295#11758222—22no—
296#11758222—22no—
297#11758222—22no—
298#11758222—22no—
299#11758222—22no—
300#11758222—22no—
301#11758222C22⋊C414yes—
302#11758222C22⋊C414yes—
303#11758222C2×D414yes—
304#11758222C2×D414yes—
305C2×D244—28no—
306C2×D244—28no—
307C2×D244—28no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—21no—
311C2×D244—21no—
312C2×D244—21no—
313C2×D244—21no—
314C2×D244—21no—
315C2×D244C22⋊C412yes—
316C2×D244C22⋊C412yes—
317C2×D244C22⋊C412yes—
318C2×D244C22×C412yes—
319C2×D244C2×D412yes—
320C2×C4×D61—28no—
321C2×C4×D61—28no—
322C2×C4×D61—28no—
323C2×C4×D61—28no—
324C2×C4×D61—28no—
325C2×C4×D61—22no—
326C2×C4×D61—22no—
327C2×C4×D61—22no—
328C2×C4×D61—22no—
329C2×C4×D61—22no—
330C2×C4×D61—22no—
331C2×C4×D61—22no—
332C2×C4×D61—22no—
333C2×C4×D61—22no—
334C2×C4×D61—22no—
335C2×C4×D61—28no—
336C2×C4×D61C22⋊C414yes—
337C2×C4×D61C22×C414yes—
338C2×Dic122—28no—
339C2×Dic122—28no—
340C2×Dic122—21no—
341C2×Dic122—21no—
342C2×Dic122—21no—
343C2×Dic122—21no—
344C2×Dic122—21no—
345C2×Dic122—21no—
346C2×Dic122—21no—
347C2×Dic122—28no—
348C2×Dic122C22⋊C412yes—
349C2×Dic122C22⋊C412yes—
350C2×Dic122C22⋊C412yes—
351C2×Dic122C22×C412yes—
352C2×Dic122C2×D412yes—
353M16×C61—22no—
354M16×C61—22no—
355M16×C61—41no—
356M16×C61—41no—
357C2×C8×C61—22no—
358C2×C8×C61—41no—
359C2×C8×C61—41no—
360C4⋊C4×C61—22no—
361C4⋊C4×C61—41no—
362C22⋊C4×C61—22no—
363C22⋊C4×C61—41no—
364C42×C61—22no—
365C42×C61—41no—
366C22⋊Dic61—22no—
367C22⋊Dic61—41no—
368C4⋊Dic61—22no—
369C4⋊Dic61—41no—
370C4×Dic61—22no—
371C4×Dic61—41no—
372#11758194—22no—
373#11758194—22no—
374#11758194—41no—
375#11758194—41no—
376C2×#92418—22no—
377C2×#92418—41no—
378C2×#92418—41no—
379C23×C61—42no—
380C23×C61C2×C22⋊C411yescharacteristic
381C23×C61C2×C22⋊C411yescharacteristic
382C23×C61#12011yescharacteristic
383C23×C61#12011yescharacteristic
384C23×C61#12011yescharacteristic
385C23×C61#12011yescharacteristic
386C23×C61C22×D411yescharacteristic
387C22×D61—22no—
388C22×D61—22no—
389C22×D61—22no—
390C22×D61—22no—
391C22×D61—22no—
392C22×D61—44no—
393C22×D61—44no—
394C22×D61C2×C22⋊C414yes—
395Q8×C61—24no—
396Q8×C61—24no—
397Q8×C61—24no—
398Q8×C61—24no—
399Q8×C61—24no—
400Q8×C61—24no—
401Q8×C61—24no—
402Q8×C61C2×C22⋊C418yes—
403C2×C4×C61—24no—
404C2×C4×C61—24no—
405C2×C4×C61—24no—
406C2×C4×C61—24no—
407C2×C4×C61—24no—
408C2×C4×C61—24no—
409C2×C4×C61—24no—
410C2×C4×C61—42no—
411C2×C4×C61—82no—
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C2×C22⋊C411yescharacteristic
417C2×C4×C61C2×C22⋊C411yescharacteristic
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61#12011yescharacteristic
423C2×C4×C61#12011yescharacteristic
424C2×C4×C61#12011yescharacteristic
425C2×C4×C61#12011yescharacteristic
426C2×C4×C61#12011yescharacteristic
427C2×C4×C61#12011yescharacteristic
428C2×C4×C61#12011yescharacteristic
429C2×C4×C61#12011yescharacteristic
430C2×C4×C61#12011yescharacteristic
431C2×C4×C61#12011yescharacteristic
432C2×C4×C61#12011yescharacteristic
433C2×C4×C61#12011yescharacteristic
434C2×C4×C61C23×C411yescharacteristic
435C2×C4×C61C22×D411yescharacteristic
436C2×C4×C61C22×D411yescharacteristic
437C2×C4×C61C22×D411yescharacteristic
438C2×C4×C61C22×D411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C22⋊D61—24no—
441C22⋊D61—24no—
442C22⋊D61—24no—
443C22⋊D61—24no—
444C22⋊D61—24no—
445C22⋊D61—24no—
446C22⋊D61—24no—
447C22⋊D61—24no—
448C2×Dic61—22no—
449C2×Dic61—22no—
450C2×Dic61—22no—
451C2×Dic61—22no—
452C2×Dic61—22no—
453C2×Dic61—42no—
454C2×Dic61—82no—
455C2×Dic61C2×C22⋊C414yes—
456D244—232no—
457D244—22no—
458D244—22no—
459D244—22no—
460D244—22no—
461D244—22no—
462D244—22no—
463D244—22no—
464D244C2×C22⋊C414yes—
465C4×D61—232no—
466C4×D61—232no—
467C4×D61—24no—
468C4×D61—24no—
469C4×D61—24no—
470C4×D61—24no—
471C4×D61—24no—
472C4×D61—24no—
473C4×D61—24no—
474C4×D61—24no—
475Dic122—232no—
476Dic122—22no—
477Dic122—22no—
478Dic122—22no—
479Dic122—22no—
480Dic122—22no—
481Dic122—22no—
482Dic122—22no—
483Dic122C2×C22⋊C414yes—
484C8×C61—42no—
485#92418—42no—
486C2×#1796—611nomaximal, Sylow
487C22×C61—22no—
488C22×C61—22no—
489C22×C61—22no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61#37911yescharacteristic
495C22×C61#37911yescharacteristic
496C22×C61#37911yescharacteristic
497C22×C61#37911yescharacteristic
498C22×C61C22×C22⋊C411yescharacteristic
499C22×C61C2×#12011yescharacteristic
500C22×C61C2×#12011yescharacteristic
501C2×D61—24no—
502C2×D61—24no—
503C2×D61—44no—
504C2×D61—44no—
505C2×D61—44no—
506C2×D61—44no—
507C2×D61—44no—
508C2×D61—44no—
509C4×C61—28no—
510C4×C61—82no—
511C4×C61#37911yescharacteristic
512C4×C61#37911yescharacteristic
513C4×C61#37911yescharacteristic
514C4×C61#37911yescharacteristic
515C4×C61C22×C22⋊C411yescharacteristic
516C4×C61C22×C22⋊C411yescharacteristic
517C4×C61C2×#12011yescharacteristic
518C4×C61C2×#12011yescharacteristic
519Dic61—24no—
520Dic61—24no—
521Dic61—82no—
522C22×2−1+4—611no—
523C2×#421—611no—
524C2×#421—611no—
525C2×#419—611no—
526C2×#419D6111yescharacteristic, complemented
527C2×#413—611no—
528C2×#410—611no—
529#1796—618no—
530C2×C61—21no—
531C2×C61—21no—
532C2×C61—21no—
533C2×C61—21no—
534C2×C61—21no—
535C2×C61—21no—
536C2×C61#179612yescomplemented
537C2×C61C2×#37911yescharacteristic
538D61—44no—
539D61—44no—
540C2×2−1+4—614no—
541C2×2−1+4—614no—
542C2×2−1+4—1222no—
543C2×2−1+4—1222no—
544C2×2−1+4—1222no—
545C2×2−1+4—1222no—
546C2×2−1+4—1222no—
547C2×2−1+4—1222no—
548C2×2−1+4—1222no—
549C2×2−1+4—1222no—
550C2×2−1+4—1222no—
551C2×2−1+4—1222no—
552C22×#41—611no—
553C22×#41—612no—
554C22×#41—611no—
555C22×#41—1222no—
556C22×#41—1221no—
557C23×Q8—612no—
558C23×Q8—1221no—
559C23×Q8C2×D6111yescharacteristic
560C22×M16—611no—
561C22×M16C2×D6111yescharacteristic
562C2×#117—611no—
563C2×#117C2×D6111yescharacteristic
564#421—614no—
565#421—614no—
566#421—1222no—
567#421—1222no—
568C2×#104—1222no—
569C2×#104—1222no—
570#419—22no—
571#419—614no—
572#419—1222no—
573#419C2×D6114yescomplemented
574C2×#103—22no—
575C2×#103—1222no—
576#413—614no—
577#413—1222no—
578C2×#101—1221no—
579C2×#100—1221no—
580#410—614no—
581#410—1222no—
582C2×#99—1222no—
583C61C2×#179611yescharacteristic, complemented, Sylow
5842−1+4—1228no—
5852−1+4—1228no—
5862−1+4—1228no—
5872−1+4—1228no—
5882−1+4—1228no—
5892−1+4—1228no—
5902−1+4—1228no—
5912−1+4—1228no—
5922−1+4—1228no—
5932−1+4—1228no—
5942−1+4—1228no—
5952−1+4—1228no—
5962−1+4—1228no—
5972−1+4—1228no—
5982−1+4—1228no—
5992−1+4—1228no—
600C2×#41—612no—
601C2×#41—612no—
602C2×#41—612no—
603C2×#41—612no—
604C2×#41—618no—
605C2×#41—612no—
606C2×#41—612no—
607C2×#41—612no—
608C2×#41—612no—
609C2×#41—612no—
610C2×#41—612no—
611C2×#41—1228no—
612C2×#41—1228no—
613C2×#41—1228no—
614C2×#41—1228no—
615C2×#41—1228no—
616C2×#41—1228no—
617C2×#41—1224no—
618C2×#41—1224no—
619C2×#41—1224no—
620C2×#41—1224no—
621C2×#41—1224no—
622C2×#41—1224no—
623C2×#41—1224no—
624C2×#41—1224no—
625C2×#41—1224no—
626C2×#41—1224no—
627C2×#41—1224no—
628C2×#41—1221no—
629C2×#41—1221no—
630C2×#41—1221no—
631C2×#41—1221no—
632C2×#41—1221no—
633C2×#41—1221no—
634C2×#41—1221no—
635C2×#41—1221no—
636C2×#41—1221no—
637C2×#41—1221no—
638C2×#41—1221no—
639C2×#41—1221no—
640C2×#41—1221no—
641C2×#41—1221no—
642C22×Q8—21no—
643C22×Q8—21no—
644C22×Q8—21no—
645C22×Q8—21no—
646C22×Q8—21no—
647C22×Q8—21no—
648C22×Q8—21no—
649C22×Q8—611no—
650C22×Q8—618no—
651C22×Q8—611no—
652C22×Q8—1222no—
653C22×Q8—1224no—
654C22×Q8—1224no—
655C22×Q8—1224no—
656C22×Q8—1224no—
657C22×Q8—1224no—
658C22×Q8—1224no—
659C22×Q8—1224no—
660C22×Q8—1224no—
661C22×Q8—1224no—
662C22×Q8—1224no—
663C22×Q8—1224no—
664C22×Q8C4×D6112yes—
665C22×Q8C4×D6112yes—
666C22×Q8D24412yes—
667C22×Q8D24412yes—
668C22×Q8C22⋊D6112yes—
669C22×Q8C22⋊D6112yes—
670C22×Q8C22×D6112yes—
671C22×D4—612no—
672C22×D4—611no—
673C22×D4—611no—
674C22×D4—1222no—
675C22×D4—1221no—
676C23×C4—21no—
677C23×C4—612no—
678C23×C4—1222no—
679C23×C4—1222no—
680C23×C4—1221no—
681C23×C4C22×D6111yescharacteristic
682C2×M16—21no—
683C2×M16—21no—
684C2×M16—21no—
685C2×M16—21no—
686C2×M16—21no—
687C2×M16—612no—
688C2×M16—1221no—
689C2×M16—1221no—
690C2×M16—1221no—
691C2×M16—1221no—
692C2×M16—1221no—
693C2×M16C22×D6112yes—
694C22×C8—21no—
695C22×C8—1221no—
696#117—21no—
697#117—21no—
698#117—21no—
699#117—612no—
700#117—1221no—
701#117—1221no—
702#117—1221no—
703#117C22×D6112yes—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—1221no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—1221no—
708C2×C42—21no—
709C2×C42—1221no—
710#104—1228no—
711#104—1228no—
712#103—28no—
713#103—1228no—
714#101—1224no—
715#100—1224no—
716#99—1228no—
717C24—612no—
718C24—1221no—
719C24D4×D6111yescharacteristic
720#41—614no—
721#41—614no—
722#41—614no—
723#41—614no—
724#41—12232no—
725#41—12232no—
726#41—12232no—
727#41—12232no—
728#41—12216no—
729#41—12216no—
730#41—12216no—
731#41—12216no—
732#41—12216no—
733#41—12216no—
734#41—12216no—
735#41—12216no—
736#41—1222no—
737#41—1222no—
738#41—1222no—
739#41—1222no—
740#41—1222no—
741#41—1222no—
742#41—1222no—
743#41—1222no—
744#41—1222no—
745#41—1222no—
746#41—1222no—
747#41—1222no—
748#41—1222no—
749#41—1222no—
750#41—1222no—
751#41—1222no—
752#41—1222no—
753#41—1222no—
754#41—1222no—
755#41—1222no—
756#41—1222no—
757#41—1222no—
758#41—1222no—
759#41—1222no—
760#41—1222no—
761#41—1222no—
762#41—1222no—
763#41—1222no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—22no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—612no—
786C2×Q8—612no—
787C2×Q8—612no—
788C2×Q8—612no—
789C2×Q8—612no—
790C2×Q8—1228no—
791C2×Q8—1228no—
792C2×Q8—1228no—
793C2×Q8—12216no—
794C2×Q8—12216no—
795C2×Q8—12216no—
796C2×Q8—12216no—
797C2×Q8—12216no—
798C2×Q8—12216no—
799C2×Q8—12216no—
800C2×Q8—12216no—
801C2×Q8—1221no—
802C2×Q8—1221no—
803C2×Q8—1221no—
804C2×Q8—1221no—
805C2×Q8—1221no—
806C2×Q8—1221no—
807C2×Q8—1221no—
808C2×Q8#1175819814yes—
809C2×Q8#1175819814yes—
810C2×Q8#1175819814yes—
811C2×Q8#1175819814yes—
812C2×Q8C2×C4×D6114yes—
813C2×Q8C2×D24414yes—
814C2×Q8C2×C22⋊D6114yes—
815C2×D4—614no—
816C2×D4—614no—
817C2×D4—612no—
818C2×D4—612no—
819C2×D4—612no—
820C2×D4—612no—
821C2×D4—612no—
822C2×D4—1228no—
823C2×D4—1228no—
824C2×D4—1228no—
825C2×D4—1222no—
826C2×D4—1222no—
827C2×D4—1222no—
828C2×D4—1222no—
829C2×D4—1222no—
830C2×D4—1222no—
831C2×D4—1222no—
832C2×D4—1222no—
833C2×D4—1222no—
834C2×D4—1222no—
835C2×D4—1221no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—1221no—
841C2×D4—1221no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—41no—
850C22×C4—612no—
851C22×C4—614no—
852C22×C4—614no—
853C22×C4—1228no—
854C22×C4—1228no—
855C22×C4—1228no—
856C22×C4—1228no—
857C22×C4—1228no—
858C22×C4—1228no—
859C22×C4—1221no—
860C22×C4—1222no—
861C22×C4—1222no—
862C22×C4—1222no—
863C22×C4—1222no—
864C22×C4—1222no—
865C22×C4—1222no—
866C22×C4—1222no—
867C22×C4—1222no—
868C22×C4—1222no—
869C22×C4—1222no—
870C22×C4—2441no—
871C22×C4C2×C4×D6111yescharacteristic
872C22×C4C2×C4×D6111yescharacteristic
873C22×C4C2×D24411yescharacteristic
874C22×C4C2×D24411yescharacteristic
875C22×C4D4×D6111yescharacteristic
876C22×C4D4×D6111yescharacteristic
877C22×C4D4×D6111yescharacteristic
878C22×C4D4×D6111yescharacteristic
879C22×C4D4×D6111yescharacteristic
880C22×C4D4×D6111yescharacteristic
881C22×C4D4×D6111yescharacteristic
882C22×C4C2×C22⋊D6111yescharacteristic
883C22×C4C2×C22⋊D6111yescharacteristic
884C22×C4C23×D6111yescharacteristic
885M16—22no—
886M16—22no—
887M16—41no—
888M16—41no—
889M16—1222no—
890M16—1222no—
891M16—2441no—
892M16—2441no—
893C2×C8—22no—
894C2×C8—41no—
895C2×C8—41no—
896C2×C8—1222no—
897C2×C8—2441no—
898C2×C8—2441no—
899C4⋊C4—22no—
900C4⋊C4—41no—
901C4⋊C4—1222no—
902C4⋊C4—2441no—
903C22⋊C4—22no—
904C22⋊C4—41no—
905C22⋊C4—1222no—
906C22⋊C4—2441no—
907C42—22no—
908C42—41no—
909C42—1222no—
910C42—2441no—
911C23—42no—
912C23—614no—
913C23—1222no—
914C23—1222no—
915C23—1222no—
916C23—1222no—
917C23—1222no—
918C23—2444no—
919C23—2444no—
920C23C22⋊C4×D6111yescharacteristic
921C23C22⋊C4×D6111yescharacteristic
922C23#1451974511yescharacteristic
923C23#1451974511yescharacteristic
924C23#1451974711yescharacteristic
925C23#1451974711yescharacteristic
926C23C2×D4×D6111yescharacteristic
927Q8—24no—
928Q8—24no—
929Q8—24no—
930Q8—24no—
931Q8—24no—
932Q8—24no—
933Q8—24no—
934Q8—614no—
935Q8—12232no—
936Q8—1222no—
937Q8—1222no—
938Q8—1222no—
939Q8—1222no—
940Q8—1222no—
941Q8—1222no—
942Q8—1222no—
943Q8C2×#1175819818yes—
944D4—614no—
945D4—12232no—
946D4—1224no—
947D4—1224no—
948D4—1224no—
949D4—1224no—
950D4—1224no—
951D4—1224no—
952D4—1224no—
953D4—1224no—
954D4—1222no—
955D4—1222no—
956D4—1222no—
957D4—1222no—
958D4—1222no—
959D4—1222no—
960D4—1222no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—24no—
967C2×C4—24no—
968C2×C4—42no—
969C2×C4—82no—
970C2×C4—614no—
971C2×C4—12232no—
972C2×C4—12232no—
973C2×C4—1222no—
974C2×C4—1222no—
975C2×C4—1222no—
976C2×C4—1222no—
977C2×C4—1222no—
978C2×C4—1224no—
979C2×C4—1224no—
980C2×C4—1224no—
981C2×C4—1224no—
982C2×C4—1224no—
983C2×C4—1224no—
984C2×C4—1224no—
985C2×C4—1224no—
986C2×C4—4882no—
987C2×C4—2442no—
988C2×C4C22⋊C4×D6111yescharacteristic
989C2×C4C22⋊C4×D6111yescharacteristic
990C2×C4C22⋊C4×D6111yescharacteristic
991C2×C4C22⋊C4×D6111yescharacteristic
992C2×C4C22⋊C4×D6111yescharacteristic
993C2×C4C22⋊C4×D6111yescharacteristic
994C2×C4C2×#1175819811yescharacteristic
995C2×C4C2×#1175819811yescharacteristic
996C2×C4C2×#1175819811yescharacteristic
997C2×C4C2×#1175819811yescharacteristic
998C2×C4#1451974511yescharacteristic
999C2×C4#1451974511yescharacteristic
1000C2×C4#1451974511yescharacteristic
1001C2×C4#1451974511yescharacteristic
1002C2×C4#1451974511yescharacteristic
1003C2×C4#1451974511yescharacteristic
1004C2×C4#1451974711yescharacteristic
1005C2×C4#1451974711yescharacteristic
1006C2×C4#1451974711yescharacteristic
1007C2×C4#1451974711yescharacteristic
1008C2×C4#1451974711yescharacteristic
1009C2×C4#1451974711yescharacteristic
1010C2×C4C22×C4×D6111yescharacteristic
1011C2×C4C2×D4×D6111yescharacteristic
1012C2×C4C2×D4×D6111yescharacteristic
1013C2×C4C2×D4×D6111yescharacteristic
1014C2×C4C22×C22⋊D6111yescharacteristic
1015C2×C4C22×D24411yescharacteristic
1016C8—42no—
1017C8—2442no—
1018C22—22no—
1019C22—22no—
1020C22—22no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—1224no—
1026C22—1224no—
1027C22—2444no—
1028C22—2444no—
1029C22—2444no—
1030C22—2444no—
1031C22—2444no—
1032C22—2444no—
1033C22#1683961711yescharacteristic
1034C22#1683961711yescharacteristic
1035C22#1683961711yescharacteristic
1036C22#1683961711yescharacteristic
1037C22C2×C22⋊C4×D6111yescharacteristic
1038C22C2×#1451974511yescharacteristic
1039C22C2×#1451974711yescharacteristic
1040C4—28no—
1041C4—82no—
1042C4—1224no—
1043C4—1224no—
1044C4—4882no—
1045C4#1683961711yescharacteristic
1046C4#1683961711yescharacteristic
1047C4#1683961711yescharacteristic
1048C4#1683961711yescharacteristic
1049C4C2×C22⋊C4×D6111yescharacteristic
1050C4C22×#1175819811yescharacteristic
1051C4C2×#1451974511yescharacteristic
1052C4C2×#1451974711yescharacteristic
1053C2—21no—
1054C2—21no—
1055C2—21no—
1056C2—21no—
1057C2—21no—
1058C2—21no—
1059C2—2444no—
1060C2—2444no—
1061C2#2144579112yesdirect product factor
1062C2C2×#1683961711yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#419C2
socleC22×C61#379
prime radicalC22×#14519825C2
cosocleC22×C4×C61C24
hypercenterC2×#419D61
hypocenterC61C2×#1796
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×#16839780C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839771C2semidirect
5. C2×#16839744C2semidirect
6. C2×#16839735C2semidirect
7. #21445791C2direct (N × H)
8. C2×C61×#419C2semidirect
19. C2×#14519825C4semidirect
22. C22×#11758226C4semidirect
27. C22×Q8×D61C4semidirect
31. #16839780C22semidirect
33. #16839778C22semidirect
37. #16839771C22semidirect
40. #16839744C22semidirect
44. #16839735C22semidirect
50. C61×#419C22semidirect
79. C2×#11758226C2×C4semidirect
124. C2×Q8×D61C2×C4semidirect
526. C2×#419D61semidirect
536. C2×C61#1796semidirect
573. #419C2×D61semidirect
583. C61C2×#1796semidirect
1061. C2#21445791direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198252
C2×#168397802
C2×#168397782
C2×#168397712
C2×#168397442
C2×#168397352
#214457912
C2×C61×#4192
C2×#179661