Finite Group Databasebeta

← C2×#21445793 #29679353

Subgroups — C2×#21445793 #29679353

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×#14519824C211yesmaximal, characteristic
2C2×#16839779C211yesmaximal, characteristic, complemented
3C2×#16839772C211yesmaximal, characteristic, complemented
4C2×#16839770C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6C2×#16839735C211yesmaximal, characteristic, complemented
7#21445793C218yesmaximal, direct product factor
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C2×#14519824—22no—
10C2×#14519824—22no—
11C2×#14519824—22no—
12C2×#14519824—22no—
13C2×#14519824—22no—
14C2×#14519824—22no—
15C2×#14519824—22no—
16C2×#14519824—22no—
17C2×#14519824—22no—
18C2×#14519824—22no—
19C2×#14519824C414yescomplemented
20C2×#14519824C2214yes—
21C22×#11758222—21no—
22C22×#11758222C2211yescharacteristic
23C22×#11758224—22no—
24C22×#11758224C412yescomplemented
25C23×Dic122—21no—
26C23×Dic122C2211yescharacteristic
27C22×Q8×D61C412yescomplemented
28C22×#11758194C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839779—22no—
31#16839779C2214yescomplemented
32C2×#14519704—22no—
33#16839772—22no—
34#16839772C2214yescomplemented
35#16839770—22no—
36#16839770C2214yescomplemented
37C2×#14519702—22no—
38C2×#14519700—22no—
39#16839744—22no—
40#16839744C2214yescomplemented
41C2×#14519695—21no—
42C2×#14519693—21no—
43#16839735—22no—
44#16839735C2214yescomplemented
45C2×#14519691—22no—
46C22×#41×C61C2211yescharacteristic
47C22×M16×C61C2211yescharacteristic
48C2×#117×C61C2211yescharacteristic
49C61×#421—22no—
50C61×#421C2214yescomplemented
51C2×#104×C61—22no—
52#14519824—28no—
53#14519824—28no—
54#14519824—28no—
55#14519824—28no—
56#14519824—28no—
57#14519824—28no—
58#14519824—28no—
59#14519824—28no—
60#14519824—28no—
61#14519824—28no—
62#14519824—28no—
63#14519824—28no—
64#14519824—28no—
65#14519824—28no—
66#14519824—28no—
67#14519824—28no—
68C2×#11758222—24no—
69C2×#11758222—24no—
70C2×#11758222—24no—
71C2×#11758222—24no—
72C2×#11758222—21no—
73C2×#11758222—21no—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222—21no—
79C2×#11758222—21no—
80C2×#11758222—24no—
81C2×#11758222—24no—
82C2×#11758222C2×C412yes—
83C2×#11758222D412yes—
84C2×#11758222D412yes—
85C2×#11758222C2312yes—
86C2×#11758224—28no—
87C2×#11758224—28no—
88C2×#11758224—28no—
89C2×#11758224—28no—
90C2×#11758224—24no—
91C2×#11758224—24no—
92C2×#11758224—28no—
93C2×#11758224—28no—
94C2×#11758224—24no—
95C2×#11758224—24no—
96C2×#11758224—24no—
97C2×#11758224C2×C418yescomplemented
98C22×Dic122—24no—
99C22×Dic122—24no—
100C22×Dic122—24no—
101C22×Dic122—24no—
102C22×Dic122—21no—
103C22×Dic122—21no—
104C22×Dic122—21no—
105C22×Dic122—21no—
106C22×Dic122—21no—
107C22×Dic122—21no—
108C22×Dic122—21no—
109C22×Dic122—22no—
110C22×Dic122—24no—
111C22×Dic122—24no—
112C22×Dic122C2×C412yes—
113C22×Dic122C2×C412yes—
114C22×Dic122D411yescharacteristic
115C22×Dic122D412yes—
116C22×Dic122D412yes—
117C22×Dic122D412yes—
118C22×Dic122D412yes—
119C22×Dic122C2312yes—
120C2×Q8×D61—24no—
121C2×Q8×D61—24no—
122C2×Q8×D61—24no—
123C2×Q8×D61—24no—
124C2×Q8×D61—24no—
125C2×Q8×D61C2×C418yescomplemented
126C22×D244D411yescharacteristic
127C22×C22⋊D61—22no—
128C22×C22⋊D61D412yes—
129C23×Dic61—21no—
130C23×Dic61—22no—
131C22×C4×D61—22no—
132C22×C4×D61C2×C412yes—
133C2×#11758194—21no—
134C2×#11758194—21no—
135C2×#11758194—21no—
136C2×#11758194—21no—
137C2×#11758194—21no—
138C2×#11758194C2312yes—
139C22×#92418—21no—
140#14519736—21no—
141#14519736—21no—
142#14519736—21no—
143#14519736C2312yes—
144C2×C4⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C4×Dic61—21no—
147#14519704—28no—
148#14519702—28no—
149#14519700—28no—
150#14519695—24no—
151#14519693—24no—
152#14519691—28no—
153C2×#41×C61—21no—
154C2×#41×C61—21no—
155C2×#41×C61—21no—
156C2×#41×C61—21no—
157C2×#41×C61—21no—
158C2×#41×C61—21no—
159C2×#41×C61C2×C412yes—
160C2×#41×C61D412yes—
161C2×#41×C61D412yes—
162C2×#41×C61D412yes—
163C2×#41×C61D412yes—
164C2×#41×C61C2312yes—
165C22×Q8×C61C2×C411yescharacteristic
166C22×D4×C61—21no—
167C22×D4×C61C2×C411yescharacteristic
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#104×C61—28no—
185C24×C61—21no—
186C24×C61C2×D411yescharacteristic
187C23×D61C22⋊C412yes—
188#41×C61—22no—
189#41×C61—22no—
190#41×C61—22no—
191#41×C61—22no—
192#41×C61—22no—
193#41×C61—22no—
194#41×C61—22no—
195#41×C61—22no—
196#41×C61—22no—
197#41×C61—22no—
198#41×C61—22no—
199#41×C61—22no—
200#41×C61C22⋊C414yes—
201#41×C61C22⋊C414yes—
202#41×C61C2×D414yes—
203#41×C61C2×D414yes—
204C2×Q8×C61—21no—
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61C22⋊C412yes—
208C2×Q8×C61C22⋊C412yes—
209C2×Q8×C61C22×C412yes—
210C2×D4×C61—22no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61C22⋊C412yes—
220C2×D4×C61C22⋊C412yes—
221C2×D4×C61C22×C412yes—
222C22×C4×C61—21no—
223C22×C4×C61—22no—
224C22×C4×C61—22no—
225C22×C4×C61—22no—
226C22×C4×C61—22no—
227C22×C4×C61—22no—
228C22×C4×C61—22no—
229C22×C4×C61—41no—
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C22×C411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2411yescharacteristic
244C2×C22⋊D61—28no—
245C2×C22⋊D61—28no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248C2×C22⋊D61—22no—
249C2×C22⋊D61—22no—
250C2×C22⋊D61—28no—
251C2×C22⋊D61C22⋊C414yes—
252C2×C22⋊D61C2×D414yes—
253C22×Dic61—28no—
254C22×Dic61—28no—
255C22×Dic61—22no—
256C22×Dic61—22no—
257C22×Dic61—22no—
258C22×Dic61—22no—
259C22×Dic61—22no—
260C22×Dic61—22no—
261C22×Dic61—22no—
262C22×Dic61—28no—
263C22×Dic61—41no—
264C22×Dic61C22⋊C412yes—
265Q8×D61—216no—
266Q8×D61—216no—
267Q8×D61—216no—
268Q8×D61—216no—
269#11758224—232no—
270#11758224—232no—
271#11758224—232no—
272#11758224—232no—
273#11758224—216no—
274#11758224—216no—
275#11758224—216no—
276#11758224—216no—
277#11758222—216no—
278#11758222—216no—
279#11758222—216no—
280#11758222—216no—
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—
297C2×D244—21no—
298C2×D244—21no—
299C2×D244—21no—
300C2×D244—21no—
301C2×D244C22⋊C412yes—
302C2×D244C2×D412yes—
303C2×C4×D61—28no—
304C2×C4×D61—28no—
305C2×C4×D61—28no—
306C2×C4×D61—22no—
307C2×C4×D61—22no—
308C2×C4×D61—22no—
309C2×C4×D61—22no—
310C2×C4×D61C22⋊C414yes—
311C2×C4×D61C22×C414yes—
312C2×Dic122—28no—
313C2×Dic122—28no—
314C2×Dic122—216no—
315C2×Dic122—216no—
316C2×Dic122—216no—
317C2×Dic122—216no—
318C2×Dic122—22no—
319C2×Dic122—22no—
320C2×Dic122—22no—
321C2×Dic122—22no—
322C2×Dic122—22no—
323C2×Dic122—22no—
324C2×Dic122—21no—
325C2×Dic122—21no—
326C2×Dic122—21no—
327C2×Dic122—21no—
328C2×Dic122—22no—
329C2×Dic122—22no—
330C2×Dic122—22no—
331C2×Dic122—22no—
332C2×Dic122—22no—
333C2×Dic122—22no—
334C2×Dic122—22no—
335C2×Dic122—22no—
336C2×Dic122—22no—
337C2×Dic122—22no—
338C2×Dic122—22no—
339C2×Dic122—22no—
340C2×Dic122—22no—
341C2×Dic122—22no—
342C2×Dic122—22no—
343C2×Dic122—28no—
344C2×Dic122C22⋊C412yes—
345C2×Dic122C22⋊C414yes—
346C2×Dic122C22⋊C414yes—
347C2×Dic122C22⋊C414yes—
348C2×Dic122C22⋊C414yes—
349C2×Dic122C22×C414yes—
350C2×Dic122C2×D412yes—
351C2×Dic122C2×D414yes—
352C2×Dic122C2×D414yes—
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—22no—
380C23×C61—22no—
381C23×C61—22no—
382C23×C61—42no—
383C23×C61—44no—
384C23×C61C2×C22⋊C411yescharacteristic
385C23×C61C2×C22⋊C411yescharacteristic
386C23×C61#12011yescharacteristic
387C23×C61#12011yescharacteristic
388C23×C61#12011yescharacteristic
389C23×C61#12011yescharacteristic
390C23×C61C22×D411yescharacteristic
391C22×D61—22no—
392C22×D61—22no—
393C22×D61—44no—
394C22×D61C2×C22⋊C414yes—
395Q8×C61—22no—
396Q8×C61—22no—
397Q8×C61—22no—
398Q8×C61C2×C22⋊C414yes—
399D4×C61—24no—
400D4×C61—24no—
401D4×C61—24no—
402D4×C61—24no—
403D4×C61—22no—
404D4×C61—22no—
405D4×C61—22no—
406D4×C61C2×C22⋊C414yes—
407C2×C4×C61—22no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—24no—
411C2×C4×C61—24no—
412C2×C4×C61—24no—
413C2×C4×C61—24no—
414C2×C4×C61—42no—
415C2×C4×C61—82no—
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×C61C2×C22⋊C411yescharacteristic
423C2×C4×C61C2×C22⋊C411yescharacteristic
424C2×C4×C61C2×C22⋊C411yescharacteristic
425C2×C4×C61C2×C22⋊C411yescharacteristic
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×C61#12011yescharacteristic
435C2×C4×C61#12011yescharacteristic
436C2×C4×C61#12011yescharacteristic
437C2×C4×C61#12011yescharacteristic
438C2×C4×C61C23×C411yescharacteristic
439C2×C4×C61C22×D411yescharacteristic
440C2×C4×C61C22×D411yescharacteristic
441C2×C4×C61C22×D411yescharacteristic
442C2×C4×C61C22×D411yescharacteristic
443C2×C4×C61C22×D411yescharacteristic
444C22⋊D61—232no—
445C22⋊D61—24no—
446C22⋊D61—24no—
447C22⋊D61—24no—
448C22⋊D61—24no—
449C2×Dic61—232no—
450C2×Dic61—24no—
451C2×Dic61—24no—
452C2×Dic61—24no—
453C2×Dic61—22no—
454C2×Dic61—22no—
455C2×Dic61—24no—
456C2×Dic61—24no—
457C2×Dic61—24no—
458C2×Dic61—24no—
459C2×Dic61—42no—
460C2×Dic61—82no—
461C2×Dic61C2×C22⋊C414yes—
462D244—22no—
463D244—22no—
464D244—22no—
465D244—22no—
466C4×D61—232no—
467C4×D61—24no—
468C4×D61—24no—
469C4×D61—24no—
470C4×D61—24no—
471Dic122—232no—
472Dic122—24no—
473Dic122—22no—
474Dic122—22no—
475Dic122—24no—
476Dic122—24no—
477Dic122—22no—
478Dic122—22no—
479Dic122—24no—
480Dic122—24no—
481Dic122—24no—
482Dic122—24no—
483Dic122C2×C22⋊C418yes—
484C8×C61—42no—
485#92418—42no—
486C2×#1796—611nomaximal, Sylow
487C22×C61—22no—
488C22×C61—22no—
489C22×C61—22no—
490C22×C61—24no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61—41no—
495C22×C61—44no—
496C22×C61—44no—
497C22×C61—44no—
498C22×C61#37911yescharacteristic
499C22×C61#37911yescharacteristic
500C22×C61#37911yescharacteristic
501C22×C61#37911yescharacteristic
502C22×C61C22×C22⋊C411yescharacteristic
503C22×C61C2×#12011yescharacteristic
504C22×C61C2×#12011yescharacteristic
505C2×D61—24no—
506C2×D61—44no—
507C2×D61—44no—
508C2×D61—44no—
509C4×C61—24no—
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—28no—
521Dic61—82no—
522C22×2−1+4—611no—
523C2×#421—611no—
524C2×#421D6111yescharacteristic, complemented
525C2×#419—611no—
526C2×#419—611no—
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—44no—
537C2×C61#179612yescomplemented
538C2×C61C2×#37911yescharacteristic
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—1221no—
555C22×#41—1222no—
556C22×#41C2×D6111yescharacteristic
557C23×Q8—612no—
558C23×Q8—611no—
559C23×Q8—1221no—
560C22×M16—611no—
561C22×M16C2×D6111yescharacteristic
562C2×#117—611no—
563C2×#117C2×D6111yescharacteristic
564#421—22no—
565#421—614no—
566#421—1222no—
567#421C2×D6114yescomplemented
568C2×#104—22no—
569C2×#104—1222no—
570#419—614no—
571#419—614no—
572#419—1222no—
573#419—1222no—
574C2×#103—1222no—
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—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—21no—
606C2×#41—612no—
607C2×#41—612no—
608C2×#41—612no—
609C2×#41—612no—
610C2×#41—618no—
611C2×#41—1224no—
612C2×#41—1224no—
613C2×#41—1224no—
614C2×#41—1224no—
615C2×#41—1224no—
616C2×#41—1224no—
617C2×#41—1224no—
618C2×#41—1228no—
619C2×#41—1228no—
620C2×#41—1224no—
621C2×#41—1224no—
622C2×#41—1228no—
623C2×#41—1228no—
624C2×#41—1228no—
625C2×#41—1228no—
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×#41C4×D6112yes—
637C2×#41D24412yes—
638C2×#41D24412yes—
639C2×#41C22⋊D6112yes—
640C2×#41C22⋊D6112yes—
641C2×#41C22×D6112yes—
642C22×Q8—611no—
643C22×Q8—618no—
644C22×Q8—612no—
645C22×Q8—612no—
646C22×Q8—612no—
647C22×Q8—612no—
648C22×Q8—612no—
649C22×Q8—612no—
650C22×Q8—612no—
651C22×Q8—1222no—
652C22×Q8—1224no—
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—1221no—
664C22×Q8—1221no—
665C22×Q8—1221no—
666C22×Q8—1221no—
667C22×Q8—1221no—
668C22×Q8—1221no—
669C22×Q8—1221no—
670C22×Q8C4×D6111yescharacteristic
671C22×D4—21no—
672C22×D4—612no—
673C22×D4—611no—
674C22×D4—1222no—
675C22×D4C4×D6111yescharacteristic
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—28no—
711#104—1228no—
712#103—1228no—
713#103—1228no—
714#101—1224no—
715#100—1224no—
716#99—1228no—
717C24—21no—
718C24—612no—
719C24D4×D6111yescharacteristic
720#41—22no—
721#41—22no—
722#41—22no—
723#41—22no—
724#41—22no—
725#41—22no—
726#41—22no—
727#41—22no—
728#41—22no—
729#41—22no—
730#41—22no—
731#41—22no—
732#41—12216no—
733#41—12216no—
734#41—12216no—
735#41—12216no—
736#41—12216no—
737#41—12232no—
738#41—12232no—
739#41—12232no—
740#41—12232no—
741#41—12216no—
742#41—12216no—
743#41—12216no—
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#1175819814yes—
761#41#1175819814yes—
762#41C2×D24414yes—
763#41C2×C22⋊D6114yes—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—612no—
768C2×Q8—612no—
769C2×Q8—614no—
770C2×Q8—614no—
771C2×Q8—614no—
772C2×Q8—614no—
773C2×Q8—614no—
774C2×Q8—614no—
775C2×Q8—614no—
776C2×Q8—1228no—
777C2×Q8—1228no—
778C2×Q8—1228no—
779C2×Q8—12216no—
780C2×Q8—12216no—
781C2×Q8—12216no—
782C2×Q8—12216no—
783C2×Q8—12216no—
784C2×Q8—12216no—
785C2×Q8—12216no—
786C2×Q8—12216no—
787C2×Q8—1222no—
788C2×Q8—1222no—
789C2×Q8—1222no—
790C2×Q8—1222no—
791C2×Q8—1222no—
792C2×Q8—1222no—
793C2×Q8—1222no—
794C2×Q8—1222no—
795C2×Q8—1222no—
796C2×Q8—1221no—
797C2×Q8—1222no—
798C2×Q8—1221no—
799C2×Q8—1222no—
800C2×Q8—1222no—
801C2×Q8—1222no—
802C2×Q8—1222no—
803C2×Q8—1222no—
804C2×Q8—1221no—
805C2×Q8—1222no—
806C2×Q8—1221no—
807C2×Q8—1222no—
808C2×Q8—1222no—
809C2×Q8—1222no—
810C2×Q8—1222no—
811C2×Q8—1222no—
812C2×Q8#1175819812yes—
813C2×Q8#1175819812yes—
814C2×Q8C2×C4×D6112yes—
815C2×D4—22no—
816C2×D4—22no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—22no—
820C2×D4—22no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—614no—
825C2×D4—614no—
826C2×D4—612no—
827C2×D4—612no—
828C2×D4—1228no—
829C2×D4—1228no—
830C2×D4—1228no—
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#1175819812yes—
840C2×D4#1175819812yes—
841C2×D4C2×C4×D6112yes—
842C22×C4—21no—
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—1222no—
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—22no—
912C23—22no—
913C23—22no—
914C23—42no—
915C23—44no—
916C23—614no—
917C23—1222no—
918C23—1222no—
919C23—2444no—
920C23C22⋊C4×D6111yescharacteristic
921C23C22⋊C4×D6111yescharacteristic
922C23#1451974511yescharacteristic
923C23#1451974511yescharacteristic
924C23#1451974711yescharacteristic
925C23#1451974711yescharacteristic
926C23C2×D4×D6111yescharacteristic
927Q8—22no—
928Q8—22no—
929Q8—22no—
930Q8—618no—
931Q8—12232no—
932Q8—1224no—
933Q8—1222no—
934Q8—1224no—
935Q8—1222no—
936Q8—1224no—
937Q8—1222no—
938Q8—1222no—
939Q8—1224no—
940Q8—1224no—
941Q8—1224no—
942Q8—1224no—
943Q8C2×#1175819814yes—
944D4—24no—
945D4—24no—
946D4—24no—
947D4—24no—
948D4—22no—
949D4—22no—
950D4—22no—
951D4—12232no—
952D4—1224no—
953D4—1224no—
954D4—1224no—
955D4—1224no—
956D4—1222no—
957D4—1222no—
958D4—1222no—
959D4—1222no—
960D4C2×#1175819814yes—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
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—1224no—
974C2×C4—1224no—
975C2×C4—1224no—
976C2×C4—1222no—
977C2×C4—1224no—
978C2×C4—1224no—
979C2×C4—1224no—
980C2×C4—1222no—
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—24no—
1022C22—41no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—1224no—
1030C22—2444no—
1031C22—2444no—
1032C22—2444no—
1033C22#1683961711yescharacteristic
1034C22#1683961711yescharacteristic
1035C22#1683961711yescharacteristic
1036C22#1683961711yescharacteristic
1037C22C2×C22⋊C4×D6111yescharacteristic
1038C22C2×#1451974511yescharacteristic
1039C22C2×#1451974711yescharacteristic
1040C4—24no—
1041C4—82no—
1042C4—1224no—
1043C4—1228no—
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—44no—
1060C2—2444no—
1061C2#2144579312yesdirect product factor
1062C2C2×#1683961711yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#379
prime radicalC22×#14519824C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1796
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#16839779C2semidirect
3. C2×#16839772C2semidirect
4. C2×#16839770C2semidirect
5. C2×#16839744C2semidirect
6. C2×#16839735C2semidirect
7. #21445793C2direct (N × H)
8. C2×C61×#421C2semidirect
19. C2×#14519824C4semidirect
24. C22×#11758224C4semidirect
27. C22×Q8×D61C4semidirect
31. #16839779C22semidirect
34. #16839772C22semidirect
36. #16839770C22semidirect
40. #16839744C22semidirect
44. #16839735C22semidirect
50. C61×#421C22semidirect
97. C2×#11758224C2×C4semidirect
125. C2×Q8×D61C2×C4semidirect
524. C2×#421D61semidirect
537. C2×C61#1796semidirect
567. #421C2×D61semidirect
583. C61C2×#1796semidirect
1061. C2#21445793direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198242
C2×#168397792
C2×#168397722
C2×#168397702
C2×#168397442
C2×#168397352
#214457932
C2×C61×#4212
C2×#179661