Finite Group Databasebeta

← C2×#21445788 #29679347

Subgroups — C2×#21445788 #29679347

Order 15616.

3946 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519823C211yesmaximal, characteristic
2C2×#16839779C211yesmaximal, characteristic, complemented
3C2×#16839768C211yesmaximal, characteristic, complemented
4C2×#16839766C211yesmaximal, characteristic, complemented
5C2×#16839744C211yesmaximal, characteristic, complemented
6C2×#16839735C211yesmaximal, characteristic, complemented
7#21445788C218yesmaximal, direct product factor
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C2×#14519823—22no—
10C2×#14519823—22no—
11C2×#14519823—22no—
12C2×#14519823—22no—
13C2×#14519823—22no—
14C2×#14519823—22no—
15C2×#14519823—22no—
16C2×#14519823—22no—
17C2×#14519823—22no—
18C2×#14519823—22no—
19C2×#14519823C414yescomplemented
20C2×#14519823C2214yes—
21C22×#11758226C412yescomplemented
22C22×#11758222—21no—
23C22×#11758222C2211yescharacteristic
24C23×D244—21no—
25C23×D244C2211yescharacteristic
26C22×D4×D61—22no—
27C22×D4×D61C412yescomplemented
28C22×#11758194C2211yescharacteristic, complemented
29C2×#14519736C2211yescharacteristic, complemented
30#16839779—22no—
31#16839779C2214yescomplemented
32C2×#14519704—22no—
33#16839768—22no—
34#16839768C2214yescomplemented
35#16839766—22no—
36#16839766C2214yescomplemented
37C2×#14519699—22no—
38C2×#14519697—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, complemented
48C2×#117×C61C2211yescharacteristic, complemented
49C61×#421—22no—
50C61×#421C2214yescomplemented
51C2×#104×C61—22no—
52C24×D61—21no—
53C24×D61—22no—
54#14519823—28no—
55#14519823—28no—
56#14519823—28no—
57#14519823—28no—
58#14519823—28no—
59#14519823—28no—
60#14519823—28no—
61#14519823—28no—
62#14519823—28no—
63#14519823—28no—
64#14519823—28no—
65#14519823—28no—
66#14519823—28no—
67#14519823—28no—
68#14519823—28no—
69#14519823—28no—
70C2×#11758226—24no—
71C2×#11758226—24no—
72C2×#11758226—24no—
73C2×#11758226—24no—
74C2×#11758226—24no—
75C2×#11758226C2×C418yescomplemented
76C2×#11758222—24no—
77C2×#11758222—24no—
78C2×#11758222—24no—
79C2×#11758222—24no—
80C2×#11758222—21no—
81C2×#11758222—21no—
82C2×#11758222—21no—
83C2×#11758222—21no—
84C2×#11758222—21no—
85C2×#11758222—21no—
86C2×#11758222—21no—
87C2×#11758222—21no—
88C2×#11758222—24no—
89C2×#11758222—24no—
90C2×#11758222C2×C412yes—
91C2×#11758222D412yes—
92C2×#11758222D412yes—
93C2×#11758222C2312yes—
94C22×Dic122D411yescharacteristic
95C22×D244—24no—
96C22×D244—24no—
97C22×D244—24no—
98C22×D244—24no—
99C22×D244—22no—
100C22×D244—21no—
101C22×D244—21no—
102C22×D244—21no—
103C22×D244—21no—
104C22×D244—21no—
105C22×D244—21no—
106C22×D244—21no—
107C22×D244—24no—
108C22×D244—24no—
109C22×D244C2×C412yes—
110C22×D244C2×C412yes—
111C22×D244D411yescharacteristic
112C22×D244D412yes—
113C22×D244D412yes—
114C22×D244D412yes—
115C22×D244D412yes—
116C22×D244C2312yes—
117C22×C22⋊D61—22no—
118C22×C22⋊D61D412yes—
119C2×D4×D61—28no—
120C2×D4×D61—28no—
121C2×D4×D61—28no—
122C2×D4×D61—28no—
123C2×D4×D61—24no—
124C2×D4×D61—24no—
125C2×D4×D61—28no—
126C2×D4×D61—28no—
127C2×D4×D61—24no—
128C2×D4×D61—24no—
129C2×D4×D61—24no—
130C2×D4×D61C2×C418yescomplemented
131C22×C4×D61—22no—
132C22×C4×D61C2×C412yes—
133C2×#11758194—21no—
134C2×#11758194—21no—
135C2×#11758194—21no—
136C2×#11758194—21no—
137C2×#11758194—21no—
138C2×#11758194C2312yescomplemented
139C22×#92418—21no—
140#14519736—21no—
141#14519736—21no—
142#14519736—21no—
143#14519736C2312yescomplemented
144C2×C4⋊Dic61—21no—
145C2×C22⋊Dic61—21no—
146C2×C4×Dic61—21no—
147#14519704—28no—
148#14519699—28no—
149#14519697—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×C61C2312yescomplemented
176C22×C8×C61—21no—
177#117×C61—21no—
178#117×C61—21no—
179#117×C61—21no—
180#117×C61C2312yescomplemented
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×D61—22no—
188C23×D61—28no—
189C23×D61—28no—
190C23×D61—22no—
191C23×D61—22no—
192C23×D61—22no—
193C23×D61—22no—
194C23×D61—22no—
195C23×D61—22no—
196C23×D61—28no—
197C23×D61—84no—
198C23×D61—88no—
199C23×D61C22⋊C412yes—
200#41×C61—22no—
201#41×C61—22no—
202#41×C61—22no—
203#41×C61—22no—
204#41×C61—22no—
205#41×C61—22no—
206#41×C61—22no—
207#41×C61—22no—
208#41×C61—22no—
209#41×C61—22no—
210#41×C61—22no—
211#41×C61—22no—
212#41×C61C22⋊C414yes—
213#41×C61C22⋊C414yes—
214#41×C61C2×D414yes—
215#41×C61C2×D414yes—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61C22⋊C412yes—
220C2×Q8×C61C22⋊C412yes—
221C2×Q8×C61C22×C412yes—
222C2×D4×C61—22no—
223C2×D4×C61—22no—
224C2×D4×C61—22no—
225C2×D4×C61—22no—
226C2×D4×C61—22no—
227C2×D4×C61—22no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—21no—
231C2×D4×C61C22⋊C412yes—
232C2×D4×C61C22⋊C412yes—
233C2×D4×C61C22×C412yes—
234C22×C4×C61—21no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—22no—
239C22×C4×C61—22no—
240C22×C4×C61—22no—
241C22×C4×C61—41no—
242C22×C4×C61C22×C411yescharacteristic
243C22×C4×C61C22×C411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C22×C4×C61C2411yescharacteristic
256C2×C22⋊D61—28no—
257C2×C22⋊D61—28no—
258C2×C22⋊D61—22no—
259C2×C22⋊D61—22no—
260C2×C22⋊D61—22no—
261C2×C22⋊D61—22no—
262C2×C22⋊D61—28no—
263C2×C22⋊D61C22⋊C414yes—
264C2×C22⋊D61C2×D414yes—
265C22×Dic61—41no—
266C22×Dic61C22⋊C412yes—
267#11758226—216no—
268#11758226—216no—
269#11758226—216no—
270#11758226—216no—
271D4×D61—232no—
272D4×D61—232no—
273D4×D61—232no—
274D4×D61—232no—
275D4×D61—216no—
276D4×D61—216no—
277D4×D61—216no—
278D4×D61—216no—
279#11758222—216no—
280#11758222—216no—
281#11758222—216no—
282#11758222—216no—
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—
299C2×D244—28no—
300C2×D244—28no—
301C2×D244—216no—
302C2×D244—216no—
303C2×D244—216no—
304C2×D244—216no—
305C2×D244—28no—
306C2×D244—22no—
307C2×D244—22no—
308C2×D244—22no—
309C2×D244—22no—
310C2×D244—22no—
311C2×D244—22no—
312C2×D244—21no—
313C2×D244—22no—
314C2×D244—21no—
315C2×D244—22no—
316C2×D244—21no—
317C2×D244—22no—
318C2×D244—21no—
319C2×D244—22no—
320C2×D244—22no—
321C2×D244—22no—
322C2×D244—22no—
323C2×D244—22no—
324C2×D244—22no—
325C2×D244—22no—
326C2×D244—22no—
327C2×D244—22no—
328C2×D244—22no—
329C2×D244—22no—
330C2×D244—22no—
331C2×D244C22⋊C412yes—
332C2×D244C22⋊C414yes—
333C2×D244C22⋊C414yes—
334C2×D244C22⋊C414yes—
335C2×D244C22⋊C414yes—
336C2×D244C22×C414yes—
337C2×D244C2×D412yes—
338C2×D244C2×D414yes—
339C2×D244C2×D414yes—
340C2×C4×D61—28no—
341C2×C4×D61—28no—
342C2×C4×D61—22no—
343C2×C4×D61—22no—
344C2×C4×D61—22no—
345C2×C4×D61—22no—
346C2×C4×D61—28no—
347C2×C4×D61C22⋊C414yes—
348C2×C4×D61C22×C414yes—
349C2×Dic122—21no—
350C2×Dic122—21no—
351C2×Dic122—21no—
352C2×Dic122—21no—
353C2×Dic122C22⋊C412yes—
354C2×Dic122C2×D412yes—
355M16×C61—22no—
356M16×C61—22no—
357M16×C61—41no—
358M16×C61—41no—
359C2×C8×C61—22no—
360C2×C8×C61—41no—
361C2×C8×C61—41no—
362C4⋊C4×C61—22no—
363C4⋊C4×C61—41no—
364C22⋊C4×C61—22no—
365C22⋊C4×C61—41no—
366C42×C61—22no—
367C42×C61—41no—
368C22⋊Dic61—22no—
369C22⋊Dic61—41no—
370C4⋊Dic61—22no—
371C4⋊Dic61—41no—
372C4×Dic61—22no—
373C4×Dic61—41no—
374#11758194—22no—
375#11758194—22no—
376#11758194—41no—
377#11758194—41no—
378C2×#92418—22no—
379C2×#92418—41no—
380C2×#92418—41no—
381C23×C61—22no—
382C23×C61—22no—
383C23×C61—22no—
384C23×C61—42no—
385C23×C61—44no—
386C23×C61C2×C22⋊C411yescharacteristic
387C23×C61C2×C22⋊C411yescharacteristic
388C23×C61#12011yescharacteristic
389C23×C61#12011yescharacteristic
390C23×C61#12011yescharacteristic
391C23×C61#12011yescharacteristic
392C23×C61C22×D411yescharacteristic
393C22×D61—24no—
394C22×D61—22no—
395C22×D61—22no—
396C22×D61—24no—
397C22×D61—24no—
398C22×D61—232no—
399C22×D61—24no—
400C22×D61—24no—
401C22×D61—24no—
402C22×D61—24no—
403C22×D61—48no—
404C22×D61—44no—
405C22×D61—84no—
406C22×D61—84no—
407C22×D61—84no—
408C22×D61—84no—
409C22×D61—84no—
410C22×D61—84no—
411C22×D61—816no—
412C22×D61—816no—
413C22×D61—816no—
414C22×D61C2×C22⋊C414yes—
415Q8×C61—22no—
416Q8×C61—22no—
417Q8×C61—22no—
418Q8×C61C2×C22⋊C414yes—
419D4×C61—24no—
420D4×C61—24no—
421D4×C61—24no—
422D4×C61—24no—
423D4×C61—22no—
424D4×C61—22no—
425D4×C61—22no—
426D4×C61C2×C22⋊C414yes—
427C2×C4×C61—22no—
428C2×C4×C61—22no—
429C2×C4×C61—22no—
430C2×C4×C61—24no—
431C2×C4×C61—24no—
432C2×C4×C61—24no—
433C2×C4×C61—24no—
434C2×C4×C61—42no—
435C2×C4×C61—82no—
436C2×C4×C61C2×C22⋊C411yescharacteristic
437C2×C4×C61C2×C22⋊C411yescharacteristic
438C2×C4×C61C2×C22⋊C411yescharacteristic
439C2×C4×C61C2×C22⋊C411yescharacteristic
440C2×C4×C61C2×C22⋊C411yescharacteristic
441C2×C4×C61C2×C22⋊C411yescharacteristic
442C2×C4×C61C2×C22⋊C411yescharacteristic
443C2×C4×C61C2×C22⋊C411yescharacteristic
444C2×C4×C61C2×C22⋊C411yescharacteristic
445C2×C4×C61C2×C22⋊C411yescharacteristic
446C2×C4×C61#12011yescharacteristic
447C2×C4×C61#12011yescharacteristic
448C2×C4×C61#12011yescharacteristic
449C2×C4×C61#12011yescharacteristic
450C2×C4×C61#12011yescharacteristic
451C2×C4×C61#12011yescharacteristic
452C2×C4×C61#12011yescharacteristic
453C2×C4×C61#12011yescharacteristic
454C2×C4×C61#12011yescharacteristic
455C2×C4×C61#12011yescharacteristic
456C2×C4×C61#12011yescharacteristic
457C2×C4×C61#12011yescharacteristic
458C2×C4×C61C23×C411yescharacteristic
459C2×C4×C61C22×D411yescharacteristic
460C2×C4×C61C22×D411yescharacteristic
461C2×C4×C61C22×D411yescharacteristic
462C2×C4×C61C22×D411yescharacteristic
463C2×C4×C61C22×D411yescharacteristic
464C22⋊D61—232no—
465C22⋊D61—24no—
466C22⋊D61—24no—
467C22⋊D61—24no—
468C22⋊D61—24no—
469C2×Dic61—22no—
470C2×Dic61—22no—
471C2×Dic61—42no—
472C2×Dic61—82no—
473C2×Dic61C2×C22⋊C414yes—
474D244—232no—
475D244—24no—
476D244—22no—
477D244—24no—
478D244—22no—
479D244—24no—
480D244—22no—
481D244—22no—
482D244—24no—
483D244—24no—
484D244—24no—
485D244—24no—
486D244C2×C22⋊C418yes—
487C4×D61—232no—
488C4×D61—24no—
489C4×D61—24no—
490C4×D61—24no—
491C4×D61—24no—
492Dic122—22no—
493Dic122—22no—
494Dic122—22no—
495Dic122—22no—
496C8×C61—42no—
497#92418—42no—
498C2×#1795—611nomaximal, Sylow
499C22×C61—22no—
500C22×C61—22no—
501C22×C61—22no—
502C22×C61—24no—
503C22×C61—41no—
504C22×C61—41no—
505C22×C61—41no—
506C22×C61—41no—
507C22×C61—44no—
508C22×C61—44no—
509C22×C61—44no—
510C22×C61#37911yescharacteristic
511C22×C61#37911yescharacteristic
512C22×C61#37911yescharacteristic
513C22×C61#37911yescharacteristic
514C22×C61C22×C22⋊C411yescharacteristic
515C22×C61C2×#12011yescharacteristic
516C22×C61C2×#12011yescharacteristic
517C2×D61—24no—
518C2×D61—28no—
519C2×D61—48no—
520C2×D61—48no—
521C2×D61—44no—
522C2×D61—48no—
523C2×D61—44no—
524C2×D61—44no—
525C2×D61—84no—
526C2×D61—84no—
527C2×D61—84no—
528C2×D61—84no—
529C2×D61—832no—
530C4×C61—24no—
531C4×C61—82no—
532C4×C61#37911yescharacteristic
533C4×C61#37911yescharacteristic
534C4×C61#37911yescharacteristic
535C4×C61#37911yescharacteristic
536C4×C61C22×C22⋊C411yescharacteristic
537C4×C61C22×C22⋊C411yescharacteristic
538C4×C61C2×#12011yescharacteristic
539C4×C61C2×#12011yescharacteristic
540Dic61—24no—
541Dic61—82no—
542C22×H(5,𝔽2)—611no—
543C2×#421—611no—
544C2×#421D6111yescharacteristic, complemented
545C2×#418—611no—
546C2×#418—611no—
547C2×#413—611no—
548C2×#410—611no—
549#1795—618no—
550C2×C61—21no—
551C2×C61—21no—
552C2×C61—21no—
553C2×C61—21no—
554C2×C61—21no—
555C2×C61—21no—
556C2×C61—44no—
557C2×C61#179512yescomplemented
558C2×C61C2×#37911yescharacteristic
559D61—48no—
560D61—44no—
561C2×H(5,𝔽2)—614no—
562C2×H(5,𝔽2)—614no—
563C2×H(5,𝔽2)—1222no—
564C2×H(5,𝔽2)—1222no—
565C2×H(5,𝔽2)—1222no—
566C2×H(5,𝔽2)—1222no—
567C2×H(5,𝔽2)—1222no—
568C2×H(5,𝔽2)—1222no—
569C2×H(5,𝔽2)—1222no—
570C2×H(5,𝔽2)—1222no—
571C2×H(5,𝔽2)—1222no—
572C2×H(5,𝔽2)—1222no—
573C22×#41—611no—
574C22×#41—612no—
575C22×#41—1221no—
576C22×#41C2×D6111yescharacteristic
577C23×D4—612no—
578C23×D4—611no—
579C23×D4—1221no—
580C23×D4—1222no—
581C22×M16—611no—
582C22×M16C2×D6111yescharacteristic, complemented
583C2×#117—611no—
584C2×#117C2×D6111yescharacteristic, complemented
585#421—22no—
586#421—614no—
587#421—1222no—
588#421C2×D6114yescomplemented
589C2×#104—22no—
590C2×#104—1222no—
591#418—614no—
592#418—614no—
593#418—1222no—
594#418—1222no—
595C2×#102—1222no—
596C2×#102—1222no—
597#413—614no—
598#413—1222no—
599C2×#101—1221no—
600C2×#100—1221no—
601#410—614no—
602#410—1222no—
603C2×#99—1222no—
604C61C2×#179511yescharacteristic, complemented, Sylow
605C25—1222no—
606C25—1221no—
607H(5,𝔽2)—1228no—
608H(5,𝔽2)—1228no—
609H(5,𝔽2)—1228no—
610H(5,𝔽2)—1228no—
611H(5,𝔽2)—1228no—
612H(5,𝔽2)—1228no—
613H(5,𝔽2)—1228no—
614H(5,𝔽2)—1228no—
615H(5,𝔽2)—1228no—
616H(5,𝔽2)—1228no—
617H(5,𝔽2)—1228no—
618H(5,𝔽2)—1228no—
619H(5,𝔽2)—1228no—
620H(5,𝔽2)—1228no—
621H(5,𝔽2)—1228no—
622H(5,𝔽2)—1228no—
623C2×#41—21no—
624C2×#41—21no—
625C2×#41—21no—
626C2×#41—21no—
627C2×#41—21no—
628C2×#41—21no—
629C2×#41—612no—
630C2×#41—612no—
631C2×#41—612no—
632C2×#41—612no—
633C2×#41—618no—
634C2×#41—1224no—
635C2×#41—1224no—
636C2×#41—1224no—
637C2×#41—1224no—
638C2×#41—1224no—
639C2×#41—1224no—
640C2×#41—1224no—
641C2×#41—1224no—
642C2×#41—1224no—
643C2×#41—1224no—
644C2×#41—1224no—
645C2×#41—1221no—
646C2×#41—1221no—
647C2×#41—1221no—
648C2×#41—1221no—
649C2×#41—1221no—
650C2×#41—1221no—
651C2×#41—1221no—
652C2×#41—1221no—
653C2×#41C4×D6112yes—
654C2×#41D24412yes—
655C2×#41D24412yes—
656C2×#41C22⋊D6112yes—
657C2×#41C22⋊D6112yes—
658C2×#41C22×D6112yes—
659C22×Q8—611no—
660C22×Q8C4×D6111yescharacteristic
661C22×D4—21no—
662C22×D4—612no—
663C22×D4—618no—
664C22×D4—612no—
665C22×D4—612no—
666C22×D4—612no—
667C22×D4—612no—
668C22×D4—612no—
669C22×D4—612no—
670C22×D4—611no—
671C22×D4—612no—
672C22×D4—1224no—
673C22×D4—1224no—
674C22×D4—1222no—
675C22×D4—1224no—
676C22×D4—1224no—
677C22×D4—1224no—
678C22×D4—1224no—
679C22×D4—1224no—
680C22×D4—1222no—
681C22×D4—1224no—
682C22×D4—1224no—
683C22×D4—1228no—
684C22×D4—1228no—
685C22×D4—1228no—
686C22×D4—1228no—
687C22×D4—1228no—
688C22×D4—1228no—
689C22×D4—1224no—
690C22×D4—1224no—
691C22×D4—1221no—
692C22×D4—1221no—
693C22×D4—1221no—
694C22×D4—1221no—
695C22×D4—1221no—
696C22×D4—1221no—
697C22×D4—1221no—
698C22×D4C4×D6111yescharacteristic
699C23×C4—21no—
700C23×C4—612no—
701C23×C4—1222no—
702C23×C4C22×D6111yescharacteristic
703C2×M16—21no—
704C2×M16—21no—
705C2×M16—21no—
706C2×M16—21no—
707C2×M16—21no—
708C2×M16—612no—
709C2×M16—1221no—
710C2×M16—1221no—
711C2×M16—1221no—
712C2×M16—1221no—
713C2×M16—1221no—
714C2×M16C22×D6112yescomplemented
715C22×C8—21no—
716C22×C8—1221no—
717#117—21no—
718#117—21no—
719#117—21no—
720#117—612no—
721#117—1221no—
722#117—1221no—
723#117—1221no—
724#117C22×D6112yescomplemented
725C2×C4⋊C4—21no—
726C2×C4⋊C4—1221no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—1221no—
729C2×C42—21no—
730C2×C42—1221no—
731#104—28no—
732#104—1228no—
733#102—1228no—
734#102—1228no—
735#101—1224no—
736#100—1224no—
737#99—1228no—
738C24—21no—
739C24—612no—
740C24—1228no—
741C24—1228no—
742C24—1228no—
743C24—1222no—
744C24—1222no—
745C24—1222no—
746C24—1222no—
747C24—1222no—
748C24—1222no—
749C24—1222no—
750C24—4884no—
751C24—4888no—
752C24D4×D6111yescharacteristic
753#41—22no—
754#41—22no—
755#41—22no—
756#41—22no—
757#41—22no—
758#41—22no—
759#41—22no—
760#41—22no—
761#41—22no—
762#41—22no—
763#41—22no—
764#41—22no—
765#41—12216no—
766#41—12216no—
767#41—12216no—
768#41—12216no—
769#41—12216no—
770#41—12216no—
771#41—12216no—
772#41—12216no—
773#41—1222no—
774#41—1222no—
775#41—1222no—
776#41—1222no—
777#41—1222no—
778#41—1222no—
779#41—1222no—
780#41—1222no—
781#41—1222no—
782#41—1222no—
783#41—1222no—
784#41—1222no—
785#41—1222no—
786#41—1222no—
787#41—1222no—
788#41—1222no—
789#41#1175819814yes—
790#41#1175819814yes—
791#41C2×D24414yes—
792#41C2×C22⋊D6114yes—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—612no—
797C2×Q8—612no—
798C2×Q8—1221no—
799C2×Q8—1221no—
800C2×Q8—1221no—
801C2×Q8—1221no—
802C2×Q8#1175819812yes—
803C2×Q8#1175819812yes—
804C2×Q8C2×C4×D6112yes—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—614no—
815C2×D4—614no—
816C2×D4—614no—
817C2×D4—614no—
818C2×D4—614no—
819C2×D4—612no—
820C2×D4—614no—
821C2×D4—614no—
822C2×D4—614no—
823C2×D4—614no—
824C2×D4—612no—
825C2×D4—1228no—
826C2×D4—1228no—
827C2×D4—1228no—
828C2×D4—12216no—
829C2×D4—12216no—
830C2×D4—12216no—
831C2×D4—12216no—
832C2×D4—1228no—
833C2×D4—12216no—
834C2×D4—12232no—
835C2×D4—12232no—
836C2×D4—12232no—
837C2×D4—12232no—
838C2×D4—12216no—
839C2×D4—12216no—
840C2×D4—1228no—
841C2×D4—1228no—
842C2×D4—1222no—
843C2×D4—1222no—
844C2×D4—1222no—
845C2×D4—1222no—
846C2×D4—12216no—
847C2×D4—1222no—
848C2×D4—1222no—
849C2×D4—1222no—
850C2×D4—1222no—
851C2×D4—1222no—
852C2×D4—1222no—
853C2×D4—1222no—
854C2×D4—1222no—
855C2×D4—1222no—
856C2×D4—1222no—
857C2×D4—1221no—
858C2×D4—1222no—
859C2×D4—1221no—
860C2×D4—1222no—
861C2×D4—1222no—
862C2×D4—1222no—
863C2×D4—1222no—
864C2×D4—1222no—
865C2×D4—1221no—
866C2×D4—1222no—
867C2×D4—1221no—
868C2×D4—1222no—
869C2×D4—1222no—
870C2×D4—1222no—
871C2×D4—1222no—
872C2×D4#1175819812yes—
873C2×D4#1175819812yes—
874C2×D4C2×C4×D6112yes—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—41no—
883C22×C4—612no—
884C22×C4—614no—
885C22×C4—614no—
886C22×C4—1228no—
887C22×C4—1228no—
888C22×C4—1228no—
889C22×C4—1222no—
890C22×C4—1222no—
891C22×C4—1222no—
892C22×C4—1222no—
893C22×C4—2441no—
894C22×C4C2×C4×D6111yescharacteristic
895C22×C4C2×C4×D6111yescharacteristic
896C22×C4C2×D24411yescharacteristic
897C22×C4C2×D24411yescharacteristic
898C22×C4D4×D6111yescharacteristic
899C22×C4D4×D6111yescharacteristic
900C22×C4D4×D6111yescharacteristic
901C22×C4D4×D6111yescharacteristic
902C22×C4D4×D6111yescharacteristic
903C22×C4D4×D6111yescharacteristic
904C22×C4D4×D6111yescharacteristic
905C22×C4C2×C22⋊D6111yescharacteristic
906C22×C4C2×C22⋊D6111yescharacteristic
907C22×C4C23×D6111yescharacteristic
908M16—22no—
909M16—22no—
910M16—41no—
911M16—41no—
912M16—1222no—
913M16—1222no—
914M16—2441no—
915M16—2441no—
916C2×C8—22no—
917C2×C8—41no—
918C2×C8—41no—
919C2×C8—1222no—
920C2×C8—2441no—
921C2×C8—2441no—
922C4⋊C4—22no—
923C4⋊C4—41no—
924C4⋊C4—1222no—
925C4⋊C4—2441no—
926C22⋊C4—22no—
927C22⋊C4—41no—
928C22⋊C4—1222no—
929C22⋊C4—2441no—
930C42—22no—
931C42—41no—
932C42—1222no—
933C42—2441no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—42no—
938C23—44no—
939C23—614no—
940C23—12232no—
941C23—1224no—
942C23—1224no—
943C23—1224no—
944C23—1224no—
945C23—1224no—
946C23—1224no—
947C23—1222no—
948C23—1224no—
949C23—1222no—
950C23—4884no—
951C23—4884no—
952C23—4884no—
953C23—4884no—
954C23—4884no—
955C23—4884no—
956C23—48816no—
957C23—48816no—
958C23—48816no—
959C23—2444no—
960C23—2448no—
961C23C22⋊C4×D6111yescharacteristic
962C23C22⋊C4×D6111yescharacteristic
963C23#1451974511yescharacteristic
964C23#1451974511yescharacteristic
965C23#1451974711yescharacteristic
966C23#1451974711yescharacteristic
967C23C2×D4×D6111yescharacteristic
968Q8—22no—
969Q8—22no—
970Q8—22no—
971Q8—1222no—
972Q8—1222no—
973Q8—1222no—
974Q8—1222no—
975Q8C2×#1175819814yes—
976D4—24no—
977D4—24no—
978D4—24no—
979D4—24no—
980D4—22no—
981D4—22no—
982D4—22no—
983D4—618no—
984D4—12232no—
985D4—12232no—
986D4—1224no—
987D4—1224no—
988D4—1224no—
989D4—1224no—
990D4—1224no—
991D4—1224no—
992D4—1222no—
993D4—1224no—
994D4—1222no—
995D4—1224no—
996D4—1224no—
997D4—1222no—
998D4—1222no—
999D4—1224no—
1000D4—1224no—
1001D4C2×#1175819814yes—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—42no—
1010C2×C4—82no—
1011C2×C4—614no—
1012C2×C4—12232no—
1013C2×C4—1222no—
1014C2×C4—1222no—
1015C2×C4—1224no—
1016C2×C4—1224no—
1017C2×C4—1224no—
1018C2×C4—1224no—
1019C2×C4—4882no—
1020C2×C4—2442no—
1021C2×C4C22⋊C4×D6111yescharacteristic
1022C2×C4C22⋊C4×D6111yescharacteristic
1023C2×C4C22⋊C4×D6111yescharacteristic
1024C2×C4C22⋊C4×D6111yescharacteristic
1025C2×C4C22⋊C4×D6111yescharacteristic
1026C2×C4C22⋊C4×D6111yescharacteristic
1027C2×C4C2×#1175819811yescharacteristic
1028C2×C4C2×#1175819811yescharacteristic
1029C2×C4C2×#1175819811yescharacteristic
1030C2×C4C2×#1175819811yescharacteristic
1031C2×C4#1451974511yescharacteristic
1032C2×C4#1451974511yescharacteristic
1033C2×C4#1451974511yescharacteristic
1034C2×C4#1451974511yescharacteristic
1035C2×C4#1451974511yescharacteristic
1036C2×C4#1451974511yescharacteristic
1037C2×C4#1451974711yescharacteristic
1038C2×C4#1451974711yescharacteristic
1039C2×C4#1451974711yescharacteristic
1040C2×C4#1451974711yescharacteristic
1041C2×C4#1451974711yescharacteristic
1042C2×C4#1451974711yescharacteristic
1043C2×C4C22×C4×D6111yescharacteristic
1044C2×C4C2×D4×D6111yescharacteristic
1045C2×C4C2×D4×D6111yescharacteristic
1046C2×C4C2×D4×D6111yescharacteristic
1047C2×C4C22×C22⋊D6111yescharacteristic
1048C2×C4C22×D24411yescharacteristic
1049C8—42no—
1050C8—2442no—
1051C22—22no—
1052C22—22no—
1053C22—22no—
1054C22—24no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—41no—
1059C22—44no—
1060C22—44no—
1061C22—44no—
1062C22—1228no—
1063C22—1224no—
1064C22—4884no—
1065C22—4884no—
1066C22—4884no—
1067C22—4884no—
1068C22—48832no—
1069C22—2444no—
1070C22—2448no—
1071C22—2448no—
1072C22—2444no—
1073C22—2444no—
1074C22—2448no—
1075C22#1683961711yescharacteristic
1076C22#1683961711yescharacteristic
1077C22#1683961711yescharacteristic
1078C22#1683961711yescharacteristic
1079C22C2×C22⋊C4×D6111yescharacteristic
1080C22C2×#1451974511yescharacteristic
1081C22C2×#1451974711yescharacteristic
1082C4—24no—
1083C4—82no—
1084C4—1224no—
1085C4—4882no—
1086C4#1683961711yescharacteristic
1087C4#1683961711yescharacteristic
1088C4#1683961711yescharacteristic
1089C4#1683961711yescharacteristic
1090C4C2×C22⋊C4×D6111yescharacteristic
1091C4C22×#1175819811yescharacteristic
1092C4C2×#1451974511yescharacteristic
1093C4C2×#1451974711yescharacteristic
1094C2—21no—
1095C2—21no—
1096C2—21no—
1097C2—21no—
1098C2—21no—
1099C2—21no—
1100C2—44no—
1101C2—2448no—
1102C2—2444no—
1103C2#2144578812yesdirect product factor
1104C2C2×#1683961711yescharacteristic
subgroupG/H
centerC22#16839617
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC22×C61#379
prime radicalC22×#14519823C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61C2×#1795
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×#16839768C2semidirect
4. C2×#16839766C2semidirect
5. C2×#16839744C2semidirect
6. C2×#16839735C2semidirect
7. #21445788C2direct (N × H)
8. C2×C61×#421C2semidirect
19. C2×#14519823C4semidirect
21. C22×#11758226C4semidirect
27. C22×D4×D61C4semidirect
28. C22×#11758194C22semidirect
29. C2×#14519736C22semidirect
31. #16839779C22semidirect
34. #16839768C22semidirect
36. #16839766C22semidirect
40. #16839744C22semidirect
44. #16839735C22semidirect
47. C22×M16×C61C22semidirect
48. C2×#117×C61C22semidirect
50. C61×#421C22semidirect
75. C2×#11758226C2×C4semidirect
130. C2×D4×D61C2×C4semidirect
138. C2×#11758194C23semidirect
143. #14519736C23semidirect
175. C2×M16×C61C23semidirect
180. #117×C61C23semidirect
544. C2×#421D61semidirect
557. C2×C61#1795semidirect
582. C22×M16C2×D61semidirect
584. C2×#117C2×D61semidirect
588. #421C2×D61semidirect
604. C61C2×#1795semidirect
714. C2×M16C22×D61semidirect
724. #117C22×D61semidirect
1103. C2#21445788direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198232
C2×#168397792
C2×#168397682
C2×#168397662
C2×#168397442
C2×#168397352
#214457882
C2×C61×#4212
C2×#179561