Finite Group Databasebeta

← C2×#21455649 #30547571

Subgroups — C2×#21455649 #30547571

Order 15616.

2234 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840392C211yesmaximal, characteristic, complemented
2C2×#16840234C211yesmaximal, characteristic
3#21455649C2116yesmaximal, direct product factor
4C2×#16840064C211yesmaximal, characteristic, complemented
5C2×#16840061C211yesmaximal, characteristic, complemented
6C2×#16840059C211yesmaximal, characteristic, complemented
7C2×#16840053C211yesmaximal, characteristic, complemented
8C2×#16840050C211yesmaximal, characteristic, complemented
9C2×#16840042C211yesmaximal, characteristic, complemented
10C2×#16840041C211yesmaximal, characteristic, complemented
11C2×#16839803C211yesmaximal, characteristic, complemented
12C2×#16839797C211yesmaximal, characteristic, complemented
13C2×#16839787C211yesmaximal, characteristic, complemented
14C2×#16839765C211yesmaximal, characteristic
15C2×#102×D61C211yesmaximal, characteristic
16C2×C61×#478C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840392—24no—
21#16840392C2218yescomplemented
22C2×#14519777C2211yescharacteristic, complemented
23C2×#14519776—21no—
24C2×#14519776C2211yescharacteristic, complemented
25C2×#14519768C2211yescharacteristic, complemented
26C2×#14519767—21no—
27C2×#14519757—21no—
28C2×#14519755—21no—
29#16840234—24no—
30#16840234C2218yes—
31C2×C4×D244C2211yescharacteristic
32C2×D4×Dic61C2211yescharacteristic
33C2×#14519739C2211yescharacteristic
34C2×C4×C22⋊D61—21no—
35C2×#14519737—21no—
36C2×#14519735C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519734C2211yescharacteristic
39C2×C4⋊C4×D61C2211yescharacteristic
40C22×#11758198—21no—
41C2×C22⋊C4×D61—21no—
42#16840064C2218yescomplemented
43#16840061C2218yescomplemented
44#16840059C2218yescomplemented
45#16840053C2218yescomplemented
46#16840050C2218yescomplemented
47#16840042C2218yescomplemented
48#16840041C2218yescomplemented
49#16839803C2218yescomplemented
50#16839797C2218yescomplemented
51C2×#14519710C2211yescharacteristic, complemented
52C2×#14519710C2211yescharacteristic, complemented
53C2×#14519710C2211yescharacteristic, complemented
54C2×#14519709C2211yescharacteristic, complemented
55C2×#14519709C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57#16839787C2218yescomplemented
58C2×C4⋊#92418C2211yescharacteristic, complemented
59C2×#14519706C2211yescharacteristic, complemented
60C2×#14519706C2211yescharacteristic, complemented
61#16839765C2218yes—
62C2×#14519699C2211yescharacteristic
63C2×#14519699C2211yescharacteristic
64C2×#14519698C2211yescharacteristic
65C2×#14519698C2211yescharacteristic
66C2×#14519697C2211yescharacteristic
67C2×#14519697C2211yescharacteristic
68#102×D61C2218yes—
69C2×#125×C61C2211yescharacteristic, complemented
70C2×C4×D4×C61C2211yescharacteristic
71C61×#478C2218yescomplemented
72C2×#107×C61C2211yescharacteristic, complemented
73C2×#106×C61C2211yescharacteristic, complemented
74C2×C4⋊C8×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C22×Dic122—21no—
79C22×Dic122—21no—
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C2×D4×D61—22no—
83C2×D4×D61—24no—
84C2×D4×D61Q818yescomplemented
85C2×D4×D61C2314yes—
86C23×Dic61—21no—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758189—24no—
92C2×#11758189C2314yes—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—24no—
96C2×C8×D61C2314yes—
97#14519777—22no—
98#14519777C2314yescomplemented
99#14519776—28no—
100#14519776—22no—
101#14519776C2314yescomplemented
102#14519768—22no—
103#14519768C2314yescomplemented
104#14519767—28no—
105#14519757—28no—
106#14519755—28no—
107C4×D244—22no—
108C4×D244C2314yes—
109D4×Dic61—22no—
110D4×Dic61C2314yes—
111#14519739—22no—
112#14519739C2314yes—
113C4×C22⋊D61—28no—
114#14519737—28no—
115#14519735—22no—
116#14519735—22no—
117#14519735C2314yes—
118#14519735C2314yes—
119#14519734D414yes—
120#14519734C2314yes—
121C2×C4⋊Dic61—21no—
122C2×C4⋊Dic61—21no—
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×C4⋊Dic61C2311yescharacteristic
126C2×#11758196—21no—
127C2×#11758196—21no—
128C2×#11758196—21no—
129C2×#11758196D411yescharacteristic
130C2×#11758196D411yescharacteristic
131C4⋊C4×D61—22no—
132C4⋊C4×D61C2314yes—
133C2×C22⋊Dic61—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×#11758198—28no—
139C2×#11758198D411yescharacteristic
140C2×#11758198D411yescharacteristic
141C22⋊C4×D61—28no—
142C2×C4×Dic61—21no—
143C2×C4×Dic61—21no—
144C2×C4×Dic61C2311yescharacteristic
145#14519710C2314yescomplemented
146#14519710C2314yescomplemented
147#14519710C2314yescomplemented
148#14519709C2314yescomplemented
149#14519709C2314yescomplemented
150#14519708C2314yescomplemented
151C4⋊#92418C2314yescomplemented
152#14519706C2314yescomplemented
153#14519706C2314yescomplemented
154#14519699C2314yes—
155#14519699C2314yes—
156#14519698C2314yes—
157#14519698C2314yes—
158#14519697C2314yes—
159#14519697C2314yes—
160C22×D4×C61C2311yescharacteristic
161C23×C4×C61—21no—
162C22×C8×C61C2311yescharacteristic
163C22×C8×C61C2311yescharacteristic
164#125×C61—22no—
165#125×C61C2314yescomplemented
166C4×D4×C61—22no—
167C4×D4×C61C2314yes—
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61—21no—
170C2×C4⋊C4×C61C2311yescharacteristic
171C2×C4⋊C4×C61C2311yescharacteristic
172C2×C4⋊C4×C61C2311yescharacteristic
173C2×C22⋊C4×C61—21no—
174C2×C42×C61C2311yescharacteristic
175#107×C61C2314yescomplemented
176#106×C61C2314yescomplemented
177C4⋊C8×C61C2314yescomplemented
178#102×C61C2314yes—
179#102×C61C2314yes—
180C24×C61—21no—
181C23×D61—21no—
182C23×D61—28no—
183C23×D61—24no—
184C23×D61—82no—
185C23×D61—82no—
186C23×D61C2×D411yescharacteristic
187C2×D4×C61—21no—
188C2×D4×C61—22no—
189C2×D4×C61C2×Q814yes—
190C2×D4×C61C2412yes—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—24no—
195C22×C4×C61—82no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—28no—
200C2×C22⋊D61—24no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61—21no—
204C22×Dic61—24no—
205C22×Dic61—82no—
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208C22×Dic61C2×D411yescharacteristic
209D4×D61—216no—
210D4×D61—28no—
211D4×D61C2×Q8116yescomplemented
212C2×D244—21no—
213C2×D244—22no—
214C2×D244C2×Q814yes—
215C2×D244C2412yes—
216C2×C4×D61—24no—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—82no—
220C2×C4×D61—82no—
221C2×C4×D61—82no—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2×Q814yes—
224C2×C4×D61#4114yes—
225C2×C4×D61C2412yes—
226C2×Dic122—24no—
227C2×Dic122—24no—
228C2×Dic122—82no—
229C2×Dic122—82no—
230C2×C8×C61—22no—
231C2×C8×C61—22no—
232C2×C8×C61C2412yes—
233C2×C8×C61C2412yes—
234C4⋊C4×C61—24no—
235C4⋊C4×C61—24no—
236C4⋊C4×C61—21no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61C2412yes—
240C4⋊C4×C61C2412yes—
241C4⋊C4×C61C2412yes—
242C22⋊C4×C61—24no—
243C42×C61C2×D412yes—
244C42×C61C2412yes—
245C22⋊Dic61—24no—
246#11758198—24no—
247#11758198—24no—
248#11758198—24no—
249#11758198—24no—
250#11758198C2×D414yes—
251#11758198C2×D414yes—
252C4⋊Dic61—21no—
253C4⋊Dic61—24no—
254C4⋊Dic61—21no—
255C4⋊Dic61—21no—
256C4⋊Dic61—24no—
257C4⋊Dic61C2412yes—
258C4⋊Dic61C2412yes—
259C4⋊Dic61C2412yes—
260#11758196—24no—
261#11758196—24no—
262#11758196—24no—
263#11758196C2×D414yes—
264#11758196C2×D414yes—
265C4×Dic61—24no—
266C4×Dic61—24no—
267C4×Dic61C2×D412yes—
268C4×Dic61C2412yes—
269C2×#92418—22no—
270C2×#92418—22no—
271C2×#92418C2412yes—
272C2×#92418C2412yes—
273#11758189—28no—
274C8×D61—28no—
275C23×C61—24no—
276C23×C61—22no—
277C23×C61—42no—
278C23×C61—42no—
279C23×C61C22×D411yescharacteristic
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—24no—
283C22×D61—22no—
284C22×D61—216no—
285C22×D61—42no—
286C22×D61—42no—
287C22×D61—816no—
288C22×D61—84no—
289C22×D61—84no—
290C22×D61C22⋊Q814yes—
291C22×D61C22×D412yes—
292D4×C61—24no—
293D4×C61—22no—
294D4×C61C22×Q814yes—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—42no—
301C2×C4×C61—42no—
302C2×C4×C61—42no—
303C2×C4×C61—84no—
304C2×C4×C61C22×D412yes—
305C2×C4×C61C22×D412yes—
306C2×C4×C61C22×D411yescharacteristic
307C2×C4×C61C22×Q812yes—
308C2×C4×C61C2×#4112yes—
309C2×C4×C61C2511yescharacteristic
310C22⋊D61—216no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—84no—
320C2×Dic61C22⋊Q814yes—
321C2×Dic61C22×D412yes—
322C2×Dic61C22×D412yes—
323C2×Dic61C22×D412yes—
324D244—24no—
325D244—22no—
326D244C22×Q814yes—
327C4×D61—84no—
328C4×D61—84no—
329C4×D61—84no—
330C4×D61C22⋊Q818yes—
331C4×D61C22×Q814yes—
332C4×D61C2×#4114yes—
333Dic122—84no—
334Dic122—84no—
335C8×C61—22no—
336C8×C61—22no—
337#92418—22no—
338#92418—22no—
339C2×#3081—611nomaximal, Sylow
340C22×C61—24no—
341C22×C61—48no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61C2×C22⋊Q812yes—
345C22×C61#57612yes—
346C22×C61#57712yes—
347C22×C61C23×D411yescharacteristic
348C2×D61—28no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—24no—
352C2×D61—48no—
353C2×D61—42no—
354C2×D61—42no—
355C2×D61—816no—
356C2×D61C2×C22⋊Q814yes—
357C4×C61—22no—
358C4×C61—22no—
359C4×C61—42no—
360C4×C61—42no—
361C4×C61—42no—
362C4×C61C2×C22⋊Q812yes—
363C4×C61C23×Q811yescharacteristic
364C4×C61C22×#4111yescharacteristic
365Dic61—22no—
366Dic61—22no—
367Dic61—42no—
368Dic61—42no—
369Dic61—42no—
370Dic61C2×C22⋊Q814yes—
371C2×#544—611no—
372C2×#518—611no—
373#3081—6116no—
374C2×#478—611no—
375C2×#478—611no—
376C2×#478—611no—
377C2×#478D6111yescharacteristic, complemented
378C2×#476—611no—
379C2×#476—611no—
380C2×#474—611no—
381C2×#474—611no—
382C2×#428—611no—
383C2×#427—611no—
384C2×#424—611no—
385C2×#418—611no—
386C22×#102—611no—
387C2×C61—44no—
388C2×C61#308114yescomplemented
389C2×C61C22×C22⋊Q811yescharacteristic
390C2×C61C2×#57611yescharacteristic
391C2×C61C2×#57711yescharacteristic
392D61—24no—
393D61—44no—
394C23×D4—611no—
395C22×M16—611no—
396C23×C8—611no—
397#544—618no—
398#544—1224no—
399C2×C4⋊Q8—611no—
400C2×C4⋊Q8—611no—
401C2×C4⋊Q8—1221no—
402C2×#125—611no—
403C2×#125—1221no—
404C2×#125C2×D6111yescharacteristic, complemented
405C2×C22⋊Q8—1221no—
406C2×C22⋊Q8—1221no—
407#518—618no—
408#518—1224no—
409C2×C4×D4—611no—
410C2×C4×D4—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C2×C4×D4—1221no—
414C2×C4×D4C2×D6111yescharacteristic
415C2×#117—611no—
416C2×#117—611no—
417C2×#117—611no—
418C22×C4⋊C4—611no—
419C22×C22⋊C4—1221no—
420C22×C22⋊C4—1221no—
421#478—618no—
422#478—618no—
423#478—618no—
424#478C2×D6118yescomplemented
425#476—618no—
426#476—618no—
427#474—618no—
428#474—618no—
429#428—618no—
430#427—618no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#107—611no—
434C2×#107C2×D6111yescharacteristic, complemented
435C2×#106—611no—
436C2×#106—611no—
437C2×#106—611no—
438C2×#106C2×D6111yescharacteristic, complemented
439#424—618no—
440C2×C4⋊C8—611no—
441C2×C4⋊C8—611no—
442C2×C4⋊C8—611no—
443C2×C4⋊C8C2×D6111yescharacteristic, complemented
444#418—618no—
445C2×#102—611no—
446C2×#102—611no—
447C2×#102—611no—
448C2×#102—611no—
449C2×#102—611no—
450C2×#102—611no—
451C2×#102—618no—
452C2×#102C2×D6111yescharacteristic
453C2×#102C2×D6111yescharacteristic
454C61C2×#308111yescharacteristic, complemented, Sylow
455C25—1221no—
456C22×Q8—1221no—
457C22×Q8—1221no—
458C22×D4—618no—
459C22×D4—614no—
460C22×D4—611no—
461C22×D4—1222no—
462C22×D4—1224no—
463C22×D4—1221no—
464C22×D4C22×D6111yescharacteristic
465C23×C4—21no—
466C23×C4—611no—
467C23×C4—1221no—
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4—1221no—
471C2×M16—614no—
472C2×M16—1224no—
473C22×C8—611no—
474C22×C8—611no—
475C22×C8—614no—
476C22×C8—1224no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479C4⋊Q8—614no—
480C4⋊Q8—614no—
481C4⋊Q8—1222no—
482C4⋊Q8—1228no—
483C4⋊Q8—1222no—
484#125—22no—
485#125—614no—
486#125—1222no—
487#125—1228no—
488#125C22×D6114yescomplemented
489C22⋊Q8—1228no—
490C22⋊Q8—1228no—
491C4×D4—22no—
492C4×D4—614no—
493C4×D4—614no—
494C4×D4—614no—
495C4×D4—1222no—
496C4×D4—1222no—
497C4×D4—1228no—
498C4×D4—1228no—
499C4×D4—1222no—
500C4×D4C22×D6114yes—
501#117—614no—
502#117—614no—
503#117—614no—
504#117—614no—
505#117—1222no—
506#117—1222no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—611no—
510C2×C4⋊C4—611no—
511C2×C4⋊C4—611no—
512C2×C4⋊C4—611no—
513C2×C4⋊C4—611no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—1222no—
516C2×C4⋊C4—1221no—
517C2×C4⋊C4—1221no—
518C2×C4⋊C4—1221no—
519C2×C4⋊C4—1221no—
520C2×C4⋊C4—1221no—
521C2×C4⋊C4C22×D6111yescharacteristic
522C2×C4⋊C4C22×D6111yescharacteristic
523C2×C4⋊C4C22×D6111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—611no—
526C2×C22⋊C4—611no—
527C2×C22⋊C4—1228no—
528C2×C22⋊C4—1228no—
529C2×C22⋊C4—1221no—
530C2×C22⋊C4—1221no—
531C2×C22⋊C4—1221no—
532C2×C22⋊C4—1221no—
533C2×C22⋊C4—1221no—
534C2×C42—611no—
535C2×C42—1221no—
536C2×C42—1221no—
537C2×C42C22×D6111yescharacteristic
538#107—614no—
539#107—614no—
540#107—614no—
541#107C22×D6114yescomplemented
542#106—614no—
543#106—614no—
544#106—614no—
545#106C22×D6114yescomplemented
546C4⋊C8—614no—
547C4⋊C8—614no—
548C4⋊C8—614no—
549C4⋊C8C22×D6114yescomplemented
550#102—614no—
551#102—614no—
552#102—614no—
553#102—614no—
554#102—614no—
555#102—614no—
556#102C22×D6114yes—
557#102C22×D6114yes—
558C24—21no—
559C24—611no—
560C24—1224no—
561C24—1228no—
562C24—1221no—
563C24—4882no—
564C24—4882no—
565C2×Q8—1224no—
566C2×Q8—1224no—
567C2×Q8—4882no—
568C2×Q8—4882no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—6116no—
572C2×D4—614no—
573C2×D4—612no—
574C2×D4—12216no—
575C2×D4—1228no—
576C2×D4—1224no—
577C2×D4—1228no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4Q8×D6114yes—
581C2×D4C23×D6112yes—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—24no—
586C22×C4—82no—
587C22×C4—611no—
588C22×C4—612no—
589C22×C4—614no—
590C22×C4—614no—
591C22×C4—612no—
592C22×C4—611no—
593C22×C4—611no—
594C22×C4—1224no—
595C22×C4—1224no—
596C22×C4—1224no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1224no—
601C22×C4—4882no—
602C22×C4—4882no—
603C22×C4—4882no—
604C22×C4—4882no—
605C22×C4D4×D6111yescharacteristic
606C22×C4D4×D6111yescharacteristic
607C22×C4C23×D6111yescharacteristic
608M16—1228no—
609C2×C8—22no—
610C2×C8—22no—
611C2×C8—612no—
612C2×C8—612no—
613C2×C8—1228no—
614C2×C8—1222no—
615C2×C8—1222no—
616C2×C8C23×D6112yes—
617C2×C8C23×D6112yes—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—614no—
624C4⋊C4—614no—
625C4⋊C4—612no—
626C4⋊C4—612no—
627C4⋊C4—612no—
628C4⋊C4—1224no—
629C4⋊C4—1224no—
630C4⋊C4—1224no—
631C4⋊C4—1224no—
632C4⋊C4—1221no—
633C4⋊C4—1221no—
634C4⋊C4—1221no—
635C4⋊C4—1224no—
636C4⋊C4C23×D6112yes—
637C4⋊C4C23×D6112yes—
638C4⋊C4C23×D6112yes—
639C22⋊C4—24no—
640C22⋊C4—614no—
641C22⋊C4—614no—
642C22⋊C4—1224no—
643C22⋊C4—1224no—
644C22⋊C4—1224no—
645C22⋊C4—1224no—
646C22⋊C4—1224no—
647C42—612no—
648C42—612no—
649C42—1224no—
650C42—1224no—
651C42D4×D6112yes—
652C42C23×D6112yes—
653C23—24no—
654C23—22no—
655C23—42no—
656C23—42no—
657C23—614no—
658C23—612no—
659C23—12216no—
660C23—1222no—
661C23—1222no—
662C23—1224no—
663C23—1222no—
664C23—48816no—
665C23—4884no—
666C23—4884no—
667C23—2442no—
668C23—2442no—
669C23C2×D4×D6111yescharacteristic
670Q8—4884no—
671Q8—4884no—
672D4—24no—
673D4—22no—
674D4—614no—
675D4—12216no—
676D4—1224no—
677D4—1222no—
678D4C2×Q8×D6114yes—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—84no—
688C2×C4—614no—
689C2×C4—612no—
690C2×C4—618no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—612no—
694C2×C4—612no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—4884no—
701C2×C4—4884no—
702C2×C4—4884no—
703C2×C4—4884no—
704C2×C4—2442no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4C2×D4×D6112yes—
708C2×C4C2×D4×D6112yes—
709C2×C4C2×D4×D6111yescharacteristic
710C2×C4C2×Q8×D6112yes—
711C2×C4#41×D6112yes—
712C2×C4C24×D6111yescharacteristic
713C8—22no—
714C8—22no—
715C8—1222no—
716C8—1222no—
717C22—24no—
718C22—48no—
719C22—42no—
720C22—42no—
721C22—614no—
722C22—1228no—
723C22—1222no—
724C22—1222no—
725C22—1224no—
726C22—48816no—
727C22—2448no—
728C22—2442no—
729C22—2442no—
730C22C22⋊Q8×D6112yes—
731C22#1684056612yes—
732C22#1684056912yes—
733C22C22×D4×D6111yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—614no—
740C4—1222no—
741C4—1222no—
742C4—2442no—
743C4—2442no—
744C4—2442no—
745C4C22⋊Q8×D6112yes—
746C4C22×Q8×D6111yescharacteristic
747C4C2×#41×D6111yescharacteristic
748C2—44no—
749C2—1224no—
750C2—2444no—
751C2#2145564914yesdirect product factor
752C2C2×C22⋊Q8×D6111yescharacteristic
753C2C2×#1684056611yescharacteristic
754C2C2×#1684056911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#478C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
hypercenterC2×#478D61
hypocenterC61C2×#3081
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#16840392C2semidirect
3. #21455649C2direct (N × H)
4. C2×#16840064C2semidirect
5. C2×#16840061C2semidirect
6. C2×#16840059C2semidirect
7. C2×#16840053C2semidirect
8. C2×#16840050C2semidirect
9. C2×#16840042C2semidirect
10. C2×#16840041C2semidirect
11. C2×#16839803C2semidirect
12. C2×#16839797C2semidirect
13. C2×#16839787C2semidirect
16. C2×C61×#478C2semidirect
21. #16840392C22semidirect
22. C2×#14519777C22semidirect
24. C2×#14519776C22semidirect
25. C2×#14519768C22semidirect
42. #16840064C22semidirect
43. #16840061C22semidirect
44. #16840059C22semidirect
45. #16840053C22semidirect
46. #16840050C22semidirect
47. #16840042C22semidirect
48. #16840041C22semidirect
49. #16839803C22semidirect
50. #16839797C22semidirect
51. C2×#14519710C22semidirect
52. C2×#14519710C22semidirect
53. C2×#14519710C22semidirect
54. C2×#14519709C22semidirect
55. C2×#14519709C22semidirect
56. C2×#14519708C22semidirect
57. #16839787C22semidirect
58. C2×C4⋊#92418C22semidirect
59. C2×#14519706C22semidirect
60. C2×#14519706C22semidirect
69. C2×#125×C61C22semidirect
71. C61×#478C22semidirect
72. C2×#107×C61C22semidirect
73. C2×#106×C61C22semidirect
74. C2×C4⋊C8×C61C22semidirect
84. C2×D4×D61Q8semidirect
98. #14519777C23semidirect
101. #14519776C23semidirect
103. #14519768C23semidirect
145. #14519710C23semidirect
146. #14519710C23semidirect
147. #14519710C23semidirect
148. #14519709C23semidirect
149. #14519709C23semidirect
150. #14519708C23semidirect
151. C4⋊#92418C23semidirect
152. #14519706C23semidirect
153. #14519706C23semidirect
165. #125×C61C23semidirect
175. #107×C61C23semidirect
176. #106×C61C23semidirect
177. C4⋊C8×C61C23semidirect
211. D4×D61C2×Q8semidirect
377. C2×#478D61semidirect
388. C2×C61#3081semidirect
404. C2×#125C2×D61semidirect
424. #478C2×D61semidirect
434. C2×#107C2×D61semidirect
438. C2×#106C2×D61semidirect
443. C2×C4⋊C8C2×D61semidirect
454. C61C2×#3081semidirect
488. #125C22×D61semidirect
541. #107C22×D61semidirect
545. #106C22×D61semidirect
549. C4⋊C8C22×D61semidirect
751. C2#21455649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403922
C2×#168402342
#214556492
C2×#168400642
C2×#168400612
C2×#168400592
C2×#168400532
C2×#168400502
C2×#168400422
C2×#168400412
C2×#168398032
C2×#168397972
C2×#168397872
C2×#168397652
C2×#102×D612
C2×C61×#4782
C2×#308161