Finite Group Databasebeta

← #30621749

Subgroups — #30621749

Order 15616.

1314 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C22×#14519839C211yesmaximal, characteristic
3#21462343C211yesmaximal, characteristic, complemented
4D4×C22⋊#6923C211yesmaximal, characteristic
5#21461964C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461832C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461769C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461554C211yesmaximal, characteristic, complemented
15#450×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic, complemented
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21C22×C22⋊#6923—21no—
22SD16×#6923—24no—
23C2×#14519845C2211yescharacteristic, complemented
24C2×#14519845C2211yescharacteristic, complemented
25C2×#14519840C2211yescharacteristic, complemented
26C2×#14519840C2211yescharacteristic, complemented
27C2×#14519839—24no—
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic, complemented
33C2×C8×#6923C2211yescharacteristic, complemented
34(C2×#6923)⋊Q8C2211yescharacteristic, complemented
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713—21no—
38#16840713C2211yescharacteristic, complemented
39#16840711—21no—
40#16840710—21no—
41#16840710—21no—
42#16840709—21no—
43#16840704C2211yescharacteristic
44#16840703—21no—
45C4⋊C4×#6923C2211yescharacteristic, complemented
46C22⋊C4×#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic, complemented
49#16840636C2211yescharacteristic, complemented
50#16840635C2211yescharacteristic, complemented
51#16840635C2211yescharacteristic, complemented
52(C2×#6923)⋊C8C2211yescharacteristic, complemented
53(C2×#6923)⋊C8C2211yescharacteristic, complemented
54C22×D4×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×SD16×D61C2211yescharacteristic
57C22⋊Q8×D61C2211yescharacteristic
58#16839915C411yescharacteristic, complemented
59#16839914C411yescharacteristic, complemented
60#16839914C411yescharacteristic, complemented
61#16839913C411yescharacteristic, complemented
62#16839912C411yescharacteristic, complemented
63#16839911C411yescharacteristic, complemented
64#16839911C411yescharacteristic, complemented
65#102×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#450C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C2×D61⋊C8—22no—
73C2×D61⋊C8—21no—
74C2×D61⋊C8—41no—
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77C22×#92420—21no—
78Q8×#6923—22no—
79Q8×#6923—41no—
80D4×#6923—22no—
81D4×#6923—22no—
82D4×#6923—41no—
83D4×#6923—41no—
84C2×C4⋊#6923—22no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923—21no—
88C2×C4⋊#6923—41no—
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C4⋊#6923C2311yescharacteristic
92C2×C4⋊#6923C2311yescharacteristic
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C22⋊#6923—44no—
101C2×C22⋊#6923D411yescharacteristic
102C2×C22⋊#6923D411yescharacteristic
103C2×C4×#6923—21no—
104C2×C4×#6923—21no—
105C2×C4×#6923C2311yescharacteristic
106C2×C4×#6923C2311yescharacteristic
107#14519845—22no—
108#14519845—41no—
109#14519840—22no—
110#14519840—41no—
111#14519839—22no—
112#14519839—22no—
113#14519839—22no—
114#14519839D414yes—
115C8×#6923—22no—
116C8×#6923—41no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4—21no—
122(C2×#6923)⋊C4D411yescharacteristic
123(C2×#6923)⋊C4D411yescharacteristic
124C24×D61—21no—
125C2×Q8×D61C2311yescharacteristic
126C22×D244C2×C411yescharacteristic
127C22×C22⋊D61—21no—
128C2×D4×D61—22no—
129C2×D4×D61—22no—
130C2×D4×D61—21no—
131C2×D4×D61—21no—
132C2×D4×D61—41no—
133C2×D4×D61—41no—
134C2×D4×D61C2×C411yescharacteristic
135C2×D4×D61C2×C411yescharacteristic
136C2×D4×D61C2311yescharacteristic
137C2×D4×D61C2311yescharacteristic
138C22×C4×D61C2311yescharacteristic
139C2×#11758190C2×C411yescharacteristic, complemented
140C2×#11758190C2×C411yescharacteristic, complemented
141C2×#11758200C2×C411yescharacteristic, complemented
142C2×#11758200C2×C411yescharacteristic, complemented
143C2×#11758201C2×C411yescharacteristic, complemented
144C2×#11758201C2×C411yescharacteristic, complemented
145SD16×D61—22no—
146SD16×D61—22no—
147SD16×D61—41no—
148SD16×D61—41no—
149C2×C8×D61C2311yescharacteristic
150C2×C8×D61C2311yescharacteristic
151#14519757C2×C411yescharacteristic, complemented
152#14519756C2×C411yescharacteristic, complemented
153#14519755—21no—
154#14519754—21no—
155#14519753C2×C411yescharacteristic, complemented
156C4⋊C4×D61—21no—
157C4⋊C4×D61C2311yescharacteristic
158C22⋊C4×D61—21no—
159#14519699C2×C411yescharacteristic, complemented
160#14519699C2×C411yescharacteristic, complemented
161#14519698C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic, complemented
164#14519697C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C22×D4×C61C2×C411yescharacteristic
169C2×SD16×C61C2×C411yescharacteristic, complemented
170C2×SD16×C61C2×C411yescharacteristic, complemented
171C22⋊Q8×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173#102×C61C2×C411yescharacteristic, complemented
174C22⋊C8×C61C2×C411yescharacteristic, complemented
175C24×C61—21no—
176C23×D61—21no—
177C23×D61—21no—
178C23×D61—21no—
179C23×D61—21no—
180C23×D61—21no—
181C23×D61—42no—
182C23×D61—42no—
183C23×D61—42no—
184C23×D61—42no—
185C23×D61—81no—
186C23×D61—81no—
187C23×D61C2×D411yescharacteristic
188C22×#6923—21no—
189C22×#6923—21no—
190C22×#6923—21no—
191C22×#6923—21no—
192C22×#6923—42no—
193C22×#6923—42no—
194C22×#6923—42no—
195C22×#6923—42no—
196C22×#6923—42no—
197C22×#6923—42no—
198C22×#6923—81no—
199C22×#6923—81no—
200C22×#6923—81no—
201C22×#6923C2×D411yescharacteristic
202C22×#6923C2×D411yescharacteristic
203C22×#6923C2×D411yescharacteristic
204C22×#6923C2×D411yescharacteristic
205C2×Q8×C61C22×C411yescharacteristic
206C2×D4×C61—22no—
207C2×D4×C61—21no—
208C2×D4×C61—41no—
209C2×D4×C61C22×C411yescharacteristic
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—42no—
217C2×C22⋊D61—42no—
218C22×Dic61#4111yescharacteristic
219Q8×D61—21no—
220Q8×D61—21no—
221Q8×D61—21no—
222Q8×D61—21no—
223D4×D61—22no—
224D4×D61—22no—
225D4×D61—21no—
226D4×D61—21no—
227D4×D61—21no—
228D4×D61—21no—
229D4×D61—21no—
230D4×D61—21no—
231D4×D61—41no—
232D4×D61—41no—
233D4×D61—42no—
234D4×D61—42no—
235D4×D61—42no—
236D4×D61—42no—
237D4×D61C2×D412yes—
238D4×D61#4112yes—
239C2×D244—22no—
240C2×D244—21no—
241C2×D244—41no—
242C2×D244C22×C411yescharacteristic
243C2×D244C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61C22×C411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61#4111yescharacteristic
253C2×C4×D61C2411yescharacteristic
254C2×Dic122—21no—
255C2×Dic122C22×C411yescharacteristic
256C22⋊#6923—22no—
257C22⋊#6923—42no—
258C22⋊#6923—42no—
259C22⋊#6923—42no—
260C22⋊#6923—42no—
261C22⋊#6923—42no—
262C22⋊#6923—81no—
263C22⋊#6923—81no—
264C22⋊#6923SD1614yescomplemented
265C2×#92420—21no—
266C2×#92420—21no—
267C2×#92420—42no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—42no—
276C4⋊#6923—42no—
277C4⋊#6923—81no—
278C4⋊#6923C2×D412yes—
279C4×#6923—21no—
280C4×#6923—21no—
281C4×#6923—21no—
282C4×#6923—21no—
283C4×#6923—42no—
284C4×#6923—81no—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8—21no—
288D61⋊C8—42no—
289D61⋊C8C2×D412yes—
290SD16×C61—22no—
291SD16×C61—41no—
292C2×C8×C61C22×C411yescharacteristic
293C2×C8×C61C22×C411yescharacteristic
294C4⋊C4×C61—21no—
295C4⋊C4×C61C22×C411yescharacteristic
296C22⋊C4×C61—21no—
297C22⋊Dic61—21no—
298#11758201—22no—
299#11758201—41no—
300#11758200—22no—
301#11758200—41no—
302#11758198—21no—
303#11758198—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61C22×C411yescharacteristic
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309C2×#92418C22×C411yescharacteristic
310C2×#92418C22×C411yescharacteristic
311#11758190—22no—
312#11758190—41no—
313C8×D61—21no—
314C8×D61—21no—
315C8×D61—21no—
316C8×D61—21no—
317C23×C61—21no—
318C23×C61—21no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—81no—
322C23×C61C4×D411yescharacteristic
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—22no—
329C22×D61—22no—
330C22×D61—21no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—42no—
339C22×D61—41no—
340C22×D61—41no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—42no—
346C22×D61—42no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61—84no—
350C22×D61—84no—
351C22×D61—84no—
352C22×D61—84no—
353C22×D61—81no—
354C22×D61C4×D411yescharacteristic
355C22×D61C2×SD1612yes—
356C22×D61#13512yes—
357C22×D61C22×D411yescharacteristic
358C2×#6923—21no—
359C2×#6923—21no—
360C2×#6923—21no—
361C2×#6923—21no—
362C2×#6923—21no—
363C2×#6923—22no—
364C2×#6923—21no—
365C2×#6923—21no—
366C2×#6923—21no—
367C2×#6923—21no—
368C2×#6923—21no—
369C2×#6923—41no—
370C2×#6923—41no—
371C2×#6923—41no—
372C2×#6923—41no—
373C2×#6923—41no—
374C2×#6923—41no—
375C2×#6923—41no—
376C2×#6923—41no—
377C2×#6923—41no—
378C2×#6923—41no—
379C2×#6923—41no—
380C2×#6923—84no—
381C2×#6923—84no—
382C2×#6923—84no—
383C2×#6923C2×SD1612yes—
384C2×#6923C2×SD1612yes—
385Q8×C61—21no—
386Q8×C61—21no—
387D4×C61—21no—
388D4×C61—21no—
389D4×C61—21no—
390D4×C61—42no—
391D4×C61C4×D412yes—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61C4×D411yescharacteristic
397C2×C4×C61C23×C411yescharacteristic
398C22⋊D61—22no—
399C22⋊D61—22no—
400C22⋊D61—42no—
401C22⋊D61—42no—
402C22⋊D61—41no—
403C22⋊D61—41no—
404C2×Dic61—21no—
405C2×Dic61—21no—
406C2×Dic61—21no—
407C2×Dic61—21no—
408C2×Dic61C4×D411yescharacteristic
409C2×Dic61C2×#4111yescharacteristic
410D244—21no—
411D244—21no—
412D244—21no—
413D244—42no—
414D244C4×D412yes—
415C4×D61—21no—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—21no—
419C4×D61—21no—
420C4×D61—21no—
421C4×D61—41no—
422C4×D61—41no—
423C4×D61—41no—
424C4×D61—41no—
425C4×D61C22×D411yescharacteristic
426C4×D61C2×#4111yescharacteristic
427C4×D61H(5,𝔽2)11yescharacteristic
428C4×D61H(5,𝔽2)11yescharacteristic
429Dic122—21no—
430Dic122—21no—
431Dic122—41no—
432Dic122—41no—
433#92420—22no—
434#92420—41no—
435C8×C61—21no—
436C8×C61—21no—
437#92418—21no—
438#92418—21no—
439#22874—611nomaximal, Sylow
440C22×C61—21no—
441C22×C61—21no—
442C22×C61—22no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—41no—
447C22×C61—41no—
448C22×C61—84no—
449C22×C61C4×SD1612yescomplemented
450C22×C61C2×C4×D411yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—22no—
454C2×D61—22no—
455C2×D61—22no—
456C2×D61—22no—
457C2×D61—22no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—42no—
461C2×D61—42no—
462C2×D61—42no—
463C2×D61—42no—
464C2×D61—41no—
465C2×D61—41no—
466C2×D61—41no—
467C2×D61—84no—
468C2×D61—84no—
469C2×D61—84no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61—81no—
473C2×D61—81no—
474C2×D61C4×SD1612yescomplemented
475C2×D61D4211yescharacteristic
476C2×D61#54611yescharacteristic
477C2×D61C22×SD1611yescharacteristic
478C2×D61C2×#13511yescharacteristic
479C2×D61#57611yescharacteristic
480C2×D61#57711yescharacteristic
481#6923—22no—
482#6923—22no—
483#6923—41no—
484#6923—42no—
485#6923—41no—
486#6923—81no—
487#6923—81no—
488#6923—81no—
489C4×C61—21no—
490C4×C61—41no—
491C4×C61—41no—
492C4×C61C2×C4×D411yescharacteristic
493C4×C61#51811yescharacteristic
494Dic61—21no—
495Dic61—41no—
496Dic61—41no—
497Dic61#54611yescharacteristic
498Dic61#55111yescharacteristic
499C2×#450—611no—
500C2×C4×SD16—611no—
501C22×#102—611no—
502#2360—611no—
503D4×C22⋊C4—611no—
504#1968—611no—
505#1934—611no—
506#1926—611no—
507#1892—611no—
508#1880—611no—
509#1877—611no—
510#1864—611no—
511#1853—611no—
512C4×#102—611no—
513C8×C22⋊C4—611no—
514C2×C61—22no—
515C2×C61—42no—
516C2×C61—81no—
517C2×C61#235811yescharacteristic
518C2×C61C2×C4×SD1611yescharacteristic
519C2×C61#294611yescharacteristic
520D61—22no—
521D61—42no—
522D61—81no—
523D61#328011yescharacteristic
524D61D4×SD1611yescharacteristic
525D61#329511yescharacteristic
526D61#329611yescharacteristic
527C23×D4—611no—
528C22×SD16—611no—
529C22×SD16—611no—
530C23×C8—611no—
531C2×C22⋊Q8—611no—
532C2×C4×Q8—611no—
533C2×C4×D4—611no—
534C2×C4×D4—611no—
535C22×C4⋊C4—611no—
536C22×C22⋊C4—1221no—
537#450—611no—
538#450—611no—
539#450—611no—
540#450—611no—
541#450—611no—
542#450—611no—
543#450—611no—
544#450#692311yescharacteristic, complemented
545C4×SD16—1224no—
546C2×#106—611no—
547C2×#106—611no—
548C2×#103—611no—
549C2×#103—611no—
550C2×#102—611no—
551C2×#102—611no—
552C2×#102—611no—
553C2×#102—611no—
554C2×#102—611no—
555C2×#102—611no—
556C2×#102—1224no—
557C2×C22⋊C8—611no—
558C2×C4×C8—611no—
559C2×C4×C8—611no—
560#391—611no—
561#390—611no—
562#390—611no—
563#389—611no—
564#389—1221no—
565#387—1221no—
566#386—1221no—
567#386—1221no—
568#385—1221no—
569#380—611no—
570#379—1221no—
571C4×C4⋊C4—611no—
572C4×C22⋊C4—611no—
573C4×C22⋊C4—1221no—
574#340—611no—
575#340—611no—
576#340—611no—
577#340—611no—
578#336—611no—
579#336—611no—
580C61#2287411yescharacteristic, complemented, Sylow
581C25—1221no—
582C22×Q8—611no—
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—611no—
586C22×D4—611no—
587C22×D4—611no—
588C22×D4—1221no—
589C22×D4—1221no—
590C22×D4—1221no—
591C22×D4—1222no—
592C22×D4—1222no—
593C22×D4—2441no—
594C22×D4—2441no—
595C22×D4C2×#692311yescharacteristic
596C23×C4—611no—
597C23×C4—1221no—
598C23×C4—1221no—
599C23×C4—1221no—
600C2×SD16—611no—
601C2×SD16—611no—
602C2×SD16—611no—
603C2×SD16—611no—
604C2×SD16—611no—
605C2×SD16—611no—
606C2×SD16—1222no—
607C2×SD16—1222no—
608C2×SD16—2441no—
609C2×SD16—2441no—
610C2×SD16C2×#692311yescharacteristic, complemented
611C2×SD16C2×#692311yescharacteristic, complemented
612C22×C8—611no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—611no—
616C22×C8—1222no—
617C22×C8—1221no—
618C22×C8—1221no—
619C22×C8—2441no—
620C22⋊Q8—611no—
621C22⋊Q8—611no—
622C22⋊Q8—611no—
623C22⋊Q8—1221no—
624C22⋊Q8—1221no—
625C22⋊Q8C2×#692311yescharacteristic, complemented
626C4×Q8—1222no—
627C4×Q8—2441no—
628C4×D4—1222no—
629C4×D4—1222no—
630C4×D4—2441no—
631C4×D4—2441no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—611no—
636C2×C4⋊C4—611no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1222no—
639C2×C4⋊C4—1221no—
640C2×C4⋊C4—1221no—
641C2×C4⋊C4—1221no—
642C2×C4⋊C4—2441no—
643C2×C22⋊C4—611no—
644C2×C22⋊C4—611no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—2444no—
654C2×C42—611no—
655C2×C42—611no—
656C2×C42—1221no—
657C2×C42—1221no—
658#106—1222no—
659#106—2441no—
660#103—1222no—
661#103—2441no—
662#102—614no—
663#102—611no—
664#102—611no—
665#102—611no—
666#102—611no—
667#102—611no—
668#102—611no—
669#102—1222no—
670#102—1222no—
671#102—1222no—
672#102C2×#692311yescharacteristic, complemented
673#102C2×#692311yescharacteristic, complemented
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8C2×#692311yescharacteristic, complemented
678C4×C8—1222no—
679C4×C8—2441no—
680#95—611no—
681#95—611no—
682#95—1221no—
683#95—1221no—
684#95—1221no—
685#95—1221no—
686#95—1221no—
687C24—21no—
688C24—611no—
689C24—1221no—
690C24—1221no—
691C24—1221no—
692C24—1221no—
693C24—1221no—
694C24—4881no—
695C24—4881no—
696C24—2442no—
697C24—2442no—
698C24—2442no—
699C24—2442no—
700C2×Q8—611no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8—1221no—
704C2×Q8—1221no—
705C2×Q8—1221no—
706C2×Q8C22×#692311yescharacteristic
707C2×D4—22no—
708C2×D4—21no—
709C2×D4—41no—
710C2×D4—612no—
711C2×D4—612no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—1222no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1222no—
726C2×D4—1222no—
727C2×D4—1221no—
728C2×D4—2441no—
729C2×D4—2441no—
730C2×D4—2441no—
731C2×D4—2442no—
732C2×D4—2442no—
733C2×D4—2442no—
734C2×D4—2442no—
735C2×D4—2442no—
736C2×D4—2442no—
737C2×D4C22×#692311yescharacteristic
738C2×D4C22×#692311yescharacteristic
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—611no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—4881no—
759C22×C4—4881no—
760C22×C4—4881no—
761C22×C4—2442no—
762C22×C4—2442no—
763C22×C4—2442no—
764C22×C4—2442no—
765C22×C4—2442no—
766C22×C4—2442no—
767C22×C4C22×#692311yescharacteristic
768SD16—22no—
769SD16—41no—
770SD16—1222no—
771SD16—1222no—
772SD16—1222no—
773SD16—2441no—
774SD16—2441no—
775SD16—2441no—
776C2×C8—612no—
777C2×C8—611no—
778C2×C8—611no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8—1221no—
785C2×C8—1221no—
786C2×C8—1221no—
787C2×C8—1221no—
788C2×C8—2442no—
789C2×C8—2442no—
790C2×C8C22×#692311yescharacteristic
791C2×C8C22×#692311yescharacteristic
792C4⋊C4—21no—
793C4⋊C4—612no—
794C4⋊C4—611no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—1221no—
801C4⋊C4—1221no—
802C4⋊C4—1221no—
803C4⋊C4—1221no—
804C4⋊C4—1221no—
805C4⋊C4—1221no—
806C4⋊C4—4881no—
807C4⋊C4—2442no—
808C4⋊C4—2442no—
809C4⋊C4C22×#692311yescharacteristic
810C22⋊C4—21no—
811C22⋊C4—614no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1222no—
815C22⋊C4—1221no—
816C22⋊C4—4881no—
817C22⋊C4—4881no—
818C22⋊C4—2442no—
819C22⋊C4—2442no—
820C22⋊C4—2442no—
821C22⋊C4—2442no—
822C22⋊C4—2442no—
823C42—1221no—
824C42—1221no—
825C42—1221no—
826C42—1221no—
827C42—4881no—
828C42—2442no—
829C23—21no—
830C23—21no—
831C23—42no—
832C23—42no—
833C23—81no—
834C23—611no—
835C23—612no—
836C23—612no—
837C23—611no—
838C23—1221no—
839C23—1221no—
840C23—1221no—
841C23—1221no—
842C23—1222no—
843C23—1222no—
844C23—1221no—
845C23—1221no—
846C23—4881no—
847C23—4881no—
848C23—4881no—
849C23—4884no—
850C23—4884no—
851C23—4884no—
852C23—4884no—
853C23—2442no—
854C23—2442no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2441no—
859C23—2441no—
860C23—2442no—
861C23—2441no—
862C23—2442no—
863C23—2441no—
864C23—2441no—
865C23—2441no—
866C23—2441no—
867C23—2442no—
868C23—2442no—
869C23D4×#692311yescharacteristic
870Q8—21no—
871Q8—21no—
872Q8—1221no—
873Q8—1221no—
874Q8—2441no—
875Q8—2441no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—42no—
880D4—612no—
881D4—1222no—
882D4—1222no—
883D4—1221no—
884D4—1221no—
885D4—1221no—
886D4—2442no—
887D4—2441no—
888D4—2441no—
889D4—2442no—
890D4—2442no—
891D4D4×#692312yes—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—611no—
897C2×C4—611no—
898C2×C4—611no—
899C2×C4—611no—
900C2×C4—611no—
901C2×C4—612no—
902C2×C4—612no—
903C2×C4—611no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1221no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1222no—
919C2×C4—1221no—
920C2×C4—1221no—
921C2×C4—1221no—
922C2×C4—1221no—
923C2×C4—1221no—
924C2×C4—1221no—
925C2×C4—4884no—
926C2×C4—4884no—
927C2×C4—4884no—
928C2×C4—2441no—
929C2×C4—2441no—
930C2×C4—2441no—
931C2×C4—2441no—
932C2×C4—2441no—
933C2×C4—2441no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4—2441no—
940C2×C4—2441no—
941C2×C4—2441no—
942C2×C4—2441no—
943C2×C4D4×#692311yescharacteristic
944C2×C4C23×#692311yescharacteristic
945C8—21no—
946C8—21no—
947C8—1222no—
948C8—1221no—
949C8—1221no—
950C8—2441no—
951C22—21no—
952C22—21no—
953C22—22no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—84no—
960C22—611no—
961C22—611no—
962C22—611no—
963C22—611no—
964C22—611no—
965C22—611no—
966C22—612no—
967C22—1222no—
968C22—1222no—
969C22—1222no—
970C22—1222no—
971C22—1221no—
972C22—1221no—
973C22—1222no—
974C22—4884no—
975C22—4884no—
976C22—4881no—
977C22—4881no—
978C22—4881no—
979C22—4881no—
980C22—4884no—
981C22—2442no—
982C22—2442no—
983C22—2442no—
984C22—2442no—
985C22—2441no—
986C22—2441no—
987C22—2441no—
988C22—2441no—
989C22—2441no—
990C22SD16×#692312yescomplemented
991C22C2×D4×#692311yescharacteristic
992C4—21no—
993C4—41no—
994C4—41no—
995C4—611no—
996C4—611no—
997C4—1222no—
998C4—1222no—
999C4—1221no—
1000C4—4881no—
1001C4—4881no—
1002C4—4881no—
1003C4—2441no—
1004C4—2441no—
1005C4—2442no—
1006C4—2441no—
1007C4—2441no—
1008C4C2×D4×#692311yescharacteristic
1009C4#1684082911yescharacteristic
1010C2—22no—
1011C2—42no—
1012C2—81no—
1013C2—611no—
1014C2—611no—
1015C2—611no—
1016C2—611no—
1017C2—1222no—
1018C2—4881no—
1019C2—2442no—
1020C2#2146234111yescharacteristic
1021C2C2×SD16×#692311yescharacteristic
1022C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#450C4
socleC22×C61C2×C4×D4
prime radicalC22×D4×D61C22
cosocleC2×C4×D61C24
hypercenter#450#6923
hypocenterC61#22874
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C2×SD16×#6923C2semidirect
3. #21462343C2semidirect
5. #21461964C2semidirect
6. #21461909C2semidirect
7. #21461897C2semidirect
8. #21461832C2semidirect
9. #21461815C2semidirect
10. #21461812C2semidirect
11. #21461784C2semidirect
12. #21461769C2semidirect
13. #102×#6923C2semidirect
14. #21461554C2semidirect
17. C2×Q8×#6923C22semidirect
23. C2×#14519845C22semidirect
24. C2×#14519845C22semidirect
25. C2×#14519840C22semidirect
26. C2×#14519840C22semidirect
32. C2×C8×#6923C22semidirect
33. C2×C8×#6923C22semidirect
34. (C2×#6923)⋊Q8C22semidirect
38. #16840713C22semidirect
45. C4⋊C4×#6923C22semidirect
48. #16840636C22semidirect
49. #16840636C22semidirect
50. #16840635C22semidirect
51. #16840635C22semidirect
52. (C2×#6923)⋊C8C22semidirect
53. (C2×#6923)⋊C8C22semidirect
58. #16839915C4semidirect
59. #16839914C4semidirect
60. #16839914C4semidirect
61. #16839913C4semidirect
62. #16839912C4semidirect
63. #16839911C4semidirect
64. #16839911C4semidirect
68. C61×#450C4semidirect
139. C2×#11758190C2×C4semidirect
140. C2×#11758190C2×C4semidirect
141. C2×#11758200C2×C4semidirect
142. C2×#11758200C2×C4semidirect
143. C2×#11758201C2×C4semidirect
144. C2×#11758201C2×C4semidirect
151. #14519757C2×C4semidirect
152. #14519756C2×C4semidirect
155. #14519753C2×C4semidirect
159. #14519699C2×C4semidirect
160. #14519699C2×C4semidirect
161. #14519698C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519697C2×C4semidirect
164. #14519697C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
169. C2×SD16×C61C2×C4semidirect
170. C2×SD16×C61C2×C4semidirect
171. C22⋊Q8×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
264. C22⋊#6923SD16semidirect
449. C22×C61C4×SD16semidirect
474. C2×D61C4×SD16semidirect
544. #450#6923semidirect
580. C61#22874semidirect
610. C2×SD16C2×#6923semidirect
611. C2×SD16C2×#6923semidirect
625. C22⋊Q8C2×#6923semidirect
672. #102C2×#6923semidirect
673. #102C2×#6923semidirect
677. C22⋊C8C2×#6923semidirect
990. C22SD16×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C22×#145198392
#214623432
D4×C22⋊#69232
#214619642
#214619092
#214618972
#214618322
#214618152
#214618122
#214617842
#214617692
#102×#69232
#214615542
#450×D612
#2287461