Finite Group Databasebeta

← #30621747

Subgroups — #30621747

Order 15616.

1186 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×#6923C211yesmaximal, characteristic, complemented
2C2×#16840752C211yesmaximal, characteristic, complemented
3#21462346C211yesmaximal, characteristic, complemented
4#21462322C211yesmaximal, characteristic, complemented
5#21461964C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461833C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461784C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#102×#6923C211yesmaximal, characteristic, complemented
14#21461554C211yesmaximal, characteristic, complemented
15#449×D61C211yesmaximal, characteristic
16C22×D61⋊C8C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21D8×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840752—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×C8×#6923C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8C2211yescharacteristic
34(C2×#6923)⋊Q8C2211yescharacteristic
35#16840714—21no—
36#16840714C2211yescharacteristic
37#16840713C2211yescharacteristic
38#16840712—21no—
39#16840710—21no—
40#16840710—21no—
41#16840710—21no—
42#16840705—21no—
43#16840704C2211yescharacteristic
44C4⋊C4×#6923C2211yescharacteristic
45C22⋊C4×#6923—21no—
46C4×C22⋊#6923C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×#41×D61C2211yescharacteristic
55C2×SD16×D61C2211yescharacteristic
56C2×D8×D61C2211yescharacteristic
57#121×D61C2211yescharacteristic
58#16839910C411yescharacteristic, complemented
59#16839909C411yescharacteristic, complemented
60#16839908C411yescharacteristic, complemented
61#16839907C411yescharacteristic, complemented
62#16839906C411yescharacteristic, complemented
63#16839905C411yescharacteristic, complemented
64#16839904C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#449C411yescharacteristic, 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—
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—41no—
82D4×#6923—41no—
83D4×#6923—41no—
84#14519856—22no—
85#14519856—41no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923D411yescharacteristic
99C2×C22⋊#6923D411yescharacteristic
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519846—22no—
105#14519845—41no—
106#14519840—22no—
107#14519840—22no—
108#14519839—22no—
109#14519839—22no—
110#14519839—41no—
111#14519839D414yescomplemented
112C8×#6923—22no—
113C8×#6923—41no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C2×#11758226C2×C411yescharacteristic, complemented
124C2×#11758222—21no—
125C2×#11758222C2×C411yescharacteristic, complemented
126C2×#11758224—21no—
127C2×#11758224C2×C411yescharacteristic, complemented
128#41×D61—22no—
129#41×D61—22no—
130#41×D61—41no—
131#41×D61—41no—
132C2×Q8×D61C2311yescharacteristic
133C2×D4×D61—21no—
134C2×D4×D61—21no—
135C2×D4×D61C2311yescharacteristic
136C2×D4×D61C2311yescharacteristic
137C22×C4×D61—21no—
138C22×C4×D61C2311yescharacteristic
139C2×#11758190C2×C411yescharacteristic, complemented
140C2×#11758200C2×C411yescharacteristic, complemented
141C2×#11758201C2×C411yescharacteristic, complemented
142SD16×D61—41no—
143SD16×D61—41no—
144C2×D488C2×C411yescharacteristic
145C2×#11758199C2×C411yescharacteristic
146C2×#11758199C2×C411yescharacteristic
147D8×D61—22no—
148D8×D61—22no—
149C2×C8×D61C2311yescharacteristic
150C2×C8×D61C2311yescharacteristic
151#14519752C2×C411yescharacteristic, complemented
152#14519751C2×C411yescharacteristic, complemented
153#14519750—21no—
154#14519749—21no—
155#14519748C2×C411yescharacteristic, complemented
156C4⋊C4×D61C2311yescharacteristic
157C22⋊C4×D61—21no—
158#14519702C2×C411yescharacteristic, complemented
159#14519701C2×C411yescharacteristic, complemented
160#14519700C2×C411yescharacteristic, complemented
161#14519699C2×C411yescharacteristic, complemented
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic, complemented
164C22⋊#92418C2×C411yescharacteristic, complemented
165#14519689C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167C2×#41×C61C2×C411yescharacteristic, complemented
168C2×SD16×C61C2×C411yescharacteristic, complemented
169C2×D8×C61C2×C411yescharacteristic
170#121×C61C2×C411yescharacteristic, complemented
171#103×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic, complemented
173C22⋊C8×C61C2×C411yescharacteristic, complemented
174C23×D61—21no—
175C23×D61—21no—
176C23×D61C2×D411yescharacteristic
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923—21no—
180C22×#6923—21no—
181C22×#6923—42no—
182C22×#6923—42no—
183C22×#6923—42no—
184C22×#6923—42no—
185C22×#6923—42no—
186C22×#6923—42no—
187C22×#6923—81no—
188C22×#6923—81no—
189C22×#6923—81no—
190C22×#6923C2×D411yescharacteristic
191C22×#6923C2×D411yescharacteristic
192C22×#6923C2×D411yescharacteristic
193C22×#6923C2×D411yescharacteristic
194#41×C61—22no—
195#41×C61—41no—
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61C22×C411yescharacteristic
200C2×D4×C61C22×C411yescharacteristic
201C22×C4×C61—21no—
202C22×C4×C61C22×C411yescharacteristic
203C2×C22⋊D61—21no—
204C2×C22⋊D61—21no—
205C2×C22⋊D61—21no—
206C2×C22⋊D61—21no—
207C2×C22⋊D61—21no—
208C2×C22⋊D61—21no—
209C22×Dic61—21no—
210C22×Dic61#4111yescharacteristic
211#11758226—22no—
212#11758226—41no—
213Q8×D61—21no—
214Q8×D61—21no—
215Q8×D61—21no—
216Q8×D61—21no—
217#11758224—22no—
218#11758224—41no—
219#11758224—42no—
220#11758224—42no—
221D4×D61—21no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—21no—
225D4×D61—21no—
226D4×D61—21no—
227D4×D61—42no—
228D4×D61—42no—
229D4×D61—81no—
230D4×D61—81no—
231D4×D61C2×D412yes—
232D4×D61#4112yes—
233#11758222—22no—
234#11758222—41no—
235#11758222—42no—
236#11758222—42no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244C22×C411yescharacteristic
240C2×D244C22×C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61C22×C411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×C4×D61#4111yescharacteristic
254C2×C4×D61C2411yescharacteristic
255C2×Dic122—21no—
256C2×Dic122C22×C411yescharacteristic
257C22⋊#6923—22no—
258C22⋊#6923—22no—
259C22⋊#6923—42no—
260C22⋊#6923—42no—
261C22⋊#6923—42no—
262C22⋊#6923—42no—
263C22⋊#6923—42no—
264C22⋊#6923—81no—
265C22⋊#6923—81no—
266C2×#92420—21no—
267C2×#92420—21no—
268C2×#92420—42no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—21no—
274C4⋊#6923—21no—
275C4⋊#6923—21no—
276C4⋊#6923—81no—
277C4⋊#6923C2×D412yes—
278C4×#6923—21no—
279C4×#6923—21no—
280C4×#6923—21no—
281C4×#6923—21no—
282C4×#6923—42no—
283C4×#6923—81no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8—42no—
288D61⋊C8C2×D412yes—
289SD16×C61—41no—
290D8×C61—22no—
291C2×C8×C61C22×C411yescharacteristic
292C2×C8×C61C22×C411yescharacteristic
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊Dic61—21no—
296#11758201—41no—
297#11758200—41no—
298#11758199—22no—
299#11758199—22no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304C2×#92418C22×C411yescharacteristic
305C2×#92418C22×C411yescharacteristic
306D488—22no—
307#11758190—41no—
308C8×D61—21no—
309C8×D61—21no—
310C8×D61—21no—
311C8×D61—21no—
312C23×C61—21no—
313C23×C61—21no—
314C23×C61C4×D411yescharacteristic
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—22no—
318C22×D61—22no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61C4×D411yescharacteristic
336C22×D61C22×D411yescharacteristic
337C2×#6923—21no—
338C2×#6923—21no—
339C2×#6923—21no—
340C2×#6923—21no—
341C2×#6923—21no—
342C2×#6923—22no—
343C2×#6923—21no—
344C2×#6923—21no—
345C2×#6923—21no—
346C2×#6923—21no—
347C2×#6923—21no—
348C2×#6923—41no—
349C2×#6923—41no—
350C2×#6923—41no—
351C2×#6923—41no—
352C2×#6923—41no—
353C2×#6923—41no—
354C2×#6923—41no—
355C2×#6923—41no—
356C2×#6923—41no—
357C2×#6923—41no—
358C2×#6923—41no—
359C2×#6923—84no—
360C2×#6923—84no—
361C2×#6923—84no—
362C2×#6923#13512yes—
363C2×#6923#13512yes—
364Q8×C61—21no—
365Q8×C61—21no—
366D4×C61—21no—
367D4×C61—21no—
368D4×C61—21no—
369D4×C61—42no—
370D4×C61—81no—
371D4×C61C4×D412yes—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—42no—
377C2×C4×C61C4×D411yescharacteristic
378C2×C4×C61C23×C411yescharacteristic
379C22⋊D61—22no—
380C22⋊D61—22no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—42no—
392C2×Dic61C4×D411yescharacteristic
393C2×Dic61C2×#4111yescharacteristic
394D244—21no—
395D244—21no—
396D244—21no—
397D244—42no—
398D244—81no—
399D244C4×D412yes—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—21no—
405C4×D61—21no—
406C4×D61—42no—
407C4×D61—42no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61C22×D411yescharacteristic
413C4×D61C2×#4111yescharacteristic
414C4×D61H(5,𝔽2)11yescharacteristic
415C4×D61H(5,𝔽2)11yescharacteristic
416Dic122—21no—
417Dic122—21no—
418Dic122—41no—
419Dic122—41no—
420#92420—22no—
421#92420—41no—
422C8×C61—21no—
423C8×C61—21no—
424#92418—21no—
425#92418—21no—
426#22872—611nomaximal, Sylow
427C22×C61—21no—
428C22×C61—22no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61C2×C4×D411yescharacteristic
437C2×D61—21no—
438C2×D61—22no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—41no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—81no—
455C2×D61—81no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61D4211yescharacteristic
459C2×D61#54611yescharacteristic
460C2×D61C2×#13511yescharacteristic
461C2×D61C2×#13511yescharacteristic
462C2×D61#57611yescharacteristic
463C2×D61#57711yescharacteristic
464#6923—22no—
465#6923—22no—
466#6923—42no—
467#6923—41no—
468#6923—41no—
469#6923—81no—
470#6923—81no—
471#6923—81no—
472C4×C61—21no—
473C4×C61—41no—
474C4×C61—41no—
475C4×C61C2×C4×D411yescharacteristic
476C4×C61#51811yescharacteristic
477Dic61—21no—
478Dic61—41no—
479Dic61—41no—
480Dic61#54611yescharacteristic
481Dic61#55111yescharacteristic
482C2×#449—611no—
483C2×C4×D8—611no—
484C2×#416—611no—
485#2363—611no—
486#2339—611no—
487#1968—611no—
488#1933—611no—
489#1928—611no—
490#1893—611no—
491#1879—611no—
492#1877—611no—
493#1864—611no—
494#1854—611no—
495C4×#102—611no—
496C8×C22⋊C4—611no—
497C2×C61—41no—
498C2×C61—42no—
499C2×C61—81no—
500C2×C61#235811yescharacteristic
501C2×C61C4×#13511yescharacteristic
502C2×C61#294611yescharacteristic
503D61—41no—
504D61—42no—
505D61—81no—
506D61#328011yescharacteristic
507D61#328411yescharacteristic
508D61#329711yescharacteristic
509D61#330311yescharacteristic
510C22×#41—611no—
511C22×SD16—611no—
512C22×D8—611no—
513C23×C8—611no—
514C2×#121—611no—
515C2×C4×D4—611no—
516C2×C4×D4—611no—
517C2×C4×D4—611no—
518C2×#117—611no—
519#449—611no—
520#449—611no—
521#449—611no—
522#449—611no—
523#449—611no—
524#449—611no—
525#449—611no—
526#449#692311yescharacteristic, complemented
527C4×D8—1224no—
528C2×#107—611no—
529C2×#106—611no—
530#416—1224no—
531C2×#103—611no—
532C2×#103—611no—
533C2×#103—611no—
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—611no—
537C2×#102—611no—
538C2×#102—611no—
539C2×C22⋊C8—611no—
540C2×C4×C8—611no—
541C2×C4×C8—611no—
542#391—611no—
543#391—611no—
544#390—611no—
545#390—1221no—
546#389—611no—
547#388—1221no—
548#386—1221no—
549#386—1221no—
550#386—1221no—
551#381—1221no—
552#380—611no—
553C4×C4⋊C4—611no—
554C4×C22⋊C4—611no—
555C4×C22⋊C4—1221no—
556C2×#95—1221no—
557#340—611no—
558#340—611no—
559#340—611no—
560#340—611no—
561#336—611no—
562#336—611no—
563C61#2287211yescharacteristic, complemented, Sylow
564C2×#41—611no—
565C2×#41—611no—
566C2×#41—611no—
567C2×#41—1221no—
568C2×#41—1221no—
569C2×#41—1222no—
570C2×#41—1222no—
571C2×#41—2441no—
572C2×#41—2441no—
573C2×#41C2×#692311yescharacteristic, complemented
574C22×Q8—611no—
575C22×D4—611no—
576C22×D4—611no—
577C22×D4—1221no—
578C22×D4—1221no—
579C23×C4—611no—
580C23×C4—1221no—
581C23×C4—1221no—
582C23×C4—1221no—
583C23×C4—1221no—
584C2×SD16—611no—
585C2×SD16—611no—
586C2×SD16—611no—
587C2×SD16—2441no—
588C2×SD16—2441no—
589C2×SD16C2×#692311yescharacteristic, complemented
590C2×D8—611no—
591C2×D8—611no—
592C2×D8—611no—
593C2×D8—1222no—
594C2×D8—1222no—
595C2×D8C2×#692311yescharacteristic
596C22×C8—611no—
597C22×C8—611no—
598C22×C8—611no—
599C22×C8—611no—
600C22×C8—1222no—
601C22×C8—1221no—
602C22×C8—1221no—
603C22×C8—2441no—
604#121—611no—
605#121—611no—
606#121—611no—
607#121—1221no—
608#121—1221no—
609#121C2×#692311yescharacteristic, complemented
610C4×D4—1222no—
611C4×D4—1222no—
612C4×D4—1222no—
613C4×D4—2441no—
614C4×D4—2441no—
615C4×D4—2441no—
616#117—1222no—
617#117—2441no—
618C2×C4⋊C4—611no—
619C2×C4⋊C4—611no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—1221no—
624C2×C22⋊C4—611no—
625C2×C22⋊C4—611no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1221no—
630C2×C22⋊C4—1221no—
631C2×C22⋊C4—1221no—
632C2×C22⋊C4—1221no—
633C2×C22⋊C4—1221no—
634C2×C42—611no—
635C2×C42—611no—
636C2×C42—1221no—
637C2×C42—1221no—
638#107—1222no—
639#106—2441no—
640#103—611no—
641#103—611no—
642#103—611no—
643#103—1222no—
644#103—1222no—
645#103C2×#692311yescharacteristic, complemented
646#102—614no—
647#102—611no—
648#102—611no—
649#102—611no—
650#102—1222no—
651#102—1222no—
652#102—2441no—
653#102C2×#692311yescharacteristic, complemented
654C22⋊C8—611no—
655C22⋊C8—611no—
656C22⋊C8—611no—
657C22⋊C8C2×#692311yescharacteristic, complemented
658C4×C8—1222no—
659C4×C8—2441no—
660#95—611no—
661#95—611no—
662#95—1221no—
663#95—1221no—
664#95—1221no—
665#95—1221no—
666#95—1221no—
667#95—1221no—
668#95—1221no—
669C24—611no—
670C24—1221no—
671C24—1221no—
672#41—22no—
673#41—41no—
674#41—1222no—
675#41—1222no—
676#41—1222no—
677#41—2441no—
678#41—2442no—
679#41—2442no—
680#41—2441no—
681#41—2442no—
682#41—2442no—
683#41—2441no—
684C2×Q8—611no—
685C2×Q8—1221no—
686C2×Q8—1221no—
687C2×Q8—1221no—
688C2×Q8—1221no—
689C2×Q8—1221no—
690C2×Q8C22×#692311yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—612no—
694C2×D4—612no—
695C2×D4—611no—
696C2×D4—611no—
697C2×D4—1221no—
698C2×D4—1221no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1221no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—1221no—
709C2×D4—1221no—
710C2×D4—1221no—
711C2×D4—4881no—
712C2×D4—4881no—
713C2×D4—2442no—
714C2×D4—2442no—
715C2×D4C22×#692311yescharacteristic
716C2×D4C22×#692311yescharacteristic
717C22×C4—21no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—4881no—
741C22×C4—4881no—
742C22×C4—4881no—
743C22×C4—2442no—
744C22×C4—2442no—
745C22×C4—2442no—
746C22×C4—2442no—
747C22×C4—2442no—
748C22×C4—2442no—
749C22×C4—2442no—
750C22×C4—2442no—
751C22×C4C22×#692311yescharacteristic
752SD16—41no—
753SD16—2441no—
754SD16—2441no—
755SD16—2441no—
756D8—22no—
757D8—1222no—
758D8—1222no—
759D8—1222no—
760C2×C8—612no—
761C2×C8—611no—
762C2×C8—611no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—1221no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—1221no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—2442no—
773C2×C8—2442no—
774C2×C8C22×#692311yescharacteristic
775C2×C8C22×#692311yescharacteristic
776C4⋊C4—612no—
777C4⋊C4—611no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—4881no—
787C4⋊C4C22×#692311yescharacteristic
788C22⋊C4—21no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1222no—
792C22⋊C4—1222no—
793C22⋊C4—1221no—
794C22⋊C4—4881no—
795C22⋊C4—4881no—
796C22⋊C4—2442no—
797C22⋊C4—2442no—
798C22⋊C4—2442no—
799C22⋊C4—2442no—
800C22⋊C4—2442no—
801C42—1221no—
802C42—1221no—
803C42—1221no—
804C42—1221no—
805C42—4881no—
806C42—2442no—
807C23—21no—
808C23—21no—
809C23—611no—
810C23—611no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1222no—
816C23—1222no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1221no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23D4×#692311yescharacteristic
832Q8—21no—
833Q8—21no—
834Q8—1221no—
835Q8—1221no—
836Q8—2441no—
837Q8—2441no—
838D4—21no—
839D4—21no—
840D4—21no—
841D4—42no—
842D4—81no—
843D4—612no—
844D4—1222no—
845D4—1222no—
846D4—1221no—
847D4—1221no—
848D4—1221no—
849D4—4881no—
850D4—4881no—
851D4—4881no—
852D4—2442no—
853D4—2441no—
854D4—2441no—
855D4—2442no—
856D4—2442no—
857D4D4×#692312yes—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—42no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—611no—
867C2×C4—611no—
868C2×C4—612no—
869C2×C4—612no—
870C2×C4—611no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—1222no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—4884no—
893C2×C4—4884no—
894C2×C4—4884no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4—2442no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2441no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4D4×#692311yescharacteristic
914C2×C4C23×#692311yescharacteristic
915C8—21no—
916C8—21no—
917C8—1222no—
918C8—1221no—
919C8—1221no—
920C8—2441no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—22no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—611no—
931C22—611no—
932C22—611no—
933C22—611no—
934C22—611no—
935C22—611no—
936C22—1221no—
937C22—1221no—
938C22—1221no—
939C22—1222no—
940C22—4881no—
941C22—4881no—
942C22—4881no—
943C22—4881no—
944C22—2442no—
945C22—2442no—
946C22—2441no—
947C22—2441no—
948C22—2441no—
949C22—2441no—
950C22—2442no—
951C22—2442no—
952C22—2441no—
953C22—2441no—
954C22—2441no—
955C22—2441no—
956C22—2441no—
957C22C2×D4×#692311yescharacteristic
958C4—21no—
959C4—41no—
960C4—41no—
961C4—611no—
962C4—611no—
963C4—1222no—
964C4—1222no—
965C4—1221no—
966C4—4881no—
967C4—4881no—
968C4—4881no—
969C4—2441no—
970C4—2441no—
971C4—2442no—
972C4—2441no—
973C4—2441no—
974C4C2×D4×#692311yescharacteristic
975C4#1684082911yescharacteristic
976C2—41no—
977C2—42no—
978C2—81no—
979C2—611no—
980C2—611no—
981C2—611no—
982C2—611no—
983C2—4881no—
984C2—2441no—
985C2—2442no—
986C2#2146234111yescharacteristic
987C2#135×#692311yescharacteristic
988C2#2146257611yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#449C4
socleC22×C61C2×C4×D4
prime radical#449×D61C2
cosocleC2×C4×D61C24
hypercenter#449#6923
hypocenterC61#22872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×D8×#6923C2semidirect
2. C2×#16840752C2semidirect
3. #21462346C2semidirect
4. #21462322C2semidirect
5. #21461964C2semidirect
6. #21461908C2semidirect
7. #21461899C2semidirect
8. #21461833C2semidirect
9. #21461814C2semidirect
10. #21461812C2semidirect
11. #21461784C2semidirect
12. #21461770C2semidirect
13. #102×#6923C2semidirect
14. #21461554C2semidirect
58. #16839910C4semidirect
59. #16839909C4semidirect
60. #16839908C4semidirect
61. #16839907C4semidirect
62. #16839906C4semidirect
63. #16839905C4semidirect
64. #16839904C4semidirect
68. C61×#449C4semidirect
111. #14519839D4semidirect
123. C2×#11758226C2×C4semidirect
125. C2×#11758222C2×C4semidirect
127. C2×#11758224C2×C4semidirect
139. C2×#11758190C2×C4semidirect
140. C2×#11758200C2×C4semidirect
141. C2×#11758201C2×C4semidirect
151. #14519752C2×C4semidirect
152. #14519751C2×C4semidirect
155. #14519748C2×C4semidirect
158. #14519702C2×C4semidirect
159. #14519701C2×C4semidirect
160. #14519700C2×C4semidirect
161. #14519699C2×C4semidirect
162. #14519698C2×C4semidirect
163. #14519697C2×C4semidirect
164. C22⋊#92418C2×C4semidirect
165. #14519689C2×C4semidirect
166. #14519689C2×C4semidirect
167. C2×#41×C61C2×C4semidirect
168. C2×SD16×C61C2×C4semidirect
170. #121×C61C2×C4semidirect
171. #103×C61C2×C4semidirect
172. #102×C61C2×C4semidirect
173. C22⋊C8×C61C2×C4semidirect
526. #449#6923semidirect
563. C61#22872semidirect
573. C2×#41C2×#6923semidirect
589. C2×SD16C2×#6923semidirect
609. #121C2×#6923semidirect
645. #103C2×#6923semidirect
653. #102C2×#6923semidirect
657. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D8×#69232
C2×#168407522
#214623462
#214623222
#214619642
#214619082
#214618992
#214618332
#214618142
#214618122
#214617842
#214617702
#102×#69232
#214615542
#449×D612
#2287261