Finite Group Databasebeta

← #30621759

Subgroups — #30621759

Order 15616.

1274 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840754C211yesmaximal, characteristic
3#21462345C211yesmaximal, characteristic, complemented
4D4×C22⋊#6923C211yesmaximal, characteristic
5#21461969C211yesmaximal, characteristic, complemented
6#21461909C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461834C211yesmaximal, characteristic, complemented
9#21461815C211yesmaximal, characteristic, complemented
10#21461812C211yesmaximal, characteristic, complemented
11#21461782C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic, complemented
15#450×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic, complemented
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21C22×C22⋊#6923—21no—
22SD16×#6923—24no—
23C2×#14519846C2211yescharacteristic, complemented
24C2×#14519845C2211yescharacteristic, complemented
25#16840754—24no—
26C2×#14519840C2211yescharacteristic, complemented
27C2×#14519840C2211yescharacteristic, complemented
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519839C2211yescharacteristic
32C2×#14519831C2211yescharacteristic, complemented
33C2×C8×#6923C2211yescharacteristic, complemented
34(C2×#6923)⋊Q8C2211yescharacteristic, complemented
35#16840714C2211yescharacteristic
36#16840714C2211yescharacteristic
37#16840713C2211yescharacteristic, complemented
38#16840712—21no—
39#16840712—21no—
40#16840711—21no—
41#16840710—21no—
42#16840710—21no—
43#16840704C2211yescharacteristic
44#16840703—21no—
45C4⋊C4×#6923—21no—
46C4⋊C4×#6923C2211yescharacteristic, complemented
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—
71C2×#11758213—21no—
72D61⋊M16—22no—
73D61⋊M16—41no—
74C2×#11758217—21no—
75C2×D61⋊C8C2311yescharacteristic
76C2×D61⋊C8C2311yescharacteristic
77Q8×#6923—22no—
78Q8×#6923—41no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—41no—
82D4×#6923—41no—
83#14519856—22no—
84#14519856—41no—
85C2×C4⋊#6923—21no—
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⋊#6923—21no—
99C2×C22⋊#6923—44no—
100C2×C22⋊#6923D411yescharacteristic
101C2×C22⋊#6923D411yescharacteristic
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104C2×C4×#6923—21no—
105C2×C4×#6923C2311yescharacteristic
106C2×C4×#6923C2311yescharacteristic
107#14519846—41no—
108#14519845—22no—
109#14519840—22no—
110#14519840—41no—
111#14519839—22no—
112#14519839—22no—
113#14519839—22no—
114#14519839D414yes—
115#14519831—41no—
116C8×#6923—22no—
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
140C2×#11758190C2×C411yescharacteristic, complemented
141C2×#11758200C2×C411yescharacteristic
142C2×#11758200C2×C411yescharacteristic, complemented
143C2×#11758201C2×C411yescharacteristic
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
160#14519699C2×C411yescharacteristic, complemented
161#14519698C2×C411yescharacteristic
162#14519698C2×C411yescharacteristic, complemented
163#14519697C2×C411yescharacteristic
164#14519697C2×C411yescharacteristic, complemented
165C22⋊#92418C2×C411yescharacteristic, complemented
166#14519689C2×C411yescharacteristic, complemented
167#14519689C2×C411yescharacteristic, complemented
168C22×D4×C61C2×C411yescharacteristic
169C2×SD16×C61C2×C411yescharacteristic
170C2×SD16×C61C2×C411yescharacteristic, complemented
171C22⋊Q8×C61C2×C411yescharacteristic, complemented
172#102×C61C2×C411yescharacteristic
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—81no—
197C22×#6923—81no—
198C22×#6923C2×D411yescharacteristic
199C22×#6923C2×D411yescharacteristic
200C22×#6923C2×D411yescharacteristic
201C22×#6923C2×D411yescharacteristic
202C2×Q8×C61C22×C411yescharacteristic
203C2×D4×C61—22no—
204C2×D4×C61—21no—
205C2×D4×C61—41no—
206C2×D4×C61C22×C411yescharacteristic
207C2×D4×C61C22×C411yescharacteristic
208C22×C4×C61C22×C411yescharacteristic
209C2×C22⋊D61—21no—
210C2×C22⋊D61—21no—
211C2×C22⋊D61—21no—
212C2×C22⋊D61—21no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C22×Dic61#4111yescharacteristic
216Q8×D61—21no—
217Q8×D61—21no—
218Q8×D61—21no—
219Q8×D61—21no—
220D4×D61—22no—
221D4×D61—22no—
222D4×D61—21no—
223D4×D61—21no—
224D4×D61—21no—
225D4×D61—21no—
226D4×D61—21no—
227D4×D61—21no—
228D4×D61—41no—
229D4×D61—41no—
230D4×D61—42no—
231D4×D61—42no—
232D4×D61—42no—
233D4×D61—42no—
234D4×D61C2×D412yes—
235D4×D61#4112yes—
236C2×D244—22no—
237C2×D244—21no—
238C2×D244—41no—
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×D61C22×C411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×C4×D61#4111yescharacteristic
250C2×C4×D61C2411yescharacteristic
251C2×Dic122—21no—
252C2×Dic122C22×C411yescharacteristic
253C22⋊#6923—22no—
254C22⋊#6923—41no—
255C22⋊#6923—42no—
256C22⋊#6923—42no—
257C22⋊#6923—42no—
258C22⋊#6923—42no—
259C22⋊#6923—42no—
260C22⋊#6923—42no—
261C22⋊#6923—81no—
262C22⋊#6923—81no—
263#11758217—42no—
264C2×#92420—21no—
265C2×#92420—21no—
266C4⋊#6923—21no—
267C4⋊#6923—21no—
268C4⋊#6923—21no—
269C4⋊#6923—21no—
270C4⋊#6923—21no—
271C4⋊#6923—21no—
272C4⋊#6923—21no—
273C4⋊#6923—42no—
274C4⋊#6923—42no—
275C4⋊#6923C2×D412yes—
276C4×#6923—21no—
277C4×#6923—21no—
278C4×#6923—21no—
279C4×#6923—21no—
280C4×#6923—42no—
281C4×#6923—42no—
282C4×#6923—42no—
283#11758213—42no—
284D61⋊C8—21no—
285D61⋊C8—21no—
286D61⋊C8—21no—
287D61⋊C8C2×D412yes—
288SD16×C61—22no—
289SD16×C61—41no—
290C2×C8×C61C22×C411yescharacteristic
291C2×C8×C61C22×C411yescharacteristic
292C4⋊C4×C61—21no—
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295C22⋊Dic61—21no—
296#11758201—22no—
297#11758201—41no—
298#11758200—22no—
299#11758200—41no—
300#11758198—21no—
301#11758198—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307C2×#92418C22×C411yescharacteristic
308C2×#92418C22×C411yescharacteristic
309#11758190—22no—
310#11758190—41no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C8×D61—21no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—81no—
320C23×C61C4×D411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—41no—
339C22×D61—41no—
340C22×D61—42no—
341C22×D61—41no—
342C22×D61—41no—
343C22×D61—41no—
344C22×D61—41no—
345C22×D61—41no—
346C22×D61—41no—
347C22×D61—81no—
348C22×D61—81no—
349C22×D61—81no—
350C22×D61—84no—
351C22×D61—84no—
352C22×D61—84no—
353C22×D61—84no—
354C22×D61C4×D411yescharacteristic
355C22×D61C22×D411yescharacteristic
356C2×#6923—21no—
357C2×#6923—21no—
358C2×#6923—21no—
359C2×#6923—22no—
360C2×#6923—21no—
361C2×#6923—21no—
362C2×#6923—21no—
363C2×#6923—21no—
364C2×#6923—21no—
365C2×#6923—21no—
366C2×#6923—21no—
367C2×#6923—21no—
368C2×#6923—41no—
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—84no—
380C2×#6923—84no—
381C2×#6923AGL(1,ℤ/8)12yes—
382Q8×C61—21no—
383Q8×C61—21no—
384D4×C61—21no—
385D4×C61—21no—
386D4×C61—21no—
387D4×C61—42no—
388D4×C61C4×D412yes—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61C4×D411yescharacteristic
394C2×C4×C61C23×C411yescharacteristic
395C22⋊D61—22no—
396C22⋊D61—22no—
397C22⋊D61—42no—
398C22⋊D61—42no—
399C22⋊D61—41no—
400C22⋊D61—41no—
401C2×Dic61—21no—
402C2×Dic61—21no—
403C2×Dic61—21no—
404C2×Dic61—21no—
405C2×Dic61C4×D411yescharacteristic
406C2×Dic61C2×#4111yescharacteristic
407D244—21no—
408D244—21no—
409D244—21no—
410D244—42no—
411D244C4×D412yes—
412C4×D61—21no—
413C4×D61—21no—
414C4×D61—21no—
415C4×D61—21no—
416C4×D61—21no—
417C4×D61—21no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—41no—
422C4×D61C22×D411yescharacteristic
423C4×D61C2×#4111yescharacteristic
424C4×D61H(5,𝔽2)11yescharacteristic
425C4×D61H(5,𝔽2)11yescharacteristic
426Dic122—21no—
427Dic122—21no—
428Dic122—41no—
429Dic122—41no—
430#92420—22no—
431#92420—41no—
432C8×C61—21no—
433C8×C61—21no—
434#92418—21no—
435#92418—21no—
436#22884—611nomaximal, Sylow
437C22×C61—21no—
438C22×C61—22no—
439C22×C61—21no—
440C22×C61—21no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—41no—
446C22×C61—84no—
447C22×C61C2×C4×D411yescharacteristic
448C2×D61—21no—
449C2×D61—22no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—41no—
453C2×D61—41no—
454C2×D61—42no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—42no—
458C2×D61—41no—
459C2×D61—42no—
460C2×D61—42no—
461C2×D61—41no—
462C2×D61—41no—
463C2×D61—41no—
464C2×D61—41no—
465C2×D61—84no—
466C2×D61—84no—
467C2×D61—84no—
468C2×D61—81no—
469C2×D61—81no—
470C2×D61—81no—
471C2×D61—81no—
472C2×D61D4211yescharacteristic
473C2×D61#54611yescharacteristic
474C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
475C2×D61#57511yescharacteristic
476C2×D61#57711yescharacteristic
477C2×D61#57711yescharacteristic
478#6923—22no—
479#6923—41no—
480#6923—42no—
481#6923—41no—
482#6923—41no—
483#6923—81no—
484#6923—81no—
485#6923—81no—
486C4×C61—21no—
487C4×C61—41no—
488C4×C61—41no—
489C4×C61C2×C4×D411yescharacteristic
490C4×C61#51811yescharacteristic
491Dic61—21no—
492Dic61—41no—
493Dic61—41no—
494Dic61#54611yescharacteristic
495Dic61#55111yescharacteristic
496C2×#450—611no—
497C2×C4×SD16—611no—
498C2×#418—611no—
499#2362—611no—
500D4×C22⋊C4—611no—
501#1973—611no—
502#1934—611no—
503#1926—611no—
504#1894—611no—
505#1880—611no—
506#1877—611no—
507#1862—611no—
508#1854—611no—
509#1762—611no—
510#1753—611no—
511C2×C61—41no—
512C2×C61—42no—
513C2×C61—81no—
514C2×C61#235811yescharacteristic
515C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
516C2×C61#294911yescharacteristic
517D61—41no—
518D61—42no—
519D61—81no—
520D61#326511yescharacteristic
521D61#326711yescharacteristic
522D61#332311yescharacteristic
523D61#332411yescharacteristic
524C23×D4—611no—
525C22×SD16—611no—
526C22×SD16—611no—
527C22×M16—611no—
528C2×C22⋊Q8—611no—
529C2×C4×Q8—611no—
530C2×C4×D4—611no—
531C2×C4×D4—611no—
532C2×#117—611no—
533C22×C22⋊C4—1221no—
534#450—611no—
535#450—611no—
536#450—611no—
537#450—611no—
538#450—611no—
539#450—611no—
540#450—611no—
541#450#692311yescharacteristic, complemented
542C4×SD16—1224no—
543C2×#107—611no—
544C2×#106—611no—
545#418—1224no—
546C2×#103—611no—
547C2×#103—611no—
548C2×#102—611no—
549C2×#102—611no—
550C2×#102—611no—
551C2×#102—611no—
552C2×#102—611no—
553C2×#102—611no—
554C2×C22⋊C8—611no—
555C2×#97—611no—
556C2×C4×C8—611no—
557#391—611no—
558#390—611no—
559#390—611no—
560#389—611no—
561#388—1221no—
562#388—1221no—
563#387—1221no—
564#386—1221no—
565#386—1221no—
566#380—611no—
567#379—1221no—
568C4×C4⋊C4—611no—
569C4×C4⋊C4—1221no—
570C4×C22⋊C4—611no—
571#340—611no—
572#340—611no—
573#340—611no—
574#340—611no—
575#336—611no—
576#336—611no—
577C61#2288411yescharacteristic, complemented, Sylow
578C25—1221no—
579C22×Q8—611no—
580C22×D4—611no—
581C22×D4—611no—
582C22×D4—611no—
583C22×D4—611no—
584C22×D4—611no—
585C22×D4—1221no—
586C22×D4—1221no—
587C22×D4—1221no—
588C22×D4—1222no—
589C22×D4—1222no—
590C22×D4—2441no—
591C22×D4—2441no—
592C22×D4C2×#692311yescharacteristic
593C23×C4—611no—
594C23×C4—1221no—
595C23×C4—1221no—
596C2×SD16—611no—
597C2×SD16—611no—
598C2×SD16—611no—
599C2×SD16—611no—
600C2×SD16—611no—
601C2×SD16—611no—
602C2×SD16—1222no—
603C2×SD16—1222no—
604C2×SD16—2441no—
605C2×SD16—2441no—
606C2×SD16C2×#692311yescharacteristic
607C2×SD16C2×#692311yescharacteristic, complemented
608C2×M16—1222no—
609C2×M16—1221no—
610C2×M16—1221no—
611C2×M16—2441no—
612C22×C8—611no—
613C22×C8—611no—
614C22×C8—611no—
615C22×C8—611no—
616C22⋊Q8—611no—
617C22⋊Q8—611no—
618C22⋊Q8—611no—
619C22⋊Q8—1221no—
620C22⋊Q8—1221no—
621C22⋊Q8C2×#692311yescharacteristic, complemented
622C4×Q8—1222no—
623C4×Q8—2441no—
624C4×D4—1222no—
625C4×D4—1222no—
626C4×D4—2441no—
627C4×D4—2441no—
628#117—1222no—
629#117—2441no—
630C2×C4⋊C4—611no—
631C2×C4⋊C4—611no—
632C2×C4⋊C4—611no—
633C2×C4⋊C4—611no—
634C2×C4⋊C4—611no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C4⋊C4—1221no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—1221no—
641C2×C22⋊C4—1221no—
642C2×C22⋊C4—1221no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—2444no—
650C2×C42—611no—
651C2×C42—611no—
652C2×C42—1221no—
653C2×C42—1221no—
654C2×C42—1221no—
655#107—2441no—
656#106—1222no—
657#103—1222no—
658#103—2441no—
659#102—614no—
660#102—611no—
661#102—611no—
662#102—611no—
663#102—611no—
664#102—611no—
665#102—611no—
666#102—1222no—
667#102—1222no—
668#102—1222no—
669#102C2×#692311yescharacteristic
670#102C2×#692311yescharacteristic, complemented
671C22⋊C8—611no—
672C22⋊C8—611no—
673C22⋊C8—611no—
674C22⋊C8C2×#692311yescharacteristic, complemented
675#97—2441no—
676C4×C8—1222no—
677#95—611no—
678#95—611no—
679#95—1221no—
680#95—1221no—
681#95—1221no—
682#95—1221no—
683#95—1221no—
684C24—21no—
685C24—611no—
686C24—1221no—
687C24—1221no—
688C24—1221no—
689C24—1221no—
690C24—1221no—
691C24—4881no—
692C24—4881no—
693C24—2442no—
694C24—2442no—
695C24—2442no—
696C24—2442no—
697C2×Q8—611no—
698C2×Q8—1221no—
699C2×Q8—1221no—
700C2×Q8—1221no—
701C2×Q8—1221no—
702C2×Q8—1221no—
703C2×Q8C22×#692311yescharacteristic
704C2×D4—22no—
705C2×D4—21no—
706C2×D4—41no—
707C2×D4—612no—
708C2×D4—612no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—1222no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1222no—
723C2×D4—1222no—
724C2×D4—1221no—
725C2×D4—2441no—
726C2×D4—2441no—
727C2×D4—2441no—
728C2×D4—2442no—
729C2×D4—2442no—
730C2×D4—2442no—
731C2×D4—2442no—
732C2×D4—2442no—
733C2×D4—2442no—
734C2×D4C22×#692311yescharacteristic
735C2×D4C22×#692311yescharacteristic
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—611no—
744C22×C4—611no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—1221no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—4881no—
756C22×C4—4881no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4—2442no—
760C22×C4—2442no—
761C22×C4C22×#692311yescharacteristic
762SD16—22no—
763SD16—41no—
764SD16—1222no—
765SD16—1222no—
766SD16—1222no—
767SD16—2441no—
768SD16—2441no—
769SD16—2441no—
770M16—2442no—
771M16—2442no—
772C2×C8—612no—
773C2×C8—611no—
774C2×C8—611no—
775C2×C8—1221no—
776C2×C8—1221no—
777C2×C8—1221no—
778C2×C8—1221no—
779C2×C8—1221no—
780C2×C8—1221no—
781C2×C8—1221no—
782C2×C8—1221no—
783C2×C8—1221no—
784C2×C8C22×#692311yescharacteristic
785C2×C8C22×#692311yescharacteristic
786C4⋊C4—21no—
787C4⋊C4—612no—
788C4⋊C4—611no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—1221no—
792C4⋊C4—1221no—
793C4⋊C4—1221no—
794C4⋊C4—1221no—
795C4⋊C4—1221no—
796C4⋊C4—1221no—
797C4⋊C4—1221no—
798C4⋊C4—1221no—
799C4⋊C4—1221no—
800C4⋊C4—2442no—
801C4⋊C4—2442no—
802C4⋊C4C22×#692311yescharacteristic
803C22⋊C4—21no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1222no—
807C22⋊C4—1221no—
808C22⋊C4—4881no—
809C22⋊C4—4881no—
810C22⋊C4—2442no—
811C22⋊C4—2441no—
812C22⋊C4—2442no—
813C22⋊C4—2442no—
814C22⋊C4—2442no—
815C22⋊C4—2442no—
816C22⋊C4—2442no—
817C42—1221no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—2442no—
822C42—2442no—
823C42—2442no—
824C23—21no—
825C23—21no—
826C23—42no—
827C23—42no—
828C23—81no—
829C23—611no—
830C23—611no—
831C23—1221no—
832C23—1221no—
833C23—1222no—
834C23—1222no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1221no—
839C23—1221no—
840C23—1221no—
841C23—4881no—
842C23—4881no—
843C23—4881no—
844C23—4884no—
845C23—4884no—
846C23—4884no—
847C23—4884no—
848C23—2442no—
849C23—2442no—
850C23—2442no—
851C23—2441no—
852C23—2441no—
853C23—2441no—
854C23—2441no—
855C23—2441no—
856C23—2441no—
857C23—2441no—
858C23—2441no—
859C23—2441no—
860C23—2441no—
861C23—2442no—
862C23—2442no—
863C23—2442no—
864C23D4×#692311yescharacteristic
865Q8—21no—
866Q8—21no—
867Q8—1221no—
868Q8—1221no—
869Q8—2441no—
870Q8—2441no—
871D4—21no—
872D4—21no—
873D4—21no—
874D4—42no—
875D4—612no—
876D4—1222no—
877D4—1222no—
878D4—1221no—
879D4—1221no—
880D4—1221no—
881D4—2442no—
882D4—2441no—
883D4—2441no—
884D4—2442no—
885D4—2442no—
886D4D4×#692312yes—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—611no—
892C2×C4—611no—
893C2×C4—611no—
894C2×C4—611no—
895C2×C4—611no—
896C2×C4—612no—
897C2×C4—611no—
898C2×C4—1221no—
899C2×C4—1221no—
900C2×C4—1221no—
901C2×C4—1221no—
902C2×C4—1221no—
903C2×C4—1221no—
904C2×C4—1221no—
905C2×C4—1221no—
906C2×C4—1221no—
907C2×C4—1221no—
908C2×C4—1221no—
909C2×C4—1221no—
910C2×C4—1221no—
911C2×C4—1222no—
912C2×C4—1221no—
913C2×C4—1221no—
914C2×C4—1221no—
915C2×C4—1221no—
916C2×C4—1221no—
917C2×C4—1221no—
918C2×C4—1221no—
919C2×C4—1221no—
920C2×C4—4884no—
921C2×C4—4884no—
922C2×C4—2441no—
923C2×C4—2441no—
924C2×C4—2441no—
925C2×C4—2441no—
926C2×C4—2441no—
927C2×C4—2441no—
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×C4D4×#692311yescharacteristic
938C2×C4C23×#692311yescharacteristic
939C8—21no—
940C8—21no—
941C8—1222no—
942C8—1221no—
943C8—1221no—
944C8—2441no—
945C22—21no—
946C22—21no—
947C22—21no—
948C22—22no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—84no—
955C22—611no—
956C22—611no—
957C22—611no—
958C22—611no—
959C22—611no—
960C22—611no—
961C22—1221no—
962C22—1221no—
963C22—1221no—
964C22—1222no—
965C22—4884no—
966C22—4884no—
967C22—4881no—
968C22—4881no—
969C22—4881no—
970C22—4881no—
971C22—4884no—
972C22—2442no—
973C22—2442no—
974C22—2441no—
975C22—2441no—
976C22—2441no—
977C22—2441no—
978C22—2442no—
979C22—2442no—
980C22—2441no—
981C22—2441no—
982C22—2441no—
983C22—2441no—
984C22—2441no—
985C22C2×D4×#692311yescharacteristic
986C4—21no—
987C4—41no—
988C4—41no—
989C4—611no—
990C4—611no—
991C4—1222no—
992C4—1221no—
993C4—4881no—
994C4—4881no—
995C4—4881no—
996C4—2441no—
997C4—2441no—
998C4—2441no—
999C4—2442no—
1000C4—2441no—
1001C4—2441no—
1002C4C2×D4×#692311yescharacteristic
1003C4#1684082911yescharacteristic
1004C2—41no—
1005C2—42no—
1006C2—81no—
1007C2—611no—
1008C2—611no—
1009C2—611no—
1010C2—611no—
1011C2—4881no—
1012C2—2441no—
1013C2—2442no—
1014C2#2146234111yescharacteristic
1015C2AGL(1,ℤ/8)×#692311yescharacteristic
1016C2#2146257911yescharacteristic
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#22884
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. #21462345C2semidirect
5. #21461969C2semidirect
6. #21461909C2semidirect
7. #21461897C2semidirect
8. #21461834C2semidirect
9. #21461815C2semidirect
10. #21461812C2semidirect
11. #21461782C2semidirect
12. #21461770C2semidirect
13. #21461590C2semidirect
14. #21461562C2semidirect
17. C2×Q8×#6923C22semidirect
23. C2×#14519846C22semidirect
24. C2×#14519845C22semidirect
26. C2×#14519840C22semidirect
27. C2×#14519840C22semidirect
32. C2×#14519831C22semidirect
33. C2×C8×#6923C22semidirect
34. (C2×#6923)⋊Q8C22semidirect
37. #16840713C22semidirect
46. 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
140. C2×#11758190C2×C4semidirect
142. C2×#11758200C2×C4semidirect
144. C2×#11758201C2×C4semidirect
151. #14519757C2×C4semidirect
152. #14519756C2×C4semidirect
155. #14519753C2×C4semidirect
160. #14519699C2×C4semidirect
162. #14519698C2×C4semidirect
164. #14519697C2×C4semidirect
165. C22⋊#92418C2×C4semidirect
166. #14519689C2×C4semidirect
167. #14519689C2×C4semidirect
170. C2×SD16×C61C2×C4semidirect
171. C22⋊Q8×C61C2×C4semidirect
173. #102×C61C2×C4semidirect
174. C22⋊C8×C61C2×C4semidirect
541. #450#6923semidirect
577. C61#22884semidirect
607. C2×SD16C2×#6923semidirect
621. C22⋊Q8C2×#6923semidirect
670. #102C2×#6923semidirect
674. C22⋊C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×#69232
C2×#168407542
#214623452
D4×C22⋊#69232
#214619692
#214619092
#214618972
#214618342
#214618152
#214618122
#214617822
#214617702
#214615902
#214615622
#450×D612
#2288461