Finite Group Databasebeta

← #29646988

Subgroups — #29646988

Order 15616.

1096 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459425C211yesmaximal, characteristic
2#21454946C211yesmaximal, characteristic, complemented
3C4×#14519783C211yesmaximal, characteristic, complemented
4#21444278C211yesmaximal, characteristic, complemented
5#21444268C211yesmaximal, characteristic, complemented
6#21444261C211yesmaximal, characteristic, complemented
7#21444260C211yesmaximal, characteristic, complemented
8#21444257C211yesmaximal, characteristic, complemented
9#21444234C211yesmaximal, characteristic, complemented
10#21444232C211yesmaximal, characteristic, complemented
11#21444231C211yesmaximal, characteristic, complemented
12#21444200C211yesmaximal, characteristic, complemented
13C2×#16839491C211yesmaximal, characteristic, complemented
14D4⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic, complemented
16C2×#14519783—21no—
17#16840494C411yescharacteristic
18#16840470C411yescharacteristic
19#16840468C411yescharacteristic
20#16840465C411yescharacteristic
21#16840464C411yescharacteristic
22#16840463—21no—
23#16840437—21no—
24#16840435—21no—
25#16840405C411yescharacteristic
26#16840404—21no—
27#16840403C411yescharacteristic
28#16840396C411yescharacteristic
29#16840309C2211yescharacteristic
30#16840299C2211yescharacteristic
31#16840290—21no—
32#16840274—21no—
33#16840271—21no—
34C4×#11758226C2211yescharacteristic
35C4×#11758222C2211yescharacteristic
36C2×C4×D244C2211yescharacteristic
37C4×D4×D61—21no—
38C4×D4×D61C2211yescharacteristic
39#16839890—21no—
40#16839835—21no—
41#16839830—21no—
42#16839825—21no—
43#16839818C2211yescharacteristic, complemented
44#16839814C2211yescharacteristic, complemented
45#16839784C2211yescharacteristic, complemented
46C2×C4⋊#92418C2211yescharacteristic, complemented
47C4⋊C8×D61C2211yescharacteristic, complemented
48#16839717—21no—
49#16839716—21no—
50#16839716—21no—
51C4×#11758194C2211yescharacteristic, complemented
52C4×#11758189C2211yescharacteristic, complemented
53C4×#11758189C2211yescharacteristic, complemented
54C4×C8×D61C2211yescharacteristic, complemented
55C4×C8×D61C2211yescharacteristic, complemented
56Q8⋊#92418C2211yescharacteristic, complemented
57Q8⋊#92418C2211yescharacteristic, complemented
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60#16839491C2211yescharacteristic, complemented
61#16839491C2211yescharacteristic, complemented
62D4⋊#92418C2211yescharacteristic, complemented
63D4⋊#92418C2211yescharacteristic, complemented
64#16839489C2211yescharacteristic
65#16839489C2211yescharacteristic
66#16839489C2211yescharacteristic, complemented
67#16839489C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C2×C4×C8×C61C2211yescharacteristic, complemented
71C61×Q8⋊C8C2211yescharacteristic, complemented
72C61×Q8⋊C8C2211yescharacteristic, complemented
73C61×D4⋊C8C2211yescharacteristic, complemented
74C61×D4⋊C8C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222—21no—
77C2×#11758222D411yescharacteristic
78C22×D244C2×C411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83#14519783—28no—
84C2×#11758194—21no—
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×#11758189—21no—
88C22×#92418—21no—
89C2×C8×D61—21no—
90C2×C8×D61—21no—
91C2×C8×D61—21no—
92#14519776C2×C411yescharacteristic
93#14519773C2×C411yescharacteristic
94#14519772—21no—
95#14519772—21no—
96#14519770—21no—
97#14519768C2×C411yescharacteristic
98#14519767—21no—
99#14519766C2×C411yescharacteristic
100#14519763—21no—
101#14519763—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519761—21no—
106#14519761—21no—
107#14519759—21no—
108#14519759—21no—
109#14519757—21no—
110#14519757—21no—
111#14519755—21no—
112#14519755—21no—
113#14519754—21no—
114#14519753C2×C411yescharacteristic
115#14519752—21no—
116#14519752—21no—
117#14519752C2×C411yescharacteristic
118#14519752C2×C411yescharacteristic
119#14519750—21no—
120#14519750—21no—
121#14519750—21no—
122#14519749—21no—
123#14519748C2×C411yescharacteristic
124#14519747—21no—
125#14519747—21no—
126#14519747—21no—
127#14519745—21no—
128Q8×Dic61C2×C411yescharacteristic
129C4×Dic122C2×C411yescharacteristic
130C4×Dic122D411yescharacteristic
131C4×D244—21no—
132C4×D244—21no—
133C4×D244—21no—
134C4×D244—21no—
135C4×D244C2×C411yescharacteristic
136C4×D244C2×C411yescharacteristic
137C4×D244C2×C411yescharacteristic
138C4×D244D411yescharacteristic
139C4×D244C2311yescharacteristic
140C4×D244C2311yescharacteristic
141D4×Dic61—21no—
142D4×Dic61C2×C411yescharacteristic
143#14519739—21no—
144#14519739—21no—
145#14519739C2×C411yescharacteristic
146#14519739C2×C411yescharacteristic
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61C2×C411yescharacteristic
150C4×C22⋊D61C2×C411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153#14519737—21no—
154#14519737—21no—
155#14519737—21no—
156#14519736D411yescharacteristic
157#14519735—21no—
158#14519735C2×C411yescharacteristic
159#14519734—21no—
160#14519734D411yescharacteristic
161#14519734D411yescharacteristic
162C2×C4⋊Dic61C2×C411yescharacteristic
163C4⋊C4×D61—21no—
164C4⋊C4×D61C2×C411yescharacteristic
165C2×#11758198—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C22⋊C4×D61—21no—
169C42×D61—21no—
170C42×D61C2311yescharacteristic
171C42×D61C2311yescharacteristic
172C4⋊#92418—21no—
173C4⋊#92418C2311yescharacteristic
174C4⋊#92418C2311yescharacteristic
175#14519706—21no—
176#14519706—21no—
177#14519689—21no—
178#14519689—21no—
179#14519688—21no—
180#14519687—21no—
181#14519687—21no—
182#14519687—21no—
183C4×#92418C2311yescharacteristic
184C4×#92418C2311yescharacteristic
185C8×Dic61—21no—
186C8×Dic61—21no—
187C8×Dic61—21no—
188C22×C8×C61—21no—
189#126×C61—21no—
190#125×C61C2×C411yescharacteristic
191#124×C61C2×C411yescharacteristic
192#123×C61—21no—
193C22⋊Q8×C61C2×C411yescharacteristic
194#121×C61C2×C411yescharacteristic
195C4×Q8×C61C2311yescharacteristic
196C4×D4×C61—21no—
197C4×D4×C61C2311yescharacteristic
198#117×C61—21no—
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61C2311yescharacteristic
201C4⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61—21no—
203#97×C61—21no—
204C4×C8×C61—21no—
205C4×C8×C61C2311yescharacteristic
206C4×C8×C61C2311yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61C22×C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61—21no—
220C2×C22⋊D61C22⋊C411yescharacteristic
221C2×C22⋊D61C22⋊C411yescharacteristic
222C22×Dic61—21no—
223C22×Dic61—21no—
224#11758226—22no—
225#11758226—41no—
226D4×D61—22no—
227D4×D61—41no—
228D4×D61—44no—
229#11758222—24no—
230#11758222—81no—
231#11758222—81no—
232C2×D244—22no—
233C2×D244—21no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—41no—
238C2×D244C22⋊C411yescharacteristic
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—81no—
250C2×C4×D61—81no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61C22×C411yescharacteristic
254C2×C4×D61C22×C411yescharacteristic
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122C22⋊C411yescharacteristic
261C2×C8×C61—24no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61C22×C411yescharacteristic
271C4⋊C4×C61C22×C411yescharacteristic
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C42×C61—21no—
278C42×C61C22×C411yescharacteristic
279C42×C61C2×D411yescharacteristic
280C42×C61C2×D411yescharacteristic
281C42×C61C2411yescharacteristic
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61C22⋊C411yescharacteristic
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22×C411yescharacteristic
308C4⋊Dic61C22×C411yescharacteristic
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325#11758194—24no—
326C2×#92418—21no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—81no—
331#11758189—24no—
332#11758189—24no—
333#11758189—81no—
334C8×D61—24no—
335C8×D61—24no—
336C8×D61—81no—
337C23×C61—21no—
338C23×C61C2×C22⋊C411yescharacteristic
339C22×D61—21no—
340C22×D61—21no—
341C22×D61—42no—
342C22×D61—42no—
343C22×D61—42no—
344C22×D61—42no—
345C22×D61—81no—
346C22×D61—81no—
347C22×D61C2×C22⋊C411yescharacteristic
348C22×D61C2×C22⋊C411yescharacteristic
349Q8×C61—21no—
350Q8×C61—21no—
351D4×C61—21no—
352D4×C61—21no—
353D4×C61—42no—
354C2×C4×C61—22no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C2×C22⋊C411yescharacteristic
365C2×C4×C61C2×C22⋊C411yescharacteristic
366C2×C4×C61C2×C22⋊C411yescharacteristic
367C2×C4×C61C23×C411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C22×D411yescharacteristic
370C22⋊D61—22no—
371C22⋊D61—42no—
372C22⋊D61—42no—
373C22⋊D61—81no—
374C22⋊D61—81no—
375C22⋊D61#10414yes—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—81no—
379C2×Dic61—81no—
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61C2×C22⋊C411yescharacteristic
384C2×Dic61C2×C22⋊C411yescharacteristic
385C2×Dic61C2×C22⋊C411yescharacteristic
386D244—22no—
387D244—21no—
388D244—21no—
389D244—21no—
390D244—42no—
391D244—42no—
392D244—42no—
393D244—81no—
394D244#13112yescomplemented
395C4×D61—22no—
396C4×D61—21no—
397C4×D61—21no—
398C4×D61—21no—
399C4×D61—21no—
400C4×D61—21no—
401C4×D61—21no—
402C4×D61—21no—
403C4×D61—21no—
404C4×D61—22no—
405C4×D61—42no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—42no—
411C4×D61—81no—
412C4×D61—81no—
413C4×D61—81no—
414C4×D61—81no—
415Dic122—22no—
416Dic122—81no—
417C8×C61—22no—
418C8×C61—22no—
419C8×C61—41no—
420C8×C61—41no—
421#92418—22no—
422#92418—22no—
423#92418—41no—
424#92418—41no—
425#17517—611nomaximal, Sylow
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61C2×#10412yes—
432C22×C61C22×C22⋊C411yescharacteristic
433C2×D61—21no—
434C2×D61—21no—
435C2×D61—21no—
436C2×D61—22no—
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—41no—
440C2×D61—41no—
441C2×D61—41no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—84no—
445C2×D61—84no—
446C2×D61C2×#10412yes—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—21no—
450C4×C61—21no—
451C4×C61—41no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61C2×#13111yescharacteristic
455C4×C61#56811yescharacteristic
456C4×C61#57611yescharacteristic
457C4×C61#57711yescharacteristic
458Dic61—21no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—41no—
464Dic61—41no—
465Dic61C2×#10412yes—
466#3481—611no—
467#2990—611no—
468C4×#131—611no—
469#1494—611no—
470#1494D6111yescharacteristic, complemented
471#1492—611no—
472#1490—611no—
473#1490—611no—
474#1489—611no—
475#1484—611no—
476#1483—611no—
477#1483—611no—
478#1476—611no—
479C2×D4⋊C8—611no—
480C2×D4⋊C8—611no—
481C2×C61—22no—
482C2×C61—81no—
483C2×C61#288011yescharacteristic
484C2×C61#289711yescharacteristic
485C2×C61C22×#10411yescharacteristic
486D61—22no—
487D61—41no—
488D61—42no—
489D61—81no—
490C2×#131—1221no—
491#559—611no—
492#554—611no—
493#554—611no—
494#553—611no—
495#553—611no—
496#553—1221no—
497#551—1221no—
498#551—1221no—
499#546—611no—
500#546—611no—
501#546—1221no—
502D42—611no—
503#532—611no—
504#529—611no—
505#529—1221no—
506#529C2×D6111yescharacteristic
507#525—1221no—
508#525—1221no—
509C4×#41—611no—
510C4×#41—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×C4×D4—1221no—
514#446—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#432C2×D6111yescharacteristic, complemented
520#431—611no—
521#423—611no—
522C2×C4⋊C8—611no—
523C2×C4⋊C8—611no—
524#405—1221no—
525#405—1221no—
526#405—1221no—
527C4×M16—611no—
528C4×M16—611no—
529C4×M16—611no—
530C2×C4×C8—611no—
531C2×C4×C8—611no—
532C2×C4×C8C2×D6111yescharacteristic, complemented
533Q8⋊C8—611no—
534Q8⋊C8—611no—
535Q8⋊C8C2×D6111yescharacteristic, complemented
536Q8⋊C8C2×D6111yescharacteristic, complemented
537D4⋊C8—611no—
538D4⋊C8—611no—
539D4⋊C8—611no—
540D4⋊C8—611no—
541D4⋊C8—611no—
542D4⋊C8—611no—
543D4⋊C8—611no—
544D4⋊C8—611no—
545D4⋊C8—611no—
546D4⋊C8—611no—
547D4⋊C8C2×D6111yescharacteristic, complemented
548D4⋊C8C2×D6111yescharacteristic, complemented
549C61#1751711yescharacteristic, complemented, Sylow
550C2×#41—611no—
551C2×#41—611no—
552C2×#41—1221no—
553C22×D4—611no—
554C22×D4—611no—
555C22×D4—1221no—
556C23×C4—1221no—
557C23×C4—1221no—
558#131—1228no—
559C2×M16—1221no—
560C2×M16—1221no—
561C2×M16—1221no—
562C2×M16—1221no—
563C22×C8—21no—
564C22×C8—1221no—
565C22×C8—1221no—
566C22×C8—1221no—
567C22×C8—1221no—
568C4⋊Q8—611no—
569#127—611no—
570#126—21no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#125—611no—
575#125—1221no—
576#125C4×D6111yescharacteristic
577#124—611no—
578#124—1221no—
579#124—1221no—
580#124C4×D6111yescharacteristic
581#123—21no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—1221no—
591C22⋊Q8—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8C4×D6111yescharacteristic
596#121—611no—
597#121—611no—
598#121—611no—
599#121—1221no—
600#121—1221no—
601#121—1221no—
602#121—1221no—
603#121—1221no—
604#121—1221no—
605#121C4×D6111yescharacteristic
606#120—1221no—
607#120—1221no—
608#120—1221no—
609#120—1221no—
610C4×Q8—611no—
611C4×Q8—611no—
612C4×Q8—611no—
613C4×Q8C22×D6111yescharacteristic
614C4×D4—21no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638C4×D4—1221no—
639C4×D4—1221no—
640C4×D4C22×D6111yescharacteristic
641#117—21no—
642#117—611no—
643#117—611no—
644#117—611no—
645#117—611no—
646#117—1221no—
647#117—1221no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—1221no—
651C2×C22⋊C4—1221no—
652C2×C22⋊C4—1221no—
653C2×C22⋊C4—1221no—
654C2×C22⋊C4—1221no—
655C2×C42—611no—
656C2×C42—611no—
657C2×C42—1221no—
658C2×C42C22×D6111yescharacteristic
659C4⋊C8—611no—
660C4⋊C8—611no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C4⋊C8—1221no—
664C4⋊C8C22×D6111yescharacteristic
665C4⋊C8C22×D6111yescharacteristic
666C22⋊C8—21no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669#97—21no—
670#97—1221no—
671#97—1221no—
672#97—1221no—
673#97—1221no—
674C4×C8—21no—
675C4×C8—611no—
676C4×C8—611no—
677C4×C8—1221no—
678C4×C8—1221no—
679C4×C8—1221no—
680C4×C8C22×D6111yescharacteristic
681C4×C8C22×D6111yescharacteristic
682C24—1221no—
683C24—1221no—
684#41—1224no—
685#41—1222no—
686#41—4881no—
687#41—4881no—
688#41—2441no—
689C2×Q8—611no—
690C2×Q8—1221no—
691C2×Q8C2×C4×D6111yescharacteristic
692C2×D4—21no—
693C2×D4—611no—
694C2×D4—611no—
695C2×D4—611no—
696C2×D4—611no—
697C2×D4—611no—
698C2×D4—1222no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1222no—
706C2×D4—1221no—
707C2×D4—1221no—
708C2×D4—2441no—
709C2×D4—2441no—
710C2×D4—2444no—
711C2×D4C2×C4×D6111yescharacteristic
712C22×C4—21no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—611no—
718C22×C4—611no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1221no—
727C22×C4—1221no—
728C22×C4—1221no—
729C22×C4—4881no—
730C22×C4—4881no—
731C22×C4—4881no—
732C22×C4—4881no—
733C22×C4C2×C4×D6111yescharacteristic
734C22×C4D4×D6111yescharacteristic
735C22×C4D4×D6111yescharacteristic
736M16—1224no—
737M16—1224no—
738M16—1224no—
739M16—4881no—
740C2×C8—24no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—1224no—
746C2×C8—1224no—
747C2×C8—1221no—
748C2×C8—1221no—
749C2×C8—1221no—
750C2×C8—1221no—
751C2×C8—4881no—
752C2×C8—4881no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—611no—
762C4⋊C4—611no—
763C4⋊C4—611no—
764C4⋊C4—611no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—1221no—
771C4⋊C4—1221no—
772C4⋊C4C2×C4×D6111yescharacteristic
773C4⋊C4C2×C4×D6111yescharacteristic
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C42—21no—
800C42—611no—
801C42—611no—
802C42—611no—
803C42—611no—
804C42—611no—
805C42—611no—
806C42—1221no—
807C42—1221no—
808C42C2×C4×D6111yescharacteristic
809C42D4×D6111yescharacteristic
810C42D4×D6111yescharacteristic
811C42C23×D6111yescharacteristic
812C23—21no—
813C23—611no—
814C23—611no—
815C23—1221no—
816C23—1221no—
817C23—4881no—
818C23—4881no—
819C23—2442no—
820C23—2442no—
821C23—2442no—
822C23—2442no—
823C23C22⋊C4×D6111yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—1222no—
827Q8—4881no—
828D4—21no—
829D4—21no—
830D4—42no—
831D4—614no—
832D4—612no—
833D4—1222no—
834D4—1222no—
835D4—1221no—
836D4—1221no—
837D4—1221no—
838D4—4881no—
839D4—4881no—
840D4—4881no—
841D4—2442no—
842D4—2442no—
843D4—2442no—
844D4—2442no—
845D4—2442no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—611no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—1221no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—4881no—
875C2×C4—4881no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4881no—
879C2×C4—4881no—
880C2×C4—2442no—
881C2×C4—2442no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4C22⋊C4×D6111yescharacteristic
887C2×C4C22⋊C4×D6111yescharacteristic
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22×C4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C8—22no—
893C8—22no—
894C8—41no—
895C8—41no—
896C8—1222no—
897C8—1222no—
898C8—2441no—
899C8—2441no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—612no—
906C22—1221no—
907C22—1221no—
908C22—1221no—
909C22—1221no—
910C22—1221no—
911C22—1222no—
912C22—4884no—
913C22—4884no—
914C22—2441no—
915C22—2441no—
916C22—2441no—
917C22—2441no—
918C22—2441no—
919C22#104×D6112yes—
920C22C2×C22⋊C4×D6111yescharacteristic
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—612no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—2441no—
935C4—2441no—
936C4#131×D6111yescharacteristic
937C4#1684052711yescharacteristic
938C4#1684056411yescharacteristic
939C4#1684056911yescharacteristic
940C2—22no—
941C2—81no—
942C2—1222no—
943C2—4881no—
944C2—2441no—
945C2—2442no—
946C2#2145426711yescharacteristic
947C2#2145434111yescharacteristic
948C2C2×#104×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C22×C22⋊C4
prime radical#21459425C2
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#17517
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #21454946C2semidirect
3. C4×#14519783C2semidirect
4. #21444278C2semidirect
5. #21444268C2semidirect
6. #21444261C2semidirect
7. #21444260C2semidirect
8. #21444257C2semidirect
9. #21444234C2semidirect
10. #21444232C2semidirect
11. #21444231C2semidirect
12. #21444200C2semidirect
13. C2×#16839491C2semidirect
14. D4⋊C8×D61C2semidirect
15. C61×#1494C2semidirect
43. #16839818C22semidirect
44. #16839814C22semidirect
45. #16839784C22semidirect
46. C2×C4⋊#92418C22semidirect
47. C4⋊C8×D61C22semidirect
51. C4×#11758194C22semidirect
52. C4×#11758189C22semidirect
53. C4×#11758189C22semidirect
54. C4×C8×D61C22semidirect
55. C4×C8×D61C22semidirect
56. Q8⋊#92418C22semidirect
57. Q8⋊#92418C22semidirect
60. #16839491C22semidirect
61. #16839491C22semidirect
62. D4⋊#92418C22semidirect
63. D4⋊#92418C22semidirect
66. #16839489C22semidirect
67. #16839489C22semidirect
69. C61×#432C22semidirect
70. C2×C4×C8×C61C22semidirect
71. C61×Q8⋊C8C22semidirect
72. C61×Q8⋊C8C22semidirect
73. C61×D4⋊C8C22semidirect
74. C61×D4⋊C8C22semidirect
394. D244#131semidirect
470. #1494D61semidirect
519. #432C2×D61semidirect
532. C2×C4×C8C2×D61semidirect
535. Q8⋊C8C2×D61semidirect
536. Q8⋊C8C2×D61semidirect
547. D4⋊C8C2×D61semidirect
548. D4⋊C8C2×D61semidirect
549. C61#17517semidirect

Maximal subgroups

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

subgroupindex
#214594252
#214549462
C4×#145197832
#214442782
#214442682
#214442612
#214442602
#214442572
#214442342
#214442322
#214442312
#214442002
C2×#168394912
D4⋊C8×D612
C61×#14942
#1751761