Finite Group Databasebeta

← #29648228

Subgroups — #29648228

Order 15616.

1152 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459606C211yesmaximal, characteristic
2#21454830C211yesmaximal, characteristic, complemented
3#21454828C211yesmaximal, characteristic, complemented
4#21444452C211yesmaximal, characteristic, complemented
5#21444442C211yesmaximal, characteristic, complemented
6#21444441C211yesmaximal, characteristic, complemented
7#21444430C211yesmaximal, characteristic, complemented
8#21444428C211yesmaximal, characteristic, complemented
9#21444428C211yesmaximal, characteristic, complemented
10#21444415C211yesmaximal, characteristic, complemented
11#21444415C211yesmaximal, characteristic, complemented
12#21444409C211yesmaximal, characteristic, complemented
13C2×#16839501C211yesmaximal, characteristic, complemented
14#329×D61C211yesmaximal, characteristic, complemented
15C61×#1530C211yesmaximal, characteristic, complemented
16C2×#14519824C411yescharacteristic
17C2×#14519823C411yescharacteristic
18#16840421—21no—
19#16840421—21no—
20#16840408—21no—
21#16840408—21no—
22#16840401—21no—
23#16840401—21no—
24#16840401—21no—
25#16840401—21no—
26#16840337C411yescharacteristic
27#16840337C411yescharacteristic
28#16840333C411yescharacteristic
29#16840326C411yescharacteristic
30#16840325C411yescharacteristic
31#16840325C411yescharacteristic
32#16840311C2211yescharacteristic
33#16840311C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35#124×D61C2211yescharacteristic
36#124×D61C2211yescharacteristic
37C4×#11758222C2211yescharacteristic
38#16839891—21no—
39#16839890—21no—
40#16839835—21no—
41#16839833—21no—
42#16839832—21no—
43#16839830—21no—
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839819C2211yescharacteristic, complemented
47#16839817C2211yescharacteristic, complemented
48#16839817C2211yescharacteristic, complemented
49#16839817C2211yescharacteristic, complemented
50#16839817C2211yescharacteristic, complemented
51#16839714C2211yescharacteristic, complemented
52#16839714C2211yescharacteristic, complemented
53C2×#14519688C2211yescharacteristic, complemented
54#97×D61C2211yescharacteristic, complemented
55#97×D61C2211yescharacteristic, complemented
56#16839502C2211yescharacteristic, complemented
57#16839502C2211yescharacteristic, complemented
58#16839502C2211yescharacteristic, complemented
59#16839502C2211yescharacteristic, complemented
60#16839501C2211yescharacteristic, complemented
61#16839501C2211yescharacteristic, complemented
62#16839501C2211yescharacteristic, complemented
63#16839501C2211yescharacteristic, complemented
64#16839501C2211yescharacteristic, complemented
65#16839501C2211yescharacteristic, complemented
66#16839501C2211yescharacteristic, complemented
67#16839501C2211yescharacteristic, complemented
68C61×#532C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C2×#97×C61C2211yescharacteristic, complemented
71C61×#329C2211yescharacteristic, complemented
72C61×#329C2211yescharacteristic, complemented
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75#14519824—44no—
76#14519823—44no—
77C2×#11758226C2×C411yescharacteristic
78C2×#11758226C2×C411yescharacteristic
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222C2×C411yescharacteristic
82C2×#11758224—21no—
83C2×#11758224—21no—
84C2×#11758224C2×C411yescharacteristic
85C2×#11758224C2×C411yescharacteristic
86C22×Dic122—21no—
87C22×Dic122C2×C411yescharacteristic
88C2×Q8×D61C2×C411yescharacteristic
89C2×Q8×D61C2×C411yescharacteristic
90C22×D244—21no—
91C22×D244C2×C411yescharacteristic
92C2×D4×D61—21no—
93C2×D4×D61—21no—
94C2×D4×D61C2×C411yescharacteristic
95C2×D4×D61C2×C411yescharacteristic
96C2×#11758189—21no—
97C2×#11758189—21no—
98C22×#92418—21no—
99C2×C8×D61—21no—
100C2×C8×D61—21no—
101#14519775C2×C411yescharacteristic
102#14519775C2×C411yescharacteristic
103#14519773C2×C411yescharacteristic
104#14519773C2×C411yescharacteristic
105#14519766C2×C411yescharacteristic
106#14519766C2×C411yescharacteristic
107#14519765—21no—
108#14519765—21no—
109#14519765C2×C411yescharacteristic
110#14519765C2×C411yescharacteristic
111#14519765C2311yescharacteristic
112#14519765C2311yescharacteristic
113#14519764C2×C411yescharacteristic
114#14519764C2×C411yescharacteristic
115#14519763—21no—
116#14519763—21no—
117#14519763—21no—
118#14519763—21no—
119#14519762—21no—
120#14519762—21no—
121#14519762—21no—
122#14519762—21no—
123#14519758—21no—
124#14519758—21no—
125#14519756—21no—
126#14519756—21no—
127#14519755—21no—
128#14519755—21no—
129#14519755—21no—
130#14519755—21no—
131#14519751—21no—
132#14519751—21no—
133#14519750—21no—
134#14519750—21no—
135#14519750—21no—
136#14519750—21no—
137#14519749—21no—
138#14519749—21no—
139#14519749—21no—
140#14519749—21no—
141#14519745—21no—
142#14519745—21no—
143#14519745—21no—
144#14519745—21no—
145#14519745—21no—
146#14519745—21no—
147C4×Dic122D411yescharacteristic
148C4×Dic122D411yescharacteristic
149C4×D244D411yescharacteristic
150C4×D244D411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154C4×C22⋊D61D411yescharacteristic
155#14519737—21no—
156#14519737—21no—
157#14519737—21no—
158#14519737—21no—
159#14519736C2×C411yescharacteristic
160#14519734C2×C411yescharacteristic
161#14519734C2×C411yescharacteristic
162C2×#11758198—21no—
163C2×#11758198—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C22⋊C4×D61—21no—
167C22⋊C4×D61—21no—
168C42×D61C2311yescharacteristic
169C42×D61C2311yescharacteristic
170C4⋊#92418—21no—
171#14519706—21no—
172#14519706—21no—
173#14519706—21no—
174#14519706—21no—
175C22⋊#92418—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519688—21no—
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519688C2311yescharacteristic
184#14519688C2311yescharacteristic
185#14519687—21no—
186#14519687—21no—
187C8×Dic61—21no—
188C8×Dic61—21no—
189C2×#41×C61C2×C411yescharacteristic
190C2×#41×C61C2×C411yescharacteristic
191C22×C8×C61—21no—
192C4⋊Q8×C61C2×C411yescharacteristic
193#127×C61C2×C411yescharacteristic
194#124×C61C2311yescharacteristic
195#124×C61C2311yescharacteristic
196#121×C61—21no—
197#121×C61—21no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61—21no—
202C22⋊C8×C61—21no—
203#97×C61—21no—
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206#97×C61C2311yescharacteristic
207#97×C61C2311yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—21no—
211#41×C61—42no—
212#41×C61—42no—
213C2×Q8×C61C22×C411yescharacteristic
214C2×Q8×C61C22×C411yescharacteristic
215C2×D4×C61—21no—
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—21no—
219C2×D4×C61C22×C411yescharacteristic
220C2×D4×C61C22×C411yescharacteristic
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239#11758226—42no—
240#11758226—42no—
241Q8×D61—42no—
242Q8×D61—42no—
243#11758224—42no—
244#11758224—42no—
245#11758224—44no—
246#11758224—44no—
247D4×D61—42no—
248D4×D61—42no—
249D4×D61—44no—
250D4×D61—44no—
251#11758222—24no—
252#11758222—44no—
253#11758222—44no—
254C2×D244—21no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—44no—
258C2×D244—42no—
259C2×D244C22⋊C411yescharacteristic
260C2×D244C22×C411yescharacteristic
261C2×D244C22×C411yescharacteristic
262C2×C4×D61—21no—
263C2×C4×D61—21no—
264C2×C4×D61—21no—
265C2×C4×D61—21no—
266C2×C4×D61C22×C411yescharacteristic
267C2×C4×D61C22×C411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—44no—
276C2×Dic122—42no—
277C2×Dic122C22⋊C411yescharacteristic
278C2×Dic122C22×C411yescharacteristic
279C2×Dic122C22×C411yescharacteristic
280C2×C8×C61—21no—
281C2×C8×C61—21no—
282C2×C8×C61—21no—
283C2×C8×C61—21no—
284C2×C8×C61—42no—
285C4⋊C4×C61—21no—
286C4⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—21no—
289C22⋊C4×C61—21no—
290C22⋊C4×C61—21no—
291C42×C61C22×C411yescharacteristic
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D411yescharacteristic
294C42×C61C2411yescharacteristic
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298C22⋊Dic61—21no—
299C22⋊Dic61C22⋊C411yescharacteristic
300C22⋊Dic61C22⋊C411yescharacteristic
301#11758198—21no—
302#11758198—21no—
303#11758198—21no—
304#11758198—21no—
305#11758198—21no—
306#11758198—21no—
307#11758198—21no—
308#11758198—21no—
309#11758198—21no—
310#11758198—21no—
311#11758198—21no—
312#11758198—21no—
313#11758198C22⋊C411yescharacteristic
314#11758198C22⋊C411yescharacteristic
315#11758198C22⋊C411yescharacteristic
316#11758198C22⋊C411yescharacteristic
317C4⋊Dic61C22⋊C411yescharacteristic
318C4⋊Dic61C22⋊C411yescharacteristic
319#11758196—21no—
320#11758196—21no—
321#11758196—21no—
322#11758196—21no—
323#11758196C22⋊C411yescharacteristic
324#11758196C22⋊C411yescharacteristic
325#11758196C22⋊C411yescharacteristic
326#11758196C22⋊C411yescharacteristic
327C4×Dic61C22×C411yescharacteristic
328C4×Dic61C22×C411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2×D411yescharacteristic
333C2×#92418—21no—
334C2×#92418—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337C2×#92418—42no—
338#11758189—42no—
339#11758189—42no—
340C8×D61—42no—
341C8×D61—42no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61C2×C22⋊C411yescharacteristic
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—42no—
348C22×D61—42no—
349C22×D61—42no—
350C22×D61—81no—
351C22×D61—81no—
352C22×D61—81no—
353C22×D61—81no—
354C22×D61—81no—
355C22×D61—81no—
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61C2×C22⋊C411yescharacteristic
358Q8×C61—41no—
359Q8×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—42no—
363D4×C61—42no—
364D4×C61—81no—
365D4×C61—81no—
366C2×C4×C61—22no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—42no—
372C2×C4×C61—42no—
373C2×C4×C61C2×C22⋊C411yescharacteristic
374C2×C4×C61C2×C22⋊C411yescharacteristic
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C23×C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C22×D411yescharacteristic
379C22⋊D61—22no—
380C22⋊D61—42no—
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—42no—
384C22⋊D61—81no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C22⋊D61—81no—
388C22⋊D61#10014yes—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—42no—
392C2×Dic61—42no—
393C2×Dic61—42no—
394C2×Dic61C2×C22⋊C411yescharacteristic
395C2×Dic61C2×C22⋊C411yescharacteristic
396C2×Dic61C2×C22⋊C411yescharacteristic
397C2×Dic61C2×C22⋊C411yescharacteristic
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400D244—22no—
401D244—41no—
402D244—41no—
403D244—42no—
404D244—42no—
405D244—42no—
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—41no—
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—42no—
413C4×D61—42no—
414C4×D61—42no—
415C4×D61—42no—
416Dic122—22no—
417Dic122—42no—
418Dic122—42no—
419Dic122—42no—
420Dic122—41no—
421Dic122—41no—
422C8×C61—22no—
423C8×C61—41no—
424C8×C61—41no—
425C8×C61—41no—
426#92418—22no—
427#92418—41no—
428#92418—41no—
429#92418—41no—
430#17685—611nomaximal, Sylow
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—41no—
434C22×C61—41no—
435C22×C61—41no—
436C22×C61—41no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61C2×#10012yes—
440C22×C61C22×C22⋊C411yescharacteristic
441C2×D61—21no—
442C2×D61—21no—
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—41no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—162no—
453C2×D61—162no—
454C2×D61—162no—
455C2×D61C2×#10012yes—
456C4×C61—21no—
457C4×C61—21no—
458C4×C61—21no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—41no—
463C4×C61—41no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—41no—
470Dic61—41no—
471Dic61C2×#10012yes—
472#3500—611no—
473#2970—611no—
474#2970—611no—
475#1536—611no—
476#1533—611no—
477#1533—611no—
478#1530—611no—
479#1530—611no—
480#1530—611no—
481#1530D6111yescharacteristic, complemented
482#1527—611no—
483#1527—611no—
484#1525—611no—
485C2×#329—611no—
486C2×#329—611no—
487C2×C61—22no—
488C2×C61—81no—
489C2×C61—81no—
490C2×C61C22×#10011yescharacteristic
491C2×C61#290111yescharacteristic
492C2×C61#290111yescharacteristic
493D61—22no—
494D61—41no—
495D61—81no—
496D61—81no—
497C2×2−1+4—611no—
498C2×H(5,𝔽2)—611no—
499#548—1221no—
500#548—1221no—
501#546—1221no—
502#546—1221no—
503#546—1221no—
504#546—1221no—
505#546—1221no—
506#546—1221no—
507#536—611no—
508#536—611no—
509#536—611no—
510#535—611no—
511#535—611no—
512#535—611no—
513#532—611no—
514#532—611no—
515#532C2×D6111yescharacteristic
516C2×#124—611no—
517C2×#124—611no—
518C2×#124—611no—
519C4×#41—611no—
520#446—1221no—
521#446—1221no—
522#435—1221no—
523#435—1221no—
524#435—1221no—
525#435—1221no—
526C8×D4—1221no—
527C8×D4—1221no—
528#432—611no—
529#432—611no—
530#432—611no—
531#432—611no—
532#432—611no—
533#432C2×D6111yescharacteristic, complemented
534C4×M16—611no—
535C4×M16—611no—
536C2×#97—611no—
537C2×#97—611no—
538C2×#97—611no—
539C2×#97C2×D6111yescharacteristic, complemented
540#329—611no—
541#329—611no—
542#329—611no—
543#329—611no—
544#329—611no—
545#329—611no—
546#329—611no—
547#329—611no—
548#329—611no—
549#329—611no—
550#329—611no—
551#329—611no—
552#329C2×D6111yescharacteristic, complemented
553#329C2×D6111yescharacteristic, complemented
554#329C2×D6111yescharacteristic, complemented
555#329C2×D6111yescharacteristic, complemented
556C61#1768511yescharacteristic, complemented, Sylow
5572−1+4—2444no—
558H(5,𝔽2)—2444no—
559C2×#41—611no—
560C2×#41—611no—
561C2×#41—611no—
562C2×#41—611no—
563C2×#41—611no—
564C2×#41—1221no—
565C2×#41—1221no—
566C2×#41—1221no—
567C2×#41—1221no—
568C2×#41C4×D6111yescharacteristic
569C2×#41C4×D6111yescharacteristic
570C22×Q8—611no—
571C22×Q8—611no—
572C22×Q8—611no—
573C22×Q8—1221no—
574C22×D4—611no—
575C22×D4—611no—
576C22×D4—611no—
577C22×D4—1221no—
578C22×D4—1221no—
579C22×D4—1221no—
580C2×M16—1221no—
581C2×M16—1221no—
582C22×C8—21no—
583C22×C8—1221no—
584C22×C8—1221no—
585C22×C8—1221no—
586C4⋊Q8—611no—
587C4⋊Q8—611no—
588C4⋊Q8C4×D6111yescharacteristic
589#127—611no—
590#127—611no—
591#127C4×D6111yescharacteristic
592#124—611no—
593#124—611no—
594#124—611no—
595#124—611no—
596#124—611no—
597#124—611no—
598#124—611no—
599#124—611no—
600#124—1221no—
601#124—1221no—
602#124—1221no—
603#124—1221no—
604#124—1221no—
605#124—1221no—
606#124C22×D6111yescharacteristic
607#124C22×D6111yescharacteristic
608#123—1221no—
609#123—1221no—
610#123—1221no—
611#123—1221no—
612#123—1221no—
613#123—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8—1221no—
617C22⋊Q8—1221no—
618C22⋊Q8—1221no—
619C22⋊Q8—1221no—
620#121—21no—
621#121—21no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121—1221no—
630#121—1221no—
631#121—1221no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635#120—1221no—
636#120—1221no—
637#120—1221no—
638C4×Q8—611no—
639C4×Q8—611no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
647C4×D4—611no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652#117—611no—
653#117—611no—
654#117—611no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C42—611no—
662C2×C42—611no—
663C2×C42C22×D6111yescharacteristic
664C4⋊C8—21no—
665C4⋊C8—1221no—
666C4⋊C8—1221no—
667C4⋊C8—1221no—
668C4⋊C8—1221no—
669C4⋊C8—1221no—
670C22⋊C8—21no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8—1221no—
674C22⋊C8—1221no—
675C22⋊C8—1221no—
676#97—21no—
677#97—611no—
678#97—611no—
679#97—611no—
680#97—611no—
681#97—1221no—
682#97—1221no—
683#97—1221no—
684#97C22×D6111yescharacteristic
685#97C22×D6111yescharacteristic
686#97C22×D6111yescharacteristic
687#97C22×D6111yescharacteristic
688C4×C8—1221no—
689C4×C8—1221no—
690C24—1221no—
691C24—1221no—
692C24—1221no—
693#41—42no—
694#41—42no—
695#41—1224no—
696#41—2444no—
697#41—2444no—
698#41—2442no—
699#41—2442no—
700#41—2442no—
701#41—2442no—
702#41—2444no—
703#41—2444no—
704C2×Q8—611no—
705C2×Q8—611no—
706C2×Q8—611no—
707C2×Q8—1221no—
708C2×Q8—1221no—
709C2×Q8—1221no—
710C2×Q8—2442no—
711C2×Q8—2444no—
712C2×Q8—2442no—
713C2×Q8—2442no—
714C2×Q8C2×C4×D6111yescharacteristic
715C2×Q8C2×C4×D6111yescharacteristic
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—611no—
721C2×D4—611no—
722C2×D4—611no—
723C2×D4—611no—
724C2×D4—611no—
725C2×D4—1221no—
726C2×D4—1221no—
727C2×D4—1221no—
728C2×D4—1221no—
729C2×D4—1221no—
730C2×D4—1221no—
731C2×D4—1221no—
732C2×D4—1221no—
733C2×D4—1221no—
734C2×D4—1221no—
735C2×D4—1221no—
736C2×D4—2442no—
737C2×D4—2444no—
738C2×D4—2442no—
739C2×D4—2442no—
740C2×D4—2444no—
741C2×D4—2444no—
742C2×D4C2×C4×D6111yescharacteristic
743C2×D4C2×C4×D6111yescharacteristic
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—611no—
747C22×C4—611no—
748C22×C4—611no—
749C22×C4—611no—
750C22×C4—611no—
751C22×C4—611no—
752C22×C4—1221no—
753C22×C4—1221no—
754C22×C4—1221no—
755C22×C4—1221no—
756C22×C4—1221no—
757C22×C4—1221no—
758C22×C4—1221no—
759C22×C4C2×C4×D6111yescharacteristic
760C22×C4D4×D6111yescharacteristic
761C22×C4D4×D6111yescharacteristic
762M16—2442no—
763M16—2442no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—42no—
769C2×C8—1221no—
770C2×C8—1221no—
771C2×C8—1221no—
772C2×C8—1221no—
773C2×C8—2442no—
774C2×C8—2442no—
775C2×C8—2442no—
776C4⋊C4—21no—
777C4⋊C4—21no—
778C4⋊C4—611no—
779C4⋊C4—611no—
780C4⋊C4—611no—
781C4⋊C4—611no—
782C4⋊C4—611no—
783C4⋊C4—611no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—611no—
819C42—611no—
820C42C2×C4×D6111yescharacteristic
821C42D4×D6111yescharacteristic
822C42D4×D6111yescharacteristic
823C42C23×D6111yescharacteristic
824C23—21no—
825C23—21no—
826C23—611no—
827C23—611no—
828C23—1221no—
829C23—1221no—
830C23—4881no—
831C23—4881no—
832C23—4881no—
833C23—4881no—
834C23—4881no—
835C23—4881no—
836C23—2442no—
837C23—2442no—
838C23—2442no—
839C23C22⋊C4×D6111yescharacteristic
840Q8—41no—
841Q8—41no—
842Q8—1222no—
843Q8—2441no—
844Q8—2441no—
845Q8—2442no—
846Q8—2442no—
847Q8—2442no—
848D4—41no—
849D4—41no—
850D4—42no—
851D4—42no—
852D4—81no—
853D4—81no—
854D4—614no—
855D4—1222no—
856D4—1222no—
857D4—4881no—
858D4—4881no—
859D4—4881no—
860D4—4881no—
861D4—2441no—
862D4—2441no—
863D4—2442no—
864D4—2442no—
865D4—2442no—
866D4—2442no—
867D4—2442no—
868D4—2442no—
869D4—2442no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—611no—
878C2×C4—611no—
879C2×C4—611no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1221no—
886C2×C4—1221no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2442no—
892C2×C4—2442no—
893C2×C4—2442no—
894C2×C4—2442no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2442no—
898C2×C4C22⋊C4×D6111yescharacteristic
899C2×C4C22⋊C4×D6111yescharacteristic
900C2×C4C22⋊C4×D6111yescharacteristic
901C2×C4C22×C4×D6111yescharacteristic
902C2×C4C2×D4×D6111yescharacteristic
903C2×C4C2×D4×D6111yescharacteristic
904C8—22no—
905C8—41no—
906C8—41no—
907C8—41no—
908C8—1222no—
909C8—2441no—
910C8—2441no—
911C8—2441no—
912C22—21no—
913C22—21no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—612no—
921C22—1221no—
922C22—1221no—
923C22—1221no—
924C22—1221no—
925C22—1221no—
926C22—9762no—
927C22—9762no—
928C22—9762no—
929C22—2441no—
930C22—2441no—
931C22—2441no—
932C22—2441no—
933C22—2441no—
934C22—2441no—
935C22#100×D6112yes—
936C22C2×C22⋊C4×D6111yescharacteristic
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—21no—
943C4—41no—
944C4—41no—
945C4—612no—
946C4—1221no—
947C4—1221no—
948C4—1221no—
949C4—1221no—
950C4—1221no—
951C4—2441no—
952C4—2441no—
953C2—22no—
954C2—81no—
955C2—81no—
956C2—1222no—
957C2—4881no—
958C2—4881no—
959C2—2441no—
960C2C2×#100×D6111yescharacteristic
961C2#2145436311yescharacteristic
962C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1530C2
socleC22×C61C22×C22⋊C4
prime radical#21459606C2
cosocleC42×C61C24
hypercenter#1530D61
hypocenterC61#17685
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1530

Complements

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

NH ≅ G/Ntype
2. #21454830C2semidirect
3. #21454828C2semidirect
4. #21444452C2semidirect
5. #21444442C2semidirect
6. #21444441C2semidirect
7. #21444430C2semidirect
8. #21444428C2semidirect
9. #21444428C2semidirect
10. #21444415C2semidirect
11. #21444415C2semidirect
12. #21444409C2semidirect
13. C2×#16839501C2semidirect
14. #329×D61C2semidirect
15. C61×#1530C2semidirect
46. #16839819C22semidirect
47. #16839817C22semidirect
48. #16839817C22semidirect
49. #16839817C22semidirect
50. #16839817C22semidirect
51. #16839714C22semidirect
52. #16839714C22semidirect
53. C2×#14519688C22semidirect
54. #97×D61C22semidirect
55. #97×D61C22semidirect
56. #16839502C22semidirect
57. #16839502C22semidirect
58. #16839502C22semidirect
59. #16839502C22semidirect
60. #16839501C22semidirect
61. #16839501C22semidirect
62. #16839501C22semidirect
63. #16839501C22semidirect
64. #16839501C22semidirect
65. #16839501C22semidirect
66. #16839501C22semidirect
67. #16839501C22semidirect
69. C61×#432C22semidirect
70. C2×#97×C61C22semidirect
71. C61×#329C22semidirect
72. C61×#329C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
481. #1530D61semidirect
533. #432C2×D61semidirect
539. C2×#97C2×D61semidirect
552. #329C2×D61semidirect
553. #329C2×D61semidirect
554. #329C2×D61semidirect
555. #329C2×D61semidirect
556. C61#17685semidirect

Maximal subgroups

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

subgroupindex
#214596062
#214548302
#214548282
#214444522
#214444422
#214444412
#214444302
#214444282
#214444152
#214444092
C2×#168395012
#329×D612
C61×#15302
#1768561