Finite Group Databasebeta

← #11866258

Subgroups — #11866258

Order 1152.

1048 conjugacy classes of subgroups.

The subgroup lattice has 849 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63795C211yesmaximal, characteristic
2C2×D3×#204C211yesmaximal, characteristic, complemented
3#10593994C211yesmaximal, characteristic, complemented
4#10593894C211yesmaximal, characteristic, complemented
5#10592540C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590954C211yesmaximal, characteristic, complemented
9#10590948C211yesmaximal, characteristic, complemented
10#10590860C211yesmaximal, characteristic, complemented
11#10590760C211yesmaximal, characteristic, complemented
12#10590755C211yesmaximal, characteristic, complemented
13#10590752C211yesmaximal, characteristic, complemented
14#10590365C211yesmaximal, characteristic, complemented
15#10590356C211yesmaximal, characteristic, complemented
16#80537—31nomaximal
17#79087—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24#64078C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#875C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63904—21no—
35#63894C2211yescharacteristic
36#63893—21no—
37#63893—21no—
38Dic3×D12C2211yescharacteristic
39#63891—21no—
40#63891—21no—
41#63881—21no—
42#63866C2211yescharacteristic, complemented
43#63860C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic
46C2×#3716C2211yescharacteristic
47C2×#3716C2211yescharacteristic
48C2×#3714C2211yescharacteristic
49#63795—24no—
50D3×#204—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63643C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63567C2211yescharacteristic, complemented
61#63566C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×D3×SD16—31no—
64C2×#911—31no—
65C2×#908—31no—
66C22×#204—31no—
67#5675—31no—
68#5545—31no—
69#5526—31no—
70#5521—31no—
71C3×#463—31no—
72C3×#424—31no—
73#5162—31no—
74#5153—31no—
75#5120—31no—
76#5113—31no—
77#5057—31no—
78#5019—31no—
79#4844—31no—
80#4844—31no—
81#4844—31no—
82#4844D311yescharacteristic, complemented
83#4841—31no—
84#4841—31no—
85#4841—31no—
86#4841—31no—
87#4841—31no—
88#4841—61no—
89#4839D311yescharacteristic, complemented
90#4818—31no—
91#4802—31no—
92#4787—31no—
93#4772—31no—
94C22×D32—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#626—21no—
106C2×#625—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12D414yes—
113#3795—22no—
114#3795—22no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C42C2311yescharacteristic
120#3752—21no—
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124#3744—22no—
125#3744—22no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D24—22no—
138C3×#204—22no—
139C3×ΓL(1,𝔽25)—22no—
140C3×D3×C8—22no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143#3722—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3717—22no—
150#3716—22no—
151#3716—22no—
152#3714—22no—
153#3042—91noSylow
154C2×D3×Q8—31no—
155C2×#237—31no—
156C2×D3×D4—31no—
157C2×#235—31no—
158C22×D12—31no—
159C22×Dic6—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×#124—31no—
165C3×C4×D4—31no—
166C3×#117—31no—
167#944—31no—
168C2×#215—31no—
169#936—31no—
170D4×Dic3—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#213—31no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177D3×SD16—64no—
178#911—64no—
179#908—64no—
180C2×D24—31no—
181C2×D24C2×D311yescharacteristic
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—31no—
185C2×#204—31no—
186C2×#204—31no—
187C2×#204—31no—
188C2×#204—31no—
189C2×#204—61no—
190C2×#204—61no—
191C2×#204—64no—
192C2×#204C2×D311yescharacteristic
193C2×ΓL(1,𝔽25)C2×D311yescharacteristic
194C2×D3×C8C2×D311yescharacteristic
195#897—61no—
196#897—61no—
197#893—31no—
198#893—61no—
199#893—61no—
200#892—31no—
201#886—61no—
202#886—61no—
203#883—61no—
204#883—61no—
205#67⋊C4—61no—
206D3×C22⋊C4—61no—
207D3×C22⋊C4—61no—
208D3×C22⋊C4—61no—
209#878—61no—
210#878—61no—
211#875—31no—
212#875C2×D311yescharacteristic, complemented
213C4×D12—31no—
214C4×D12—31no—
215C4×D12—31no—
216C4×D12—31no—
217C4×D12—61no—
218C4×D12C2×D311yescharacteristic
219#872C2×D311yescharacteristic
220#869—31no—
221#869—31no—
222#869—31no—
223#869—61no—
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#821—31no—
235#821C2×D311yescharacteristic, complemented
236#816—31no—
237#816—31no—
238#816—31no—
239#816—31no—
240#816—31no—
241#816—31no—
242#816—31no—
243#816—61no—
244#816—61no—
245#816C2×D311yescharacteristic, complemented
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#810—31no—
249#810—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3C2×D411yescharacteristic
255C2×D32—24no—
256C2×D32—81no—
257C2×D32—81no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C2×C3⋊Dic3—21no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C4⋊(C3⋊D3)—21no—
265C4⋊(C3⋊D3)C2×D412yes—
266C4×C3⋊D3—81no—
267#634—21no—
268#634—21no—
269#634—21no—
270#634—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12C2×D412yes—
280C3×C4×D3—81no—
281C3×C4×D3C2×D412yes—
282C3×C4×D3#4112yes—
283C3×Dic6—21no—
284C3×Dic6—21no—
285#627—42no—
286#626—24no—
287#625—42no—
288#624—81no—
289D3×Dic3—42no—
290D3×Dic3—42no—
291D3×Dic3—81no—
292C32×C8—21no—
293C32×C8—21no—
294C3×C3⋊C8—21no—
295C3×C3⋊C8—21no—
296C2×AGL(1,ℤ/8)—91no—
297C22×SD16—91no—
298#536—91no—
299#518—91no—
300#463—31no—
301#463—91no—
302#463—91no—
303#463—91no—
304#461—91no—
305#461—91no—
306#461—91no—
307#461—91no—
308#424—31no—
309#419—91no—
310#416—91no—
311C23×D3—61no—
312C23×D3—61no—
313C2×C3×Q8—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C22×C3×C4—31no—
317C22×C3×C4—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324D3×Q8—62no—
325D3×Q8—62no—
326#237—62no—
327#237—62no—
328D3×D4—34no—
329D3×D4—62no—
330#235—62no—
331#235—62no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—34no—
335C2×D12—61no—
336C2×D12—62no—
337C2×D12—61no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—121no—
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6—62no—
358C2×Dic6—61no—
359C2×Dic6—61no—
360C2×Dic6C22×D311yescharacteristic
361C3×SD16—62no—
362C3×D8—62no—
363C3×M16—62no—
364C2×C3×C8—21no—
365C2×C3×C8—21no—
366C2×C3×C8—31no—
367C2×C3×C8—31no—
368C2×C3×C8—62no—
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C2×C3×C8C22×D311yescharacteristic
372C2×C3×C8C22×D311yescharacteristic
373C3×C4⋊C4—31no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—31no—
378C3×C22⋊C4—61no—
379C3×C22⋊C4—61no—
380C3×C22⋊C4—61no—
381C3×C42—21no—
382C3×C42—31no—
383C3×C42C22×D311yescharacteristic
384C3×C42C22×D311yescharacteristic
385#217—61no—
386#217—61no—
387#217—61no—
388#217—61no—
389#215—62no—
390#214—62no—
391#214—62no—
392#213—62no—
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—61no—
403(C2×D3)⋊C4—61no—
404(C2×D3)⋊C4—121no—
405(C2×D3)⋊C4D1211yescharacteristic
406(C2×D3)⋊C4D1211yescharacteristic
407C4⋊Dic3—31no—
408C4⋊Dic3—31no—
409C4⋊Dic3—61no—
410C4⋊Dic3—61no—
411C4⋊Dic3—61no—
412C4⋊Dic3—61no—
413C4⋊Dic3—61no—
414C4⋊Dic3—61no—
415C4⋊Dic3—61no—
416C4⋊Dic3—121no—
417C4⋊Dic3—121no—
418C4⋊Dic3C22×D311yescharacteristic
419Dic3⋊C4—61no—
420Dic3⋊C4—61no—
421Dic3⋊C4D1211yescharacteristic
422Dic3⋊C4D1211yescharacteristic
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428D24—22no—
429D24—62no—
430#204—22no—
431#204—62no—
432#204—62no—
433#204—62no—
434#204—62no—
435#204—62no—
436#204—62no—
437#204—62no—
438#204—122no—
439#204—122no—
440ΓL(1,𝔽25)—22no—
441D3×C8—22no—
442C22×C32C22×D411yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—41no—
445C2×C3⋊D3—41no—
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—22no—
449C2×C3×D3—41no—
450C2×C3×D3—41no—
451C2×C3×D3—41no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3#12112yes—
455D32—84no—
456C32×C4—21no—
457C32×C4—21no—
458C32×C4C22×D411yescharacteristic
459C32×C4C2×#4111yescharacteristic
460C3⋊Dic3—41no—
461C3⋊Dic3—41no—
462C3⋊Dic3—41no—
463C3×Dic3—21no—
464C3×Dic3—21no—
465C3×Dic3—41no—
466C3×Dic3—41no—
467C3×Dic3#12112yes—
468C2×#41—91no—
469C22×Q8—91no—
470C22×D4—91no—
471AGL(1,ℤ/8)—184no—
472C2×SD16—31no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C2×SD16—91no—
477C2×SD16—91no—
478C2×SD16—184no—
479C2×D8—31no—
480C2×D8—91no—
481C2×M16—31no—
482C22×C8—31no—
483C4⋊Q8—91no—
484C4⋊Q8—91no—
485#124—31no—
486#124—91no—
487#123—181no—
488#123—181no—
489C22⋊Q8—181no—
490C22⋊Q8—181no—
491C4×D4—31no—
492C4×D4—91no—
493C4×D4—91no—
494C4×D4—91no—
495C4×D4—181no—
496C4×D4—181no—
497#117—31no—
498#117—91no—
499C2×C22⋊C4—181no—
500C2×C22⋊C4—181no—
501C4⋊C8—31no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8D3211yescharacteristic, complemented
505#103—31no—
506#103—91no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511#102—31no—
512#102—91no—
513C23×C3—31no—
514C23×C3—61no—
515C23×C3—61no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—64no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—64no—
522C22×D3—121no—
523C22×D3—241no—
524C22×D3—241no—
525C22×D3—241no—
526C22×D3—241no—
527C22×D3C2×D1211yescharacteristic
528C3×Q8—61no—
529C3×Q8—61no—
530C3×D4—32no—
531C3×D4—61no—
532C3×D4—61no—
533C3×D4—61no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—31no—
541C2×C3×C4—31no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—241no—
545C2×C3×C4C2×D1211yescharacteristic
546C2×C3×C4C2×D1211yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550C2×C3×C4C23×D311yescharacteristic
551#67—64no—
552#67—122no—
553#67—122no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—122no—
566C2×Dic3—122no—
567C2×Dic3—241no—
568C2×Dic3C2×D1211yescharacteristic
569C2×Dic3C2×D1211yescharacteristic
570C2×Dic3C2×D1211yescharacteristic
571D12—21no—
572D12—21no—
573D12—21no—
574D12—32no—
575D12—32no—
576D12—62no—
577D12—64no—
578D12—61no—
579D12—61no—
580D12—121no—
581D12D3×D412yes—
582C4×D3—81no—
583C4×D3—122no—
584C4×D3—122no—
585C4×D3—241no—
586C4×D3—241no—
587C4×D3—241no—
588C4×D3—241no—
589C4×D3—241no—
590C4×D3—242no—
591C4×D3D3×D412yes—
592C4×D3#23912yes—
593Dic6—21no—
594Dic6—21no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—61no—
602Dic6—61no—
603Dic6—121no—
604Dic6—121no—
605Dic6—121no—
606Dic6—121no—
607Dic6—122no—
608Dic6—122no—
609C3×C8—21no—
610C3×C8—21no—
611C3×C8—21no—
612C3×C8—21no—
613C3×C8—41no—
614C3×C8—41no—
615C3×C8—61no—
616C3×C8—61no—
617C3⋊C8—21no—
618C3⋊C8—21no—
619C2×C32C2×#12111yescharacteristic
620C2×C32#57711yescharacteristic
621C2×C32#57711yescharacteristic
622C3⋊D3—42no—
623C3×D3—22no—
624C3×D3—42no—
625C3×D3—81no—
626C24—181no—
627#41—182no—
628#41—182no—
629C2×Q8—31no—
630C2×Q8—91no—
631C2×Q8—91no—
632C2×Q8—181no—
633C2×Q8—182no—
634C2×Q8—182no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—94no—
638C2×D4—91no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C22×C4—31no—
643C22×C4—61no—
644C22×C4—181no—
645C22×C4—181no—
646C22×C4—181no—
647C22×C4—181no—
648C22×C4—181no—
649SD16—62no—
650SD16—182no—
651SD16—182no—
652SD16—182no—
653SD16—182no—
654SD16—182no—
655D8—62no—
656D8—182no—
657M16—62no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8C2×D3211yescharacteristic
662C2×C8C2×D3211yescharacteristic
663C4⋊C4—31no—
664C4⋊C4—31no—
665C4⋊C4—31no—
666C4⋊C4—91no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C22⋊C4—31no—
672C22⋊C4—31no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—181no—
677C22⋊C4—181no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C42—181no—
684C42C2×D3211yescharacteristic
685C22×C3—21no—
686C22×C3—32no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—62no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3C22×D1211yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C2×D3—21no—
698C2×D3—21no—
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—62no—
706C2×D3—62no—
707C2×D3—122no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—121no—
711C2×D3—121no—
712C2×D3—241no—
713C2×D3—241no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3#89512yes—
717C3×C4—22no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4C2×D3×D411yescharacteristic
731C3×C4C2×D3×D411yescharacteristic
732C3×C4C2×#23911yescharacteristic
733C3×C4D3×#4111yescharacteristic
734Dic3—21no—
735Dic3—21no—
736Dic3—41no—
737Dic3—41no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746Dic3—241no—
747Dic3#89512yes—
748C32#304211yescharacteristic, complemented, Sylow
749C23—31no—
750C23—61no—
751C23—61no—
752C23—184no—
753C23—181no—
754C23—721no—
755C23—721no—
756Q8—61no—
757Q8—61no—
758Q8—181no—
759Q8—181no—
760Q8—181no—
761Q8—181no—
762Q8—362no—
763D4—32no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—92no—
768D4—184no—
769D4—181no—
770D4—362no—
771C2×C4—31no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—181no—
779C2×C4—181no—
780C2×C4—181no—
781C2×C4—241no—
782C2×C4—362no—
783C2×C4—362no—
784C2×C4—721no—
785C2×C4—721no—
786C2×C4—721no—
787C2×C4D3×D1211yescharacteristic
788C2×C4D3×D1211yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C8—21no—
791C8—21no—
792C8—61no—
793C8—61no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—62no—
798C2×C3—122no—
799C2×C3—241no—
800C2×C3C2×#89511yescharacteristic
801C2×C3D3×#12111yescharacteristic
802C2×C3#575111yescharacteristic
803C2×C3#575111yescharacteristic
804C2×C3#577011yescharacteristic
805C2×C3#577511yescharacteristic
806D3—22no—
807D3—42no—
808D3—81no—
809D3—122no—
810D3—122no—
811D3—242no—
812C22—32no—
813C22—61no—
814C22—61no—
815C22—62no—
816C22—121no—
817C22—121no—
818C22—121no—
819C22—121no—
820C22—121no—
821C22—182no—
822C22—361no—
823C22—361no—
824C22—724no—
825C22C2×D3×D1211yescharacteristic
826C4—21no—
827C4—21no—
828C4—32no—
829C4—61no—
830C4—61no—
831C4—121no—
832C4—121no—
833C4—361no—
834C4—361no—
835C4—361no—
836C4D32×D411yescharacteristic
837C4D3×#23911yescharacteristic
838C3—21no—
839C3#7908711yescharacteristic, complemented
840C3#8053711yescharacteristic, complemented
841C2—62no—
842C2—122no—
843C2—241no—
844C2—362no—
845C2D3×#89511yescharacteristic
846C2#1059467911yescharacteristic
847C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#63795C2
hypercenterC4⋊C8D32
hypocenterC32#3042
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×D3×#204C2semidirect
3. #10593994C2semidirect
4. #10593894C2semidirect
5. #10592540C2semidirect
6. C3×#4844C2semidirect
7. C3×#4839C2semidirect
8. #10590954C2semidirect
9. #10590948C2semidirect
10. #10590860C2semidirect
11. #10590760C2semidirect
12. #10590755C2semidirect
13. #10590752C2semidirect
14. #10590365C2semidirect
15. #10590356C2semidirect
24. #64078C22semidirect
29. C3×#875C22semidirect
42. #63866C22semidirect
43. #63860C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63643C22semidirect
53. #63643C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63567C22semidirect
60. #63567C22semidirect
61. #63566C22semidirect
62. #63563C22semidirect
82. #4844D3semidirect
89. #4839D3semidirect
212. #875C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
235. #821C2×D3semidirect
245. #816C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
504. C4⋊C8D32semidirect
748. C32#3042semidirect
839. C3#79087semidirect
840. C3#80537semidirect

Maximal subgroups

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

subgroupindex
C2×#637952
C2×D3×#2042
#105939942
#105938942
#105925402
C3×#48442
C3×#48392
#105909542
#105909482
#105908602
#105907602
#105907552
#105907522
#105903652
#105903562
#805373
#790873