Finite Group Databasebeta

← #11860509

Subgroups — #11860509

Order 1152.

1072 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic
3#10593994C211yesmaximal, characteristic, complemented
4#10592725C211yesmaximal, characteristic, complemented
5C3×C4×#215C211yesmaximal, characteristic, complemented
6#10591566C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9D3×#809C211yesmaximal, characteristic, complemented
10#10590589C211yesmaximal, characteristic, complemented
11#10590581C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13C4×#3714C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590318C211yesmaximal, characteristic, complemented
16#82564—31nomaximal
17#79647—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C2×#3755C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic, complemented
24C2×C3×#215C2211yescharacteristic
25C3×#893—21no—
26C3×#893C2211yescharacteristic, complemented
27C3×D3×C4⋊C4—21no—
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic, complemented
32C3×#872—21no—
33C3×#872C2211yescharacteristic
34#63939C418yescomplemented
35#63921—21no—
36D3×(C2×D3)⋊C4—21no—
37#63904—21no—
38#63894C2211yescharacteristic
39Dic3×D12C2211yescharacteristic
40#63881—21no—
41#63841C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63662C2211yescharacteristic, complemented
47#63636C2211yescharacteristic
48#63634C2211yescharacteristic, complemented
49#63630C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×#520—31no—
63C2×#949—31no—
64C2×#914—31no—
65#5574D311yescharacteristic, complemented
66#5545—31no—
67#5521—31no—
68C3×C4×SD16—31no—
69#5233—31no—
70#5164—31no—
71#5026—31no—
72#5026—31no—
73#5026—31no—
74#5026—61no—
75C4×#215—31no—
76C4×#215D311yescharacteristic, complemented
77#5014—31no—
78#5014—31no—
79#5014—31no—
80C4×#213—31no—
81C4×#213—31no—
82#4997—31no—
83C2×#809—31no—
84#4964—31no—
85#4869—31no—
86#4861—31no—
87#4804—31no—
88#4788—31no—
89D3×#102—31no—
90#4756—31no—
91C4×D24—31no—
92#4689—31no—
93C22×D32—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C3×#239—22no—
98C3×#239C2×C414yescomplemented
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×#626—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12C2×C414yescomplemented
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C42—21no—
116C32×C42C2311yescharacteristic
117#3755C2×C414yescomplemented
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#215C2×C414yescomplemented
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3714C2×C414yescomplemented
143#3713C2×C414yescomplemented
144#3711C2×C414yescomplemented
145D3×C3⋊C8—22no—
146#2946—91noSylow
147C2×C3×#41—31no—
148C2×#239C2×D311yescharacteristic
149C2×D3×D4—31no—
150C22×D12—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—21no—
153C3×C4×Q8—31no—
154C3×C4×Q8C2×D311yescharacteristic, complemented
155C3×C4×Q8C2×D311yescharacteristic, complemented
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×C4×D4—61no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4—61no—
165#949—38no—
166Q8×Dic3C2×D311yescharacteristic, complemented
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—61no—
170C2×#215C2×D311yescharacteristic
171D4×Dic3—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C4×#67—61no—
176C2×(C2×D3)⋊C4—61no—
177#926—31no—
178C2×#208—31no—
179C22×C3⋊C8—31no—
180#914—38no—
181C2×D24—31no—
182C2×ΓL(1,𝔽25)—31no—
183C2×D3×C8—31no—
184#893—21no—
185#893—31no—
186#893—61no—
187#893—61no—
188#893C2×D311yescharacteristic, complemented
189#892—31no—
190D3×C4⋊C4—21no—
191D3×C4⋊C4C2×D311yescharacteristic
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196C4×D12—21no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C4×D12—61no—
202C4×D12C2×D311yescharacteristic
203C4×D12C2×D311yescharacteristic, complemented
204#872—21no—
205#872C2×D311yescharacteristic
206C3×#106—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835C2×D311yescharacteristic, complemented
214#832—31no—
215#832—31no—
216#832—31no—
217#821—31no—
218#821—31no—
219#818—31no—
220#815—31no—
221C8×Dic3—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—61no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236#803—31no—
237#803—31no—
238#803—31no—
239#803—61no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8C2×D311yescharacteristic, complemented
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—24no—
247C2×D32—81no—
248C2×D32—81no—
249C32×Q8—21no—
250C32×Q8C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256C2×C3⋊Dic3—21no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)C22×C412yes—
259C4×C3⋊D3—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—24no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12C22×C412yes—
269C3×D12C22×C412yes—
270C3×C4×D3—24no—
271C3×C4×D3—81no—
272C3×C4×D3—81no—
273C3×C4×D3—81no—
274C3×C4×D3—81no—
275C3×C4×D3C22×C412yes—
276C3×C4×D3#4112yes—
277#626—24no—
278#624—81no—
279D3×Dic3—81no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)C22×C412yes—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C2×AGL(1,ℤ/8)—91no—
285#520—31no—
286#518—91no—
287#442—91no—
288#442—91no—
289#440—91no—
290#440—91no—
291C4×SD16—31no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—91no—
296#416—91no—
297C2×#102—91no—
298#405—91no—
299C23×D3—61no—
300C23×D3—61no—
301C3×#41—34no—
302C3×#41—62no—
303C2×C3×Q8—21no—
304C2×C3×Q8C22×D311yescharacteristic
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C2×#67—61no—
316C22×Dic3—61no—
317#239—22no—
318#239C4×D314yescomplemented
319D3×D4—34no—
320D3×D4—62no—
321C2×D12—21no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—34no—
325C2×D12—61no—
326C2×D12—62no—
327C2×D12—61no—
328C2×D12C22×D311yescharacteristic
329C2×D12C22×D311yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—121no—
341C2×C4×D3C22×D311yescharacteristic
342C3×SD16—34no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42—21no—
364C3×C42—21no—
365C3×C42—31no—
366C3×C42—41no—
367C3×C42—61no—
368C3×C42C22×D311yescharacteristic
369C3×C42C22×D311yescharacteristic
370#217—61no—
371#217—61no—
372#215—34no—
373#215—34no—
374#215—64no—
375#215C4×D314yescomplemented
376#213—34no—
377#213—34no—
378#213—34no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389(C2×D3)⋊C4#6711yescharacteristic
390(C2×D3)⋊C4#6711yescharacteristic
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4#6711yescharacteristic
399Dic3⋊C4#6711yescharacteristic
400C4×Dic3—21no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404#208—34no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—62no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D24—34no—
415ΓL(1,𝔽25)—34no—
416D3×C8—62no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—22no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3C4×D412yes—
430D32—84no—
431C32×C4—22no—
432C32×C4—21no—
433C32×C4—21no—
434C32×C4—41no—
435C32×C4C23×C411yescharacteristic
436C32×C4C2×#4111yescharacteristic
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—31no—
444C22×D4—91no—
445AGL(1,ℤ/8)—98no—
446C2×SD16—31no—
447C2×SD16—91no—
448C2×D8—91no—
449C2×D8—91no—
450C2×M16—91no—
451C22×C8—91no—
452C4×Q8—31no—
453C4×Q8D3211yescharacteristic, complemented
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4—61no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C4×D4—181no—
464#117—31no—
465#117—61no—
466#117—91no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—61no—
469C2×C22⋊C4—181no—
470C2×C22⋊C4—181no—
471#107—91no—
472#107—91no—
473#106—31no—
474#106—91no—
475#103—31no—
476#103—91no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#97—91no—
484#97—91no—
485C4×C8—31no—
486C4×C8—91no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—64no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—64no—
496C22×D3—121no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—241no—
501C22×D3C2×#6711yescharacteristic
502C3×Q8—21no—
503C3×Q8—21no—
504C3×Q8—22no—
505C3×Q8—41no—
506C3×Q8C2×C4×D312yes—
507C3×Q8C2×C4×D312yes—
508C3×D4—32no—
509C3×D4—32no—
510C3×D4—64no—
511C3×D4—61no—
512C3×D4—61no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—32no—
522C2×C3×C4—32no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—64no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—241no—
531C2×C3×C4—241no—
532C2×C3×C4—241no—
533C2×C3×C4—241no—
534C2×C3×C4D3×D411yescharacteristic
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C2×#6711yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540#67—64no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—241no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—24no—
551D12—21no—
552D12—21no—
553D12—32no—
554D12—32no—
555D12—62no—
556D12—64no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12C2×C4×D312yes—
561D12C2×C4×D312yes—
562C4×D3—24no—
563C4×D3—81no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—81no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—242no—
573C4×D3C2×C4×D312yes—
574C4×D3#23512yes—
575C3×C8—32no—
576C3×C8—61no—
577C3⋊C8—21no—
578C3⋊C8—32no—
579C3⋊C8—32no—
580C3⋊C8—62no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C3⋊C8C2×C4×D312yes—
585C2×C32C2×C4×D411yescharacteristic
586C2×C32#57611yescharacteristic
587C2×C32#57711yescharacteristic
588C3⋊D3—42no—
589C3×D3—22no—
590C3×D3—42no—
591C3×D3—42no—
592C24—181no—
593#41—34no—
594#41—62no—
595C2×Q8C2×D3211yescharacteristic
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—61no—
599C2×D4—94no—
600C2×D4—91no—
601C2×D4—182no—
602C2×D4—181no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—34no—
613SD16—94no—
614D8—94no—
615D8—94no—
616M16—94no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—91no—
621C2×C8—182no—
622C4⋊C4—21no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—91no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C42—21no—
641C42—31no—
642C42—61no—
643C42—181no—
644C42C2×D3211yescharacteristic
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—62no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—22no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—122no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—241no—
673C2×D3—241no—
674C2×D3—244no—
675C2×D3—244no—
676C2×D3C4×#6712yes—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—22no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—32no—
686C3×C4—41no—
687C3×C4—41no—
688C3×C4—42no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4C22×C4×D311yescharacteristic
697C3×C4C22×C4×D311yescharacteristic
698C3×C4C2×#23511yescharacteristic
699C3×C4D3×#4111yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3C4×#6712yes—
708C32#294611yescharacteristic, complemented, Sylow
709C23—31no—
710C23—61no—
711C23—61no—
712C23—184no—
713C23—181no—
714C23—721no—
715C23—721no—
716Q8—21no—
717Q8C4×D3212yes—
718D4—32no—
719D4—32no—
720D4—64no—
721D4—61no—
722D4—61no—
723D4—92no—
724D4—184no—
725D4—181no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—31no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—64no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—181no—
737C2×C4—241no—
738C2×C4—241no—
739C2×C4—241no—
740C2×C4—241no—
741C2×C4—721no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4D3×#6711yescharacteristic
745C2×C4D3×#6711yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—32no—
748C8—61no—
749C8—92no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—62no—
755C2×C3—122no—
756C2×C3—122no—
757C2×C3C4×D3×D411yescharacteristic
758C2×C3#576211yescharacteristic
759C2×C3#576911yescharacteristic
760C2×C3C2×C4×#6711yescharacteristic
761C2×C3#583511yescharacteristic
762C2×C3#583711yescharacteristic
763D3—22no—
764D3—42no—
765D3—42no—
766D3—122no—
767D3—122no—
768D3—242no—
769C22—32no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—62no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—182no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22C2×D3×#6711yescharacteristic
783C4—21no—
784C4—22no—
785C4—21no—
786C4—32no—
787C4—41no—
788C4—61no—
789C4—61no—
790C4—121no—
791C4—121no—
792C4—361no—
793C4C2×C4×D3211yescharacteristic
794C4D3×#23511yescharacteristic
795C3—21no—
796C3#7964711yescharacteristic, complemented
797C3#8256411yescharacteristic, complemented
798C2—62no—
799C2—122no—
800C2—122no—
801C2—362no—
802C2C4×D3×#6711yescharacteristic
803C2#1059531811yescharacteristic
804C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#63939C2
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5574C2semidirect
3. #10593994C2semidirect
4. #10592725C2semidirect
5. C3×C4×#215C2semidirect
6. #10591566C2semidirect
7. #10591556C2semidirect
8. #10591536C2semidirect
9. D3×#809C2semidirect
10. #10590589C2semidirect
11. #10590581C2semidirect
12. #10590452C2semidirect
13. C4×#3714C2semidirect
14. #10590344C2semidirect
15. #10590318C2semidirect
20. C32×C4×Q8C22semidirect
23. C3×Q8×Dic3C22semidirect
26. C3×#893C22semidirect
31. C3×C4×D12C22semidirect
34. #63939C4semidirect
46. #63662C22semidirect
48. #63634C22semidirect
49. #63630C22semidirect
50. C3×#835C22semidirect
52. C3×#808C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
57. #63563C22semidirect
59. #63562C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
65. #5574D3semidirect
76. C4×#215D3semidirect
98. C3×#239C2×C4semidirect
112. D3×D12C2×C4semidirect
117. #3755C2×C4semidirect
122. C3×#215C2×C4semidirect
142. #3714C2×C4semidirect
143. #3713C2×C4semidirect
144. #3711C2×C4semidirect
154. C3×C4×Q8C2×D3semidirect
155. C3×C4×Q8C2×D3semidirect
166. Q8×Dic3C2×D3semidirect
188. #893C2×D3semidirect
203. C4×D12C2×D3semidirect
213. #835C2×D3semidirect
231. #808C2×D3semidirect
241. C4×C3⋊C8C2×D3semidirect
318. #239C4×D3semidirect
375. #215C4×D3semidirect
453. C4×Q8D32semidirect
708. C32#2946semidirect
796. C3#79647semidirect
797. C3#82564semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
C2×#639392
#105939942
#105927252
C3×C4×#2152
#105915662
#105915562
#105915362
D3×#8092
#105905892
#105905812
#105904522
C4×#37142
#105903442
#105903182
#825643
#796473