Finite Group Databasebeta

← #11860503

Subgroups — #11860503

Order 1152.

1079 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic
3#10593890C211yesmaximal, characteristic, complemented
4C4×#3753C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic, complemented
6Dic3×#214C211yesmaximal, characteristic, complemented
7D3×#832C211yesmaximal, characteristic, complemented
8#10591404C211yesmaximal, characteristic, complemented
9#10590610C211yesmaximal, characteristic, complemented
10#10590478C211yesmaximal, characteristic, complemented
11#10590456C211yesmaximal, characteristic, complemented
12#10590436C211yesmaximal, characteristic, complemented
13C4×#3715C211yesmaximal, characteristic, complemented
14#10590346C211yesmaximal, characteristic, complemented
15#10590319C211yesmaximal, characteristic, complemented
16#82537—31nomaximal
17#79775—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
23C3×D4×Dic3C2211yescharacteristic
24C2×C3×#214C2211yescharacteristic
25C3×C4×#67—21no—
26C2×C3×(C2×D3)⋊C4—21no—
27C3×#893C2211yescharacteristic
28C3×#892C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic, complemented
34#63934C418yescomplemented
35#63894C2211yescharacteristic, complemented
36D3×C4⋊Dic3C2211yescharacteristic
37#63883—21no—
38#63881—21no—
39#63880—21no—
40Dic3×Dic6C2211yescharacteristic, complemented
41#63836—21no—
42C2×#3715C2211yescharacteristic
43C2×#3714C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C2×D3×C3⋊C8C2211yescharacteristic
46#63659C2211yescharacteristic
47#63636C2211yescharacteristic, complemented
48#63634C2211yescharacteristic, complemented
49C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#810C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53C3×#803C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63562C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61Dic3×C3⋊C8C2211yescharacteristic, complemented
62C3×#518—31no—
63C2×#932—31no—
64C2×#914—31no—
65#5574—31no—
66#5545D311yescharacteristic, complemented
67#5523—31no—
68C3×#440—31no—
69C2×#832—31no—
70Dic3×SD16—31no—
71C4×#215—31no—
72#5018—31no—
73#5018D311yescharacteristic, complemented
74C4×#214—31no—
75C4×#214—31no—
76#5014—31no—
77#5014—31no—
78C4×#213—31no—
79C4×#213—31no—
80C4×#213—31no—
81C4×#213—61no—
82#5002—31no—
83#4997—31no—
84#4995—31no—
85#4881—31no—
86#4872—31no—
87#4817—31no—
88#4804—31no—
89#4785—31no—
90D3×#102—31no—
91#4711—31no—
92#4708—31no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C3×D3×D4—22no—
101C3×D3×D4C2×C414yescomplemented
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111#3799—22no—
112#3799C2×C414yescomplemented
113C32×C4⋊C4C2311yescharacteristic
114C32×C22⋊C4—21no—
115C32×C42C2311yescharacteristic
116#3753C2×C414yescomplemented
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#214C2×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⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3715C2×C414yescomplemented
143#3714C2×C414yescomplemented
144#3711C2×C414yescomplemented
145D3×C3⋊C8—22no—
146#2946—91noSylow
147C22×C3×D4—31no—
148C2×#239—31no—
149C2×D3×D4C2×D311yescharacteristic
150C2×#235—31no—
151C2×C3×SD16—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—21no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—31no—
157C3×C4×D4—61no—
158C3×C4×D4—61no—
159C3×C4×D4C2×D311yescharacteristic
160C3×C4×D4C2×D311yescharacteristic
161C3×#117—31no—
162C3×#117—31no—
163C2×C3×C22⋊C4—61no—
164C2×C3×C22⋊C4—61no—
165Q8×Dic3—31no—
166C2×#215—31no—
167D4×Dic3C2×D311yescharacteristic
168C2×#214—31no—
169C2×#214C2×D311yescharacteristic
170#932—38no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—61no—
175C4×#67—21no—
176C2×(C2×D3)⋊C4—21no—
177C2×C4⋊Dic3—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—31no—
185#893—61no—
186#893C2×D311yescharacteristic
187#892—61no—
188#892C2×D311yescharacteristic
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4—61no—
192#67⋊C4—21no—
193#67⋊C4—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—21no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200C4×D12—61no—
201C4×D12C2×D311yescharacteristic
202#872—61no—
203#872C2×D311yescharacteristic
204C4×Dic6—31no—
205C4×Dic6C2×D311yescharacteristic, complemented
206C3×#107—31no—
207C3×#103—31no—
208C3×#102—31no—
209C3×#97—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—61no—
216#832C2×D311yescharacteristic
217#821—31no—
218#821—31no—
219#817—31no—
220#815—31no—
221C8×Dic3—31no—
222#810—31no—
223#810C2×D311yescharacteristic, complemented
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—61no—
229#808—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236#803—31no—
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C23×C32—21no—
243C22×C3⋊D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—24no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
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—
260C3×#67—24no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—21no—
269C3×D12C22×C412yes—
270C3×C4×D3—81no—
271C3×C4×D3—81no—
272C3×C4×D3C22×C412yes—
273C3×C4×D3#4112yes—
274C3×Dic6—21no—
275C3×Dic6C22×C412yes—
276#626—24no—
277#624—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—91no—
286#518—31no—
287#442—91no—
288#442—91no—
289#440—31no—
290#440—91no—
291C4×SD16—91no—
292C4×SD16—91no—
293C4×D8—91no—
294C4×D8—91no—
295#428—91no—
296#416—91no—
297C2×#102—91no—
298#405—91no—
299C24×C3—61no—
300C23×D3—21no—
301C2×C3×Q8—31no—
302C2×C3×D4—21no—
303C2×C3×D4—34no—
304C2×C3×D4—31no—
305C2×C3×D4—62no—
306C2×C3×D4—61no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—41no—
313C22×C3×C4—61no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C2×#67—21no—
317C2×#67—61no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320#239—34no—
321#239—62no—
322D3×D4—22no—
323D3×D4C4×D314yescomplemented
324#235—34no—
325#235—62no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—21no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
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
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—34no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—21no—
355C3×C22⋊C4—21no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—41no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—21no—
364C3×C42—31no—
365C3×C42—61no—
366C3×C42—61no—
367C3×C42C22×D311yescharacteristic
368C3×C42C22×D311yescharacteristic
369#217—21no—
370#215—34no—
371#214—34no—
372#214C4×D314yescomplemented
373#213—34no—
374#213—34no—
375#213—34no—
376#213—64no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4#6711yescharacteristic
386(C2×D3)⋊C4#6711yescharacteristic
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398Dic3⋊C4#6711yescharacteristic
399C4×Dic3—21no—
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×C32—22no—
418C22×C32—41no—
419C22×C32—41no—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—84no—
430C2×C3×D3C4×D412yes—
431C32×C4—21no—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C23×C411yescharacteristic
435C32×C4C2×#4111yescharacteristic
436C3⋊Dic3—41no—
437C3×Dic3—22no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3C4×D412yes—
443C2×#41—91no—
444C22×D4—31no—
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×Q8—91no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—61no—
458C4×D4—61no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4—181no—
463C4×D4D3211yescharacteristic
464#117—31no—
465#117—31no—
466#117—181no—
467C2×C4⋊C4—91no—
468C2×C4⋊C4—181no—
469C2×C22⋊C4—61no—
470C2×C22⋊C4—61no—
471#107—31no—
472#107—91no—
473#106—91no—
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—31no—
484#97—91no—
485C4×C8—91no—
486C4×C8—91no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—64no—
492C23×C3—61no—
493C23×C3—241no—
494C23×C3—241no—
495C22×D3—21no—
496C22×D3—24no—
497C22×D3—61no—
498C22×D3—61no—
499C22×D3—81no—
500C22×D3—81no—
501C22×D3—121no—
502C22×D3C2×#6711yescharacteristic
503C3×Q8—32no—
504C3×Q8—61no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—22no—
508C3×D4—32no—
509C3×D4—41no—
510C3×D4—64no—
511C3×D4—61no—
512C3×D4C2×C4×D312yes—
513C3×D4C2×C4×D312yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—32no—
521C2×C3×C4—32no—
522C2×C3×C4—31no—
523C2×C3×C4—31no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—81no—
529C2×C3×C4—81no—
530C2×C3×C4—82no—
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—24no—
541#67—64no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—81no—
548C2×Dic3—121no—
549C2×Dic3—241no—
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552C2×Dic3C2×#6711yescharacteristic
553D12—21no—
554D12—32no—
555D12—32no—
556D12—62no—
557D12—64no—
558D12—61no—
559D12—61no—
560D12—121no—
561D12C2×C4×D312yes—
562C4×D3—64no—
563C4×D3—64no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—242no—
572C4×D3C2×C4×D312yes—
573C4×D3#23512yes—
574Dic6—21no—
575Dic6C2×C4×D312yes—
576C3×C8—32no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—32no—
580C3⋊C8—32no—
581C3⋊C8—62no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C3⋊C8C2×C4×D312yes—
586C2×C32—42no—
587C2×C32C2×C4×D411yescharacteristic
588C2×C32#57611yescharacteristic
589C2×C32#57711yescharacteristic
590C3⋊D3—42no—
591C3×D3—22no—
592C3×D3—42no—
593C24—61no—
594#41—94no—
595#41—182no—
596C2×Q8—31no—
597C2×D4—34no—
598C2×D4—31no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—91no—
602C2×D4—181no—
603C2×D4C2×D3211yescharacteristic
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613SD16—34no—
614SD16—94no—
615D8—94no—
616D8—94no—
617M16—94no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—91no—
622C2×C8—182no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—21no—
633C22⋊C4—31no—
634C22⋊C4—31no—
635C22⋊C4—61no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—61no—
644C42—181no—
645C42C2×D3211yescharacteristic
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—32no—
650C22×C3—42no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—62no—
658C22×C3—81no—
659C22×C3—81no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—244no—
663C22×C3C2×D3×D411yescharacteristic
664C22×C3C22×#6711yescharacteristic
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—62no—
671C2×D3—62no—
672C2×D3—84no—
673C2×D3—122no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3C4×#6712yes—
681C3×C4—22no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—32no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—61no—
693C3×C4—61no—
694C3×C4—62no—
695C3×C4—81no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4C22×C4×D311yescharacteristic
699C3×C4C22×C4×D311yescharacteristic
700C3×C4C2×#23511yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—22no—
703Dic3—21no—
704Dic3—21no—
705Dic3—41no—
706Dic3—41no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3C4×#6712yes—
711C32#294611yescharacteristic, complemented, Sylow
712C23—21no—
713C23—31no—
714C23—64no—
715C23—61no—
716C23—181no—
717C23—241no—
718C23—241no—
719Q8—32no—
720Q8—61no—
721D4—21no—
722D4—32no—
723D4—64no—
724D4—61no—
725D4—92no—
726D4—184no—
727D4—181no—
728D4C4×D3212yes—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—81no—
739C2×C4—184no—
740C2×C4—181no—
741C2×C4—241no—
742C2×C4—241no—
743C2×C4—241no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4—721no—
747C2×C4D3×#6711yescharacteristic
748C2×C4D3×#6711yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—32no—
751C8—61no—
752C8—92no—
753C8—181no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—42no—
758C2×C3—42no—
759C2×C3—62no—
760C2×C3—82no—
761C2×C3—122no—
762C2×C3C4×D3×D411yescharacteristic
763C2×C3#577411yescharacteristic
764C2×C3#577811yescharacteristic
765C2×C3C2×C4×#6711yescharacteristic
766C2×C3#583511yescharacteristic
767C2×C3#583611yescharacteristic
768D3—22no—
769D3—42no—
770D3—122no—
771D3—122no—
772D3—242no—
773C22—22no—
774C22—32no—
775C22—41no—
776C22—41no—
777C22—61no—
778C22—61no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—182no—
783C22—244no—
784C22—361no—
785C22—361no—
786C22C2×D3×#6711yescharacteristic
787C4—21no—
788C4—21no—
789C4—32no—
790C4—41no—
791C4—61no—
792C4—61no—
793C4—62no—
794C4—121no—
795C4—121no—
796C4—361no—
797C4C2×C4×D3211yescharacteristic
798C4D3×#23511yescharacteristic
799C3—21no—
800C3#7977511yescharacteristic, complemented
801C3#8253711yescharacteristic, complemented
802C2—42no—
803C2—62no—
804C2—122no—
805C2—362no—
806C2C4×D3×#6711yescharacteristic
807C2#1059509711yescharacteristic
808C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63934C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2946
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5545C2semidirect
3. #10593890C2semidirect
4. C4×#3753C2semidirect
5. C3×#5018C2semidirect
6. Dic3×#214C2semidirect
7. D3×#832C2semidirect
8. #10591404C2semidirect
9. #10590610C2semidirect
10. #10590478C2semidirect
11. #10590456C2semidirect
12. #10590436C2semidirect
13. C4×#3715C2semidirect
14. #10590346C2semidirect
15. #10590319C2semidirect
22. C4×C4⋊(C3⋊D3)C22semidirect
33. C3×C4×Dic6C22semidirect
34. #63934C4semidirect
35. #63894C22semidirect
40. Dic3×Dic6C22semidirect
47. #63636C22semidirect
48. #63634C22semidirect
49. C4×C3⋊(C3⋊C8)C22semidirect
51. C3×#810C22semidirect
52. C3×#807C22semidirect
53. C3×#803C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63565C22semidirect
57. #63564C22semidirect
60. #63554C22semidirect
61. Dic3×C3⋊C8C22semidirect
66. #5545D3semidirect
73. #5018D3semidirect
101. C3×D3×D4C2×C4semidirect
112. #3799C2×C4semidirect
116. #3753C2×C4semidirect
122. C3×#214C2×C4semidirect
142. #3715C2×C4semidirect
143. #3714C2×C4semidirect
144. #3711C2×C4semidirect
205. C4×Dic6C2×D3semidirect
223. #810C2×D3semidirect
235. #807C2×D3semidirect
237. #803C2×D3semidirect
323. D3×D4C4×D3semidirect
372. #214C4×D3semidirect
711. C32#2946semidirect
800. C3#79775semidirect
801. C3#82537semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
C2×#639342
#105938902
C4×#37532
C3×#50182
Dic3×#2142
D3×#8322
#105914042
#105906102
#105904782
#105904562
#105904362
C4×#37152
#105903462
#105903192
#825373
#797753