Finite Group Databasebeta

← #11872165

Subgroups — #11872165

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5582C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic, complemented
3C4×#3755C211yesmaximal, characteristic, complemented
4C3×#5026C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6#10591568C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10590595C211yesmaximal, characteristic
10#10590465C211yesmaximal, characteristic, complemented
11#10590464C211yesmaximal, characteristic, complemented
12#10590446C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14C4×#3713C211yesmaximal, characteristic, complemented
15#10590265C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#79785—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic, complemented
20C2×#3755C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#947C2211yescharacteristic, complemented
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#896—21no—
26C3×#895C2211yescharacteristic
27C3×#894—21no—
28C3×#888C2211yescharacteristic, complemented
29C3×#876—21no—
30C3×#875—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×#872C2211yescharacteristic
34#63921—21no—
35D3×(C2×D3)⋊C4—21no—
36#63904—21no—
37#63894C2211yescharacteristic
38Dic3×D12C2211yescharacteristic
39#63881—21no—
40#63841C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63636C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic
49C3×#807C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#542—31no—
62#5582D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#440—31no—
66#5169—31no—
67#5165—31no—
68#5087—31no—
69#5084—31no—
70#5057—31no—
71#5057—31no—
72#5046—31no—
73#5045—31no—
74#5036—31no—
75#5035—31no—
76#5026D311yescharacteristic, complemented
77C4×#215—31no—
78C4×#215—31no—
79C4×#215—61no—
80#5014—31no—
81C4×#213—31no—
82C4×#213—31no—
83#5000—31no—
84#4890—31no—
85#4885—31no—
86#4819—31no—
87#4815—31no—
88#4773—31no—
89#4761—31no—
90#4711—31no—
91#4709—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×#626—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—22no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112#3755—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#215—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3713—22no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#124—31no—
148C3×#124—61no—
149C3×#123—61no—
150C3×C22⋊Q8—31no—
151C3×C22⋊Q8—61no—
152C3×#121—31no—
153C3×C4×Q8—21no—
154C3×C4×Q8C2×D311yescharacteristic, complemented
155C3×C4×Q8C2×D311yescharacteristic, complemented
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159#947C2×D311yescharacteristic, complemented
160#946C2×D311yescharacteristic
161C2×#215—31no—
162C2×#215—31no—
163C2×#215—61no—
164C2×#215C2×D311yescharacteristic
165D4×Dic3—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#926—31no—
172C2×D24—31no—
173#896—21no—
174#895C2×D311yescharacteristic
175#894—21no—
176#893—31no—
177#893—61no—
178#893—61no—
179#892—31no—
180#888C2×D311yescharacteristic, complemented
181#67⋊C4—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185#876—21no—
186#875—21no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12C2×D311yescharacteristic
193C4×D12C2×D311yescharacteristic, complemented
194#872C2×D311yescharacteristic
195C3×#107—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×#97—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic, complemented
203#832—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#817—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#809—31no—
216#809—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—61no—
221#809C2×D311yescharacteristic
222#808—31no—
223#808—31no—
224#808—31no—
225#808—61no—
226#807—31no—
227#807—31no—
228#807C2×D311yescharacteristic, complemented
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803C2×D311yescharacteristic, complemented
232C4×C3⋊C8—31no—
233C4×C3⋊C8—31no—
234C4×C3⋊C8—61no—
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—24no—
240C2×D32—81no—
241C2×D32—81no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×Dic6—81no—
268#626—24no—
269#624—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—31no—
276#518—91no—
277#485—91no—
278#482—91no—
279#476—91no—
280#474—91no—
281#463—91no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—31no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C23×D3—61no—
291C23×D3—61no—
292C2×C3×Q8—21no—
293C2×C3×Q8—61no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306C2×D12—21no—
307C2×D12—31no—
308C2×D12—31no—
309C2×D12—61no—
310C2×D12—62no—
311C2×D12—61no—
312C2×D12—62no—
313C2×D12C22×D311yescharacteristic
314C2×D12C22×D311yescharacteristic
315C2×C4×D3—21no—
316C2×C4×D3—21no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—121no—
323C2×C4×D3C22×D311yescharacteristic
324C2×Dic6—21no—
325C3×SD16—62no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C22⋊C4—31no—
341C3×C22⋊C4—31no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42—21no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—41no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#215—22no—
358#215—62no—
359#215—62no—
360#215—64no—
361#213—62no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—121no—
377(C2×D3)⋊C4#6711yescharacteristic
378(C2×D3)⋊C4#6711yescharacteristic
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D24—62no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3×D3—22no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413D32—84no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—91no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8—91no—
431C4⋊Q8—31no—
432#126—61no—
433#124—31no—
434#124—61no—
435#123—61no—
436C22⋊Q8—31no—
437C22⋊Q8—61no—
438#121—31no—
439C4×Q8D3211yescharacteristic, complemented
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—181no—
446C4×D4—181no—
447#117—31no—
448#117—91no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451#107—31no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—91no—
456C4⋊C8—91no—
457#103—31no—
458#103—91no—
459#102—31no—
460#102—91no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465C22⋊C8—91no—
466C22⋊C8—91no—
467#97—31no—
468C4×C8—91no—
469C23×C3—31no—
470C23×C3—61no—
471C23×C3—61no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—64no—
475C22×D3—64no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3—241no—
480C22×D3—241no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3C2×#6711yescharacteristic
484C3×Q8—22no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—241no—
491C3×D4—32no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—241no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—64no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3C2×#6711yescharacteristic
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530D12—21no—
531D12—21no—
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—61no—
538D12—61no—
539D12—81no—
540D12—121no—
541D12#23512yes—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—241no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—242no—
552Dic6—81no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32#52511yescharacteristic
564C2×C32#57611yescharacteristic
565C2×C32#57711yescharacteristic
566C3⋊D3—42no—
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—181no—
571C2×Q8—61no—
572C2×Q8C2×D3211yescharacteristic
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—91no—
577C2×D4—181no—
578C2×D4—182no—
579C2×D4—182no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4—181no—
586SD16—62no—
587SD16—182no—
588D8—182no—
589D8—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8—91no—
594C4⋊C4—21no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C42—21no—
616C42—31no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—21no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—62no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3—121no—
628C22×C3—121no—
629C22×C3C2×D3×D411yescharacteristic
630C22×C3C22×#6711yescharacteristic
631C2×D3—22no—
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—122no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—121no—
647C2×D3—241no—
648C2×D3—241no—
649C2×D3—244no—
650C2×D3—244no—
651C3×C4—22no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—41no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—81no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4C2×#23511yescharacteristic
671C3×C4D3×#4111yescharacteristic
672C3×C4D3×#4111yescharacteristic
673C3×C4D3×#4111yescharacteristic
674Dic3—21no—
675Dic3—21no—
676Dic3—21no—
677Dic3—41no—
678Dic3—41no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—31no—
684C23—61no—
685C23—61no—
686C23—184no—
687C23—181no—
688C23—721no—
689C23—721no—
690Q8—21no—
691Q8—21no—
692Q8—241no—
693D4—32no—
694D4—61no—
695D4—61no—
696D4—61no—
697D4—92no—
698D4—184no—
699D4—181no—
700D4—241no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—181no—
711C2×C4—241no—
712C2×C4—241no—
713C2×C4—721no—
714C2×C4—721no—
715C2×C4—721no—
716C2×C4D3×#6711yescharacteristic
717C2×C4D3×#6711yescharacteristic
718C2×C4C22×D3211yescharacteristic
719C8—61no—
720C8—61no—
721C8—181no—
722C8—181no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—122no—
727C2×C3—121no—
728C2×C3—241no—
729C2×C3#554711yescharacteristic
730C2×C3#577411yescharacteristic
731C2×C3#577811yescharacteristic
732C2×C3#582811yescharacteristic
733C2×C3#583511yescharacteristic
734C2×C3#583711yescharacteristic
735D3—41no—
736D3—42no—
737D3—81no—
738D3—122no—
739D3—122no—
740D3—242no—
741C22—61no—
742C22—61no—
743C22—62no—
744C22—61no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—121no—
749C22—121no—
750C22—182no—
751C22—361no—
752C22—361no—
753C22—724no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—41no—
759C4—61no—
760C4—61no—
761C4—61no—
762C4—121no—
763C4—121no—
764C4—361no—
765C4D3×#23511yescharacteristic
766C4#6430611yescharacteristic
767C3—21no—
768C3#7978511yescharacteristic, complemented
769C3#8346011yescharacteristic, complemented
770C2—121no—
771C2—122no—
772C2—241no—
773C2—362no—
774C2#1059506011yescharacteristic
775C2#1059531911yescharacteristic
776C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590595C2
hypercenterC4×Q8D32
hypocenterC32#3118
LCSG ▷ C2×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×#5582C2semidirect
2. #10593994C2semidirect
3. C4×#3755C2semidirect
4. C3×#5026C2semidirect
5. #10591651C2semidirect
6. #10591568C2semidirect
7. #10591567C2semidirect
8. #10591559C2semidirect
10. #10590465C2semidirect
11. #10590464C2semidirect
12. #10590446C2semidirect
13. #10590346C2semidirect
14. C4×#3713C2semidirect
15. #10590265C2semidirect
19. C32×C4×Q8C22semidirect
22. C3×#947C22semidirect
28. C3×#888C22semidirect
32. C3×C4×D12C22semidirect
43. #63662C22semidirect
45. #63635C22semidirect
46. C4×C3⋊(C3⋊C8)C22semidirect
47. C3×#835C22semidirect
49. C3×#807C22semidirect
50. C3×#803C22semidirect
51. #63576C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
62. #5582D3semidirect
76. #5026D3semidirect
154. C3×C4×Q8C2×D3semidirect
155. C3×C4×Q8C2×D3semidirect
159. #947C2×D3semidirect
180. #888C2×D3semidirect
193. C4×D12C2×D3semidirect
202. #835C2×D3semidirect
228. #807C2×D3semidirect
231. #803C2×D3semidirect
439. C4×Q8D32semidirect
682. C32#3118semidirect
768. C3#79785semidirect
769. C3#83460semidirect

Maximal subgroups

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

subgroupindex
C3×#55822
#105939942
C4×#37552
C3×#50262
#105916512
#105915682
#105915672
#105915592
#105905952
#105904652
#105904642
#105904462
#105903462
C4×#37132
#105902652
#834603
#797853