Finite Group Databasebeta

← #11872169

Subgroups — #11872169

Order 1152.

878 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5545C211yesmaximal, characteristic, complemented
2#10593878C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591471C211yesmaximal, characteristic, complemented
6#10591458C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic
8#10591410C211yesmaximal, characteristic, complemented
9#10590558C211yesmaximal, characteristic, complemented
10#10590534C211yesmaximal, characteristic, complemented
11#10590519C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13#10590358C211yesmaximal, characteristic, complemented
14C4×#3714C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17#79696—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×(C2×D3)⋊C4—21no—
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×D3×C22⋊C4—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic, complemented
33#63918C2211yescharacteristic, complemented
34#63909C2211yescharacteristic
35#63868—21no—
36#63865—21no—
37#63864C2211yescharacteristic, complemented
38#63856C2211yescharacteristic
39#63853—21no—
40#63852—21no—
41C2×#3715C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46#63630C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#518—31no—
62#5582—31no—
63#5545D311yescharacteristic, complemented
64#5534—31no—
65C3×C4×SD16—31no—
66#5218—31no—
67#5217—31no—
68#5169—31no—
69#5165—31no—
70#5026—31no—
71#5018—31no—
72C4×#214D311yescharacteristic, complemented
73#5016—31no—
74#5016—31no—
75#5014—31no—
76#5014—31no—
77#5014—61no—
78C4×#213—31no—
79#5008—31no—
80#5007—31no—
81#5003—31no—
82#5000—31no—
83#4996—31no—
84#4870—31no—
85#4866—31no—
86#4819—31no—
87#4814—31no—
88#4773—31no—
89#4759—31no—
90C4×D24—31no—
91#4690—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#627—21no—
107C2×#626—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3753—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#214—22no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4D411yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3715—22no—
140#3714—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C3×C4×Q8—31no—
146C3×C4×D4—21no—
147C3×C4×D4—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—31no—
156C2×C3×C22⋊C4—61no—
157C2×C3×C22⋊C4—61no—
158#947—31no—
159#946—31no—
160C2×#215—31no—
161D4×Dic3C2×D311yescharacteristic
162C2×#214—31no—
163C2×#214C2×D311yescharacteristic
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169C4×#67—21no—
170C2×(C2×D3)⋊C4—21no—
171#924—31no—
172C2×D24—31no—
173#898—61no—
174#896—61no—
175#896—61no—
176#895—31no—
177#894—61no—
178#893C2×D311yescharacteristic
179#892C2×D311yescharacteristic
180#888—31no—
181#885—61no—
182#883—61no—
183#67⋊C4—21no—
184D3×C22⋊C4—21no—
185#876—61no—
186#875—31no—
187#875—61no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—61no—
191C4×D12C2×D311yescharacteristic
192#872C2×D311yescharacteristic
193#869—31no—
194C4×Dic6C2×D311yescharacteristic, complemented
195C3×#106—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209#821—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212#818—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810C2×D311yescharacteristic, complemented
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#808—31no—
223#808—31no—
224#808—61no—
225#808C2×D311yescharacteristic, complemented
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231#803—31no—
232#803—31no—
233#803—61no—
234C4×C3⋊C8C2×D311yescharacteristic, complemented
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—81no—
240C22×C3×D3—81no—
241C22×C3×D3C2×D411yescharacteristic
242C32×D4—21no—
243C32×D4#4112yes—
244C2×C32×C4—21no—
245C2×C32×C4—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—81no—
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#627—81no—
270#626—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#542—91no—
276#518—31no—
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—91no—
287C4×SD16—31no—
288C4×D8—91no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×Q8—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—61no—
296C2×C3×D4—62no—
297C2×C3×D4—62no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—41no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—21no—
308C2×#67—61no—
309C22×Dic3—21no—
310D3×D4—22no—
311D3×D4—22no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—121no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—62no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—41no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42—61no—
350C3×C42C22×D311yescharacteristic
351C3×C42C22×D311yescharacteristic
352#217—21no—
353#217—61no—
354#215—62no—
355#214—22no—
356#214—62no—
357#213—62no—
358#213—64no—
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374(C2×D3)⋊C4#6711yescharacteristic
375(C2×D3)⋊C4#6711yescharacteristic
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
389C4×Dic3—21no—
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×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3×D3—21no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—84no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—31no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×D8—91no—
430C2×D8—91no—
431C4⋊Q8—91no—
432#126—181no—
433#124—91no—
434#124—181no—
435#123—181no—
436C22⋊Q8—91no—
437C22⋊Q8—181no—
438#121—91no—
439C4×Q8—31no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—61no—
444C4×D4—61no—
445C4×D4—91no—
446C4×D4D3211yescharacteristic
447#117—31no—
448#117—31no—
449C2×C22⋊C4—61no—
450C2×C22⋊C4—61no—
451#107—91no—
452#107—91no—
453#106—31no—
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—91no—
468C4×C8—31no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—31no—
472C23×C3—41no—
473C23×C3—64no—
474C23×C3—61no—
475C23×C3—241no—
476C23×C3—241no—
477C22×D3—21no—
478C22×D3—24no—
479C22×D3—61no—
480C22×D3—61no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3—121no—
484C22×D3C2×#6711yescharacteristic
485C3×Q8—61no—
486C3×Q8—61no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—22no—
490C3×D4—32no—
491C3×D4—41no—
492C3×D4—64no—
493C3×D4—61no—
494C3×D4#23512yes—
495C3×D4#23512yes—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—81no—
511C2×C3×C4—81no—
512C2×C3×C4—82no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4—241no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—24no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—81no—
530C2×Dic3—121no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534D12—21no—
535D12—62no—
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12—241no—
542D12#23512yes—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—81no—
546C4×D3—81no—
547C4×D3—241no—
548C4×D3—241no—
549C4×D3—242no—
550Dic6—21no—
551Dic6—21no—
552Dic6—241no—
553Dic6—241no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—62no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—121no—
564C2×C32—42no—
565C2×C32#52511yescharacteristic
566C2×C32#57611yescharacteristic
567C2×C32#57711yescharacteristic
568C3⋊D3—81no—
569C3×D3—41no—
570C3×D3—42no—
571C24—61no—
572C2×Q8—31no—
573C2×Q8—181no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4C2×D3211yescharacteristic
581C22×C4—21no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587SD16—62no—
588SD16—182no—
589D8—182no—
590D8—182no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4C2×D3211yescharacteristic
604C22⋊C4—21no—
605C22⋊C4—31no—
606C22⋊C4—31no—
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C22⋊C4—181no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C42—31no—
617C42—61no—
618C42—61no—
619C42C2×D3211yescharacteristic
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—21no—
623C22×C3—42no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—244no—
637C22×C3C2×D3×D411yescharacteristic
638C22×C3C22×#6711yescharacteristic
639C2×D3—21no—
640C2×D3—22no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—84no—
646C2×D3—122no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—61no—
668C3×C4—81no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4C2×#23511yescharacteristic
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23511yescharacteristic
675C3×C4D3×#4111yescharacteristic
676Dic3—21no—
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—121no—
683Dic3—121no—
684Dic3—241no—
685C32#311811yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23—64no—
689C23—61no—
690C23—181no—
691C23—241no—
692C23—241no—
693Q8—61no—
694Q8—61no—
695Q8—721no—
696D4—21no—
697D4—32no—
698D4—64no—
699D4—61no—
700D4—181no—
701D4—181no—
702D4—721no—
703D4#379812yes—
704C2×C4—21no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—81no—
714C2×C4—181no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—241no—
718C2×C4—721no—
719C2×C4D3×#6711yescharacteristic
720C2×C4D3×#6711yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—61no—
723C8—61no—
724C8—181no—
725C8—181no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—82no—
732C2×C3—121no—
733C2×C3—122no—
734C2×C3#554711yescharacteristic
735C2×C3#576211yescharacteristic
736C2×C3#576911yescharacteristic
737C2×C3#579111yescharacteristic
738C2×C3#583511yescharacteristic
739C2×C3#583611yescharacteristic
740D3—41no—
741D3—42no—
742D3—242no—
743D3—241no—
744D3—241no—
745C22—22no—
746C22—41no—
747C22—41no—
748C22—61no—
749C22—61no—
750C22—61no—
751C22—62no—
752C22—121no—
753C22—121no—
754C22—244no—
755C22—361no—
756C22—361no—
757C22—361no—
758C22C2×D3×#6711yescharacteristic
759C4—21no—
760C4—21no—
761C4—41no—
762C4—61no—
763C4—61no—
764C4—61no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—361no—
769C4C2×#379811yescharacteristic
770C4D3×#23511yescharacteristic
771C3—21no—
772C3#7969611yescharacteristic, complemented
773C3#8254111yescharacteristic, complemented
774C2—42no—
775C2—121no—
776C2—122no—
777C2—721no—
778C2#1059500211yescharacteristic
779C2#1059510511yescharacteristic
780C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591448C2
hypercenterC4×D4D32
hypocenterC32#3118
LCSG ▷ C2×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
2. #10593878C2semidirect
3. #10592713C2semidirect
4. C3×C4×#214C2semidirect
5. #10591471C2semidirect
6. #10591458C2semidirect
8. #10591410C2semidirect
9. #10590558C2semidirect
10. #10590534C2semidirect
11. #10590519C2semidirect
12. #10590425C2semidirect
13. #10590358C2semidirect
14. C4×#3714C2semidirect
15. #10590264C2semidirect
21. C4×C4⋊(C3⋊D3)C22semidirect
32. C3×C4×Dic6C22semidirect
33. #63918C22semidirect
37. #63864C22semidirect
44. #63636C22semidirect
45. #63635C22semidirect
46. #63630C22semidirect
48. C3×#810C22semidirect
49. C3×#808C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63564C22semidirect
63. #5545D3semidirect
72. C4×#214D3semidirect
194. C4×Dic6C2×D3semidirect
216. #810C2×D3semidirect
225. #808C2×D3semidirect
234. C4×C3⋊C8C2×D3semidirect
685. C32#3118semidirect
772. C3#79696semidirect
773. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105938782
#105927132
C3×C4×#2142
#105914712
#105914582
#105914482
#105914102
#105905582
#105905342
#105905192
#105904252
#105903582
C4×#37142
#105902642
#825413
#796963