Finite Group Databasebeta

← #11872162

Subgroups — #11872162

Order 1152.

872 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×#5545C211yesmaximal, characteristic, complemented
2#10593983C211yesmaximal, characteristic, complemented
3#10592717C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591468C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic
8#10591408C211yesmaximal, characteristic, complemented
9#10590555C211yesmaximal, characteristic, complemented
10#10590530C211yesmaximal, characteristic, complemented
11#10590502C211yesmaximal, characteristic, complemented
12#10590429C211yesmaximal, characteristic, complemented
13C4×#3716C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590264C211yesmaximal, characteristic, complemented
16#82541—31nomaximal
17#79594—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C4×#634C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
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×C4×D12C2211yescharacteristic, complemented
32C3×#872C2211yescharacteristic
33#63918C2211yescharacteristic, complemented
34#63915—21no—
35#63908C2211yescharacteristic
36#63905—21no—
37#63862—21no—
38#63860C2211yescharacteristic, complemented
39#63857C2211yescharacteristic
40#63851—21no—
41C2×#3716C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63637C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46#63630C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#809C2211yescharacteristic, complemented
49C3×#807C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#518—31no—
62#5561—31no—
63#5545D311yescharacteristic, complemented
64#5534—31no—
65C3×C4×D8—31no—
66#5218—31no—
67#5217—31no—
68#5156—31no—
69#5153—31no—
70#5018—31no—
71#5018—31no—
72#5018—61no—
73C4×#214—31no—
74#5016—31no—
75#5016—31no—
76#5014—31no—
77#5014—31no—
78C4×#213D311yescharacteristic, complemented
79#5008—31no—
80#5007—31no—
81#5003—31no—
82#5000—31no—
83#4996—31no—
84#4890—31no—
85#4888—31no—
86#4787—31no—
87#4779—31no—
88#4776—31no—
89#4761—31no—
90C4×#204—31no—
91#4690—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C3×D3×D4—22no—
99C3×D3×D4—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#627—21no—
107C2×#625—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3754—22no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#213—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4D411yescharacteristic
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3716—22no—
140#3713—22no—
141#3118—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C3×C4×D4—21no—
146C3×C4×D4—31no—
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#938—31no—
159#936—31no—
160D4×Dic3C2×D311yescharacteristic
161C2×#214—31no—
162C2×#214—31no—
163C2×#214—31no—
164C2×#214—61no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213C2×D311yescharacteristic
168#930—31no—
169#929—61no—
170C4×#67—21no—
171C2×(C2×D3)⋊C4—21no—
172#924—31no—
173#924—61no—
174C2×#204—31no—
175#898—61no—
176#897—31no—
177#896—61no—
178#893C2×D311yescharacteristic
179#892C2×D311yescharacteristic
180#888—31no—
181#885—61no—
182#885—61no—
183#883—61no—
184#67⋊C4—21no—
185D3×C22⋊C4—21no—
186#879—61no—
187#875—31no—
188C4×D12C2×D311yescharacteristic
189C4×D12C2×D311yescharacteristic, complemented
190#872C2×D311yescharacteristic
191#869—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C3×#107—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#832—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(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—61no—
219#809—31no—
220#809—31no—
221#809C2×D311yescharacteristic, complemented
222#808—31no—
223#808—31no—
224#808—31no—
225#807—31no—
226#807—31no—
227#807—61no—
228#807C2×D311yescharacteristic, complemented
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—24no—
238C22×C3×D3—21no—
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—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253C3×#67—24no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—81no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269#627—81no—
270#625—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—91no—
288C4×D8—31no—
289#433—91no—
290C24×C3—61no—
291C23×D3—21no—
292C2×C3×D4—21no—
293C2×C3×D4—31no—
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—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—21no—
312D3×D4—22no—
313D3×D4—22no—
314C2×D12C22×D311yescharacteristic
315C2×D12C22×D311yescharacteristic
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3C22×D311yescharacteristic
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C3×D8—62no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C4⋊C4C22×D311yescharacteristic
335C3×C22⋊C4—21no—
336C3×C22⋊C4—21no—
337C3×C22⋊C4—31no—
338C3×C22⋊C4—31no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C42—21no—
346C3×C42—31no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C22×D311yescharacteristic
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#214—62no—
356#214—64no—
357#214—62no—
358#214—62no—
359#213—22no—
360#213—62no—
361#213—62no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4#6711yescharacteristic
371(C2×D3)⋊C4#6711yescharacteristic
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—121no—
384Dic3⋊C4#6711yescharacteristic
385Dic3⋊C4#6711yescharacteristic
386C4×Dic3—21no—
387C4×Dic3—61no—
388C4×Dic3—61no—
389C4×Dic3—121no—
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
399#204—62no—
400C22×C32—22no—
401C22×C32—41no—
402C22×C32—41no—
403C22×C32C22×D411yescharacteristic
404C2×C3×D3—21no—
405C2×C3×D3—22no—
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—
413C2×C3×D3—84no—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4C2×#4111yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×D4—31no—
427C2×SD16—91no—
428C2×SD16—91no—
429C2×D8—31no—
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—91no—
440C4×D4—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—31no—
444C4×D4—61no—
445C4×D4—61no—
446C4×D4D3211yescharacteristic
447#117—31no—
448#117—31no—
449C2×C22⋊C4—61no—
450C2×C22⋊C4—61no—
451#107—31no—
452#107—91no—
453#106—91no—
454#106—91no—
455C4⋊C8—91no—
456C4⋊C8—91no—
457#103—91no—
458#103—91no—
459#102—31no—
460#102—31no—
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—61no—
476C23×C3—241no—
477C23×C3—241no—
478C22×D3—21no—
479C22×D3—24no—
480C22×D3—21no—
481C22×D3—81no—
482C22×D3—81no—
483C22×D3C2×#6711yescharacteristic
484C3×D4—21no—
485C3×D4—21no—
486C3×D4—22no—
487C3×D4—32no—
488C3×D4—41no—
489C3×D4—64no—
490C3×D4—61no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4#23512yes—
494C3×D4#23512yes—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—81no—
509C2×C3×C4—81no—
510C2×C3×C4—82no—
511C2×C3×C4—241no—
512C2×C3×C4—241no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—24no—
522#67—241no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—81no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536D12—21no—
537D12—21no—
538D12—21no—
539D12#23512yes—
540C4×D3—21no—
541C4×D3—21no—
542C4×D3—81no—
543C4×D3—81no—
544C4×D3—81no—
545Dic6—62no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—241no—
552Dic6—241no—
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—42no—
564C2×C32#52511yescharacteristic
565C2×C32#57611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—41no—
568C3×D3—42no—
569C3×D3—81no—
570C24—61no—
571C2×Q8—91no—
572C2×Q8—181no—
573C2×D4—31no—
574C2×D4—31no—
575C2×D4—61no—
576C2×D4—62no—
577C2×D4—62no—
578C2×D4—181no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4—61no—
585C22×C4—61no—
586SD16—182no—
587SD16—182no—
588D8—62no—
589D8—182no—
590C2×C8—31no—
591C2×C8—31no—
592C2×C8—91no—
593C2×C8—91no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
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—31no—
616C42—61no—
617C42—181no—
618C42C2×D3211yescharacteristic
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—21no—
622C22×C3—42no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3—62no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—244no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—22no—
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—41no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—84no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23511yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—122no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—241no—
682C32#311811yescharacteristic, complemented, Sylow
683C23—21no—
684C23—31no—
685C23—64no—
686C23—61no—
687C23—61no—
688C23—241no—
689C23—241no—
690Q8—181no—
691Q8—181no—
692Q8—721no—
693D4—21no—
694D4—32no—
695D4—64no—
696D4—61no—
697D4—61no—
698D4—61no—
699D4—721no—
700D4#379812yes—
701C2×C4—21no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—81no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—241no—
714C2×C4—241no—
715C2×C4—241no—
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—42no—
727C2×C3—42no—
728C2×C3—82no—
729C2×C3—121no—
730C2×C3—122no—
731C2×C3—241no—
732C2×C3#554711yescharacteristic
733C2×C3#575711yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3#579111yescharacteristic
736C2×C3#583511yescharacteristic
737C2×C3#583611yescharacteristic
738D3—41no—
739D3—42no—
740D3—81no—
741C22—22no—
742C22—41no—
743C22—41no—
744C22—61no—
745C22—61no—
746C22—61no—
747C22—62no—
748C22—121no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—244no—
754C22C2×D3×#6711yescharacteristic
755C4—21no—
756C4—21no—
757C4—41no—
758C4—61no—
759C4—61no—
760C4—61no—
761C4—121no—
762C4—121no—
763C4—361no—
764C4—361no—
765C4C2×#379811yescharacteristic
766C4D3×#23511yescharacteristic
767C3—21no—
768C3#7959411yescharacteristic, complemented
769C3#8254111yescharacteristic, complemented
770C2—42no—
771C2—121no—
772C2—122no—
773C2—241no—
774C2#1059500211yescharacteristic
775C2#1059509611yescharacteristic
776C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591447C2
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. #10593983C2semidirect
3. #10592717C2semidirect
4. C3×C4×#213C2semidirect
5. #10591468C2semidirect
6. #10591459C2semidirect
8. #10591408C2semidirect
9. #10590555C2semidirect
10. #10590530C2semidirect
11. #10590502C2semidirect
12. #10590429C2semidirect
13. C4×#3716C2semidirect
14. #10590344C2semidirect
15. #10590264C2semidirect
21. C4×#634C22semidirect
31. C3×C4×D12C22semidirect
33. #63918C22semidirect
38. #63860C22semidirect
44. #63637C22semidirect
45. #63634C22semidirect
46. #63630C22semidirect
48. C3×#809C22semidirect
49. C3×#807C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
58. #63562C22semidirect
63. #5545D3semidirect
78. C4×#213D3semidirect
189. C4×D12C2×D3semidirect
221. #809C2×D3semidirect
228. #807C2×D3semidirect
234. C4×C3⋊C8C2×D3semidirect
682. C32#3118semidirect
768. C3#79594semidirect
769. C3#82541semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105939832
#105927172
C3×C4×#2132
#105914682
#105914592
#105914472
#105914082
#105905552
#105905302
#105905022
#105904292
C4×#37162
#105903442
#105902642
#825413
#795943