Finite Group Databasebeta

← #11872187

Subgroups — #11872187

Order 1152.

874 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5682C211yesmaximal, characteristic, complemented
2#10593994C211yesmaximal, characteristic, complemented
3#10592756C211yesmaximal, characteristic, complemented
4C3×#5057C211yesmaximal, characteristic, complemented
5#10591651C211yesmaximal, characteristic, complemented
6Dic3×#215C211yesmaximal, characteristic, complemented
7#10591559C211yesmaximal, characteristic, complemented
8#10591540C211yesmaximal, characteristic, complemented
9#10591515C211yesmaximal, characteristic
10#10591430C211yesmaximal, characteristic, complemented
11#10591422C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10590300C211yesmaximal, characteristic, complemented
14#10590269C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#83460—31nomaximal
17#80509—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C32×#124C2211yescharacteristic, complemented
20C2×#3755C2211yescharacteristic
21C2×#3753C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C3×D4×Dic3C2211yescharacteristic, complemented
28C2×C3×#213C2211yescharacteristic
29C3×#886—21no—
30C3×#885—21no—
31C3×#879—21no—
32C3×#878—21no—
33C3×C4×D12C2211yescharacteristic
34C3×#872C2211yescharacteristic
35C3×#869C2211yescharacteristic, complemented
36#63921—21no—
37D3×(C2×D3)⋊C4—21no—
38#63904—21no—
39#63894C2211yescharacteristic
40Dic3×D12C2211yescharacteristic
41#63881—21no—
42#63841C2211yescharacteristic
43#63662C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
49#63576C2211yescharacteristic, complemented
50#63576C2211yescharacteristic, complemented
51#63573C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63564C2211yescharacteristic
54#63564C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#542—31no—
62#5682D311yescharacteristic, complemented
63#5545—31no—
64#5521—31no—
65C3×#463—31no—
66#5169—31no—
67Dic3×SD16—31no—
68#5156—31no—
69#5152—31no—
70#5087—31no—
71#5084—31no—
72#5057—31no—
73#5057—31no—
74#5057—61no—
75#5057D311yescharacteristic, complemented
76#5046—31no—
77#5045—31no—
78#5036—31no—
79#5035—31no—
80#5026—31no—
81C4×#215—31no—
82#5014—31no—
83C4×#213—31no—
84#5007—31no—
85#5000—31no—
86#4842—31no—
87#4840—31no—
88#4817—31no—
89#4815—31no—
90#4779—31no—
91#4756—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C2×C3×D12C2311yescharacteristic
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×C22⋊C4—21no—
109C32×C22⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3755—22no—
112#3753—22no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#215—22no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3118—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×SD16—31no—
145C2×C3×D8—31no—
146C3×C4⋊Q8—31no—
147C3×#126—61no—
148C3×#124—21no—
149C3×#124—61no—
150C3×#124C2×D311yescharacteristic, complemented
151C3×#124C2×D311yescharacteristic, complemented
152C3×#123—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×#121—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×C4×D4—31no—
159C3×#117—31no—
160#946C2×D311yescharacteristic
161Q8×Dic3C2×D311yescharacteristic, complemented
162C2×#215—31no—
163C2×#215—31no—
164C2×#215—61no—
165C2×#215C2×D311yescharacteristic
166#938C2×D311yescharacteristic
167D4×Dic3—31no—
168D4×Dic3C2×D311yescharacteristic, complemented
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175#926—31no—
176#893—31no—
177#893—61no—
178#893—61no—
179#892—31no—
180#886—21no—
181#885—21no—
182#67⋊C4—61no—
183D3×C22⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#879—21no—
187#878—21no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194#872C2×D311yescharacteristic
195#869C2×D311yescharacteristic, complemented
196C3×C4⋊C8—31no—
197C3×#103—31no—
198C3×#102—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835C2×D311yescharacteristic, complemented
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic, complemented
209#830—31no—
210#830—31no—
211#821—31no—
212#821—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—31no—
215#817—31no—
216#817—31no—
217#815—31no—
218C8×Dic3—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—31no—
223#808—31no—
224#808—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—31no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32—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—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)#4112yes—
253C4×C3⋊D3—81no—
254C3×#67—81no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—81no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
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—31no—
282#463—91no—
283#450—91no—
284#447—91no—
285#442—91no—
286#440—91no—
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—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C2×#67—21no—
305C2×#67—61no—
306C22×Dic3—21no—
307C22×Dic3—61no—
308D3×D4—62no—
309D3×D4—62no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—61no—
313C2×D12—62no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—121no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C3×SD16—62no—
327C3×D8—62no—
328C2×C3×C8—31no—
329C2×C3×C8—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—21no—
340C3×C22⋊C4—21no—
341C3×C22⋊C4—21no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—41no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—31no—
352C3×C42—61no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—21no—
356#217—21no—
357#217—61no—
358#217—61no—
359#215—22no—
360#215—62no—
361#215—62no—
362#215—122no—
363#213—22no—
364#213—62no—
365#213—62no—
366#213—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—61no—
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—121no—
376(C2×D3)⋊C4#6711yescharacteristic
377(C2×D3)⋊C4#6711yescharacteristic
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401C22×C32—41no—
402C22×C32—41no—
403C22×C32—41no—
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—22no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3×D3—22no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414D32—84no—
415C32×C4—21no—
416C32×C4—21no—
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—
426C3×Dic3—41no—
427C22×D4—91no—
428C2×SD16—31no—
429C2×SD16—91no—
430C2×D8—31no—
431C2×D8—91no—
432C4⋊Q8—31no—
433#126—61no—
434#124—61no—
435#124D3211yescharacteristic, complemented
436#123—61no—
437C22⋊Q8—31no—
438C22⋊Q8—61no—
439#121—31no—
440C4×Q8—31no—
441C4×D4—31no—
442C4×D4—31no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—181no—
447C4×D4—181no—
448#117—31no—
449#117—91no—
450C2×C22⋊C4—181no—
451C2×C22⋊C4—181no—
452#107—91no—
453#107—91no—
454#106—91no—
455#106—91no—
456C4⋊C8—31no—
457C4⋊C8—91no—
458#103—31no—
459#103—91no—
460#102—31no—
461#102—91no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—91no—
469C4×C8—91no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3—41no—
474C23×C3—61no—
475C22×D3—21no—
476C22×D3—64no—
477C22×D3—64no—
478C22×D3—61no—
479C22×D3—61no—
480C22×D3—121no—
481C22×D3—241no—
482C22×D3—241no—
483C22×D3—241no—
484C22×D3—241no—
485C22×D3C2×#6711yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—241no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—32no—
498C3×D4—41no—
499C3×D4—41no—
500C3×D4—61no—
501C3×D4—241no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—64no—
525#67—81no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—81no—
532C2×Dic3—121no—
533C2×Dic3—241no—
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537D12—21no—
538D12—32no—
539D12—32no—
540D12—62no—
541D12—64no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12#23712yes—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—81no—
549C4×D3—241no—
550C4×D3—241no—
551C4×D3—241no—
552C4×D3—241no—
553C4×D3—241no—
554C4×D3—242no—
555Dic6—81no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32—81no—
567C2×C32#52511yescharacteristic
568C2×C32#57611yescharacteristic
569C2×C32#57711yescharacteristic
570C3⋊D3—42no—
571C3×D3—41no—
572C3×D3—42no—
573C24—181no—
574C2×Q8—61no—
575C2×Q8C2×D3211yescharacteristic
576C2×D4—31no—
577C2×D4—61no—
578C2×D4—91no—
579C2×D4—181no—
580C2×D4—182no—
581C2×D4—182no—
582C2×D4C2×D3211yescharacteristic
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588C22×C4—181no—
589SD16—62no—
590SD16—182no—
591D8—62no—
592D8—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—91no—
596C2×C8—91no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—31no—
609C22⋊C4—31no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C42—31no—
619C42—61no—
620C42—181no—
621C42C2×D3211yescharacteristic
622C22×C3—21no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—61no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C22×#6711yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—22no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—62no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—241no—
654C2×D3—241no—
655C2×D3—244no—
656C2×D3—244no—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—61no—
668C3×C4—61no—
669C3×C4—61no—
670C3×C4—81no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4C2×#23711yescharacteristic
675C3×C4D3×#4111yescharacteristic
676C3×C4D3×#4111yescharacteristic
677C3×C4D3×#4111yescharacteristic
678Dic3—21no—
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—121no—
685Dic3—121no—
686Dic3—241no—
687C32#311811yescharacteristic, complemented, Sylow
688C23—21no—
689C23—31no—
690C23—61no—
691C23—184no—
692C23—181no—
693C23—721no—
694C23—721no—
695Q8—21no—
696Q8—21no—
697Q8—241no—
698D4—21no—
699D4—21no—
700D4—32no—
701D4—61no—
702D4—92no—
703D4—184no—
704D4—181no—
705D4—241no—
706C2×C4—21no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—31no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—181no—
716C2×C4—241no—
717C2×C4—241no—
718C2×C4—721no—
719C2×C4—721no—
720C2×C4—721no—
721C2×C4D3×#6711yescharacteristic
722C2×C4D3×#6711yescharacteristic
723C2×C4C22×D3211yescharacteristic
724C8—61no—
725C8—61no—
726C8—181no—
727C8—181no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—81no—
732C2×C3—81no—
733C2×C3—122no—
734C2×C3—121no—
735C2×C3—161no—
736C2×C3#560611yescharacteristic
737C2×C3#577011yescharacteristic
738C2×C3#577411yescharacteristic
739C2×C3#582811yescharacteristic
740C2×C3#583511yescharacteristic
741C2×C3#583711yescharacteristic
742D3—41no—
743D3—42no—
744D3—122no—
745D3—122no—
746D3—242no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—61no—
751C22—61no—
752C22—61no—
753C22—62no—
754C22—121no—
755C22—121no—
756C22—182no—
757C22—361no—
758C22—361no—
759C22—724no—
760C22C2×D3×#6711yescharacteristic
761C4—21no—
762C4—21no—
763C4—41no—
764C4—61no—
765C4—61no—
766C4—61no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—361no—
771C4D3×#23711yescharacteristic
772C4#6431211yescharacteristic
773C3—21no—
774C3#8050911yescharacteristic, complemented
775C3#8346011yescharacteristic, complemented
776C2—81no—
777C2—121no—
778C2—122no—
779C2—362no—
780C2#1059530111yescharacteristic
781C2#1059545411yescharacteristic
782C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#124C22
socleC22×C32C22×D4
prime radical#10591515C2
hypercenter#124D32
hypocenterC32#3118
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#5682C2semidirect
2. #10593994C2semidirect
3. #10592756C2semidirect
4. C3×#5057C2semidirect
5. #10591651C2semidirect
6. Dic3×#215C2semidirect
7. #10591559C2semidirect
8. #10591540C2semidirect
10. #10591430C2semidirect
11. #10591422C2semidirect
12. #10591400C2semidirect
13. #10590300C2semidirect
14. #10590269C2semidirect
15. #10590253C2semidirect
19. C32×#124C22semidirect
24. C3×Q8×Dic3C22semidirect
27. C3×D4×Dic3C22semidirect
35. C3×#869C22semidirect
43. #63662C22semidirect
44. #63659C22semidirect
45. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#835C22semidirect
47. C3×#832C22semidirect
48. C3×C4⋊(C3⋊C8)C22semidirect
49. #63576C22semidirect
50. #63576C22semidirect
51. #63573C22semidirect
52. #63573C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5682D3semidirect
75. #5057D3semidirect
150. C3×#124C2×D3semidirect
151. C3×#124C2×D3semidirect
161. Q8×Dic3C2×D3semidirect
168. D4×Dic3C2×D3semidirect
195. #869C2×D3semidirect
202. #835C2×D3semidirect
208. #832C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
435. #124D32semidirect
687. C32#3118semidirect
774. C3#80509semidirect
775. C3#83460semidirect

Maximal subgroups

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

subgroupindex
C3×#56822
#105939942
#105927562
C3×#50572
#105916512
Dic3×#2152
#105915592
#105915402
#105915152
#105914302
#105914222
#105914002
#105903002
#105902692
#105902532
#834603
#805093