Finite Group Databasebeta

← #11872762

Subgroups — #11872762

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593994C211yesmaximal, characteristic, complemented
2#10593949C211yesmaximal, characteristic, complemented
3#10592546C211yesmaximal, characteristic, complemented
4C3×#4843C211yesmaximal, characteristic, complemented
5C3×#4840C211yesmaximal, characteristic, complemented
6#10590944C211yesmaximal, characteristic, complemented
7#10590944C211yesmaximal, characteristic, complemented
8#10590837C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10#10590771C211yesmaximal, characteristic, complemented
11Dic3×D24C211yesmaximal, characteristic, complemented
12#10590746C211yesmaximal, characteristic, complemented
13#10590745C211yesmaximal, characteristic, complemented
14#10590355C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#80317—31nomaximal
17#79386—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64079C2211yescharacteristic, complemented
21C2×C3×D24C2211yescharacteristic
22C2×C3×D24C2211yescharacteristic
23C3×#874C2211yescharacteristic, complemented
24C3×C4×D12C2211yescharacteristic
25C3×#872C2211yescharacteristic
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63908C2211yescharacteristic
29#63908C2211yescharacteristic
30#63904—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33Dic3×D12C2211yescharacteristic, complemented
34Dic3×D12C2211yescharacteristic, complemented
35#63885—21no—
36#63885—21no—
37#63884—21no—
38#63884—21no—
39#63881—21no—
40#63841C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63645C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#815C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5719—31no—
62#5545—31no—
63#5535—31no—
64#5521—31no—
65C3×#459—31no—
66C3×#433—31no—
67#5156—31no—
68#5156—31no—
69#5152—31no—
70Dic3×D8—31no—
71#5072—31no—
72#5009—31no—
73#4847—31no—
74#4847—31no—
75#4847—31no—
76#4847—61no—
77#4843—31no—
78#4843D311yescharacteristic, complemented
79#4840D311yescharacteristic, complemented
80#4785—31no—
81#4784—31no—
82#4779—31no—
83#4756—31no—
84#4737—31no—
85#4737—31no—
86#4732—31no—
87#4732—31no—
88#4711—31no—
89#4711—31no—
90C4×D24—31no—
91C4×D24—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#625—21no—
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4D411yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130C3×D24—22no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#939—61no—
150#939—61no—
151#938—31no—
152#938—31no—
153#935—61no—
154#935—61no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158C2×#213—31no—
159C2×#213—31no—
160#930—31no—
161#930—31no—
162C4×#67—61no—
163C2×(C2×D3)⋊C4—61no—
164#926—31no—
165C2×D24—31no—
166C2×D24—31no—
167C2×D24C2×D311yescharacteristic
168C2×D24C2×D311yescharacteristic
169#894—61no—
170#894—61no—
171#893—31no—
172#893—61no—
173#893—61no—
174#892—31no—
175#884—61no—
176#884—61no—
177#67⋊C4—61no—
178D3×C22⋊C4—61no—
179D3×C22⋊C4—61no—
180D3×C22⋊C4—61no—
181#874C2×D311yescharacteristic, complemented
182C4×D12—31no—
183C4×D12—31no—
184C4×D12—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12—61no—
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191#870—31no—
192#870—31no—
193#870—61no—
194C3×C4⋊C8—21no—
195C3×C4⋊C8—31no—
196C3×C4⋊C8C2×D311yescharacteristic, complemented
197C3×C4⋊C8C2×D311yescharacteristic, complemented
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201C3×C22⋊C8—31no—
202C3×#97—31no—
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#821—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—61no—
217#821—61no—
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#817—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#815C2×D311yescharacteristic, complemented
231C8×Dic3C2×D311yescharacteristic, complemented
232#808—31no—
233#807—31no—
234C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
235C22×C3⋊D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12—81no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267#626—24no—
268#625—81no—
269#625—81no—
270#624—81no—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—31no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—31no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310D3×D4—62no—
311D3×D4—62no—
312C2×D12—21no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C3×D8—62no—
334C3×D8—62no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C42—21no—
350C3×C42—31no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
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—121no—
373(C2×D3)⋊C4D1211yescharacteristic
374(C2×D3)⋊C4D1211yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
390Dic3⋊C4—121no—
391Dic3⋊C4D1211yescharacteristic
392Dic3⋊C4D1211yescharacteristic
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—22no—
399D24—22no—
400D24—62no—
401D24—62no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—22no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418D32—84no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—91no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435#127—31no—
436#125—91no—
437#123—181no—
438#123—181no—
439#121—91no—
440#121—91no—
441#121—181no—
442#121—181no—
443C4×D4—31no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—31no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—91no—
456#107—91no—
457#106—91no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8D3211yescharacteristic, complemented
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—31no—
470C22⋊C8—31no—
471#97—31no—
472C4×C8—31no—
473C23×C3—31no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—241no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3C2×D1211yescharacteristic
490C3×D4—32no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—241no—
497C3×D4—241no—
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—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4C2×D1211yescharacteristic
509C2×C3×C4C2×D1211yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—241no—
516#67—241no—
517#67—241no—
518#67—241no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—241no—
530C2×Dic3—241no—
531C2×Dic3—241no—
532C2×Dic3C2×D1211yescharacteristic
533C2×Dic3C2×D1211yescharacteristic
534C2×Dic3C2×D1211yescharacteristic
535D12—21no—
536D12—21no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12—32no—
541D12—32no—
542D12—62no—
543D12—64no—
544D12—61no—
545D12—61no—
546D12—81no—
547D12—81no—
548D12—121no—
549D12#23712yes—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—81no—
553C4×D3—241no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32#52511yescharacteristic
572C2×C32#57611yescharacteristic
573C2×C32#57611yescharacteristic
574C3⋊D3—42no—
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—181no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—91no—
586C2×D4—181no—
587C2×D4—182no—
588C2×D4—182no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598D8—62no—
599D8—62no—
600D8—182no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8C2×D3211yescharacteristic
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C22⋊C4—31no—
615C22⋊C4—31no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—181no—
627C42C2×D3211yescharacteristic
628C22×C3—21no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—62no—
632C22×C3—61no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C22×D1211yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—244no—
665C2×D3—244no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—121no—
678C3×C4C2×#23711yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—241no—
693Dic3—241no—
694Dic3—241no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—184no—
701C23—181no—
702C23—721no—
703C23—721no—
704D4—32no—
705D4—61no—
706D4—61no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—184no—
712D4—181no—
713D4—241no—
714D4—241no—
715D4—721no—
716D4—721no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—241no—
727C2×C4—721no—
728C2×C4—721no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4D3×D1211yescharacteristic
733C2×C4D3×D1211yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—21no—
737C8—61no—
738C8—61no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—122no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3—241no—
746C2×C3#552411yescharacteristic
747C2×C3#560611yescharacteristic
748C2×C3#575211yescharacteristic
749C2×C3#575211yescharacteristic
750C2×C3#575711yescharacteristic
751C2×C3#577411yescharacteristic
752D3—41no—
753D3—42no—
754D3—81no—
755D3—81no—
756D3—122no—
757D3—122no—
758D3—242no—
759C22—61no—
760C22—62no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—182no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22C2×D3×D1211yescharacteristic
776C4—21no—
777C4—21no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—361no—
783C4—361no—
784C4—361no—
785C4D3×#23711yescharacteristic
786C4#6431911yescharacteristic
787C3—21no—
788C3#7938611yescharacteristic, complemented
789C3#8031711yescharacteristic, complemented
790C2—121no—
791C2—122no—
792C2—241no—
793C2—241no—
794C2—362no—
795C2#1059462611yescharacteristic
796C2#1059467811yescharacteristic
797C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593994C2semidirect
2. #10593949C2semidirect
3. #10592546C2semidirect
4. C3×#4843C2semidirect
5. C3×#4840C2semidirect
6. #10590944C2semidirect
7. #10590944C2semidirect
8. #10590837C2semidirect
9. #10590834C2semidirect
10. #10590771C2semidirect
11. Dic3×D24C2semidirect
12. #10590746C2semidirect
13. #10590745C2semidirect
14. #10590355C2semidirect
15. #10590271C2semidirect
20. #64079C22semidirect
23. C3×#874C22semidirect
33. Dic3×D12C22semidirect
34. Dic3×D12C22semidirect
43. C32×C4⋊C8C22semidirect
46. #63645C22semidirect
47. #63644C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
52. C3×#815C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
78. #4843D3semidirect
79. #4840D3semidirect
181. #874C2×D3semidirect
196. C3×C4⋊C8C2×D3semidirect
197. C3×C4⋊C8C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
230. #815C2×D3semidirect
231. C8×Dic3C2×D3semidirect
234. C4⋊(C3⋊C8)C2×D3semidirect
460. C4⋊C8D32semidirect
695. C32#3122semidirect
788. C3#79386semidirect
789. C3#80317semidirect

Maximal subgroups

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

subgroupindex
#105939942
#105939492
#105925462
C3×#48432
C3×#48402
#105909442
#105908372
#105908342
#105907712
Dic3×D242
#105907462
#105907452
#105903552
#105902712
#803173
#793863