Finite Group Databasebeta

← #11872741

Subgroups — #11872741

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
1C3×#5545C211yesmaximal, characteristic, complemented
2#10593949C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic, complemented
5#10591447C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590505C211yesmaximal, characteristic, complemented
10#10590502C211yesmaximal, characteristic, complemented
11#10590455C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13#10590347C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82542—31nomaximal
17#80317—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20#64079C2211yescharacteristic, complemented
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
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×#874C2211yescharacteristic, complemented
31C3×C4×D12C2211yescharacteristic
32C3×#872C2211yescharacteristic
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic, complemented
37#63885—21no—
38#63885—21no—
39#63884—21no—
40#63884—21no—
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63635C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#809C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic, complemented
50C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#518—31no—
62#5719—31no—
63#5545D311yescharacteristic, complemented
64#5535—31no—
65C3×#459—31no—
66#5217—31no—
67#5217—31no—
68#5156—31no—
69#5156—31no—
70#5152—31no—
71Dic3×D8—31no—
72#5072—31no—
73#5015—31no—
74#5015D311yescharacteristic, complemented
75#5014—31no—
76#5014—31no—
77C4×#213—31no—
78C4×#213—31no—
79#5009—31no—
80#5009—31no—
81#5009—31no—
82#5009—61no—
83#5003—31no—
84#5003—31no—
85#5000—31no—
86#4847—31no—
87#4840—31no—
88#4785—31no—
89#4784—31no—
90#4779—31no—
91#4756—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625—21no—
108C2×#625—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C22⋊C4—21no—
113C32×C42C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#213—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×C4×D4—21no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151C3×C4×D4—61no—
152C3×C4×D4—61no—
153C3×C4×D4C2×D311yescharacteristic
154C3×C4×D4C2×D311yescharacteristic
155C3×#117—31no—
156C3×#117—31no—
157C2×C3×C22⋊C4—61no—
158C2×C3×C22⋊C4—61no—
159#939—61no—
160#939—61no—
161#938—31no—
162#938—31no—
163#935—61no—
164#935—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3C2×D311yescharacteristic
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213C2×D311yescharacteristic
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—31no—
176C4×#67—21no—
177C2×(C2×D3)⋊C4—21no—
178#894—61no—
179#894—61no—
180#893C2×D311yescharacteristic
181#892C2×D311yescharacteristic
182#884—61no—
183#884—61no—
184#67⋊C4—21no—
185D3×C22⋊C4—21no—
186#874C2×D311yescharacteristic, complemented
187C4×D12—31no—
188C4×D12—31no—
189C4×D12C2×D311yescharacteristic
190#872C2×D311yescharacteristic
191#870—31no—
192#870—31no—
193#870—61no—
194C3×C4⋊C8—31no—
195C3×#102—31no—
196C3×#102—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#817—31no—
215#815—31no—
216C8×Dic3—31no—
217#809—31no—
218#809—31no—
219#809C2×D311yescharacteristic, complemented
220#809C2×D311yescharacteristic, complemented
221#808—31no—
222#808—31no—
223#808—31no—
224#808—61no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
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—24no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—81no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269C3×C4×D3—81no—
270#625—81no—
271#625—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C3⋊(C3⋊C8)—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—31no—
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—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4—41no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C22×Dic3—21no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321D3×D4—22no—
322D3×D4—22no—
323C2×D12—21no—
324C2×D12—21no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C3×D8—62no—
334C3×D8—62no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42—31no—
354C3×C42—61no—
355C3×C42C22×D311yescharacteristic
356C3×C42C22×D311yescharacteristic
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#213—22no—
363#213—22no—
364#213—62no—
365#213—62no—
366#213—62no—
367#213—62no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—21no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4#6711yescharacteristic
376(C2×D3)⋊C4#6711yescharacteristic
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389Dic3⋊C4—121no—
390Dic3⋊C4#6711yescharacteristic
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402C22×C32—22no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—22no—
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—
418C2×C3×D3—84no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
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—31no—
445C4×D4—31no—
446C4×D4—61no—
447C4×D4—61no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4D3211yescharacteristic
451#117—31no—
452#117—31no—
453C2×C22⋊C4—61no—
454C2×C22⋊C4—61no—
455#107—91no—
456#107—91no—
457#106—91no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—91no—
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—91no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—81no—
488C22×D3—81no—
489C22×D3C2×#6711yescharacteristic
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C3×D4—241no—
503C3×D4#23512yes—
504C3×D4#23712yes—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—81no—
518C2×C3×C4—81no—
519C2×C3×C4—82no—
520C2×C3×C4—241no—
521C2×C3×C4—241no—
522C2×C3×C4—241no—
523C2×C3×C4D3×D411yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—24no—
530#67—241no—
531#67—241no—
532#67—241no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—81no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547D12—21no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12—81no—
553D12—81no—
554D12#23512yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—81no—
558C4×D3—81no—
559C4×D3—241no—
560C4×D3—241no—
561C3×C8—61no—
562C3×C8—61no—
563C3⋊C8—21no—
564C3⋊C8—21no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—121no—
570C3⋊C8—121no—
571C2×C32—42no—
572C2×C32#52511yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57611yescharacteristic
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—61no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—62no—
585C2×D4—62no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—21no—
592C22×C4—31no—
593C22×C4—61no—
594C22×C4—61no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—181no—
598D8—62no—
599D8—62no—
600D8—182no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—91no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—31no—
616C22⋊C4—31no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42C2×D3211yescharacteristic
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—42no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C2×D3—21no—
654C2×D3—22no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—84no—
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—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4C2×#23511yescharacteristic
683C3×C4C2×#23711yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—64no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—241no—
703C23—241no—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—241no—
713D4—241no—
714D4—721no—
715D4—721no—
716D4#379512yes—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—81no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—241no—
748C2×C3—241no—
749C2×C3#560611yescharacteristic
750C2×C3#575711yescharacteristic
751C2×C3#577411yescharacteristic
752C2×C3#579111yescharacteristic
753C2×C3#583511yescharacteristic
754C2×C3#583511yescharacteristic
755D3—41no—
756D3—42no—
757D3—81no—
758D3—81no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—61no—
764C22—62no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—244no—
775C22C2×D3×#6711yescharacteristic
776C4—21no—
777C4—21no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—61no—
782C4—121no—
783C4—361no—
784C4—361no—
785C4C2×#379511yescharacteristic
786C4D3×#23511yescharacteristic
787C3—21no—
788C3#8031711yescharacteristic, complemented
789C3#8254211yescharacteristic, complemented
790C2—42no—
791C2—121no—
792C2—122no—
793C2—241no—
794C2—241no—
795C2#1059489211yescharacteristic
796C2#1059509611yescharacteristic
797C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3122
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. #10593949C2semidirect
3. #10592708C2semidirect
4. C3×#5015C2semidirect
5. #10591447C2semidirect
6. #10591447C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10590505C2semidirect
10. #10590502C2semidirect
11. #10590455C2semidirect
12. #10590452C2semidirect
13. #10590347C2semidirect
14. #10590271C2semidirect
15. #10590253C2semidirect
20. #64079C22semidirect
30. C3×#874C22semidirect
35. Dic3×D12C22semidirect
36. Dic3×D12C22semidirect
45. #63635C22semidirect
46. #63634C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
48. C3×#809C22semidirect
49. C3×#809C22semidirect
50. C3×C4⋊(C3⋊C8)C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
59. #63554C22semidirect
60. Dic3×C3⋊C8C22semidirect
63. #5545D3semidirect
74. #5015D3semidirect
186. #874C2×D3semidirect
219. #809C2×D3semidirect
220. #809C2×D3semidirect
232. C4⋊(C3⋊C8)C2×D3semidirect
695. C32#3122semidirect
788. C3#80317semidirect
789. C3#82542semidirect

Maximal subgroups

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

subgroupindex
C3×#55452
#105939492
#105927082
C3×#50152
#105914472
#105914302
Dic3×#2132
#105905052
#105905022
#105904552
#105904522
#105903472
#105902712
#105902532
#825423
#803173