Finite Group Databasebeta

← #11871287

Subgroups — #11871287

Order 1152.

1042 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic, complemented
2#10593968C211yesmaximal, characteristic, complemented
3#10592713C211yesmaximal, characteristic, complemented
4C3×#5014C211yesmaximal, characteristic, complemented
5#10591481C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10590558C211yesmaximal, characteristic, complemented
10#10590547C211yesmaximal, characteristic, complemented
11#10590500C211yesmaximal, characteristic, complemented
12#10590423C211yesmaximal, characteristic, complemented
13#10590346C211yesmaximal, characteristic, complemented
14#10590344C211yesmaximal, characteristic, complemented
15#10590262C211yesmaximal, characteristic, complemented
16#82310—31nomaximal
17#79869—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C2×#3798—21no—
21C32×C4×D4C2211yescharacteristic
22C2×#3753C2211yescharacteristic
23C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C3×C4×#67—21no—
27C3×#893C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29C3×#67⋊C4—21no—
30C3×D3×C22⋊C4—21no—
31C3×C4×D12C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic, complemented
33C3×C42×D3C2211yescharacteristic
34#63918C2211yescharacteristic, complemented
35#63911C2211yescharacteristic, complemented
36#63909C2211yescharacteristic
37#63908C2211yescharacteristic
38#63906—21no—
39C4×#626—21no—
40#63852—21no—
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic, complemented
45#63635C2211yescharacteristic, complemented
46#63630C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#809C2211yescharacteristic, complemented
49C3×#808C2211yescharacteristic, complemented
50C3×#803C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×C3×C4×D4—31no—
62#5548—31no—
63C4×D3×D4D311yescharacteristic, complemented
64#5477—31no—
65C3×#442—31no—
66#5217—31no—
67#5217—31no—
68#5156—31no—
69#5150—31no—
70#5015—31no—
71#5015—31no—
72#5014—31no—
73#5014—31no—
74#5014—31no—
75#5014—31no—
76#5014—31no—
77#5014—61no—
78#5014D311yescharacteristic, complemented
79#5008—31no—
80#5008—31no—
81#4968—31no—
82#4968—31no—
83#4926—31no—
84#4870—31no—
85#4863—31no—
86#4786—31no—
87#4777—31no—
88#4773—31no—
89#4761—31no—
90#4711—31no—
91#4705—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×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—44no—
108C2×C3×C4×D3D411yescharacteristic
109C2×C3×C4×D3D411yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#625—21no—
116#3798—44no—
117C32×C4⋊C4C2311yescharacteristic
118C32×C22⋊C4—21no—
119C32×C42C2311yescharacteristic
120#3753—22no—
121#3752—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C3×#217—21no—
126C3×#213—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3D411yescharacteristic
134C3×C4×Dic3D411yescharacteristic
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141#3714—22no—
142#3713—22no—
143#3109—91noSylow
144C22×C3×D4—31no—
145C23×C3×C4—61no—
146C2×D3×D4C2×D311yescharacteristic
147C2×#235—61no—
148C2×#235—61no—
149C22×C4×D3—21no—
150C2×C3×D8—31no—
151C3×C4×D4—21no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155C3×C4×D4—31no—
156C3×C4×D4—61no—
157C3×C4×D4—61no—
158C3×C4×D4C2×D311yescharacteristic
159C3×C4×D4C2×D311yescharacteristic
160C2×C3×C4⋊C4—31no—
161C2×C3×C22⋊C4—61no—
162C2×C3×C42—31no—
163#940—31no—
164#938—31no—
165D4×Dic3C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172C2×#213C2×D311yescharacteristic
173#930—31no—
174#930—31no—
175#930—61no—
176C4×#67—21no—
177C4×#67—61no—
178C2×D24—31no—
179#895—31no—
180#893C2×D311yescharacteristic
181D3×C4⋊C4C2×D311yescharacteristic
182#888—31no—
183#885—61no—
184#884—61no—
185#67⋊C4—21no—
186D3×C22⋊C4—21no—
187#875—61no—
188#874—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193C4×D12C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic, complemented
195C42×D3C2×D311yescharacteristic
196#869—31no—
197C3×#106—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#97—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—61no—
207#832C2×D311yescharacteristic
208#830—31no—
209#830—31no—
210#821—31no—
211#821—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214#817—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217#809—31no—
218#809—31no—
219#809—31no—
220#809—31no—
221#809—31no—
222#809—61no—
223#809C2×D311yescharacteristic, complemented
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic, complemented
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234#803—31no—
235#803—61no—
236#803C2×D311yescharacteristic, complemented
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—24no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4#4112yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4—42no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4×C3⋊D3—42no—
256C3×#67—24no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12#4112yescomplemented
267C3×C4×D3—22no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—22no—
271C3×C4×D3—42no—
272C3×C4×D3—42no—
273C3×C4×D3—42no—
274C3×C4×D3—42no—
275#627—42no—
276#626—42no—
277#626—42no—
278#626—42no—
279#625—42no—
280C3⋊(C3⋊C8)—21no—
281C3⋊(C3⋊C8)—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284#532—91no—
285C2×C4×D4—31no—
286#481—91no—
287#481—91no—
288#476—91no—
289#476—91no—
290#459—91no—
291#459—91no—
292#447—91no—
293#447—91no—
294#442—31no—
295#442—91no—
296#442—91no—
297#442—91no—
298#432—91no—
299C24×C3—61no—
300C23×D3—21no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—62no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4—124no—
321C2×#67—21no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C22×Dic3—21no—
328D3×D4—22no—
329D3×D4—22no—
330#235—124no—
331#235—124no—
332C2×D12—31no—
333C2×D12—31no—
334C2×D12—61no—
335C2×D12—61no—
336C2×D12—61no—
337C2×D12—61no—
338C2×D12C22×D311yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—44no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—121no—
348C2×C4×D3#6711yescharacteristic
349C2×C4×D3#6711yescharacteristic
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C3×D8—62no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C22⋊C4—61no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—21no—
370C3×C42—31no—
371C3×C42—31no—
372C3×C42—31no—
373C3×C42C22×D311yescharacteristic
374C3×C42C22×D311yescharacteristic
375#217—21no—
376#217—61no—
377#213—22no—
378#213—62no—
379#213—62no—
380#213—64no—
381#213—62no—
382#213—62no—
383#213—62no—
384(C2×D3)⋊C4—21no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392(C2×D3)⋊C4—121no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401C4×Dic3#6711yescharacteristic
402C4×Dic3#6711yescharacteristic
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D24—62no—
413C22×C32—22no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—22no—
423C2×C3×D3—48no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3AGL(1,ℤ/8)12yes—
430C32×C4—21no—
431C32×C4—21no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3AGL(1,ℤ/8)12yes—
441C2×#41—181no—
442C22×D4—31no—
443C23×C4—61no—
444C2×D8—31no—
445C2×D8—91no—
446C2×D8—91no—
447C2×D8—91no—
448C4⋊Q8—91no—
449#127—91no—
450#124—181no—
451#121—91no—
452#121—91no—
453#121—181no—
454C4×D4—31no—
455C4×D4—31no—
456C4×D4—31no—
457C4×D4—31no—
458C4×D4—61no—
459C4×D4—61no—
460C4×D4—91no—
461C4×D4—181no—
462C4×D4D3211yescharacteristic
463C2×C4⋊C4—31no—
464C2×C22⋊C4—61no—
465C2×C42—31no—
466#106—31no—
467#106—91no—
468#106—91no—
469#106—91no—
470C4⋊C8—91no—
471C4⋊C8—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482#97—31no—
483#97—91no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—41no—
488C23×C3—64no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—122no—
492C23×C3—122no—
493C22×D3—24no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—61no—
500C22×D3—121no—
501C22×D3C2×#6711yescharacteristic
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—22no—
505C3×D4—32no—
506C3×D4—41no—
507C3×D4—64no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—61no—
511C3×D4#23512yescomplemented
512C3×D4#23512yescomplemented
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4—62no—
525C2×C3×C4—62no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—82no—
531C2×C3×C4—122no—
532C2×C3×C4—122no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4—122no—
536C2×C3×C4D3×D411yescharacteristic
537C2×C3×C4D3×D411yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—24no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—42no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—121no—
554C2×Dic3C2×#6711yescharacteristic
555C2×Dic3C2×#6711yescharacteristic
556C2×Dic3C2×#6711yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—62no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—121no—
566D12—122no—
567D12—122no—
568D12—122no—
569D12#23512yescomplemented
570C4×D3—22no—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—22no—
574C4×D3—42no—
575C4×D3—42no—
576C4×D3—42no—
577C4×D3—42no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—242no—
581Dic6—122no—
582Dic6—122no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C3⋊C8—62no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—61no—
591C3⋊C8—61no—
592C3⋊C8—121no—
593C2×C32—42no—
594C2×C32#52511yescharacteristic
595C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C3⋊D3—81no—
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—81no—
601C24—61no—
602#41—364no—
603C2×Q8—181no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—62no—
608C2×D4—62no—
609C2×D4—91no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4C2×D3211yescharacteristic
615C22×C4—21no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—124no—
625C22×C4—181no—
626D8—62no—
627D8—182no—
628D8—182no—
629D8—182no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4C2×D3211yescharacteristic
640C22⋊C4—21no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—31no—
650C42—31no—
651C42C2×D3211yescharacteristic
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—21no—
655C22×C3—32no—
656C22×C3—42no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—81no—
665C22×C3—81no—
666C22×C3—128no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3—121no—
672C22×C3C2×D3×D411yescharacteristic
673C22×C3C22×#6711yescharacteristic
674C2×D3—21no—
675C2×D3—21no—
676C2×D3—22no—
677C2×D3—48no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—122no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—241no—
691C2×D3—241no—
692C2×D3#94912yes—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—32no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23511yescharacteristic
710C3×C4C2×#23511yescharacteristic
711C3×C4C2×#23511yescharacteristic
712C3×C4D3×#4111yescharacteristic
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—41no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720Dic3#93212yes—
721C32#310911yescharacteristic, complemented, Sylow
722C23—21no—
723C23—31no—
724C23—64no—
725C23—61no—
726C23—61no—
727C23—122no—
728C23—122no—
729C23—181no—
730Q8—362no—
731D4—21no—
732D4—32no—
733D4—64no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—181no—
738D4—181no—
739D4—362no—
740D4—362no—
741D4—362no—
742D4—362no—
743D4#379812yescomplemented
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—42no—
749C2×C4—62no—
750C2×C4—62no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—122no—
760C2×C4—181no—
761C2×C4—362no—
762C2×C4D3×#6711yescharacteristic
763C2×C4D3×#6711yescharacteristic
764C2×C4C22×D3211yescharacteristic
765C8—61no—
766C8—61no—
767C8—181no—
768C8—181no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—42no—
773C2×C3—42no—
774C2×C3—62no—
775C2×C3—82no—
776C2×C3—122no—
777C2×C3—241no—
778C2×C3#554711yescharacteristic
779C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
780C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
781C2×C3#579111yescharacteristic
782C2×C3C2×#93211yescharacteristic
783C2×C3C2×#94911yescharacteristic
784D3—22no—
785D3—42no—
786D3—81no—
787D3—242no—
788D3—241no—
789D3—241no—
790C22—22no—
791C22—32no—
792C22—41no—
793C22—41no—
794C22—61no—
795C22—61no—
796C22—62no—
797C22—128no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—121no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22C2×D3×#6711yescharacteristic
807C4—21no—
808C4—21no—
809C4—32no—
810C4—41no—
811C4—61no—
812C4—61no—
813C4—121no—
814C4—121no—
815C4—361no—
816C4C2×#379811yescharacteristic
817C4D3×#23511yescharacteristic
818C3—21no—
819C3#7986911yescharacteristic, complemented
820C3#8231011yescharacteristic, complemented
821C2—42no—
822C2—62no—
823C2—122no—
824C2—241no—
825C2—721no—
826C2#1059500211yescharacteristic
827C2D3×#93211yescharacteristic
828C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3109
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×C4×D3×D4C2semidirect
2. #10593968C2semidirect
3. #10592713C2semidirect
4. C3×#5014C2semidirect
5. #10591481C2semidirect
6. #10591448C2semidirect
7. #10591447C2semidirect
8. #10591408C2semidirect
9. #10590558C2semidirect
10. #10590547C2semidirect
11. #10590500C2semidirect
12. #10590423C2semidirect
13. #10590346C2semidirect
14. #10590344C2semidirect
15. #10590262C2semidirect
23. C4×C4⋊(C3⋊D3)C22semidirect
32. C3×C4×D12C22semidirect
34. #63918C22semidirect
35. #63911C22semidirect
44. #63636C22semidirect
45. #63635C22semidirect
46. #63630C22semidirect
48. C3×#809C22semidirect
49. C3×#808C22semidirect
50. C3×#803C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. Dic3⋊(C3⋊C8)C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
58. #63562C22semidirect
63. C4×D3×D4D3semidirect
78. #5014D3semidirect
194. C4×D12C2×D3semidirect
223. #809C2×D3semidirect
230. #808C2×D3semidirect
236. #803C2×D3semidirect
246. C32×D4#41semidirect
266. C3×D12#41semidirect
511. C3×D4#235semidirect
512. C3×D4#235semidirect
569. D12#235semidirect
721. C32#3109semidirect
743. D4#3798semidirect
819. C3#79869semidirect
820. C3#82310semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105939682
#105927132
C3×#50142
#105914812
#105914482
#105914472
#105914082
#105905582
#105905472
#105905002
#105904232
#105903462
#105903442
#105902622
#823103
#798693