Finite Group Databasebeta

← #11887036

Subgroups — #11887036

Order 1152.

1055 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5609C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic, complemented
3#10592737C211yesmaximal, characteristic, complemented
4C3×#5033C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591448C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10591162C211yesmaximal, characteristic, complemented
10#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11C2×#63562C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590555C211yesmaximal, characteristic, complemented
14#10590456C211yesmaximal, characteristic, complemented
15#10590438C211yesmaximal, characteristic, complemented
16#83482—31nomaximal
17#81302—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C2×#3804—21no—
22C32×#121C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24#64139C2211yescharacteristic, complemented
25C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
26C3×#940C2211yescharacteristic
27C3×#937—21no—
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#884—21no—
33C3×#882—21no—
34#63966—21no—
35#63918C2211yescharacteristic, complemented
36#63909C2211yescharacteristic, complemented
37#63895—21no—
38#63894C2211yescharacteristic, complemented
39#63890—21no—
40D3×C4⋊Dic3C2211yescharacteristic, complemented
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#830C2211yescharacteristic, complemented
50C3×#807C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic, complemented
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62#5609D311yescharacteristic, complemented
63#5555—31no—
64#5507—31no—
65C3×#480—31no—
66#5217—31no—
67#5217—31no—
68C2×#832—31no—
69C2×#832—31no—
70#5072—31no—
71#5070—31no—
72#5038—31no—
73#5038—31no—
74#5038—31no—
75#5038—61no—
76#5033—31no—
77#5033D311yescharacteristic, complemented
78C4×#213—31no—
79D4×C3⋊C8—31no—
80#5007—31no—
81C2×#809—31no—
82#4890—31no—
83#4883—31no—
84#4882—31no—
85#4872—31no—
86#4786—31no—
87#4773—31no—
88D3×#102—31no—
89#4760—31no—
90#4732—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C22×C3×Dic3—21no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C3×D3×D4—44no—
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3C2311yescharacteristic
115C2×#627—21no—
116C2×#626—21no—
117C2×#624—21no—
118#3804—44no—
119C2×D3×Dic3—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122#3753—41no—
123#3752—21no—
124C4⋊(C3⋊Dic3)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)—41no—
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C2×C3⋊(C3⋊C8)C2311yescharacteristic
128C3×#217D411yescharacteristic
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142#3722—21no—
143#3714—22no—
144#3714—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—31no—
148C22×C3×D4—31no—
149C22×C3×D4—61no—
150C2×#237—61no—
151C2×D3×D4—21no—
152C2×D3×D4C2×D311yescharacteristic
153C2×#235—61no—
154C22×D12C2×D311yescharacteristic
155C3×#127—31no—
156C3×#121—21no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#121C2×D311yescharacteristic
160C3×#121C2×D311yescharacteristic
161C3×#120—61no—
162C3×#120—61no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C2×C3×C4⋊C4—31no—
166#940C2×D311yescharacteristic
167#937—21no—
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—61no—
173#930—31no—
174#930—31no—
175#930—31no—
176#930—61no—
177#929—61no—
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3C2×D311yescharacteristic, complemented
181C22×C3⋊C8—31no—
182C22×C3⋊C8—31no—
183C22×C3⋊C8—31no—
184C22×C3⋊C8—61no—
185C2×D24—31no—
186C2×D24—31no—
187C2×D3×C8—31no—
188#897—61no—
189#896—61no—
190#895—31no—
191#895C2×D311yescharacteristic
192#894—61no—
193#893—31no—
194#893C2×D311yescharacteristic
195D3×C4⋊C4—31no—
196#888—31no—
197#886—61no—
198#886—61no—
199#884—21no—
200#882—21no—
201C4×D12—31no—
202#869—31no—
203C3×#107—31no—
204C3×#107—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—61no—
217#832C2×D311yescharacteristic, complemented
218#832C2×D311yescharacteristic, complemented
219#830—31no—
220#830C2×D311yescharacteristic, complemented
221#821—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224Dic3⋊C8—31no—
225C8×Dic3—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#807—31no—
234#807—31no—
235#807—61no—
236#807C2×D311yescharacteristic, complemented
237#807C2×D311yescharacteristic, complemented
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C23×C32C2×D411yescharacteristic
242C22×C3⋊D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—21no—
245C22×C3×D3—42no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—81no—
250C22×C3×D3—81no—
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—42no—
261C2×C3⋊Dic3—21no—
262C4⋊(C3⋊D3)—21no—
263C4⋊(C3⋊D3)—21no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—81no—
267C3×#67D814yescomplemented
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—42no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—42no—
278C3×D12—42no—
279C3×D12#4112yescomplemented
280C3×C4×D3—21no—
281C3×C4×D3—21no—
282C3×C4×D3—42no—
283#627—42no—
284#626—42no—
285#624—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—31no—
293#486—91no—
294#480—31no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—91no—
305C2×#102—91no—
306C24×C3—61no—
307C24×C3—61no—
308C23×D3—21no—
309C23×D3—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—31no—
316C2×C3×D4—41no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—62no—
323C2×C3×D4—61no—
324C2×C3×D4—121no—
325C2×C3×D4—121no—
326C2×C3×D4—124no—
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C22×D311yescharacteristic
329C22×C3×C4—21no—
330C22×C3×C4—31no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67#6711yescharacteristic
343C22×Dic3—21no—
344C22×Dic3—61no—
345#237—124no—
346D3×D4—22no—
347D3×D4—41no—
348D3×D4—44no—
349#235—124no—
350C2×D12—22no—
351C2×D12—21no—
352C2×D12—21no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—41no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12C22×D311yescharacteristic
359C2×D12C22×D311yescharacteristic
360C2×C4×D3—21no—
361C2×C4×D3—61no—
362C2×C4×D3—61no—
363C2×C4×D3—61no—
364C2×C4×D3C22×D311yescharacteristic
365C2×Dic6—61no—
366C2×Dic6—61no—
367C2×C3×C8—31no—
368C2×C3×C8—31no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4C22×D311yescharacteristic
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—31no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—41no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C42—31no—
384#217#6711yescharacteristic
385#213—62no—
386#213—121no—
387#213—121no—
388#213—121no—
389#213—122no—
390(C2×D3)⋊C4—21no—
391(C2×D3)⋊C4—21no—
392(C2×D3)⋊C4—61no—
393(C2×D3)⋊C4—61no—
394(C2×D3)⋊C4—61no—
395(C2×D3)⋊C4—61no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—121no—
399(C2×D3)⋊C4#6711yescharacteristic
400C4⋊Dic3—21no—
401C4⋊Dic3—31no—
402C4⋊Dic3—31no—
403C4⋊Dic3—61no—
404C4⋊Dic3—61no—
405C4⋊Dic3—61no—
406C4⋊Dic3C22×D311yescharacteristic
407C4⋊Dic3C22×D311yescharacteristic
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4#6711yescharacteristic
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—31no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8—121no—
420C2×C3⋊C8—121no—
421C2×C3⋊C8—122no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424D24—62no—
425D24—121no—
426D3×C8—121no—
427C22×C32—21no—
428C22×C32—21no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32C2×D812yes—
433C22×C32C22×D411yescharacteristic
434C2×C3⋊D3—41no—
435C2×C3⋊D3—41no—
436C2×C3⋊D3—41no—
437C2×C3×D3—21no—
438C2×C3×D3—21no—
439C2×C3×D3—22no—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C2×C3×D3—41no—
444C2×C3×D3—41no—
445C2×C3×D3—84no—
446C2×C3×D3—84no—
447C2×C3×D3C2×D812yes—
448C32×C4—21no—
449C32×C4—41no—
450C32×C4C2×#4111yescharacteristic
451C32×C4H(5,𝔽2)11yescharacteristic
452C3⋊Dic3—41no—
453C3×Dic3—21no—
454C3×Dic3—21no—
455C3×Dic3—41no—
456C3×Dic3—41no—
457C3×Dic3C2×D812yes—
458C2×#41—181no—
459C22×D4—31no—
460C22×D4—31no—
461C22×D4—61no—
462C2×D8—91no—
463C2×D8—91no—
464C2×D8—91no—
465C22×C8—91no—
466C22×C8—91no—
467C4⋊Q8—91no—
468#127—31no—
469#123—181no—
470#123—181no—
471C22⋊Q8—181no—
472#121—31no—
473#121—61no—
474#121—91no—
475#121—91no—
476#121D3211yescharacteristic
477#120—61no—
478#120—61no—
479C4×D4—31no—
480C4×D4—31no—
481C4×D4—91no—
482C2×C4⋊C4—31no—
483C2×C4⋊C4—91no—
484#107—31no—
485#107—31no—
486#107—91no—
487C4⋊C8—91no—
488#102—31no—
489#102—31no—
490#102—91no—
491#102—91no—
492#102—91no—
493#102—91no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498C22⋊C8—31no—
499C22⋊C8—91no—
500C4×C8—91no—
501C23×C3—21no—
502C23×C3—21no—
503C23×C3—21no—
504C23×C3—31no—
505C23×C3—41no—
506C23×C3—61no—
507C23×C3—61no—
508C23×C3—122no—
509C23×C3—122no—
510C23×C3—122no—
511C23×C3—122no—
512C23×C3—241no—
513C23×C3—241no—
514C23×C3D3×D411yescharacteristic
515C23×C3C2×#6711yescharacteristic
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—42no—
522C22×D3—61no—
523C22×D3—61no—
524C22×D3—81no—
525C22×D3—81no—
526C22×D3—121no—
527C22×D3C2×#6711yescharacteristic
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—21no—
532C3×D4—34no—
533C3×D4—32no—
534C3×D4—41no—
535C3×D4—41no—
536C3×D4—42no—
537C3×D4—42no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—61no—
541C3×D4—82no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—122no—
545C3×D4—122no—
546C3×D4—241no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—31no—
556C2×C3×C4—31no—
557C2×C3×C4—31no—
558C2×C3×C4—41no—
559C2×C3×C4—41no—
560C2×C3×C4—41no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—122no—
566C2×C3×C4—122no—
567C2×C3×C4D3×D411yescharacteristic
568C2×C3×C4C2×#6711yescharacteristic
569C2×C3×C4C23×D311yescharacteristic
570C2×C3×C4C23×D311yescharacteristic
571#67—42no—
572#67—42no—
573#67—81no—
574#67—122no—
575#67—122no—
576#67—122no—
577#67—242no—
578#67#21314yescomplemented
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—42no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—121no—
585C2×Dic3—122no—
586C2×Dic3C2×#6711yescharacteristic
587C2×Dic3C2×#6711yescharacteristic
588C2×Dic3C2×#6711yescharacteristic
589D12—21no—
590D12—21no—
591D12—21no—
592D12—42no—
593D12—42no—
594D12—61no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—121no—
599D12—121no—
600D12—122no—
601D12#23712yescomplemented
602C4×D3—21no—
603C4×D3—21no—
604C4×D3—42no—
605C4×D3—122no—
606C4×D3—122no—
607C4×D3—122no—
608Dic6—122no—
609Dic6—122no—
610C3×C8—61no—
611C3×C8—61no—
612C3⋊C8—21no—
613C3⋊C8—21no—
614C3⋊C8—62no—
615C3⋊C8—61no—
616C3⋊C8—61no—
617C3⋊C8—61no—
618C3⋊C8—61no—
619C3⋊C8—121no—
620C2×C32—22no—
621C2×C32—81no—
622C2×C32#54611yescharacteristic
623C2×C32C22×D811yescharacteristic
624C2×C32#57711yescharacteristic
625C3⋊D3—81no—
626C3×D3—22no—
627C3×D3—42no—
628C3×D3—81no—
629C24—61no—
630C24—61no—
631#41—364no—
632C2×Q8—181no—
633C2×D4—21no—
634C2×D4—31no—
635C2×D4—31no—
636C2×D4—31no—
637C2×D4—62no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
642C2×D4—62no—
643C2×D4—61no—
644C2×D4—91no—
645C2×D4—121no—
646C2×D4—121no—
647C2×D4—124no—
648C2×D4—181no—
649C2×D4—181no—
650C2×D4C2×D3211yescharacteristic
651C22×C4—31no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—181no—
655C22×C4—181no—
656C22×C4C2×D3211yescharacteristic
657D8—182no—
658D8—361no—
659D8—361no—
660C2×C8—31no—
661C2×C8—31no—
662C2×C8—91no—
663C2×C8—91no—
664C2×C8—361no—
665C2×C8—361no—
666C4⋊C4—31no—
667C4⋊C4—31no—
668C4⋊C4—31no—
669C4⋊C4—61no—
670C4⋊C4—91no—
671C4⋊C4—181no—
672C4⋊C4—181no—
673C4⋊C4C2×D3211yescharacteristic
674C22⋊C4—21no—
675C22⋊C4—31no—
676C22⋊C4—31no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22⋊C4—181no—
682C42—31no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—22no—
689C22×C3—32no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—61no—
699C22×C3—61no—
700C22×C3—62no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—244no—
710C22×C3—244no—
711C22×C3D3×D812yes—
712C22×C3C2×#21312yes—
713C22×C3C2×D3×D411yescharacteristic
714C22×C3C22×#6711yescharacteristic
715C2×D3—21no—
716C2×D3—21no—
717C2×D3—22no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—84no—
724C2×D3—84no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—121no—
730C2×D3—121no—
731C2×D3—241no—
732C2×D3—241no—
733C2×D3—241no—
734C2×D3C2×#21312yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—21no—
738C3×C4—21no—
739C3×C4—32no—
740C3×C4—41no—
741C3×C4—41no—
742C3×C4—41no—
743C3×C4—61no—
744C3×C4—61no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748C3×C4C2×#23711yescharacteristic
749C3×C4#100411yescharacteristic
750C3×C4D3×#4111yescharacteristic
751C3×C4#100911yescharacteristic
752Dic3—21no—
753Dic3—21no—
754Dic3—41no—
755Dic3—41no—
756Dic3—121no—
757Dic3—121no—
758Dic3—241no—
759Dic3C2×#21312yes—
760C32#329411yescharacteristic, complemented, Sylow
761C23—21no—
762C23—31no—
763C23—61no—
764C23—61no—
765C23—122no—
766C23—122no—
767C23—122no—
768C23—122no—
769C23—181no—
770C23—241no—
771C23—241no—
772C23D3×#6711yescharacteristic
773Q8—362no—
774D4—21no—
775D4—21no—
776D4—34no—
777D4—32no—
778D4—42no—
779D4—61no—
780D4—61no—
781D4—61no—
782D4—122no—
783D4—122no—
784D4—122no—
785D4—122no—
786D4—181no—
787D4—181no—
788D4—241no—
789D4—362no—
790D4—362no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—31no—
795C2×C4—31no—
796C2×C4—31no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—122no—
802C2×C4—122no—
803C2×C4—181no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4D3×#6711yescharacteristic
807C2×C4C22×D3211yescharacteristic
808C8—61no—
809C8—61no—
810C8—181no—
811C8—181no—
812C2×C3—22no—
813C2×C3—22no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—42no—
818C2×C3—62no—
819C2×C3—81no—
820C2×C3—81no—
821C2×C3—122no—
822C2×C3—161no—
823C2×C3—241no—
824C2×C3#565411yescharacteristic
825C2×C3C2×D3×D811yescharacteristic
826C2×C3#577811yescharacteristic
827C2×C3C22×#21311yescharacteristic
828C2×C3#580611yescharacteristic
829C2×C3#583611yescharacteristic
830D3—22no—
831D3—42no—
832D3—81no—
833D3—241no—
834D3—241no—
835D3—481no—
836C22—21no—
837C22—21no—
838C22—32no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—61no—
843C22—61no—
844C22—62no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—121no—
850C22—244no—
851C22—244no—
852C22—361no—
853C22—361no—
854C22—361no—
855C22D3×#21312yes—
856C22C2×D3×#6711yescharacteristic
857C4—21no—
858C4—32no—
859C4—41no—
860C4—61no—
861C4—61no—
862C4—121no—
863C4—121no—
864C4—361no—
865C4D3×#23711yescharacteristic
866C4#6431411yescharacteristic
867C3—21no—
868C3#8130211yescharacteristic, complemented
869C3#8348211yescharacteristic, complemented
870C2—22no—
871C2—62no—
872C2—81no—
873C2—122no—
874C2—241no—
875C2—721no—
876C2C2×D3×#21311yescharacteristic
877C2#1059514811yescharacteristic
878C2#1059546411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3294
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C3×#5609C2semidirect
2. #10594906C2semidirect
3. #10592737C2semidirect
4. C3×#5033C2semidirect
5. #10591487C2semidirect
6. #10591448C2semidirect
7. #10591429C2semidirect
8. D3×#832C2semidirect
9. #10591162C2semidirect
10. #67⋊(C3⋊C8)C2semidirect
11. C2×#63562C2semidirect
12. #10590576C2semidirect
13. #10590555C2semidirect
14. #10590456C2semidirect
15. #10590438C2semidirect
23. C2×#3753C22semidirect
24. #64139C22semidirect
25. C22×C3⋊(C3⋊C8)C22semidirect
29. C2×C3×C4⋊Dic3C22semidirect
35. #63918C22semidirect
36. #63909C22semidirect
38. #63894C22semidirect
40. D3×C4⋊Dic3C22semidirect
42. C2×#3714C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63636C22semidirect
46. #63634C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#830C22semidirect
50. C3×#807C22semidirect
51. C3×#807C22semidirect
52. Dic3⋊(C3⋊C8)C22semidirect
54. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5609D3semidirect
77. #5033D3semidirect
180. C2×C4⋊Dic3C2×D3semidirect
217. #832C2×D3semidirect
218. #832C2×D3semidirect
220. #830C2×D3semidirect
236. #807C2×D3semidirect
237. #807C2×D3semidirect
267. C3×#67D8semidirect
279. C3×D12#41semidirect
578. #67#213semidirect
601. D12#237semidirect
760. C32#3294semidirect
868. C3#81302semidirect
869. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×#56092
#105949062
#105927372
C3×#50332
#105914872
#105914482
#105914292
D3×#8322
#105911622
#67⋊(C3⋊C8)2
C2×#635622
#105905762
#105905552
#105904562
#105904382
#834823
#813023