Finite Group Databasebeta

← #11887124

Subgroups — #11887124

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591499C211yesmaximal, characteristic, complemented
6#10591487C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591438C211yesmaximal, characteristic, complemented
9Dic3×#214C211yesmaximal, characteristic, complemented
10#10591415C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10591408C211yesmaximal, characteristic, complemented
13#10591179C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591092C211yesmaximal, characteristic, complemented
16#83483—31nomaximal
17#80158—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×#953—21no—
24C3×#940C2211yescharacteristic
25C3×#939—21no—
26C3×#938C2211yescharacteristic
27C3×#937—21no—
28C3×D4×Dic3C2211yescharacteristic
29C2×C3×#214C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic, complemented
31C3×#930C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34#63982—21no—
35#67⋊Dic3—21no—
36#63918C2211yescharacteristic, complemented
37#63893—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63856C2211yescharacteristic, complemented
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3715C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#830C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic
63#5635—31no—
64#5543—31no—
65C3×#450—31no—
66#5218—31no—
67#5218D311yescharacteristic, complemented
68C2×#832—31no—
69C2×#832—31no—
70C2×#832—31no—
71C2×#832—61no—
72#5171—31no—
73#5169—31no—
74#5163—31no—
75Dic3×SD16—31no—
76#5075—31no—
77#5070—31no—
78#5048—31no—
79#5041—31no—
80#5041—31no—
81#5034—31no—
82#5034—31no—
83C4×#214—31no—
84D4×C3⋊C8—31no—
85#5008—31no—
86#4777—31no—
87D3×#102—31no—
88#4761—31no—
89#4760—31no—
90#4735—31no—
91#67⋊C8—31no—
92C24×C32—21no—
93C23×C3×D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—44no—
107C2×C3×#67D411yescharacteristic
108C22×C3×Dic3—21no—
109C3×D3×D4—22no—
110C3×D3×D4—41no—
111C2×C3×D12C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×C3×Dic6C2311yescharacteristic
114C2×#627—21no—
115C2×D3×Dic3—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)—41no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×#217—21no—
125C3×#217D411yescharacteristic
126C3×#214—22no—
127C3×#214—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4D411yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—21no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C22×C3×D4C2×D311yescharacteristic
150C22×C3×D4C2×D311yescharacteristic
151C22×#67—21no—
152C2×D3×D4C2×D311yescharacteristic
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×#127—31no—
156C3×C22⋊Q8—31no—
157C3×#121—31no—
158C3×#121—31no—
159C3×#121—61no—
160C3×#120—61no—
161C3×#120—61no—
162C3×C4×D4—31no—
163C3×C4×D4—31no—
164#953—21no—
165#946—31no—
166Q8×Dic3—31no—
167C2×#215—31no—
168#940C2×D311yescharacteristic
169#939—21no—
170#938C2×D311yescharacteristic
171#937—21no—
172D4×Dic3—61no—
173D4×Dic3C2×D311yescharacteristic
174C2×#214—31no—
175C2×#214C2×D311yescharacteristic
176C2×#214C2×D311yescharacteristic, complemented
177#930C2×D311yescharacteristic
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—61no—
183#924—31no—
184#924C2×D311yescharacteristic, complemented
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×D3×C8—31no—
190#897—61no—
191D3×C4⋊C4—31no—
192#890—61no—
193#889—61no—
194#888—31no—
195#67⋊C4—61no—
196#878—61no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—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#832—61no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic, complemented
222#830—31no—
223#830C2×D311yescharacteristic, complemented
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227#817—31no—
228#817—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231#810—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4#4112yes—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3—81no—
262C3×#67—42no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—81no—
267C3×#67SD1614yescomplemented
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—42no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281#627—81no—
282D3×Dic3—81no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—31no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—91no—
301C2×#102—91no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3—41no—
305C24×C3—61no—
306C23×D3—21no—
307C2×C3×Q8—31no—
308C2×C3×D4—24no—
309C2×C3×D4—22no—
310C2×C3×D4—22no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—31no—
316C2×C3×D4—31no—
317C2×C3×D4—41no—
318C2×C3×D4—41no—
319C2×C3×D4—41no—
320C2×C3×D4—42no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—62no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—121no—
328C2×C3×D4—124no—
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C22×C3×C4—21no—
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—44no—
344C2×#67#6711yescharacteristic
345C22×Dic3—21no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—121no—
350D3×D4—22no—
351D3×D4—41no—
352C2×D12C22×D311yescharacteristic
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6C22×D311yescharacteristic
358C3×SD16—62no—
359C3×SD16—121no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373#217—21no—
374#217—21no—
375#217—21no—
376#217—61no—
377#217#6711yescharacteristic
378#215—121no—
379#214—22no—
380#214—41no—
381#214—121no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—121no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4#6711yescharacteristic
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—61no—
414C2×C3⋊C8—61no—
415C2×C3⋊C8—121no—
416C2×C3⋊C8—121no—
417C2×C3⋊C8—121no—
418C2×C3⋊C8—122no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421D3×C8—121no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32—22no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—84no—
431C22×C32C2×SD1612yes—
432C22×C32C22×D411yescharacteristic
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C2×C3×D3C2×SD1612yes—
440C32×C4—21no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3C2×SD1612yes—
451C22×D4—31no—
452C22×D4—61no—
453C22×D4D3211yescharacteristic
454C2×SD16—31no—
455C2×SD16—31no—
456C2×SD16—91no—
457C22×C8—91no—
458C22×C8—91no—
459C4⋊Q8—91no—
460#127—31no—
461#125—181no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466#121—31no—
467#121—31no—
468#121—61no—
469#120—61no—
470#120—61no—
471C4×Q8—91no—
472C4×D4—31no—
473C4×D4—31no—
474C4×D4—181no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477#106—91no—
478#106—91no—
479#106—91no—
480C4⋊C8—91no—
481#103—91no—
482#102—31no—
483#102—31no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491C22⋊C8—31no—
492C22⋊C8—91no—
493C4×C8—91no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—31no—
500C23×C3—41no—
501C23×C3—41no—
502C23×C3—42no—
503C23×C3—42no—
504C23×C3—44no—
505C23×C3—42no—
506C23×C3—42no—
507C23×C3—61no—
508C23×C3—82no—
509C23×C3—81no—
510C23×C3—81no—
511C23×C3—82no—
512C23×C3—122no—
513C23×C3—122no—
514C23×C3—241no—
515C23×C3D3×D411yescharacteristic
516C23×C3C2×#6711yescharacteristic
517C22×D3—21no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—81no—
521C22×D3C2×#6711yescharacteristic
522C3×Q8—61no—
523C3×Q8—61no—
524C3×D4—22no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—21no—
531C3×D4—22no—
532C3×D4—34no—
533C3×D4—41no—
534C3×D4—41no—
535C3×D4—42no—
536C3×D4—42no—
537C3×D4—44no—
538C3×D4—61no—
539C3×D4—61no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—122no—
544C3×D4—241no—
545C3×D4#23712yes—
546C3×D4#23712yes—
547C2×C3×C4—22no—
548C2×C3×C4—22no—
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—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—122no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—42no—
569#67—42no—
570#67—42no—
571#67—42no—
572#67—81no—
573#67#21414yescomplemented
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—42no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—121no—
583C2×Dic3—121no—
584C2×Dic3—241no—
585C2×Dic3—241no—
586C2×Dic3—241no—
587C2×Dic3—242no—
588C2×Dic3C2×#6711yescharacteristic
589C2×Dic3C2×#6711yescharacteristic
590C2×Dic3C2×#6711yescharacteristic
591D12—21no—
592D12—21no—
593C4×D3—21no—
594C4×D3—21no—
595C4×D3—241no—
596Dic6—21no—
597Dic6—21no—
598Dic6—241no—
599Dic6—241no—
600C3×C8—61no—
601C3×C8—61no—
602C3⋊C8—21no—
603C3⋊C8—21no—
604C3⋊C8—61no—
605C3⋊C8—61no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—121no—
609C3⋊C8—121no—
610C2×C32—22no—
611C2×C32—42no—
612C2×C32—81no—
613C2×C32#54611yescharacteristic
614C2×C32C22×SD1611yescharacteristic
615C2×C32#57611yescharacteristic
616C3×D3—22no—
617C3×D3—81no—
618C24—21no—
619C24—61no—
620C2×Q8—31no—
621C2×Q8—181no—
622C2×D4—22no—
623C2×D4—21no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—41no—
627C2×D4—61no—
628C2×D4—61no—
629C2×D4—61no—
630C2×D4—62no—
631C2×D4—61no—
632C2×D4—61no—
633C2×D4—121no—
634C2×D4—124no—
635C2×D4C2×D3211yescharacteristic
636C2×D4C2×D3211yescharacteristic
637C22×C4—31no—
638C22×C4—61no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4C2×D3211yescharacteristic
642SD16—62no—
643SD16—121no—
644SD16—361no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—91no—
648C2×C8—91no—
649C2×C8—361no—
650C2×C8—361no—
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—61no—
655C4⋊C4—91no—
656C4⋊C4—91no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—31no—
663C22⋊C4—31no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—181no—
669C42—31no—
670C42—181no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—22no—
681C22×C3—32no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—81no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—84no—
701C22×C3—84no—
702C22×C3—88no—
703C22×C3—121no—
704C22×C3—121no—
705C22×C3—121no—
706C22×C3—244no—
707C22×C3D3×SD1612yes—
708C22×C3C2×#21412yes—
709C22×C3C2×D3×D411yescharacteristic
710C22×C3C22×#6711yescharacteristic
711C2×D3—21no—
712C2×D3—21no—
713C2×D3—41no—
714C2×D3—41no—
715C2×D3—41no—
716C2×D3—84no—
717C2×D3C2×#21412yes—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4C2×#23711yescharacteristic
730C3×C4C2×#23711yescharacteristic
731C3×C4#100411yescharacteristic
732C3×C4#100411yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—241no—
743Dic3—241no—
744Dic3C2×#21412yes—
745C32#329511yescharacteristic, complemented, Sylow
746C23—21no—
747C23—21no—
748C23—31no—
749C23—42no—
750C23—42no—
751C23—61no—
752C23—81no—
753C23—122no—
754C23—122no—
755C23—241no—
756C23D3×#6711yescharacteristic
757Q8—61no—
758Q8—61no—
759Q8—721no—
760D4—21no—
761D4—21no—
762D4—21no—
763D4—34no—
764D4—42no—
765D4—61no—
766D4—61no—
767D4—122no—
768D4—122no—
769D4—122no—
770D4—122no—
771D4—241no—
772D4#380512yes—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—122no—
784C2×C4—181no—
785C2×C4—181no—
786C2×C4—721no—
787C2×C4—721no—
788C2×C4D3×#6711yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C8—61no—
791C8—61no—
792C8—181no—
793C8—181no—
794C2×C3—24no—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—42no—
801C2×C3—42no—
802C2×C3—62no—
803C2×C3—82no—
804C2×C3—82no—
805C2×C3—81no—
806C2×C3—81no—
807C2×C3—241no—
808C2×C3#559111yescharacteristic
809C2×C3C2×D3×SD1611yescharacteristic
810C2×C3#577411yescharacteristic
811C2×C3C22×#21411yescharacteristic
812C2×C3#580611yescharacteristic
813C2×C3#583511yescharacteristic
814D3—22no—
815D3—81no—
816C22—21no—
817C22—21no—
818C22—22no—
819C22—32no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—61no—
826C22—61no—
827C22—84no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—244no—
832C22D3×#21412yes—
833C22C2×D3×#6711yescharacteristic
834C4—21no—
835C4—32no—
836C4—61no—
837C4—61no—
838C4—121no—
839C4—121no—
840C4—121no—
841C4—361no—
842C4—361no—
843C4C2×#380511yescharacteristic
844C4#6433011yescharacteristic
845C3—21no—
846C3#8015811yescharacteristic, complemented
847C3#8348311yescharacteristic, complemented
848C2—22no—
849C2—42no—
850C2—62no—
851C2—81no—
852C2—241no—
853C2#1059509711yescharacteristic
854C2C2×D3×#21411yescharacteristic
855C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×#67C2
hypercenterC22×D4D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594993C2semidirect
3. C2×#63659C2semidirect
4. C3×#5218C2semidirect
5. #10591499C2semidirect
6. #10591487C2semidirect
7. #10591458C2semidirect
8. #10591438C2semidirect
9. Dic3×#214C2semidirect
10. #10591415C2semidirect
11. D3×#832C2semidirect
12. #10591408C2semidirect
13. #10591179C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591092C2semidirect
21. C2×C4⋊(C3⋊Dic3)C22semidirect
22. C22×C3⋊(C3⋊C8)C22semidirect
30. C2×C3×#214C22semidirect
33. C3×#924C22semidirect
36. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. Dic3×Dic6C22semidirect
42. C2×#3715C22semidirect
43. C2×D3×C3⋊C8C22semidirect
46. #63659C22semidirect
47. #63659C22semidirect
49. C3×#832C22semidirect
50. C3×#830C22semidirect
51. #63574C22semidirect
52. #63573C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63565C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
67. #5218D3semidirect
176. C2×#214C2×D3semidirect
184. #924C2×D3semidirect
221. #832C2×D3semidirect
223. #830C2×D3semidirect
267. C3×#67SD16semidirect
573. #67#214semidirect
745. C32#3295semidirect
846. C3#80158semidirect
847. C3#83483semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105949932
C2×#636592
C3×#52182
#105914992
#105914872
#105914582
#105914382
Dic3×#2142
#105914152
D3×#8322
#105914082
#105911792
#67⋊(C3⋊C8)2
#105910922
#834833
#801583