Finite Group Databasebeta

← #11887392

Subgroups — #11887392

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5829C211yesmaximal, characteristic, complemented
2#10594945C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5238C211yesmaximal, characteristic, complemented
5#10591634C211yesmaximal, characteristic, complemented
6#10591614C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9#10591447C211yesmaximal, characteristic, complemented
10Dic3×#213C211yesmaximal, characteristic, complemented
11D3×#832C211yesmaximal, characteristic, complemented
12#10591409C211yesmaximal, characteristic, complemented
13#10591166C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591093C211yesmaximal, characteristic, complemented
16#83495—31nomaximal
17#80102—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20#64135C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic, complemented
25C3×#939—21no—
26C3×#937—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic
29C3×#930C2211yescharacteristic
30C3×#930C2211yescharacteristic, complemented
31C3×#929—21no—
32C3×C4×#67C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4—21no—
34#63970—21no—
35#63969—21no—
36#63908C2211yescharacteristic
37#63902—21no—
38Dic3×D12C2211yescharacteristic, complemented
39D3×C4⋊Dic3C2211yescharacteristic
40#63869C2211yescharacteristic, complemented
41#63862—21no—
42C2×#3713C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63575C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#546—31no—
62#5829D311yescharacteristic, complemented
63#5614—31no—
64#5565—31no—
65C3×#449—31no—
66#5238D311yescharacteristic, complemented
67#5233—31no—
68#5233—31no—
69#5233—61no—
70#5217—31no—
71C2×#832—31no—
72#5171—31no—
73#5165—31no—
74#5156—31no—
75Dic3×D8—31no—
76#5057—31no—
77#5056—31no—
78#5048—31no—
79#5044—31no—
80#5038—31no—
81#5038—31no—
82#5035—31no—
83C4×#213—31no—
84D4×C3⋊C8—31no—
85#5009—31no—
86#4811—31no—
87#4800—31no—
88D3×#102—31no—
89#4763—31no—
90#4737—31no—
91#67⋊C8—31no—
92C23×C3×D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C22×C3×Dic3—21no—
105C3×D3×D4—22no—
106C3×D3×D4—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×#625—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3—21no—
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#215—41no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
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—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3713—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C2×D311yescharacteristic
148C22×C3×D4—31no—
149C2×D3×D4C2×D311yescharacteristic
150C2×C3×SD16—31no—
151C2×C3×D8—31no—
152C3×#124—31no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C22⋊C4—61no—
162#947C2×D311yescharacteristic
163#946C2×D311yescharacteristic
164C2×#215C2×D311yescharacteristic, complemented
165#939—21no—
166#939—61no—
167#938—31no—
168#938—61no—
169#937—21no—
170#935—61no—
171D4×Dic3—31no—
172D4×Dic3C2×D311yescharacteristic
173C2×#213—31no—
174C2×#213—31no—
175C2×#213C2×D311yescharacteristic
176#930—31no—
177#930C2×D311yescharacteristic
178#930C2×D311yescharacteristic, complemented
179#929—21no—
180C4×#67C2×D311yescharacteristic
181C2×(C2×D3)⋊C4—21no—
182#926—31no—
183#926—31no—
184#926—61no—
185C2×C4⋊Dic3—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190C2×D3×C8—31no—
191#898—61no—
192D3×C4⋊C4—31no—
193#890—31no—
194#883—61no—
195#67⋊C4—61no—
196#67⋊C4—61no—
197#879—61no—
198C4×D12—31no—
199#870—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—61no—
208#835—61no—
209#835C2×D311yescharacteristic, complemented
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225(C2×D3)⋊C8—31no—
226#818—31no—
227#817—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×Q8—21no—
247C32×Q8—21no—
248C32×D4—21no—
249C32×D4—42no—
250C32×D4#4112yes—
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—42no—
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259C3×#67—22no—
260C3×#67—42no—
261C3×#67—81no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×C4×D3—21no—
274C3×C4×D3—21no—
275#625—42no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—31no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—31no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C3×#41—24no—
300C3×#41—22no—
301C3×#41—22no—
302C3×#41—41no—
303C3×#41—41no—
304C3×#41—42no—
305C2×C3×Q8—21no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—41no—
315C2×C3×D4—61no—
316C2×C3×D4—62no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4—121no—
320C2×C3×D4C22×D311yescharacteristic
321C2×C3×D4C22×D311yescharacteristic
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—41no—
327C22×C3×C4—61no—
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—21no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67#6711yescharacteristic
336C22×Dic3—21no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339D3×D4—22no—
340D3×D4—41no—
341C2×D12C22×D311yescharacteristic
342C2×D12C22×D311yescharacteristic
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3C22×D311yescharacteristic
346C3×SD16—121no—
347C3×D8—62no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363#217—21no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#217#6711yescharacteristic
370#215—41no—
371#213—22no—
372#213—121no—
373#213—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—122no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—22no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—84no—
431C2×C3×D3#13512yes—
432C32×C4—21no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41D3211yescharacteristic
444C22×D4—31no—
445C2×SD16—31no—
446C2×D8—31no—
447C2×D8—91no—
448C22×C8—91no—
449C22×C8—91no—
450#126—181no—
451#125—91no—
452#124—31no—
453#123—61no—
454#123—181no—
455C22⋊Q8—31no—
456#121—31no—
457#121—31no—
458#121—61no—
459#121—91no—
460#121—181no—
461#120—61no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—61no—
469#107—91no—
470#107—91no—
471#106—91no—
472C4⋊C8—91no—
473#103—31no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—31no—
484C22⋊C8—91no—
485C4×C8—91no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—21no—
489C23×C3—31no—
490C23×C3—41no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—122no—
494C23×C3—122no—
495C23×C3—241no—
496C23×C3D3×D411yescharacteristic
497C23×C3C2×#6711yescharacteristic
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—42no—
501C22×D3—42no—
502C22×D3—81no—
503C22×D3C2×#6711yescharacteristic
504C3×Q8—22no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—22no—
513C3×D4—41no—
514C3×D4—42no—
515C3×D4—42no—
516C3×D4—44no—
517C3×D4—62no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—241no—
524C3×D4—241no—
525C3×D4#23712yes—
526C3×D4#23712yes—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—31no—
540C2×C3×C4—41no—
541C2×C3×C4—42no—
542C2×C3×C4—42no—
543C2×C3×C4—44no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—241no—
549C2×C3×C4D3×D411yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—22no—
554#67—42no—
555#67—81no—
556#67—81no—
557#67—122no—
558#67—122no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—81no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—241no—
569C2×Dic3—241no—
570C2×Dic3C2×#6711yescharacteristic
571C2×Dic3C2×#6711yescharacteristic
572C2×Dic3C2×#6711yescharacteristic
573D12—21no—
574D12—21no—
575D12—21no—
576D12—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—241no—
580C4×D3—241no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C3⋊C8—61no—
586C3⋊C8—61no—
587C3⋊C8—61no—
588C3⋊C8—61no—
589C3⋊C8—121no—
590C3⋊C8—121no—
591C2×C32—41no—
592C2×C32—42no—
593C2×C32#54611yescharacteristic
594C2×C32C2×#13511yescharacteristic
595C2×C32#57611yescharacteristic
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—61no—
600#41—22no—
601#41—41no—
602C2×Q8C2×D3211yescharacteristic
603C2×D4—21no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—31no—
607C2×D4—61no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4—121no—
612C2×D4—181no—
613C2×D4C2×D3211yescharacteristic
614C22×C4—21no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620SD16—121no—
621D8—62no—
622D8—361no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—91no—
626C2×C8—91no—
627C2×C8—361no—
628C2×C8—361no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—61no—
633C4⋊C4—91no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—181no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—22no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—42no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—61no—
670C22×C3—61no—
671C22×C3—81no—
672C22×C3—81no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—244no—
680C22×C3C2×D3×D411yescharacteristic
681C22×C3C22×#6711yescharacteristic
682C2×D3—21no—
683C2×D3—21no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—84no—
691C2×D3#95012yes—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—42no—
698C3×C4—41no—
699C3×C4—41no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—61no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4C2×#23711yescharacteristic
706C3×C4C2×#23711yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4#100411yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3—241no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—21no—
722C23—31no—
723C23—61no—
724C23—61no—
725C23—122no—
726C23—122no—
727C23—241no—
728C23D3×#6711yescharacteristic
729Q8—21no—
730Q8—21no—
731D4—21no—
732D4—42no—
733D4—62no—
734D4—61no—
735D4—61no—
736D4—61no—
737D4—61no—
738D4—122no—
739D4—241no—
740D4—241no—
741D4—362no—
742D4#380512yes—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—42no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—241no—
757C2×C4—721no—
758C2×C4—721no—
759C2×C4D3×#6711yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—61no—
762C8—61no—
763C8—181no—
764C8—181no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—42no—
773C2×C3—62no—
774C2×C3—82no—
775C2×C3—241no—
776C2×C3—241no—
777C2×C3#559111yescharacteristic
778C2×C3D3×#13511yescharacteristic
779C2×C3#577411yescharacteristic
780C2×C3#580611yescharacteristic
781C2×C3C2×#95011yescharacteristic
782C2×C3#583511yescharacteristic
783D3—22no—
784D3—81no—
785D3—81no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—22no—
790C22—32no—
791C22—41no—
792C22—41no—
793C22—61no—
794C22—61no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—121no—
800C22—121no—
801C22—244no—
802C22C2×D3×#6711yescharacteristic
803C4—21no—
804C4—41no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—121no—
809C4—121no—
810C4—361no—
811C4—361no—
812C4C2×#380511yescharacteristic
813C4#6433011yescharacteristic
814C3—21no—
815C3#8010211yescharacteristic, complemented
816C3#8349511yescharacteristic, complemented
817C2—41no—
818C2—42no—
819C2—62no—
820C2—241no—
821C2—241no—
822C2D3×#95011yescharacteristic
823C2#1059545411yescharacteristic
824C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5829C2semidirect
2. #10594945C2semidirect
3. #10592932C2semidirect
4. C3×#5238C2semidirect
5. #10591634C2semidirect
6. #10591614C2semidirect
7. #10591567C2semidirect
8. #10591551C2semidirect
9. #10591447C2semidirect
10. Dic3×#213C2semidirect
11. D3×#832C2semidirect
12. #10591409C2semidirect
13. #10591166C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591093C2semidirect
20. #64135C22semidirect
21. C22×C3⋊(C3⋊C8)C22semidirect
24. C2×C3×#215C22semidirect
30. C3×#930C22semidirect
38. Dic3×D12C22semidirect
40. #63869C22semidirect
44. #63662C22semidirect
45. #63662C22semidirect
48. C3×#835C22semidirect
50. C3×#830C22semidirect
51. #63576C22semidirect
52. #63575C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. #5829D3semidirect
66. #5238D3semidirect
164. C2×#215C2×D3semidirect
178. #930C2×D3semidirect
209. #835C2×D3semidirect
222. #830C2×D3semidirect
720. C32#3297semidirect
815. C3#80102semidirect
816. C3#83495semidirect

Maximal subgroups

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

subgroupindex
C3×#58292
#105949452
#105929322
C3×#52382
#105916342
#105916142
#105915672
#105915512
#105914472
Dic3×#2132
D3×#8322
#105914092
#105911662
#67⋊(C3⋊C8)2
#105910932
#834953
#801023