Finite Group Databasebeta

← #11889086

Subgroups — #11889086

Order 1152.

960 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×D12C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3#10592717C211yesmaximal, characteristic, complemented
4C3×#5009C211yesmaximal, characteristic, complemented
5#10591459C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591421C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590588C211yesmaximal, characteristic, complemented
10#10590578C211yesmaximal, characteristic, complemented
11#10590449C211yesmaximal, characteristic, complemented
12#10590438C211yesmaximal, characteristic, complemented
13#10590377C211yesmaximal, characteristic, complemented
14#10590330C211yesmaximal, characteristic, complemented
15#10590279C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#81189—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12—21no—
21C32×C4×D4C2211yescharacteristic
22C2×#3754C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C3×#930—21no—
25C3×#895C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#882—21no—
28C3×#882—21no—
29C3×#874C2211yescharacteristic
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic, complemented
32D3×C4⋊Dic3C2211yescharacteristic, complemented
33#63884—21no—
34#63878—21no—
35#63862—21no—
36#63857C2211yescharacteristic, complemented
37#63857C2211yescharacteristic, complemented
38#63846—21no—
39#63841C2211yescharacteristic, complemented
40C2×#3716C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic, complemented
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47#63630C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#808C2211yescharacteristic, complemented
51C3×#807C2211yescharacteristic, complemented
52C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
53#63563C2211yescharacteristic, complemented
54#63563C2211yescharacteristic, complemented
55#63562C2211yescharacteristic, complemented
56#63562C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×D42—31no—
62#5694—31no—
63D4×D12D311yescharacteristic
64#5541—31no—
65C3×#478—31no—
66#5218—31no—
67#5218—31no—
68#5215—31no—
69C2×#832—31no—
70#5075—31no—
71#5071—31no—
72#5067—31no—
73#5042—31no—
74#5041—31no—
75#5035—31no—
76#5033—31no—
77#5018—31no—
78#5018—31no—
79#5018—61no—
80#5011—31no—
81#5009D311yescharacteristic, complemented
82#4886—31no—
83#4882—31no—
84#4866—31no—
85#4864—31no—
86#4848—31no—
87#4836—31no—
88#4776—31no—
89#4776—31no—
90#4770—31no—
91D3×#102—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C22×C32×C4—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C3×D3×D4—41no—
102C3×D3×D4—41no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—44no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×D3×Dic3—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116C32×C42C2311yescharacteristic
117#3754—22no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3716—41no—
142#3716—41no—
143#3711—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4C2×D311yescharacteristic
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—21no—
152C3×#127—31no—
153C3×#125—31no—
154C3×#121—31no—
155C3×#121—31no—
156C3×#121—61no—
157C3×#120—61no—
158C3×#120—61no—
159C3×C4×D4—21no—
160C3×C4×D4—31no—
161C3×C4×D4C2×D311yescharacteristic
162C3×C4×D4C2×D311yescharacteristic
163#935—61no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—61no—
169#930—21no—
170#926—31no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173#924—31no—
174C2×#208—31no—
175C22×C3⋊C8—31no—
176C2×#204—31no—
177C2×#204—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—61no—
181#897—31no—
182#897—31no—
183#895C2×D311yescharacteristic
184#895C2×D311yescharacteristic
185#894—61no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—31no—
189#890—61no—
190#889—61no—
191#882—21no—
192#882—21no—
193#879—61no—
194#877—61no—
195#874C2×D311yescharacteristic
196C4×D12C2×D311yescharacteristic
197#870C2×D311yescharacteristic, complemented
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—31no—
205C3×#102—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—61no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#830—31no—
218#830—31no—
219#821—31no—
220#821—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#810—31no—
224#810—31no—
225#810—61no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—61no—
234#807C2×D311yescharacteristic, complemented
235C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
236#803—31no—
237#803—31no—
238#803—61no—
239C23×C32—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—42no—
246C22×C3×D3—81no—
247C22×C3×D3—81no—
248C22×C3×D3C2×D411yescharacteristic
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—42no—
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2×D411yescharacteristic
256C2×C32×C4C2411yescharacteristic
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—21no—
259#634—21no—
260#634—21no—
261C3×#67—42no—
262C3×#67—42no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—22no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12—42no—
274C3×D12—42no—
275C3×D12—81no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280D3×Dic3—42no—
281C3⋊(C3⋊C8)—21no—
282C3⋊(C3⋊C8)—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285#552—91no—
286D42—31no—
287#490—91no—
288#482—91no—
289#480—91no—
290#478—31no—
291#468—91no—
292#465—91no—
293#460—91no—
294#450—91no—
295#450—91no—
296#440—91no—
297#435—91no—
298#418—91no—
299C2×#102—91no—
300C24×C3—61no—
301C24×C3—61no—
302C23×D3—21no—
303C23×D3—21no—
304C2×C3×D4—21no—
305C2×C3×D4—31no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—61no—
309C2×C3×D4—61no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—62no—
313C2×C3×D4—62no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—124no—
317C2×C3×D4—121no—
318C2×C3×D4—121no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C2×#67—21no—
327C2×#67—21no—
328C22×Dic3—61no—
329D3×D4—22no—
330D3×D4—22no—
331D3×D4—41no—
332D3×D4—41no—
333C2×D12—21no—
334C2×D12—21no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12—44no—
338C2×D12#6711yescharacteristic
339C2×D12C22×D311yescharacteristic
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×C3×C8—31no—
348C2×C3×C8—31no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4C22×D311yescharacteristic
356C3×C4⋊C4C22×D311yescharacteristic
357C3×C22⋊C4—21no—
358C3×C22⋊C4—21no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—41no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42C22×D311yescharacteristic
366C3×C42C22×D311yescharacteristic
367#217—61no—
368#217—61no—
369#217—61no—
370#214—64no—
371#214—62no—
372#214—62no—
373#214—121no—
374#214—121no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4#6711yescharacteristic
381(C2×D3)⋊C4#6711yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3#6711yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—121no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404#208—121no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—61no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414#204—121no—
415#204—121no—
416ΓL(1,𝔽25)—121no—
417D3×C8—121no—
418C22×C32—22no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—84no—
434C2×C3×D3—84no—
435C2×C3×D3AGL(1,ℤ/8)12yes—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4C2×#4111yescharacteristic
440C32×C4H(5,𝔽2)11yescharacteristic
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C22×D4—31no—
448C22×D4—31no—
449C22×D4—61no—
450C2×SD16—91no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×M16—91no—
454C22×C8—91no—
455#127—31no—
456#126—181no—
457#125—31no—
458#125—181no—
459#123—181no—
460C22⋊Q8—91no—
461C22⋊Q8—91no—
462#121—31no—
463#121—31no—
464#121—61no—
465#120—61no—
466#120—61no—
467C4×Q8—91no—
468C4×D4—31no—
469C4×D4D3211yescharacteristic
470#117—91no—
471#117—181no—
472C2×C4⋊C4—91no—
473#107—31no—
474#107—91no—
475#106—31no—
476C4⋊C8—31no—
477#103—91no—
478#102—31no—
479#102—31no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487C22⋊C8—91no—
488C22⋊C8—91no—
489#97—91no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—31no—
494C23×C3—41no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—241no—
502C23×C3—241no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—81no—
510C22×D3—81no—
511C22×D3C2×#6711yescharacteristic
512C22×D3C2×#6711yescharacteristic
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—22no—
516C3×D4—41no—
517C3×D4—62no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C3×D4—122no—
524C3×D4—122no—
525C3×D4—122no—
526C3×D4—122no—
527C3×D4—241no—
528C3×D4#23712yes—
529C3×D4#23912yes—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—41no—
538C2×C3×C4—42no—
539C2×C3×C4—42no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—82no—
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4D3×D411yescharacteristic
549C2×C3×C4C2×#6711yescharacteristic
550C2×C3×C4C2×#6711yescharacteristic
551C2×C3×C4C23×D311yescharacteristic
552C2×C3×C4C23×D311yescharacteristic
553#67—42no—
554#67—42no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—122no—
564C2×Dic3C2×#6711yescharacteristic
565C2×Dic3C2×#6711yescharacteristic
566D12—22no—
567D12—21no—
568D12—21no—
569D12—21no—
570D12—21no—
571D12—42no—
572D12—42no—
573D12—42no—
574D12—81no—
575C4×D3—21no—
576C4×D3—21no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—122no—
580Dic6—62no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—61no—
585Dic6—121no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C3⋊C8—62no—
591C3⋊C8—61no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—61no—
595C3⋊C8—121no—
596C2×C32—42no—
597C2×C32#54611yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57711yescharacteristic
600C3×D3—22no—
601C3×D3—41no—
602C3×D3—81no—
603C3×D3—81no—
604C24—61no—
605C24—61no—
606C2×Q8—91no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—61no—
611C2×D4—61no—
612C2×D4—61no—
613C2×D4—61no—
614C2×D4—62no—
615C2×D4—62no—
616C2×D4—61no—
617C2×D4—61no—
618C2×D4—124no—
619C2×D4—121no—
620C2×D4—121no—
621C2×D4C2×D3211yescharacteristic
622C22×C4—21no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—181no—
626SD16—182no—
627SD16—361no—
628SD16—361no—
629M16—361no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—91no—
633C2×C8—91no—
634C2×C8—361no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—91no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4—181no—
645C4⋊C4C2×D3211yescharacteristic
646C22⋊C4—21no—
647C22⋊C4—31no—
648C22⋊C4—31no—
649C22⋊C4—61no—
650C22⋊C4—61no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C42—181no—
655C42—181no—
656C42C2×D3211yescharacteristic
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—32no—
661C22×C3—42no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—61no—
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×C3—244no—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C22×#6711yescharacteristic
683C2×D3—21no—
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—21no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—84no—
695C2×D3—84no—
696C2×D3#93212yes—
697C3×C4—21no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4C2×#23711yescharacteristic
713C3×C4#100411yescharacteristic
714C3×C4C2×#23911yescharacteristic
715C3×C4#100911yescharacteristic
716Dic3—21no—
717Dic3—21no—
718Dic3—41no—
719Dic3—41no—
720Dic3—122no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#331011yescharacteristic, complemented, Sylow
727C23—21no—
728C23—31no—
729C23—31no—
730C23—61no—
731C23—61no—
732C23—122no—
733C23—122no—
734C23—122no—
735C23—122no—
736C23—241no—
737C23—241no—
738Q8—181no—
739Q8—181no—
740D4—21no—
741D4—62no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—61no—
746D4—122no—
747D4—122no—
748D4—122no—
749D4—122no—
750D4—122no—
751D4—241no—
752D4#379612yes—
753C2×C4—21no—
754C2×C4—31no—
755C2×C4—31no—
756C2×C4—42no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—362no—
766C2×C4D3×#6711yescharacteristic
767C2×C4D3×#6711yescharacteristic
768C2×C4C22×D3211yescharacteristic
769C8—61no—
770C8—61no—
771C8—181no—
772C8—181no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—42no—
777C2×C3—42no—
778C2×C3—62no—
779C2×C3—82no—
780C2×C3—121no—
781C2×C3—241no—
782C2×C3—241no—
783C2×C3#563011yescharacteristic
784C2×C3#577011yescharacteristic
785C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
786C2×C3C2×#93211yescharacteristic
787C2×C3#580611yescharacteristic
788C2×C3#583611yescharacteristic
789D3—22no—
790D3—41no—
791D3—81no—
792D3—81no—
793C22—22no—
794C22—32no—
795C22—41no—
796C22—41no—
797C22—61no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22—61no—
802C22—121no—
803C22—121no—
804C22—121no—
805C22—121no—
806C22—121no—
807C22—121no—
808C22—244no—
809C22—244no—
810C22C2×D3×#6711yescharacteristic
811C4—21no—
812C4—21no—
813C4—41no—
814C4—61no—
815C4—61no—
816C4—121no—
817C4—121no—
818C4—361no—
819C4—361no—
820C4C2×#379611yescharacteristic
821C4#6430711yescharacteristic
822C3—21no—
823C3#8118911yescharacteristic, complemented
824C3#8348411yescharacteristic, complemented
825C2—42no—
826C2—62no—
827C2—121no—
828C2—241no—
829C2—241no—
830C2#1059488911yescharacteristic
831C2D3×#93211yescharacteristic
832C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×D12C2
hypercenterC4×D4D32
hypocenterC32#3310
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
2. #10593920C2semidirect
3. #10592717C2semidirect
4. C3×#5009C2semidirect
5. #10591459C2semidirect
6. #10591459C2semidirect
7. #10591421C2semidirect
8. D3×#832C2semidirect
9. #10590588C2semidirect
10. #10590578C2semidirect
11. #10590449C2semidirect
12. #10590438C2semidirect
13. #10590377C2semidirect
14. #10590330C2semidirect
15. #10590279C2semidirect
23. C4×#634C22semidirect
31. C3×#870C22semidirect
32. D3×C4⋊Dic3C22semidirect
36. #63857C22semidirect
37. #63857C22semidirect
39. #63841C22semidirect
40. C2×#3716C22semidirect
41. C2×#3716C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63637C22semidirect
46. #63634C22semidirect
47. #63630C22semidirect
50. C3×#808C22semidirect
51. C3×#807C22semidirect
52. C3×C4⋊(C3⋊C8)C22semidirect
53. #63563C22semidirect
54. #63563C22semidirect
55. #63562C22semidirect
56. #63562C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
81. #5009D3semidirect
197. #870C2×D3semidirect
230. #808C2×D3semidirect
234. #807C2×D3semidirect
235. C4⋊(C3⋊C8)C2×D3semidirect
726. C32#3310semidirect
823. C3#81189semidirect
824. C3#83484semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
#105939202
#105927172
C3×#50092
#105914592
#105914212
D3×#8322
#105905882
#105905782
#105904492
#105904382
#105903772
#105903302
#105902792
#834843
#811893