Finite Group Databasebeta

← #11889149

Subgroups — #11889149

Order 1152.

964 conjugacy classes of subgroups.

The subgroup lattice has 841 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5717C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic, complemented
4C3×#5071C211yesmaximal, characteristic, complemented
5#10591462C211yesmaximal, characteristic, complemented
6#10591460C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591423C211yesmaximal, characteristic, complemented
10#10591421C211yesmaximal, characteristic, complemented
11#10591413C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#81725—31nomaximal
18C2×C3×D3×D4—21no—
19C2×C3×D3×D4C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C32×#127C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23C2×#3754C2211yescharacteristic, complemented
24C4×#634C2211yescharacteristic, complemented
25C3×#938—21no—
26C3×#938C2211yescharacteristic
27C3×#938C2211yescharacteristic
28C3×#937—21no—
29C3×#937—21no—
30C3×C4×D12C2211yescharacteristic
31C3×C4×D12C2211yescharacteristic
32C3×#870C2211yescharacteristic, complemented
33D3×C4⋊Dic3C2211yescharacteristic, complemented
34#63884—21no—
35#63878—21no—
36#63862—21no—
37#63857C2211yescharacteristic, complemented
38#63857C2211yescharacteristic, complemented
39#63846—21no—
40#63841C2211yescharacteristic, complemented
41C2×#3716C2211yescharacteristic
42C2×#3711C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic, complemented
45#63659C2211yescharacteristic, complemented
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#832C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#803C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
61C3×D42—31no—
62#5717D311yescharacteristic
63#5694—31no—
64#5541—31no—
65C3×#490—31no—
66#5218—31no—
67#5218—31no—
68#5215—31no—
69C2×#832—31no—
70#5075—31no—
71#5075—31no—
72#5075—61no—
73#5071D311yescharacteristic, complemented
74#5066—31no—
75#5042—31no—
76#5041—31no—
77#5035—31no—
78#5033—31no—
79#5018—31no—
80#5011—31no—
81#5009—31no—
82#4784—31no—
83#4780—31no—
84#4778—31no—
85#4776—31no—
86#4776—31no—
87#4774—31no—
88#4770—31no—
89D3×#102—31no—
90#4710—31no—
91#4706—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C2×C32×D4—21no—
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C3×D3×D4—41no—
106C3×D3×D4—41no—
107C3×D3×D4—44no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×C4×D3C2311yescharacteristic
113C2×D3×Dic3—21no—
114C32×C42C2311yescharacteristic
115#3754—41no—
116#3754—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#217—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—22no—
143#3711—41no—
144D3×C3⋊C8—41no—
145#3310—91noSylow
146C22×C3×D4—31no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C2×D3×D4—21no—
150C2×D3×D4C2×D311yescharacteristic
151C2×D3×D4C2×D311yescharacteristic
152C3×#127—21no—
153C3×#127C2×D311yescharacteristic
154C3×#127C2×D311yescharacteristic
155C3×#125—31no—
156C3×#121—31no—
157C3×#121—31no—
158C3×#121—61no—
159C3×#120—61no—
160C3×#120—61no—
161C3×C4×D4—31no—
162C3×C4×D4—31no—
163#938—21no—
164#938C2×D311yescharacteristic
165#938C2×D311yescharacteristic
166#937—21no—
167#937—21no—
168#935—61no—
169C2×#214—31no—
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—61no—
175C2×#214—61no—
176#926—31no—
177C2×C4⋊Dic3—31no—
178#924—31no—
179#924—31no—
180C2×#208—31no—
181C22×C3⋊C8—31no—
182C2×#204—31no—
183C2×ΓL(1,𝔽25)—31no—
184C2×D3×C8—31no—
185#898—61no—
186#897—31no—
187#897—31no—
188#894—61no—
189#892—31no—
190#892—61no—
191D3×C4⋊C4—31no—
192#890—61no—
193#889—61no—
194#879—61no—
195#877—61no—
196C4×D12C2×D311yescharacteristic
197C4×D12C2×D311yescharacteristic
198#870C2×D311yescharacteristic, complemented
199C4×Dic6—31no—
200C4×Dic6—31no—
201C4×Dic6—61no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#97—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#832—61no—
216#832C2×D311yescharacteristic, complemented
217#832C2×D311yescharacteristic, complemented
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#830—31no—
221#830—31no—
222#821—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#816—31no—
227#810—31no—
228#809—31no—
229#809—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
238#803C2×D311yescharacteristic, complemented
239C23×C32—21no—
240C23×C32—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—21no—
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—42no—
255C32×D4—81no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—22no—
273C3×D12—21no—
274C3×D12#4112yes—
275C3×C4×D3—21no—
276C3×C4×D3—21no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—42no—
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—31no—
288#482—91no—
289#480—91no—
290#478—91no—
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—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—31no—
311C2×C3×D4—31no—
312C2×C3×D4—41no—
313C2×C3×D4—41no—
314C2×C3×D4—61no—
315C2×C3×D4—61no—
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—121no—
321C2×C3×D4—121no—
322C2×C3×D4—124no—
323C2×C3×D4C22×D311yescharacteristic
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C2×C3×D4C22×D311yescharacteristic
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—61no—
330C2×#67—21no—
331C2×#67—21no—
332C2×#67—21no—
333C2×#67—21no—
334C22×Dic3—61no—
335D3×D4—22no—
336D3×D4—22no—
337D3×D4—41no—
338D3×D4—41no—
339D3×D4—44no—
340C2×D12#6711yescharacteristic
341C2×D12C22×D311yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×C4×D3C22×D311yescharacteristic
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—61no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—31no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—21no—
363C3×C42C22×D311yescharacteristic
364C3×C42C22×D311yescharacteristic
365#217—21no—
366#217—21no—
367#217—61no—
368#217—61no—
369#217—61no—
370#214—62no—
371#214—121no—
372#214—121no—
373#214—121no—
374#214—121no—
375#214—122no—
376#214—122no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4#6711yescharacteristic
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3#6711yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—121no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—121no—
406#208—121no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416#204—62no—
417ΓL(1,𝔽25)—121no—
418D3×C8—121no—
419C22×C32—41no—
420C22×C32—41no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—21no—
429C2×C3×D3—22no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3—84no—
436C2×C3×D3AGL(1,ℤ/8)12yes—
437C32×C4—21no—
438C32×C4—21no—
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—
447C3×Dic3—41no—
448C22×D4—31no—
449C22×D4—31no—
450C22×D4—61no—
451C2×SD16—91no—
452C2×SD16—91no—
453C2×SD16—91no—
454C2×M16—91no—
455C22×C8—91no—
456#127D3211yescharacteristic
457#126—181no—
458#125—31no—
459#125—181no—
460#123—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463#121—31no—
464#121—31no—
465#121—61no—
466#120—61no—
467#120—61no—
468C4×Q8—91no—
469C4×D4—31no—
470C4×D4—31no—
471#117—91no—
472#117—181no—
473C2×C4⋊C4—91no—
474#107—91no—
475#107—91no—
476#106—91no—
477C4⋊C8—91no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—91no—
489C22⋊C8—91no—
490#97—31no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—61no—
500C23×C3—122no—
501C23×C3—122no—
502C23×C3—122no—
503C23×C3—122no—
504C23×C3—241no—
505C23×C3—241no—
506C22×D3—21no—
507C22×D3—42no—
508C22×D3—42no—
509C22×D3—42no—
510C22×D3—42no—
511C22×D3—81no—
512C22×D3—81no—
513C22×D3C2×#6711yescharacteristic
514C22×D3C2×#6711yescharacteristic
515C3×D4—21no—
516C3×D4—21no—
517C3×D4—21no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—21no—
523C3×D4—32no—
524C3×D4—41no—
525C3×D4—41no—
526C3×D4—41no—
527C3×D4—41no—
528C3×D4—42no—
529C3×D4—42no—
530C3×D4—62no—
531C3×D4—61no—
532C3×D4—82no—
533C3×D4—81no—
534C3×D4—81no—
535C3×D4—82no—
536C3×D4—122no—
537C3×D4—122no—
538C3×D4—122no—
539C3×D4—122no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—31no—
544C2×C3×C4—31no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—122no—
553C2×C3×C4D3×D411yescharacteristic
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4C2×#6711yescharacteristic
556C2×C3×C4C2×#6711yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559#67—42no—
560#67—42no—
561#67—42no—
562#67—42no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—122no—
573C2×Dic3C2×#6711yescharacteristic
574C2×Dic3C2×#6711yescharacteristic
575D12—22no—
576D12—21no—
577D12#23712yes—
578C4×D3—21no—
579C4×D3—21no—
580C4×D3—21no—
581C4×D3—21no—
582C4×D3—42no—
583C4×D3—122no—
584Dic6—62no—
585Dic6—61no—
586Dic6—61no—
587Dic6—61no—
588Dic6—61no—
589Dic6—121no—
590C3×C8—61no—
591C3×C8—61no—
592C3⋊C8—21no—
593C3⋊C8—21no—
594C3⋊C8—61no—
595C3⋊C8—61no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C3⋊C8—121no—
600C2×C32—81no—
601C2×C32—81no—
602C2×C32#54611yescharacteristic
603C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
604C2×C32#57711yescharacteristic
605C3×D3—22no—
606C3×D3—41no—
607C3×D3—42no—
608C24—61no—
609C24—61no—
610C2×Q8—91no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—31no—
614C2×D4—31no—
615C2×D4—61no—
616C2×D4—61no—
617C2×D4—62no—
618C2×D4—62no—
619C2×D4—61no—
620C2×D4—61no—
621C2×D4—121no—
622C2×D4—121no—
623C2×D4—124no—
624C2×D4C2×D3211yescharacteristic
625C2×D4C2×D3211yescharacteristic
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—61no—
629C22×C4—181no—
630SD16—182no—
631SD16—361no—
632SD16—361no—
633M16—361no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—91no—
637C2×C8—91no—
638C2×C8—361no—
639C4⋊C4—31no—
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—31no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C22⋊C4—31no—
651C22⋊C4—31no—
652C22⋊C4—61no—
653C22⋊C4—61no—
654C22⋊C4—61no—
655C22⋊C4—181no—
656C22⋊C4—181no—
657C22⋊C4—181no—
658C42—181no—
659C42—181no—
660C42C2×D3211yescharacteristic
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—61no—
678C22×C3—62no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—81no—
682C22×C3—81no—
683C22×C3—81no—
684C22×C3—81no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—121no—
688C22×C3—121no—
689C22×C3—244no—
690C22×C3—244no—
691C22×C3C2×D3×D411yescharacteristic
692C22×C3C22×#6711yescharacteristic
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—21no—
697C2×D3—22no—
698C2×D3—21no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—84no—
702C2×D3—84no—
703C2×D3#93212yes—
704C3×C4—22no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4C2×#23711yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4D3×#4111yescharacteristic
720C3×C4#100911yescharacteristic
721Dic3—21no—
722Dic3—21no—
723Dic3—41no—
724Dic3—41no—
725Dic3—41no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—241no—
732C32#331011yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—31no—
736C23—31no—
737C23—61no—
738C23—122no—
739C23—122no—
740C23—122no—
741C23—122no—
742C23—241no—
743C23—241no—
744Q8—181no—
745Q8—181no—
746D4—21no—
747D4—21no—
748D4—21no—
749D4—21no—
750D4—32no—
751D4—42no—
752D4—62no—
753D4—61no—
754D4—81no—
755D4—122no—
756D4—122no—
757D4—122no—
758D4—122no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—122no—
769C2×C4—181no—
770C2×C4—181no—
771C2×C4—362no—
772C2×C4D3×#6711yescharacteristic
773C2×C4D3×#6711yescharacteristic
774C2×C4C22×D3211yescharacteristic
775C8—61no—
776C8—61no—
777C8—181no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—62no—
783C2×C3—81no—
784C2×C3—81no—
785C2×C3—81no—
786C2×C3—81no—
787C2×C3—121no—
788C2×C3—122no—
789C2×C3—161no—
790C2×C3—161no—
791C2×C3#567611yescharacteristic
792C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
793C2×C3#577511yescharacteristic
794C2×C3C2×#93211yescharacteristic
795C2×C3#580611yescharacteristic
796C2×C3#583611yescharacteristic
797D3—22no—
798D3—41no—
799D3—42no—
800C22—32no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—61no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—61no—
812C22—62no—
813C22—121no—
814C22—121no—
815C22—244no—
816C22—244no—
817C22C2×D3×#6711yescharacteristic
818C4—21no—
819C4—21no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—361no—
826C4—361no—
827C4D3×#23711yescharacteristic
828C4#6431411yescharacteristic
829C3—21no—
830C3#8172511yescharacteristic, complemented
831C3#8348411yescharacteristic, complemented
832C2—62no—
833C2—81no—
834C2—81no—
835C2—121no—
836C2—122no—
837C2D3×#93211yescharacteristic
838C2#1059510611yescharacteristic
839C2#1059522911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radicalC3×#5717C2
hypercenter#127D32
hypocenterC32#3310
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593920C2semidirect
3. #10592774C2semidirect
4. C3×#5071C2semidirect
5. #10591462C2semidirect
6. #10591460C2semidirect
7. #10591459C2semidirect
8. #10591459C2semidirect
9. #10591423C2semidirect
10. #10591421C2semidirect
11. #10591413C2semidirect
12. D3×#832C2semidirect
13. #10590360C2semidirect
14. #10590326C2semidirect
15. #10590270C2semidirect
22. C2×#3754C22semidirect
23. C2×#3754C22semidirect
24. C4×#634C22semidirect
32. C3×#870C22semidirect
33. D3×C4⋊Dic3C22semidirect
37. #63857C22semidirect
38. #63857C22semidirect
40. #63841C22semidirect
42. C2×#3711C22semidirect
43. C2×D3×C3⋊C8C22semidirect
44. #63659C22semidirect
45. #63659C22semidirect
46. C4⋊(C3⋊(C3⋊C8))C22semidirect
47. C3×#832C22semidirect
48. C3×#832C22semidirect
49. C3×#832C22semidirect
50. C3×#832C22semidirect
51. C3×#803C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. (C2×D3)⋊(C3⋊C8)C22semidirect
73. #5071D3semidirect
198. #870C2×D3semidirect
216. #832C2×D3semidirect
217. #832C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
238. #803C2×D3semidirect
732. C32#3310semidirect
830. C3#81725semidirect
831. C3#83484semidirect

Maximal subgroups

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

subgroupindex
C3×#57172
#105939202
#105927742
C3×#50712
#105914622
#105914602
#105914592
#105914232
#105914212
#105914132
D3×#8322
#105903602
#105903262
#105902702
#834843
#817253