Finite Group Databasebeta

← #11889098

Subgroups — #11889098

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 851 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591477C211yesmaximal, characteristic, complemented
6#10591462C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591439C211yesmaximal, characteristic, complemented
9#10591422C211yesmaximal, characteristic, complemented
10#10591421C211yesmaximal, characteristic, complemented
11#10591409C211yesmaximal, characteristic, complemented
12#10591405C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14#10591155C211yesmaximal, characteristic, complemented
15#10591089C211yesmaximal, characteristic, complemented
16#83484—31nomaximal
17#78762—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23#64133C2211yescharacteristic, complemented
24C3×#953—21no—
25C3×#940C2211yescharacteristic
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C3×#937—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63961—21no—
35#63955—21no—
36#63869C2211yescharacteristic, complemented
37#63858—21no—
38#63857C2211yescharacteristic, complemented
39#63847—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3711C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic, complemented
46#63657C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51#63576C2211yescharacteristic, complemented
52#63576C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic
63#5541—31no—
64#5513—31no—
65C2×C3×#102—31no—
66#5218—31no—
67#5218—31no—
68#5218—31no—
69#5218—61no—
70#5215—31no—
71C2×#832D311yescharacteristic, complemented
72#5114—31no—
73#5111—31no—
74#5075—31no—
75#5071—31no—
76#5042—31no—
77#5041—31no—
78#5035—31no—
79#5033—31no—
80#5018—31no—
81#5011—31no—
82#5009—31no—
83#4967—31no—
84#4780—31no—
85#4779—31no—
86#4776—31no—
87#4770—31no—
88#4764—31no—
89#4763—31no—
90#4762—31no—
91#4757—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
100C2×#634C2311yescharacteristic
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—
109C22×C3×Dic3—21no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114#3757—21no—
115#3754—22no—
116#3754—41no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3716—41no—
144#3711—41no—
145#3310—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
153C22×C3×C8—31no—
154C3×#127—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C4⋊C4—31no—
163#953—21no—
164#940C2×D311yescharacteristic
165#939—21no—
166#938C2×D311yescharacteristic
167#937—21no—
168#935—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—31no—
175C2×#214—61no—
176C2×#214—61no—
177#930C2×D311yescharacteristic
178#929—61no—
179C4×#67C2×D311yescharacteristic
180#926—31no—
181#926—61no—
182C2×C4⋊Dic3C2×D311yescharacteristic, complemented
183#924—31no—
184#924—31no—
185#924—31no—
186#924—61no—
187C2×#208—31no—
188C22×C3⋊C8C2×D311yescharacteristic, complemented
189C2×#204—31no—
190C2×ΓL(1,𝔽25)—31no—
191#898—61no—
192#897—31no—
193#892—31no—
194#890—31no—
195#889—61no—
196#889—61no—
197#887—31no—
198#879—61no—
199#877—61no—
200#870—31no—
201C4×Dic6—31no—
202C3×#102—31no—
203C3×#102—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—61no—
214#832—61no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic, complemented
218#832C2×D311yescharacteristic, complemented
219#830—31no—
220#830—31no—
221#830—31no—
222#830—61no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#816—31no—
227#815—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238#803—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—
261#634—21no—
262#634—21no—
263C3×#67—22no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—42no—
268C3×#67—81no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3—42no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
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—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—31no—
300C24×C3—21no—
301C24×C3—21no—
302C24×C3—41no—
303C24×C3—61no—
304C23×D3—21no—
305C2×C3×D4—22no—
306C2×C3×D4—22no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—41no—
314C2×C3×D4—42no—
315C2×C3×D4—41no—
316C2×C3×D4—41no—
317C2×C3×D4—42no—
318C2×C3×D4—61no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—62no—
322C2×C3×D4—61no—
323C2×C3×D4—61no—
324C2×C3×D4—121no—
325C2×C3×D4—124no—
326C2×C3×D4C22×D311yescharacteristic
327C2×C3×D4C22×D311yescharacteristic
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—61no—
333C22×C3×C4—61no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—44no—
342C2×#67#6711yescharacteristic
343C22×Dic3—21no—
344C22×Dic3—21no—
345D3×D4—22no—
346D3×D4—41no—
347C2×D12C22×D311yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—121no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366#217—21no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—121no—
373#217#6711yescharacteristic
374#214—62no—
375#214—62no—
376#214—122no—
377#214—121no—
378#214—121no—
379#214—121no—
380#214—122no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4#6711yescharacteristic
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403Dic3⋊C4#6711yescharacteristic
404C4×Dic3—61no—
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—61no—
408C4×Dic3C22×D311yescharacteristic
409#208—121no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—41no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419#204—121no—
420ΓL(1,𝔽25)—121no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—22no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—84no—
430C22×C32AGL(1,ℤ/8)12yes—
431C22×C32C22×D411yescharacteristic
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—84no—
439C32×C4—21no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3×Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C22×D4—31no—
451C22×D4—61no—
452C22×D4D3211yescharacteristic
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C2×M16—91no—
457C22×C8—31no—
458#127—31no—
459#126—181no—
460#125—91no—
461#125—181no—
462#123—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465#121—31no—
466#121—31no—
467#121—61no—
468#120—61no—
469#120—61no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—31no—
473#117—91no—
474#117—181no—
475C2×C4⋊C4—31no—
476#107—91no—
477#107—91no—
478#106—91no—
479C4⋊C8—91no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—91no—
491C22⋊C8—91no—
492#97—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—31no—
499C23×C3—41no—
500C23×C3—41no—
501C23×C3—42no—
502C23×C3—42no—
503C23×C3—44no—
504C23×C3—42no—
505C23×C3—42no—
506C23×C3—61no—
507C23×C3—82no—
508C23×C3—81no—
509C23×C3—81no—
510C23×C3—82no—
511C23×C3—122no—
512C23×C3—122no—
513C23×C3—241no—
514C23×C3D3×D411yescharacteristic
515C23×C3C2×#6711yescharacteristic
516C22×D3—21no—
517C22×D3—42no—
518C22×D3—42no—
519C22×D3—81no—
520C22×D3C2×#6711yescharacteristic
521C3×D4—22no—
522C3×D4—21no—
523C3×D4—21no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—22no—
529C3×D4—41no—
530C3×D4—41no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—44no—
534C3×D4—62no—
535C3×D4—61no—
536C3×D4—61no—
537C3×D4—122no—
538C3×D4—122no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—241no—
542C3×D4#23512yes—
543C3×D4#23712yes—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—31no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—41no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—122no—
561C2×C3×C4—122no—
562C2×C3×C4D3×D411yescharacteristic
563C2×C3×C4C2×#6711yescharacteristic
564C2×C3×C4C23×D311yescharacteristic
565C2×C3×C4C23×D311yescharacteristic
566#67—22no—
567#67—42no—
568#67—42no—
569#67—42no—
570#67—42no—
571#67—81no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—42no—
576C2×Dic3—42no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—121no—
582C2×Dic3—121no—
583C2×Dic3C2×#6711yescharacteristic
584C2×Dic3C2×#6711yescharacteristic
585C2×Dic3C2×#6711yescharacteristic
586D12—21no—
587D12—21no—
588C4×D3—21no—
589C4×D3—21no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596C3×C8—61no—
597C3×C8—61no—
598C3⋊C8—21no—
599C3⋊C8—21no—
600C3⋊C8—61no—
601C3⋊C8—61no—
602C3⋊C8—61no—
603C3⋊C8—61no—
604C3⋊C8—121no—
605C3⋊C8—121no—
606C2×C32—22no—
607C2×C32—42no—
608C2×C32—81no—
609C2×C32#54611yescharacteristic
610C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
611C2×C32#57711yescharacteristic
612C3×D3—41no—
613C3×D3—81no—
614C24—21no—
615C24—61no—
616C2×Q8—91no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—31no—
620C2×D4—31no—
621C2×D4—41no—
622C2×D4—61no—
623C2×D4—61no—
624C2×D4—61no—
625C2×D4—62no—
626C2×D4—61no—
627C2×D4—61no—
628C2×D4—121no—
629C2×D4—124no—
630C2×D4C2×D3211yescharacteristic
631C2×D4C2×D3211yescharacteristic
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4C2×D3211yescharacteristic
636SD16—182no—
637SD16—361no—
638SD16—361no—
639M16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—91no—
643C2×C8—91no—
644C2×C8—121no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C22⋊C4—31no—
657C22⋊C4—31no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—61no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—181no—
666C42—181no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—22no—
675C22×C3—41no—
676C22×C3—41no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3—81no—
695C22×C3—81no—
696C22×C3—84no—
697C22×C3—84no—
698C22×C3—88no—
699C22×C3—121no—
700C22×C3—121no—
701C22×C3—121no—
702C22×C3—244no—
703C22×C3#91112yes—
704C22×C3#93212yes—
705C22×C3C2×D3×D411yescharacteristic
706C22×C3C22×#6711yescharacteristic
707C2×D3—21no—
708C2×D3—21no—
709C2×D3—21no—
710C2×D3—41no—
711C2×D3—41no—
712C2×D3—41no—
713C2×D3—84no—
714C3×C4—21no—
715C3×C4—21no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—41no—
719C3×C4—61no—
720C3×C4—61no—
721C3×C4—61no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4—121no—
725C3×C4C2×#23511yescharacteristic
726C3×C4C2×#23711yescharacteristic
727C3×C4#100411yescharacteristic
728C3×C4#100411yescharacteristic
729Dic3—21no—
730Dic3—21no—
731Dic3—21no—
732Dic3—41no—
733Dic3—41no—
734Dic3—41no—
735Dic3—121no—
736Dic3—121no—
737Dic3—121no—
738Dic3—121no—
739Dic3—241no—
740Dic3—241no—
741C32#331011yescharacteristic, complemented, Sylow
742C23—21no—
743C23—21no—
744C23—31no—
745C23—42no—
746C23—42no—
747C23—61no—
748C23—81no—
749C23—122no—
750C23—122no—
751C23—241no—
752C23D3×#6711yescharacteristic
753Q8—181no—
754Q8—181no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—62no—
760D4—61no—
761D4—61no—
762D4—122no—
763D4—122no—
764D4—122no—
765D4—122no—
766D4—241no—
767D4#380412yes—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—31no—
771C2×C4—31no—
772C2×C4—31no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—181no—
781C2×C4—181no—
782C2×C4D3×#6711yescharacteristic
783C2×C4C22×D3211yescharacteristic
784C8—61no—
785C8—61no—
786C8—181no—
787C8—181no—
788C2×C3—22no—
789C2×C3—22no—
790C2×C3—21no—
791C2×C3—21no—
792C2×C3—21no—
793C2×C3—42no—
794C2×C3—42no—
795C2×C3—42no—
796C2×C3—82no—
797C2×C3—82no—
798C2×C3—81no—
799C2×C3—81no—
800C2×C3—121no—
801C2×C3—241no—
802C2×C3#549011yescharacteristic
803C2×C3C2×#91111yescharacteristic
804C2×C3#576211yescharacteristic
805C2×C3C2×#93211yescharacteristic
806C2×C3#580611yescharacteristic
807C2×C3#583611yescharacteristic
808D3—41no—
809D3—81no—
810C22—21no—
811C22—21no—
812C22—22no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—61no—
819C22—61no—
820C22—61no—
821C22—84no—
822C22—121no—
823C22—121no—
824C22—121no—
825C22—244no—
826C22#6393212yes—
827C22C2×D3×#6711yescharacteristic
828C4—21no—
829C4—61no—
830C4—61no—
831C4—61no—
832C4—121no—
833C4—121no—
834C4—121no—
835C4—361no—
836C4—361no—
837C4C2×#380411yescharacteristic
838C4#6433011yescharacteristic
839C3—21no—
840C3#7876211yescharacteristic, complemented
841C3#8348411yescharacteristic, complemented
842C2—22no—
843C2—42no—
844C2—81no—
845C2—121no—
846C2—241no—
847C2#1059510511yescharacteristic
848C2C2×#6393211yescharacteristic
849C2#1059549311yescharacteristic
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#3310
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. #10594849C2semidirect
3. #10592917C2semidirect
4. C2×C3×#832C2semidirect
5. #10591477C2semidirect
6. #10591462C2semidirect
7. #10591459C2semidirect
8. #10591439C2semidirect
9. #10591422C2semidirect
10. #10591421C2semidirect
11. #10591409C2semidirect
12. #10591405C2semidirect
13. #10591175C2semidirect
14. #10591155C2semidirect
15. #10591089C2semidirect
22. C2×#3754C22semidirect
23. #64133C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C22×C3×C3⋊C8C22semidirect
36. #63869C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
41. #63841C22semidirect
42. C2×#3716C22semidirect
43. C2×#3711C22semidirect
45. #63659C22semidirect
46. #63657C22semidirect
49. C3×#832C22semidirect
50. C3×#832C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63554C22semidirect
71. C2×#832D3semidirect
182. C2×C4⋊Dic3C2×D3semidirect
188. C22×C3⋊C8C2×D3semidirect
217. #832C2×D3semidirect
218. #832C2×D3semidirect
741. C32#3310semidirect
840. C3#78762semidirect
841. C3#83484semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105948492
#105929172
C2×C3×#8322
#105914772
#105914622
#105914592
#105914392
#105914222
#105914212
#105914092
#105914052
#105911752
#105911552
#105910892
#834843
#787623