Finite Group Databasebeta

← #11887021

Subgroups — #11887021

Order 1152.

1087 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic, complemented
3#10592916C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591449C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10591413C211yesmaximal, characteristic, complemented
10D3×#832C211yesmaximal, characteristic, complemented
11#10591410C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591089C211yesmaximal, characteristic, complemented
16#83482—31nomaximal
17#78757—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3804—21no—
22C2×#3753C2211yescharacteristic
23C2×#3753C2211yescharacteristic, complemented
24#64139C2211yescharacteristic, complemented
25C3×#953—21no—
26C3×#940C2211yescharacteristic
27C3×#939—21no—
28C3×#938C2211yescharacteristic
29C3×#937—21no—
30C3×D4×Dic3C2211yescharacteristic
31C3×#930C2211yescharacteristic
32C3×C4×#67C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
34C22×C3×C3⋊C8C2211yescharacteristic, complemented
35#63966—21no—
36#63918C2211yescharacteristic, complemented
37#63909C2211yescharacteristic, complemented
38#63895—21no—
39#63894C2211yescharacteristic, complemented
40#63890—21no—
41D3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×#3714C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, 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#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic, complemented
63#5555—31no—
64#5507—31no—
65C2×C3×#102—31no—
66#5217—31no—
67#5217—31no—
68#5217—31no—
69#5217—61no—
70C2×#832—31no—
71C2×#832D311yescharacteristic, complemented
72#5115—31no—
73C8×#67—31no—
74#5072—31no—
75#5070—31no—
76#5038—31no—
77#5038—31no—
78#5033—31no—
79#5033—31no—
80C4×#213—31no—
81D4×C3⋊C8—31no—
82#5007—31no—
83#4967—31no—
84#4786—31no—
85#4775—31no—
86#4774—31no—
87#4773—31no—
88D3×#102—31no—
89#4760—31no—
90#4759—31no—
91#4756—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×#638—21no—
101C2×C4⋊(C3⋊D3)C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—21no—
107C2×C3×#67—44no—
108C2×C3×#67D411yescharacteristic
109C22×C3×Dic3—21no—
110C22×C3×Dic3—21no—
111C3×D3×D4—22no—
112C3×D3×D4—41no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×#627—21no—
116C2×#626—21no—
117C2×#624—21no—
118#3804—44no—
119C2×D3×Dic3—21no—
120#3753—22no—
121#3753—41no—
122#3752—21no—
123C4⋊(C3⋊Dic3)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#217—21no—
127C3×#217—21no—
128C3×#217D411yescharacteristic
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4D411yescharacteristic
131C3×C4⋊Dic3—21no—
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8—41no—
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140Dic3⋊Dic3—21no—
141Dic3⋊Dic3—21no—
142#3722—21no—
143#3722—21no—
144#3714—41no—
145D3×C3⋊C8—41no—
146#3294—91noSylow
147C22×C3×D4—21no—
148C22×C3×D4—31no—
149C22×C3×D4—61no—
150C22×C3×D4C2×D311yescharacteristic
151C22×C3×D4C2×D311yescharacteristic
152C22×#67—21no—
153C2×#237—61no—
154C2×D3×D4C2×D311yescharacteristic
155C2×#235—61no—
156C22×C3×C8—31no—
157C3×#127—31no—
158C3×#121—31no—
159C3×#121—31no—
160C3×#121—61no—
161C3×#120—61no—
162C3×#120—61no—
163C3×C4×D4—31no—
164C3×C4×D4—31no—
165C2×C3×C4⋊C4—31no—
166#953—21no—
167#940C2×D311yescharacteristic
168#939—21no—
169#938C2×D311yescharacteristic
170#937—21no—
171D4×Dic3C2×D311yescharacteristic
172C2×#213—31no—
173C2×#213—31no—
174C2×#213—31no—
175C2×#213—31no—
176C2×#213—31no—
177C2×#213—61no—
178C2×#213—61no—
179#930—31no—
180#930—31no—
181#930—31no—
182#930—61no—
183#930C2×D311yescharacteristic
184#929—61no—
185C4×#67C2×D311yescharacteristic
186C2×C4⋊Dic3—31no—
187C2×C4⋊Dic3C2×D311yescharacteristic, complemented
188C22×C3⋊C8—31no—
189C22×C3⋊C8C2×D311yescharacteristic, complemented
190C2×D24—31no—
191C2×D3×C8—31no—
192#897—61no—
193#896—61no—
194#895—31no—
195#894—61no—
196#893—31no—
197D3×C4⋊C4—31no—
198#888—31no—
199#886—61no—
200#886—61no—
201C4×D12—31no—
202#869—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—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
217#832C2×D311yescharacteristic
218#832C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic, complemented
220#830—31no—
221#830—31no—
222#830—31no—
223#830—61no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227#818—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238C4⋊(C3⋊C8)—31no—
239C4×C3⋊C8—31no—
240C23×C32—21no—
241C23×C32—21no—
242C23×C32—42no—
243C23×C32—42no—
244C23×C32—81no—
245C23×C32C2×D411yescharacteristic
246C22×C3⋊D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3—81no—
251C22×C3×D3C2×D411yescharacteristic
252C32×D4—21no—
253C32×D4—21no—
254C32×D4—21no—
255C32×D4—42no—
256C32×D4#4112yescomplemented
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261#638—42no—
262C2×C3⋊Dic3—21no—
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—42no—
268C3×#67—42no—
269C3×#67—81no—
270C3×#67D814yescomplemented
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—42no—
275C2×C3×Dic3—42no—
276C2×C3×Dic3C2×D411yescharacteristic
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C3×D12—21no—
280C3×D12—21no—
281C3×C4×D3—21no—
282C3×C4×D3—21no—
283#627—42no—
284#626—42no—
285#624—42no—
286D3×Dic3—42no—
287C3⋊(C3⋊C8)—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291#547—91no—
292D42—31no—
293#486—91no—
294#480—91no—
295#480—91no—
296#474—91no—
297#466—91no—
298#466—91no—
299#459—91no—
300#447—91no—
301#447—91no—
302C4×D8—91no—
303C8×D4—91no—
304C2×#102—31no—
305C2×#102—91no—
306C24×C3—21no—
307C24×C3—21no—
308C24×C3—41no—
309C24×C3—61no—
310C23×D3—21no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—41no—
320C2×C3×D4—42no—
321C2×C3×D4—41no—
322C2×C3×D4—41no—
323C2×C3×D4—42no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—61no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C2×C3×D4—124no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—21no—
337C22×C3×C4—31no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—44no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—121no—
352C2×#67#6711yescharacteristic
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—61no—
356#237—124no—
357D3×D4—22no—
358D3×D4—41no—
359#235—124no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—61no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3C22×D311yescharacteristic
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×C3×C8—31no—
372C2×C3×C8—31no—
373C2×C3×C8—121no—
374C3×C4⋊C4—31no—
375C3×C4⋊C4—31no—
376C3×C4⋊C4—31no—
377C3×C4⋊C4—31no—
378C3×C4⋊C4—61no—
379C3×C22⋊C4—31no—
380C3×C22⋊C4—31no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384C3×C42—31no—
385#217—21no—
386#217—21no—
387#217#6711yescharacteristic
388#213—62no—
389#213—62no—
390#213—122no—
391#213—121no—
392#213—121no—
393#213—121no—
394#213—122no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—61no—
397(C2×D3)⋊C4—61no—
398(C2×D3)⋊C4—61no—
399(C2×D3)⋊C4—61no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402(C2×D3)⋊C4—121no—
403(C2×D3)⋊C4#6711yescharacteristic
404C4⋊Dic3—21no—
405C4⋊Dic3—31no—
406C4⋊Dic3—31no—
407C4⋊Dic3—61no—
408C4⋊Dic3—61no—
409C4⋊Dic3—61no—
410C4⋊Dic3C22×D311yescharacteristic
411C4⋊Dic3C22×D311yescharacteristic
412C4⋊Dic3C22×D311yescharacteristic
413Dic3⋊C4—61no—
414Dic3⋊C4—61no—
415Dic3⋊C4#6711yescharacteristic
416C4×Dic3C22×D311yescharacteristic
417C2×C3⋊C8—31no—
418C2×C3⋊C8—31no—
419C2×C3⋊C8—31no—
420C2×C3⋊C8—31no—
421C2×C3⋊C8—41no—
422C2×C3⋊C8—61no—
423C2×C3⋊C8—61no—
424C2×C3⋊C8—121no—
425C2×C3⋊C8C22×D311yescharacteristic
426C2×C3⋊C8C22×D311yescharacteristic
427D24—121no—
428D3×C8—121no—
429C22×C32—21no—
430C22×C32—21no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—84no—
438C22×C32C2×D812yes—
439C22×C32C22×D411yescharacteristic
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3⋊D3—41no—
443C2×C3×D3—21no—
444C2×C3×D3—21no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—84no—
449C2×C3×D3C2×D812yes—
450C32×C4—21no—
451C32×C4C2×#4111yescharacteristic
452C32×C4H(5,𝔽2)11yescharacteristic
453C3⋊Dic3—41no—
454C3×Dic3—21no—
455C3×Dic3—21no—
456C3×Dic3—41no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3C2×D812yes—
460C2×#41—181no—
461C22×D4—31no—
462C22×D4—61no—
463C22×D4D3211yescharacteristic
464C2×D8—91no—
465C2×D8—91no—
466C2×D8—91no—
467C22×C8—31no—
468C22×C8—91no—
469C4⋊Q8—91no—
470#127—31no—
471#123—181no—
472#123—181no—
473C22⋊Q8—181no—
474#121—31no—
475#121—31no—
476#121—61no—
477#121—91no—
478#121—91no—
479#120—61no—
480#120—61no—
481C4×D4—31no—
482C4×D4—31no—
483C4×D4—91no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486#107—91no—
487#107—91no—
488#107—91no—
489C4⋊C8—91no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—31no—
494#102—91no—
495#102—91no—
496#102—91no—
497#102—91no—
498#102—91no—
499#102—91no—
500C22⋊C8—91no—
501C22⋊C8—91no—
502C4×C8—91no—
503C23×C3—21no—
504C23×C3—21no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—31no—
509C23×C3—41no—
510C23×C3—41no—
511C23×C3—42no—
512C23×C3—42no—
513C23×C3—44no—
514C23×C3—42no—
515C23×C3—42no—
516C23×C3—61no—
517C23×C3—82no—
518C23×C3—81no—
519C23×C3—81no—
520C23×C3—82no—
521C23×C3—122no—
522C23×C3—122no—
523C23×C3—241no—
524C23×C3D3×D411yescharacteristic
525C23×C3C2×#6711yescharacteristic
526C22×D3—21no—
527C22×D3—42no—
528C22×D3—42no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—81no—
532C22×D3—121no—
533C22×D3C2×#6711yescharacteristic
534C3×D4—22no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—21no—
540C3×D4—21no—
541C3×D4—22no—
542C3×D4—34no—
543C3×D4—41no—
544C3×D4—41no—
545C3×D4—42no—
546C3×D4—42no—
547C3×D4—44no—
548C3×D4—61no—
549C3×D4—61no—
550C3×D4—122no—
551C3×D4—122no—
552C3×D4—122no—
553C3×D4—122no—
554C3×D4—241no—
555C3×D4#23512yescomplemented
556C3×D4#23712yescomplemented
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—31no—
566C2×C3×C4—41no—
567C2×C3×C4—41no—
568C2×C3×C4—61no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—122no—
574C2×C3×C4—122no—
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C2×#6711yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578C2×C3×C4C23×D311yescharacteristic
579#67—42no—
580#67—42no—
581#67—42no—
582#67—42no—
583#67—81no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—242no—
588#67#21314yescomplemented
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—21no—
592C2×Dic3—42no—
593C2×Dic3—42no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3—122no—
598C2×Dic3C2×#6711yescharacteristic
599C2×Dic3C2×#6711yescharacteristic
600C2×Dic3C2×#6711yescharacteristic
601D12—21no—
602D12—21no—
603D12—61no—
604D12—61no—
605D12—61no—
606D12—61no—
607D12—121no—
608D12—121no—
609D12—122no—
610C4×D3—21no—
611C4×D3—21no—
612C4×D3—122no—
613C4×D3—122no—
614C4×D3—122no—
615Dic6—122no—
616Dic6—122no—
617C3×C8—61no—
618C3×C8—61no—
619C3⋊C8—21no—
620C3⋊C8—21no—
621C3⋊C8—61no—
622C3⋊C8—61no—
623C3⋊C8—61no—
624C3⋊C8—61no—
625C3⋊C8—121no—
626C3⋊C8—121no—
627C2×C32—22no—
628C2×C32—42no—
629C2×C32—81no—
630C2×C32#54611yescharacteristic
631C2×C32C22×D811yescharacteristic
632C2×C32#57711yescharacteristic
633C3⋊D3—81no—
634C3×D3—22no—
635C3×D3—81no—
636C24—21no—
637C24—61no—
638#41—364no—
639C2×Q8—181no—
640C2×D4—22no—
641C2×D4—21no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—41no—
645C2×D4—61no—
646C2×D4—61no—
647C2×D4—61no—
648C2×D4—62no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—91no—
652C2×D4—121no—
653C2×D4—124no—
654C2×D4—181no—
655C2×D4—181no—
656C2×D4C2×D3211yescharacteristic
657C2×D4C2×D3211yescharacteristic
658C22×C4—31no—
659C22×C4—61no—
660C22×C4—61no—
661C22×C4—181no—
662C22×C4—181no—
663C22×C4C2×D3211yescharacteristic
664D8—182no—
665D8—361no—
666D8—361no—
667C2×C8—31no—
668C2×C8—31no—
669C2×C8—91no—
670C2×C8—91no—
671C2×C8—121no—
672C2×C8—361no—
673C4⋊C4—31no—
674C4⋊C4—31no—
675C4⋊C4—31no—
676C4⋊C4—31no—
677C4⋊C4—61no—
678C4⋊C4—91no—
679C4⋊C4—181no—
680C4⋊C4—181no—
681C22⋊C4—31no—
682C22⋊C4—31no—
683C22⋊C4—61no—
684C22⋊C4—61no—
685C22⋊C4—61no—
686C22⋊C4—181no—
687C22⋊C4—181no—
688C22⋊C4—181no—
689C42—31no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—22no—
698C22×C3—32no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—42no—
702C22×C3—42no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—41no—
709C22×C3—41no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—61no—
714C22×C3—61no—
715C22×C3—81no—
716C22×C3—81no—
717C22×C3—81no—
718C22×C3—81no—
719C22×C3—84no—
720C22×C3—84no—
721C22×C3—88no—
722C22×C3—121no—
723C22×C3—121no—
724C22×C3—121no—
725C22×C3—244no—
726C22×C3D3×D812yes—
727C22×C3C2×#21312yes—
728C22×C3C2×D3×D411yescharacteristic
729C22×C3C22×#6711yescharacteristic
730C2×D3—21no—
731C2×D3—21no—
732C2×D3—41no—
733C2×D3—41no—
734C2×D3—41no—
735C2×D3—84no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—241no—
743C2×D3—241no—
744C2×D3—241no—
745C2×D3C2×#21312yes—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—32no—
751C3×C4—41no—
752C3×C4—61no—
753C3×C4—61no—
754C3×C4—121no—
755C3×C4—121no—
756C3×C4—121no—
757C3×C4C2×#23511yescharacteristic
758C3×C4C2×#23711yescharacteristic
759C3×C4#100411yescharacteristic
760C3×C4#100411yescharacteristic
761Dic3—21no—
762Dic3—21no—
763Dic3—41no—
764Dic3—41no—
765Dic3—41no—
766Dic3—121no—
767Dic3—121no—
768Dic3—241no—
769Dic3C2×#21312yes—
770C32#329411yescharacteristic, complemented, Sylow
771C23—21no—
772C23—21no—
773C23—31no—
774C23—42no—
775C23—42no—
776C23—61no—
777C23—81no—
778C23—122no—
779C23—122no—
780C23—181no—
781C23—241no—
782C23D3×#6711yescharacteristic
783Q8—362no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—34no—
788D4—42no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—122no—
794D4—122no—
795D4—181no—
796D4—181no—
797D4—241no—
798D4—362no—
799D4—362no—
800D4#380412yescomplemented
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—31no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—61no—
807C2×C4—61no—
808C2×C4—61no—
809C2×C4—61no—
810C2×C4—61no—
811C2×C4—122no—
812C2×C4—122no—
813C2×C4—181no—
814C2×C4—362no—
815C2×C4—362no—
816C2×C4D3×#6711yescharacteristic
817C2×C4C22×D3211yescharacteristic
818C8—61no—
819C8—61no—
820C8—181no—
821C8—181no—
822C2×C3—22no—
823C2×C3—22no—
824C2×C3—21no—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—42no—
828C2×C3—42no—
829C2×C3—42no—
830C2×C3—62no—
831C2×C3—82no—
832C2×C3—82no—
833C2×C3—81no—
834C2×C3—81no—
835C2×C3—241no—
836C2×C3#549011yescharacteristic
837C2×C3C2×D3×D811yescharacteristic
838C2×C3#576211yescharacteristic
839C2×C3C22×#21311yescharacteristic
840C2×C3#580611yescharacteristic
841C2×C3#583611yescharacteristic
842D3—22no—
843D3—81no—
844D3—241no—
845D3—241no—
846D3—481no—
847C22—21no—
848C22—21no—
849C22—22no—
850C22—32no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—61no—
857C22—61no—
858C22—84no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—244no—
863C22—361no—
864C22—361no—
865C22—361no—
866C22D3×#21312yes—
867C22C2×D3×#6711yescharacteristic
868C4—21no—
869C4—32no—
870C4—61no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4—121no—
875C4—361no—
876C4C2×#380411yescharacteristic
877C4#6433011yescharacteristic
878C3—21no—
879C3#7875711yescharacteristic, complemented
880C3#8348211yescharacteristic, complemented
881C2—22no—
882C2—42no—
883C2—62no—
884C2—81no—
885C2—241no—
886C2—721no—
887C2C2×D3×#21311yescharacteristic
888C2#1059510511yescharacteristic
889C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3294
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
1. C3×D4×#67C2semidirect
2. #10594906C2semidirect
3. #10592916C2semidirect
4. C2×C3×#832C2semidirect
5. #10591487C2semidirect
6. #10591449C2semidirect
7. #10591448C2semidirect
8. #10591429C2semidirect
9. #10591413C2semidirect
10. D3×#832C2semidirect
11. #10591410C2semidirect
12. #10591400C2semidirect
13. #10591164C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591089C2semidirect
23. C2×#3753C22semidirect
24. #64139C22semidirect
33. C2×C3×C4⋊Dic3C22semidirect
34. C22×C3×C3⋊C8C22semidirect
36. #63918C22semidirect
37. #63909C22semidirect
39. #63894C22semidirect
41. D3×C4⋊Dic3C22semidirect
42. C2×#3714C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63659C22semidirect
46. #63657C22semidirect
49. C3×#832C22semidirect
50. C3×#832C22semidirect
51. #63576C22semidirect
52. #63576C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
62. D4×#67D3semidirect
71. C2×#832D3semidirect
187. C2×C4⋊Dic3C2×D3semidirect
189. C22×C3⋊C8C2×D3semidirect
218. #832C2×D3semidirect
219. #832C2×D3semidirect
256. C32×D4#41semidirect
270. C3×#67D8semidirect
555. C3×D4#235semidirect
556. C3×D4#237semidirect
588. #67#213semidirect
770. C32#3294semidirect
800. D4#3804semidirect
879. C3#78757semidirect
880. C3#83482semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105949062
#105929162
C2×C3×#8322
#105914872
#105914492
#105914482
#105914292
#105914132
D3×#8322
#105914102
#105914002
#105911642
C3⋊C8×#672
#105910892
#834823
#787573