Finite Group Databasebeta

← D3×#4764 #11873575

Subgroups — D3×#4764 #11873575

Order 1152.

1031 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
1D3×#940C211yesmaximal, characteristic
2D3×#890C211yesmaximal, characteristic, complemented
3#10592463C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4764C211yesmaximal, characteristic, complemented
6#10591480C211yesmaximal, characteristic, complemented
7#10591477C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590888C211yesmaximal, characteristic, complemented
11#10590882C211yesmaximal, characteristic, complemented
12D3×#815C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590554C211yesmaximal, characteristic, complemented
15#10590550C211yesmaximal, characteristic, complemented
16D3×#490—31nomaximal
17C2×#4764—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22#64149C2211yescharacteristic
23#64099C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63979—21no—
29#63979—21no—
30#63914C2211yescharacteristic
31#63911C2211yescharacteristic
32D3×C4⋊Dic3—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×Dic3⋊C4—21no—
35C4×D3×Dic3C2211yescharacteristic
36#63872C2211yescharacteristic, complemented
37#63869C2211yescharacteristic, complemented
38#63846—21no—
39#63845—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#102C2211yescharacteristic, complemented
42#63659C2211yescharacteristic, complemented
43#63648C2211yescharacteristic, complemented
44#63642C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×#815C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic, complemented
53#63564C2211yescharacteristic, complemented
54#63564C2211yescharacteristic, complemented
55#63563C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59#63555C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C2×#940—31no—
62D3×#127—31no—
63D3×#125—31no—
64C2×#890—31no—
65C3×#490—31no—
66C2×C3×#102—31no—
67C2×#832—31no—
68C2×#821—31no—
69C2×#815—31no—
70#5071—31no—
71#5067—31no—
72C2×#809—31no—
73D3×#102—31no—
74D3×#102—31no—
75D3×#102—31no—
76D3×#102D311yescharacteristic, complemented
77#4764—31no—
78#4764—31no—
79#4764—31no—
80#4764—31no—
81#4764—31no—
82#4764—31no—
83#4764—31no—
84#4764—31no—
85#4764—31no—
86#4764—31no—
87#4764—31no—
88#4764—61no—
89#4764D311yescharacteristic, direct product factor
90#4713—31no—
91D3×#97—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107D3×#67—44no—
108D3×#67—44no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#625—21no—
113C2×#625—21no—
114C2×D3×Dic3—21no—
115C2×D3×Dic3D411yescharacteristic
116C2×D3×Dic3D411yescharacteristic
117D3×D12—22no—
118D3×D12—22no—
119C2×C32×C8C2311yescharacteristic
120C32×C4⋊C4C2311yescharacteristic
121C4⋊(C3⋊Dic3)—21no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—22no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic32D411yescharacteristic
141Dic32D411yescharacteristic
142D3×C3⋊C8—22no—
143C2×#490—91noSylow
144C22×C3×D4—31no—
145C22×#67—61no—
146C22×#67—61no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×D3×D4—61no—
150C2×D3×D4C2×D311yescharacteristic
151C22×D12—31no—
152C22×C3×C8—31no—
153C3×#127—31no—
154C3×#125—31no—
155C2×C3×C4⋊C4—31no—
156#940—31no—
157#940—31no—
158#940—31no—
159#940—31no—
160#940—31no—
161#940—61no—
162#940—61no—
163#940—61no—
164#940—61no—
165#940—61no—
166#940C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—61no—
169C2×Dic3⋊C4—61no—
170C2×C4×Dic3—31no—
171C22×C3⋊C8—31no—
172C2×D3×C8—31no—
173C2×D3×C8C2×D311yescharacteristic
174D3×C4⋊C4—31no—
175D3×C4⋊C4—61no—
176D3×C4⋊C4—61no—
177D3×C4⋊C4C2×D311yescharacteristic
178#890—31no—
179#890—31no—
180#890—31no—
181#890—31no—
182#890—31no—
183#890—61no—
184#890—61no—
185#890—61no—
186#890C2×D311yescharacteristic, complemented
187#889—61no—
188#889—61no—
189#874—31no—
190C42×D3—31no—
191#870—31no—
192C3×#102—21no—
193C3×#102—31no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102C2×D311yescharacteristic, complemented
200C3×#102C2×D311yescharacteristic, complemented
201C3×#97—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#832C2×D311yescharacteristic, complemented
210#832C2×D311yescharacteristic, complemented
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic, complemented
219#821C2×D311yescharacteristic, complemented
220#815—31no—
221#815—31no—
222#815—31no—
223#815—31no—
224#815—31no—
225#815—61no—
226#815C2×D311yescharacteristic, complemented
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic, complemented
235#809C2×D311yescharacteristic, complemented
236#803—31no—
237C23×C32—21no—
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3C2×D411yescharacteristic
245C2×D32—42no—
246C2×D32—42no—
247C2×D32—42no—
248C32×D4—21no—
249C32×D4—21no—
250C2×C32×C4—21no—
251C2×C32×C4C2411yescharacteristic
252#638—42no—
253#638—42no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C3×#67—42no—
260C3×#67—42no—
261C3×#67—42no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—42no—
272C3×C4×D3#4112yes—
273C3×C4×D3#4112yes—
274#626—42no—
275#626—42no—
276#626—42no—
277#625—42no—
278#625—42no—
279D3×Dic3—22no—
280D3×Dic3—22no—
281D3×Dic3—42no—
282C32×C8—21no—
283C3⋊(C3⋊C8)—21no—
284C3×C3⋊C8—21no—
285C3×C3⋊C8—21no—
286C2×#127—91no—
287C2×#125—91no—
288#490—31no—
289#490—91no—
290#490—91no—
291#490—91no—
292#490—91no—
293#490—91no—
294#490—91no—
295#490—91no—
296C2×#102—31no—
297C2×#102—91no—
298C2×#102—91no—
299C2×#102—91no—
300C2×#97—91no—
301C24×C3—61no—
302C23×D3—21no—
303C23×D3—61no—
304C23×D3—61no—
305C2×C3×D4—21no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—62no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4C22×D311yescharacteristic
314C2×C3×D4C22×D311yescharacteristic
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C2×#67—21no—
318C2×#67—21no—
319C2×#67—21no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—61no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—121no—
332C2×#67—121no—
333C2×#67—124no—
334C2×#67—124no—
335C22×Dic3—31no—
336C22×Dic3—31no—
337C22×Dic3—61no—
338D3×D4—22no—
339D3×D4—22no—
340D3×D4—62no—
341D3×D4—62no—
342D3×D4—124no—
343D3×D4—124no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—61no—
347C2×D12—62no—
348C2×D12—62no—
349C2×D12—61no—
350C2×D12—61no—
351C2×D12—61no—
352C2×D12C22×D311yescharacteristic
353C2×D12C22×D311yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—31no—
356C2×C4×D3—31no—
357C2×C4×D3—61no—
358C2×C4×D3C22×D311yescharacteristic
359C2×C3×C8—21no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—62no—
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C3×C4⋊C4—21no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4C22×D311yescharacteristic
372C3×C4⋊C4C22×D311yescharacteristic
373C3×C42—31no—
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—121no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—31no—
401C4×Dic3—31no—
402C4×Dic3—31no—
403C4×Dic3—31no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—62no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D3×C8—22no—
413D3×C8—62no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32—41no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#12412yes—
429C2×C3×D3AGL(1,ℤ/8)12yes—
430C2×C3×D3AGL(1,ℤ/8)12yes—
431D32—84no—
432C32×C4—41no—
433C32×C4C2×#4111yescharacteristic
434C32×C4C2×#4111yescharacteristic
435C3⋊Dic3—21no—
436C3⋊Dic3—21no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3#12412yes—
443C22×D4—31no—
444C22×D4—91no—
445C22×D4—181no—
446C22×D4—181no—
447C22×C8—31no—
448C22×C8—91no—
449#127—31no—
450#127—91no—
451#127—91no—
452#127—91no—
453#127—181no—
454#127—181no—
455#125—31no—
456#125—91no—
457#125—91no—
458#125—91no—
459#125—181no—
460#125—181no—
461C2×C4⋊C4—31no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—181no—
464C2×C4⋊C4—181no—
465C2×C42—91no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102D3211yescharacteristic, complemented
482#97—31no—
483#97—91no—
484#97—91no—
485#97—91no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—41no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—122no—
493C23×C3—122no—
494C23×C3—122no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—42no—
498C22×D3—42no—
499C22×D3—42no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—121no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—122no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3D3×D411yescharacteristic
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—41no—
515C3×D4—41no—
516C3×D4—61no—
517C3×D4—61no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—122no—
521C3×D4—122no—
522C3×D4—122no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—31no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—41no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—122no—
535C2×C3×C4C23×D311yescharacteristic
536C2×C3×C4C23×D311yescharacteristic
537#67—42no—
538#67—42no—
539#67—42no—
540#67—122no—
541#67—122no—
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—242no—
552#67—242no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—31no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—62no—
562C2×Dic3—62no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—121no—
566C2×Dic3—122no—
567C2×Dic3D3×D411yescharacteristic
568C2×Dic3D3×D411yescharacteristic
569C2×Dic3D3×D411yescharacteristic
570D12—21no—
571D12—21no—
572D12—21no—
573D12—21no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—121no—
579D12—121no—
580D12—122no—
581D12—122no—
582D12—122no—
583C4×D3—42no—
584C4×D3—62no—
585C4×D3—62no—
586C4×D3—122no—
587C4×D3#23512yes—
588C4×D3#23712yes—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8—61no—
597C3⋊C8—61no—
598C3⋊C8—121no—
599C2×C32—81no—
600C2×C32C2×#12411yescharacteristic
601C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
602C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
603C3⋊D3—81no—
604C3×D3—81no—
605C3×D3—81no—
606C3×D3#49014yescomplemented
607C24—61no—
608C24—181no—
609C2×D4—31no—
610C2×D4—31no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—61no—
616C2×D4—91no—
617C2×D4—182no—
618C2×D4—182no—
619C2×D4—181no—
620C2×D4—181no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—364no—
627C2×D4—364no—
628C2×D4C2×D3211yescharacteristic
629C22×C4—31no—
630C22×C4—61no—
631C22×C4—91no—
632C22×C4—91no—
633C22×C4—181no—
634C2×C8—31no—
635C2×C8—31no—
636C2×C8—62no—
637C2×C8—91no—
638C2×C8—182no—
639C2×C8C2×D3211yescharacteristic
640C4⋊C4—31no—
641C4⋊C4—31no—
642C4⋊C4—61no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—91no—
646C4⋊C4—181no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4C2×D3211yescharacteristic
654C42—31no—
655C42—91no—
656C42—91no—
657C42—91no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—32no—
661C22×C3—32no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—81no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—244no—
678C22×C3C2×D3×D411yescharacteristic
679C22×C3C2×D3×D411yescharacteristic
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3—84no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3#88512yes—
699C2×D3#91112yes—
700C2×D3#91412yes—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—32no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—81no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4C2×#23511yescharacteristic
712C3×C4C2×#23711yescharacteristic
713C3×C4D3×#4111yescharacteristic
714C3×C4D3×#4111yescharacteristic
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—241no—
728Dic3#88512yes—
729C32C2×#49011yescharacteristic, complemented, Sylow
730C23—21no—
731C23—31no—
732C23—61no—
733C23—61no—
734C23—122no—
735C23—122no—
736C23—122no—
737C23—181no—
738C23—362no—
739C23—362no—
740C23—362no—
741D4—21no—
742D4—21no—
743D4—61no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
748D4—122no—
749D4—122no—
750D4—181no—
751D4—181no—
752D4—362no—
753D4—362no—
754D4—362no—
755D4—362no—
756D4—362no—
757D4—362no—
758D4—362no—
759C2×C4—21no—
760C2×C4—31no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—122no—
770C2×C4—182no—
771C2×C4—182no—
772C2×C4—181no—
773C2×C4—362no—
774C2×C4C22×D3211yescharacteristic
775C8—21no—
776C8—61no—
777C8—61no—
778C8—181no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—21no—
782C2×C3—34no—
783C2×C3—81no—
784C2×C3—81no—
785C2×C3—161no—
786C2×C3—241no—
787C2×C3—241no—
788C2×C3C2×#88511yescharacteristic
789C2×C3D3×#12411yescharacteristic
790C2×C3C2×#91111yescharacteristic
791C2×C3C2×#91411yescharacteristic
792C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
793C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
794D3—81no—
795D3—81no—
796D3—241no—
797D3—241no—
798D3—481no—
799D3#476414yesdirect product factor
800C22—32no—
801C22—32no—
802C22—32no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—121no—
807C22—121no—
808C22—121no—
809C22—121no—
810C22—121no—
811C22—121no—
812C22—244no—
813C22—361no—
814C22—361no—
815C22—361no—
816C22—724no—
817C22D32×D411yescharacteristic
818C4—32no—
819C4—41no—
820C4—61no—
821C4—61no—
822C4—121no—
823C4—121no—
824C4—181no—
825C4—181no—
826C4—361no—
827C4D3×#23511yescharacteristic
828C4D3×#23711yescharacteristic
829C3—21no—
830C3C2×#476411yescharacteristic, complemented
831C3D3×#49011yescharacteristic, complemented
832C2—34no—
833C2—81no—
834C2—241no—
835C2—241no—
836C2—721no—
837C2D3×#88511yescharacteristic
838C2D3×#91111yescharacteristic
839C2D3×#91411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenter#102D32
hypocenterC32C2×#490
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. D3×#890C2semidirect
3. #10592463C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4764C2semidirect
6. #10591480C2semidirect
7. #10591477C2semidirect
8. D3×#832C2semidirect
9. D3×#821C2semidirect
10. #10590888C2semidirect
11. #10590882C2semidirect
12. D3×#815C2semidirect
13. D3×#809C2semidirect
14. #10590554C2semidirect
15. #10590550C2semidirect
23. #64099C22semidirect
27. C3×#890C22semidirect
36. #63872C22semidirect
37. #63869C22semidirect
41. C32×#102C22semidirect
42. #63659C22semidirect
43. #63648C22semidirect
44. #63642C22semidirect
45. #63636C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
50. C3×#815C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63555C22semidirect
60. #63554C22semidirect
76. D3×#102D3semidirect
89. #4764D3direct (N × H)
186. #890C2×D3semidirect
199. C3×#102C2×D3semidirect
200. C3×#102C2×D3semidirect
209. #832C2×D3semidirect
210. #832C2×D3semidirect
218. #821C2×D3semidirect
219. #821C2×D3semidirect
226. #815C2×D3semidirect
234. #809C2×D3semidirect
235. #809C2×D3semidirect
481. #102D32semidirect
606. C3×D3#490semidirect
729. C32C2×#490semidirect
799. D3#4764direct (N × H)
830. C3C2×#4764semidirect
831. C3D3×#490semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
D3×#8902
#105924632
C3×D3×#1022
C3×#47642
#105914802
#105914772
D3×#8322
D3×#8212
#105908882
#105908822
D3×#8152
D3×#8092
#105905542
#105905502
D3×#4903
C2×#47643