Finite Group Databasebeta

← D3×#4760 #11873362

Subgroups — D3×#4760 #11873362

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic
2D3×#888C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591487C211yesmaximal, characteristic, complemented
7D3×#832C211yesmaximal, characteristic, complemented
8#10591402C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590885C211yesmaximal, characteristic, complemented
11#10590878C211yesmaximal, characteristic, complemented
12D3×C8×Dic3C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590552C211yesmaximal, characteristic, complemented
15#10590548C211yesmaximal, characteristic, complemented
16D3×#486—31nomaximal
17C2×#4760—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6—21no—
23#64149C2211yescharacteristic
24#64097C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#888C2211yescharacteristic, complemented
29#63979—21no—
30#63979—21no—
31#63919C2211yescharacteristic, complemented
32#63918C2211yescharacteristic, complemented
33#63914C2211yescharacteristic
34#63911C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36D3×Dic3⋊C4—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63840—21no—
39#63839—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#102C2211yescharacteristic, complemented
42#63659C2211yescharacteristic, complemented
43#63648C2211yescharacteristic, complemented
44C8×C3⋊Dic3C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×C8×Dic3C2211yescharacteristic, 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#63553C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#940—31no—
62D3×C4⋊Q8—31no—
63D3×#127—31no—
64C2×#888—31no—
65C3×#486—31no—
66C2×C3×#102—31no—
67C2×#832—31no—
68C2×#821—31no—
69C2×C8×Dic3—31no—
70#5088—31no—
71#5070—31no—
72C2×#809—31no—
73D3×#102—31no—
74D3×#102—31no—
75D3×#102—31no—
76D3×#102D311yescharacteristic, complemented
77#4760—31no—
78#4760—31no—
79#4760—31no—
80#4760—31no—
81#4760—31no—
82#4760—31no—
83#4760—31no—
84#4760—31no—
85#4760—31no—
86#4760—31no—
87#4760—31no—
88#4760—61no—
89#4760D311yescharacteristic, direct product factor
90#4694—31no—
91C4×D3×C8—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×Dic6—21no—
109D3×#67—44no—
110D3×#67—44no—
111C2×#627—21no—
112C2×#627—21no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119C2×D3×Dic3D411yescharacteristic
120C2×D3×Dic3D411yescharacteristic
121D3×D12—22no—
122D3×D12—22no—
123D3×Dic6—44no—
124C2×C32×C8C2311yescharacteristic
125C32×C4⋊C4C2311yescharacteristic
126C4⋊(C3⋊Dic3)C2311yescharacteristic
127#3750—21no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×D3×C8—22no—
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141Dic32D411yescharacteristic
142Dic32D411yescharacteristic
143D3×C3⋊C8—22no—
144C2×#486—91noSylow
145C22×C3×D4—31no—
146C22×#67—61no—
147C22×#67—61no—
148C2×D3×Q8—61no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×D3×D4—61no—
152C2×D3×D4C2×D311yescharacteristic
153C22×D12—31no—
154C22×Dic6—61no—
155C22×C3×C8—31no—
156C3×C4⋊Q8—31no—
157C3×#127—31no—
158C2×C3×C4⋊C4—31no—
159#944—61no—
160#940—31no—
161#940—31no—
162#940—31no—
163#940—31no—
164#940—31no—
165#940—61no—
166#940—61no—
167#940—61no—
168#940—61no—
169#940—61no—
170#940C2×D311yescharacteristic
171C2×C4⋊Dic3—31no—
172C2×Dic3⋊C4—61no—
173C2×C4×Dic3—31no—
174C22×C3⋊C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8C2×D311yescharacteristic
177D3×C4⋊C4—31no—
178D3×C4⋊C4—61no—
179D3×C4⋊C4C2×D311yescharacteristic
180#888—31no—
181#888—31no—
182#888—31no—
183#888—31no—
184#888—31no—
185#888—61no—
186#888—61no—
187#888—61no—
188#888—61no—
189#888C2×D311yescharacteristic, complemented
190#874—31no—
191C42×D3—31no—
192#869—31no—
193C3×#102—21no—
194C3×#102—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102C2×D311yescharacteristic, complemented
201C3×#102C2×D311yescharacteristic, complemented
202C3×C4×C8—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic, complemented
211#832C2×D311yescharacteristic, complemented
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic, complemented
220#821C2×D311yescharacteristic, complemented
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—31no—
234#809—61no—
235#809C2×D311yescharacteristic, complemented
236#809C2×D311yescharacteristic, complemented
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3C2×D411yescharacteristic
246C2×D32—42no—
247C2×D32—42no—
248C2×D32—42no—
249C32×D4—21no—
250C32×D4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2411yescharacteristic
253#638—42no—
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3C2×D411yescharacteristic
257C2×C3⋊Dic3C2×D411yescharacteristic
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260#634—42no—
261C3×#67—42no—
262C3×#67—42no—
263C3×#67—42no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—21no—
273C3×C4×D3—42no—
274C3×C4×D3#4112yes—
275C3×C4×D3#4112yes—
276C3×Dic6—42no—
277#627—42no—
278#627—42no—
279#626—42no—
280#626—42no—
281#626—42no—
282#625—42no—
283#625—42no—
284D3×Dic3—42no—
285D3×Dic3D814yes—
286D3×Dic3SD1614yes—
287C32×C8—21no—
288C3⋊(C3⋊C8)—21no—
289C3×C3⋊C8—21no—
290C3×C3⋊C8—21no—
291C2×C4⋊Q8—91no—
292C2×#127—91no—
293#486—31no—
294#486—91no—
295#486—91no—
296#486—91no—
297#486—91no—
298#486—91no—
299#486—91no—
300#486—91no—
301C2×#102—31no—
302C2×#102—91no—
303C2×#102—91no—
304C2×#102—91no—
305C2×C4×C8—91no—
306C24×C3—61no—
307C23×D3—21no—
308C23×D3—61no—
309C23×D3—61no—
310C2×C3×Q8—61no—
311C2×C3×D4—21no—
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—62no—
315C2×C3×D4—62no—
316C2×C3×D4—61no—
317C2×C3×D4—61no—
318C2×C3×D4—61no—
319C2×C3×D4C22×D311yescharacteristic
320C2×C3×D4C22×D311yescharacteristic
321C22×C3×C4—31no—
322C22×C3×C4—61no—
323C2×#67—21no—
324C2×#67—21no—
325C2×#67—21no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—121no—
338C2×#67—121no—
339C2×#67—124no—
340C2×#67—124no—
341C22×Dic3—31no—
342C22×Dic3—31no—
343C22×Dic3—61no—
344D3×Q8—124no—
345D3×D4—22no—
346D3×D4—22no—
347D3×D4—62no—
348D3×D4—62no—
349D3×D4—124no—
350D3×D4—124no—
351C2×D12—31no—
352C2×D12—31no—
353C2×D12—61no—
354C2×D12—62no—
355C2×D12—62no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12C22×D311yescharacteristic
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—21no—
362C2×C4×D3—31no—
363C2×C4×D3—31no—
364C2×C4×D3—61no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—21no—
367C2×Dic6—61no—
368C2×Dic6—61no—
369C2×Dic6—61no—
370C2×Dic6—61no—
371C2×Dic6—61no—
372C2×Dic6—61no—
373C2×Dic6—121no—
374C2×Dic6—124no—
375C2×C3×C8—21no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8—62no—
379C2×C3×C8C22×D311yescharacteristic
380C2×C3×C8C22×D311yescharacteristic
381C3×C4⋊C4—21no—
382C3×C4⋊C4—31no—
383C3×C4⋊C4—31no—
384C3×C4⋊C4—61no—
385C3×C4⋊C4—61no—
386C3×C4⋊C4C22×D311yescharacteristic
387C3×C4⋊C4C22×D311yescharacteristic
388C3×C42—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—121no—
405C4×Dic3—31no—
406C4×Dic3—31no—
407C4×Dic3—31no—
408C4×Dic3—31no—
409C4×Dic3—31no—
410C4×Dic3—31no—
411C4×Dic3—61no—
412C4×Dic3C22×D311yescharacteristic
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—61no—
416C2×C3⋊C8—62no—
417C2×C3⋊C8C22×D311yescharacteristic
418C2×C3⋊C8C22×D311yescharacteristic
419D3×C8—22no—
420D3×C8—62no—
421C22×C32—41no—
422C22×C32—41no—
423C22×C32—41no—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
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—41no—
434C2×C3×D3—84no—
435C2×C3×D3#12412yes—
436C2×C3×D3C2×D812yes—
437C2×C3×D3C2×SD1612yes—
438D32—84no—
439C32×C4—41no—
440C32×C4C2×#4111yescharacteristic
441C32×C4C2×#4111yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3C2×D812yes—
444C3⋊Dic3C2×SD1612yes—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3#12412yes—
448C3×Dic3C2×D812yes—
449C3×Dic3C2×SD1612yes—
450C22×Q8—181no—
451C22×D4—31no—
452C22×D4—91no—
453C22×D4—181no—
454C22×D4—181no—
455C22×C8—31no—
456C22×C8—91no—
457C4⋊Q8—31no—
458C4⋊Q8—91no—
459C4⋊Q8—91no—
460C4⋊Q8—91no—
461C4⋊Q8—181no—
462C4⋊Q8—181no—
463#127—31no—
464#127—91no—
465#127—91no—
466#127—91no—
467#127—181no—
468#127—181no—
469C2×C4⋊C4—31no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—181no—
472C2×C42—91no—
473#102—31no—
474#102—31no—
475#102—31no—
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102D3211yescharacteristic, complemented
489C4×C8—31no—
490C4×C8—91no—
491C4×C8—91no—
492C4×C8—91no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—41no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C23×C3—122no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3—61no—
508C22×D3—61no—
509C22×D3—121no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3D3×D411yescharacteristic
517C3×Q8—122no—
518C3×D4—21no—
519C3×D4—21no—
520C3×D4—21no—
521C3×D4—21no—
522C3×D4—41no—
523C3×D4—41no—
524C3×D4—61no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—61no—
528C3×D4—122no—
529C3×D4—122no—
530C3×D4—122no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—31no—
537C2×C3×C4—32no—
538C2×C3×C4—32no—
539C2×C3×C4—41no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545#67—42no—
546#67—42no—
547#67—42no—
548#67—122no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—122no—
553#67—122no—
554#67—122no—
555#67—122no—
556#67—122no—
557#67—122no—
558#67—122no—
559#67—242no—
560#67—242no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—31no—
564C2×Dic3—31no—
565C2×Dic3—31no—
566C2×Dic3—31no—
567C2×Dic3—34no—
568C2×Dic3—34no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—122no—
575C2×Dic3D3×D411yescharacteristic
576C2×Dic3D3×D411yescharacteristic
577C2×Dic3D3×D411yescharacteristic
578D12—21no—
579D12—21no—
580D12—21no—
581D12—21no—
582D12—61no—
583D12—61no—
584D12—61no—
585D12—61no—
586D12—121no—
587D12—121no—
588D12—122no—
589D12—122no—
590D12—122no—
591C4×D3—34no—
592C4×D3—34no—
593C4×D3—42no—
594C4×D3—122no—
595C4×D3#23512yes—
596C4×D3#23712yes—
597Dic6—42no—
598Dic6—122no—
599Dic6—122no—
600Dic6—122no—
601Dic6—122no—
602Dic6—122no—
603Dic6—122no—
604Dic6—242no—
605C3×C8—21no—
606C3×C8—21no—
607C3×C8—41no—
608C3×C8—61no—
609C3×C8—61no—
610C3⋊C8—21no—
611C3⋊C8—21no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—121no—
615C2×C32—81no—
616C2×C32C2×#12411yescharacteristic
617C2×C32C22×D811yescharacteristic
618C2×C32C22×SD1611yescharacteristic
619C3⋊D3—81no—
620C3×D3—81no—
621C3×D3—81no—
622C3×D3#48614yescomplemented
623C24—61no—
624C24—181no—
625C2×Q8—61no—
626C2×Q8—181no—
627C2×Q8—181no—
628C2×Q8—181no—
629C2×Q8—364no—
630C2×D4—31no—
631C2×D4—31no—
632C2×D4—62no—
633C2×D4—62no—
634C2×D4—61no—
635C2×D4—61no—
636C2×D4—61no—
637C2×D4—91no—
638C2×D4—182no—
639C2×D4—182no—
640C2×D4—181no—
641C2×D4—181no—
642C2×D4—181no—
643C2×D4—181no—
644C2×D4—181no—
645C2×D4—181no—
646C2×D4—181no—
647C2×D4—364no—
648C2×D4—364no—
649C2×D4C2×D3211yescharacteristic
650C22×C4—31no—
651C22×C4—61no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—181no—
655C2×C8—31no—
656C2×C8—31no—
657C2×C8—62no—
658C2×C8—91no—
659C2×C8—182no—
660C2×C8C2×D3211yescharacteristic
661C4⋊C4—31no—
662C4⋊C4—31no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—91no—
666C4⋊C4—181no—
667C4⋊C4—181no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4C2×D3211yescharacteristic
671C42—31no—
672C42—91no—
673C42—91no—
674C42—91no—
675C22×C3—21no—
676C22×C3—32no—
677C22×C3—32no—
678C22×C3—32no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—81no—
686C22×C3—81no—
687C22×C3—81no—
688C22×C3—121no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—121no—
694C22×C3—244no—
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—84no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—121no—
709C2×D3—121no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—241no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3#88512yes—
716C2×D3D3×D812yes—
717C2×D3D3×SD1612yes—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—32no—
721C3×C4—32no—
722C3×C4—32no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—81no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4C2×#23511yescharacteristic
729C3×C4C2×#23711yescharacteristic
730C3×C4D3×#4111yescharacteristic
731C3×C4D3×#4111yescharacteristic
732Dic3—32no—
733Dic3—32no—
734Dic3—32no—
735Dic3—32no—
736Dic3—41no—
737Dic3—41no—
738Dic3—62no—
739Dic3—62no—
740Dic3—121no—
741Dic3—121no—
742Dic3—241no—
743Dic3#88512yes—
744Dic3D3×D812yes—
745Dic3D3×SD1612yes—
746C32C2×#48611yescharacteristic, complemented, Sylow
747C23—21no—
748C23—31no—
749C23—61no—
750C23—61no—
751C23—122no—
752C23—122no—
753C23—122no—
754C23—181no—
755C23—362no—
756C23—362no—
757C23—362no—
758Q8—122no—
759Q8—362no—
760Q8—362no—
761Q8—362no—
762D4—21no—
763D4—21no—
764D4—61no—
765D4—61no—
766D4—61no—
767D4—61no—
768D4—122no—
769D4—122no—
770D4—122no—
771D4—181no—
772D4—181no—
773D4—362no—
774D4—362no—
775D4—362no—
776D4—362no—
777D4—362no—
778D4—362no—
779D4—362no—
780C2×C4—21no—
781C2×C4—31no—
782C2×C4—31no—
783C2×C4—31no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—94no—
789C2×C4—94no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—122no—
793C2×C4—181no—
794C2×C4—362no—
795C2×C4C22×D3211yescharacteristic
796C8—21no—
797C8—61no—
798C8—61no—
799C8—181no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—34no—
804C2×C3—81no—
805C2×C3—81no—
806C2×C3—161no—
807C2×C3—241no—
808C2×C3—241no—
809C2×C3C2×#88511yescharacteristic
810C2×C3D3×#12411yescharacteristic
811C2×C3C2×D3×D811yescharacteristic
812C2×C3C2×D3×D811yescharacteristic
813C2×C3C2×D3×SD1611yescharacteristic
814C2×C3C2×D3×SD1611yescharacteristic
815D3—81no—
816D3—81no—
817D3—241no—
818D3—241no—
819D3—481no—
820D3#476014yesdirect product factor
821C22—32no—
822C22—32no—
823C22—32no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22—361no—
835C22—361no—
836C22—361no—
837C22—724no—
838C22D32×D411yescharacteristic
839C4—32no—
840C4—32no—
841C4—32no—
842C4—41no—
843C4—92no—
844C4—92no—
845C4—121no—
846C4—121no—
847C4—361no—
848C4D3×#23511yescharacteristic
849C4D3×#23711yescharacteristic
850C3—21no—
851C3C2×#476011yescharacteristic, complemented
852C3D3×#48611yescharacteristic, complemented
853C2—34no—
854C2—81no—
855C2—241no—
856C2—241no—
857C2—721no—
858C2D3×#88511yescharacteristic
859C2D32×D811yescharacteristic
860C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenter#102D32
hypocenterC32C2×#486
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×#888C2semidirect
3. #10592459C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4760C2semidirect
6. #10591487C2semidirect
7. D3×#832C2semidirect
8. #10591402C2semidirect
9. D3×#821C2semidirect
10. #10590885C2semidirect
11. #10590878C2semidirect
12. D3×C8×Dic3C2semidirect
13. D3×#809C2semidirect
14. #10590552C2semidirect
15. #10590548C2semidirect
24. #64097C22semidirect
28. C3×#888C22semidirect
31. #63919C22semidirect
32. #63918C22semidirect
41. C32×#102C22semidirect
42. #63659C22semidirect
43. #63648C22semidirect
44. C8×C3⋊Dic3C22semidirect
45. #63636C22semidirect
46. C3×#832C22semidirect
47. C3×#832C22semidirect
48. C3×#821C22semidirect
49. C3×#821C22semidirect
50. C3×C8×Dic3C22semidirect
51. C3×#809C22semidirect
52. C3×#809C22semidirect
53. #63564C22semidirect
54. #63564C22semidirect
55. #63563C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. #63553C22semidirect
60. Dic3×C3⋊C8C22semidirect
76. D3×#102D3semidirect
89. #4760D3direct (N × H)
189. #888C2×D3semidirect
200. C3×#102C2×D3semidirect
201. C3×#102C2×D3semidirect
210. #832C2×D3semidirect
211. #832C2×D3semidirect
219. #821C2×D3semidirect
220. #821C2×D3semidirect
227. C8×Dic3C2×D3semidirect
235. #809C2×D3semidirect
236. #809C2×D3semidirect
488. #102D32semidirect
622. C3×D3#486semidirect
746. C32C2×#486semidirect
820. D3#4760direct (N × H)
851. C3C2×#4760semidirect
852. C3D3×#486semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
D3×#8882
#105924592
C3×D3×#1022
C3×#47602
#105914872
D3×#8322
#105914022
D3×#8212
#105908852
#105908782
D3×C8×Dic32
D3×#8092
#105905522
#105905482
D3×#4863
C2×#47603