Finite Group Databasebeta

← D3×#4794 #11873536

Subgroups — D3×#4794 #11873536

Order 1152.

922 conjugacy classes of subgroups.

The subgroup lattice has 781 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#947C211yesmaximal, characteristic
2D3×#888C211yesmaximal, characteristic, complemented
3#10592493C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4794C211yesmaximal, characteristic, complemented
6#10591632C211yesmaximal, characteristic, complemented
7#10591624C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic
10#10590893C211yesmaximal, characteristic, complemented
11#10590866C211yesmaximal, characteristic, complemented
12D3×#815C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic
14#10590541C211yesmaximal, characteristic, complemented
15#10590535C211yesmaximal, characteristic, complemented
16D3×#489—31nomaximal
17C2×#4794—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×D3×Dic6—21no—
21#64156C2211yescharacteristic
22#64097C2211yescharacteristic, complemented
23C3×#947C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#888C2211yescharacteristic, complemented
27D3×(C2×D3)⋊C4—21no—
28D3×(C2×D3)⋊C4—21no—
29#63919C2211yescharacteristic, complemented
30#63918C2211yescharacteristic, complemented
31#63907—21no—
32#63907—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×Dic3⋊C4—21no—
35C4×D3×Dic3C2211yescharacteristic
36#63864C2211yescharacteristic
37#63863C2211yescharacteristic
38#63840—21no—
39#63839—21no—
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63648C2211yescharacteristic
44#63642C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#816C2211yescharacteristic, complemented
50C3×#815C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53#63566C2211yescharacteristic, complemented
54#63565C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59#63555C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C2×#947—31no—
62D3×C4⋊Q8—31no—
63D3×#124—31no—
64C2×#888—31no—
65C3×#489—31no—
66C2×C3×#103—31no—
67C2×#835—31no—
68C2×#821—31no—
69C2×#815—31no—
70#5089—31no—
71#5055—31no—
72C2×#809—31no—
73D3×#103—31no—
74D3×#103D311yescharacteristic, complemented
75#4794—31no—
76#4794—31no—
77#4794—31no—
78#4794—31no—
79#4794—31no—
80#4794—31no—
81#4794—31no—
82#4794—31no—
83#4794—31no—
84#4794—61no—
85#4794D311yescharacteristic, direct product factor
86D3×#102—31no—
87D3×#102—31no—
88#4765—31no—
89#4765—31no—
90#4714—31no—
91D3×#97—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634—21no—
96C3×D3×Q8—22no—
97C3×D3×Q8—22no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111D3×D12—22no—
112D3×D12—22no—
113D3×Dic6—44no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—22no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141D3×C3⋊C8—22no—
142C2×#489—91noSylow
143C22×C3×Q8—31no—
144C2×D3×Q8—61no—
145C2×D3×Q8C2×D311yescharacteristic
146C2×D3×D4—31no—
147C22×D12—31no—
148C22×Dic6—61no—
149C22×C3×C8—31no—
150C3×C4⋊Q8—31no—
151C3×#124—31no—
152C2×C3×C4⋊C4—31no—
153#947—31no—
154#947—31no—
155#947—31no—
156#947—31no—
157#947—61no—
158#947—61no—
159#947—61no—
160#947C2×D311yescharacteristic
161#944—61no—
162#936—31no—
163C2×(C2×D3)⋊C4—61no—
164C2×(C2×D3)⋊C4—61no—
165C2×C4⋊Dic3—31no—
166C2×Dic3⋊C4—61no—
167C2×C4×Dic3—31no—
168C22×C3⋊C8—31no—
169C2×D3×C8—31no—
170C2×D3×C8C2×D311yescharacteristic
171D3×C4⋊C4—31no—
172D3×C4⋊C4—61no—
173D3×C4⋊C4C2×D311yescharacteristic
174#888—31no—
175#888—31no—
176#888—31no—
177#888—31no—
178#888—31no—
179#888—61no—
180#888—61no—
181#888—61no—
182#888—61no—
183#888C2×D311yescharacteristic, complemented
184#885—61no—
185#885—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188#875—31no—
189C42×D3—31no—
190#869—31no—
191C3×#103—21no—
192C3×#103—31no—
193C3×#103—31no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103C2×D311yescharacteristic, complemented
197C3×#103C2×D311yescharacteristic, complemented
198C3×#102—31no—
199C3×#102—31no—
200C3×#97—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—61no—
206#835C2×D311yescharacteristic, complemented
207#835C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—61no—
216#821C2×D311yescharacteristic
217#816—31no—
218#816C2×D311yescharacteristic, complemented
219#815—31no—
220#815—31no—
221#815—31no—
222#815—31no—
223#815—31no—
224#815—61no—
225#815C2×D311yescharacteristic, complemented
226#810—31no—
227#810C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#803—31no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—42no—
240C2×D32—42no—
241C2×D32—42no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252#634—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3#4112yes—
264C3×C4×D3#4112yes—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6—42no—
269#627—42no—
270#627—42no—
271#626—42no—
272D3×Dic3—22no—
273D3×Dic3—22no—
274D3×Dic3—42no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279C2×C4⋊Q8—91no—
280C2×#124—91no—
281#489—31no—
282#489—91no—
283#489—91no—
284#489—91no—
285#489—91no—
286#489—91no—
287#489—91no—
288#489—91no—
289C2×#103—31no—
290C2×#103—91no—
291C2×#102—91no—
292C2×#102—91no—
293C2×#97—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—62no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—61no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—61no—
312D3×Q8—22no—
313D3×Q8—22no—
314D3×Q8—124no—
315D3×D4—62no—
316D3×D4—62no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—62no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—21no—
331C2×Dic6—21no—
332C2×Dic6—61no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—121no—
339C2×Dic6—124no—
340C2×Dic6C22×D311yescharacteristic
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8—62no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C42—31no—
357#217—61no—
358#217—61no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372(C2×D3)⋊C4—121no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—62no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403D3×C8—22no—
404D3×C8—62no—
405C22×C32C22×D411yescharacteristic
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3#12412yes—
413C2×C3×D3AGL(1,ℤ/8)12yes—
414C2×C3×D3#13712yes—
415D32—84no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—21no—
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#12412yes—
429C22×Q8—31no—
430C22×Q8—181no—
431C22×D4—91no—
432C22×C8—31no—
433C22×C8—91no—
434C4⋊Q8—31no—
435C4⋊Q8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—91no—
438C4⋊Q8—181no—
439C4⋊Q8—181no—
440#124—31no—
441#124—91no—
442#124—91no—
443#124—91no—
444#124—181no—
445#124—181no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449C2×C22⋊C4—181no—
450C2×C22⋊C4—181no—
451C2×C42—91no—
452#103—31no—
453#103—31no—
454#103—31no—
455#103—31no—
456#103—91no—
457#103—91no—
458#103—91no—
459#103D3211yescharacteristic, complemented
460#102—31no—
461#102—31no—
462#102—91no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#97—31no—
469#97—91no—
470#97—91no—
471#97—91no—
472C23×C3—31no—
473C23×C3—61no—
474C22×D3—21no—
475C22×D3—61no—
476C22×D3—61no—
477C22×D3—121no—
478C22×D3—122no—
479C22×D3—122no—
480C22×D3—122no—
481C22×D3—122no—
482C22×D3—122no—
483C22×D3—122no—
484C22×D3D3×D411yescharacteristic
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—41no—
490C3×Q8—41no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×Q8—122no—
495C3×D4—61no—
496C3×D4—61no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—32no—
504C2×C3×C4—32no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—122no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—62no—
527C2×Dic3—62no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535D12—21no—
536D12—21no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—121no—
543D12—122no—
544C4×D3—42no—
545C4×D3—42no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—122no—
549C4×D3#23512yes—
550C4×D3#23712yes—
551Dic6—21no—
552Dic6—21no—
553Dic6—42no—
554Dic6—42no—
555Dic6—122no—
556Dic6—122no—
557Dic6—122no—
558Dic6—122no—
559Dic6—122no—
560Dic6—122no—
561Dic6—242no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—61no—
566C3×C8—61no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—121no—
572C2×C32C2×#12411yescharacteristic
573C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
574C2×C32C2×#13711yescharacteristic
575C3⋊D3—81no—
576C3×D3—81no—
577C3×D3#48914yescomplemented
578C24—181no—
579C2×Q8—31no—
580C2×Q8—61no—
581C2×Q8—61no—
582C2×Q8—62no—
583C2×Q8—62no—
584C2×Q8—181no—
585C2×Q8—181no—
586C2×Q8—181no—
587C2×Q8—364no—
588C2×Q8C2×D3211yescharacteristic
589C2×D4—31no—
590C2×D4—91no—
591C2×D4—182no—
592C2×D4—182no—
593C2×D4—181no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—61no—
597C22×C4—91no—
598C22×C4—91no—
599C22×C4—181no—
600C2×C8—31no—
601C2×C8—31no—
602C2×C8—62no—
603C2×C8—91no—
604C2×C8—182no—
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4C2×D3211yescharacteristic
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—31no—
625C42—91no—
626C42—91no—
627C42—91no—
628C22×C3—21no—
629C22×C3—32no—
630C22×C3—32no—
631C22×C3—32no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3C2×D3×D411yescharacteristic
636C22×C3C2×D3×D411yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—121no—
644C2×D3—121no—
645C2×D3—121no—
646C2×D3—241no—
647C2×D3—241no—
648C2×D3—241no—
649C2×D3—244no—
650C2×D3—244no—
651C2×D3#88512yes—
652C2×D3#91412yes—
653C2×D3#91812yes—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—81no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23511yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4D3×#4111yescharacteristic
671C3×C4D3×#4111yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—61no—
678Dic3—61no—
679Dic3—61no—
680Dic3—61no—
681Dic3—121no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686Dic3#88512yes—
687C32C2×#48911yescharacteristic, complemented, Sylow
688C23—31no—
689C23—61no—
690C23—181no—
691C23—362no—
692C23—362no—
693C23—362no—
694Q8—21no—
695Q8—21no—
696Q8—61no—
697Q8—61no—
698Q8—122no—
699Q8—122no—
700Q8—362no—
701Q8—362no—
702Q8—362no—
703D4—61no—
704D4—61no—
705D4—181no—
706D4—181no—
707D4—362no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—31no—
711C2×C4—32no—
712C2×C4—32no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—91no—
719C2×C4—91no—
720C2×C4—122no—
721C2×C4—122no—
722C2×C4—182no—
723C2×C4—182no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4C22×D3211yescharacteristic
727C8—21no—
728C8—61no—
729C8—61no—
730C8—181no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—34no—
735C2×C3—241no—
736C2×C3C2×#88511yescharacteristic
737C2×C3D3×#12411yescharacteristic
738C2×C3C2×#91411yescharacteristic
739C2×C3C2×#91811yescharacteristic
740C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
741C2×C3D3×#13711yescharacteristic
742D3—81no—
743D3—241no—
744D3—241no—
745D3—481no—
746D3#479414yesdirect product factor
747C22—32no—
748C22—32no—
749C22—32no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22—361no—
754C22—361no—
755C22—361no—
756C22—724no—
757C22D32×D411yescharacteristic
758C4—32no—
759C4—41no—
760C4—41no—
761C4—61no—
762C4—61no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—181no—
767C4—181no—
768C4—361no—
769C4D3×#23511yescharacteristic
770C4D3×#23711yescharacteristic
771C3—21no—
772C3C2×#479411yescharacteristic, complemented
773C3D3×#48911yescharacteristic, complemented
774C2—34no—
775C2—241no—
776C2—721no—
777C2D3×#88511yescharacteristic
778C2D3×#91411yescharacteristic
779C2D3×#91811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC2×D3×D12C22
hypercenter#103D32
hypocenterC32C2×#489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. D3×#888C2semidirect
3. #10592493C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4794C2semidirect
6. #10591632C2semidirect
7. #10591624C2semidirect
8. D3×#835C2semidirect
10. #10590893C2semidirect
11. #10590866C2semidirect
12. D3×#815C2semidirect
14. #10590541C2semidirect
15. #10590535C2semidirect
22. #64097C22semidirect
26. C3×#888C22semidirect
29. #63919C22semidirect
30. #63918C22semidirect
41. C32×#103C22semidirect
42. #63662C22semidirect
44. #63642C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#816C22semidirect
50. C3×#815C22semidirect
51. C3×#810C22semidirect
53. #63566C22semidirect
54. #63565C22semidirect
59. #63555C22semidirect
60. #63554C22semidirect
74. D3×#103D3semidirect
85. #4794D3direct (N × H)
183. #888C2×D3semidirect
196. C3×#103C2×D3semidirect
197. C3×#103C2×D3semidirect
206. #835C2×D3semidirect
207. #835C2×D3semidirect
218. #816C2×D3semidirect
225. #815C2×D3semidirect
227. #810C2×D3semidirect
459. #103D32semidirect
577. C3×D3#489semidirect
687. C32C2×#489semidirect
746. D3#4794direct (N × H)
772. C3C2×#4794semidirect
773. C3D3×#489semidirect

Maximal subgroups

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

subgroupindex
D3×#9472
D3×#8882
#105924932
C3×D3×#1032
C3×#47942
#105916322
#105916242
D3×#8352
D3×#8212
#105908932
#105908662
D3×#8152
D3×#8092
#105905412
#105905352
D3×#4893
C2×#47943