Finite Group Databasebeta

← D3×#4811 #11869600

Subgroups — D3×#4811 #11869600

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#946C211yesmaximal, characteristic
2D32×C4⋊C4C211yesmaximal, characteristic
3#10592510C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591555C211yesmaximal, characteristic, complemented
7#10591551C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9D3×(C2×D3)⋊C8C211yesmaximal, characteristic
10#10590689C211yesmaximal, characteristic, complemented
11#10590682C211yesmaximal, characteristic, complemented
12D3×#818C211yesmaximal, characteristic, complemented
13D3×#807C211yesmaximal, characteristic, complemented
14#10590528C211yesmaximal, characteristic, complemented
15#10590517C211yesmaximal, characteristic, complemented
16D3×#484—31nomaximal
17C2×#4811—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C4×D32—21no—
20C2×C4×D32C2211yescharacteristic
21#64155C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27D3×(C2×D3)⋊C4—21no—
28#63900C2211yescharacteristic
29D3×C4⋊Dic3C2211yescharacteristic
30D3×C4⋊Dic3C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32#63888—21no—
33#63887—21no—
34#63883—21no—
35D3×Dic3⋊C4—21no—
36D3×Dic3⋊C4—21no—
37D3×Dic3⋊C4—21no—
38#63871C2211yescharacteristic
39#63856C2211yescharacteristic
40C2×D3×C3⋊C8C2211yescharacteristic
41C32×#103C2211yescharacteristic, complemented
42#63662C2211yescharacteristic, complemented
43#63647C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63634C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#835C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#810C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C2×#946—31no—
62D3×C22⋊Q8—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C3×#484—31no—
66C2×C3×#103—31no—
67C2×#835—31no—
68C2×(C2×D3)⋊C8—31no—
69C2×#818—31no—
70#5044—31no—
71#4970—31no—
72C2×#807—31no—
73#4884—31no—
74#4884—31no—
75D3×#107—31no—
76D3×#107—31no—
77#4811—31no—
78#4811—31no—
79#4811—31no—
80#4811—31no—
81#4811—31no—
82#4811—31no—
83#4811—31no—
84#4811—31no—
85#4811—31no—
86#4811—61no—
87#4811D311yescharacteristic, direct product factor
88D3×#103—31no—
89D3×#103D311yescharacteristic, complemented
90D3×C22⋊C8—31no—
91#4722—31no—
92C22×D32D411yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C3×D3×Q8—22no—
97C3×D3×Q8—22no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#624—21no—
106C2×#624D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3D411yescharacteristic
111C2×D3×Dic3D411yescharacteristic
112C4×D32—22no—
113C4×D32—22no—
114C4×D32—44no—
115C2×C32×C8C2311yescharacteristic
116C32×C4⋊C4C2311yescharacteristic
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—22no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141D3×C3⋊C8—22no—
142C2×#484—91noSylow
143C22×C3×Q8—31no—
144C2×D3×Q8C2×D311yescharacteristic
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3—61no—
148C22×C4×D3—61no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4—31no—
153#946—31no—
154#946—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158#946—61no—
159#946—61no—
160#946C2×D311yescharacteristic
161C2×(C2×D3)⋊C4—61no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165#924—31no—
166C2×Dic3⋊C4—61no—
167C2×Dic3⋊C4—61no—
168C2×Dic3⋊C4—61no—
169C22×C3⋊C8—31no—
170C2×D3×C8—31no—
171C2×D3×C8C2×D311yescharacteristic
172#897—31no—
173#896—61no—
174D3×C4⋊C4—31no—
175D3×C4⋊C4—31no—
176D3×C4⋊C4—31no—
177D3×C4⋊C4—31no—
178D3×C4⋊C4—31no—
179D3×C4⋊C4—31no—
180D3×C4⋊C4—31no—
181D3×C4⋊C4—61no—
182D3×C4⋊C4—61no—
183D3×C4⋊C4—61no—
184D3×C4⋊C4—61no—
185D3×C4⋊C4—61no—
186D3×C4⋊C4—61no—
187D3×C4⋊C4C2×D311yescharacteristic
188D3×C4⋊C4C2×D311yescharacteristic
189D3×C22⋊C4—61no—
190#878—61no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#103—21no—
194C3×#103—31no—
195C3×#103—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103C2×D311yescharacteristic, complemented
199C3×#103C2×D311yescharacteristic, complemented
200C3×C22⋊C8—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#830—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818—31no—
217#818—31no—
218#818—31no—
219#818—31no—
220#818—31no—
221#818—61no—
222#818C2×D311yescharacteristic, complemented
223#816—31no—
224#816C2×D311yescharacteristic, complemented
225#810—31no—
226#810C2×D311yescharacteristic, complemented
227#807—31no—
228#807—31no—
229#807—31no—
230#807—31no—
231#807—31no—
232#807—31no—
233#807—31no—
234#807—61no—
235#807C2×D311yescharacteristic, complemented
236C22×C3⋊D3C2×D411yescharacteristic
237C22×C3×D3C2×D411yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C2×D32—22no—
240C2×D32—22no—
241C2×D32Q1614yes—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3#4112yes—
265C3×C4×D3#4112yes—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269#624—22no—
270#624—42no—
271D3×Dic3—22no—
272D3×Dic3—22no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275D3×Dic3—42no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8—21no—
279C3×C3⋊C8—21no—
280C2×C22⋊Q8—91no—
281C22×C4⋊C4—91no—
282#484—31no—
283#484—91no—
284#484—91no—
285#484—91no—
286#484—91no—
287#484—91no—
288#484—91no—
289#484—91no—
290C2×#107—91no—
291C2×#107—91no—
292C2×#103—31no—
293C2×#103—91no—
294C2×C22⋊C8—91no—
295C23×D3—31no—
296C23×D3—31no—
297C2×C3×Q8—21no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—62no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314D3×Q8—22no—
315D3×Q8—22no—
316C2×C4×D3—21no—
317C2×C4×D3—21no—
318C2×C4×D3—21no—
319C2×C4×D3—31no—
320C2×C4×D3—31no—
321C2×C4×D3—31no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—62no—
329C2×C4×D3—62no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—121no—
338C2×C4×D3—124no—
339C2×C4×D3—124no—
340C2×C4×D3C22×D311yescharacteristic
341C2×C4×D3C22×D311yescharacteristic
342C2×Dic6—21no—
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—62no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360#217—61no—
361(C2×D3)⋊C4—21no—
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—121no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397Dic3⋊C4—121no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—62no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D3×C8—22no—
405D3×C8—62no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—21no—
408C2×C3⋊D3—21no—
409C2×C3⋊D3C2×Q1612yes—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3#12312yes—
413C2×C3×D3C2×Q1612yes—
414C2×C3×D3C2×Q1612yes—
415C2×C3×D3AGL(1,ℤ/8)12yes—
416D32—28no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4C2×#4111yescharacteristic
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3#12312yes—
430C22×Q8—31no—
431C23×C4—91no—
432C23×C4—181no—
433C22×C8—31no—
434C22×C8—91no—
435C22⋊Q8—31no—
436C22⋊Q8—91no—
437C22⋊Q8—91no—
438C22⋊Q8—91no—
439C22⋊Q8—181no—
440C22⋊Q8—181no—
441C2×C4⋊C4—31no—
442C2×C4⋊C4—31no—
443C2×C4⋊C4—91no—
444C2×C4⋊C4—91no—
445C2×C4⋊C4—91no—
446C2×C4⋊C4—91no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—181no—
449C2×C4⋊C4—181no—
450C2×C4⋊C4—181no—
451C2×C4⋊C4—181no—
452C2×C22⋊C4—181no—
453#107—31no—
454#107—31no—
455#107—91no—
456#107—91no—
457#107—91no—
458#107—91no—
459#107—91no—
460#107—91no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103D3211yescharacteristic, complemented
469C22⋊C8—31no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472C22⋊C8—91no—
473C23×C3—31no—
474C23×C3—31no—
475C22×D3—31no—
476C22×D3—31no—
477C22×D3—34no—
478C22×D3—34no—
479C22×D3—61no—
480C22×D3—62no—
481C22×D3—62no—
482C22×D3—62no—
483C22×D3—62no—
484C22×D3D3×D411yescharacteristic
485C22×D3D3×D411yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—41no—
491C3×Q8—41no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—122no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—61no—
524C2×Dic3—62no—
525C2×Dic3—62no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C4×D3—21no—
538C4×D3—21no—
539C4×D3—42no—
540C4×D3—42no—
541C4×D3—42no—
542C4×D3—62no—
543C4×D3—62no—
544C4×D3—62no—
545C4×D3—61no—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—62no—
550C4×D3—121no—
551C4×D3—121no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—242no—
560C4×D3#23512yes—
561C4×D3#23712yes—
562Dic6—21no—
563Dic6—21no—
564Dic6—42no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32C2×#12311yescharacteristic
576C2×C32C22×Q1611yescharacteristic
577C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
578C3⋊D3—22no—
579C3×D3—22no—
580C3×D3#48414yescomplemented
581C24—91no—
582C2×Q8—31no—
583C2×Q8—61no—
584C2×Q8—62no—
585C2×Q8—62no—
586C2×Q8C2×D3211yescharacteristic
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—61no—
592C22×C4—91no—
593C22×C4—91no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—182no—
598C22×C4—182no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—364no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8—62no—
607C2×C8—91no—
608C2×C8—182no—
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—61no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22×C3—21no—
632C22×C3—32no—
633C22×C3—32no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3C2×D3×D411yescharacteristic
639C22×C3C2×D3×D411yescharacteristic
640C2×D3—21no—
641C2×D3—21no—
642C2×D3—32no—
643C2×D3—32no—
644C2×D3—62no—
645C2×D3—68no—
646C2×D3—61no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—68no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3#88312yes—
654C2×D3#91412yes—
655C2×D3D3×Q1612yes—
656C2×D3D3×Q1612yes—
657C3×C4—21no—
658C3×C4—21no—
659C3×C4—32no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—61no—
665C3×C4—81no—
666C3×C4—81no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4C2×#23511yescharacteristic
672C3×C4C2×#23711yescharacteristic
673C3×C4D3×#4111yescharacteristic
674C3×C4D3×#4111yescharacteristic
675Dic3—21no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—61no—
681Dic3—61no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—241no—
688Dic3—241no—
689Dic3#88312yes—
690C32C2×#48411yescharacteristic, complemented, Sylow
691C23—31no—
692C23—31no—
693C23—94no—
694C23—91no—
695C23—182no—
696C23—182no—
697Q8—21no—
698Q8—21no—
699Q8—61no—
700Q8—61no—
701Q8—122no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—31no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—91no—
715C2×C4—122no—
716C2×C4—122no—
717C2×C4—122no—
718C2×C4—182no—
719C2×C4—182no—
720C2×C4—182no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4—362no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4C22×D3211yescharacteristic
731C8—21no—
732C8—61no—
733C8—61no—
734C8—181no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—34no—
739C2×C3—62no—
740C2×C3C2×#88311yescharacteristic
741C2×C3D3×#12311yescharacteristic
742C2×C3C2×#91411yescharacteristic
743C2×C3C2×D3×Q1611yescharacteristic
744C2×C3C2×D3×Q1611yescharacteristic
745C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
746D3—22no—
747D3—62no—
748D3—62no—
749D3—122no—
750D3#481114yesdirect product factor
751C22—32no—
752C22—32no—
753C22—32no—
754C22—32no—
755C22—61no—
756C22—61no—
757C22—92no—
758C22—188no—
759C22—181no—
760C22—181no—
761C22D32×D411yescharacteristic
762C4—32no—
763C4—41no—
764C4—41no—
765C4—61no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—181no—
771C4—361no—
772C4—361no—
773C4D3×#23511yescharacteristic
774C4D3×#23711yescharacteristic
775C3—21no—
776C3C2×#481111yescharacteristic, complemented
777C3D3×#48411yescharacteristic, complemented
778C2—34no—
779C2—62no—
780C2—182no—
781C2D3×#88311yescharacteristic
782C2D3×#91411yescharacteristic
783C2D32×Q1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radicalC22×D32D4
hypercenter#103D32
hypocenterC32C2×#484
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
3. #10592510C2semidirect
4. C3×#4811C2semidirect
5. C3×D3×#103C2semidirect
6. #10591555C2semidirect
7. #10591551C2semidirect
8. D3×#835C2semidirect
10. #10590689C2semidirect
11. #10590682C2semidirect
12. D3×#818C2semidirect
13. D3×#807C2semidirect
14. #10590528C2semidirect
15. #10590517C2semidirect
41. C32×#103C22semidirect
42. #63662C22semidirect
44. #63645C22semidirect
45. #63634C22semidirect
46. C3×#835C22semidirect
47. C3×#835C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#810C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63575C22semidirect
55. #63575C22semidirect
56. #63575C22semidirect
57. #63566C22semidirect
58. #63565C22semidirect
87. #4811D3direct (N × H)
89. D3×#103D3semidirect
198. C3×#103C2×D3semidirect
199. C3×#103C2×D3semidirect
206. #835C2×D3semidirect
207. #835C2×D3semidirect
222. #818C2×D3semidirect
224. #816C2×D3semidirect
226. #810C2×D3semidirect
235. #807C2×D3semidirect
468. #103D32semidirect
580. C3×D3#484semidirect
690. C32C2×#484semidirect
750. D3#4811direct (N × H)
776. C3C2×#4811semidirect
777. C3D3×#484semidirect

Maximal subgroups

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

subgroupindex
D3×#9462
D32×C4⋊C42
#105925102
C3×#48112
C3×D3×#1032
#105915552
#105915512
D3×#8352
D3×(C2×D3)⋊C82
#105906892
#105906822
D3×#8182
D3×#8072
#105905282
#105905172
D3×#4843
C2×#48113