Finite Group Databasebeta

← D3×#5182 #11865639

Subgroups — D3×#5182 #11865639

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Q16C211yesmaximal, characteristic
2D3×Q8×Dic3C211yesmaximal, characteristic
3D3×#944C211yesmaximal, characteristic
4C2×D3×#216C211yesmaximal, characteristic
5#10592881C211yesmaximal, characteristic, complemented
6C3×#5182C211yesmaximal, characteristic, complemented
7#10591633C211yesmaximal, characteristic, complemented
8#10591625C211yesmaximal, characteristic, complemented
9#10591580C211yesmaximal, characteristic, complemented
10#10591574C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic
12#10590800C211yesmaximal, characteristic, complemented
13#10590798C211yesmaximal, characteristic, complemented
14D3×#816C211yesmaximal, characteristic
15D3×Dic3⋊C8C211yesmaximal, characteristic
16C2×#5182—31nomaximal
17D3×#462—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C2×C32×Q16C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23#64153C2211yescharacteristic
24C2×#3756C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C2×C3×#216C2211yescharacteristic
30C3×D3×Q16—24no—
31C2×C3×Dic12C2211yescharacteristic
32C2×C3×D3×C8C2211yescharacteristic
33D3×#216—24no—
34D3×C4⋊Dic3—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36D3×Dic3⋊C4—21no—
37D3×Dic3⋊C4—21no—
38C4×D3×Dic3—21no—
39C4×D3×Dic3C2211yescharacteristic
40#63873C2211yescharacteristic
41#63866C2211yescharacteristic
42#63843—21no—
43#63843C2211yescharacteristic
44Dic3×Dic6—21no—
45Dic3×Dic6C2211yescharacteristic
46#63839—21no—
47#63839—21no—
48C2×#3719C2211yescharacteristic
49C2×#3718C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic
52#63643C2211yescharacteristic
53#63641C2211yescharacteristic
54C3×#835C2211yescharacteristic
55C3×#816C2211yescharacteristic
56C3×Dic3⋊C8C2211yescharacteristic
57#63572C2211yescharacteristic
58Dic3⋊(C3⋊C8)C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#63566C2211yescharacteristic
62#63565C2211yescharacteristic
63C22×C3×Q16—31no—
64C2×Q8×Dic3—31no—
65C2×#944—31no—
66C22×#216—31no—
67C2×D3×Q16—31no—
68C2×D3×Q16D311yescharacteristic
69D3×C4⋊Q8—31no—
70C4×D3×Q8—31no—
71C3×#462—31no—
72C2×#835—31no—
73#5182—31no—
74#5182—31no—
75#5182—31no—
76#5182—31no—
77#5182—31no—
78#5182—31no—
79#5182—31no—
80#5182—31no—
81#5182—31no—
82#5182—61no—
83#5182D311yescharacteristic, direct product factor
84C2×#816—31no—
85C2×Dic3⋊C8—31no—
86#5090—31no—
87#5031—31no—
88#4849—31no—
89D3×C4⋊C8—31no—
90D3×#103—31no—
91D3×#103—31no—
92#4795—31no—
93#4795—31no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C3×D3×Q8—22no—
98C3×D3×Q8—22no—
99C3×D3×Q8—22no—
100C3×D3×Q8D414yes—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112C2×D3×Dic3D411yescharacteristic
113C2×D3×Dic3D411yescharacteristic
114D3×Dic6—22no—
115D3×Dic6—22no—
116C32×Q16—22no—
117C2×C32×C8C2311yescharacteristic
118#3756—22no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121#3750—21no—
122#3750—21no—
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#216—22no—
127C3×#216—22no—
128C3×#216—22no—
129C3×C4⋊Dic3—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C3×Dic12—22no—
138C3×D3×C8—22no—
139#3724—21no—
140#3724—21no—
141Dic3⋊Dic3—21no—
142Dic3⋊Dic3—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146Dic32—21no—
147Dic32—21no—
148Dic32D411yescharacteristic
149Dic32D411yescharacteristic
150#3719—22no—
151#3718—22no—
152D3×C3⋊C8—22no—
153C2×#462—91noSylow
154C22×C3×Q8—31no—
155C22×C3×Q8—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C2×D3×Q8C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—21no—
161C2×C3×Q16—31no—
162C2×C3×Q16—31no—
163C2×C3×Q16—31no—
164C2×C3×Q16—31no—
165C2×C3×Q16—64no—
166C2×C3×Q16C2×D311yescharacteristic
167C2×C3×Q16C2×D311yescharacteristic
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×C4×Q8—31no—
171Q8×Dic3—31no—
172Q8×Dic3—31no—
173Q8×Dic3—31no—
174Q8×Dic3—31no—
175Q8×Dic3—61no—
176Q8×Dic3—61no—
177Q8×Dic3—61no—
178Q8×Dic3C2×D311yescharacteristic
179#944—31no—
180#944—31no—
181#944—31no—
182#944—31no—
183#944—31no—
184#944—61no—
185#944—61no—
186#944—61no—
187#944C2×D311yescharacteristic
188C2×#216—31no—
189C2×#216—31no—
190C2×#216—31no—
191C2×#216—31no—
192C2×#216—31no—
193C2×#216—61no—
194C2×#216—64no—
195C2×#216C2×D311yescharacteristic
196C2×#216C2×D311yescharacteristic
197C2×#216C2×D311yescharacteristic
198C2×C4⋊Dic3—31no—
199C2×C4⋊Dic3—61no—
200C2×Dic3⋊C4—61no—
201C2×Dic3⋊C4—61no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—61no—
204C22×C3⋊C8—31no—
205D3×Q16—24no—
206D3×Q16—64no—
207C2×Dic12—31no—
208C2×Dic12C2×D311yescharacteristic
209C2×D3×C8—31no—
210C2×D3×C8C2×D311yescharacteristic
211D3×C4⋊C4—31no—
212D3×C4⋊C4—61no—
213D3×C4⋊C4—61no—
214D3×C4⋊C4—61no—
215#888—61no—
216#888—61no—
217#887—31no—
218#887—61no—
219C42×D3—31no—
220C42×D3—61no—
221#869—31no—
222C4×Dic6—31no—
223C4×Dic6—61no—
224C3×C4⋊C8—31no—
225C3×#103—31no—
226C3×#103—31no—
227#835—31no—
228#835—31no—
229#835—31no—
230#835—31no—
231#835—31no—
232#835—61no—
233#835C2×D311yescharacteristic
234#816—31no—
235#816—31no—
236#816—31no—
237#816—31no—
238#816—31no—
239#816—61no—
240#816C2×D311yescharacteristic
241Dic3⋊C8—31no—
242Dic3⋊C8—31no—
243Dic3⋊C8—31no—
244Dic3⋊C8—31no—
245Dic3⋊C8—31no—
246Dic3⋊C8—61no—
247Dic3⋊C8C2×D311yescharacteristic
248#810—31no—
249#810—31no—
250C4⋊(C3⋊C8)—31no—
251C22×C3×D3C2×D411yescharacteristic
252C32×Q8—21no—
253C32×Q8—21no—
254C32×Q8—21no—
255C32×Q8C2×D412yes—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263#634—21no—
264#634—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×C4×D3—24no—
273C3×C4×D3—42no—
274C3×C4×D3C2×D412yes—
275C3×C4×D3#4112yes—
276C3×Dic6—21no—
277C3×Dic6—24no—
278C3×Dic6—21no—
279C3×Dic6—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—42no—
283C3×Dic6C2×D412yes—
284#627—42no—
285D3×Dic3—22no—
286D3×Dic3—42no—
287D3×Dic3—42no—
288D3×Dic3Q1614yescomplemented
289C32×C8—21no—
290C3⋊(C3⋊C8)—21no—
291C3×C3⋊C8—21no—
292C3×C3⋊C8—21no—
293C22×Q16—31no—
294C22×Q16—91no—
295C2×C4⋊Q8—91no—
296C2×C4×Q8—91no—
297#462—31no—
298#462—91no—
299#462—91no—
300#462—91no—
301#462—91no—
302#462—91no—
303#462—91no—
304#462—91no—
305C2×C4⋊C8—91no—
306C2×#103—91no—
307C2×#103—91no—
308C2×C3×Q8—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—34no—
311C2×C3×Q8—31no—
312C2×C3×Q8—31no—
313C2×C3×Q8—31no—
314C2×C3×Q8—61no—
315C2×C3×Q8—61no—
316C2×C3×Q8—62no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C2×C3×Q8C22×D311yescharacteristic
322C2×C3×Q8C22×D311yescharacteristic
323C22×C3×C4—31no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×Q8—22no—
331D3×Q8—22no—
332D3×Q8—22no—
333D3×Q8—62no—
334D3×Q8—62no—
335D3×Q8#6714yes—
336C2×C4×D3—21no—
337C2×C4×D3—21no—
338C2×C4×D3—31no—
339C2×C4×D3—31no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6—21no—
344C2×Dic6—21no—
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
348C2×Dic6—62no—
349C2×Dic6—62no—
350C2×Dic6—61no—
351C2×Dic6—61no—
352C2×Dic6C22×D311yescharacteristic
353C2×Dic6C22×D311yescharacteristic
354C2×Dic6C22×D311yescharacteristic
355C3×Q16—22no—
356C3×Q16—22no—
357C3×Q16—42no—
358C3×Q16—62no—
359C3×Q16—62no—
360C3×Q16—62no—
361C3×Q16—62no—
362C2×C3×C8—21no—
363C2×C3×C8—31no—
364C2×C3×C8—31no—
365C2×C3×C8—62no—
366C2×C3×C8C22×D311yescharacteristic
367C2×C3×C8C22×D311yescharacteristic
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C42—31no—
373C3×C42—61no—
374#216—22no—
375#216—22no—
376#216—22no—
377#216—62no—
378#216—62no—
379#216—62no—
380#216—62no—
381#216—62no—
382#216—122no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—121no—
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—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—121no—
412Dic3⋊C4—121no—
413C4×Dic3—21no—
414C4×Dic3—31no—
415C4×Dic3—31no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—61no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3—61no—
426C4×Dic3—61no—
427C4×Dic3—121no—
428C4×Dic3C22×D311yescharacteristic
429C2×C3⋊C8—31no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8—62no—
433C2×C3⋊C8C22×D311yescharacteristic
434C2×C3⋊C8C22×D311yescharacteristic
435Dic12—22no—
436Dic12—62no—
437D3×C8—22no—
438D3×C8—62no—
439C22×C32C22×D411yescharacteristic
440C2×C3×D3#12112yes—
441C2×C3×D3C2×Q1612yes—
442C2×C3×D3#13712yes—
443C32×C4—22no—
444C32×C4—41no—
445C32×C4C22×D411yescharacteristic
446C32×C4C2×#4111yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—41no—
449C3⋊Dic3—41no—
450C3⋊Dic3C2×Q1612yescomplemented
451C3×Dic3—22no—
452C3×Dic3—21no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3#12112yes—
457C3×Dic3C2×Q1612yescomplemented
458C22×Q8—31no—
459C22×Q8—31no—
460C22×Q8—91no—
461C2×Q16—31no—
462C2×Q16—31no—
463C2×Q16—31no—
464C2×Q16—31no—
465C2×Q16—64no—
466C2×Q16—91no—
467C2×Q16—91no—
468C2×Q16—91no—
469C2×Q16—184no—
470C2×Q16D3211yescharacteristic
471C22×C8—31no—
472C22×C8—91no—
473C4⋊Q8—31no—
474C4⋊Q8—91no—
475C4⋊Q8—91no—
476C4⋊Q8—91no—
477C4⋊Q8—181no—
478C4⋊Q8—181no—
479C4×Q8—31no—
480C4×Q8—91no—
481C4×Q8—91no—
482C4×Q8—91no—
483C4×Q8—181no—
484C4×Q8—181no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—181no—
487C2×C4⋊C4—181no—
488C2×C4⋊C4—181no—
489C2×C42—91no—
490C2×C42—181no—
491C4⋊C8—31no—
492C4⋊C8—91no—
493C4⋊C8—91no—
494C4⋊C8—91no—
495#103—31no—
496#103—31no—
497#103—91no—
498#103—91no—
499#103—91no—
500#103—91no—
501#103—91no—
502#103—91no—
503C23×C3—31no—
504C22×D3D3×D411yescharacteristic
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—22no—
512C3×Q8—32no—
513C3×Q8—41no—
514C3×Q8—41no—
515C3×Q8—41no—
516C3×Q8—64no—
517C3×Q8—61no—
518C3×Q8—61no—
519C3×Q8—61no—
520C3×Q8—61no—
521C3×Q8—61no—
522C3×Q8—122no—
523C3×Q8D3×D412yes—
524C3×Q8C2×#6712yes—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—31no—
535C2×C3×C4—41no—
536C2×C3×C4—41no—
537C2×C3×C4—64no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—122no—
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—34no—
552C2×Dic3—31no—
553C2×Dic3—31no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—62no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3D3×D411yescharacteristic
566C2×Dic3D3×D411yescharacteristic
567C2×Dic3D3×D411yescharacteristic
568C4×D3—24no—
569C4×D3—34no—
570C4×D3—42no—
571C4×D3—62no—
572C4×D3—122no—
573C4×D3—122no—
574C4×D3#23712yes—
575C4×D3C2×#6712yes—
576Dic6—21no—
577Dic6—24no—
578Dic6—21no—
579Dic6—21no—
580Dic6—21no—
581Dic6—21no—
582Dic6—42no—
583Dic6—61no—
584Dic6—61no—
585Dic6—61no—
586Dic6—61no—
587Dic6—121no—
588Dic6—121no—
589Dic6—122no—
590Dic6—122no—
591Dic6C2×#6712yes—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—41no—
595C3×C8—61no—
596C3×C8—61no—
597C3⋊C8—21no—
598C3⋊C8—21no—
599C3⋊C8—61no—
600C3⋊C8—61no—
601C3⋊C8—121no—
602C2×C32C2×#12111yescharacteristic
603C2×C32C22×Q1611yescharacteristic
604C2×C32C2×#13711yescharacteristic
605C3×D3#46214yescomplemented
606C2×Q8—34no—
607C2×Q8—31no—
608C2×Q8—31no—
609C2×Q8—31no—
610C2×Q8—61no—
611C2×Q8—61no—
612C2×Q8—62no—
613C2×Q8—62no—
614C2×Q8—62no—
615C2×Q8—91no—
616C2×Q8—181no—
617C2×Q8—182no—
618C2×Q8—182no—
619C2×Q8C2×D3211yescharacteristic
620C2×Q8C2×D3211yescharacteristic
621C22×C4—31no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—91no—
625C22×C4—91no—
626C22×C4—181no—
627C22×C4—181no—
628Q16—22no—
629Q16—62no—
630Q16—62no—
631Q16—62no—
632Q16—62no—
633Q16—182no—
634Q16—182no—
635Q16—182no—
636C2×C8—31no—
637C2×C8—31no—
638C2×C8—62no—
639C2×C8—91no—
640C2×C8—182no—
641C2×C8C2×D3211yescharacteristic
642C4⋊C4—31no—
643C4⋊C4—61no—
644C4⋊C4—61no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—181no—
648C4⋊C4—181no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C42—31no—
658C42—61no—
659C42—91no—
660C42—91no—
661C42—91no—
662C42—181no—
663C42—181no—
664C42—181no—
665C22×C3—21no—
666C22×C3—32no—
667C22×C3—32no—
668C22×C3—32no—
669C22×C3C2×D3×D411yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C2×D3D3×Q1612yes—
672C2×D3#91812yes—
673C2×D3#93912yes—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—32no—
679C3×C4—32no—
680C3×C4—42no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—61no—
684C3×C4—62no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4C2×D3×D411yescharacteristic
690C3×C4C2×#23711yescharacteristic
691C3×C4D3×#4111yescharacteristic
692C3×C4C22×#6711yescharacteristic
693Dic3—21no—
694Dic3—22no—
695Dic3—32no—
696Dic3—32no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—62no—
701Dic3—61no—
702Dic3—61no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710Dic3D3×Q1612yescomplemented
711Dic3#93912yes—
712C32C2×#46211yescharacteristic, complemented, Sylow
713C23—31no—
714Q8—21no—
715Q8—21no—
716Q8—21no—
717Q8—32no—
718Q8—64no—
719Q8—61no—
720Q8—61no—
721Q8—61no—
722Q8—61no—
723Q8—61no—
724Q8—122no—
725Q8—181no—
726Q8—181no—
727Q8—362no—
728Q8D3×#6712yes—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—32no—
734C2×C4—32no—
735C2×C4—31no—
736C2×C4—64no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—94no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—122no—
745C2×C4—182no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—362no—
749C2×C4—362no—
750C2×C4C22×D3211yescharacteristic
751C8—21no—
752C8—61no—
753C8—61no—
754C8—181no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—34no—
759C2×C3D3×#12111yescharacteristic
760C2×C3C2×D3×Q1611yescharacteristic
761C2×C3C2×D3×Q1611yescharacteristic
762C2×C3C2×#91811yescharacteristic
763C2×C3D3×#13711yescharacteristic
764C2×C3C2×#93911yescharacteristic
765D3#518214yesdirect product factor
766C22—32no—
767C22—32no—
768C22—32no—
769C22D32×D411yescharacteristic
770C4—22no—
771C4—32no—
772C4—32no—
773C4—41no—
774C4—61no—
775C4—62no—
776C4—92no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4C2×D3×#6711yescharacteristic
785C3—21no—
786C3D3×#46211yescharacteristic, complemented
787C3C2×#518211yescharacteristic, complemented
788C2—34no—
789C2D32×Q1611yescharacteristic
790C2D3×#91811yescharacteristic
791C2D3×#93911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC2×Q16D32
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
5. #10592881C2semidirect
6. C3×#5182C2semidirect
7. #10591633C2semidirect
8. #10591625C2semidirect
9. #10591580C2semidirect
10. #10591574C2semidirect
12. #10590800C2semidirect
13. #10590798C2semidirect
83. #5182D3direct (N × H)
288. D3×Dic3Q16semidirect
450. C3⋊Dic3C2×Q16semidirect
457. C3×Dic3C2×Q16semidirect
605. C3×D3#462semidirect
710. Dic3D3×Q16semidirect
712. C32C2×#462semidirect
765. D3#5182direct (N × H)
786. C3D3×#462semidirect
787. C3C2×#5182semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Q162
D3×Q8×Dic32
D3×#9442
C2×D3×#2162
#105928812
C3×#51822
#105916332
#105916252
#105915802
#105915742
D3×#8352
#105908002
#105907982
D3×#8162
D3×Dic3⋊C82
C2×#51823
D3×#4623