Finite Group Databasebeta

← D3×#5052 #11867011

Subgroups — D3×#5052 #11867011

Order 1152.

1039 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×C22⋊Q8C211yesmaximal, characteristic
2C2×D3×#216C211yesmaximal, characteristic, complemented
3D3×#924C211yesmaximal, characteristic
4C2×D3×#208C211yesmaximal, characteristic
5#10592751C211yesmaximal, characteristic, complemented
6C3×#5052C211yesmaximal, characteristic, complemented
7#10591638C211yesmaximal, characteristic, complemented
8#10591598C211yesmaximal, characteristic, complemented
9D3×#835C211yesmaximal, characteristic, complemented
10#10591189C211yesmaximal, characteristic, complemented
11#10591121C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590587C211yesmaximal, characteristic, complemented
14D3×#808C211yesmaximal, characteristic, complemented
15#10590520C211yesmaximal, characteristic, complemented
16C2×#5052—31nomaximal
17D3×#470—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C2×D3×Dic6C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3756C2211yescharacteristic, complemented
23#64133C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic, complemented
27C3×#924C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#897C2211yescharacteristic
31C3×#896—21no—
32C3×D3×C4⋊C4—21no—
33C3×D3×C4⋊C4C2211yescharacteristic
34C3×D3×C22⋊C4—21no—
35C3×#878—21no—
36D3×#217—21no—
37#63964—21no—
38D3×#216—24no—
39D3×C4⋊Dic3C2211yescharacteristic
40D3×Dic3⋊C4—21no—
41#63857C2211yescharacteristic
42#63856C2211yescharacteristic
43#63851—21no—
44C2×#3719C2211yescharacteristic, complemented
45C2×#3718C2211yescharacteristic, complemented
46C2×#3711C2211yescharacteristic
47C2×#3711C2211yescharacteristic
48D3×#208—24no—
49C2×D3×C3⋊C8C2211yescharacteristic
50C2×D3×C3⋊C8C2211yescharacteristic
51#63662C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63635C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#808C2211yescharacteristic, complemented
57#63574C2211yescharacteristic, complemented
58#63573C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63C2×C3×C22⋊Q8—31no—
64C22×#216—31no—
65C2×#924—31no—
66C22×#208—31no—
67C2×D3×Q16—31no—
68C2×D3×M16—31no—
69D3×C22⋊Q8—31no—
70D3×C22⋊Q8D311yescharacteristic
71C3×#470—31no—
72C2×#835—31no—
73#5189—31no—
74#5137—31no—
75#5052—31no—
76#5052—31no—
77#5052—31no—
78#5052—31no—
79#5052—31no—
80#5052—31no—
81#5052—31no—
82#5052—31no—
83#5052—31no—
84#5052—61no—
85#5052D311yescharacteristic, direct product factor
86C2×#810—31no—
87C2×#808—31no—
88#4867—31no—
89D3×#106—31no—
90#4816—31no—
91#4816—31no—
92D3×#103—31no—
93D3×#103—31no—
94C23×C3×D3D411yescharacteristic
95C2×C32×Q8C2311yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C22×C3×Dic3D411yescharacteristic
99C3×D3×Q8—22no—
100C3×D3×Q8—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6—21no—
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×#627—21no—
113C2×D3×Dic3—21no—
114C2×D3×Dic3—21no—
115D3×Dic6—22no—
116D3×Dic6—22no—
117C32×C4⋊C4—21no—
118C32×C4⋊C4C2311yescharacteristic
119C32×C22⋊C4—21no—
120#3757—21no—
121#3756—22no—
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124#3748—22no—
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127C3×#217—21no—
128C3×#217—21no—
129C3×#216—22no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×C4⋊Dic3—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×#208—22no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142#3724—21no—
143Dic3⋊Dic3—21no—
144Dic3⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146(C2×D3)⋊Dic3—21no—
147#3719—22no—
148#3718—22no—
149#3711—22no—
150#3711—22no—
151D3×C3⋊C8—22no—
152D3×C3⋊C8D414yes—
153C2×#470—91noSylow
154C22×C3×Q8—31no—
155C23×C3×C4—31no—
156C2×D3×Q8—31no—
157C2×D3×Q8C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C22×Dic6—31no—
160C2×C3×Q16—31no—
161C2×C3×M16—31no—
162C3×C22⋊Q8—21no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8—31no—
165C3×C22⋊Q8—31no—
166C3×C22⋊Q8—31no—
167C3×C22⋊Q8—61no—
168C3×C22⋊Q8—61no—
169C3×C22⋊Q8C2×D311yescharacteristic
170C3×C22⋊Q8C2×D311yescharacteristic
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4—61no—
173C2×C3×C22⋊C4—61no—
174C2×#217—61no—
175#946—31no—
176#946C2×D311yescharacteristic
177C2×#216—31no—
178C2×#216—31no—
179C2×#216—31no—
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—61no—
183C2×#216—64no—
184C2×#216C2×D311yescharacteristic, complemented
185C2×C4⋊Dic3—31no—
186#924—31no—
187#924—31no—
188#924—31no—
189#924—31no—
190#924—61no—
191#924—61no—
192#924—61no—
193#924C2×D311yescharacteristic
194#924C2×D311yescharacteristic
195C2×Dic3⋊C4—61no—
196C2×#208—31no—
197C2×#208—31no—
198C2×#208—31no—
199C2×#208—31no—
200C2×#208—61no—
201C2×#208—64no—
202C2×#208C2×D311yescharacteristic
203C22×C3⋊C8—31no—
204C22×C3⋊C8—31no—
205D3×Q16—64no—
206D3×M16—64no—
207C2×Dic12—31no—
208C2×ΓL(1,𝔽25)—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211C2×D3×C8—31no—
212#897—31no—
213#897C2×D311yescharacteristic
214#896—21no—
215#896—61no—
216D3×C4⋊C4—21no—
217D3×C4⋊C4—31no—
218D3×C4⋊C4—61no—
219D3×C4⋊C4C2×D311yescharacteristic
220D3×C22⋊C4—21no—
221D3×C22⋊C4—61no—
222#878—21no—
223#878—61no—
224C3×#106—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, complemented
234#817—31no—
235#816—31no—
236#816—31no—
237#810—31no—
238#810—31no—
239#810—31no—
240#810—31no—
241#810—31no—
242#810—61no—
243#810C2×D311yescharacteristic, complemented
244#808—31no—
245#808—31no—
246#808—31no—
247#808—31no—
248#808—31no—
249#808—61no—
250#808C2×D311yescharacteristic, complemented
251C23×C32C2×D411yescharacteristic
252C22×C3×D3—22no—
253C22×C3×D3—22no—
254C22×C3×D3—22no—
255C22×C3×D3C2×D411yescharacteristic
256C22×C3×D3C2×D411yescharacteristic
257C32×Q8—21no—
258C32×Q8—21no—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2411yescharacteristic
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267#634—21no—
268#634—21no—
269C2×C3×Dic3—22no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C3×C4×D3—22no—
277C3×C4×D3—21no—
278C3×C4×D3—21no—
279C3×C4×D3—22no—
280C3×C4×D3—42no—
281C3×C4×D3—42no—
282C3×C4×D3C2×D412yes—
283C3×C4×D3#4112yes—
284C3×Dic6—21no—
285C3×Dic6—21no—
286C3×Dic6—21no—
287C3×Dic6—21no—
288C3×Dic6—42no—
289#627—42no—
290D3×Dic3—42no—
291D3×Dic3—42no—
292C3⋊(C3⋊C8)—21no—
293C3⋊(C3⋊C8)C2×D412yes—
294C3×C3⋊C8—21no—
295C3×C3⋊C8C2×D412yes—
296C22×Q16—91no—
297C22×M16—91no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8—91no—
300#470—31no—
301#470—91no—
302#470—91no—
303#470—91no—
304#470—91no—
305#470—91no—
306#470—91no—
307#470—91no—
308C2×#106—91no—
309C2×#103—91no—
310C2×#103—91no—
311C24×C3—31no—
312C23×D3#6711yescharacteristic
313C2×C3×Q8—21no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×Q8—61no—
317C2×C3×Q8—62no—
318C2×C3×Q8—62no—
319C2×C3×Q8C22×D311yescharacteristic
320C2×C3×Q8C22×D311yescharacteristic
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×Dic3—61no—
334C22×Dic3—61no—
335C22×Dic3#6711yescharacteristic
336D3×Q8—22no—
337D3×Q8—22no—
338D3×Q8—62no—
339D3×Q8—62no—
340C2×C4×D3—22no—
341C2×C4×D3—22no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3#6711yescharacteristic
347C2×C4×D3#6711yescharacteristic
348C2×C4×D3C22×D311yescharacteristic
349C2×C4×D3C22×D311yescharacteristic
350C2×Dic6—21no—
351C2×Dic6—31no—
352C2×Dic6—31no—
353C2×Dic6—61no—
354C2×Dic6—62no—
355C2×Dic6—62no—
356C2×Dic6—61no—
357C2×Dic6—61no—
358C2×Dic6C22×D311yescharacteristic
359C2×Dic6C22×D311yescharacteristic
360C3×Q16—62no—
361C3×M16—62no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4—21no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—41no—
370C3×C4⋊C4—61no—
371C3×C4⋊C4—61no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—61no—
381C3×C22⋊C4—61no—
382C3×C22⋊C4—61no—
383C3×C22⋊C4—61no—
384#217—21no—
385#217—21no—
386#217—61no—
387#217—61no—
388#217—61no—
389#217—61no—
390#217—121no—
391#216—22no—
392#216—62no—
393#216—62no—
394#216—62no—
395#216—62no—
396#216—62no—
397#216—122no—
398(C2×D3)⋊C4—21no—
399(C2×D3)⋊C4—21no—
400(C2×D3)⋊C4—61no—
401(C2×D3)⋊C4—61no—
402C4⋊Dic3—21no—
403C4⋊Dic3—31no—
404C4⋊Dic3—31no—
405C4⋊Dic3—61no—
406C4⋊Dic3—61no—
407C4⋊Dic3—61no—
408C4⋊Dic3C22×D311yescharacteristic
409C4⋊Dic3C22×D311yescharacteristic
410Dic3⋊C4—21no—
411Dic3⋊C4—21no—
412Dic3⋊C4—21no—
413Dic3⋊C4—21no—
414Dic3⋊C4—61no—
415Dic3⋊C4—61no—
416Dic3⋊C4—61no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419Dic3⋊C4—61no—
420Dic3⋊C4—121no—
421#208—22no—
422#208—62no—
423#208—62no—
424#208—62no—
425#208—62no—
426#208—122no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—31no—
429C2×C3⋊C8—34no—
430C2×C3⋊C8—31no—
431C2×C3⋊C8—31no—
432C2×C3⋊C8—61no—
433C2×C3⋊C8—61no—
434C2×C3⋊C8—62no—
435C2×C3⋊C8C22×D311yescharacteristic
436C2×C3⋊C8C22×D311yescharacteristic
437Dic12—62no—
438ΓL(1,𝔽25)—62no—
439ΓL(1,𝔽25)—62no—
440D3×C8—34no—
441D3×C8—62no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32C22×D411yescharacteristic
446C2×C3×D3—21no—
447C2×C3×D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—44no—
450C2×C3×D3#12112yes—
451C2×C3×D3#13712yes—
452C2×C3×D3#13712yes—
453C32×C4—21no—
454C32×C4—41no—
455C32×C4—41no—
456C32×C4C22×D411yescharacteristic
457C32×C4C2×#4111yescharacteristic
458C3⋊Dic3—41no—
459C3⋊Dic3—41no—
460C3×Dic3—21no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3—41no—
464C3×Dic3—41no—
465C3×Dic3#12112yes—
466C22×Q8—31no—
467C22×Q8—91no—
468C23×C4—31no—
469C2×Q16—31no—
470C2×Q16—91no—
471C2×Q16—91no—
472C2×Q16—91no—
473C2×Q16—184no—
474C2×M16—31no—
475C2×M16—91no—
476C2×M16—91no—
477C2×M16—91no—
478C2×M16—184no—
479C22×C8—91no—
480C22×C8—91no—
481C22⋊Q8—31no—
482C22⋊Q8—31no—
483C22⋊Q8—31no—
484C22⋊Q8—31no—
485C22⋊Q8—61no—
486C22⋊Q8—61no—
487C22⋊Q8—91no—
488C22⋊Q8—91no—
489C22⋊Q8—91no—
490C22⋊Q8—181no—
491C22⋊Q8—181no—
492C22⋊Q8D3211yescharacteristic
493C2×C4⋊C4—31no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—91no—
496C2×C4⋊C4—181no—
497C2×C22⋊C4—61no—
498C2×C22⋊C4—181no—
499#106—31no—
500#106—91no—
501#106—91no—
502#106—91no—
503#103—31no—
504#103—31no—
505#103—91no—
506#103—91no—
507#103—91no—
508#103—91no—
509#103—91no—
510#103—91no—
511C23×C3—21no—
512C23×C3—31no—
513C23×C3—31no—
514C23×C3—62no—
515C23×C3—62no—
516C23×C3—62no—
517C23×C3D3×D411yescharacteristic
518C23×C3C2×#6711yescharacteristic
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3C2×#6711yescharacteristic
523C22×D3C2×#6711yescharacteristic
524C3×Q8—21no—
525C3×Q8—21no—
526C3×Q8—21no—
527C3×Q8—21no—
528C3×Q8—41no—
529C3×Q8—41no—
530C3×Q8—61no—
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8—122no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—31no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—31no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—41no—
553C2×C3×C4—62no—
554C2×C3×C4—62no—
555C2×C3×C4—62no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4—122no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568C2×Dic3—22no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—61no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—121no—
578C2×Dic3—121no—
579C2×Dic3—122no—
580C2×Dic3—122no—
581C2×Dic3C2×#6711yescharacteristic
582C2×Dic3C2×#6711yescharacteristic
583C4×D3—22no—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—22no—
587C4×D3—42no—
588C4×D3—42no—
589C4×D3—122no—
590C4×D3—122no—
591C4×D3D3×D412yes—
592C4×D3#23712yes—
593Dic6—21no—
594Dic6—21no—
595Dic6—21no—
596Dic6—21no—
597Dic6—42no—
598Dic6—61no—
599Dic6—61no—
600Dic6—61no—
601Dic6—61no—
602Dic6—121no—
603Dic6—121no—
604Dic6—122no—
605Dic6—122no—
606C3×C8—32no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—32no—
610C3⋊C8—32no—
611C3⋊C8—62no—
612C3⋊C8—61no—
613C3⋊C8—61no—
614C3⋊C8—121no—
615C3⋊C8D3×D412yes—
616C2×C32—41no—
617C2×C32C2×#12111yescharacteristic
618C2×C32C2×#13711yescharacteristic
619C2×C32C2×#13711yescharacteristic
620C3×D3—41no—
621C3×D3#47014yescomplemented
622C24—31no—
623C2×Q8—31no—
624C2×Q8—31no—
625C2×Q8—61no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—91no—
629C2×Q8—181no—
630C2×Q8—182no—
631C2×Q8—182no—
632C2×Q8C2×D3211yescharacteristic
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—181no—
643C22×C4—181no—
644C22×C4C2×D3211yescharacteristic
645Q16—62no—
646Q16—182no—
647Q16—182no—
648Q16—182no—
649M16—62no—
650M16—182no—
651M16—182no—
652M16—182no—
653C2×C8—31no—
654C2×C8—31no—
655C2×C8—94no—
656C2×C8—91no—
657C2×C8—91no—
658C2×C8—182no—
659C4⋊C4—21no—
660C4⋊C4—31no—
661C4⋊C4—31no—
662C4⋊C4—61no—
663C4⋊C4—61no—
664C4⋊C4—61no—
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—91no—
668C4⋊C4—181no—
669C4⋊C4—181no—
670C4⋊C4—181no—
671C4⋊C4—181no—
672C4⋊C4C2×D3211yescharacteristic
673C22⋊C4—21no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—181no—
679C22⋊C4—181no—
680C22⋊C4—181no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—32no—
689C22×C3—32no—
690C22×C3—32no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—61no—
695C22×C3—61no—
696C22×C3—61no—
697C22×C3—124no—
698C22×C3C2×D3×D411yescharacteristic
699C22×C3C22×#6711yescharacteristic
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—44no—
704C2×D3#93912yes—
705C2×D3#94212yes—
706C2×D3#95112yes—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—32no—
712C3×C4—41no—
713C3×C4—41no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—61no—
718C3×C4—81no—
719C3×C4—81no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4—121no—
724C3×C4C2×D3×D411yescharacteristic
725C3×C4C2×D3×D411yescharacteristic
726C3×C4C2×#23711yescharacteristic
727C3×C4D3×#4111yescharacteristic
728Dic3—21no—
729Dic3—41no—
730Dic3—41no—
731Dic3—41no—
732Dic3—41no—
733Dic3—121no—
734Dic3—121no—
735Dic3—121no—
736Dic3—121no—
737Dic3—241no—
738Dic3—241no—
739Dic3#93912yes—
740C32C2×#47011yescharacteristic, complemented, Sylow
741C23—31no—
742C23—31no—
743C23—62no—
744C23—62no—
745C23—62no—
746C23D3×#6711yescharacteristic
747Q8—21no—
748Q8—21no—
749Q8—61no—
750Q8—61no—
751Q8—61no—
752Q8—61no—
753Q8—122no—
754Q8—181no—
755Q8—181no—
756Q8—362no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—31no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—31no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—122no—
775C2×C4—122no—
776C2×C4—181no—
777C2×C4—181no—
778C2×C4—362no—
779C2×C4—362no—
780C2×C4D3×#6711yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—32no—
783C8—61no—
784C8—92no—
785C8—181no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—34no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—81no—
793C2×C3—121no—
794C2×C3D3×#12111yescharacteristic
795C2×C3D3×#13711yescharacteristic
796C2×C3D3×#13711yescharacteristic
797C2×C3C2×#93911yescharacteristic
798C2×C3C2×#94211yescharacteristic
799C2×C3C2×#95111yescharacteristic
800D3—41no—
801D3#505214yesdirect product factor
802C22—21no—
803C22—21no—
804C22—21no—
805C22—32no—
806C22—32no—
807C22—32no—
808C22—61no—
809C22—61no—
810C22—61no—
811C22—124no—
812C22C2×D3×#6711yescharacteristic
813C4—21no—
814C4—32no—
815C4—41no—
816C4—41no—
817C4—61no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—361no—
823C4—361no—
824C4D32×D411yescharacteristic
825C4D3×#23711yescharacteristic
826C3—21no—
827C3D3×#47011yescharacteristic, complemented
828C3C2×#505211yescharacteristic, complemented
829C2—34no—
830C2—41no—
831C2—121no—
832C2D3×#93911yescharacteristic
833C2D3×#94211yescharacteristic
834C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC23×C3×D3D4
hypercenterC22⋊Q8D32
hypocenterC32C2×#470
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×D3×#216C2semidirect
5. #10592751C2semidirect
6. C3×#5052C2semidirect
7. #10591638C2semidirect
8. #10591598C2semidirect
9. D3×#835C2semidirect
10. #10591189C2semidirect
11. #10591121C2semidirect
12. D3×#810C2semidirect
13. #10590587C2semidirect
14. D3×#808C2semidirect
15. #10590520C2semidirect
22. C2×#3756C22semidirect
26. C2×C3×#216C22semidirect
44. C2×#3719C22semidirect
45. C2×#3718C22semidirect
51. #63662C22semidirect
52. #63637C22semidirect
53. #63635C22semidirect
54. C3×#835C22semidirect
55. C3×#810C22semidirect
56. C3×#808C22semidirect
57. #63574C22semidirect
58. #63573C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63565C22semidirect
85. #5052D3direct (N × H)
184. C2×#216C2×D3semidirect
233. #835C2×D3semidirect
243. #810C2×D3semidirect
250. #808C2×D3semidirect
621. C3×D3#470semidirect
740. C32C2×#470semidirect
801. D3#5052direct (N × H)
827. C3D3×#470semidirect
828. C3C2×#5052semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C22⋊Q82
C2×D3×#2162
D3×#9242
C2×D3×#2082
#105927512
C3×#50522
#105916382
#105915982
D3×#8352
#105911892
#105911212
D3×#8102
#105905872
D3×#8082
#105905202
C2×#50523
D3×#4703