Finite Group Databasebeta

← D3×#5134 #11866911

Subgroups — D3×#5134 #11866911

Order 1152.

1148 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic, complemented
2D3×#930C211yesmaximal, characteristic
3D3×#924C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592833C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7#10591178C211yesmaximal, characteristic, complemented
8#10591176C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590850C211yesmaximal, characteristic, complemented
11#10590838C211yesmaximal, characteristic, complemented
12#10590833C211yesmaximal, characteristic, complemented
13#10590828C211yesmaximal, characteristic, complemented
14D3×#818C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16C2×#5134—31nomaximal
17D3×#468—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C2×D3×Dic6C2211yescharacteristic
22C2×C32×M16C2211yescharacteristic, complemented
23#64139C2211yescharacteristic
24#64133C2211yescharacteristic, complemented
25C2×#3744C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×D3×M16—24no—
30C2×C3×#204C2211yescharacteristic, complemented
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic
34C2×C3×D3×C8C2211yescharacteristic
35#63978—21no—
36D3×#217—21no—
37#63964—21no—
38D3×(C2×D3)⋊C4—21no—
39#63909C2211yescharacteristic
40#63908C2211yescharacteristic
41#63906—21no—
42D3×C4⋊Dic3C2211yescharacteristic
43D3×C4⋊Dic3C2211yescharacteristic
44D3×Dic3⋊C4—21no—
45#63857C2211yescharacteristic, complemented
46#63856C2211yescharacteristic, complemented
47#63851—21no—
48C2×#3717C2211yescharacteristic, complemented
49C2×#3716C2211yescharacteristic, complemented
50D3×#204—24no—
51#63648C2211yescharacteristic, complemented
52#63645C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#818C2211yescharacteristic, complemented
56C3×#816C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C22×C3×M16—31no—
64C2×#930—31no—
65C2×#924—31no—
66C2×D3×SD16—31no—
67C2×D3×M16D311yescharacteristic, complemented
68C22×#204—31no—
69D3×C22⋊Q8—31no—
70D3×#121—31no—
71C3×#468—31no—
72#5174—31no—
73#5134—31no—
74#5134—31no—
75#5134—31no—
76#5134—31no—
77#5134—31no—
78#5134—31no—
79#5134—31no—
80#5134—31no—
81#5134—61no—
82#5134D311yescharacteristic, direct product factor
83C2×#821—31no—
84C2×#818—31no—
85C2×#816—31no—
86#5049—31no—
87#5042—31no—
88#4886—31no—
89D3×#107—31no—
90#4812—31no—
91D3×#103—31no—
92#4780—31no—
93D3×#102—31no—
94C23×C3×D3D411yescharacteristic
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C22×C3×Dic3D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—22no—
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3D411yescharacteristic
106C2×C3×C4×D3D411yescharacteristic
107C2×C3×C4×D3C2311yescharacteristic
108C2×C3×C4×D3C2311yescharacteristic
109C2×C3×Dic6C2311yescharacteristic
110D3×#67—44no—
111C2×#627—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625—21no—
115C2×D3×Dic3—21no—
116C2×D3×Dic3—21no—
117C2×D3×Dic3—21no—
118D3×D12—22no—
119D3×D12—22no—
120D3×Dic6—22no—
121D3×Dic6—22no—
122C32×M16—22no—
123C2×C32×C8C2311yescharacteristic
124C2×C32×C8C2311yescharacteristic
125#3757—21no—
126#3752—21no—
127C4⋊(C3⋊Dic3)C2311yescharacteristic
128C4⋊(C3⋊Dic3)C2311yescharacteristic
129#3750—21no—
130#3744—22no—
131C3×#217—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3C2311yescharacteristic
134C3×C4⋊Dic3C2311yescharacteristic
135C3×Dic3⋊C4—21no—
136C3×#208—22no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×#204—22no—
140C3×ΓL(1,𝔽25)—22no—
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143C3×D3×C8D414yescomplemented
144#3724—21no—
145Dic3⋊Dic3—21no—
146Dic3⋊Dic3—21no—
147Dic3⋊Dic3—21no—
148#3722—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152#3717—22no—
153#3716—22no—
154C2×#468—91noSylow
155C23×C3×C4—31no—
156C22×#67—61no—
157C2×D3×Q8—31no—
158C2×D3×D4—31no—
159C2×D3×D4—61no—
160C22×D12—31no—
161C22×C4×D3C2×D311yescharacteristic
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C2×C3×M16—21no—
165C2×C3×M16—31no—
166C2×C3×M16—31no—
167C2×C3×M16—31no—
168C2×C3×M16—64no—
169C2×C3×M16C2×D311yescharacteristic, complemented
170C2×C3×M16C2×D311yescharacteristic, complemented
171C22×C3×C8—31no—
172C22×C3×C8—31no—
173C3×C22⋊Q8—31no—
174C3×#121—31no—
175C2×#217—61no—
176#946—31no—
177C2×#215—31no—
178#939—61no—
179#938—31no—
180C2×#214—31no—
181#930—31no—
182#930—31no—
183#930—31no—
184#930—31no—
185#930—61no—
186#930—61no—
187#930—61no—
188#930C2×D311yescharacteristic
189C2×(C2×D3)⋊C4—61no—
190C2×C4⋊Dic3—31no—
191C2×C4⋊Dic3—31no—
192#924—31no—
193#924—31no—
194#924—31no—
195#924—31no—
196#924—61no—
197#924—61no—
198#924—61no—
199#924C2×D311yescharacteristic, complemented
200C2×Dic3⋊C4—61no—
201C2×#208C2×D311yescharacteristic, complemented
202D3×SD16—64no—
203D3×M16—24no—
204C2×#204—31no—
205C2×#204—31no—
206C2×#204—31no—
207C2×#204—31no—
208C2×#204—61no—
209C2×#204—64no—
210C2×#204C2×D311yescharacteristic, complemented
211C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
212C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
213C2×D3×C8C2×D311yescharacteristic
214C2×D3×C8C2×D311yescharacteristic
215#897—31no—
216#896—61no—
217#895—31no—
218D3×C4⋊C4—31no—
219D3×C4⋊C4—31no—
220D3×C4⋊C4—61no—
221#884—61no—
222D3×C22⋊C4—61no—
223D3×C22⋊C4—61no—
224#878—61no—
225C3×#107—31no—
226C3×#103—31no—
227C3×#102—31no—
228#835—31no—
229#832—31no—
230#821—31no—
231#821—31no—
232#821—31no—
233#821—31no—
234#821—61no—
235#821C2×D311yescharacteristic, complemented
236#818—31no—
237#818—31no—
238#818—31no—
239#818—31no—
240#818—61no—
241#818C2×D311yescharacteristic, complemented
242#816—31no—
243#816—31no—
244#816—31no—
245#816—31no—
246#816—61no—
247#816C2×D311yescharacteristic, complemented
248#810—31no—
249#809—31no—
250#807—31no—
251#807—31no—
252C23×C32C2×D411yescharacteristic
253C22×C3⋊D3—21no—
254C22×C3×D3—22no—
255C22×C3×D3—22no—
256C22×C3×D3—22no—
257C22×C3×D3—21no—
258C22×C3×D3C2×D411yescharacteristic
259C22×C3×D3C2×D411yescharacteristic
260C2×D32—42no—
261C2×D32—42no—
262C2×D32—42no—
263C2×C32×C4—21no—
264C2×C32×C4—21no—
265C2×C32×C4C2×D411yescharacteristic
266C2×C32×C4C2411yescharacteristic
267#638—42no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—21no—
273#634—21no—
274#634—21no—
275C3×#67—42no—
276C2×C3×Dic3—22no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C3×D12—21no—
283C3×D12—21no—
284C3×C4×D3—22no—
285C3×C4×D3—21no—
286C3×C4×D3—21no—
287C3×C4×D3—22no—
288C3×C4×D3C2×D412yes—
289C3×C4×D3#4112yes—
290C3×Dic6—21no—
291C3×Dic6—21no—
292#627—42no—
293#626—42no—
294#626—42no—
295#625—42no—
296D3×Dic3—42no—
297D3×Dic3—42no—
298D3×Dic3—42no—
299C32×C8—21no—
300C32×C8C2×D412yescomplemented
301C3×C3⋊C8—21no—
302C3×C3⋊C8C2×D412yescomplemented
303C22×SD16—91no—
304C22×M16—31no—
305C2×C22⋊Q8—91no—
306C2×#121—91no—
307#468—31no—
308#468—91no—
309#468—91no—
310#468—91no—
311#468—91no—
312#468—91no—
313#468—91no—
314#468—91no—
315C2×#107—91no—
316C2×#103—91no—
317C2×#102—91no—
318C24×C3—31no—
319C23×D3—61no—
320C23×D3—61no—
321C23×D3D1211yescharacteristic
322C2×C3×Q8—31no—
323C2×C3×D4—31no—
324C2×C3×D4—61no—
325C22×C3×C4—21no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—21no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—121no—
343C2×#67—124no—
344C22×Dic3—61no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3D1211yescharacteristic
348D3×Q8—62no—
349D3×Q8—62no—
350D3×D4—62no—
351D3×D4—62no—
352D3×D4—124no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—62no—
357C2×D12—62no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12C22×D311yescharacteristic
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3—61no—
364C2×C4×D3—61no—
365C2×C4×D3—61no—
366C2×C4×D3D1211yescharacteristic
367C2×C4×D3D1211yescharacteristic
368C2×C4×D3C22×D311yescharacteristic
369C2×C4×D3C22×D311yescharacteristic
370C2×Dic6—31no—
371C2×Dic6—31no—
372C2×Dic6—61no—
373C2×Dic6—62no—
374C2×Dic6—62no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6C22×D311yescharacteristic
378C3×SD16—62no—
379C3×M16—22no—
380C3×M16—22no—
381C3×M16—42no—
382C3×M16—62no—
383C3×M16—62no—
384C3×M16—62no—
385C2×C3×C8—21no—
386C2×C3×C8—21no—
387C2×C3×C8—31no—
388C2×C3×C8—34no—
389C2×C3×C8—31no—
390C2×C3×C8—62no—
391C2×C3×C8C22×D311yescharacteristic
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C2×C3×C8C22×D311yescharacteristic
395C3×C4⋊C4—31no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—61no—
398C3×C22⋊C4—61no—
399C3×C22⋊C4—61no—
400#217—21no—
401#217—61no—
402#217—61no—
403#217—61no—
404#217—61no—
405#217—61no—
406#217—121no—
407#215—62no—
408#214—62no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—121no—
418C4⋊Dic3—31no—
419C4⋊Dic3—31no—
420C4⋊Dic3—31no—
421C4⋊Dic3—31no—
422C4⋊Dic3—61no—
423C4⋊Dic3—61no—
424C4⋊Dic3—61no—
425C4⋊Dic3—61no—
426C4⋊Dic3—61no—
427C4⋊Dic3C22×D311yescharacteristic
428C4⋊Dic3C22×D311yescharacteristic
429Dic3⋊C4—21no—
430Dic3⋊C4—61no—
431Dic3⋊C4—61no—
432Dic3⋊C4—61no—
433Dic3⋊C4—61no—
434Dic3⋊C4—61no—
435Dic3⋊C4—61no—
436Dic3⋊C4—61no—
437Dic3⋊C4—121no—
438#208—22no—
439C2×C3⋊C8C22×D311yescharacteristic
440C2×C3⋊C8C22×D311yescharacteristic
441#204—22no—
442#204—62no—
443#204—62no—
444#204—62no—
445#204—62no—
446#204—122no—
447ΓL(1,𝔽25)—22no—
448ΓL(1,𝔽25)—22no—
449D3×C8—22no—
450D3×C8#6714yescomplemented
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32C22×D411yescharacteristic
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—21no—
461C2×C3×D3—44no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3#12112yes—
466C2×C3×D3AGL(1,ℤ/8)12yes—
467C2×C3×D3#13712yes—
468D32—84no—
469C32×C4—21no—
470C32×C4C22×D411yescharacteristic
471C32×C4C2×#4111yescharacteristic
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3⋊Dic3—41no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3#12112yes—
480C22×Q8—91no—
481C22×D4—91no—
482C22×D4—181no—
483C23×C4—31no—
484C2×SD16—31no—
485C2×SD16—91no—
486C2×SD16—91no—
487C2×SD16—91no—
488C2×SD16—184no—
489C2×M16—31no—
490C2×M16—31no—
491C2×M16—31no—
492C2×M16—64no—
493C2×M16D3211yescharacteristic, complemented
494C22×C8—31no—
495C22×C8—31no—
496C22⋊Q8—31no—
497C22⋊Q8—91no—
498C22⋊Q8—91no—
499C22⋊Q8—91no—
500C22⋊Q8—181no—
501C22⋊Q8—181no—
502#121—31no—
503#121—91no—
504#121—91no—
505#121—91no—
506#121—181no—
507#121—181no—
508C2×C4⋊C4—91no—
509C2×C4⋊C4—91no—
510C2×C4⋊C4—181no—
511C2×C22⋊C4—181no—
512C2×C22⋊C4—181no—
513#107—31no—
514#107—91no—
515#107—91no—
516#107—91no—
517#103—31no—
518#103—91no—
519#103—91no—
520#103—91no—
521#102—31no—
522#102—91no—
523#102—91no—
524#102—91no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—62no—
529C23×C3—62no—
530C23×C3—62no—
531C23×C3—61no—
532C23×C3C2×D1211yescharacteristic
533C23×C3D3×D411yescharacteristic
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—22no—
537C22×D3—21no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3C2×D1211yescharacteristic
548C22×D3C2×D1211yescharacteristic
549C3×Q8—61no—
550C3×Q8—61no—
551C3×D4—61no—
552C3×D4—61no—
553C3×D4—122no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—41no—
565C2×C3×C4—41no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—62no—
569C2×C3×C4—61no—
570C2×C3×C4—61no—
571C2×C3×C4—61no—
572C2×C3×C4—61no—
573C2×C3×C4—61no—
574C2×C3×C4C2×D1211yescharacteristic
575C2×C3×C4D3×D411yescharacteristic
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—122no—
580#67—122no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—242no—
586C2×Dic3—22no—
587C2×Dic3—21no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—122no—
600C2×Dic3—122no—
601C2×Dic3—122no—
602C2×Dic3C2×D1211yescharacteristic
603C2×Dic3C2×D1211yescharacteristic
604D12—21no—
605D12—21no—
606D12—61no—
607D12—61no—
608D12—61no—
609D12—61no—
610D12—121no—
611D12—121no—
612D12—122no—
613D12—122no—
614C4×D3—22no—
615C4×D3—21no—
616C4×D3—21no—
617C4×D3—22no—
618C4×D3—122no—
619C4×D3—122no—
620C4×D3—122no—
621C4×D3#23512yes—
622C4×D3C2×#6712yes—
623Dic6—21no—
624Dic6—21no—
625Dic6—61no—
626Dic6—61no—
627Dic6—61no—
628Dic6—61no—
629Dic6—121no—
630Dic6—121no—
631Dic6—122no—
632Dic6—122no—
633C3×C8—21no—
634C3×C8—21no—
635C3×C8—22no—
636C3×C8—32no—
637C3×C8—41no—
638C3×C8—61no—
639C3×C8D3×D412yescomplemented
640C3×C8C2×#6712yescomplemented
641C3⋊C8—21no—
642C3⋊C8C2×#6712yescomplemented
643C2×C32—41no—
644C2×C32C2×#12111yescharacteristic
645C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
646C2×C32C2×#13711yescharacteristic
647C3⋊D3—81no—
648C3×D3—41no—
649C3×D3—81no—
650C3×D3#46814yescomplemented
651C24—31no—
652C24—181no—
653C2×Q8—31no—
654C2×Q8—91no—
655C2×Q8—181no—
656C2×Q8—182no—
657C2×Q8—182no—
658C2×D4—31no—
659C2×D4—61no—
660C2×D4—91no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—181no—
665C2×D4—181no—
666C2×D4—181no—
667C2×D4—364no—
668C22×C4—31no—
669C22×C4—31no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—181no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4C2×D3211yescharacteristic
679SD16—62no—
680SD16—182no—
681SD16—182no—
682SD16—182no—
683M16—22no—
684M16—62no—
685M16—62no—
686M16—62no—
687C2×C8—31no—
688C2×C8—34no—
689C2×C8—31no—
690C2×C8—62no—
691C2×C8C2×D3211yescharacteristic
692C2×C8C2×D3211yescharacteristic
693C4⋊C4—31no—
694C4⋊C4—31no—
695C4⋊C4—61no—
696C4⋊C4—91no—
697C4⋊C4—91no—
698C4⋊C4—181no—
699C4⋊C4—181no—
700C4⋊C4—181no—
701C4⋊C4—181no—
702C4⋊C4—181no—
703C22⋊C4—61no—
704C22⋊C4—61no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C22⋊C4—181no—
710C22⋊C4—181no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—32no—
719C22×C3—32no—
720C22×C3—32no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—124no—
728C22×C3—121no—
729C22×C3—121no—
730C22×C3—121no—
731C22×C3C22×D1211yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—44no—
737C2×D3—41no—
738C2×D3—41no—
739C2×D3—41no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—241no—
747C2×D3—241no—
748C2×D3—241no—
749C2×D3—244no—
750C2×D3—244no—
751C2×D3#90812yes—
752C2×D3#90912yes—
753C2×D3#93012yes—
754C3×C4—21no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—32no—
759C3×C4—41no—
760C3×C4—61no—
761C3×C4—121no—
762C3×C4—121no—
763C3×C4—121no—
764C3×C4C2×#23511yescharacteristic
765C3×C4C2×D3×D411yescharacteristic
766C3×C4D3×#4111yescharacteristic
767C3×C4C22×#6711yescharacteristic
768Dic3—21no—
769Dic3—41no—
770Dic3—41no—
771Dic3—41no—
772Dic3—121no—
773Dic3—121no—
774Dic3—121no—
775Dic3—121no—
776Dic3—121no—
777Dic3—121no—
778Dic3—241no—
779Dic3—241no—
780Dic3—241no—
781Dic3#93012yes—
782C32C2×#46811yescharacteristic, complemented, Sylow
783C23—31no—
784C23—31no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—61no—
789C23—181no—
790C23—362no—
791C23—362no—
792C23—362no—
793C23D3×D1211yescharacteristic
794Q8—61no—
795Q8—61no—
796Q8—181no—
797Q8—181no—
798Q8—362no—
799D4—61no—
800D4—61no—
801D4—122no—
802D4—181no—
803D4—181no—
804D4—362no—
805D4—362no—
806D4—362no—
807D4—362no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—31no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—31no—
814C2×C4—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—181no—
823C2×C4—181no—
824C2×C4—181no—
825C2×C4—362no—
826C2×C4—362no—
827C2×C4—362no—
828C2×C4D3×D1211yescharacteristic
829C2×C4C22×D3211yescharacteristic
830C8—21no—
831C8—32no—
832C8—61no—
833C8D3×#6712yescomplemented
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—34no—
838C2×C3—41no—
839C2×C3—41no—
840C2×C3—81no—
841C2×C3—121no—
842C2×C3—241no—
843C2×C3D3×#12111yescharacteristic
844C2×C3C2×#90811yescharacteristic
845C2×C3C2×#90911yescharacteristic
846C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
847C2×C3D3×#13711yescharacteristic
848C2×C3C2×#93011yescharacteristic
849D3—41no—
850D3—81no—
851D3—241no—
852D3—241no—
853D3—481no—
854D3#513414yesdirect product factor
855C22—21no—
856C22—21no—
857C22—21no—
858C22—32no—
859C22—32no—
860C22—32no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—124no—
865C22—121no—
866C22—121no—
867C22—121no—
868C22—361no—
869C22—361no—
870C22—361no—
871C22—724no—
872C22C2×D3×D1211yescharacteristic
873C4—21no—
874C4—32no—
875C4—61no—
876C4—121no—
877C4—121no—
878C4—121no—
879C4—361no—
880C4—361no—
881C4—361no—
882C4D3×#23511yescharacteristic
883C4C2×D3×#6711yescharacteristic
884C3—21no—
885C3D3×#46811yescharacteristic, complemented
886C3C2×#513411yescharacteristic, complemented
887C2—34no—
888C2—41no—
889C2—121no—
890C2—241no—
891C2—721no—
892C2D3×#90811yescharacteristic
893C2D3×#90911yescharacteristic
894C2D3×#93011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalD3×#930C2
hypercenterC2×M16D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×M16C2semidirect
3. D3×#924C2semidirect
4. C2×D3×#204C2semidirect
5. #10592833C2semidirect
6. C3×#5134C2semidirect
7. #10591178C2semidirect
8. #10591176C2semidirect
9. D3×#821C2semidirect
10. #10590850C2semidirect
11. #10590838C2semidirect
12. #10590833C2semidirect
13. #10590828C2semidirect
14. D3×#818C2semidirect
15. D3×#816C2semidirect
22. C2×C32×M16C22semidirect
24. #64133C22semidirect
25. C2×#3744C22semidirect
27. C3×#924C22semidirect
28. C2×C3×#208C22semidirect
30. C2×C3×#204C22semidirect
31. C2×C3×ΓL(1,𝔽25)C22semidirect
32. C2×C3×ΓL(1,𝔽25)C22semidirect
45. #63857C22semidirect
46. #63856C22semidirect
48. C2×#3717C22semidirect
49. C2×#3716C22semidirect
51. #63648C22semidirect
52. #63645C22semidirect
53. #63643C22semidirect
54. C3×#821C22semidirect
55. C3×#818C22semidirect
56. C3×#816C22semidirect
57. #63575C22semidirect
58. #63575C22semidirect
59. #63567C22semidirect
60. #63566C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
67. C2×D3×M16D3semidirect
82. #5134D3direct (N × H)
143. C3×D3×C8D4semidirect
169. C2×C3×M16C2×D3semidirect
170. C2×C3×M16C2×D3semidirect
199. #924C2×D3semidirect
201. C2×#208C2×D3semidirect
210. C2×#204C2×D3semidirect
211. C2×ΓL(1,𝔽25)C2×D3semidirect
212. C2×ΓL(1,𝔽25)C2×D3semidirect
235. #821C2×D3semidirect
241. #818C2×D3semidirect
247. #816C2×D3semidirect
300. C32×C8C2×D4semidirect
302. C3×C3⋊C8C2×D4semidirect
450. D3×C8#67semidirect
493. C2×M16D32semidirect
639. C3×C8D3×D4semidirect
640. C3×C8C2×#67semidirect
642. C3⋊C8C2×#67semidirect
650. C3×D3#468semidirect
782. C32C2×#468semidirect
833. C8D3×#67semidirect
854. D3#5134direct (N × H)
885. C3D3×#468semidirect
886. C3C2×#5134semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
D3×#9302
D3×#9242
C2×D3×#2042
#105928332
C3×#51342
#105911782
#105911762
D3×#8212
#105908502
#105908382
#105908332
#105908282
D3×#8182
D3×#8162
C2×#51343
D3×#4683