Finite Group Databasebeta

← D3×#5154 #11874345

Subgroups — D3×#5154 #11874345

Order 1152.

1408 conjugacy classes of subgroups.

The subgroup lattice has 875 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×D8C211yesmaximal, characteristic, complemented
2D3×#940C211yesmaximal, characteristic, complemented
3D3×#936C211yesmaximal, characteristic, complemented
4C2×D3×#214C211yesmaximal, characteristic, complemented
5C2×D3×#213C211yesmaximal, characteristic, complemented
6C2×D3×#204C211yesmaximal, characteristic, complemented
7#10592853C211yesmaximal, characteristic, complemented
8C3×#5154C211yesmaximal, characteristic, complemented
9#10591485C211yesmaximal, characteristic, complemented
10#10591483C211yesmaximal, characteristic, complemented
11#10591475C211yesmaximal, characteristic, complemented
12#10591469C211yesmaximal, characteristic, complemented
13#10590887C211yesmaximal, characteristic, complemented
14#10590883C211yesmaximal, characteristic, complemented
15D3×#815C211yesmaximal, characteristic, complemented
16C2×#5154—31nomaximal
17D3×#496—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C2×D3×#67—22no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic, complemented
24#64149C2211yescharacteristic, complemented
25#64145C2211yescharacteristic, complemented
26C2×#3754C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28C2×#3744C2211yescharacteristic, complemented
29C3×#940C2211yescharacteristic, complemented
30C3×#936C2211yescharacteristic, complemented
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C3×D3×D8—24no—
36C2×C3×D24C2211yescharacteristic, complemented
37C2×C3×#204C2211yescharacteristic, complemented
38C2×C3×D3×C8C2211yescharacteristic
39#63979—22no—
40D3×#217—22no—
41#63959—22no—
42D3×#214—24no—
43D3×#213—24no—
44#63914C2211yescharacteristic, complemented
45#63911C2211yescharacteristic, complemented
46C4×D3×Dic3C2211yescharacteristic
47#63863C2211yescharacteristic, complemented
48#63860C2211yescharacteristic, complemented
49C2×#3717C2211yescharacteristic, complemented
50C2×#3716C2211yescharacteristic, complemented
51C2×#3716C2211yescharacteristic, complemented
52C2×#3715C2211yescharacteristic, complemented
53C2×#3714C2211yescharacteristic, complemented
54C2×#3713C2211yescharacteristic, complemented
55C2×D3×C3⋊C8C2211yescharacteristic
56D3×#204—24no—
57#63642C2211yescharacteristic, complemented
58C3×#815C2211yescharacteristic, complemented
59#63555C2211yescharacteristic, complemented
60#63554C2211yescharacteristic, complemented
61C22×C3×D8—31no—
62C2×#940—31no—
63C2×#936—31no—
64C22×#214—31no—
65C22×#213—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68C2×D3×D8—31no—
69C2×D3×D8D311yescharacteristic, complemented
70C22×#204—31no—
71D3×#127—31no—
72D3×#124—31no—
73C3×#496—31no—
74#5176—31no—
75#5176—31no—
76#5154—31no—
77#5154—31no—
78#5154—31no—
79#5154—31no—
80#5154—31no—
81#5154—31no—
82#5154—31no—
83#5154—31no—
84#5154—31no—
85#5154—61no—
86#5154D311yescharacteristic, direct product factor
87C2×#815—31no—
88#5074—31no—
89#5058—31no—
90#4712—31no—
91D3×#97—31no—
92C23×C3×D3—21no—
93C23×C3×D3—21no—
94C22×D32—21no—
95C2×C32×D4C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×#638—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—22no—
104C3×D3×D4—22no—
105C3×D3×D4—22no—
106C3×D3×D4—22no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112D3×#67—48no—
113C2×#627—21no—
114C2×#626—21no—
115C2×#626—22no—
116C2×#625—22no—
117C2×D3×Dic3—21no—
118C2×D3×Dic3D412yes—
119D3×D12—22no—
120D3×D12—22no—
121D3×Dic6—22no—
122D3×Dic6—22no—
123C32×D8—22no—
124C2×C32×C8C2311yescharacteristic
125#3757—22no—
126#3754—22no—
127#3753—22no—
128C4×C3⋊Dic3C2311yescharacteristic
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130#3744—22no—
131C3×#217—22no—
132C3×#214—22no—
133C3×#213—22no—
134C3×#213—22no—
135C3×#213—22no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×#204—22no—
141C3×D3×C8D414yescomplemented
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144Dic32D412yes—
145#3717—22no—
146#3716—22no—
147#3716—22no—
148#3715—22no—
149#3714—22no—
150#3713—22no—
151D3×C3⋊C8D414yescomplemented
152C2×#496—91noSylow
153C22×C3×D4—31no—
154C22×C3×D4—31no—
155C22×#67—62no—
156C2×D3×Q8—31no—
157C2×D3×D4—31no—
158C2×D3×D4—62no—
159C2×D3×D4C2×D311yescharacteristic
160C2×D3×D4C2×D311yescharacteristic
161C22×D12—31no—
162C22×Dic6—31no—
163C2×C3×SD16—31no—
164C2×C3×SD16—31no—
165C2×C3×D8—21no—
166C2×C3×D8—31no—
167C2×C3×D8—31no—
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C2×C3×D8—64no—
171C2×C3×D8C2×D311yescharacteristic, complemented
172C2×C3×D8C2×D311yescharacteristic, complemented
173C22×C3×C8—31no—
174C3×#127—31no—
175C3×#124—31no—
176C2×#217—62no—
177#947—31no—
178C2×#215—31no—
179C2×#215—31no—
180#940—31no—
181#940—31no—
182#940—31no—
183#940—31no—
184#940—31no—
185#940—61no—
186#940—62no—
187#940—62no—
188#940C2×D311yescharacteristic, complemented
189#936—31no—
190#936—31no—
191#936—31no—
192#936—31no—
193#936—61no—
194#936—62no—
195#936C2×D311yescharacteristic, complemented
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#214—31no—
200C2×#214—31no—
201C2×#214—61no—
202C2×#214—64no—
203C2×#214C2×D311yescharacteristic, complemented
204C2×#213—31no—
205C2×#213—31no—
206C2×#213—31no—
207C2×#213—31no—
208C2×#213—31no—
209C2×#213—61no—
210C2×#213—64no—
211C2×#213C2×D311yescharacteristic, complemented
212C2×#213C2×D311yescharacteristic, complemented
213C2×#213C2×D311yescharacteristic, complemented
214C2×C4×Dic3—31no—
215C22×C3⋊C8—31no—
216D3×SD16—64no—
217D3×SD16—64no—
218D3×D8—24no—
219D3×D8—64no—
220C2×D24—31no—
221C2×D24C2×D311yescharacteristic, complemented
222C2×#204—31no—
223C2×#204—31no—
224C2×#204—31no—
225C2×#204—31no—
226C2×#204—31no—
227C2×#204—61no—
228C2×#204—64no—
229C2×#204C2×D311yescharacteristic, complemented
230C2×D3×C8—31no—
231C2×D3×C8C2×D311yescharacteristic
232#885—62no—
233D3×C22⋊C4—62no—
234#875—31no—
235#874—31no—
236C42×D3—31no—
237C3×#97—31no—
238#815—31no—
239#815—31no—
240#815—31no—
241#815—31no—
242#815—31no—
243#815—61no—
244#815C2×D311yescharacteristic, complemented
245#803—31no—
246C23×C32—21no—
247C23×C32—21no—
248C22×C3⋊D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—21no—
252C22×C3×D3—42no—
253C22×C3×D3—42no—
254C22×C3×D3—44no—
255C22×C3×D3—44no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—42no—
258C2×D32—44no—
259C32×D4—21no—
260C32×D4—21no—
261C32×D4—21no—
262C32×D4—21no—
263C2×C32×C4C2411yescharacteristic
264#638—44no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3C2×D412yes—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269#634—21no—
270#634—21no—
271C3×#67—44no—
272C3×#67—42no—
273C3×#67—42no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3C2×D412yes—
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×C4×D3C2×D412yes—
284C3×C4×D3C2×D412yes—
285C3×Dic6—21no—
286C3×Dic6—21no—
287#627—42no—
288#626—44no—
289#626—42no—
290#625—44no—
291D3×Dic3—24no—
292D3×Dic3—42no—
293C32×C8C2×D412yescomplemented
294C3⋊(C3⋊C8)C2×D412yescomplemented
295C3×C3⋊C8C2×D412yescomplemented
296C3×C3⋊C8C2×D412yescomplemented
297C22×SD16—91no—
298C22×SD16—91no—
299C22×D8—31no—
300C22×D8—91no—
301C2×#127—91no—
302C2×#124—91no—
303#496—31no—
304#496—91no—
305#496—91no—
306#496—91no—
307#496—91no—
308#496—91no—
309#496—91no—
310#496—91no—
311C2×#97—91no—
312C24×C3—61no—
313C24×C3—61no—
314C23×D3—21no—
315C23×D3—21no—
316C23×D3—61no—
317C23×D3—61no—
318C2×C3×Q8—31no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—62no—
325C2×C3×D4—62no—
326C2×C3×D4—62no—
327C2×C3×D4—62no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—62no—
331C2×C3×D4C22×D311yescharacteristic
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C2×C3×D4C22×D311yescharacteristic
335C22×C3×C4—31no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—22no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—61no—
345C2×#67—122no—
346C2×#67—128no—
347C22×Dic3—32no—
348C22×Dic3—61no—
349D3×Q8—62no—
350D3×Q8—62no—
351D3×D4—22no—
352D3×D4—22no—
353D3×D4—22no—
354D3×D4—22no—
355D3×D4—62no—
356D3×D4—62no—
357D3×D4—128no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—61no—
361C2×D12—62no—
362C2×D12—62no—
363C2×D12—62no—
364C2×D12—61no—
365C2×D12C22×D311yescharacteristic
366C2×D12C22×D311yescharacteristic
367C2×D12C22×D311yescharacteristic
368C2×C4×D3—32no—
369C2×C4×D3—61no—
370C2×C4×D3C22×D311yescharacteristic
371C2×Dic6—31no—
372C2×Dic6—31no—
373C2×Dic6—61no—
374C2×Dic6—62no—
375C2×Dic6—62no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6C22×D311yescharacteristic
379C3×SD16—62no—
380C3×SD16—62no—
381C3×D8—22no—
382C3×D8—22no—
383C3×D8—42no—
384C3×D8—62no—
385C3×D8—62no—
386C3×D8—62no—
387C3×D8—62no—
388C2×C3×C8—21no—
389C2×C3×C8—31no—
390C2×C3×C8—31no—
391C2×C3×C8—34no—
392C2×C3×C8C22×D311yescharacteristic
393C2×C3×C8C22×D311yescharacteristic
394C3×C22⋊C4—62no—
395C3×C42—31no—
396#217—22no—
397#217—62no—
398#217—62no—
399#217—62no—
400#217—62no—
401#217—122no—
402#215—62no—
403#215—62no—
404#214—22no—
405#214—62no—
406#214—62no—
407#214—62no—
408#214—62no—
409#214—62no—
410#214—122no—
411#213—22no—
412#213—22no—
413#213—22no—
414#213—62no—
415#213—62no—
416#213—62no—
417#213—62no—
418#213—62no—
419#213—122no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—62no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—32no—
425C4×Dic3—32no—
426C4×Dic3—61no—
427C4×Dic3C22×D311yescharacteristic
428C2×C3⋊C8—31no—
429C2×C3⋊C8—31no—
430C2×C3⋊C8—34no—
431C2×C3⋊C8—61no—
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—22no—
435D24—62no—
436#204—22no—
437#204—62no—
438#204—62no—
439#204—62no—
440#204—62no—
441#204—62no—
442#204—122no—
443D3×C8—34no—
444D3×C8#6714yescomplemented
445C22×C32—41no—
446C22×C32—41no—
447C22×C32—42no—
448C22×C32—42no—
449C22×C32C22×D411yescharacteristic
450C2×C3⋊D3—41no—
451C2×C3⋊D3—42no—
452C2×C3×D3—41no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—42no—
456C2×C3×D3—42no—
457C2×C3×D3—42no—
458C2×C3×D3—84no—
459C2×C3×D3—84no—
460C2×C3×D3#12712yes—
461C2×C3×D3AGL(1,ℤ/8)14yes—
462D32—84no—
463C32×C4C22×D411yescharacteristic
464C32×C4C22×D411yescharacteristic
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—41no—
469C3×Dic3#12712yes—
470C22×Q8—91no—
471C22×D4—31no—
472C22×D4—31no—
473C22×D4—91no—
474C22×D4—182no—
475C2×SD16—31no—
476C2×SD16—31no—
477C2×SD16—91no—
478C2×SD16—91no—
479C2×SD16—91no—
480C2×SD16—91no—
481C2×SD16—91no—
482C2×SD16—91no—
483C2×SD16—184no—
484C2×SD16—184no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—31no—
489C2×D8—64no—
490C2×D8—91no—
491C2×D8—91no—
492C2×D8—91no—
493C2×D8—184no—
494C2×D8D3211yescharacteristic, complemented
495C22×C8—31no—
496C22×C8—91no—
497#127—31no—
498#127—91no—
499#127—91no—
500#127—91no—
501#127—182no—
502#124—31no—
503#124—91no—
504#124—91no—
505#124—91no—
506#124—182no—
507C2×C22⋊C4—182no—
508C2×C42—91no—
509#97—31no—
510#97—91no—
511#97—91no—
512#97—91no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—31no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—124no—
524C23×C3—122no—
525C23×C3—122no—
526C23×C3—124no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—21no—
530C22×D3—44no—
531C22×D3—44no—
532C22×D3—42no—
533C22×D3—42no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—121no—
537C22×D3—122no—
538C22×D3—124no—
539C22×D3—124no—
540C22×D3—122no—
541C22×D3D3×D411yescharacteristic
542C3×Q8—61no—
543C3×Q8—61no—
544C3×D4—21no—
545C3×D4—21no—
546C3×D4—21no—
547C3×D4—21no—
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—41no—
555C3×D4—41no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—124no—
565C2×C3×C4—21no—
566C2×C3×C4—31no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—32no—
570C2×C3×C4—61no—
571C2×C3×C4C23×D311yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573#67—44no—
574#67—42no—
575#67—42no—
576#67—124no—
577#67—124no—
578#67—124no—
579#67—124no—
580#67—124no—
581#67—122no—
582#67—244no—
583C2×Dic3—21no—
584C2×Dic3—32no—
585C2×Dic3—32no—
586C2×Dic3—62no—
587C2×Dic3—64no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—121no—
591C2×Dic3—122no—
592C2×Dic3D3×D412yes—
593C2×Dic3D3×D411yescharacteristic
594D12—21no—
595D12—21no—
596D12—21no—
597D12—21no—
598D12—21no—
599D12—21no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—121no—
605D12—121no—
606D12—122no—
607D12—124no—
608C4×D3—64no—
609C4×D3—122no—
610C4×D3D3×D412yes—
611C4×D3C2×#6712yes—
612Dic6—21no—
613Dic6—21no—
614Dic6—61no—
615Dic6—61no—
616Dic6—61no—
617Dic6—61no—
618Dic6—121no—
619Dic6—121no—
620Dic6—122no—
621Dic6—122no—
622C3×C8—22no—
623C3×C8—32no—
624C3×C8—32no—
625C3×C8D3×D412yescomplemented
626C3×C8C2×#6712yescomplemented
627C3⋊C8—32no—
628C3⋊C8—32no—
629C3⋊C8—62no—
630C3⋊C8D3×D412yescomplemented
631C3⋊C8C2×#6712yescomplemented
632C2×C32—81no—
633C2×C32—81no—
634C2×C32C2×#12711yescharacteristic
635C2×C32C2×AGL(1,ℤ/8)12yes—
636C3⋊D3—81no—
637C3×D3—81no—
638C3×D3—81no—
639C3×D3—81no—
640C3×D3#49614yescomplemented
641C24—61no—
642C24—61no—
643C24—181no—
644C2×Q8—31no—
645C2×Q8—91no—
646C2×Q8—181no—
647C2×Q8—182no—
648C2×Q8—182no—
649C2×D4—31no—
650C2×D4—31no—
651C2×D4—31no—
652C2×D4—62no—
653C2×D4—62no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—61no—
657C2×D4—62no—
658C2×D4—61no—
659C2×D4—91no—
660C2×D4—182no—
661C2×D4—182no—
662C2×D4—182no—
663C2×D4—181no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—368no—
667C2×D4C2×D3211yescharacteristic
668C2×D4C2×D3211yescharacteristic
669C22×C4—31no—
670C22×C4—92no—
671C22×C4—181no—
672SD16—62no—
673SD16—62no—
674SD16—182no—
675SD16—182no—
676SD16—182no—
677SD16—182no—
678SD16—182no—
679SD16—182no—
680D8—22no—
681D8—62no—
682D8—62no—
683D8—62no—
684D8—62no—
685D8—182no—
686D8—182no—
687D8—182no—
688C2×C8—31no—
689C2×C8—31no—
690C2×C8—34no—
691C2×C8—94no—
692C2×C8—91no—
693C2×C8C2×D3211yescharacteristic
694C22⋊C4—62no—
695C22⋊C4—182no—
696C22⋊C4—182no—
697C22⋊C4—182no—
698C42—31no—
699C42—92no—
700C42—91no—
701C22×C3—21no—
702C22×C3—32no—
703C22×C3—34no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—41no—
711C22×C3—41no—
712C22×C3—82no—
713C22×C3—81no—
714C22×C3—81no—
715C22×C3—82no—
716C22×C3—121no—
717C22×C3—121no—
718C22×C3—122no—
719C22×C3—122no—
720C22×C3—122no—
721C22×C3—121no—
722C22×C3—244no—
723C22×C3—244no—
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D411yescharacteristic
726C2×D3—41no—
727C2×D3—42no—
728C2×D3—42no—
729C2×D3—42no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—84no—
733C2×D3—84no—
734C2×D3—121no—
735C2×D3—122no—
736C2×D3—122no—
737C2×D3—121no—
738C2×D3—241no—
739C2×D3—242no—
740C2×D3—244no—
741C2×D3—244no—
742C2×D3#91114yes—
743C2×D3#94012yes—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—32no—
747C3×C4—62no—
748C3×C4—121no—
749C3×C4C2×D3×D411yescharacteristic
750C3×C4C2×D3×D411yescharacteristic
751C3×C4C2×D3×D411yescharacteristic
752C3×C4C22×#6711yescharacteristic
753Dic3—22no—
754Dic3—41no—
755Dic3—62no—
756Dic3—62no—
757Dic3—122no—
758Dic3—121no—
759Dic3—121no—
760Dic3—241no—
761Dic3#94012yes—
762C32C2×#49611yescharacteristic, complemented, Sylow
763C23—21no—
764C23—21no—
765C23—31no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—122no—
770C23—122no—
771C23—124no—
772C23—124no—
773C23—181no—
774C23—362no—
775C23—364no—
776Q8—61no—
777Q8—61no—
778Q8—181no—
779Q8—181no—
780Q8—362no—
781D4—21no—
782D4—21no—
783D4—21no—
784D4—21no—
785D4—61no—
786D4—61no—
787D4—61no—
788D4—61no—
789D4—61no—
790D4—61no—
791D4—122no—
792D4—122no—
793D4—124no—
794D4—181no—
795D4—181no—
796D4—362no—
797D4—364no—
798D4—364no—
799D4—364no—
800C2×C4—31no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—61no—
805C2×C4—92no—
806C2×C4—184no—
807C2×C4—181no—
808C2×C4—362no—
809C2×C4C22×D3211yescharacteristic
810C8—32no—
811C8—32no—
812C8—92no—
813C8D3×#6712yescomplemented
814C2×C3—22no—
815C2×C3—21no—
816C2×C3—34no—
817C2×C3—81no—
818C2×C3—81no—
819C2×C3—81no—
820C2×C3—81no—
821C2×C3—161no—
822C2×C3—161no—
823C2×C3—241no—
824C2×C3—241no—
825C2×C3—241no—
826C2×C3D3×#12711yescharacteristic
827C2×C3C2×#91112yes—
828C2×C3D3×AGL(1,ℤ/8)12yes—
829C2×C3C2×#94011yescharacteristic
830D3—81no—
831D3—81no—
832D3—81no—
833D3—241no—
834D3—241no—
835D3—481no—
836D3#515414yesdirect product factor
837C22—34no—
838C22—32no—
839C22—42no—
840C22—42no—
841C22—41no—
842C22—41no—
843C22—122no—
844C22—122no—
845C22—122no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—244no—
850C22—244no—
851C22—362no—
852C22—361no—
853C22—724no—
854C22D32×D411yescharacteristic
855C4—32no—
856C4—62no—
857C4—121no—
858C4—182no—
859C4—361no—
860C4D32×D411yescharacteristic
861C4C2×D3×#6711yescharacteristic
862C3—21no—
863C3D3×#49611yescharacteristic, complemented
864C3C2×#515411yescharacteristic, complemented
865C2—34no—
866C2—81no—
867C2—81no—
868C2—241no—
869C2—241no—
870C2—241no—
871C2—721no—
872C2D3×#91112yes—
873C2D3×#94011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32C2×#496
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×D8C2semidirect
2. D3×#940C2semidirect
3. D3×#936C2semidirect
4. C2×D3×#214C2semidirect
5. C2×D3×#213C2semidirect
6. C2×D3×#204C2semidirect
7. #10592853C2semidirect
8. C3×#5154C2semidirect
9. #10591485C2semidirect
10. #10591483C2semidirect
11. #10591475C2semidirect
12. #10591469C2semidirect
13. #10590887C2semidirect
14. #10590883C2semidirect
15. D3×#815C2semidirect
23. C2×C32×D8C22semidirect
24. #64149C22semidirect
25. #64145C22semidirect
26. C2×#3754C22semidirect
27. C2×#3753C22semidirect
28. C2×#3744C22semidirect
29. C3×#940C22semidirect
30. C3×#936C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#213C22semidirect
36. C2×C3×D24C22semidirect
37. C2×C3×#204C22semidirect
44. #63914C22semidirect
45. #63911C22semidirect
47. #63863C22semidirect
48. #63860C22semidirect
49. C2×#3717C22semidirect
50. C2×#3716C22semidirect
51. C2×#3716C22semidirect
52. C2×#3715C22semidirect
53. C2×#3714C22semidirect
54. C2×#3713C22semidirect
57. #63642C22semidirect
58. C3×#815C22semidirect
59. #63555C22semidirect
60. #63554C22semidirect
69. C2×D3×D8D3semidirect
86. #5154D3direct (N × H)
141. C3×D3×C8D4semidirect
151. D3×C3⋊C8D4semidirect
171. C2×C3×D8C2×D3semidirect
172. C2×C3×D8C2×D3semidirect
188. #940C2×D3semidirect
195. #936C2×D3semidirect
203. C2×#214C2×D3semidirect
211. C2×#213C2×D3semidirect
212. C2×#213C2×D3semidirect
213. C2×#213C2×D3semidirect
221. C2×D24C2×D3semidirect
229. C2×#204C2×D3semidirect
244. #815C2×D3semidirect
293. C32×C8C2×D4semidirect
294. C3⋊(C3⋊C8)C2×D4semidirect
295. C3×C3⋊C8C2×D4semidirect
296. C3×C3⋊C8C2×D4semidirect
444. D3×C8#67semidirect
494. C2×D8D32semidirect
625. C3×C8D3×D4semidirect
626. C3×C8C2×#67semidirect
630. C3⋊C8D3×D4semidirect
631. C3⋊C8C2×#67semidirect
640. C3×D3#496semidirect
762. C32C2×#496semidirect
813. C8D3×#67semidirect
836. D3#5154direct (N × H)
863. C3D3×#496semidirect
864. C3C2×#5154semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×D82
D3×#9402
D3×#9362
C2×D3×#2142
C2×D3×#2132
C2×D3×#2042
#105928532
C3×#51542
#105914852
#105914832
#105914752
#105914692
#105908872
#105908832
D3×#8152
C2×#51543
D3×#4963