Finite Group Databasebeta

← #13178625

Subgroups — #13178625

Order 1728.

1590 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C212yesmaximal, complemented
2C3×#64149C211yesmaximal, characteristic, complemented
3C3×#64147C211yesmaximal, characteristic, complemented
4C3×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
5#11723726C212yesmaximal, complemented
6#11723725C212yesmaximal, complemented
7#11723718C212yesmaximal, complemented
8C4⋊#6296C211yesmaximal, characteristic, complemented
9#11723696C211yesmaximal, characteristic, complemented
10#11723691C211yesmaximal, characteristic, complemented
11C4×#6294C211yesmaximal, characteristic, complemented
12#10595139—31nomaximal
13#10595133—31nomaximal
14#10595131—31nomaximal
15C2×C33×D4C2211yescharacteristic
16C2×C3×#638C2212yes—
17C2×C3×#638C2212yes—
18C2×C3×#638C2212yes—
19C22×C3×C3⋊Dic3C2212yes—
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4×C3⋊D3C2211yescharacteristic
22C2×#6296C2212yes—
23C2×#6295C2212yes—
24#89046—28no—
25C2×#6294C2212yes—
26C2×#6294C2211yescharacteristic
27C2×#6294C2211yescharacteristic
28C3×#3757C2212yes—
29C3×#3757C2212yes—
30C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
32C3×C4×C3⋊Dic3C2211yescharacteristic
33C3×C4×C3⋊Dic3C2211yescharacteristic
34#88815C2212yes—
35#88814C2212yes—
36#88814C2212yes—
37#88813C2211yescharacteristic
38#88813C2211yescharacteristic
39C2×#3805—32no—
40C2×#3804—32no—
41C2×#3804—32no—
42#64149D311yescharacteristic, complemented
43#64147D311yescharacteristic, complemented
44D4×C3⋊Dic3D311yescharacteristic, complemented
45C3×#940—31no—
46C3×#940—31no—
47C3×#940—61no—
48C3×#938—31no—
49C3×#938—31no—
50C3×#938—61no—
51C3×D4×Dic3—31no—
52C3×D4×Dic3—31no—
53C3×D4×Dic3—61no—
54#67⋊Dic3—32no—
55Dic3×#67—32no—
56#63971—32no—
57#63970—32no—
58#63959—32no—
59#63959—32no—
60#63958—32no—
61#63953—32no—
62#63952—32no—
63#63919—31no—
64#63918—31no—
65#63918—31no—
66#63916—31no—
67#63909—31no—
68#63908—31no—
69#63898—31no—
70#63894—31no—
71Dic3×D12—31no—
72C4×#624—31no—
73C4×D3×Dic3—31no—
74C4×D3×Dic3—31no—
75C23×C33C2312yes—
76C22×C3×C3⋊D3C2312yes—
77C22×C3×C3⋊D3C2311yescharacteristic
78C33×D4—22no—
79C2×C33×C4C2311yescharacteristic
80C3×#638—24no—
81C3×#638—24no—
82C3×#638—24no—
83C2×C3×C3⋊Dic3—24no—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C2×C3×C3⋊Dic3C2312yes—
87C2×C3×C3⋊Dic3C2311yescharacteristic
88C2×C3×C3⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊Dic3C2311yescharacteristic
90C2×C3×C3⋊Dic3C2311yescharacteristic
91C3×C4⋊(C3⋊D3)—22no—
92C3×C4×C3⋊D3—22no—
93#6296—24no—
94#6295—24no—
95#6294—24no—
96#6294—22no—
97#6294D414yescomplemented
98#5716—91no—
99#5596—91no—
100#5548—91no—
101C2×C32×D4—21no—
102C2×C32×D4—21no—
103C2×C32×D4—21no—
104C2×C32×D4—41no—
105C2×C32×D4C2×D311yescharacteristic
106C2×C32×D4C2×D311yescharacteristic
107C2×C32×D4C2×D311yescharacteristic
108C2×#638C2×D312yes—
109C2×#638C2×D312yes—
110C2×#638C2×D312yes—
111C22×C3⋊Dic3C2×D312yes—
112C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
113C2×C4×C3⋊D3C2×D311yescharacteristic
114C2×C3×#67—32no—
115C2×C3×#67—32no—
116C2×C3×#67—32no—
117C2×C3×#67—32no—
118C2×C3×#67—32no—
119C2×C3×#67—32no—
120C2×C3×#67—62no—
121C2×C3×#67—62no—
122C2×C3×#67—62no—
123C22×C3×Dic3—32no—
124C22×C3×Dic3—32no—
125C22×C3×Dic3—62no—
126C2×C3×D12—31no—
127C2×C3×D12—31no—
128C2×C3×D12—61no—
129C2×C3×C4×D3—31no—
130C2×C3×C4×D3—31no—
131C2×C3×C4×D3—61no—
132C2×#627—32no—
133C2×#627—32no—
134C2×#627—32no—
135C2×#626—32no—
136C2×#626—32no—
137C2×#625—32no—
138C2×#624—31no—
139C2×#624—32no—
140C2×#624—31no—
141#3805—68no—
142#3804—68no—
143#3804—68no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—32no—
147C2×D3×Dic3—32no—
148C2×D3×Dic3—31no—
149C2×D3×Dic3—31no—
150#3757C2×D312yes—
151#3757C2×D312yes—
152C4⋊(C3⋊Dic3)C2×D311yescharacteristic
153C4⋊(C3⋊Dic3)C2×D311yescharacteristic
154C4×C3⋊Dic3C2×D311yescharacteristic
155C4×C3⋊Dic3C2×D311yescharacteristic
156C3×#217—32no—
157C3×#217—32no—
158C3×#217—32no—
159C3×#217—32no—
160C3×#217—62no—
161C3×#217—62no—
162C3×C4⋊Dic3—31no—
163C3×C4⋊Dic3—31no—
164C3×C4⋊Dic3—31no—
165C3×C4⋊Dic3—31no—
166C3×C4⋊Dic3—61no—
167C3×C4⋊Dic3—61no—
168C3×C4×Dic3—31no—
169C3×C4×Dic3—31no—
170C3×C4×Dic3—31no—
171C3×C4×Dic3—31no—
172C3×C4×Dic3—61no—
173C3×C4×Dic3—61no—
174#3724—32no—
175Dic3⋊Dic3—32no—
176Dic3⋊Dic3—32no—
177#3722—32no—
178#3722—32no—
179(C2×D3)⋊Dic3—32no—
180(C2×D3)⋊Dic3—32no—
181(C2×D3)⋊Dic3—32no—
182(C2×D3)⋊Dic3—32no—
183Dic32—31no—
184Dic32—31no—
185Dic32—31no—
186Dic32—31no—
187Dic32—31no—
188Dic32—31no—
189C22×C33—22no—
190C22×C33—22no—
191C22×C33—22no—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—22no—
196C2×C3×C3⋊D3—22no—
197C2×C3×C3⋊D3—22no—
198C2×C3×C3⋊D3C2×D412yes—
199C33×C4#4112yescomplemented
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—22no—
202C3×C3⋊Dic3—21no—
203C3×C3⋊Dic3—21no—
204C3×C3⋊Dic3C2×D412yes—
205C3×C3⋊Dic3C2×D412yes—
206C3×C3⋊Dic3#4112yescomplemented
207C2×#237—92no—
208C2×#237—92no—
209C2×#235—92no—
210C3×#127—91no—
211C3×#121—91no—
212C3×C4×D4—91no—
213#940—31no—
214#940—31no—
215#940—61no—
216#939—92no—
217#938—31no—
218#938—31no—
219#938—61no—
220#938—91no—
221#938—92no—
222#936—92no—
223D4×Dic3—31no—
224D4×Dic3—31no—
225D4×Dic3—61no—
226D4×Dic3—91no—
227D4×Dic3—92no—
228#930—91no—
229C4×#67—92no—
230C2×C4×Dic3—91no—
231#895—91no—
232#893—91no—
233#888—91no—
234#888—91no—
235#885—92no—
236#885—92no—
237#884—92no—
238#67⋊C4—92no—
239C4×D12—91no—
240C42×D3—91no—
241C42×D3—91no—
242#869—91no—
243C23×C32—22no—
244C23×C32—22no—
245C23×C32—22no—
246C23×C32—42no—
247C23×C32C22×D312yes—
248C23×C32C22×D312yes—
249C23×C32C22×D312yes—
250C22×C3⋊D3C22×D312yes—
251C22×C3⋊D3C22×D311yescharacteristic
252C22×C3×D3—31no—
253C22×C3×D3—31no—
254C22×C3×D3—32no—
255C22×C3×D3—32no—
256C22×C3×D3—61no—
257C22×C3×D3—62no—
258C32×D4—22no—
259C32×D4—24no—
260C32×D4—22no—
261C32×D4—22no—
262C32×D4—42no—
263C32×D4—42no—
264C32×D4—44no—
265C2×C32×C4—21no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—41no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272#638—24no—
273#638—24no—
274#638—24no—
275C2×C3⋊Dic3—24no—
276C2×C3⋊Dic3C22×D311yescharacteristic
277C2×C3⋊Dic3C22×D311yescharacteristic
278C2×C3⋊Dic3C22×D312yes—
279C2×C3⋊Dic3C22×D312yes—
280C2×C3⋊Dic3C22×D311yescharacteristic
281C2×C3⋊Dic3C22×D311yescharacteristic
282C2×C3⋊Dic3C22×D311yescharacteristic
283C4⋊(C3⋊D3)—22no—
284C4×C3⋊D3—22no—
285C3×#67—64no—
286C3×#67—64no—
287C3×#67—64no—
288C3×#67—64no—
289C3×#67—64no—
290C3×#67—64no—
291C3×#67—124no—
292C3×#67—124no—
293C3×#67—124no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—31no—
298C2×C3×Dic3—31no—
299C2×C3×Dic3—31no—
300C2×C3×Dic3—31no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—31no—
303C2×C3×Dic3—31no—
304C2×C3×Dic3—32no—
305C2×C3×Dic3—32no—
306C2×C3×Dic3—32no—
307C2×C3×Dic3—32no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—62no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—64no—
316C2×C3×Dic3—64no—
317C2×C3×Dic3—124no—
318C3×D12—62no—
319C3×D12—62no—
320C3×D12—122no—
321C3×C4×D3—62no—
322C3×C4×D3—62no—
323C3×C4×D3—122no—
324#627—64no—
325#627—64no—
326#627—64no—
327#626—64no—
328#626—64no—
329#625—64no—
330#624—34no—
331#624—64no—
332#624—62no—
333D3×Dic3—34no—
334D3×Dic3—34no—
335D3×Dic3—62no—
336D3×Dic3—64no—
337D3×Dic3—64no—
338D3×Dic3—62no—
339#532—271noSylow
340C2×C33—42no—
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3×C3⋊D3—22no—
345C3×C3⋊D3—42no—
346C2×C3×D4—21no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—41no—
350C2×C3×D4—92no—
351C2×C3×D4—92no—
352C2×C3×D4—92no—
353C2×C3×D4—91no—
354C2×C3×D4D3211yescharacteristic
355C2×C3×D4D3211yescharacteristic
356C2×C3×D4D3211yescharacteristic
357C22×C3×C4—92no—
358C22×C3×C4—91no—
359C2×#67—32no—
360C2×#67—32no—
361C2×#67—32no—
362C2×#67—32no—
363C2×#67—32no—
364C2×#67—32no—
365C2×#67—62no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—92no—
369C2×#67—92no—
370C22×Dic3—32no—
371C22×Dic3—32no—
372C22×Dic3—62no—
373C22×Dic3—91no—
374C22×Dic3—91no—
375C22×Dic3—92no—
376#237—188no—
377#237—188no—
378#235—188no—
379C2×D12—31no—
380C2×D12—31no—
381C2×D12—61no—
382C2×D12—92no—
383C2×C4×D3—31no—
384C2×C4×D3—31no—
385C2×C4×D3—61no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—92no—
391C2×C4×D3—92no—
392C2×Dic6—92no—
393C2×Dic6—92no—
394C2×Dic6—92no—
395C3×C4⋊C4—91no—
396C3×C4⋊C4—91no—
397C3×C22⋊C4—92no—
398C3×C22⋊C4—92no—
399C3×C42—91no—
400C3×C42—91no—
401#217—32no—
402#217—32no—
403#217—32no—
404#217—32no—
405#217—62no—
406#217—62no—
407#217—92no—
408#217—92no—
409(C2×D3)⋊C4—92no—
410(C2×D3)⋊C4—92no—
411(C2×D3)⋊C4—92no—
412(C2×D3)⋊C4—92no—
413C4⋊Dic3—31no—
414C4⋊Dic3—31no—
415C4⋊Dic3—31no—
416C4⋊Dic3—31no—
417C4⋊Dic3—61no—
418C4⋊Dic3—61no—
419C4⋊Dic3—92no—
420Dic3⋊C4—92no—
421Dic3⋊C4—92no—
422C4×Dic3—31no—
423C4×Dic3—31no—
424C4×Dic3—31no—
425C4×Dic3—31no—
426C4×Dic3—61no—
427C4×Dic3—61no—
428C4×Dic3—91no—
429C4×Dic3—91no—
430C4×Dic3—91no—
431C4×Dic3—91no—
432C4×Dic3—91no—
433C4×Dic3—91no—
434C22×C32—22no—
435C22×C32—24no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—22no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—21no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—41no—
448C22×C32—42no—
449C22×C32—42no—
450C22×C32—44no—
451C22×C32—42no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—42no—
456C22×C32—42no—
457C22×C32—82no—
458C22×C32—82no—
459C22×C32C23×D311yescharacteristic
460C22×C32C23×D311yescharacteristic
461C22×C32C23×D311yescharacteristic
462C2×C3⋊D3—21no—
463C2×C3⋊D3—21no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—22no—
466C2×C3⋊D3—22no—
467C2×C3⋊D3D3×D412yes—
468C2×C3×D3—32no—
469C2×C3×D3—32no—
470C2×C3×D3—62no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—62no—
476C2×C3×D3—62no—
477C2×C3×D3—62no—
478C2×C3×D3—62no—
479C2×C3×D3—62no—
480C2×C3×D3—62no—
481C2×C3×D3—121no—
482C2×C3×D3—121no—
483C2×C3×D3—122no—
484C2×C3×D3—122no—
485C2×C3×D3—122no—
486C32×C4—22no—
487C32×C4—22no—
488C32×C4—22no—
489C32×C4—42no—
490C32×C4#23512yescomplemented
491C32×C4#23712yescomplemented
492C32×C4#23712yescomplemented
493C3⋊Dic3—22no—
494C3⋊Dic3—22no—
495C3⋊Dic3—21no—
496C3⋊Dic3—21no—
497C3⋊Dic3D3×D412yes—
498C3⋊Dic3D3×D412yes—
499C3⋊Dic3#23712yescomplemented
500C3×Dic3—32no—
501C3×Dic3—32no—
502C3×Dic3—32no—
503C3×Dic3—32no—
504C3×Dic3—32no—
505C3×Dic3—32no—
506C3×Dic3—62no—
507C3×Dic3—62no—
508C3×Dic3—62no—
509C3×Dic3—61no—
510C3×Dic3—62no—
511C3×Dic3—62no—
512C3×Dic3—62no—
513C3×Dic3—62no—
514C3×Dic3—61no—
515C3×Dic3—61no—
516C3×Dic3—61no—
517C3×Dic3—121no—
518C3×Dic3—121no—
519C3×Dic3—122no—
520C3×Dic3—122no—
521C2×#41—272no—
522C4⋊Q8—271no—
523#127—91no—
524#124—272no—
525#121—91no—
526#121—272no—
527#121—271no—
528C4×D4—91no—
529C4×D4—271no—
530C4×D4—272no—
531C2×C42—271no—
532C33#53211yescharacteristic, complemented, Sylow
533C23×C3—22no—
534C23×C3—22no—
535C23×C3—22no—
536C23×C3—42no—
537C23×C3—91no—
538C23×C3—92no—
539C23×C3C2×D3212yes—
540C23×C3C2×D3212yes—
541C23×C3C2×D3212yes—
542C22×D3—31no—
543C22×D3—31no—
544C22×D3—32no—
545C22×D3—32no—
546C22×D3—61no—
547C22×D3—62no—
548C3×D4—24no—
549C3×D4—22no—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—42no—
553C3×D4—42no—
554C3×D4—44no—
555C3×D4—184no—
556C3×D4—184no—
557C3×D4—184no—
558C3×D4—182no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—41no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—91no—
567C2×C3×C4—91no—
568C2×C3×C4—92no—
569C2×C3×C4—92no—
570C2×C3×C4—184no—
571C2×C3×C4—182no—
572C2×C3×C4C2×D3211yescharacteristic
573C2×C3×C4C2×D3211yescharacteristic
574C2×C3×C4C2×D3211yescharacteristic
575#67—64no—
576#67—64no—
577#67—64no—
578#67—64no—
579#67—64no—
580#67—64no—
581#67—124no—
582#67—124no—
583#67—124no—
584#67—184no—
585#67—184no—
586C2×Dic3—31no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—31no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—62no—
605C2×Dic3—62no—
606C2×Dic3—61no—
607C2×Dic3—64no—
608C2×Dic3—64no—
609C2×Dic3—94no—
610C2×Dic3—124no—
611C2×Dic3—184no—
612C2×Dic3—182no—
613D12—62no—
614D12—62no—
615D12—122no—
616D12—184no—
617C4×D3—62no—
618C4×D3—62no—
619C4×D3—94no—
620C4×D3—94no—
621C4×D3—122no—
622C4×D3—182no—
623C4×D3—184no—
624C4×D3—182no—
625C4×D3—184no—
626Dic6—184no—
627Dic6—184no—
628Dic6—184no—
629C2×C32—21no—
630C2×C32—21no—
631C2×C32—21no—
632C2×C32—21no—
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—41no—
639C2×C32—41no—
640C2×C32—41no—
641C2×C32—42no—
642C2×C32—44no—
643C2×C32—42no—
644C2×C32—42no—
645C2×C32—82no—
646C2×C32—82no—
647C2×C32—84no—
648C2×C32C2×#23511yescharacteristic
649C2×C32C2×D3×D411yescharacteristic
650C2×C32C2×D3×D411yescharacteristic
651C2×C32C2×D3×D411yescharacteristic
652C2×C32C2×#23711yescharacteristic
653C2×C32C2×#23711yescharacteristic
654C2×C32C2×#23711yescharacteristic
655C2×C32D3×#4111yescharacteristic
656C2×C32D3×#4111yescharacteristic
657C3⋊D3—22no—
658C3⋊D3—42no—
659C3×D3—62no—
660C3×D3—62no—
661C3×D3—122no—
662C3×D3—122no—
663C3×D3—122no—
664C3×D3—242no—
665#41—548no—
666C2×Q8—272no—
667C2×D4—92no—
668C2×D4—92no—
669C2×D4—92no—
670C2×D4—91no—
671C2×D4—272no—
672C2×D4#111311yescharacteristic
673C22×C4—92no—
674C22×C4—91no—
675C22×C4—271no—
676C22×C4—271no—
677C22×C4—272no—
678C4⋊C4—91no—
679C4⋊C4—91no—
680C4⋊C4—272no—
681C22⋊C4—92no—
682C22⋊C4—92no—
683C22⋊C4—272no—
684C22⋊C4—272no—
685C42—91no—
686C42—91no—
687C42—271no—
688C42—271no—
689C22×C3—24no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—42no—
703C22×C3—42no—
704C22×C3—42no—
705C22×C3—42no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—42no—
709C22×C3—42no—
710C22×C3—44no—
711C22×C3—41no—
712C22×C3—82no—
713C22×C3—82no—
714C22×C3—92no—
715C22×C3—181no—
716C22×C3—181no—
717C22×C3—182no—
718C22×C3—182no—
719C22×C3—182no—
720C22×C3C22×D3211yescharacteristic
721C22×C3C22×D3211yescharacteristic
722C22×C3C22×D3211yescharacteristic
723C2×D3—32no—
724C2×D3—32no—
725C2×D3—62no—
726C2×D3—61no—
727C2×D3—61no—
728C2×D3—61no—
729C2×D3—61no—
730C2×D3—62no—
731C2×D3—62no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—122no—
741C3×C4—22no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—42no—
745C3×C4—92no—
746C3×C4—92no—
747C3×C4—92no—
748C3×C4—182no—
749C3×C4—182no—
750C3×C4—181no—
751C3×C4—181no—
752C3×C4#380412yescomplemented
753C3×C4#380412yescomplemented
754C3×C4#380512yescomplemented
755Dic3—32no—
756Dic3—32no—
757Dic3—32no—
758Dic3—32no—
759Dic3—32no—
760Dic3—32no—
761Dic3—62no—
762Dic3—62no—
763Dic3—62no—
764Dic3—62no—
765Dic3—62no—
766Dic3—62no—
767Dic3—62no—
768Dic3—61no—
769Dic3—61no—
770Dic3—61no—
771Dic3—61no—
772Dic3—121no—
773Dic3—122no—
774Dic3—122no—
775Dic3—121no—
776C32—21no—
777C32—21no—
778C32—21no—
779C32—41no—
780C32#554811yescharacteristic, complemented
781C32#559611yescharacteristic, complemented
782C32#571611yescharacteristic, complemented
783C23—91no—
784C23—92no—
785C23C2×#111312yes—
786Q8—544no—
787D4—22no—
788D4—184no—
789D4—184no—
790D4—184no—
791D4—182no—
792D4—544no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—91no—
797C2×C4—91no—
798C2×C4—92no—
799C2×C4—92no—
800C2×C4—184no—
801C2×C4—182no—
802C2×C4—274no—
803C2×C4—544no—
804C2×C4—542no—
805C2×C4C2×#111311yescharacteristic
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—44no—
816C2×C3—42no—
817C2×C3—42no—
818C2×C3—42no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—82no—
823C2×C3—82no—
824C2×C3—84no—
825C2×C3—182no—
826C2×C3—362no—
827C2×C3D32×D411yescharacteristic
828C2×C3D32×D411yescharacteristic
829C2×C3D32×D411yescharacteristic
830C2×C3D3×#23711yescharacteristic
831C2×C3D3×#23711yescharacteristic
832C2×C3#6431211yescharacteristic
833C2×C3C2×#380411yescharacteristic
834C2×C3C2×#380411yescharacteristic
835C2×C3C2×#380511yescharacteristic
836D3—62no—
837D3—62no—
838D3—122no—
839D3—122no—
840D3—122no—
841D3—242no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—92no—
846C22—181no—
847C22—181no—
848C22—182no—
849C22—182no—
850C22—182no—
851C22C22×#111311yescharacteristic
852C4—92no—
853C4—92no—
854C4—92no—
855C4—182no—
856C4—182no—
857C4—181no—
858C4—181no—
859C4#8904612yescomplemented
860C3—21no—
861C3—21no—
862C3—21no—
863C3—41no—
864C3#1059513111yescharacteristic, complemented
865C3#1059513311yescharacteristic, complemented
866C3#1059513911yescharacteristic, complemented
867C2—42no—
868C2—182no—
869C2—362no—
870C2D4×#111311yescharacteristic
871C2#1172462211yescharacteristic
872C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33#532
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×#89046C2semidirect
2. C3×#64149C2semidirect
3. C3×#64147C2semidirect
4. C3×D4×C3⋊Dic3C2semidirect
5. #11723726C2semidirect
6. #11723725C2semidirect
7. #11723718C2semidirect
8. C4⋊#6296C2semidirect
9. #11723696C2semidirect
10. #11723691C2semidirect
11. C4×#6294C2semidirect
42. #64149D3semidirect
43. #64147D3semidirect
44. D4×C3⋊Dic3D3semidirect
97. #6294D4semidirect
199. C33×C4#41semidirect
206. C3×C3⋊Dic3#41semidirect
490. C32×C4#235semidirect
491. C32×C4#237semidirect
492. C32×C4#237semidirect
499. C3⋊Dic3#237semidirect
532. C33#532semidirect
752. C3×C4#3804semidirect
753. C3×C4#3804semidirect
754. C3×C4#3805semidirect
780. C32#5548semidirect
781. C32#5596semidirect
782. C32#5716semidirect
859. C4#89046semidirect
864. C3#10595131semidirect
865. C3#10595133semidirect
866. C3#10595139semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C3×#641492
C3×#641472
C3×D4×C3⋊Dic32
#117237262
#117237252
#117237182
C4⋊#62962
#117236962
#117236912
C4×#62942
#105951393
#105951333
#105951313