Finite Group Databasebeta

← #13178702

Subgroups — #13178702

Order 1728.

3198 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#1113C211yesmaximal, characteristic, complemented
2C2×C3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#89049C212yesmaximal, complemented
4C3×#64146C212yesmaximal, complemented
5#11723729C212yesmaximal, complemented
6#11723727C212yesmaximal, complemented
7#11723723C211yesmaximal, characteristic, complemented
8#11723701C212yesmaximal, complemented
9#11723700C212yesmaximal, complemented
10#10595278—31nomaximal
11D3×#937—32nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C3×C3⋊D3C2212yescomplemented
14C23×C3×C3⋊D3C2211yescharacteristic, complemented
15C22×#1113—24no—
16C22×#1113—28no—
17C22×#1113C2212yes—
18C22×#1113C2212yescomplemented
19C2×C33×D4C2211yescharacteristic, complemented
20C2×C3×#638C2214yescomplemented
21C2×C3×#638C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic, complemented
23C3×D4×C3⋊D3—24no—
24C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
26#89049—28no—
27C2×#6295C2214yescomplemented
28C2×#6294C2212yescomplemented
29C3×#3757C2212yescomplemented
30C3×#3752C2214yescomplemented
31#88814C2214yescomplemented
32#88814C2212yescomplemented
33C23×D32—31no—
34C23×D32—32no—
35C2×D4×C3⋊D3D311yescharacteristic, complemented
36C2×C3×D3×D4—32no—
37C2×C3×D3×D4—61no—
38C2×#3811—32no—
39C2×D3×#67—34no—
40#64146D312yescomplemented
41C3×#937—32no—
42C3×#937—32no—
43C3×#937—62no—
44#63983—34no—
45#63983—32no—
46#63981—32no—
47#63977—32no—
48#63976—32no—
49#63974—31no—
50D3×#217—32no—
51#63923—32no—
52#63922—34no—
53#63921—32no—
54D3×(C2×D3)⋊C4—34no—
55C23×C33C2311yescharacteristic
56C23×C33C2311yescharacteristic, complemented
57C22×C3×C3⋊D3—24no—
58C22×C3×C3⋊D3—24no—
59C22×C3×C3⋊D3—28no—
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3—24no—
62C22×C3×C3⋊D3D414yescomplemented
63C22×C3×C3⋊D3C2314yes—
64C22×C3×C3⋊D3C2311yescharacteristic
65C22×C3×C3⋊D3C2311yescharacteristic
66C22×C3×C3⋊D3C2311yescharacteristic, complemented
67C2×#1113—232no—
68C2×#1113—24no—
69C2×#1113—24no—
70C2×#1113—28no—
71C2×#1113—24no—
72C2×#1113D418yescomplemented
73C33×D4—22no—
74C2×C33×C4C2311yescharacteristic, complemented
75C3×#638—22no—
76C3×#638—22no—
77C3×#638—28no—
78C2×C3×C3⋊Dic3C2314yescomplemented
79C2×C3×C3⋊Dic3C2311yescharacteristic, complemented
80C3×C4⋊(C3⋊D3)—22no—
81C3×C4×C3⋊D3—22no—
82#6295—28no—
83#6294—24no—
84C2×#937—91no—
85D3×#120—92no—
86C23×C3⋊D3C2×D311yescharacteristic
87C23×C3⋊D3C2×D312yescomplemented
88C23×C3⋊D3C2×D311yescharacteristic, complemented
89C23×C3×D3—32no—
90C23×C3×D3—32no—
91C23×C3×D3—32no—
92C23×C3×D3—32no—
93C23×C3×D3—61no—
94C23×C3×D3—61no—
95C23×C3×D3—62no—
96C22×D32—34no—
97C22×D32—32no—
98C22×D32—34no—
99C22×D32—32no—
100C22×D32—68no—
101C22×D32—616no—
102C22×D32—68no—
103C22×D32—64no—
104C2×C32×D4—21no—
105C2×C32×D4—22no—
106C2×C32×D4—41no—
107C2×C32×D4C2×D311yescharacteristic, complemented
108C2×C32×D4C2×D312yescomplemented
109C2×#638C2×D314yescomplemented
110C2×#638C2×D311yescharacteristic, complemented
111C2×#638C2×D311yescharacteristic, complemented
112D4×C3⋊D3—24no—
113C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
114C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
115C2×C3×#67—32no—
116C2×C3×#67—34no—
117C2×C3×#67—34no—
118C2×C3×#67—32no—
119C2×C3×#67—61no—
120C2×C3×#67—61no—
121C2×C3×#67—64no—
122C3×D3×D4—68no—
123C3×D3×D4—68no—
124C2×C3×D12—32no—
125C2×C3×D12—61no—
126C2×C3×C4×D3—32no—
127C2×C3×C4×D3—61no—
128#3811—68no—
129D3×#67—616no—
130C2×#626—34no—
131C2×#626—34no—
132C2×#625—34no—
133C2×#624—32no—
134C2×D3×Dic3—34no—
135#3757C2×D312yescomplemented
136#3752C2×D314yescomplemented
137C3×#217—32no—
138C3×#217—32no—
139C3×#217—62no—
140C3×(C2×D3)⋊C4—34no—
141C3×(C2×D3)⋊C4—34no—
142C3×(C2×D3)⋊C4—64no—
143#3722—34no—
144#3722—32no—
145(C2×D3)⋊Dic3—34no—
146(C2×D3)⋊Dic3—34no—
147(C2×D3)⋊Dic3—34no—
148C22×C33—22no—
149C22×C33—21no—
150C22×C33—22no—
151C22×C33C2×D412yescomplemented
152C22×C33C2411yescharacteristic
153C2×C3×C3⋊D3—216no—
154C2×C3×C3⋊D3—24no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—24no—
157C2×C3×C3⋊D3—28no—
158C2×C3×C3⋊D3—21no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—44no—
161C2×C3×C3⋊D3C2×D414yes—
162C2×C3×C3⋊D3C2×D412yes—
163C2×C3×C3⋊D3C2×D418yescomplemented
164C2×C3×C3⋊D3C2×D412yescomplemented
165#1113—216no—
166#1113—216no—
167C33×C4—21no—
168C3×C3⋊Dic3—21no—
169C3×C3⋊Dic3—24no—
170C24×D3—91no—
171C24×D3—92no—
172C22×C3×D4—91no—
173C22×#67—92no—
174C2×D3×D4—32no—
175C2×D3×D4—61no—
176C2×D3×D4—94no—
177C3×#120—92no—
178#953—92no—
179C2×#217—91no—
180#937—32no—
181#937—32no—
182#937—62no—
183#937—92no—
184#937—92no—
185#937—92no—
186#937—94no—
187C2×(C2×D3)⋊C4—92no—
188#882—94no—
189#882—92no—
190D3×C22⋊C4—94no—
191D3×C22⋊C4—92no—
192C23×C32—22no—
193C23×C32—21no—
194C23×C32—21no—
195C23×C32—22no—
196C23×C32—41no—
197C23×C32—41no—
198C23×C32C22×D312yes—
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D312yescomplemented
201C23×C32C22×D311yescharacteristic, complemented
202C22×C3⋊D3—22no—
203C22×C3⋊D3—24no—
204C22×C3⋊D3—24no—
205C22×C3⋊D3—28no—
206C22×C3⋊D3—24no—
207C22×C3⋊D3#6714yescomplemented
208C22×C3⋊D3C22×D314yes—
209C22×C3⋊D3C22×D311yescharacteristic
210C22×C3⋊D3C22×D311yescharacteristic
211C22×C3⋊D3C22×D311yescharacteristic, complemented
212C22×C3×D3—32no—
213C22×C3×D3—38no—
214C22×C3×D3—32no—
215C22×C3×D3—34no—
216C22×C3×D3—34no—
217C22×C3×D3—32no—
218C22×C3×D3—61no—
219C22×C3×D3—64no—
220C22×C3×D3—64no—
221C22×C3×D3—61no—
222C22×C3×D3—61no—
223C22×C3×D3—68no—
224C22×C3×D3—68no—
225C22×C3×D3—68no—
226C22×C3×D3—68no—
227C22×C3×D3—64no—
228C22×C3×D3—64no—
229C22×C3×D3—64no—
230C22×C3×D3—64no—
231C22×C3×D3—124no—
232C22×C3×D3—128no—
233C22×C3×D3—124no—
234C22×C3×D3—124no—
235C2×D32—38no—
236C2×D32—316no—
237C2×D32—68no—
238C2×D32—68no—
239C2×D32—68no—
240C2×D32—68no—
241C2×D32—68no—
242C2×D32—664no—
243C2×D32—632no—
244C2×D32—64no—
245C2×D32—68no—
246C2×D32—64no—
247C2×D32—64no—
248C32×D4—22no—
249C32×D4—24no—
250C32×D4—24no—
251C32×D4—44no—
252C32×D4—44no—
253C2×C32×C4—21no—
254C2×C32×C4—22no—
255C2×C32×C4—41no—
256C2×C32×C4C22×D311yescharacteristic, complemented
257C2×C32×C4C22×D312yescomplemented
258#638—22no—
259#638—22no—
260#638—28no—
261C2×C3⋊Dic3C22×D311yescharacteristic, complemented
262C2×C3⋊Dic3C22×D314yescomplemented
263C4⋊(C3⋊D3)—22no—
264C4×C3⋊D3—22no—
265C3×#67—68no—
266C3×#67—68no—
267C3×#67—64no—
268C3×#67—64no—
269C3×#67—64no—
270C3×#67—64no—
271C3×#67—128no—
272C2×C3×Dic3—32no—
273C2×C3×Dic3—34no—
274C2×C3×Dic3—34no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—64no—
277C3×D12—64no—
278C3×D12—64no—
279C3×C4×D3—64no—
280C3×C4×D3—64no—
281#626—68no—
282#626—68no—
283#625—68no—
284#624—64no—
285D3×Dic3—68no—
286C2×#120—271noSylow
287C2×C33—22no—
288C2×C33—41no—
289C2×C33C22×D412yes—
290C2×C33C22×D411yescharacteristic
291C3×C3⋊D3—28no—
292C3×C3⋊D3—22no—
293C3×C3⋊D3—41no—
294C3×C3⋊D3#12014yescomplemented
295C24×C3—91no—
296C24×C3—92no—
297C24×C3—91no—
298C23×D3—32no—
299C23×D3—32no—
300C23×D3—32no—
301C23×D3—32no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—62no—
305C23×D3—94no—
306C23×D3—92no—
307C23×D3—94no—
308C23×D3—92no—
309C23×D3—188no—
310C23×D3—1816no—
311C23×D3—188no—
312C23×D3—184no—
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4—41no—
316C2×C3×D4—91no—
317C2×C3×D4—91no—
318C2×C3×D4—94no—
319C2×C3×D4—91no—
320C2×C3×D4—184no—
321C2×C3×D4D3211yescharacteristic, complemented
322C2×C3×D4D3212yescomplemented
323C22×C3×C4—91no—
324C2×#67—32no—
325C2×#67—34no—
326C2×#67—34no—
327C2×#67—32no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—64no—
331C2×#67—94no—
332C2×#67—94no—
333C2×#67—188no—
334C22×Dic3—92no—
335D3×D4—68no—
336D3×D4—68no—
337D3×D4—1816no—
338C2×D12—32no—
339C2×D12—61no—
340C2×D12—94no—
341C2×C4×D3—32no—
342C2×C4×D3—61no—
343C2×C4×D3—94no—
344C3×C22⋊C4—92no—
345C3×C22⋊C4—94no—
346#217—32no—
347#217—32no—
348#217—62no—
349#217—94no—
350#217—92no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—34no—
353(C2×D3)⋊C4—64no—
354(C2×D3)⋊C4—94no—
355(C2×D3)⋊C4—94no—
356(C2×D3)⋊C4—94no—
357C22×C32—21no—
358C22×C32—22no—
359C22×C32—24no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—24no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—21no—
366C22×C32—24no—
367C22×C32—22no—
368C22×C32—41no—
369C22×C32—42no—
370C22×C32—42no—
371C22×C32—42no—
372C22×C32—44no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32—44no—
376C22×C32—82no—
377C22×C32—82no—
378C22×C32D3×D414yescomplemented
379C22×C32C2×#6712yescomplemented
380C22×C32C23×D312yes—
381C22×C32C23×D311yescharacteristic
382C2×C3⋊D3—21no—
383C2×C3⋊D3—216no—
384C2×C3⋊D3—22no—
385C2×C3⋊D3—24no—
386C2×C3⋊D3—24no—
387C2×C3⋊D3—28no—
388C2×C3⋊D3—22no—
389C2×C3⋊D3—44no—
390C2×C3⋊D3D3×D414yes—
391C2×C3⋊D3D3×D418yescomplemented
392C2×C3⋊D3C2×#6712yes—
393C2×C3⋊D3C2×#6712yescomplemented
394C2×C3×D3—38no—
395C2×C3×D3—34no—
396C2×C3×D3—38no—
397C2×C3×D3—38no—
398C2×C3×D3—34no—
399C2×C3×D3—62no—
400C2×C3×D3—64no—
401C2×C3×D3—62no—
402C2×C3×D3—68no—
403C2×C3×D3—616no—
404C2×C3×D3—616no—
405C2×C3×D3—616no—
406C2×C3×D3—64no—
407C2×C3×D3—64no—
408C2×C3×D3—64no—
409C2×C3×D3—64no—
410C2×C3×D3—64no—
411C2×C3×D3—62no—
412C2×C3×D3—64no—
413C2×C3×D3—62no—
414C2×C3×D3—128no—
415C2×C3×D3—124no—
416C2×C3×D3—122no—
417C2×C3×D3—124no—
418C2×C3×D3—122no—
419C2×C3×D3—1216no—
420C2×C3×D3—128no—
421C2×C3×D3—128no—
422D32—632no—
423D32—616no—
424D32—632no—
425D32—616no—
426C32×C4—21no—
427C32×C4—22no—
428C32×C4—22no—
429C32×C4—42no—
430C32×C4—42no—
431C3⋊Dic3—21no—
432C3⋊Dic3—24no—
433C3×Dic3—62no—
434C3×Dic3—64no—
435C3×Dic3—64no—
436C3×Dic3—62no—
437C3×Dic3—124no—
438C25—271no—
439C22×D4—91no—
440C22×D4—272no—
441#120—92no—
442#120—272no—
443#120—272no—
444#120—272no—
445C2×C22⋊C4—272no—
446C2×C22⋊C4—271no—
447C33C2×#12011yescharacteristic, complemented, Sylow
448C23×C3—22no—
449C23×C3—21no—
450C23×C3—21no—
451C23×C3—22no—
452C23×C3—41no—
453C23×C3—41no—
454C23×C3—91no—
455C23×C3—91no—
456C23×C3—94no—
457C23×C3—94no—
458C23×C3—91no—
459C23×C3—184no—
460C23×C3—188no—
461C23×C3—182no—
462C23×C3—184no—
463C23×C3—184no—
464C23×C3C2×D3212yes—
465C23×C3C2×D3211yescharacteristic
466C23×C3C2×D3211yescharacteristic, complemented
467C23×C3C2×D3212yescomplemented
468C22×D3—32no—
469C22×D3—34no—
470C22×D3—34no—
471C22×D3—32no—
472C22×D3—38no—
473C22×D3—32no—
474C22×D3—61no—
475C22×D3—64no—
476C22×D3—64no—
477C22×D3—61no—
478C22×D3—61no—
479C22×D3—68no—
480C22×D3—68no—
481C22×D3—68no—
482C22×D3—64no—
483C22×D3—68no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—64no—
487C22×D3—916no—
488C22×D3—98no—
489C22×D3—124no—
490C22×D3—128no—
491C22×D3—124no—
492C22×D3—124no—
493C22×D3—188no—
494C22×D3—188no—
495C22×D3—188no—
496C22×D3—188no—
497C22×D3—188no—
498C22×D3—184no—
499C22×D3—188no—
500C22×D3—184no—
501C22×D3—184no—
502C22×D3—1864no—
503C22×D3—1832no—
504C3×D4—24no—
505C3×D4—24no—
506C3×D4—22no—
507C3×D4—44no—
508C3×D4—44no—
509C3×D4—182no—
510C3×D4—182no—
511C3×D4—188no—
512C3×D4—182no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—41no—
516C2×C3×C4—91no—
517C2×C3×C4—94no—
518C2×C3×C4—182no—
519C2×C3×C4C2×D3211yescharacteristic, complemented
520C2×C3×C4C2×D3212yescomplemented
521#67—64no—
522#67—68no—
523#67—68no—
524#67—64no—
525#67—64no—
526#67—64no—
527#67—128no—
528#67—188no—
529#67—188no—
530C2×Dic3—34no—
531C2×Dic3—34no—
532C2×Dic3—32no—
533C2×Dic3—61no—
534C2×Dic3—64no—
535C2×Dic3—184no—
536D12—64no—
537D12—64no—
538D12—188no—
539C4×D3—64no—
540C4×D3—64no—
541C4×D3—188no—
542C2×C32—22no—
543C2×C32—24no—
544C2×C32—24no—
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—21no—
548C2×C32—41no—
549C2×C32—42no—
550C2×C32—44no—
551C2×C32—42no—
552C2×C32—41no—
553C2×C32—42no—
554C2×C32—42no—
555C2×C32—82no—
556C2×C32—82no—
557C2×C32—82no—
558C2×C32C2×D3×D412yes—
559C2×C32C2×D3×D414yes—
560C2×C32C2×D3×D412yes—
561C2×C32C22×#6711yescharacteristic
562C3⋊D3—22no—
563C3⋊D3—28no—
564C3⋊D3—41no—
565C3⋊D3#93714yescomplemented
566C3×D3—38no—
567C3×D3—64no—
568C3×D3—68no—
569C3×D3—64no—
570C3×D3—68no—
571C3×D3—128no—
572C3×D3—122no—
573C3×D3—122no—
574C3×D3—122no—
575C24—91no—
576C24—92no—
577C24—91no—
578C24—272no—
579C24—272no—
580C24—544no—
581C24—548no—
582C2×D4—91no—
583C2×D4—94no—
584C2×D4—91no—
585C2×D4—91no—
586C2×D4—184no—
587C2×D4—274no—
588C2×D4—548no—
589C2×D4#111311yescharacteristic, complemented
590C22×C4—91no—
591C22×C4—272no—
592C22⋊C4—92no—
593C22⋊C4—94no—
594C22⋊C4—272no—
595C22⋊C4—274no—
596C22×C3—24no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—22no—
604C22×C3—21no—
605C22×C3—22no—
606C22×C3—24no—
607C22×C3—44no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—44no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—41no—
614C22×C3—42no—
615C22×C3—82no—
616C22×C3—82no—
617C22×C3—94no—
618C22×C3—92no—
619C22×C3—98no—
620C22×C3—92no—
621C22×C3—188no—
622C22×C3—1816no—
623C22×C3—184no—
624C22×C3—182no—
625C22×C3—184no—
626C22×C3—182no—
627C22×C3—181no—
628C22×C3—364no—
629C22×C3D3×#6714yescomplemented
630C22×C3#381112yescomplemented
631C22×C3C22×D3212yes—
632C22×C3C22×D3211yescharacteristic
633C2×D3—38no—
634C2×D3—34no—
635C2×D3—38no—
636C2×D3—38no—
637C2×D3—34no—
638C2×D3—62no—
639C2×D3—64no—
640C2×D3—62no—
641C2×D3—68no—
642C2×D3—616no—
643C2×D3—616no—
644C2×D3—616no—
645C2×D3—64no—
646C2×D3—64no—
647C2×D3—64no—
648C2×D3—64no—
649C2×D3—64no—
650C2×D3—62no—
651C2×D3—64no—
652C2×D3—62no—
653C2×D3—128no—
654C2×D3—124no—
655C2×D3—122no—
656C2×D3—124no—
657C2×D3—122no—
658C2×D3—1216no—
659C2×D3—128no—
660C2×D3—128no—
661C2×D3—1832no—
662C2×D3—1816no—
663C2×D3—1832no—
664C2×D3—1816no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—21no—
668C3×C4—42no—
669C3×C4—42no—
670C3×C4—184no—
671C3×C4—181no—
672Dic3—62no—
673Dic3—64no—
674Dic3—64no—
675Dic3—62no—
676Dic3—124no—
677C32—22no—
678C32—21no—
679C32—41no—
680C32D3×#12012yescomplemented
681C32C2×#93711yescharacteristic, complemented
682C23—91no—
683C23—94no—
684C23—91no—
685C23—94no—
686C23—91no—
687C23—184no—
688C23—188no—
689C23—182no—
690C23—184no—
691C23—184no—
692C23—278no—
693C23—544no—
694C23—544no—
695C23—548no—
696C23—544no—
697C23—5432no—
698C23C2×#111311yescharacteristic
699C23C2×#111311yescharacteristic, complemented
700D4—22no—
701D4—182no—
702D4—182no—
703D4—188no—
704D4—182no—
705D4—548no—
706C2×C4—94no—
707C2×C4—91no—
708C2×C4—182no—
709C2×C4—544no—
710C2×C4C2×#111311yescharacteristic, complemented
711C2×C3—24no—
712C2×C3—22no—
713C2×C3—24no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—22no—
717C2×C3—42no—
718C2×C3—44no—
719C2×C3—42no—
720C2×C3—42no—
721C2×C3—41no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—82no—
725C2×C3—82no—
726C2×C3—82no—
727C2×C3—94no—
728C2×C3—188no—
729C2×C3—182no—
730C2×C3—361no—
731C2×C3D32×D414yes—
732C2×C3D32×D412yes—
733C2×C3C2×D3×#6712yes—
734C2×C3C2×#381111yescharacteristic
735D3—38no—
736D3—64no—
737D3—68no—
738D3—64no—
739D3—68no—
740D3—122no—
741D3—128no—
742D3—122no—
743D3—122no—
744C22—22no—
745C22—22no—
746C22—21no—
747C22—94no—
748C22—92no—
749C22—98no—
750C22—92no—
751C22—188no—
752C22—1816no—
753C22—184no—
754C22—182no—
755C22—184no—
756C22—182no—
757C22—181no—
758C22—364no—
759C22—5416no—
760C22—5416no—
761C22#8904912yescomplemented
762C22C22×#111311yescharacteristic
763C4—21no—
764C4—184no—
765C4—181no—
766C3—21no—
767C3—22no—
768C3—41no—
769C3D3×#93712yescomplemented
770C3#1059527811yescharacteristic, complemented
771C2—22no—
772C2—41no—
773C2—94no—
774C2—188no—
775C2—182no—
776C2—361no—
777C2D4×#111312yes—
778C2C2×#8904911yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×D4C22
hypercenterC2×D4#1113
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×#1113C2semidirect
2. C2×C3×D4×C3⋊D3C2semidirect
3. C2×#89049C2semidirect
4. C3×#64146C2semidirect
5. #11723729C2semidirect
6. #11723727C2semidirect
7. #11723723C2semidirect
8. #11723701C2semidirect
9. #11723700C2semidirect
13. C23×C3×C3⋊D3C22semidirect
14. C23×C3×C3⋊D3C22semidirect
18. C22×#1113C22semidirect
19. C2×C33×D4C22semidirect
20. C2×C3×#638C22semidirect
21. C2×C3×#638C22semidirect
22. C2×C3×#638C22semidirect
24. C2×C3×C4⋊(C3⋊D3)C22semidirect
25. C2×C3×C4×C3⋊D3C22semidirect
27. C2×#6295C22semidirect
28. C2×#6294C22semidirect
29. C3×#3757C22semidirect
30. C3×#3752C22semidirect
31. #88814C22semidirect
32. #88814C22semidirect
35. C2×D4×C3⋊D3D3semidirect
40. #64146D3semidirect
56. C23×C33C23semidirect
62. C22×C3×C3⋊D3D4semidirect
66. C22×C3×C3⋊D3C23semidirect
72. C2×#1113D4semidirect
74. C2×C33×C4C23semidirect
78. C2×C3×C3⋊Dic3C23semidirect
79. C2×C3×C3⋊Dic3C23semidirect
87. C23×C3⋊D3C2×D3semidirect
88. C23×C3⋊D3C2×D3semidirect
107. C2×C32×D4C2×D3semidirect
108. C2×C32×D4C2×D3semidirect
109. C2×#638C2×D3semidirect
110. C2×#638C2×D3semidirect
111. C2×#638C2×D3semidirect
113. C2×C4⋊(C3⋊D3)C2×D3semidirect
114. C2×C4×C3⋊D3C2×D3semidirect
135. #3757C2×D3semidirect
136. #3752C2×D3semidirect
151. C22×C33C2×D4semidirect
163. C2×C3×C3⋊D3C2×D4semidirect
164. C2×C3×C3⋊D3C2×D4semidirect
200. C23×C32C22×D3semidirect
201. C23×C32C22×D3semidirect
207. C22×C3⋊D3#67semidirect
211. C22×C3⋊D3C22×D3semidirect
256. C2×C32×C4C22×D3semidirect
257. C2×C32×C4C22×D3semidirect
261. C2×C3⋊Dic3C22×D3semidirect
262. C2×C3⋊Dic3C22×D3semidirect
294. C3×C3⋊D3#120semidirect
321. C2×C3×D4D32semidirect
322. C2×C3×D4D32semidirect
378. C22×C32D3×D4semidirect
379. C22×C32C2×#67semidirect
391. C2×C3⋊D3D3×D4semidirect
393. C2×C3⋊D3C2×#67semidirect
447. C33C2×#120semidirect
466. C23×C3C2×D32semidirect
467. C23×C3C2×D32semidirect
519. C2×C3×C4C2×D32semidirect
520. C2×C3×C4C2×D32semidirect
565. C3⋊D3#937semidirect
589. C2×D4#1113semidirect
629. C22×C3D3×#67semidirect
630. C22×C3#3811semidirect
680. C32D3×#120semidirect
681. C32C2×#937semidirect
699. C23C2×#1113semidirect
710. C2×C4C2×#1113semidirect
761. C22#89049semidirect
769. C3D3×#937semidirect
770. C3#10595278semidirect

Maximal subgroups

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

subgroupindex
C23×#11132
C2×C3×D4×C3⋊D32
C2×#890492
C3×#641462
#117237292
#117237272
#117237232
#117237012
#117237002
#105952783
D3×#9373