Finite Group Databasebeta

← C2×#11722954 #13172321

Subgroups — C2×#11722954 #13172321

Order 1728.

2322 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6290C211yesmaximal, characteristic, complemented
2C22×D3×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×#625C211yesmaximal, characteristic, complemented
5C2×#88814C211yesmaximal, characteristic, complemented
6C2×#88806C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722954C218yesmaximal, direct product factor
9C2×#63980—31nomaximal
10C2×#63971—31nomaximal
11C2×#63885—31nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C32×D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊Dic3C2211yescharacteristic
18C22×C32×Dic3C2211yescharacteristic
19C2×#6290—24no—
20C2×#6290C2214yescomplemented
21C2×D3×C3⋊Dic3—24no—
22C2×D3×C3⋊Dic3C2214yescomplemented
23C2×C3×#626—24no—
24C2×C3×#626C2214yescomplemented
25C2×C3×#625—24no—
26C2×C3×#625C2214yescomplemented
27#88814C2214yescomplemented
28#88806C2214yescomplemented
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C22×#638—31no—
31C23×C3⋊Dic3—31no—
32C22×C3×#67—31no—
33C22×C3×#67—31no—
34C22×C3×#67—31no—
35C22×C3×D12—31no—
36C22×#626D311yescharacteristic, complemented
37C22×#625—31no—
38C22×#625—31no—
39C22×#625—61no—
40C22×#625D311yescharacteristic, complemented
41C22×D3×Dic3—31no—
42C22×D3×Dic3—31no—
43C22×D3×Dic3—61no—
44C2×#3750—31no—
45C2×C3×#217—31no—
46C2×C3×(C2×D3)⋊C4—31no—
47#63980—38no—
48#63971—38no—
49C2×#3724—31no—
50C2×#3724—31no—
51C2×#3724—61no—
52C2×#3722—31no—
53C2×(C2×D3)⋊Dic3—31no—
54C2×(C2×D3)⋊Dic3—31no—
55C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
56#63885—38no—
57C23×C33C2311yescharacteristic
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3—22no—
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3C2312yes—
62C22×C32×D3—22no—
63C22×C32×D3—22no—
64C22×C32×D3—22no—
65C22×C32×D3—22no—
66C22×C32×D3—22no—
67C22×C32×D3D414yescomplemented
68C22×C32×D3C2312yes—
69C22×C32×D3C2312yes—
70C2×C3⋊(C3⋊Dic3)D414yescomplemented
71C2×C3⋊(C3⋊Dic3)C2312yes—
72C2×C3×C3⋊Dic3—22no—
73C2×C3×C3⋊Dic3—22no—
74C2×C3×C3⋊Dic3C2312yes—
75C2×C3×C3⋊Dic3C2312yes—
76C2×C32×Dic3—22no—
77C2×C32×Dic3C2312yes—
78#6290—28no—
79D3×C3⋊Dic3—28no—
80C3×#626—28no—
81C3×#625—28no—
82C2×#939—91no—
83C2×#939—91no—
84C2×#884—91no—
85C24×C32—31no—
86C24×C32—31no—
87C23×C3⋊D3C2×D311yescharacteristic
88C23×C3×D3—21no—
89C23×C3×D3—21no—
90C23×C3×D3—31no—
91C23×C3×D3—31no—
92C23×C3×D3—61no—
93C23×C3×D3C2×D311yescharacteristic
94C23×C3×D3C2×D311yescharacteristic
95C23×C3×D3C2×D311yescharacteristic
96C23×C3×D3C2×D311yescharacteristic
97C22×C32×C4—31no—
98C2×#638—34no—
99C2×#638—64no—
100C22×C3⋊Dic3—31no—
101C22×C3⋊Dic3—31no—
102C22×C3⋊Dic3—31no—
103C22×C3⋊Dic3—34no—
104C22×C3⋊Dic3—64no—
105C22×C3⋊Dic3—61no—
106C22×C3⋊Dic3—61no—
107C22×C3⋊Dic3—61no—
108C22×C3⋊Dic3—121no—
109C22×C3⋊Dic3C2×D311yescharacteristic
110C22×C3⋊Dic3C2×D311yescharacteristic
111C2×C3×#67—34no—
112C2×C3×#67—34no—
113C2×C3×#67—34no—
114C2×C3×#67—64no—
115C2×C3×#67—64no—
116C2×C3×#67—64no—
117C22×C3×Dic3—21no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3—31no—
120C22×C3×Dic3—31no—
121C22×C3×Dic3—31no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C2×C3×D12—34no—
127C2×C3×D12—64no—
128C2×#626—24no—
129C2×#626C2×D314yescomplemented
130C2×#625—24no—
131C2×#625—34no—
132C2×#625—34no—
133C2×#625—64no—
134C2×#625—64no—
135C2×#625—64no—
136C2×#625—68no—
137C2×#625C2×D314yescomplemented
138C2×D3×Dic3—34no—
139C2×D3×Dic3—34no—
140C2×D3×Dic3—64no—
141C2×D3×Dic3—64no—
142C2×D3×Dic3—64no—
143C2×D3×Dic3—68no—
144#3750—34no—
145C3×#217—34no—
146C3×(C2×D3)⋊C4—34no—
147#3724—34no—
148#3724—34no—
149#3724—64no—
150#3722—34no—
151(C2×D3)⋊Dic3—34no—
152(C2×D3)⋊Dic3—34no—
153(C2×D3)⋊Dic3C2×D314yescomplemented
154C22×C33C2×D412yes—
155C22×C33C2×D412yes—
156C22×C33#4112yes—
157C22×C33C2411yescharacteristic
158C2×C3×C3⋊D3—22no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3—44no—
162C2×C32×D3—28no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C2×C32×D3—22no—
166C2×C32×D3—22no—
167C2×C32×D3—22no—
168C2×C32×D3—44no—
169C2×C32×D3C2×D414yescomplemented
170C3⋊(C3⋊Dic3)C2×D414yescomplemented
171C3×C3⋊Dic3—22no—
172C3×C3⋊Dic3—22no—
173C32×Dic3—22no—
174C22×C3×D4—91no—
175C22×C3×D4—91no—
176C22×#67—31no—
177C22×#67—31no—
178C22×#67—31no—
179C22×#67—91no—
180C22×#67—91no—
181C22×#67—91no—
182C22×#67—181no—
183C23×Dic3—91no—
184C23×Dic3—91no—
185C23×Dic3—181no—
186C22×D12—31no—
187C22×C4×D3—91no—
188C2×C3×C22⋊C4—91no—
189C2×#217—31no—
190C2×#217—91no—
191#939—98no—
192#939—98no—
193C2×(C2×D3)⋊C4—31no—
194C2×(C2×D3)⋊C4—91no—
195C2×(C2×D3)⋊C4—91no—
196C2×Dic3⋊C4—91no—
197C2×Dic3⋊C4—91no—
198C2×Dic3⋊C4—91no—
199C2×Dic3⋊C4—181no—
200#884—98no—
201C23×C32—21no—
202C23×C32—21no—
203C23×C32—21no—
204C23×C32—34no—
205C23×C32—32no—
206C23×C32—32no—
207C23×C32—41no—
208C23×C32—62no—
209C23×C32—62no—
210C23×C32—62no—
211C23×C32—62no—
212C23×C32—62no—
213C23×C32C22×D311yescharacteristic
214C23×C32C22×D311yescharacteristic
215C23×C32C22×D311yescharacteristic
216C22×C3⋊D3—22no—
217C22×C3⋊D3—22no—
218C22×C3⋊D3—22no—
219C22×C3⋊D3C22×D312yes—
220C22×C3×D3—24no—
221C22×C3×D3—24no—
222C22×C3×D3—22no—
223C22×C3×D3—22no—
224C22×C3×D3—22no—
225C22×C3×D3—22no—
226C22×C3×D3—24no—
227C22×C3×D3—22no—
228C22×C3×D3—22no—
229C22×C3×D3—22no—
230C22×C3×D3—22no—
231C22×C3×D3—22no—
232C22×C3×D3—22no—
233C22×C3×D3—24no—
234C22×C3×D3—22no—
235C22×C3×D3—22no—
236C22×C3×D3—32no—
237C22×C3×D3—32no—
238C22×C3×D3—42no—
239C22×C3×D3—42no—
240C22×C3×D3—62no—
241C22×C3×D3—64no—
242C22×C3×D3—62no—
243C22×C3×D3—62no—
244C22×C3×D3—62no—
245C22×C3×D3—62no—
246C22×C3×D3—62no—
247C22×C3×D3—62no—
248C22×C3×D3—122no—
249C22×C3×D3—122no—
250C22×C3×D3#6714yescomplemented
251C22×C3×D3#6714yescomplemented
252C22×C3×D3C22×D312yes—
253C22×C3×D3C22×D312yes—
254C22×C3×D3C22×D312yes—
255C22×C3×D3C22×D312yes—
256C2×C32×C4—32no—
257C2×C32×C4—62no—
258#638—68no—
259C2×C3⋊Dic3—22no—
260C2×C3⋊Dic3—22no—
261C2×C3⋊Dic3—34no—
262C2×C3⋊Dic3—34no—
263C2×C3⋊Dic3—34no—
264C2×C3⋊Dic3—32no—
265C2×C3⋊Dic3—32no—
266C2×C3⋊Dic3—32no—
267C2×C3⋊Dic3—62no—
268C2×C3⋊Dic3—64no—
269C2×C3⋊Dic3—64no—
270C2×C3⋊Dic3—64no—
271C2×C3⋊Dic3—62no—
272C2×C3⋊Dic3—62no—
273C2×C3⋊Dic3—68no—
274C2×C3⋊Dic3—124no—
275C2×C3⋊Dic3—122no—
276C2×C3⋊Dic3C22×D312yes—
277C2×C3⋊Dic3C22×D312yes—
278C3×#67—68no—
279C3×#67—68no—
280C3×#67—68no—
281C2×C3×Dic3—22no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—22no—
284C2×C3×Dic3—32no—
285C2×C3×Dic3—32no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—32no—
288C2×C3×Dic3—42no—
289C2×C3×Dic3—62no—
290C2×C3×Dic3—62no—
291C2×C3×Dic3—64no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3—62no—
294C2×C3×Dic3—62no—
295C2×C3×Dic3—62no—
296C2×C3×Dic3—122no—
297C2×C3×Dic3C22×D312yes—
298C2×C3×Dic3C22×D312yes—
299C3×D12—68no—
300#626—28no—
301#625—28no—
302#625—68no—
303#625—68no—
304#625—616no—
305D3×Dic3—68no—
306D3×Dic3—68no—
307D3×Dic3—616no—
308C2×#121—271noSylow
309C2×C33#12114yescomplemented
310C2×C33C22×D411yescharacteristic
311C2×C33C22×D411yescharacteristic
312C2×C33C2×#4111yescharacteristic
313C3×C3⋊D3—42no—
314C32×D3—24no—
315C32×D3—42no—
316C24×C3—31no—
317C24×C3—31no—
318C24×C3—31no—
319C24×C3—31no—
320C24×C3—61no—
321C24×C3—61no—
322C24×C3—91no—
323C23×D3—31no—
324C23×D3—31no—
325C23×D3—61no—
326C23×D3D3211yescharacteristic
327C23×D3D3211yescharacteristic
328C2×C3×D4—94no—
329C2×C3×D4—94no—
330C2×C3×D4—184no—
331C2×C3×D4—184no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—91no—
336C22×C3×C4—91no—
337C2×#67—34no—
338C2×#67—34no—
339C2×#67—34no—
340C2×#67—64no—
341C2×#67—64no—
342C2×#67—64no—
343C2×#67—94no—
344C2×#67—94no—
345C2×#67—94no—
346C2×#67—184no—
347C2×#67—184no—
348C2×#67—184no—
349C2×#67—184no—
350C2×#67—188no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—31no—
354C22×Dic3—31no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—94no—
358C22×Dic3—94no—
359C22×Dic3—91no—
360C22×Dic3—91no—
361C22×Dic3—91no—
362C22×Dic3—184no—
363C22×Dic3—181no—
364C22×Dic3—181no—
365C22×Dic3—181no—
366C22×Dic3—184no—
367C22×Dic3—184no—
368C22×Dic3—188no—
369C22×Dic3—361no—
370C22×Dic3D3211yescharacteristic
371C2×D12—34no—
372C2×D12—64no—
373C2×C4×D3—94no—
374C2×C4×D3—184no—
375C3×C22⋊C4—94no—
376#217—34no—
377#217—94no—
378(C2×D3)⋊C4—34no—
379(C2×D3)⋊C4—94no—
380(C2×D3)⋊C4—94no—
381Dic3⋊C4—94no—
382Dic3⋊C4—94no—
383Dic3⋊C4—94no—
384Dic3⋊C4—184no—
385C22×C32—21no—
386C22×C32—21no—
387C22×C32—21no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—22no—
392C22×C32—22no—
393C22×C32—22no—
394C22×C32—22no—
395C22×C32—22no—
396C22×C32—22no—
397C22×C32—34no—
398C22×C32—42no—
399C22×C32—42no—
400C22×C32—42no—
401C22×C32—41no—
402C22×C32—68no—
403C22×C32—62no—
404C22×C32—62no—
405C22×C32—62no—
406C22×C32—62no—
407C22×C32—62no—
408C22×C32—124no—
409C22×C32#23512yes—
410C22×C32D3×D412yes—
411C22×C32D3×D412yes—
412C22×C32D3×D412yes—
413C22×C32D3×D412yes—
414C22×C32#23712yes—
415C22×C32#23712yes—
416C22×C32C2×#6712yes—
417C22×C32C2×#6712yes—
418C22×C32C23×D311yescharacteristic
419C22×C32C23×D311yescharacteristic
420C22×C32C23×D311yescharacteristic
421C2×C3⋊D3—22no—
422C2×C3⋊D3—22no—
423C2×C3⋊D3—22no—
424C2×C3⋊D3—44no—
425C2×C3×D3—24no—
426C2×C3×D3—24no—
427C2×C3×D3—216no—
428C2×C3×D3—28no—
429C2×C3×D3—28no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—24no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—22no—
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—24no—
442C2×C3×D3—42no—
443C2×C3×D3—42no—
444C2×C3×D3—48no—
445C2×C3×D3—44no—
446C2×C3×D3—44no—
447C2×C3×D3—64no—
448C2×C3×D3—62no—
449C2×C3×D3—62no—
450C2×C3×D3—62no—
451C2×C3×D3—62no—
452C2×C3×D3—62no—
453C2×C3×D3—62no—
454C2×C3×D3—122no—
455C2×C3×D3—122no—
456C2×C3×D3—128no—
457C2×C3×D3—124no—
458C2×C3×D3—124no—
459C2×C3×D3C2×#6714yescomplemented
460C2×C3×D3C2×#6714yescomplemented
461C32×C4—62no—
462C3⋊Dic3—22no—
463C3⋊Dic3—22no—
464C3⋊Dic3—34no—
465C3⋊Dic3—34no—
466C3⋊Dic3—34no—
467C3⋊Dic3—64no—
468C3⋊Dic3—64no—
469C3⋊Dic3—64no—
470C3⋊Dic3—124no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—42no—
474C3×Dic3—64no—
475C3×Dic3—62no—
476C3×Dic3—62no—
477C3×Dic3—62no—
478C3×Dic3—62no—
479C3×Dic3—122no—
480C22×D4—91no—
481C22×D4—91no—
482C22×D4—271no—
483C23×C4—271no—
484#121—278no—
485C2×C4⋊C4—271no—
486C2×C22⋊C4—91no—
487C2×C22⋊C4—271no—
488C33C2×#12111yescharacteristic, complemented, Sylow
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—32no—
493C23×C3—32no—
494C23×C3—34no—
495C23×C3—34no—
496C23×C3—32no—
497C23×C3—32no—
498C23×C3—41no—
499C23×C3—62no—
500C23×C3—64no—
501C23×C3—62no—
502C23×C3—64no—
503C23×C3—64no—
504C23×C3—64no—
505C23×C3—62no—
506C23×C3—62no—
507C23×C3—62no—
508C23×C3—62no—
509C23×C3—62no—
510C23×C3—62no—
511C23×C3—62no—
512C23×C3—62no—
513C23×C3—62no—
514C23×C3—62no—
515C23×C3—92no—
516C23×C3—122no—
517C23×C3—122no—
518C23×C3—182no—
519C23×C3—182no—
520C23×C3—182no—
521C23×C3C2×D3211yescharacteristic
522C23×C3C2×D3211yescharacteristic
523C23×C3C2×D3211yescharacteristic
524C22×D3—22no—
525C22×D3—22no—
526C22×D3—22no—
527C22×D3—22no—
528C22×D3—22no—
529C22×D3—32no—
530C22×D3—32no—
531C22×D3—62no—
532C22×D3—64no—
533C22×D3—62no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—62no—
537C22×D3—62no—
538C22×D3—62no—
539C22×D3—122no—
540C22×D3—122no—
541C22×D3#62514yescomplemented
542C22×D3C2×D3212yes—
543C22×D3C2×D3212yes—
544C3×D4—188no—
545C3×D4—188no—
546C2×C3×C4—32no—
547C2×C3×C4—32no—
548C2×C3×C4—62no—
549C2×C3×C4—62no—
550C2×C3×C4—62no—
551C2×C3×C4—92no—
552C2×C3×C4—92no—
553C2×C3×C4—122no—
554C2×C3×C4—182no—
555C2×C3×C4—182no—
556#67—68no—
557#67—68no—
558#67—68no—
559#67—188no—
560#67—188no—
561#67—188no—
562#67—1816no—
563C2×Dic3—22no—
564C2×Dic3—32no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—64no—
571C2×Dic3—62no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—62no—
575C2×Dic3—92no—
576C2×Dic3—92no—
577C2×Dic3—92no—
578C2×Dic3—94no—
579C2×Dic3—94no—
580C2×Dic3—94no—
581C2×Dic3—122no—
582C2×Dic3—182no—
583C2×Dic3—184no—
584C2×Dic3—182no—
585C2×Dic3—184no—
586C2×Dic3—182no—
587C2×Dic3—184no—
588C2×Dic3—188no—
589C2×Dic3—188no—
590C2×Dic3—1816no—
591C2×Dic3—362no—
592C2×Dic3—364no—
593C2×Dic3C2×D3212yes—
594D12—68no—
595C4×D3—188no—
596C2×C32—21no—
597C2×C32—21no—
598C2×C32—21no—
599C2×C32—21no—
600C2×C32—21no—
601C2×C32—21no—
602C2×C32—21no—
603C2×C32—21no—
604C2×C32—21no—
605C2×C32—24no—
606C2×C32—24no—
607C2×C32—24no—
608C2×C32—44no—
609C2×C32—41no—
610C2×C32—41no—
611C2×C32—41no—
612C2×C32—64no—
613C2×C32—122no—
614C2×C32#88414yescomplemented
615C2×C32#93914yescomplemented
616C2×C32#93914yescomplemented
617C2×C32C2×#23511yescharacteristic
618C2×C32C2×D3×D411yescharacteristic
619C2×C32C2×D3×D411yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32C2×D3×D411yescharacteristic
622C2×C32C2×#23711yescharacteristic
623C2×C32C2×#23711yescharacteristic
624C2×C32C22×#6711yescharacteristic
625C2×C32C22×#6711yescharacteristic
626C3⋊D3—42no—
627C3×D3—28no—
628C3×D3—24no—
629C3×D3—24no—
630C3×D3—44no—
631C3×D3—42no—
632C3×D3—42no—
633C3×D3—124no—
634C3×D3—122no—
635C3×D3—122no—
636C24—31no—
637C24—31no—
638C24—91no—
639C2×D4—94no—
640C2×D4—94no—
641C2×D4—184no—
642C2×D4—184no—
643C2×D4—274no—
644C2×D4—544no—
645C22×C4—31no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—274no—
649C22×C4—271no—
650C22×C4—544no—
651C4⋊C4—274no—
652C22⋊C4—94no—
653C22⋊C4—274no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—22no—
663C22×C3—22no—
664C22×C3—22no—
665C22×C3—22no—
666C22×C3—34no—
667C22×C3—34no—
668C22×C3—41no—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—64no—
673C22×C3—64no—
674C22×C3—64no—
675C22×C3—616no—
676C22×C3—64no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—62no—
680C22×C3—62no—
681C22×C3—68no—
682C22×C3—68no—
683C22×C3—62no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—122no—
690C22×C3—122no—
691C22×C3—128no—
692C22×C3—124no—
693C22×C3—124no—
694C22×C3—182no—
695C22×C3—182no—
696C22×C3—182no—
697C22×C3—364no—
698C22×C3#379512yes—
699C22×C3#380212yes—
700C22×C3#380412yes—
701C22×C3#380512yes—
702C22×C3C2×#62512yes—
703C22×C3D3×#6712yes—
704C22×C3D3×#6712yes—
705C22×C3#381112yes—
706C22×C3#381112yes—
707C22×C3C22×D3211yescharacteristic
708C22×C3C22×D3211yescharacteristic
709C22×C3C22×D3211yescharacteristic
710C2×D3—22no—
711C2×D3—22no—
712C2×D3—28no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—44no—
717C2×D3—64no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—122no—
725C2×D3—122no—
726C2×D3—128no—
727C2×D3—124no—
728C2×D3—124no—
729C2×D3C2×#62514yescomplemented
730C3×C4—62no—
731C3×C4—62no—
732C3×C4—122no—
733C3×C4—182no—
734C3×C4—182no—
735Dic3—22no—
736Dic3—64no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—62no—
741Dic3—94no—
742Dic3—94no—
743Dic3—94no—
744Dic3—122no—
745Dic3—184no—
746Dic3—184no—
747Dic3—184no—
748Dic3—364no—
749C32—21no—
750C32—21no—
751C32—21no—
752C32—41no—
753C32C2×#88411yescharacteristic, complemented
754C32C2×#93911yescharacteristic, complemented
755C32C2×#93911yescharacteristic, complemented
756C23—32no—
757C23—34no—
758C23—32no—
759C23—62no—
760C23—62no—
761C23—62no—
762C23—62no—
763C23—62no—
764C23—92no—
765C23—182no—
766C23—182no—
767C23—182no—
768C23D3311yescharacteristic
769D4—188no—
770D4—188no—
771D4—548no—
772C2×C4—32no—
773C2×C4—62no—
774C2×C4—92no—
775C2×C4—92no—
776C2×C4—182no—
777C2×C4—182no—
778C2×C4—272no—
779C2×C4—274no—
780C2×C4—548no—
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—24no—
791C2×C3—24no—
792C2×C3—24no—
793C2×C3—41no—
794C2×C3—41no—
795C2×C3—41no—
796C2×C3—44no—
797C2×C3—68no—
798C2×C3—64no—
799C2×C3—64no—
800C2×C3—124no—
801C2×C3—122no—
802C2×C3—122no—
803C2×C3—362no—
804C2×C3#6388514yescomplemented
805C2×C3#6397114yescomplemented
806C2×C3#6398014yescomplemented
807C2×C3C2×#379511yescharacteristic
808C2×C3C2×#380211yescharacteristic
809C2×C3C2×#380411yescharacteristic
810C2×C3C2×#380511yescharacteristic
811C2×C3C22×#62511yescharacteristic
812C2×C3C2×D3×#6711yescharacteristic
813C2×C3C2×D3×#6711yescharacteristic
814C2×C3C2×#381111yescharacteristic
815C2×C3C2×#381111yescharacteristic
816D3—24no—
817D3—42no—
818D3—124no—
819D3—122no—
820D3—122no—
821C22—34no—
822C22—62no—
823C22—62no—
824C22—68no—
825C22—62no—
826C22—62no—
827C22—62no—
828C22—124no—
829C22—182no—
830C22—182no—
831C22—182no—
832C22—364no—
833C22D3×#62512yes—
834C22#8895412yes—
835C22#8896112yes—
836C22C2×D3311yescharacteristic
837C4—62no—
838C4—182no—
839C4—182no—
840C4—274no—
841C3—21no—
842C3—21no—
843C3—21no—
844C3—41no—
845C3C2×#6388511yescharacteristic, complemented
846C3C2×#6397111yescharacteristic, complemented
847C3C2×#6398011yescharacteristic, complemented
848C2—64no—
849C2—122no—
850C2—362no—
851C2#1172295414yesdirect product factor
852C2C2×D3×#62511yescharacteristic
853C2C2×#8895411yescharacteristic
854C2C2×#8896111yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutator, cosocleC22×C33C24
FrattiniC22C2×D33
Fitting, socleC23×C33C23
hypocenterC33C2×#121
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6290C2semidirect
2. C22×D3×C3⋊Dic3C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×#625C2semidirect
5. C2×#88814C2semidirect
6. C2×#88806C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722954C2direct (N × H)
20. C2×#6290C22semidirect
22. C2×D3×C3⋊Dic3C22semidirect
24. C2×C3×#626C22semidirect
26. C2×C3×#625C22semidirect
27. #88814C22semidirect
28. #88806C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
36. C22×#626D3semidirect
40. C22×#625D3semidirect
55. C2×(C2×D3)⋊Dic3D3semidirect
67. C22×C32×D3D4semidirect
70. C2×C3⋊(C3⋊Dic3)D4semidirect
129. C2×#626C2×D3semidirect
137. C2×#625C2×D3semidirect
153. (C2×D3)⋊Dic3C2×D3semidirect
169. C2×C32×D3C2×D4semidirect
170. C3⋊(C3⋊Dic3)C2×D4semidirect
250. C22×C3×D3#67semidirect
251. C22×C3×D3#67semidirect
309. C2×C33#121semidirect
459. C2×C3×D3C2×#67semidirect
460. C2×C3×D3C2×#67semidirect
488. C33C2×#121semidirect
541. C22×D3#625semidirect
614. C2×C32#884semidirect
615. C2×C32#939semidirect
616. C2×C32#939semidirect
729. C2×D3C2×#625semidirect
753. C32C2×#884semidirect
754. C32C2×#939semidirect
755. C32C2×#939semidirect
804. C2×C3#63885semidirect
805. C2×C3#63971semidirect
806. C2×C3#63980semidirect
845. C3C2×#63885semidirect
846. C3C2×#63971semidirect
847. C3C2×#63980semidirect
851. C2#11722954direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#62902
C22×D3×C3⋊Dic32
C22×C3×#6262
C22×C3×#6252
C2×#888142
C2×#888062
C2×C3×(C2×D3)⋊Dic32
#117229542
C2×#639803
C2×#639713
C2×#638853