Finite Group Databasebeta

← C2×#11722950 #13172306

Subgroups — C2×#11722950 #13172306

Order 1728.

3898 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#6295C211yesmaximal, characteristic, complemented
3C22×#6292C211yesmaximal, characteristic, complemented
4C22×C3×#626C211yesmaximal, characteristic, complemented
5C2×#88804C211yesmaximal, characteristic, complemented
6C2×C3×#3722C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722950C218yesmaximal, direct product factor
9C2×#63981—31nomaximal
10C2×#63923—31nomaximal
11C2×#63922—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C3×C3⋊D3C2211yescharacteristic, complemented
15C23×C32×D3C2211yescharacteristic
16C22×D3×C3⋊D3—24no—
17C22×D3×C3⋊D3—24no—
18C22×D3×C3⋊D3—24no—
19C22×D3×C3⋊D3C2214yescomplemented
20C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
21C22×C32×Dic3C2211yescharacteristic, complemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C2×#6295—24no—
24C2×#6295C2214yescomplemented
25C2×#6292—24no—
26C2×#6292C2214yescomplemented
27C2×C3×#626—24no—
28C2×C3×#626C2214yescomplemented
29#88804C2214yescomplemented
30C3×#3722C2214yescomplemented
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C24×C3⋊D3—31no—
33C23×D32—31no—
34C23×D32—31no—
35C23×D32—61no—
36C22×C4⋊(C3⋊D3)—31no—
37C22×C3×#67—31no—
38C22×C3×D12—31no—
39C22×#626—31no—
40C22×#626—31no—
41C22×#626—31no—
42C22×#626—31no—
43C22×#626—61no—
44C22×#626D311yescharacteristic, complemented
45C22×#625—31no—
46C2×#3752—31no—
47C2×C3×#217—31no—
48C2×C3×(C2×D3)⋊C4—31no—
49C2×C3×(C2×D3)⋊C4—31no—
50C2×C3×(C2×D3)⋊C4—31no—
51#63981—38no—
52C2×#3722—31no—
53C2×#3722—31no—
54C2×#3722—61no—
55C2×#3722D311yescharacteristic, complemented
56C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
57#63923—38no—
58#63922—38no—
59C23×C33C2311yescharacteristic
60C22×C3⋊(C3⋊D3)—22no—
61C22×C3⋊(C3⋊D3)—22no—
62C22×C3⋊(C3⋊D3)D414yescomplemented
63C22×C3⋊(C3⋊D3)C2312yes—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3—22no—
66C22×C3×C3⋊D3—22no—
67C22×C3×C3⋊D3—22no—
68C22×C3×C3⋊D3—22no—
69C22×C3×C3⋊D3D414yescomplemented
70C22×C3×C3⋊D3C2312yes—
71C22×C3×C3⋊D3C2312yescomplemented
72C22×C32×D3—22no—
73C22×C32×D3—22no—
74C22×C32×D3D414yescomplemented
75C22×C32×D3C2312yes—
76C2×D3×C3⋊D3—232no—
77C2×D3×C3⋊D3—28no—
78C2×D3×C3⋊D3—28no—
79C2×D3×C3⋊D3—28no—
80C2×C3×C3⋊Dic3—22no—
81C2×C3×C3⋊Dic3C2312yescomplemented
82C2×C32×Dic3—22no—
83C2×C32×Dic3—22no—
84C2×C32×Dic3C2312yescomplemented
85C2×C32×Dic3C2312yescomplemented
86#6295—28no—
87#6292—28no—
88C3×#626—28no—
89C2×#937—91no—
90C2×#882—91no—
91C2×#882—91no—
92C24×C32—31no—
93C23×C3⋊D3—31no—
94C23×C3⋊D3—31no—
95C23×C3⋊D3—31no—
96C23×C3⋊D3—34no—
97C23×C3⋊D3—64no—
98C23×C3⋊D3—64no—
99C23×C3⋊D3—61no—
100C23×C3⋊D3—64no—
101C23×C3⋊D3—61no—
102C23×C3⋊D3—61no—
103C23×C3⋊D3—121no—
104C23×C3⋊D3C2×D311yescharacteristic
105C23×C3⋊D3C2×D311yescharacteristic, complemented
106C23×C3×D3—21no—
107C23×C3×D3—31no—
108C23×C3×D3—31no—
109C23×C3×D3—31no—
110C23×C3×D3—31no—
111C23×C3×D3—61no—
112C23×C3×D3—61no—
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic
115C22×D32—34no—
116C22×D32—34no—
117C22×D32—64no—
118C22×D32—64no—
119C22×D32—64no—
120C22×D32—64no—
121C22×D32—64no—
122C22×D32—68no—
123C22×D32—68no—
124C22×D32—68no—
125C22×D32—64no—
126C22×D32—64no—
127C22×C32×C4—31no—
128C22×C32×C4—31no—
129C22×C3⋊Dic3C2×D311yescharacteristic, complemented
130C2×C4⋊(C3⋊D3)—34no—
131C2×C4⋊(C3⋊D3)—64no—
132C2×C3×#67—34no—
133C2×C3×#67—64no—
134C22×C3×Dic3—21no—
135C22×C3×Dic3—21no—
136C22×C3×Dic3—31no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—61no—
139C22×C3×Dic3C2×D311yescharacteristic, complemented
140C22×C3×Dic3C2×D311yescharacteristic, complemented
141C22×C3×Dic3C2×D311yescharacteristic, complemented
142C22×C3×Dic3C2×D311yescharacteristic, complemented
143C2×C3×D12—34no—
144C2×C3×D12—64no—
145C2×#626—24no—
146C2×#626—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—64no—
151C2×#626—64no—
152C2×#626—64no—
153C2×#626—68no—
154C2×#626—64no—
155C2×#626—64no—
156C2×#626C2×D314yescomplemented
157C2×#625—34no—
158C2×#625—64no—
159#3752—34no—
160C3×#217—34no—
161C3×(C2×D3)⋊C4—34no—
162C3×(C2×D3)⋊C4—34no—
163C3×(C2×D3)⋊C4—34no—
164#3722—34no—
165#3722—34no—
166#3722—64no—
167#3722C2×D314yescomplemented
168(C2×D3)⋊Dic3C2×D314yescomplemented
169C22×C33C2×D412yes—
170C22×C33C2×D412yes—
171C22×C33C2×D412yes—
172C22×C33C2411yescharacteristic
173C2×C3⋊(C3⋊D3)—28no—
174C2×C3⋊(C3⋊D3)—22no—
175C2×C3⋊(C3⋊D3)—22no—
176C2×C3⋊(C3⋊D3)C2×D414yescomplemented
177C2×C3×C3⋊D3—28no—
178C2×C3×C3⋊D3—22no—
179C2×C3×C3⋊D3—22no—
180C2×C3×C3⋊D3—22no—
181C2×C3×C3⋊D3—22no—
182C2×C3×C3⋊D3—22no—
183C2×C3×C3⋊D3—44no—
184C2×C3×C3⋊D3C2×D414yescomplemented
185C2×C32×D3—28no—
186C2×C32×D3—22no—
187C2×C32×D3—22no—
188C2×C32×D3C2×D414yescomplemented
189D3×C3⋊D3—232no—
190C3×C3⋊Dic3—22no—
191C32×Dic3—22no—
192C32×Dic3—22no—
193C24×D3—91no—
194C24×D3—91no—
195C24×D3—91no—
196C24×D3—181no—
197C22×C3×D4—91no—
198C22×#67—31no—
199C22×#67—91no—
200C22×#67—91no—
201C22×#67—91no—
202C22×D12—31no—
203C22×D12—91no—
204C22×D12—91no—
205C22×D12—91no—
206C22×D12—181no—
207C2×C3×C22⋊C4—91no—
208C2×C3×C22⋊C4—91no—
209C2×#217—31no—
210#937—98no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—31no—
214C2×(C2×D3)⋊C4—91no—
215C2×(C2×D3)⋊C4—91no—
216C2×(C2×D3)⋊C4—91no—
217C2×(C2×D3)⋊C4—181no—
218#882—98no—
219#882—98no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—34no—
224C23×C32—32no—
225C23×C32—41no—
226C23×C32—62no—
227C23×C32—62no—
228C23×C32C22×D311yescharacteristic
229C23×C32C22×D311yescharacteristic
230C23×C32C22×D311yescharacteristic
231C22×C3⋊D3—22no—
232C22×C3⋊D3—22no—
233C22×C3⋊D3—22no—
234C22×C3⋊D3—22no—
235C22×C3⋊D3—22no—
236C22×C3⋊D3—34no—
237C22×C3⋊D3—34no—
238C22×C3⋊D3—34no—
239C22×C3⋊D3—32no—
240C22×C3⋊D3—32no—
241C22×C3⋊D3—32no—
242C22×C3⋊D3—64no—
243C22×C3⋊D3—62no—
244C22×C3⋊D3—62no—
245C22×C3⋊D3—64no—
246C22×C3⋊D3—64no—
247C22×C3⋊D3—62no—
248C22×C3⋊D3—68no—
249C22×C3⋊D3—68no—
250C22×C3⋊D3—632no—
251C22×C3⋊D3—62no—
252C22×C3⋊D3—62no—
253C22×C3⋊D3—68no—
254C22×C3⋊D3—64no—
255C22×C3⋊D3—64no—
256C22×C3⋊D3—62no—
257C22×C3⋊D3—62no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—62no—
260C22×C3⋊D3—124no—
261C22×C3⋊D3—122no—
262C22×C3⋊D3—122no—
263C22×C3⋊D3—122no—
264C22×C3⋊D3—122no—
265C22×C3⋊D3—122no—
266C22×C3⋊D3—124no—
267C22×C3⋊D3—124no—
268C22×C3⋊D3D1214yescomplemented
269C22×C3⋊D3C22×D312yes—
270C22×C3⋊D3C22×D312yescomplemented
271C22×C3×D3—24no—
272C22×C3×D3—24no—
273C22×C3×D3—22no—
274C22×C3×D3—22no—
275C22×C3×D3—22no—
276C22×C3×D3—22no—
277C22×C3×D3—24no—
278C22×C3×D3—22no—
279C22×C3×D3—34no—
280C22×C3×D3—34no—
281C22×C3×D3—32no—
282C22×C3×D3—32no—
283C22×C3×D3—32no—
284C22×C3×D3—32no—
285C22×C3×D3—64no—
286C22×C3×D3—62no—
287C22×C3×D3—62no—
288C22×C3×D3—64no—
289C22×C3×D3—64no—
290C22×C3×D3—62no—
291C22×C3×D3—62no—
292C22×C3×D3—62no—
293C22×C3×D3—62no—
294C22×C3×D3—64no—
295C22×C3×D3—62no—
296C22×C3×D3—62no—
297C22×C3×D3—62no—
298C22×C3×D3—62no—
299C22×C3×D3—62no—
300C22×C3×D3—62no—
301C22×C3×D3—122no—
302C22×C3×D3—122no—
303C22×C3×D3D1214yescomplemented
304C22×C3×D3#6714yescomplemented
305C22×C3×D3C22×D312yes—
306C22×C3×D3C22×D312yes—
307C2×D32—68no—
308C2×D32—68no—
309C2×D32—68no—
310C2×D32—68no—
311C2×D32—616no—
312C2×D32—616no—
313C2×D32—664no—
314C2×D32—632no—
315C2×D32—632no—
316C2×D32—616no—
317C2×D32—68no—
318C2×D32—68no—
319C2×C32×C4—32no—
320C2×C32×C4—32no—
321C2×C32×C4—62no—
322C2×C32×C4—62no—
323C2×C3⋊Dic3—22no—
324C2×C3⋊Dic3C22×D312yescomplemented
325C4⋊(C3⋊D3)—68no—
326C3×#67—68no—
327C2×C3×Dic3—24no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—22no—
333C2×C3×Dic3—22no—
334C2×C3×Dic3—32no—
335C2×C3×Dic3—32no—
336C2×C3×Dic3—42no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—62no—
340C2×C3×Dic3—122no—
341C2×C3×Dic3C22×D312yescomplemented
342C2×C3×Dic3C22×D312yescomplemented
343C2×C3×Dic3C22×D312yescomplemented
344C2×C3×Dic3C22×D312yescomplemented
345C3×D12—68no—
346#626—28no—
347#626—68no—
348#626—68no—
349#626—616no—
350#626—68no—
351#626—68no—
352#625—68no—
353C2×#120—271noSylow
354C2×C33#12014yescomplemented
355C2×C33C22×D411yescharacteristic
356C2×C33C22×D411yescharacteristic
357C2×C33C22×D411yescharacteristic
358C3⋊(C3⋊D3)—24no—
359C3×C3⋊D3—24no—
360C3×C3⋊D3—42no—
361C32×D3—24no—
362C24×C3—31no—
363C24×C3—31no—
364C24×C3—61no—
365C24×C3—91no—
366C24×C3—91no—
367C23×D3—31no—
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—61no—
372C23×D3—61no—
373C23×D3—94no—
374C23×D3—94no—
375C23×D3—91no—
376C23×D3—91no—
377C23×D3—91no—
378C23×D3—94no—
379C23×D3—184no—
380C23×D3—181no—
381C23×D3—181no—
382C23×D3—181no—
383C23×D3—184no—
384C23×D3—184no—
385C23×D3—184no—
386C23×D3—184no—
387C23×D3—184no—
388C23×D3—184no—
389C23×D3—184no—
390C23×D3—184no—
391C23×D3—188no—
392C23×D3—188no—
393C23×D3—188no—
394C23×D3—184no—
395C23×D3—361no—
396C23×D3D3211yescharacteristic
397C2×C3×D4—94no—
398C2×C3×D4—184no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—61no—
404C22×C3×C4—61no—
405C22×C3×C4—91no—
406C2×#67—34no—
407C2×#67—64no—
408C2×#67—94no—
409C2×#67—94no—
410C2×#67—94no—
411C2×#67—184no—
412C2×#67—184no—
413C2×#67—184no—
414C22×Dic3—31no—
415C22×Dic3—31no—
416C22×Dic3—61no—
417C22×Dic3D3211yescharacteristic, complemented
418C22×Dic3D3211yescharacteristic, complemented
419C2×D12—34no—
420C2×D12—64no—
421C2×D12—94no—
422C2×D12—94no—
423C2×D12—94no—
424C2×D12—184no—
425C2×D12—184no—
426C2×D12—184no—
427C2×D12—188no—
428C2×D12—184no—
429C3×C22⋊C4—94no—
430C3×C22⋊C4—94no—
431#217—34no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—94no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—184no—
439C22×C32—21no—
440C22×C32—21no—
441C22×C32—21no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—22no—
451C22×C32—34no—
452C22×C32—42no—
453C22×C32—42no—
454C22×C32—42no—
455C22×C32—41no—
456C22×C32—68no—
457C22×C32—62no—
458C22×C32—62no—
459C22×C32C2×D1212yes—
460C22×C32C2×D1212yes—
461C22×C32D3×D412yes—
462C22×C32D3×D412yes—
463C22×C32D3×D412yes—
464C22×C32D3×D412yes—
465C22×C32D3×D412yes—
466C22×C32D3×D412yes—
467C22×C32C2×#6712yes—
468C22×C32C23×D311yescharacteristic
469C22×C32C23×D311yescharacteristic
470C22×C32C23×D311yescharacteristic
471C2×C3⋊D3—28no—
472C2×C3⋊D3—22no—
473C2×C3⋊D3—22no—
474C2×C3⋊D3—22no—
475C2×C3⋊D3—22no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—34no—
478C2×C3⋊D3—34no—
479C2×C3⋊D3—34no—
480C2×C3⋊D3—44no—
481C2×C3⋊D3—64no—
482C2×C3⋊D3—64no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—632no—
485C2×C3⋊D3—68no—
486C2×C3⋊D3—62no—
487C2×C3⋊D3—62no—
488C2×C3⋊D3—64no—
489C2×C3⋊D3—64no—
490C2×C3⋊D3—616no—
491C2×C3⋊D3—68no—
492C2×C3⋊D3—68no—
493C2×C3⋊D3—62no—
494C2×C3⋊D3—62no—
495C2×C3⋊D3—62no—
496C2×C3⋊D3—62no—
497C2×C3⋊D3—124no—
498C2×C3⋊D3—122no—
499C2×C3⋊D3—122no—
500C2×C3⋊D3—122no—
501C2×C3⋊D3—122no—
502C2×C3⋊D3—128no—
503C2×C3⋊D3—128no—
504C2×C3⋊D3—1216no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3C2×D1214yescomplemented
508C2×C3×D3—24no—
509C2×C3×D3—24no—
510C2×C3×D3—216no—
511C2×C3×D3—28no—
512C2×C3×D3—28no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—24no—
518C2×C3×D3—34no—
519C2×C3×D3—34no—
520C2×C3×D3—64no—
521C2×C3×D3—64no—
522C2×C3×D3—64no—
523C2×C3×D3—616no—
524C2×C3×D3—68no—
525C2×C3×D3—68no—
526C2×C3×D3—62no—
527C2×C3×D3—62no—
528C2×C3×D3—62no—
529C2×C3×D3—62no—
530C2×C3×D3—64no—
531C2×C3×D3—62no—
532C2×C3×D3—62no—
533C2×C3×D3—62no—
534C2×C3×D3—62no—
535C2×C3×D3—62no—
536C2×C3×D3—62no—
537C2×C3×D3—122no—
538C2×C3×D3—122no—
539C2×C3×D3—128no—
540C2×C3×D3—124no—
541C2×C3×D3—124no—
542C2×C3×D3C2×D1214yescomplemented
543C2×C3×D3C2×#6714yescomplemented
544D32—664no—
545D32—632no—
546D32—632no—
547C32×C4—62no—
548C32×C4—62no—
549C3⋊Dic3—22no—
550C3×Dic3—24no—
551C3×Dic3—22no—
552C3×Dic3—22no—
553C3×Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—42no—
556C3×Dic3—62no—
557C3×Dic3—62no—
558C3×Dic3—122no—
559C25—271no—
560C22×D4—91no—
561C22×D4—271no—
562C22×D4—271no—
563#120—278no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—271no—
567C33C2×#12011yescharacteristic, complemented, Sylow
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—32no—
572C23×C3—32no—
573C23×C3—34no—
574C23×C3—34no—
575C23×C3—41no—
576C23×C3—62no—
577C23×C3—64no—
578C23×C3—64no—
579C23×C3—64no—
580C23×C3—62no—
581C23×C3—62no—
582C23×C3—62no—
583C23×C3—62no—
584C23×C3—92no—
585C23×C3—94no—
586C23×C3—92no—
587C23×C3—182no—
588C23×C3—182no—
589C23×C3—182no—
590C23×C3—182no—
591C23×C3—182no—
592C23×C3C2×D3211yescharacteristic
593C23×C3C2×D3211yescharacteristic
594C23×C3C2×D3211yescharacteristic
595C22×D3—22no—
596C22×D3—22no—
597C22×D3—32no—
598C22×D3—32no—
599C22×D3—34no—
600C22×D3—34no—
601C22×D3—32no—
602C22×D3—32no—
603C22×D3—64no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—64no—
607C22×D3—64no—
608C22×D3—62no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—64no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—92no—
620C22×D3—92no—
621C22×D3—92no—
622C22×D3—94no—
623C22×D3—94no—
624C22×D3—94no—
625C22×D3—122no—
626C22×D3—122no—
627C22×D3—182no—
628C22×D3—184no—
629C22×D3—182no—
630C22×D3—182no—
631C22×D3—184no—
632C22×D3—184no—
633C22×D3—188no—
634C22×D3—188no—
635C22×D3—1832no—
636C22×D3—188no—
637C22×D3—188no—
638C22×D3—188no—
639C22×D3—188no—
640C22×D3—188no—
641C22×D3—188no—
642C22×D3—1816no—
643C22×D3—1816no—
644C22×D3—1816no—
645C22×D3—1864no—
646C22×D3—1832no—
647C22×D3—1832no—
648C22×D3—184no—
649C22×D3—184no—
650C22×D3—182no—
651C22×D3—182no—
652C22×D3—182no—
653C22×D3—182no—
654C22×D3—182no—
655C22×D3—182no—
656C22×D3—188no—
657C22×D3—362no—
658C22×D3—364no—
659C22×D3—362no—
660C22×D3—362no—
661C22×D3—362no—
662C22×D3—362no—
663C22×D3—364no—
664C22×D3—364no—
665C22×D3#62614yescomplemented
666C22×D3C2×D3212yes—
667C3×D4—188no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—32no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—64no—
675C2×C3×C4—62no—
676C2×C3×C4—62no—
677C2×C3×C4—62no—
678C2×C3×C4—62no—
679C2×C3×C4—92no—
680C2×C3×C4—122no—
681C2×C3×C4—182no—
682#67—68no—
683#67—188no—
684#67—188no—
685#67—188no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—62no—
693C2×Dic3—122no—
694C2×Dic3C2×D3212yescomplemented
695C2×Dic3C2×D3212yescomplemented
696D12—68no—
697D12—188no—
698D12—188no—
699D12—1816no—
700D12—188no—
701C2×C32—21no—
702C2×C32—21no—
703C2×C32—21no—
704C2×C32—21no—
705C2×C32—21no—
706C2×C32—21no—
707C2×C32—21no—
708C2×C32—21no—
709C2×C32—21no—
710C2×C32—24no—
711C2×C32—24no—
712C2×C32—24no—
713C2×C32—44no—
714C2×C32—41no—
715C2×C32—41no—
716C2×C32—41no—
717C2×C32—64no—
718C2×C32#88214yescomplemented
719C2×C32#88214yescomplemented
720C2×C32#93714yescomplemented
721C2×C32C22×D1211yescharacteristic
722C2×C32C22×D1211yescharacteristic
723C2×C32C2×D3×D411yescharacteristic
724C2×C32C2×D3×D411yescharacteristic
725C2×C32C2×D3×D411yescharacteristic
726C2×C32C2×D3×D411yescharacteristic
727C2×C32C2×D3×D411yescharacteristic
728C2×C32C2×D3×D411yescharacteristic
729C2×C32C22×#6711yescharacteristic
730C3⋊D3—24no—
731C3⋊D3—42no—
732C3⋊D3—64no—
733C3⋊D3—68no—
734C3⋊D3—64no—
735C3⋊D3—64no—
736C3⋊D3—124no—
737C3⋊D3—124no—
738C3⋊D3—128no—
739C3×D3—28no—
740C3×D3—24no—
741C3×D3—24no—
742C3×D3—68no—
743C3×D3—64no—
744C3×D3—64no—
745C3×D3—124no—
746C3×D3—122no—
747C3×D3—122no—
748C24—31no—
749C24—91no—
750C24—91no—
751C24—274no—
752C24—271no—
753C24—544no—
754C24—544no—
755C24—544no—
756C2×D4—94no—
757C2×D4—184no—
758C2×D4—274no—
759C2×D4—274no—
760C2×D4—544no—
761C2×D4—544no—
762C22×C4—31no—
763C22×C4—31no—
764C22×C4—91no—
765C22⋊C4—94no—
766C22⋊C4—94no—
767C22⋊C4—274no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—22no—
780C22×C3—34no—
781C22×C3—34no—
782C22×C3—41no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3—64no—
787C22×C3—64no—
788C22×C3—64no—
789C22×C3—616no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—68no—
795C22×C3—68no—
796C22×C3—94no—
797C22×C3—182no—
798C22×C3—182no—
799C22×C3—188no—
800C22×C3—182no—
801C22×C3—182no—
802C22×C3—182no—
803C22×C3—364no—
804C22×C3D3×D1212yes—
805C22×C3D3×D1212yes—
806C22×C3D3×D1212yes—
807C22×C3#380212yes—
808C22×C3C2×#62612yes—
809C22×C3D3×#6712yes—
810C22×C3#381112yes—
811C22×C3#381112yes—
812C22×C3#381112yes—
813C22×C3C22×D3211yescharacteristic
814C22×C3C22×D3211yescharacteristic
815C22×C3C22×D3211yescharacteristic
816C2×D3—22no—
817C2×D3—22no—
818C2×D3—28no—
819C2×D3—34no—
820C2×D3—34no—
821C2×D3—64no—
822C2×D3—64no—
823C2×D3—64no—
824C2×D3—616no—
825C2×D3—62no—
826C2×D3—62no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—68no—
830C2×D3—68no—
831C2×D3—64no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—62no—
838C2×D3—94no—
839C2×D3—94no—
840C2×D3—94no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—128no—
844C2×D3—124no—
845C2×D3—124no—
846C2×D3—184no—
847C2×D3—184no—
848C2×D3—184no—
849C2×D3—1832no—
850C2×D3—1864no—
851C2×D3—1832no—
852C2×D3—1832no—
853C2×D3—184no—
854C2×D3—184no—
855C2×D3—1816no—
856C2×D3—182no—
857C2×D3—182no—
858C2×D3—182no—
859C2×D3—182no—
860C2×D3—182no—
861C2×D3—182no—
862C2×D3—188no—
863C2×D3—188no—
864C2×D3—188no—
865C2×D3—364no—
866C2×D3—362no—
867C2×D3—362no—
868C2×D3—362no—
869C2×D3—362no—
870C2×D3—368no—
871C2×D3—368no—
872C2×D3—364no—
873C2×D3—364no—
874C2×D3—3616no—
875C2×D3C2×#62614yescomplemented
876C3×C4—64no—
877C3×C4—62no—
878C3×C4—62no—
879C3×C4—62no—
880C3×C4—62no—
881C3×C4—122no—
882C3×C4—182no—
883Dic3—22no—
884Dic3—22no—
885Dic3—62no—
886Dic3—62no—
887Dic3—122no—
888C32—21no—
889C32—21no—
890C32—21no—
891C32—41no—
892C32C2×#88211yescharacteristic, complemented
893C32C2×#88211yescharacteristic, complemented
894C32C2×#93711yescharacteristic, complemented
895C23—32no—
896C23—34no—
897C23—62no—
898C23—62no—
899C23—92no—
900C23—94no—
901C23—92no—
902C23—182no—
903C23—182no—
904C23—182no—
905C23—182no—
906C23—182no—
907C23—272no—
908C23—274no—
909C23—548no—
910C23—548no—
911C23—548no—
912C23—5432no—
913C23—542no—
914C23—542no—
915C23D3311yescharacteristic
916D4—188no—
917D4—548no—
918D4—548no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—92no—
924C2×C4—182no—
925C2×C3—21no—
926C2×C3—21no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—24no—
935C2×C3—24no—
936C2×C3—24no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—41no—
940C2×C3—44no—
941C2×C3—68no—
942C2×C3—64no—
943C2×C3—64no—
944C2×C3—184no—
945C2×C3—362no—
946C2×C3#6392214yescomplemented
947C2×C3#6392314yescomplemented
948C2×C3#6398114yescomplemented
949C2×C3C2×D3×D1211yescharacteristic
950C2×C3C2×D3×D1211yescharacteristic
951C2×C3C2×D3×D1211yescharacteristic
952C2×C3C2×#380211yescharacteristic
953C2×C3C22×#62611yescharacteristic
954C2×C3C2×D3×#6711yescharacteristic
955C2×C3C2×#381111yescharacteristic
956C2×C3C2×#381111yescharacteristic
957C2×C3C2×#381111yescharacteristic
958D3—24no—
959D3—68no—
960D3—64no—
961D3—64no—
962D3—124no—
963D3—122no—
964D3—122no—
965D3—188no—
966D3—184no—
967D3—184no—
968D3—184no—
969D3—364no—
970D3—364no—
971D3—368no—
972C22—34no—
973C22—62no—
974C22—62no—
975C22—68no—
976C22—94no—
977C22—182no—
978C22—182no—
979C22—188no—
980C22—182no—
981C22—182no—
982C22—182no—
983C22—274no—
984C22—364no—
985C22—5432no—
986C22—542no—
987C22—542no—
988C22—548no—
989C22D3×#62612yes—
990C22#8895412yes—
991C22#8895512yes—
992C22C2×D3311yescharacteristic
993C4—62no—
994C4—62no—
995C4—182no—
996C3—21no—
997C3—21no—
998C3—21no—
999C3—41no—
1000C3C2×#6392211yescharacteristic, complemented
1001C3C2×#6392311yescharacteristic, complemented
1002C3C2×#6398111yescharacteristic, complemented
1003C2—64no—
1004C2—184no—
1005C2—362no—
1006C2—544no—
1007C2#1172295014yesdirect product factor
1008C2C2×D3×#62611yescharacteristic
1009C2C2×#8895411yescharacteristic
1010C2C2×#8895511yescharacteristic
subgroupG/H
center, hypercenterC23D33
commutator, cosocleC22×C33C24
FrattiniC22C2×D33
Fitting, socleC23×C33C23
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×D3×C3⋊D3C2semidirect
2. C22×#6295C2semidirect
3. C22×#6292C2semidirect
4. C22×C3×#626C2semidirect
5. C2×#88804C2semidirect
6. C2×C3×#3722C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722950C2direct (N × H)
14. C23×C3×C3⋊D3C22semidirect
19. C22×D3×C3⋊D3C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
21. C22×C32×Dic3C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×#6295C22semidirect
26. C2×#6292C22semidirect
28. C2×C3×#626C22semidirect
29. #88804C22semidirect
30. C3×#3722C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×#626D3semidirect
55. C2×#3722D3semidirect
56. C2×(C2×D3)⋊Dic3D3semidirect
62. C22×C3⋊(C3⋊D3)D4semidirect
69. C22×C3×C3⋊D3D4semidirect
71. C22×C3×C3⋊D3C23semidirect
74. C22×C32×D3D4semidirect
81. C2×C3×C3⋊Dic3C23semidirect
84. C2×C32×Dic3C23semidirect
85. C2×C32×Dic3C23semidirect
105. C23×C3⋊D3C2×D3semidirect
129. C22×C3⋊Dic3C2×D3semidirect
139. C22×C3×Dic3C2×D3semidirect
140. C22×C3×Dic3C2×D3semidirect
141. C22×C3×Dic3C2×D3semidirect
142. C22×C3×Dic3C2×D3semidirect
156. C2×#626C2×D3semidirect
167. #3722C2×D3semidirect
168. (C2×D3)⋊Dic3C2×D3semidirect
176. C2×C3⋊(C3⋊D3)C2×D4semidirect
184. C2×C3×C3⋊D3C2×D4semidirect
188. C2×C32×D3C2×D4semidirect
268. C22×C3⋊D3D12semidirect
270. C22×C3⋊D3C22×D3semidirect
303. C22×C3×D3D12semidirect
304. C22×C3×D3#67semidirect
324. C2×C3⋊Dic3C22×D3semidirect
341. C2×C3×Dic3C22×D3semidirect
342. C2×C3×Dic3C22×D3semidirect
343. C2×C3×Dic3C22×D3semidirect
344. C2×C3×Dic3C22×D3semidirect
354. C2×C33#120semidirect
417. C22×Dic3D32semidirect
418. C22×Dic3D32semidirect
507. C2×C3⋊D3C2×D12semidirect
542. C2×C3×D3C2×D12semidirect
543. C2×C3×D3C2×#67semidirect
567. C33C2×#120semidirect
665. C22×D3#626semidirect
694. C2×Dic3C2×D32semidirect
695. C2×Dic3C2×D32semidirect
718. C2×C32#882semidirect
719. C2×C32#882semidirect
720. C2×C32#937semidirect
875. C2×D3C2×#626semidirect
892. C32C2×#882semidirect
893. C32C2×#882semidirect
894. C32C2×#937semidirect
946. C2×C3#63922semidirect
947. C2×C3#63923semidirect
948. C2×C3#63981semidirect
1000. C3C2×#63922semidirect
1001. C3C2×#63923semidirect
1002. C3C2×#63981semidirect
1007. C2#11722950direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×C3⋊D32
C22×#62952
C22×#62922
C22×C3×#6262
C2×#888042
C2×C3×#37222
C2×C3×(C2×D3)⋊Dic32
#117229502
C2×#639813
C2×#639233
C2×#639223