Finite Group Databasebeta

← C2×#11722949 #13172305

Subgroups — C2×#11722949 #13172305

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×#6291C211yesmaximal, characteristic, complemented
3C22×C3×#626C211yesmaximal, characteristic, complemented
4C22×C3×#625C211yesmaximal, characteristic, complemented
5C2×#88814C211yesmaximal, characteristic, complemented
6C2×#88804C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722949C218yesmaximal, direct product factor
9C2×#63983—31nomaximal
10C2×#63981—31nomaximal
11C2×#63922—31nomaximal
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C23×C32×D3C2211yescharacteristic, complemented
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×C3×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C2×#6291—24no—
24C2×#6291C2214yescomplemented
25C2×C3×#626—24no—
26C2×C3×#626C2214yescomplemented
27C2×C3×#625—24no—
28C2×C3×#625C2214yescomplemented
29#88814C2214yescomplemented
30#88804C2214yescomplemented
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C24×C3⋊D3—31no—
33C23×D32—31no—
34C23×D32—31no—
35C23×D32—61no—
36C22×#638—31no—
37C22×C3×#67—31no—
38C22×C3×#67—31no—
39C22×C3×#67—31no—
40C22×C3×D12—31no—
41C22×#626—31no—
42C22×#626—31no—
43C22×#626—61no—
44C22×#626D311yescharacteristic, complemented
45C22×#625D311yescharacteristic, complemented
46C2×#3752—31no—
47C2×C3×#217—31no—
48C2×C3×(C2×D3)⋊C4—31no—
49#63983—38no—
50#63981—38no—
51C2×#3722—31no—
52C2×#3722—31no—
53C2×#3722—31no—
54C2×#3722—61no—
55C2×(C2×D3)⋊Dic3—31no—
56C2×(C2×D3)⋊Dic3—31no—
57C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
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⋊D3D414yescomplemented
67C22×C3×C3⋊D3C2312yes—
68C22×C32×D3—22no—
69C22×C32×D3—22no—
70C22×C32×D3—22no—
71C22×C32×D3—22no—
72C22×C32×D3—22no—
73C22×C32×D3D414yescomplemented
74C22×C32×D3C2312yes—
75C22×C32×D3C2312yescomplemented
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⋊Dic3—22no—
82C2×C3×C3⋊Dic3C2312yescomplemented
83C2×C3×C3⋊Dic3C2312yescomplemented
84C2×C32×Dic3—22no—
85C2×C32×Dic3C2312yescomplemented
86#6291—28no—
87C3×#626—28no—
88C3×#625—28no—
89C2×#937—91no—
90C2×#937—91no—
91C2×#882—91no—
92C24×C32—31no—
93C24×C32—31no—
94C23×C3⋊D3—31no—
95C23×C3⋊D3—31no—
96C23×C3⋊D3—31no—
97C23×C3⋊D3—34no—
98C23×C3⋊D3—64no—
99C23×C3⋊D3—64no—
100C23×C3⋊D3—61no—
101C23×C3⋊D3—64no—
102C23×C3⋊D3—61no—
103C23×C3⋊D3—61no—
104C23×C3⋊D3—121no—
105C23×C3⋊D3C2×D311yescharacteristic
106C23×C3×D3—21no—
107C23×C3×D3—21no—
108C23×C3×D3—31no—
109C23×C3×D3—31no—
110C23×C3×D3—61no—
111C23×C3×D3C2×D311yescharacteristic
112C23×C3×D3C2×D311yescharacteristic
113C23×C3×D3C2×D311yescharacteristic, complemented
114C23×C3×D3C2×D311yescharacteristic, complemented
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—
128C2×#638—34no—
129C2×#638—64no—
130C22×C3⋊Dic3C2×D311yescharacteristic, complemented
131C22×C3⋊Dic3C2×D311yescharacteristic, complemented
132C2×C3×#67—34no—
133C2×C3×#67—34no—
134C2×C3×#67—34no—
135C2×C3×#67—64no—
136C2×C3×#67—64no—
137C2×C3×#67—64no—
138C22×C3×Dic3—21no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C22×C3×Dic3—31no—
142C22×C3×Dic3—31no—
143C22×C3×Dic3—61no—
144C22×C3×Dic3—61no—
145C22×C3×Dic3C2×D311yescharacteristic, complemented
146C22×C3×Dic3C2×D311yescharacteristic, complemented
147C2×C3×D12—34no—
148C2×C3×D12—64no—
149C2×#626—24no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—64no—
153C2×#626—64no—
154C2×#626—64no—
155C2×#626—68no—
156C2×#626C2×D314yescomplemented
157C2×#625—24no—
158C2×#625C2×D314yescomplemented
159#3752—34no—
160C3×#217—34no—
161C3×(C2×D3)⋊C4—34no—
162#3722—34no—
163#3722—34no—
164#3722—34no—
165#3722—64no—
166(C2×D3)⋊Dic3—34no—
167(C2×D3)⋊Dic3—34no—
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⋊D3C2×D414yescomplemented
181C2×C32×D3—28no—
182C2×C32×D3—22no—
183C2×C32×D3—22no—
184C2×C32×D3—22no—
185C2×C32×D3—22no—
186C2×C32×D3—22no—
187C2×C32×D3—44no—
188C2×C32×D3C2×D414yescomplemented
189D3×C3⋊D3—232no—
190C3×C3⋊Dic3—22no—
191C3×C3⋊Dic3—22no—
192C32×Dic3—22no—
193C24×D3—91no—
194C24×D3—91no—
195C24×D3—91no—
196C24×D3—181no—
197C22×C3×D4—91no—
198C22×C3×D4—91no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—91no—
203C22×#67—91no—
204C22×#67—181no—
205C22×D12—31no—
206C22×D12—91no—
207C2×C3×C22⋊C4—91no—
208C2×#217—31no—
209C2×#217—91no—
210#937—98no—
211#937—98no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—91no—
214C2×(C2×D3)⋊C4—91no—
215C2×(C2×D3)⋊C4—91no—
216C2×(C2×D3)⋊C4—91no—
217C2×(C2×D3)⋊C4—91no—
218C2×(C2×D3)⋊C4—181no—
219#882—98no—
220C23×C32—21no—
221C23×C32—21no—
222C23×C32—21no—
223C23×C32—34no—
224C23×C32—32no—
225C23×C32—32no—
226C23×C32—41no—
227C23×C32—62no—
228C23×C32—62no—
229C23×C32—62no—
230C23×C32—62no—
231C23×C32—62no—
232C23×C32C22×D311yescharacteristic
233C23×C32C22×D311yescharacteristic
234C23×C32C22×D311yescharacteristic
235C22×C3⋊D3—22no—
236C22×C3⋊D3—22no—
237C22×C3⋊D3—34no—
238C22×C3⋊D3—34no—
239C22×C3⋊D3—34no—
240C22×C3⋊D3—32no—
241C22×C3⋊D3—32no—
242C22×C3⋊D3—32no—
243C22×C3⋊D3—64no—
244C22×C3⋊D3—62no—
245C22×C3⋊D3—62no—
246C22×C3⋊D3—64no—
247C22×C3⋊D3—64no—
248C22×C3⋊D3—62no—
249C22×C3⋊D3—68no—
250C22×C3⋊D3—68no—
251C22×C3⋊D3—632no—
252C22×C3⋊D3—62no—
253C22×C3⋊D3—62no—
254C22×C3⋊D3—68no—
255C22×C3⋊D3—64no—
256C22×C3⋊D3—64no—
257C22×C3⋊D3—62no—
258C22×C3⋊D3—62no—
259C22×C3⋊D3—62no—
260C22×C3⋊D3—62no—
261C22×C3⋊D3—124no—
262C22×C3⋊D3—122no—
263C22×C3⋊D3—122no—
264C22×C3⋊D3—122no—
265C22×C3⋊D3—122no—
266C22×C3⋊D3—122no—
267C22×C3⋊D3—124no—
268C22×C3⋊D3—124no—
269C22×C3⋊D3#6714yescomplemented
270C22×C3⋊D3C22×D312yes—
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—22no—
280C22×C3×D3—22no—
281C22×C3×D3—22no—
282C22×C3×D3—22no—
283C22×C3×D3—22no—
284C22×C3×D3—24no—
285C22×C3×D3—22no—
286C22×C3×D3—22no—
287C22×C3×D3—34no—
288C22×C3×D3—34no—
289C22×C3×D3—32no—
290C22×C3×D3—32no—
291C22×C3×D3—42no—
292C22×C3×D3—42no—
293C22×C3×D3—64no—
294C22×C3×D3—62no—
295C22×C3×D3—64no—
296C22×C3×D3—64no—
297C22×C3×D3—62no—
298C22×C3×D3—62no—
299C22×C3×D3—62no—
300C22×C3×D3—62no—
301C22×C3×D3D1214yescomplemented
302C22×C3×D3#6714yescomplemented
303C22×C3×D3C22×D312yes—
304C22×C3×D3C22×D312yes—
305C22×C3×D3C22×D312yescomplemented
306C22×C3×D3C22×D312yescomplemented
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—62no—
321#638—68no—
322C2×C3⋊Dic3—22no—
323C2×C3⋊Dic3—22no—
324C2×C3⋊Dic3C22×D312yescomplemented
325C2×C3⋊Dic3C22×D312yescomplemented
326C3×#67—68no—
327C3×#67—68no—
328C3×#67—68no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—32no—
333C2×C3×Dic3—32no—
334C2×C3×Dic3—32no—
335C2×C3×Dic3—32no—
336C2×C3×Dic3—42no—
337C2×C3×Dic3—62no—
338C2×C3×Dic3—62no—
339C2×C3×Dic3—64no—
340C2×C3×Dic3—62no—
341C2×C3×Dic3—62no—
342C2×C3×Dic3—62no—
343C2×C3×Dic3—62no—
344C2×C3×Dic3—122no—
345C2×C3×Dic3C22×D312yescomplemented
346C2×C3×Dic3C22×D312yescomplemented
347C3×D12—68no—
348#626—28no—
349#626—68no—
350#626—68no—
351#626—616no—
352#625—28no—
353C2×#120—271noSylow
354C2×C33#12014yescomplemented
355C2×C33C22×D411yescharacteristic
356C2×C33C22×D411yescharacteristic
357C2×C33C22×D411yescharacteristic
358C3⋊(C3⋊D3)—24no—
359C3×C3⋊D3—24no—
360C32×D3—24no—
361C32×D3—42no—
362C24×C3—31no—
363C24×C3—31no—
364C24×C3—31no—
365C24×C3—31no—
366C24×C3—61no—
367C24×C3—61no—
368C24×C3—91no—
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—61no—
372C23×D3—94no—
373C23×D3—94no—
374C23×D3—91no—
375C23×D3—91no—
376C23×D3—91no—
377C23×D3—94no—
378C23×D3—184no—
379C23×D3—181no—
380C23×D3—181no—
381C23×D3—181no—
382C23×D3—184no—
383C23×D3—184no—
384C23×D3—184no—
385C23×D3—184no—
386C23×D3—184no—
387C23×D3—184no—
388C23×D3—184no—
389C23×D3—184no—
390C23×D3—188no—
391C23×D3—188no—
392C23×D3—188no—
393C23×D3—184no—
394C23×D3—361no—
395C23×D3D3211yescharacteristic
396C23×D3D3211yescharacteristic, complemented
397C2×C3×D4—94no—
398C2×C3×D4—94no—
399C2×C3×D4—184no—
400C2×C3×D4—184no—
401C22×C3×C4—31no—
402C22×C3×C4—31no—
403C22×C3×C4—61no—
404C22×C3×C4—91no—
405C22×C3×C4—91no—
406C2×#67—34no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—64no—
410C2×#67—64no—
411C2×#67—64no—
412C2×#67—94no—
413C2×#67—94no—
414C2×#67—184no—
415C2×#67—184no—
416C2×#67—184no—
417C2×#67—188no—
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—61no—
423C22×Dic3—61no—
424C22×Dic3D3211yescharacteristic, complemented
425C2×D12—34no—
426C2×D12—64no—
427C2×D12—94no—
428C2×D12—184no—
429C3×C22⋊C4—94no—
430#217—34no—
431#217—94no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—94no—
434(C2×D3)⋊C4—94no—
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×C32—62no—
460C22×C32—62no—
461C22×C32—62no—
462C22×C32—124no—
463C22×C32C2×D1212yes—
464C22×C32D3×D412yes—
465C22×C32D3×D412yes—
466C22×C32D3×D412yes—
467C22×C32D3×D412yes—
468C22×C32D3×D412yes—
469C22×C32D3×D412yes—
470C22×C32C2×#6712yes—
471C22×C32C2×#6712yes—
472C22×C32C23×D311yescharacteristic
473C22×C32C23×D311yescharacteristic
474C22×C32C23×D311yescharacteristic
475C2×C3⋊D3—28no—
476C2×C3⋊D3—22no—
477C2×C3⋊D3—22no—
478C2×C3⋊D3—34no—
479C2×C3⋊D3—34no—
480C2×C3⋊D3—34no—
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×#6714yescomplemented
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—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—24no—
525C2×C3×D3—34no—
526C2×C3×D3—34no—
527C2×C3×D3—42no—
528C2×C3×D3—42no—
529C2×C3×D3—48no—
530C2×C3×D3—44no—
531C2×C3×D3—44no—
532C2×C3×D3—64no—
533C2×C3×D3—64no—
534C2×C3×D3—64no—
535C2×C3×D3—616no—
536C2×C3×D3—68no—
537C2×C3×D3—68no—
538C2×C3×D3—62no—
539C2×C3×D3—62no—
540C2×C3×D3—62no—
541C2×C3×D3—62no—
542C2×C3×D3C2×D1214yescomplemented
543C2×C3×D3C2×#6714yescomplemented
544D32—664no—
545D32—632no—
546D32—632no—
547C32×C4—62no—
548C3⋊Dic3—22no—
549C3⋊Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—22no—
552C3×Dic3—42no—
553C3×Dic3—64no—
554C3×Dic3—62no—
555C3×Dic3—62no—
556C3×Dic3—62no—
557C3×Dic3—62no—
558C3×Dic3—122no—
559C25—271no—
560C22×D4—91no—
561C22×D4—91no—
562C22×D4—271no—
563#120—278no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—271no—
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—32no—
576C23×C3—32no—
577C23×C3—41no—
578C23×C3—62no—
579C23×C3—64no—
580C23×C3—62no—
581C23×C3—64no—
582C23×C3—64no—
583C23×C3—64no—
584C23×C3—62no—
585C23×C3—62no—
586C23×C3—62no—
587C23×C3—62no—
588C23×C3—62no—
589C23×C3—62no—
590C23×C3—62no—
591C23×C3—62no—
592C23×C3—62no—
593C23×C3—62no—
594C23×C3—92no—
595C23×C3—94no—
596C23×C3—122no—
597C23×C3—122no—
598C23×C3—182no—
599C23×C3—182no—
600C23×C3C2×D3211yescharacteristic
601C23×C3C2×D3211yescharacteristic
602C23×C3C2×D3211yescharacteristic
603C22×D3—22no—
604C22×D3—22no—
605C22×D3—22no—
606C22×D3—22no—
607C22×D3—22no—
608C22×D3—32no—
609C22×D3—32no—
610C22×D3—34no—
611C22×D3—34no—
612C22×D3—64no—
613C22×D3—62no—
614C22×D3—64no—
615C22×D3—64no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—62no—
620C22×D3—92no—
621C22×D3—92no—
622C22×D3—92no—
623C22×D3—94no—
624C22×D3—94no—
625C22×D3—94no—
626C22×D3—182no—
627C22×D3—184no—
628C22×D3—182no—
629C22×D3—182no—
630C22×D3—184no—
631C22×D3—184no—
632C22×D3—188no—
633C22×D3—188no—
634C22×D3—1832no—
635C22×D3—188no—
636C22×D3—188no—
637C22×D3—188no—
638C22×D3—188no—
639C22×D3—188no—
640C22×D3—188no—
641C22×D3—1816no—
642C22×D3—1816no—
643C22×D3—1816no—
644C22×D3—1864no—
645C22×D3—1832no—
646C22×D3—1832no—
647C22×D3—184no—
648C22×D3—184no—
649C22×D3—182no—
650C22×D3—182no—
651C22×D3—182no—
652C22×D3—182no—
653C22×D3—182no—
654C22×D3—182no—
655C22×D3—188no—
656C22×D3—362no—
657C22×D3—364no—
658C22×D3—362no—
659C22×D3—362no—
660C22×D3—362no—
661C22×D3—362no—
662C22×D3—364no—
663C22×D3—364no—
664C22×D3#62614yescomplemented
665C22×D3C2×D3212yes—
666C22×D3C2×D3212yescomplemented
667C3×D4—188no—
668C3×D4—188no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—62no—
672C2×C3×C4—62no—
673C2×C3×C4—62no—
674C2×C3×C4—92no—
675C2×C3×C4—92no—
676C2×C3×C4—122no—
677C2×C3×C4—182no—
678C2×C3×C4—182no—
679#67—68no—
680#67—68no—
681#67—68no—
682#67—188no—
683#67—188no—
684#67—1816no—
685C2×Dic3—22no—
686C2×Dic3—32no—
687C2×Dic3—32no—
688C2×Dic3—32no—
689C2×Dic3—32no—
690C2×Dic3—62no—
691C2×Dic3—62no—
692C2×Dic3—64no—
693C2×Dic3—62no—
694C2×Dic3—62no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—122no—
698C2×Dic3C2×D3212yescomplemented
699D12—68no—
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—122no—
719C2×C32#88214yescomplemented
720C2×C32#93714yescomplemented
721C2×C32#93714yescomplemented
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
730C2×C32C22×#6711yescharacteristic
731C3⋊D3—24no—
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—44no—
743C3×D3—42no—
744C3×D3—42no—
745C3×D3—68no—
746C3×D3—64no—
747C3×D3—64no—
748C24—31no—
749C24—31no—
750C24—91no—
751C24—274no—
752C24—271no—
753C24—544no—
754C24—544no—
755C24—544no—
756C2×D4—94no—
757C2×D4—94no—
758C2×D4—184no—
759C2×D4—184no—
760C2×D4—274no—
761C2×D4—544no—
762C22×C4—31no—
763C22×C4—91no—
764C22×C4—91no—
765C22⋊C4—94no—
766C22⋊C4—274no—
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—64no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—68no—
796C22×C3—68no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—62no—
802C22×C3—62no—
803C22×C3—94no—
804C22×C3—122no—
805C22×C3—122no—
806C22×C3—128no—
807C22×C3—124no—
808C22×C3—124no—
809C22×C3—182no—
810C22×C3—182no—
811C22×C3—188no—
812C22×C3D3×D1212yes—
813C22×C3#380212yes—
814C22×C3C2×#62612yes—
815C22×C3D3×#6712yes—
816C22×C3D3×#6712yes—
817C22×C3D3×#6712yes—
818C22×C3#381112yes—
819C22×C3#381112yes—
820C22×C3#381112yes—
821C22×C3C22×D3211yescharacteristic
822C22×C3C22×D3211yescharacteristic
823C22×C3C22×D3211yescharacteristic
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—28no—
827C2×D3—22no—
828C2×D3—22no—
829C2×D3—22no—
830C2×D3—34no—
831C2×D3—34no—
832C2×D3—44no—
833C2×D3—64no—
834C2×D3—64no—
835C2×D3—64no—
836C2×D3—616no—
837C2×D3—62no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—62no—
841C2×D3—68no—
842C2×D3—68no—
843C2×D3—94no—
844C2×D3—94no—
845C2×D3—94no—
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—62no—
877C3×C4—62no—
878C3×C4—122no—
879C3×C4—182no—
880C3×C4—182no—
881Dic3—22no—
882Dic3—64no—
883Dic3—62no—
884Dic3—62no—
885Dic3—62no—
886Dic3—62no—
887Dic3—122no—
888C32—21no—
889C32—21no—
890C32—21no—
891C32—41no—
892C32C2×#88211yescharacteristic, complemented
893C32C2×#93711yescharacteristic, complemented
894C32C2×#93711yescharacteristic, complemented
895C23—32no—
896C23—34no—
897C23—32no—
898C23—62no—
899C23—62no—
900C23—62no—
901C23—62no—
902C23—62no—
903C23—92no—
904C23—94no—
905C23—182no—
906C23—182no—
907C23—272no—
908C23—274no—
909C23—548no—
910C23—548no—
911C23—548no—
912C23—5432no—
913C23—542no—
914C23—542no—
915C23D3311yescharacteristic
916D4—188no—
917D4—188no—
918D4—548no—
919C2×C4—32no—
920C2×C4—62no—
921C2×C4—92no—
922C2×C4—92no—
923C2×C4—182no—
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—124no—
945C2×C3—122no—
946C2×C3—122no—
947C2×C3—184no—
948C2×C3#6392214yescomplemented
949C2×C3#6398114yescomplemented
950C2×C3#6398314yescomplemented
951C2×C3C2×D3×D1211yescharacteristic
952C2×C3C2×#380211yescharacteristic
953C2×C3C22×#62611yescharacteristic
954C2×C3C2×D3×#6711yescharacteristic
955C2×C3C2×D3×#6711yescharacteristic
956C2×C3C2×D3×#6711yescharacteristic
957C2×C3C2×#381111yescharacteristic
958C2×C3C2×#381111yescharacteristic
959C2×C3C2×#381111yescharacteristic
960D3—24no—
961D3—42no—
962D3—68no—
963D3—64no—
964D3—64no—
965D3—188no—
966D3—184no—
967D3—184no—
968D3—184no—
969D3—364no—
970D3—364no—
971D3—368no—
972C22—34no—
973C22—62no—
974C22—62no—
975C22—68no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—94no—
980C22—124no—
981C22—182no—
982C22—182no—
983C22—188no—
984C22—274no—
985C22—5432no—
986C22—542no—
987C22—542no—
988C22—548no—
989C22D3×#62612yes—
990C22#8895212yes—
991C22#8895412yes—
992C22C2×D3311yescharacteristic
993C4—62no—
994C4—182no—
995C4—182no—
996C3—21no—
997C3—21no—
998C3—21no—
999C3—41no—
1000C3C2×#6392211yescharacteristic, complemented
1001C3C2×#6398111yescharacteristic, complemented
1002C3C2×#6398311yescharacteristic, complemented
1003C2—64no—
1004C2—122no—
1005C2—184no—
1006C2—544no—
1007C2#1172294914yesdirect product factor
1008C2C2×D3×#62611yescharacteristic
1009C2C2×#8895211yescharacteristic
1010C2C2×#8895411yescharacteristic
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×#6291C2semidirect
3. C22×C3×#626C2semidirect
4. C22×C3×#625C2semidirect
5. C2×#88814C2semidirect
6. C2×#88804C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722949C2direct (N × H)
15. C23×C32×D3C22semidirect
19. C22×D3×C3⋊D3C22semidirect
20. C22×C3×C3⋊Dic3C22semidirect
21. C22×C3×C3⋊Dic3C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×#6291C22semidirect
26. C2×C3×#626C22semidirect
28. C2×C3×#625C22semidirect
29. #88814C22semidirect
30. #88804C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
44. C22×#626D3semidirect
45. C22×#625D3semidirect
57. C2×(C2×D3)⋊Dic3D3semidirect
62. C22×C3⋊(C3⋊D3)D4semidirect
66. C22×C3×C3⋊D3D4semidirect
73. C22×C32×D3D4semidirect
75. C22×C32×D3C23semidirect
82. C2×C3×C3⋊Dic3C23semidirect
83. C2×C3×C3⋊Dic3C23semidirect
85. C2×C32×Dic3C23semidirect
113. C23×C3×D3C2×D3semidirect
114. C23×C3×D3C2×D3semidirect
130. C22×C3⋊Dic3C2×D3semidirect
131. C22×C3⋊Dic3C2×D3semidirect
145. C22×C3×Dic3C2×D3semidirect
146. C22×C3×Dic3C2×D3semidirect
156. C2×#626C2×D3semidirect
158. C2×#625C2×D3semidirect
168. (C2×D3)⋊Dic3C2×D3semidirect
176. C2×C3⋊(C3⋊D3)C2×D4semidirect
180. C2×C3×C3⋊D3C2×D4semidirect
188. C2×C32×D3C2×D4semidirect
269. C22×C3⋊D3#67semidirect
301. C22×C3×D3D12semidirect
302. C22×C3×D3#67semidirect
305. C22×C3×D3C22×D3semidirect
306. C22×C3×D3C22×D3semidirect
324. C2×C3⋊Dic3C22×D3semidirect
325. C2×C3⋊Dic3C22×D3semidirect
345. C2×C3×Dic3C22×D3semidirect
346. C2×C3×Dic3C22×D3semidirect
354. C2×C33#120semidirect
396. C23×D3D32semidirect
424. C22×Dic3D32semidirect
507. C2×C3⋊D3C2×#67semidirect
542. C2×C3×D3C2×D12semidirect
543. C2×C3×D3C2×#67semidirect
567. C33C2×#120semidirect
664. C22×D3#626semidirect
666. C22×D3C2×D32semidirect
698. C2×Dic3C2×D32semidirect
719. C2×C32#882semidirect
720. C2×C32#937semidirect
721. C2×C32#937semidirect
875. C2×D3C2×#626semidirect
892. C32C2×#882semidirect
893. C32C2×#937semidirect
894. C32C2×#937semidirect
948. C2×C3#63922semidirect
949. C2×C3#63981semidirect
950. C2×C3#63983semidirect
1000. C3C2×#63922semidirect
1001. C3C2×#63981semidirect
1002. C3C2×#63983semidirect
1007. C2#11722949direct (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×#62912
C22×C3×#6262
C22×C3×#6252
C2×#888142
C2×#888042
C2×C3×(C2×D3)⋊Dic32
#117229492
C2×#639833
C2×#639813
C2×#639223