Finite Group Databasebeta

← C2×#11722947 #13172286

Subgroups — C2×#11722947 #13172286

Order 1728.

3202 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×D32C211yesmaximal, characteristic, complemented
2C22×#6295C211yesmaximal, characteristic, complemented
3C22×#6290C211yesmaximal, characteristic, complemented
4C22×C3×#626C211yesmaximal, characteristic, complemented
5C2×#88803C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
8#11722947C218yesmaximal, direct product factor
9C2×#63977—31nomaximal
10C2×#63976—31nomaximal
11C2×#63922—31nomaximal
12C23×C3×C3⋊D3C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic, complemented
14C23×C32×D3C2211yescharacteristic
15C23×C32×D3C2211yescharacteristic
16C22×C3×D32—24no—
17C22×C3×D32—24no—
18C22×C3×D32—24no—
19C22×C3×D32C2214yescomplemented
20C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
21C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
22C22×C32×Dic3C2211yescharacteristic, complemented
23C2×#6295—24no—
24C2×#6295C2214yescomplemented
25C2×#6290—24no—
26C2×#6290C2214yescomplemented
27C2×C3×#626—24no—
28C2×C3×#626C2214yescomplemented
29#88803C2214yescomplemented
30(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
31C3×(C2×D3)⋊Dic3C2214yescomplemented
32C24×C3×D3—31no—
33C24×C3×D3—31no—
34C23×D32D311yescharacteristic, complemented
35C22×#638—31no—
36C22×C3×#67—31no—
37C22×C3×D12—31no—
38C22×#626—31no—
39C22×#626—31no—
40C22×#626D311yescharacteristic, complemented
41C22×#625—31no—
42C22×#625—31no—
43C22×#625—31no—
44C22×#625—61no—
45C2×#3757—31no—
46C2×#3752—31no—
47C2×C3×#217—31no—
48C2×C3×(C2×D3)⋊C4—31no—
49#63977—38no—
50#63976—38no—
51C2×(C2×D3)⋊Dic3—31no—
52C2×(C2×D3)⋊Dic3—31no—
53C2×(C2×D3)⋊Dic3—31no—
54C2×(C2×D3)⋊Dic3—31no—
55C2×(C2×D3)⋊Dic3—61no—
56C2×(C2×D3)⋊Dic3—61no—
57C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
58#63922—38no—
59C23×C33C2311yescharacteristic
60C22×C3×C3⋊D3—22no—
61C22×C3×C3⋊D3—22no—
62C22×C3×C3⋊D3—22no—
63C22×C3×C3⋊D3—22no—
64C22×C3×C3⋊D3—22no—
65C22×C3×C3⋊D3D414yescomplemented
66C22×C3×C3⋊D3C2312yes—
67C22×C3×C3⋊D3C2312yescomplemented
68C22×C32×D3—22no—
69C22×C32×D3—22no—
70C22×C32×D3—22no—
71C22×C32×D3—22no—
72C22×C32×D3D414yescomplemented
73C22×C32×D3D414yescomplemented
74C22×C32×D3C2312yes—
75C22×C32×D3C2312yes—
76C2×C3×D32—232no—
77C2×C3×D32—28no—
78C2×C3×D32—28no—
79C2×C3×D32—28no—
80C2×C3⋊(C3⋊Dic3)—22no—
81C2×C3⋊(C3⋊Dic3)C2312yescomplemented
82C2×C3×C3⋊Dic3—22no—
83C2×C3×C3⋊Dic3C2312yescomplemented
84C2×C32×Dic3—22no—
85C2×C32×Dic3C2312yescomplemented
86#6295—28no—
87#6290—28no—
88C3×#626—28no—
89C2×#953—91no—
90C2×#937—91no—
91C2×#882—91no—
92C24×C32—31no—
93C24×C32—31no—
94C23×C3⋊D3C2×D311yescharacteristic
95C23×C3⋊D3C2×D311yescharacteristic, complemented
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—31no—
99C23×C3×D3—31no—
100C23×C3×D3—31no—
101C23×C3×D3—31no—
102C23×C3×D3—34no—
103C23×C3×D3—34no—
104C23×C3×D3—64no—
105C23×C3×D3—64no—
106C23×C3×D3—64no—
107C23×C3×D3—64no—
108C23×C3×D3—64no—
109C23×C3×D3—64no—
110C23×C3×D3—61no—
111C23×C3×D3—61no—
112C23×C3×D3C2×D311yescharacteristic
113C23×C3×D3C2×D311yescharacteristic
114C23×C3×D3C2×D311yescharacteristic
115C23×C3×D3C2×D311yescharacteristic
116C22×D32—24no—
117C22×D32—24no—
118C22×D32—24no—
119C22×D32C2×D314yescomplemented
120C22×C32×C4—31no—
121C2×#638—34no—
122C2×#638—64no—
123C22×C3⋊Dic3—31no—
124C22×C3⋊Dic3—31no—
125C22×C3⋊Dic3—31no—
126C22×C3⋊Dic3—61no—
127C22×C3⋊Dic3—61no—
128C22×C3⋊Dic3—61no—
129C22×C3⋊Dic3—121no—
130C22×C3⋊Dic3C2×D311yescharacteristic, complemented
131C2×C3×#67—34no—
132C2×C3×#67—64no—
133C22×C3×Dic3—21no—
134C22×C3×Dic3—31no—
135C22×C3×Dic3—31no—
136C22×C3×Dic3—61no—
137C22×C3×Dic3C2×D311yescharacteristic, complemented
138C22×C3×Dic3C2×D311yescharacteristic, complemented
139C2×C3×D12—34no—
140C2×C3×D12—64no—
141C2×#626—24no—
142C2×#626—34no—
143C2×#626—34no—
144C2×#626—64no—
145C2×#626—64no—
146C2×#626C2×D314yescomplemented
147C2×#625—34no—
148C2×#625—34no—
149C2×#625—34no—
150C2×#625—64no—
151C2×#625—64no—
152C2×#625—68no—
153C2×#625—64no—
154C2×#625—64no—
155#3757—34no—
156#3752—34no—
157C3×#217—34no—
158C3×(C2×D3)⋊C4—34no—
159(C2×D3)⋊Dic3—34no—
160(C2×D3)⋊Dic3—34no—
161(C2×D3)⋊Dic3—34no—
162(C2×D3)⋊Dic3—34no—
163(C2×D3)⋊Dic3—64no—
164(C2×D3)⋊Dic3—64no—
165(C2×D3)⋊Dic3C2×D314yescomplemented
166C22×C33C2×D412yes—
167C22×C33C2×D412yes—
168C22×C33C2×D412yes—
169C22×C33C2411yescharacteristic
170C2×C3×C3⋊D3—28no—
171C2×C3×C3⋊D3—22no—
172C2×C3×C3⋊D3—22no—
173C2×C3×C3⋊D3—22no—
174C2×C3×C3⋊D3—22no—
175C2×C3×C3⋊D3—22no—
176C2×C3×C3⋊D3—44no—
177C2×C3×C3⋊D3C2×D414yescomplemented
178C2×C32×D3—28no—
179C2×C32×D3—28no—
180C2×C32×D3—22no—
181C2×C32×D3—22no—
182C2×C32×D3—22no—
183C2×C32×D3—22no—
184C2×C32×D3C2×D414yescomplemented
185C2×C32×D3C2×D414yescomplemented
186C3×D32—232no—
187C3⋊(C3⋊Dic3)—22no—
188C3×C3⋊Dic3—22no—
189C32×Dic3—22no—
190C25×C3—91no—
191C24×D3—31no—
192C24×D3—31no—
193C22×C3×D4—91no—
194C22×#67—31no—
195C22×#67—91no—
196C22×#67—91no—
197C22×#67—91no—
198C22×#67—91no—
199C22×#67—91no—
200C22×#67—181no—
201C22×D12—31no—
202C22×D12—91no—
203C2×C3×C22⋊C4—91no—
204#953—98no—
205C2×#217—31no—
206C2×#217—91no—
207C2×#217—91no—
208C2×#217—91no—
209C2×#217—181no—
210#937—98no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—91no—
213C2×(C2×D3)⋊C4—91no—
214C2×(C2×D3)⋊C4—91no—
215C2×(C2×D3)⋊C4—181no—
216#882—98no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32—21no—
220C23×C32—34no—
221C23×C32—34no—
222C23×C32—32no—
223C23×C32—32no—
224C23×C32—41no—
225C23×C32—62no—
226C23×C32—62no—
227C23×C32—62no—
228C23×C32—62no—
229C23×C32C22×D311yescharacteristic
230C23×C32C22×D311yescharacteristic
231C23×C32C22×D311yescharacteristic
232C22×C3⋊D3—22no—
233C22×C3⋊D3—22no—
234C22×C3⋊D3—22no—
235C22×C3⋊D3—22no—
236C22×C3⋊D3—22no—
237C22×C3⋊D3#6714yescomplemented
238C22×C3⋊D3C22×D312yes—
239C22×C3⋊D3C22×D312yescomplemented
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—22no—
243C22×C3×D3—22no—
244C22×C3×D3—22no—
245C22×C3×D3—22no—
246C22×C3×D3—22no—
247C22×C3×D3—22no—
248C22×C3×D3—24no—
249C22×C3×D3—24no—
250C22×C3×D3—22no—
251C22×C3×D3—22no—
252C22×C3×D3—34no—
253C22×C3×D3—34no—
254C22×C3×D3—32no—
255C22×C3×D3—32no—
256C22×C3×D3—32no—
257C22×C3×D3—32no—
258C22×C3×D3—42no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—62no—
263C22×C3×D3—64no—
264C22×C3×D3—62no—
265C22×C3×D3—68no—
266C22×C3×D3—68no—
267C22×C3×D3—68no—
268C22×C3×D3—68no—
269C22×C3×D3—632no—
270C22×C3×D3—632no—
271C22×C3×D3—62no—
272C22×C3×D3—62no—
273C22×C3×D3—62no—
274C22×C3×D3—62no—
275C22×C3×D3—68no—
276C22×C3×D3—68no—
277C22×C3×D3—64no—
278C22×C3×D3—62no—
279C22×C3×D3—62no—
280C22×C3×D3—62no—
281C22×C3×D3—62no—
282C22×C3×D3—62no—
283C22×C3×D3—62no—
284C22×C3×D3—122no—
285C22×C3×D3—122no—
286C22×C3×D3—122no—
287C22×C3×D3—122no—
288C22×C3×D3D1214yescomplemented
289C22×C3×D3#6714yescomplemented
290C22×C3×D3#6714yescomplemented
291C22×C3×D3#6714yescomplemented
292C22×C3×D3C22×D312yes—
293C22×C3×D3C22×D312yes—
294C22×C3×D3C22×D312yes—
295C22×C3×D3C22×D312yes—
296C2×D32—232no—
297C2×D32—28no—
298C2×D32—28no—
299C2×D32—28no—
300C2×C32×C4—32no—
301C2×C32×C4—62no—
302#638—68no—
303C2×C3⋊Dic3—22no—
304C2×C3⋊Dic3—32no—
305C2×C3⋊Dic3—32no—
306C2×C3⋊Dic3—32no—
307C2×C3⋊Dic3—62no—
308C2×C3⋊Dic3—62no—
309C2×C3⋊Dic3—62no—
310C2×C3⋊Dic3—62no—
311C2×C3⋊Dic3—64no—
312C2×C3⋊Dic3—62no—
313C2×C3⋊Dic3—62no—
314C2×C3⋊Dic3—122no—
315C2×C3⋊Dic3—122no—
316C2×C3⋊Dic3—122no—
317C2×C3⋊Dic3—124no—
318C2×C3⋊Dic3C22×D312yescomplemented
319C3×#67—68no—
320C2×C3×Dic3—22no—
321C2×C3×Dic3—22no—
322C2×C3×Dic3—22no—
323C2×C3×Dic3—32no—
324C2×C3×Dic3—32no—
325C2×C3×Dic3—42no—
326C2×C3×Dic3—62no—
327C2×C3×Dic3—62no—
328C2×C3×Dic3—62no—
329C2×C3×Dic3—122no—
330C2×C3×Dic3C22×D312yescomplemented
331C2×C3×Dic3C22×D312yescomplemented
332C3×D12—68no—
333#626—28no—
334#626—68no—
335#626—68no—
336#625—68no—
337#625—616no—
338#625—68no—
339#625—68no—
340C2×#120—271noSylow
341C2×C33#12014yescomplemented
342C2×C33C22×D411yescharacteristic
343C2×C33C22×D411yescharacteristic
344C2×C33C22×D411yescharacteristic
345C3×C3⋊D3—24no—
346C3×C3⋊D3—42no—
347C32×D3—24no—
348C32×D3—24no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3—31no—
352C24×C3—31no—
353C24×C3—61no—
354C24×C3—61no—
355C24×C3—94no—
356C24×C3—91no—
357C24×C3—91no—
358C24×C3—184no—
359C24×C3—184no—
360C24×C3—184no—
361C23×D3—31no—
362C23×D3—31no—
363C23×D3—31no—
364C23×D3—31no—
365C23×D3—34no—
366C23×D3—34no—
367C23×D3—61no—
368C23×D3—61no—
369C23×D3—64no—
370C23×D3—64no—
371C23×D3—64no—
372C23×D3—64no—
373C23×D3—64no—
374C23×D3—64no—
375C23×D3D3211yescharacteristic
376C23×D3D3211yescharacteristic
377C2×C3×D4—94no—
378C2×C3×D4—184no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—91no—
383C2×#67—34no—
384C2×#67—64no—
385C2×#67—94no—
386C2×#67—94no—
387C2×#67—94no—
388C2×#67—94no—
389C2×#67—94no—
390C2×#67—184no—
391C2×#67—184no—
392C2×#67—184no—
393C2×#67—184no—
394C2×#67—184no—
395C2×#67—188no—
396C2×#67—184no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—61no—
400C22×Dic3—91no—
401C22×Dic3—91no—
402C22×Dic3—91no—
403C22×Dic3—181no—
404C22×Dic3—181no—
405C22×Dic3—181no—
406C22×Dic3—361no—
407C22×Dic3D3211yescharacteristic, complemented
408C2×D12—34no—
409C2×D12—64no—
410C2×D12—94no—
411C2×D12—184no—
412C3×C22⋊C4—94no—
413#217—34no—
414#217—94no—
415#217—94no—
416#217—94no—
417#217—184no—
418(C2×D3)⋊C4—34no—
419(C2×D3)⋊C4—94no—
420(C2×D3)⋊C4—94no—
421(C2×D3)⋊C4—94no—
422(C2×D3)⋊C4—184no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—21no—
426C22×C32—22no—
427C22×C32—22no—
428C22×C32—22no—
429C22×C32—22no—
430C22×C32—22no—
431C22×C32—22no—
432C22×C32—22no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—34no—
436C22×C32—34no—
437C22×C32—42no—
438C22×C32—42no—
439C22×C32—42no—
440C22×C32—41no—
441C22×C32—68no—
442C22×C32—68no—
443C22×C32—62no—
444C22×C32—62no—
445C22×C32—62no—
446C22×C32—62no—
447C22×C32C2×D1212yes—
448C22×C32D3×D412yes—
449C22×C32D3×D412yes—
450C22×C32D3×D412yes—
451C22×C32D3×D412yes—
452C22×C32C2×#6712yes—
453C22×C32C2×#6712yes—
454C22×C32C2×#6712yes—
455C22×C32C2×#6712yes—
456C22×C32C23×D311yescharacteristic
457C22×C32C23×D311yescharacteristic
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—22no—
460C2×C3⋊D3—28no—
461C2×C3⋊D3—22no—
462C2×C3⋊D3—22no—
463C2×C3⋊D3—22no—
464C2×C3⋊D3—22no—
465C2×C3⋊D3—44no—
466C2×C3⋊D3C2×#6714yescomplemented
467C2×C3×D3—28no—
468C2×C3×D3—28no—
469C2×C3×D3—28no—
470C2×C3×D3—28no—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3—22no—
475C2×C3×D3—22no—
476C2×C3×D3—22no—
477C2×C3×D3—22no—
478C2×C3×D3—22no—
479C2×C3×D3—24no—
480C2×C3×D3—24no—
481C2×C3×D3—34no—
482C2×C3×D3—34no—
483C2×C3×D3—42no—
484C2×C3×D3—42no—
485C2×C3×D3—42no—
486C2×C3×D3—42no—
487C2×C3×D3—48no—
488C2×C3×D3—48no—
489C2×C3×D3—64no—
490C2×C3×D3—632no—
491C2×C3×D3—632no—
492C2×C3×D3—68no—
493C2×C3×D3—68no—
494C2×C3×D3—62no—
495C2×C3×D3—62no—
496C2×C3×D3—62no—
497C2×C3×D3—62no—
498C2×C3×D3—64no—
499C2×C3×D3—62no—
500C2×C3×D3—62no—
501C2×C3×D3—62no—
502C2×C3×D3—62no—
503C2×C3×D3—62no—
504C2×C3×D3—62no—
505C2×C3×D3—122no—
506C2×C3×D3—122no—
507C2×C3×D3—128no—
508C2×C3×D3—122no—
509C2×C3×D3—122no—
510C2×C3×D3—128no—
511C2×C3×D3—124no—
512C2×C3×D3—124no—
513C2×C3×D3C2×D1214yescomplemented
514C2×C3×D3C2×#6714yescomplemented
515C2×C3×D3C2×#6714yescomplemented
516C2×C3×D3C2×#6714yescomplemented
517D32—232no—
518C32×C4—62no—
519C3⋊Dic3—22no—
520C3⋊Dic3—62no—
521C3⋊Dic3—64no—
522C3⋊Dic3—62no—
523C3⋊Dic3—62no—
524C3⋊Dic3—122no—
525C3⋊Dic3—122no—
526C3⋊Dic3—124no—
527C3×Dic3—22no—
528C3×Dic3—22no—
529C3×Dic3—42no—
530C3×Dic3—62no—
531C3×Dic3—62no—
532C3×Dic3—122no—
533C25—91no—
534C22×D4—91no—
535C22×D4—271no—
536C22×D4—271no—
537#120—278no—
538C2×C22⋊C4—91no—
539C2×C22⋊C4—271no—
540C2×C22⋊C4—271no—
541C33C2×#12011yescharacteristic, complemented, Sylow
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—34no—
550C23×C3—34no—
551C23×C3—34no—
552C23×C3—34no—
553C23×C3—41no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—64no—
557C23×C3—64no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3—62no—
561C23×C3—62no—
562C23×C3—62no—
563C23×C3—62no—
564C23×C3—62no—
565C23×C3—62no—
566C23×C3—92no—
567C23×C3—94no—
568C23×C3—92no—
569C23×C3—122no—
570C23×C3—122no—
571C23×C3—122no—
572C23×C3—122no—
573C23×C3—188no—
574C23×C3—188no—
575C23×C3—188no—
576C23×C3—1832no—
577C23×C3—182no—
578C23×C3—182no—
579C23×C3—182no—
580C23×C3—182no—
581C23×C3—182no—
582C23×C3C2×D3211yescharacteristic
583C23×C3C2×D3211yescharacteristic
584C23×C3C2×D3211yescharacteristic
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—32no—
590C22×D3—32no—
591C22×D3—34no—
592C22×D3—34no—
593C22×D3—32no—
594C22×D3—32no—
595C22×D3—64no—
596C22×D3—62no—
597C22×D3—62no—
598C22×D3—68no—
599C22×D3—68no—
600C22×D3—68no—
601C22×D3—68no—
602C22×D3—632no—
603C22×D3—632no—
604C22×D3—62no—
605C22×D3—62no—
606C22×D3—62no—
607C22×D3—62no—
608C22×D3—68no—
609C22×D3—68no—
610C22×D3—64no—
611C22×D3—62no—
612C22×D3—62no—
613C22×D3—62no—
614C22×D3—62no—
615C22×D3—62no—
616C22×D3—62no—
617C22×D3—122no—
618C22×D3—122no—
619C22×D3—122no—
620C22×D3—122no—
621C22×D3#62514yescomplemented
622C22×D3#62614yescomplemented
623C22×D3C2×D3212yes—
624C22×D3C2×D3212yes—
625C3×D4—188no—
626C2×C3×C4—32no—
627C2×C3×C4—32no—
628C2×C3×C4—62no—
629C2×C3×C4—62no—
630C2×C3×C4—62no—
631C2×C3×C4—92no—
632C2×C3×C4—122no—
633C2×C3×C4—182no—
634#67—68no—
635#67—188no—
636#67—188no—
637#67—188no—
638#67—188no—
639#67—1816no—
640#67—188no—
641C2×Dic3—22no—
642C2×Dic3—32no—
643C2×Dic3—32no—
644C2×Dic3—62no—
645C2×Dic3—62no—
646C2×Dic3—62no—
647C2×Dic3—92no—
648C2×Dic3—92no—
649C2×Dic3—92no—
650C2×Dic3—122no—
651C2×Dic3—182no—
652C2×Dic3—182no—
653C2×Dic3—182no—
654C2×Dic3—184no—
655C2×Dic3—182no—
656C2×Dic3—182no—
657C2×Dic3—182no—
658C2×Dic3—362no—
659C2×Dic3—362no—
660C2×Dic3—362no—
661C2×Dic3—364no—
662C2×Dic3C2×D3212yescomplemented
663D12—68no—
664D12—188no—
665C2×C32—21no—
666C2×C32—21no—
667C2×C32—21no—
668C2×C32—21no—
669C2×C32—21no—
670C2×C32—21no—
671C2×C32—21no—
672C2×C32—21no—
673C2×C32—21no—
674C2×C32—24no—
675C2×C32—24no—
676C2×C32—24no—
677C2×C32—44no—
678C2×C32—41no—
679C2×C32—41no—
680C2×C32—41no—
681C2×C32—64no—
682C2×C32—64no—
683C2×C32#88214yescomplemented
684C2×C32#93714yescomplemented
685C2×C32#95314yescomplemented
686C2×C32C22×D1211yescharacteristic
687C2×C32C2×D3×D411yescharacteristic
688C2×C32C2×D3×D411yescharacteristic
689C2×C32C2×D3×D411yescharacteristic
690C2×C32C2×D3×D411yescharacteristic
691C2×C32C22×#6711yescharacteristic
692C2×C32C22×#6711yescharacteristic
693C2×C32C22×#6711yescharacteristic
694C2×C32C22×#6711yescharacteristic
695C3⋊D3—24no—
696C3⋊D3—42no—
697C3×D3—24no—
698C3×D3—24no—
699C3×D3—24no—
700C3×D3—24no—
701C3×D3—44no—
702C3×D3—44no—
703C3×D3—64no—
704C3×D3—64no—
705C3×D3—124no—
706C3×D3—124no—
707C3×D3—122no—
708C3×D3—122no—
709C24—31no—
710C24—31no—
711C24—94no—
712C24—91no—
713C24—91no—
714C24—184no—
715C24—184no—
716C24—184no—
717C2×D4—94no—
718C2×D4—184no—
719C2×D4—274no—
720C2×D4—274no—
721C2×D4—544no—
722C2×D4—544no—
723C22×C4—31no—
724C22×C4—91no—
725C22×C4—271no—
726C22⋊C4—94no—
727C22⋊C4—274no—
728C22⋊C4—274no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—34no—
742C22×C3—34no—
743C22×C3—34no—
744C22×C3—34no—
745C22×C3—41no—
746C22×C3—42no—
747C22×C3—42no—
748C22×C3—42no—
749C22×C3—64no—
750C22×C3—64no—
751C22×C3—62no—
752C22×C3—62no—
753C22×C3—62no—
754C22×C3—62no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—62no—
759C22×C3—68no—
760C22×C3—68no—
761C22×C3—68no—
762C22×C3—68no—
763C22×C3—94no—
764C22×C3—122no—
765C22×C3—122no—
766C22×C3—122no—
767C22×C3—122no—
768C22×C3—128no—
769C22×C3—128no—
770C22×C3—1832no—
771C22×C3—182no—
772C22×C3—182no—
773C22×C3—188no—
774C22×C3—182no—
775C22×C3—182no—
776C22×C3—182no—
777C22×C3—364no—
778C22×C3D3×D1212yes—
779C22×C3#380212yes—
780C22×C3C2×#62512yes—
781C22×C3C2×#62612yes—
782C22×C3D3×#6712yes—
783C22×C3D3×#6712yes—
784C22×C3D3×#6712yes—
785C22×C3D3×#6712yes—
786C22×C3D3×#6712yes—
787C22×C3C22×D3211yescharacteristic
788C22×C3C22×D3211yescharacteristic
789C22×C3C22×D3211yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—28no—
795C2×D3—28no—
796C2×D3—34no—
797C2×D3—34no—
798C2×D3—64no—
799C2×D3—632no—
800C2×D3—632no—
801C2×D3—62no—
802C2×D3—62no—
803C2×D3—62no—
804C2×D3—62no—
805C2×D3—68no—
806C2×D3—68no—
807C2×D3—64no—
808C2×D3—62no—
809C2×D3—62no—
810C2×D3—62no—
811C2×D3—62no—
812C2×D3—62no—
813C2×D3—62no—
814C2×D3—122no—
815C2×D3—122no—
816C2×D3—128no—
817C2×D3—122no—
818C2×D3—122no—
819C2×D3—128no—
820C2×D3—124no—
821C2×D3—124no—
822C2×D3C2×#62514yescomplemented
823C2×D3C2×#62614yescomplemented
824C3×C4—62no—
825C3×C4—62no—
826C3×C4—122no—
827C3×C4—182no—
828Dic3—22no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832Dic3—184no—
833Dic3—182no—
834Dic3—182no—
835Dic3—182no—
836Dic3—362no—
837Dic3—362no—
838Dic3—364no—
839C32—21no—
840C32—21no—
841C32—21no—
842C32—41no—
843C32C2×#88211yescharacteristic, complemented
844C32C2×#93711yescharacteristic, complemented
845C32C2×#95311yescharacteristic, complemented
846C23—32no—
847C23—32no—
848C23—34no—
849C23—34no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—92no—
855C23—94no—
856C23—92no—
857C23—188no—
858C23—188no—
859C23—188no—
860C23—1832no—
861C23—182no—
862C23—182no—
863C23—182no—
864C23—182no—
865C23—182no—
866C23D3311yescharacteristic
867D4—188no—
868D4—548no—
869D4—548no—
870C2×C4—32no—
871C2×C4—62no—
872C2×C4—92no—
873C2×C4—182no—
874C2×C4—272no—
875C2×C4—542no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—21no—
882C2×C3—21no—
883C2×C3—21no—
884C2×C3—21no—
885C2×C3—24no—
886C2×C3—24no—
887C2×C3—24no—
888C2×C3—41no—
889C2×C3—41no—
890C2×C3—41no—
891C2×C3—44no—
892C2×C3—64no—
893C2×C3—64no—
894C2×C3—64no—
895C2×C3—64no—
896C2×C3—124no—
897C2×C3—124no—
898C2×C3—184no—
899C2×C3—362no—
900C2×C3#6392214yescomplemented
901C2×C3#6397614yescomplemented
902C2×C3#6397714yescomplemented
903C2×C3C2×D3×D1211yescharacteristic
904C2×C3C2×#380211yescharacteristic
905C2×C3C22×#62511yescharacteristic
906C2×C3C22×#62611yescharacteristic
907C2×C3C2×D3×#6711yescharacteristic
908C2×C3C2×D3×#6711yescharacteristic
909C2×C3C2×D3×#6711yescharacteristic
910C2×C3C2×D3×#6711yescharacteristic
911C2×C3C2×D3×#6711yescharacteristic
912D3—24no—
913D3—24no—
914D3—64no—
915D3—64no—
916D3—124no—
917D3—124no—
918D3—122no—
919D3—122no—
920C22—34no—
921C22—34no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—68no—
927C22—68no—
928C22—94no—
929C22—1832no—
930C22—182no—
931C22—182no—
932C22—188no—
933C22—182no—
934C22—182no—
935C22—182no—
936C22—364no—
937C22D3×#62512yes—
938C22D3×#62612yes—
939C22#8895312yes—
940C22C2×D3311yescharacteristic
941C4—62no—
942C4—182no—
943C4—542no—
944C3—21no—
945C3—21no—
946C3—21no—
947C3—41no—
948C3C2×#6392211yescharacteristic, complemented
949C3C2×#6397611yescharacteristic, complemented
950C3C2×#6397711yescharacteristic, complemented
951C2—64no—
952C2—64no—
953C2—184no—
954C2—362no—
955C2#1172294714yesdirect product factor
956C2C2×D3×#62511yescharacteristic
957C2C2×D3×#62611yescharacteristic
958C2C2×#8895311yescharacteristic
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×C3×D32C2semidirect
2. C22×#6295C2semidirect
3. C22×#6290C2semidirect
4. C22×C3×#626C2semidirect
5. C2×#88803C2semidirect
6. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
7. C2×C3×(C2×D3)⋊Dic3C2semidirect
8. #11722947C2direct (N × H)
13. C23×C3×C3⋊D3C22semidirect
19. C22×C3×D32C22semidirect
20. C22×C3⋊(C3⋊Dic3)C22semidirect
21. C22×C3×C3⋊Dic3C22semidirect
22. C22×C32×Dic3C22semidirect
24. C2×#6295C22semidirect
26. C2×#6290C22semidirect
28. C2×C3×#626C22semidirect
29. #88803C22semidirect
30. (C2×D3)⋊(C3⋊Dic3)C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
34. C23×D32D3semidirect
40. C22×#626D3semidirect
57. C2×(C2×D3)⋊Dic3D3semidirect
65. C22×C3×C3⋊D3D4semidirect
67. C22×C3×C3⋊D3C23semidirect
72. C22×C32×D3D4semidirect
73. C22×C32×D3D4semidirect
81. C2×C3⋊(C3⋊Dic3)C23semidirect
83. C2×C3×C3⋊Dic3C23semidirect
85. C2×C32×Dic3C23semidirect
95. C23×C3⋊D3C2×D3semidirect
119. C22×D32C2×D3semidirect
130. C22×C3⋊Dic3C2×D3semidirect
137. C22×C3×Dic3C2×D3semidirect
138. C22×C3×Dic3C2×D3semidirect
146. C2×#626C2×D3semidirect
165. (C2×D3)⋊Dic3C2×D3semidirect
177. C2×C3×C3⋊D3C2×D4semidirect
184. C2×C32×D3C2×D4semidirect
185. C2×C32×D3C2×D4semidirect
237. C22×C3⋊D3#67semidirect
239. C22×C3⋊D3C22×D3semidirect
288. C22×C3×D3D12semidirect
289. C22×C3×D3#67semidirect
290. C22×C3×D3#67semidirect
291. C22×C3×D3#67semidirect
318. C2×C3⋊Dic3C22×D3semidirect
330. C2×C3×Dic3C22×D3semidirect
331. C2×C3×Dic3C22×D3semidirect
341. C2×C33#120semidirect
407. C22×Dic3D32semidirect
466. C2×C3⋊D3C2×#67semidirect
513. C2×C3×D3C2×D12semidirect
514. C2×C3×D3C2×#67semidirect
515. C2×C3×D3C2×#67semidirect
516. C2×C3×D3C2×#67semidirect
541. C33C2×#120semidirect
621. C22×D3#625semidirect
622. C22×D3#626semidirect
662. C2×Dic3C2×D32semidirect
683. C2×C32#882semidirect
684. C2×C32#937semidirect
685. C2×C32#953semidirect
822. C2×D3C2×#625semidirect
823. C2×D3C2×#626semidirect
843. C32C2×#882semidirect
844. C32C2×#937semidirect
845. C32C2×#953semidirect
900. C2×C3#63922semidirect
901. C2×C3#63976semidirect
902. C2×C3#63977semidirect
948. C3C2×#63922semidirect
949. C3C2×#63976semidirect
950. C3C2×#63977semidirect
955. C2#11722947direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D322
C22×#62952
C22×#62902
C22×C3×#6262
C2×#888032
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×(C2×D3)⋊Dic32
#117229472
C2×#639773
C2×#639763
C2×#639223