Finite Group Databasebeta

← #13156748

Subgroups — #13156748

Order 1728.

1394 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊Dic3C211yesmaximal, characteristic
2C2×#88815C211yesmaximal, characteristic, complemented
3C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6#11722061C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591719—31nomaximal
9#10591379—31nomaximal
10#10591373—31nomaximal
11C23×C32×D3C2211yescharacteristic
12C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×D3×C3⋊Dic3—22no—
19C2×D3×C3⋊Dic3—22no—
20C2×D3×C3⋊Dic3—22no—
21#88815—22no—
22Dic3⋊(C3⋊Dic3)—22no—
23C3×(C2×D3)⋊Dic3—22no—
24C3×(C2×D3)⋊Dic3C414yescomplemented
25C23×C3⋊Dic3—31no—
26C22×D3×Dic3—31no—
27C22×D3×Dic3—31no—
28C22×D3×Dic3—61no—
29C2×C4⋊(C3⋊Dic3)—31no—
30C2×C3×#217—31no—
31C2×C3×#217—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×#3724—31no—
35C2×Dic3⋊Dic3—31no—
36C2×Dic3⋊Dic3—31no—
37C2×Dic3⋊Dic3—31no—
38C2×Dic3⋊Dic3—31no—
39C2×Dic3⋊Dic3—61no—
40C2×(C2×D3)⋊Dic3D311yescharacteristic
41C2×(C2×D3)⋊Dic3D311yescharacteristic
42#63658—31no—
43C3×C3⋊#95—31no—
44C3×C3⋊#95—31no—
45#63579—31no—
46#63579—31no—
47#63579—61no—
48#63579D311yescharacteristic, complemented
49C23×C33C2311yescharacteristic
50C22×C32×D3—21no—
51C22×C32×D3—21no—
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3C2×C412yes—
55C22×C32×D3D412yes—
56C22×C32×D3Q812yes—
57C2×C3⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊Dic3)D412yes—
60C2×C3×C3⋊Dic3—21no—
61C2×C3×C3⋊Dic3—21no—
62C2×C3×C3⋊Dic3—21no—
63C2×C3×C3⋊Dic3—21no—
64C2×C3×C3⋊Dic3—21no—
65C2×C3×C3⋊Dic3—21no—
66C2×C3×C3⋊Dic3—21no—
67C2×C3×C3⋊Dic3C2×C412yescomplemented
68C2×C3×C3⋊Dic3D412yes—
69C2×C32×Dic3—21no—
70C2×C32×Dic3—21no—
71C2×C32×Dic3—21no—
72C2×C32×Dic3—21no—
73C2×C32×Dic3—21no—
74C2×C32×Dic3C2×C412yescomplemented
75D3×C3⋊Dic3—28no—
76#4950—91no—
77#4946—91no—
78#4668—91no—
79C24×C32—31no—
80C23×C3×D3—21no—
81C23×C3×D3C2×D311yescharacteristic
82C23×C3×D3C2×D311yescharacteristic
83C22×C32×C4—31no—
84C22×C32×C4—31no—
85C22×C3⋊Dic3—31no—
86C22×C3⋊Dic3—31no—
87C22×C3⋊Dic3—31no—
88C22×C3⋊Dic3—62no—
89C22×C3⋊Dic3—62no—
90C22×C3⋊Dic3—61no—
91C22×C3⋊Dic3—62no—
92C22×C3⋊Dic3—61no—
93C22×C3⋊Dic3—61no—
94C22×C3⋊Dic3—121no—
95C22×C3⋊Dic3C2×D311yescharacteristic
96C22×C3⋊Dic3C2×D311yescharacteristic
97C22×C3⋊Dic3C2×D311yescharacteristic
98C22×C3×Dic3—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—31no—
104C22×C3×Dic3—31no—
105C22×C3×Dic3—31no—
106C22×C3×Dic3—61no—
107C22×C3×Dic3—61no—
108C22×C3×Dic3—61no—
109C22×C3×Dic3C2×D311yescharacteristic
110C22×C3×Dic3C2×D311yescharacteristic
111C22×C3×Dic3C2×D311yescharacteristic
112C22×C3×Dic3C2×D311yescharacteristic
113C2×D3×Dic3—62no—
114C2×D3×Dic3—62no—
115C2×D3×Dic3—62no—
116C2×D3×Dic3—62no—
117C2×D3×Dic3—64no—
118C2×D3×Dic3—64no—
119C2×D3×Dic3—64no—
120C2×D3×Dic3—62no—
121C2×D3×Dic3—62no—
122C4⋊(C3⋊Dic3)—62no—
123C3×#217—34no—
124C3×#217—62no—
125C3×(C2×D3)⋊C4—34no—
126C3×(C2×D3)⋊C4—62no—
127#3724—62no—
128Dic3⋊Dic3—62no—
129Dic3⋊Dic3—62no—
130Dic3⋊Dic3—64no—
131Dic3⋊Dic3—62no—
132Dic3⋊Dic3—62no—
133(C2×D3)⋊Dic3—22no—
134(C2×D3)⋊Dic3Dic314yescomplemented
135C22×C33C22×C411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33C2×D411yescharacteristic
139C22×C33C2×Q811yescharacteristic
140C22×C33#4111yescharacteristic
141C22×C33#4111yescharacteristic
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3—22no—
146C2×C32×D3—22no—
147C2×C32×D3—22no—
148C2×C32×D3C4⋊C414yescomplemented
149C3⋊(C3⋊Dic3)—22no—
150C3×C3⋊Dic3—22no—
151C3×C3⋊Dic3—22no—
152C3×C3⋊Dic3—41no—
153C32×Dic3—22no—
154C32×Dic3—41no—
155C23×Dic3—91no—
156C23×Dic3—91no—
157C23×Dic3—181no—
158C22×C4×D3—91no—
159C2×C3×C22⋊C4—91no—
160C2×C3×C22⋊C4—91no—
161C2×#217—31no—
162C2×#217—31no—
163C2×(C2×D3)⋊C4—31no—
164C2×(C2×D3)⋊C4—31no—
165C2×C4⋊Dic3—91no—
166C2×C4⋊Dic3—91no—
167C2×C4⋊Dic3—91no—
168C2×C4⋊Dic3—181no—
169C2×Dic3⋊C4—91no—
170C2×Dic3⋊C4—91no—
171C2×Dic3⋊C4—91no—
172C3×#95—91no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—91no—
176C3⋊#95—91no—
177C3⋊#95—91no—
178C3⋊#95—181no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—21no—
182C23×C32—32no—
183C23×C32—32no—
184C23×C32—32no—
185C23×C32—41no—
186C23×C32—61no—
187C23×C32—61no—
188C23×C32—61no—
189C23×C32—61no—
190C23×C32C22×D311yescharacteristic
191C23×C32C22×D311yescharacteristic
192C23×C32C22×D311yescharacteristic
193C22×C3×D3—22no—
194C22×C3×D3—22no—
195C22×C3×D3—22no—
196C22×C3×D3—22no—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—21no—
201C22×C3×D3—21no—
202C22×C3×D3—21no—
203C22×C3×D3—21no—
204C22×C3×D3—21no—
205C22×C3×D3—22no—
206C22×C3×D3—22no—
207C22×C3×D3—22no—
208C22×C3×D3Dic612yes—
209C22×C3×D3Dic612yes—
210C22×C3×D3C4×D312yes—
211C22×C3×D3D1212yes—
212C22×C3×D3C2×Dic312yes—
213C22×C3×D3#6712yes—
214C2×C32×C4—32no—
215C2×C32×C4—61no—
216C2×C32×C4—61no—
217C2×C32×C4—61no—
218C2×C32×C4—61no—
219C2×C32×C4—61no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—32no—
228C2×C3⋊Dic3—32no—
229C2×C3⋊Dic3—32no—
230C2×C3⋊Dic3—62no—
231C2×C3⋊Dic3—62no—
232C2×C3⋊Dic3—62no—
233C2×C3⋊Dic3—68no—
234C2×C3⋊Dic3—61no—
235C2×C3⋊Dic3—61no—
236C2×C3⋊Dic3—62no—
237C2×C3⋊Dic3—62no—
238C2×C3⋊Dic3—61no—
239C2×C3⋊Dic3—61no—
240C2×C3⋊Dic3—61no—
241C2×C3⋊Dic3—61no—
242C2×C3⋊Dic3—122no—
243C2×C3⋊Dic3—121no—
244C2×C3⋊Dic3—121no—
245C2×C3⋊Dic3—121no—
246C2×C3⋊Dic3—121no—
247C2×C3⋊Dic3—122no—
248C2×C3⋊Dic3—122no—
249C2×C3⋊Dic3D1212yes—
250C2×C3⋊Dic3C2×Dic312yescomplemented
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—22no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—32no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—41no—
270C2×C3×Dic3—41no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—62no—
273C2×C3×Dic3—62no—
274C2×C3×Dic3—62no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—62no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—61no—
289C2×C3×Dic3—61no—
290C2×C3×Dic3—121no—
291C2×C3×Dic3—121no—
292C2×C3×Dic3—121no—
293C2×C3×Dic3—121no—
294C2×C3×Dic3C4×D312yescomplemented
295C2×C3×Dic3C2×Dic312yescomplemented
296D3×Dic3—616no—
297D3×Dic3—68no—
298D3×Dic3—68no—
299#385—271noSylow
300C2×C33C2×C4⋊C411yescharacteristic
301C2×C33C4×D411yescharacteristic
302C2×C33C4×D411yescharacteristic
303C2×C33#12011yescharacteristic
304C2×C33C22⋊Q811yescharacteristic
305C2×C33C22⋊Q811yescharacteristic
306C2×C33#12311yescharacteristic
307C32×D3—24no—
308C24×C3—31no—
309C24×C3—31no—
310C24×C3—61no—
311C23×D3D3211yescharacteristic
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—31no—
316C22×C3×C4—61no—
317C22×C3×C4—61no—
318C22×C3×C4—91no—
319C22×C3×C4—91no—
320C22×C3×C4—91no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—91no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—181no—
334C22×Dic3—181no—
335C22×Dic3—181no—
336C22×Dic3—182no—
337C22×Dic3—182no—
338C22×Dic3—182no—
339C22×Dic3—182no—
340C22×Dic3—182no—
341C22×Dic3—182no—
342C22×Dic3—184no—
343C22×Dic3—184no—
344C22×Dic3—184no—
345C22×Dic3—361no—
346C22×Dic3D3211yescharacteristic
347C22×Dic3D3211yescharacteristic
348C2×C4×D3—182no—
349C2×C4×D3—182no—
350C2×C4×D3—182no—
351C3×C22⋊C4—94no—
352C3×C22⋊C4—182no—
353#217—34no—
354#217—62no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—62no—
357C4⋊Dic3—182no—
358C4⋊Dic3—182no—
359C4⋊Dic3—182no—
360C4⋊Dic3—184no—
361Dic3⋊C4—182no—
362Dic3⋊C4—182no—
363Dic3⋊C4—182no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32—21no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—21no—
375C22×C32—21no—
376C22×C32—21no—
377C22×C32—21no—
378C22×C32—21no—
379C22×C32—21no—
380C22×C32—21no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—21no—
385C22×C32—34no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—41no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—62no—
394C22×C32—62no—
395C22×C32—62no—
396C22×C32—62no—
397C22×C32—62no—
398C22×C32—62no—
399C22×C32C2×Dic611yescharacteristic
400C22×C32C2×Dic611yescharacteristic
401C22×C32C2×C4×D311yescharacteristic
402C22×C32C2×C4×D311yescharacteristic
403C22×C32C2×D1211yescharacteristic
404C22×C32C2×D1211yescharacteristic
405C22×C32#23511yescharacteristic
406C22×C32D3×D411yescharacteristic
407C22×C32D3×D411yescharacteristic
408C22×C32D3×D411yescharacteristic
409C22×C32D3×D411yescharacteristic
410C22×C32D3×D411yescharacteristic
411C22×C32D3×D411yescharacteristic
412C22×C32#23711yescharacteristic
413C22×C32#23711yescharacteristic
414C22×C32#23711yescharacteristic
415C22×C32#23711yescharacteristic
416C22×C32#23711yescharacteristic
417C22×C32D3×Q811yescharacteristic
418C22×C32C22×Dic311yescharacteristic
419C22×C32C2×#6711yescharacteristic
420C2×C3×D3—24no—
421C2×C3×D3—24no—
422C2×C3×D3—24no—
423C2×C3×D3—24no—
424C2×C3×D3—24no—
425C2×C3×D3—24no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—22no—
433C2×C3×D3—22no—
434C2×C3×D3—22no—
435C2×C3×D3—22no—
436C2×C3×D3—22no—
437C2×C3×D3—22no—
438C2×C3×D3—24no—
439C2×C3×D3Dic3⋊C414yescomplemented
440C2×C3×D3C4⋊Dic314yescomplemented
441C32×C4—62no—
442C32×C4—121no—
443C3⋊Dic3—22no—
444C3⋊Dic3—22no—
445C3⋊Dic3—41no—
446C3⋊Dic3—62no—
447C3⋊Dic3—64no—
448C3⋊Dic3—62no—
449C3⋊Dic3—62no—
450C3⋊Dic3—122no—
451C3⋊Dic3—122no—
452C3⋊Dic3—124no—
453C3×Dic3—24no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—42no—
457C3×Dic3—41no—
458C3×Dic3—41no—
459C3×Dic3—64no—
460C3×Dic3—62no—
461C3×Dic3—62no—
462C3×Dic3—62no—
463C3×Dic3—62no—
464C3×Dic3—122no—
465C3×Dic3—122no—
466C3×Dic3—121no—
467C3×Dic3—121no—
468C23×C4—271no—
469C2×C4⋊C4—271no—
470C2×C4⋊C4—271no—
471C2×C22⋊C4—91no—
472C2×C22⋊C4—91no—
473#95—91no—
474#95—271no—
475C33#38511yescharacteristic, complemented, Sylow
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—32no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—32no—
484C23×C3—32no—
485C23×C3—41no—
486C23×C3—62no—
487C23×C3—62no—
488C23×C3—62no—
489C23×C3—62no—
490C23×C3—62no—
491C23×C3—62no—
492C23×C3—62no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—61no—
500C23×C3—61no—
501C23×C3C2×D3211yescharacteristic
502C23×C3C2×D3211yescharacteristic
503C23×C3C2×D3211yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3D3×Dic312yes—
509C22×D3#62612yes—
510C22×D3#62712yes—
511C2×C3×C4—32no—
512C2×C3×C4—32no—
513C2×C3×C4—62no—
514C2×C3×C4—62no—
515C2×C3×C4—62no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—62no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—92no—
528C2×C3×C4—92no—
529C2×C3×C4—121no—
530C2×C3×C4—121no—
531C2×C3×C4—181no—
532C2×C3×C4—181no—
533C2×C3×C4—181no—
534C2×C3×C4—181no—
535C2×C3×C4—181no—
536C2×C3×C4—181no—
537C2×C3×C4—181no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—62no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—92no—
567C2×Dic3—92no—
568C2×Dic3—92no—
569C2×Dic3—121no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—182no—
574C2×Dic3—182no—
575C2×Dic3—182no—
576C2×Dic3—1816no—
577C2×Dic3—188no—
578C2×Dic3—188no—
579C2×Dic3—182no—
580C2×Dic3—182no—
581C2×Dic3—181no—
582C2×Dic3—181no—
583C2×Dic3—181no—
584C2×Dic3—181no—
585C2×Dic3—181no—
586C2×Dic3—181no—
587C2×Dic3—362no—
588C2×Dic3—361no—
589C2×Dic3—361no—
590C2×Dic3—361no—
591C2×Dic3—361no—
592C2×Dic3—362no—
593C2×Dic3—362no—
594C2×Dic3D3×Dic312yescomplemented
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—21no—
606C2×C32—21no—
607C2×C32—21no—
608C2×C32—21no—
609C2×C32—21no—
610C2×C32—21no—
611C2×C32—21no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32—41no—
620C2×C32—41no—
621C2×C32—41no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—64no—
625C2×C32C4×D1211yescharacteristic
626C2×C32#87811yescharacteristic
627C2×C32#87811yescharacteristic
628C2×C32#87811yescharacteristic
629C2×C32#87811yescharacteristic
630C2×C32#67⋊C411yescharacteristic
631C2×C32#67⋊C411yescharacteristic
632C2×C32#67⋊C411yescharacteristic
633C2×C32#88211yescharacteristic
634C2×C32#88211yescharacteristic
635C2×C32#88311yescharacteristic
636C2×C32#88611yescharacteristic
637C2×C32D3×C4⋊C411yescharacteristic
638C2×C32#89611yescharacteristic
639C2×C32#89711yescharacteristic
640C2×C32C2×Dic3⋊C411yescharacteristic
641C2×C32C2×C4⋊Dic311yescharacteristic
642C2×C32D4×Dic311yescharacteristic
643C2×C32D4×Dic311yescharacteristic
644C2×C32#93511yescharacteristic
645C2×C32#93711yescharacteristic
646C3×D3—28no—
647C3×D3—24no—
648C3×D3—24no—
649C24—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—91no—
653C22×C4—91no—
654C22×C4—91no—
655C22×C4—271no—
656C22×C4—542no—
657C22×C4—542no—
658C22×C4—542no—
659C4⋊C4—542no—
660C4⋊C4—542no—
661C22⋊C4—94no—
662C22⋊C4—182no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—34no—
685C22×C3—34no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—64no—
696C22×C3—64no—
697C22×C3—64no—
698C22×C3—64no—
699C22×C3—64no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3—62no—
704C22×C3—62no—
705C22×C3—62no—
706C22×C3—62no—
707C22×C3—62no—
708C22×C3—62no—
709C22×C3—62no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3D3×Dic611yescharacteristic
713C22×C3D3×Dic611yescharacteristic
714C22×C3#379511yescharacteristic
715C22×C3C4×D3211yescharacteristic
716C22×C3D3×D1211yescharacteristic
717C22×C3D3×D1211yescharacteristic
718C22×C3D3×D1211yescharacteristic
719C22×C3#380211yescharacteristic
720C22×C3C2×D3×Dic311yescharacteristic
721C22×C3C2×D3×Dic311yescharacteristic
722C22×C3#380411yescharacteristic
723C22×C3#380511yescharacteristic
724C22×C3#380511yescharacteristic
725C22×C3#380511yescharacteristic
726C22×C3#380511yescharacteristic
727C22×C3C2×#62611yescharacteristic
728C22×C3C2×#62711yescharacteristic
729C22×C3D3×#6711yescharacteristic
730C22×C3#381111yescharacteristic
731C22×C3#381111yescharacteristic
732C22×C3#381111yescharacteristic
733C2×D3—22no—
734C2×D3—22no—
735C2×D3—22no—
736C2×D3—22no—
737C2×D3—22no—
738C2×D3—22no—
739C2×D3Dic3⋊Dic314yescomplemented
740C3×C4—64no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—122no—
744C3×C4—121no—
745C3×C4—121no—
746C3×C4—182no—
747C3×C4—182no—
748C3×C4—361no—
749Dic3—22no—
750Dic3—41no—
751Dic3—64no—
752Dic3—62no—
753Dic3—62no—
754Dic3—62no—
755Dic3—62no—
756Dic3—122no—
757Dic3—122no—
758Dic3—121no—
759Dic3—121no—
760Dic3—184no—
761Dic3—182no—
762Dic3—182no—
763Dic3—182no—
764Dic3—362no—
765Dic3—362no—
766Dic3—364no—
767C32—21no—
768C32—21no—
769C32—21no—
770C32—41no—
771C32#466811yescharacteristic, complemented
772C32#494611yescharacteristic, complemented
773C32#495011yescharacteristic, complemented
774C23—32no—
775C23—32no—
776C23—32no—
777C23—61no—
778C23—61no—
779C23—61no—
780C23—61no—
781C23D3311yescharacteristic
782C2×C4—32no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—61no—
786C2×C4—61no—
787C2×C4—61no—
788C2×C4—92no—
789C2×C4—92no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—272no—
798C2×C4—548no—
799C2×C4—541no—
800C2×C4—541no—
801C2×C3—21no—
802C2×C3—21no—
803C2×C3—21no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—41no—
827C2×C3—41no—
828C2×C3—41no—
829C2×C3—68no—
830C2×C3—64no—
831C2×C3—64no—
832C2×C3D3×Dic3⋊C411yescharacteristic
833C2×C3#6388011yescharacteristic
834C2×C3D3×C4⋊Dic311yescharacteristic
835C2×C3#6389111yescharacteristic
836C2×C3Dic3×D1211yescharacteristic
837C2×C3#6389311yescharacteristic
838C2×C3#6389311yescharacteristic
839C2×C3#6389611yescharacteristic
840C2×C3#6389911yescharacteristic
841C2×C3#6390211yescharacteristic
842C2×C3#6392211yescharacteristic
843C2×C3#6392311yescharacteristic
844C2×C3#6396211yescharacteristic
845C2×C3C2×Dic3⋊Dic311yescharacteristic
846C2×C3#6396911yescharacteristic
847C2×C3#67⋊Dic311yescharacteristic
848C2×C3#67⋊Dic311yescharacteristic
849C2×C3#67⋊Dic311yescharacteristic
850C2×C3#6398111yescharacteristic
851C2×C3#6398211yescharacteristic
852C2×C3#6398211yescharacteristic
853D3—24no—
854C22—34no—
855C22—62no—
856C22—62no—
857C22—62no—
858C22—62no—
859C22—62no—
860C22—62no—
861C22D32×Dic311yescharacteristic
862C22D3×#62611yescharacteristic
863C22#8895411yescharacteristic
864C22#8895511yescharacteristic
865C22D3×#62711yescharacteristic
866C22#8896111yescharacteristic
867C22#8896311yescharacteristic
868C4—62no—
869C4—121no—
870C4—182no—
871C4—182no—
872C4—361no—
873C4—542no—
874C3—21no—
875C3—21no—
876C3—21no—
877C3—41no—
878C3#1059137311yescharacteristic, complemented
879C3#1059137911yescharacteristic, complemented
880C3#1059171911yescharacteristic, complemented
881C2—64no—
882C2D3×Dic3⋊Dic311yescharacteristic
883C2#1172292511yescharacteristic
884C2#1172292811yescharacteristic
885C2#1172295011yescharacteristic
886C2#1172298011yescharacteristic
887C2#1172298111yescharacteristic
888C2#1172298911yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC23×C32×D3C22
hypocenterC33#385
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88815C2semidirect
3. C2×Dic3⋊(C3⋊Dic3)C2semidirect
6. #11722061C2semidirect
7. C3×#63579C2semidirect
24. C3×(C2×D3)⋊Dic3C4semidirect
48. #63579D3semidirect
67. C2×C3×C3⋊Dic3C2×C4semidirect
74. C2×C32×Dic3C2×C4semidirect
134. (C2×D3)⋊Dic3Dic3semidirect
148. C2×C32×D3C4⋊C4semidirect
250. C2×C3⋊Dic3C2×Dic3semidirect
294. C2×C3×Dic3C4×D3semidirect
295. C2×C3×Dic3C2×Dic3semidirect
439. C2×C3×D3Dic3⋊C4semidirect
440. C2×C3×D3C4⋊Dic3semidirect
475. C33#385semidirect
594. C2×Dic3D3×Dic3semidirect
739. C2×D3Dic3⋊Dic3semidirect
771. C32#4668semidirect
772. C32#4946semidirect
773. C32#4950semidirect
878. C3#10591373semidirect
879. C3#10591379semidirect
880. C3#10591719semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊Dic32
C2×#888152
C2×Dic3⋊(C3⋊Dic3)2
C2×C3×(C2×D3)⋊Dic32
#117220612
C3×#635792
#105917193
#105913793
#105913733