Finite Group Databasebeta

← #13156747

Subgroups — #13156747

Order 1728.

1306 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Dic3C211yesmaximal, characteristic
2C2×#88807C211yesmaximal, characteristic, complemented
3C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
6#11722082C211yesmaximal, characteristic, complemented
7C3×#63579C211yesmaximal, characteristic, complemented
8#10591718—31nomaximal
9#10591379—31nomaximal
10#10591278—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×C3×D3×Dic3—22no—
19C2×C3×D3×Dic3—22no—
20C2×C3×D3×Dic3—22no—
21#88807—22no—
22Dic3⋊(C3⋊Dic3)—22no—
23(C2×D3)⋊(C3⋊Dic3)—22no—
24C3×(C2×D3)⋊Dic3C414yescomplemented
25C23×C3×Dic3—31no—
26C22×C3×C4×D3—31no—
27C22×D3×Dic3D311yescharacteristic
28C2×#3757—31no—
29C2×C4⋊(C3⋊Dic3)—31no—
30C2×#3750—31no—
31C2×C3×#217—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C2×Dic3⋊Dic3—31no—
34C2×Dic3⋊Dic3—31no—
35C2×Dic3⋊Dic3—31no—
36C2×Dic3⋊Dic3—31no—
37C2×Dic3⋊Dic3—61no—
38C2×Dic3⋊Dic3—61no—
39C2×(C2×D3)⋊Dic3—31no—
40C2×(C2×D3)⋊Dic3—31no—
41C2×(C2×D3)⋊Dic3—61no—
42C2×(C2×D3)⋊Dic3D311yescharacteristic
43C3×C3⋊#95—31no—
44C3×C3⋊#95—31no—
45#63579—31no—
46#63579—31no—
47#63579—31no—
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)—21no—
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×Dic3C2×C412yescomplemented
74C2×C32×Dic3D412yes—
75C3×D3×Dic3—28no—
76#5210—91no—
77#4950—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—61no—
89C22×C3⋊Dic3—61no—
90C22×C3⋊Dic3—61no—
91C22×C3⋊Dic3—121no—
92C22×C3⋊Dic3C2×D311yescharacteristic
93C22×C3⋊Dic3C2×D311yescharacteristic
94C22×C3⋊Dic3C2×D311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—31no—
98C22×C3×Dic3—31no—
99C22×C3×Dic3—31no—
100C22×C3×Dic3—31no—
101C22×C3×Dic3—31no—
102C22×C3×Dic3—31no—
103C22×C3×Dic3—62no—
104C22×C3×Dic3—62no—
105C22×C3×Dic3—61no—
106C22×C3×Dic3—62no—
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×C3×C4×D3—62no—
114C2×C3×C4×D3—62no—
115C2×C3×C4×D3—62no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119#3757—62no—
120C4⋊(C3⋊Dic3)—62no—
121#3750—62no—
122C3×#217—34no—
123C3×(C2×D3)⋊C4—34no—
124Dic3⋊Dic3—62no—
125Dic3⋊Dic3—62no—
126Dic3⋊Dic3—64no—
127Dic3⋊Dic3—64no—
128Dic3⋊Dic3—62no—
129Dic3⋊Dic3—62no—
130(C2×D3)⋊Dic3—64no—
131(C2×D3)⋊Dic3—62no—
132(C2×D3)⋊Dic3—62no—
133(C2×D3)⋊Dic3Dic314yescomplemented
134C22×C33C22×C411yescharacteristic
135C22×C33C2×D411yescharacteristic
136C22×C33C2×D411yescharacteristic
137C22×C33C2×D411yescharacteristic
138C22×C33C2×Q811yescharacteristic
139C22×C33#4111yescharacteristic
140C22×C33#4111yescharacteristic
141C2×C32×D3—22no—
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3—22no—
145C2×C32×D3—22no—
146C2×C32×D3—22no—
147C2×C32×D3C4⋊C414yescomplemented
148C3⋊(C3⋊Dic3)—41no—
149C3×C3⋊Dic3—22no—
150C3×C3⋊Dic3—22no—
151C3×C3⋊Dic3—41no—
152C32×Dic3—22no—
153C32×Dic3—22no—
154C23×C3×C4—91no—
155C23×Dic3—31no—
156C22×C4×D3—31no—
157C2×C3×C22⋊C4—91no—
158C2×#217—31no—
159C2×#217—91no—
160C2×#217—91no—
161C2×#217—181no—
162C2×(C2×D3)⋊C4—31no—
163C2×(C2×D3)⋊C4—91no—
164C2×C4⋊Dic3—91no—
165C2×C4⋊Dic3—91no—
166C2×C4⋊Dic3—91no—
167C2×C4⋊Dic3—181no—
168C2×Dic3⋊C4—91no—
169C2×Dic3⋊C4—91no—
170C2×Dic3⋊C4—91no—
171C2×Dic3⋊C4—181no—
172C3×#95—91no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—91no—
176C3⋊#95—91no—
177C3⋊#95—91no—
178C23×C32—21no—
179C23×C32—21no—
180C23×C32—21no—
181C23×C32—32no—
182C23×C32—32no—
183C23×C32—32no—
184C23×C32—41no—
185C23×C32—61no—
186C23×C32—61no—
187C23×C32—61no—
188C23×C32—61no—
189C23×C32C22×D311yescharacteristic
190C23×C32C22×D311yescharacteristic
191C23×C32C22×D311yescharacteristic
192C22×C3×D3—21no—
193C22×C3×D3—21no—
194C22×C3×D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C22×C3×D3—21no—
200C22×C3×D3—22no—
201C22×C3×D3—22no—
202C22×C3×D3—22no—
203C22×C3×D3—41no—
204C22×C3×D3—41no—
205C22×C3×D3—41no—
206C22×C3×D3—41no—
207C22×C3×D3Dic612yes—
208C22×C3×D3Dic612yes—
209C22×C3×D3C4×D312yes—
210C22×C3×D3D1212yes—
211C22×C3×D3C2×Dic312yes—
212C22×C3×D3#6712yes—
213C2×C32×C4—32no—
214C2×C32×C4—32no—
215C2×C32×C4—61no—
216C2×C32×C4—61no—
217C2×C32×C4—61no—
218C2×C32×C4—61no—
219C2×C3⋊Dic3—21no—
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—61no—
227C2×C3⋊Dic3—61no—
228C2×C3⋊Dic3—61no—
229C2×C3⋊Dic3—62no—
230C2×C3⋊Dic3—62no—
231C2×C3⋊Dic3—62no—
232C2×C3⋊Dic3—61no—
233C2×C3⋊Dic3—61no—
234C2×C3⋊Dic3—61no—
235C2×C3⋊Dic3—61no—
236C2×C3⋊Dic3—61no—
237C2×C3⋊Dic3—61no—
238C2×C3⋊Dic3—121no—
239C2×C3⋊Dic3—121no—
240C2×C3⋊Dic3—121no—
241C2×C3⋊Dic3—121no—
242C2×C3⋊Dic3—121no—
243C2×C3⋊Dic3—121no—
244C2×C3⋊Dic3—122no—
245C2×C3⋊Dic3—122no—
246C2×C3⋊Dic3—122no—
247C2×C3⋊Dic3C2×Dic312yescomplemented
248C2×C3⋊Dic3#6712yes—
249C2×C3×Dic3—22no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—22no—
261C2×C3×Dic3—32no—
262C2×C3×Dic3—32no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—41no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3—62no—
268C2×C3×Dic3—62no—
269C2×C3×Dic3—68no—
270C2×C3×Dic3—62no—
271C2×C3×Dic3—62no—
272C2×C3×Dic3—61no—
273C2×C3×Dic3—61no—
274C2×C3×Dic3—61no—
275C2×C3×Dic3—61no—
276C2×C3×Dic3—61no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—62no—
281C2×C3×Dic3—61no—
282C2×C3×Dic3—61no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—61no—
285C2×C3×Dic3—61no—
286C2×C3×Dic3—61no—
287C2×C3×Dic3—121no—
288C2×C3×Dic3—121no—
289C2×C3×Dic3—121no—
290C2×C3×Dic3—121no—
291C2×C3×Dic3C4×D312yescomplemented
292C2×C3×Dic3D1212yes—
293C2×C3×Dic3C2×Dic312yescomplemented
294C2×C3×Dic3#6712yes—
295C3×C4×D3—68no—
296D3×Dic3—28no—
297#385—271noSylow
298C2×C33C2×C4⋊C411yescharacteristic
299C2×C33C4×D411yescharacteristic
300C2×C33C4×D411yescharacteristic
301C2×C33#12011yescharacteristic
302C2×C33C22⋊Q811yescharacteristic
303C2×C33C22⋊Q811yescharacteristic
304C2×C33#12311yescharacteristic
305C32×D3—24no—
306C24×C3—31no—
307C24×C3—31no—
308C24×C3—61no—
309C23×D3D3211yescharacteristic
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4—61no—
316C22×C3×C4—91no—
317C22×C3×C4—91no—
318C22×C3×C4—91no—
319C22×C3×C4—182no—
320C22×C3×C4—182no—
321C22×C3×C4—182no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—31no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—62no—
332C22×Dic3—62no—
333C22×Dic3—62no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—91no—
337C22×Dic3—181no—
338C22×Dic3—181no—
339C22×Dic3—181no—
340C22×Dic3—361no—
341C22×Dic3D3211yescharacteristic
342C22×Dic3D3211yescharacteristic
343C2×C4×D3—62no—
344C2×C4×D3—62no—
345C2×C4×D3—62no—
346C3×C22⋊C4—94no—
347#217—34no—
348#217—182no—
349#217—182no—
350#217—184no—
351(C2×D3)⋊C4—34no—
352(C2×D3)⋊C4—182no—
353C4⋊Dic3—182no—
354C4⋊Dic3—182no—
355C4⋊Dic3—184no—
356C4⋊Dic3—182no—
357Dic3⋊C4—182no—
358Dic3⋊C4—182no—
359Dic3⋊C4—182no—
360Dic3⋊C4—184no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
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—34no—
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32—62no—
393C22×C32—62no—
394C22×C32—62no—
395C22×C32—62no—
396C22×C32C2×Dic611yescharacteristic
397C22×C32C2×Dic611yescharacteristic
398C22×C32C2×C4×D311yescharacteristic
399C22×C32C2×C4×D311yescharacteristic
400C22×C32C2×D1211yescharacteristic
401C22×C32C2×D1211yescharacteristic
402C22×C32#23511yescharacteristic
403C22×C32#23511yescharacteristic
404C22×C32#23511yescharacteristic
405C22×C32D3×D411yescharacteristic
406C22×C32D3×D411yescharacteristic
407C22×C32D3×D411yescharacteristic
408C22×C32D3×D411yescharacteristic
409C22×C32#23711yescharacteristic
410C22×C32#23711yescharacteristic
411C22×C32#23711yescharacteristic
412C22×C32D3×Q811yescharacteristic
413C22×C32C22×Dic311yescharacteristic
414C22×C32C2×#6711yescharacteristic
415C22×C32C2×#6711yescharacteristic
416C22×C32C2×#6711yescharacteristic
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—22no—
422C2×C3×D3—22no—
423C2×C3×D3—22no—
424C2×C3×D3—22no—
425C2×C3×D3—22no—
426C2×C3×D3—22no—
427C2×C3×D3—22no—
428C2×C3×D3—22no—
429C2×C3×D3—24no—
430C2×C3×D3—42no—
431C2×C3×D3—42no—
432C2×C3×D3—42no—
433C2×C3×D3—42no—
434C2×C3×D3—42no—
435C2×C3×D3—42no—
436C2×C3×D3Dic3⋊C414yescomplemented
437C2×C3×D3C4⋊Dic314yescomplemented
438C32×C4—62no—
439C32×C4—62no—
440C3⋊Dic3—22no—
441C3⋊Dic3—22no—
442C3⋊Dic3—41no—
443C3⋊Dic3—122no—
444C3⋊Dic3—122no—
445C3⋊Dic3—122no—
446C3⋊Dic3—124no—
447C3⋊Dic3—121no—
448C3⋊Dic3—121no—
449C3⋊Dic3—121no—
450C3×Dic3—24no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
455C3×Dic3—42no—
456C3×Dic3—64no—
457C3×Dic3—62no—
458C3×Dic3—62no—
459C3×Dic3—62no—
460C3×Dic3—62no—
461C3×Dic3—122no—
462C3×Dic3—122no—
463C3×Dic3—121no—
464C3×Dic3—121no—
465C23×C4—91no—
466C2×C4⋊C4—271no—
467C2×C4⋊C4—271no—
468C2×C22⋊C4—91no—
469C2×C22⋊C4—271no—
470#95—91no—
471#95—271no—
472C33#38511yescharacteristic, complemented, Sylow
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—32no—
477C23×C3—32no—
478C23×C3—32no—
479C23×C3—32no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—41no—
483C23×C3—62no—
484C23×C3—62no—
485C23×C3—62no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3—61no—
493C23×C3—61no—
494C23×C3—121no—
495C23×C3—121no—
496C23×C3—121no—
497C23×C3—121no—
498C23×C3C2×D3211yescharacteristic
499C23×C3C2×D3211yescharacteristic
500C23×C3C2×D3211yescharacteristic
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—21no—
505C22×D3D3×Dic312yes—
506C22×D3#62612yes—
507C22×D3#62712yes—
508C2×C3×C4—32no—
509C2×C3×C4—32no—
510C2×C3×C4—32no—
511C2×C3×C4—32no—
512C2×C3×C4—62no—
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—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—92no—
525C2×C3×C4—92no—
526C2×C3×C4—121no—
527C2×C3×C4—121no—
528C2×C3×C4—188no—
529C2×C3×C4—181no—
530C2×C3×C4—181no—
531C2×C3×C4—181no—
532C2×C3×C4—181no—
533C2×C3×C4—181no—
534C2×C3×C4—181no—
535C2×C3×C4—181no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—62no—
545C2×Dic3—62no—
546C2×Dic3—68no—
547C2×Dic3—62no—
548C2×Dic3—62no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—62no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—182no—
569C2×Dic3—182no—
570C2×Dic3—182no—
571C2×Dic3—181no—
572C2×Dic3—181no—
573C2×Dic3—181no—
574C2×Dic3—181no—
575C2×Dic3—181no—
576C2×Dic3—181no—
577C2×Dic3—181no—
578C2×Dic3—181no—
579C2×Dic3—181no—
580C2×Dic3—361no—
581C2×Dic3—361no—
582C2×Dic3—361no—
583C2×Dic3—361no—
584C2×Dic3—361no—
585C2×Dic3—361no—
586C2×Dic3—362no—
587C2×Dic3—362no—
588C2×Dic3—362no—
589C2×Dic3D3×Dic312yescomplemented
590C2×Dic3#62612yes—
591C4×D3—68no—
592C2×C32—21no—
593C2×C32—21no—
594C2×C32—21no—
595C2×C32—21no—
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—41no—
614C2×C32—41no—
615C2×C32—41no—
616C2×C32—41no—
617C2×C32—41no—
618C2×C32—41no—
619C2×C32—41no—
620C2×C32—64no—
621C2×C32C4×D1211yescharacteristic
622C2×C32#87811yescharacteristic
623C2×C32#87811yescharacteristic
624C2×C32#67⋊C411yescharacteristic
625C2×C32#88211yescharacteristic
626C2×C32#88211yescharacteristic
627C2×C32#88311yescharacteristic
628C2×C32#88611yescharacteristic
629C2×C32D3×C4⋊C411yescharacteristic
630C2×C32#89611yescharacteristic
631C2×C32#89711yescharacteristic
632C2×C32C2×Dic3⋊C411yescharacteristic
633C2×C32#92411yescharacteristic
634C2×C32#92411yescharacteristic
635C2×C32C2×C4⋊Dic311yescharacteristic
636C2×C32C4×#6711yescharacteristic
637C2×C32C4×#6711yescharacteristic
638C2×C32#92911yescharacteristic
639C2×C32D4×Dic311yescharacteristic
640C2×C32D4×Dic311yescharacteristic
641C2×C32#95311yescharacteristic
642C3×D3—24no—
643C3×D3—24no—
644C3×D3—44no—
645C24—31no—
646C22×C4—31no—
647C22×C4—31no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—91no—
651C22×C4—182no—
652C22×C4—182no—
653C22×C4—182no—
654C22×C4—271no—
655C4⋊C4—542no—
656C4⋊C4—542no—
657C22⋊C4—94no—
658C22⋊C4—542no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—21no—
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—34no—
681C22×C3—34no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—64no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—62no—
694C22×C3—62no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—62no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—62no—
701C22×C3—62no—
702C22×C3—122no—
703C22×C3—122no—
704C22×C3—122no—
705C22×C3—122no—
706C22×C3—122no—
707C22×C3—122no—
708C22×C3D3×Dic611yescharacteristic
709C22×C3D3×Dic611yescharacteristic
710C22×C3#379511yescharacteristic
711C22×C3#379511yescharacteristic
712C22×C3#379811yescharacteristic
713C22×C3C4×D3211yescharacteristic
714C22×C3D3×D1211yescharacteristic
715C22×C3D3×D1211yescharacteristic
716C22×C3C2×D3×Dic311yescharacteristic
717C22×C3C2×D3×Dic311yescharacteristic
718C22×C3#380411yescharacteristic
719C22×C3#380411yescharacteristic
720C22×C3#380511yescharacteristic
721C22×C3C2×#62611yescharacteristic
722C22×C3C2×#62611yescharacteristic
723C22×C3C2×#62711yescharacteristic
724C22×C3D3×#6711yescharacteristic
725C22×C3D3×#6711yescharacteristic
726C22×C3D3×#6711yescharacteristic
727C22×C3D3×#6711yescharacteristic
728C22×C3#381111yescharacteristic
729C2×D3—22no—
730C2×D3—22no—
731C2×D3—22no—
732C2×D3—22no—
733C2×D3—22no—
734C2×D3—22no—
735C2×D3Dic3⋊Dic314yescomplemented
736C3×C4—64no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4—62no—
741C3×C4—122no—
742C3×C4—182no—
743C3×C4—182no—
744C3×C4—361no—
745Dic3—22no—
746Dic3—22no—
747Dic3—64no—
748Dic3—62no—
749Dic3—62no—
750Dic3—62no—
751Dic3—62no—
752Dic3—122no—
753Dic3—122no—
754Dic3—121no—
755Dic3—121no—
756Dic3—362no—
757Dic3—362no—
758Dic3—362no—
759Dic3—364no—
760Dic3—361no—
761Dic3—361no—
762Dic3—361no—
763C32—21no—
764C32—21no—
765C32—21no—
766C32—41no—
767C32#466811yescharacteristic, complemented
768C32#495011yescharacteristic, complemented
769C32#521011yescharacteristic, complemented
770C23—32no—
771C23—32no—
772C23—32no—
773C23—61no—
774C23—61no—
775C23—61no—
776C23—61no—
777C23D3311yescharacteristic
778C2×C4—32no—
779C2×C4—32no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—92no—
785C2×C4—92no—
786C2×C4—188no—
787C2×C4—181no—
788C2×C4—181no—
789C2×C4—181no—
790C2×C4—181no—
791C2×C4—181no—
792C2×C4—181no—
793C2×C4—181no—
794C2×C4—541no—
795C2×C4—541no—
796C2×C4—541no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
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—41no—
819C2×C3—41no—
820C2×C3—41no—
821C2×C3—41no—
822C2×C3—41no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—64no—
826C2×C3—64no—
827C2×C3—124no—
828C2×C3#6385111yescharacteristic
829C2×C3#6385711yescharacteristic
830C2×C3D3×Dic3⋊C411yescharacteristic
831C2×C3#6387911yescharacteristic
832C2×C3D3×C4⋊Dic311yescharacteristic
833C2×C3#6389111yescharacteristic
834C2×C3Dic3×D1211yescharacteristic
835C2×C3#6389311yescharacteristic
836C2×C3#6389611yescharacteristic
837C2×C3C4×#62611yescharacteristic
838C2×C3#6390511yescharacteristic
839C2×C3#6392311yescharacteristic
840C2×C3#6396411yescharacteristic
841C2×C3#6396411yescharacteristic
842C2×C3C2×Dic3⋊Dic311yescharacteristic
843C2×C3#6396611yescharacteristic
844C2×C3Dic3×#6711yescharacteristic
845C2×C3Dic3×#6711yescharacteristic
846C2×C3#67⋊Dic311yescharacteristic
847C2×C3#6397711yescharacteristic
848C2×C3#6397711yescharacteristic
849D3—24no—
850C22—34no—
851C22—62no—
852C22—62no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22D32×Dic311yescharacteristic
858C22D3×#62611yescharacteristic
859C22D3×#62611yescharacteristic
860C22#8895211yescharacteristic
861C22D3×#62711yescharacteristic
862C22#8896011yescharacteristic
863C22#8896111yescharacteristic
864C4—62no—
865C4—62no—
866C4—182no—
867C4—182no—
868C4—361no—
869C4—1081no—
870C3—21no—
871C3—21no—
872C3—21no—
873C3—41no—
874C3#1059127811yescharacteristic, complemented
875C3#1059137911yescharacteristic, complemented
876C3#1059171811yescharacteristic, complemented
877C2—64no—
878C2D3×Dic3⋊Dic311yescharacteristic
879C2#1172292411yescharacteristic
880C2Dic3×#62611yescharacteristic
881C2#1172294811yescharacteristic
882C2#1172297111yescharacteristic
883C2#1172297511yescharacteristic
884C2#1172298811yescharacteristic
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×#88807C2semidirect
3. C2×Dic3⋊(C3⋊Dic3)C2semidirect
6. #11722082C2semidirect
7. C3×#63579C2semidirect
24. C3×(C2×D3)⋊Dic3C4semidirect
48. #63579D3semidirect
67. C2×C3×C3⋊Dic3C2×C4semidirect
73. C2×C32×Dic3C2×C4semidirect
133. (C2×D3)⋊Dic3Dic3semidirect
147. C2×C32×D3C4⋊C4semidirect
247. C2×C3⋊Dic3C2×Dic3semidirect
291. C2×C3×Dic3C4×D3semidirect
293. C2×C3×Dic3C2×Dic3semidirect
436. C2×C3×D3Dic3⋊C4semidirect
437. C2×C3×D3C4⋊Dic3semidirect
472. C33#385semidirect
589. C2×Dic3D3×Dic3semidirect
735. C2×D3Dic3⋊Dic3semidirect
767. C32#4668semidirect
768. C32#4950semidirect
769. C32#5210semidirect
874. C3#10591278semidirect
875. C3#10591379semidirect
876. C3#10591718semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Dic32
C2×#888072
C2×Dic3⋊(C3⋊Dic3)2
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×(C2×D3)⋊Dic32
#117220822
C3×#635792
#105917183
#105913793
#105912783