Finite Group Databasebeta

← #13156849

Subgroups — #13156849

Order 1728.

1442 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
1C22×C3×#626C211yesmaximal, characteristic
2C2×#88814C211yesmaximal, characteristic, complemented
3C2×Dic3⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C2×#88803C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C2×C3×Dic32C211yesmaximal, characteristic, complemented
8#10591707—31nomaximal
9#10591383—31nomaximal
10#10591318—31nomaximal
11C23×C3×C3⋊D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C32×Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#626—22no—
19C2×C3×#626—22no—
20C2×C3×#626C414yescomplemented
21#88814—22no—
22Dic3⋊(C3⋊Dic3)—22no—
23#88803—22no—
24(C2×D3)⋊(C3⋊Dic3)—22no—
25C3×(C2×D3)⋊Dic3—22no—
26C3×Dic32—22no—
27C22×C3×#67—31no—
28C22×C3×D12—31no—
29C22×#626D311yescharacteristic
30C2×#3757—31no—
31C2×#3752—31no—
32C2×C4⋊(C3⋊Dic3)—31no—
33C2×C3×#217—31no—
34C2×C3×(C2×D3)⋊C4—31no—
35C2×C3×C4×Dic3—31no—
36C2×C3×C4×Dic3—31no—
37C2×Dic3⋊Dic3—31no—
38C2×Dic3⋊Dic3—31no—
39C2×Dic3⋊Dic3—61no—
40C2×#3722—31no—
41C2×(C2×D3)⋊Dic3—31no—
42C2×(C2×D3)⋊Dic3—31no—
43C2×(C2×D3)⋊Dic3—31no—
44C2×(C2×D3)⋊Dic3—31no—
45C2×(C2×D3)⋊Dic3—31no—
46C2×(C2×D3)⋊Dic3—31no—
47C2×(C2×D3)⋊Dic3—61no—
48C2×(C2×D3)⋊Dic3—61no—
49C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
50C2×Dic32D311yescharacteristic, complemented
51C23×C33C2311yescharacteristic
52C22×C3×C3⋊D3—21no—
53C22×C3×C3⋊D3—21no—
54C22×C3×C3⋊D3—21no—
55C22×C3×C3⋊D3—21no—
56C22×C3×C3⋊D3—21no—
57C22×C3×C3⋊D3—21no—
58C22×C3×C3⋊D3C2×C412yes—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3—21no—
63C22×C32×D3—21no—
64C22×C32×D3—21no—
65C22×C32×D3C2×C412yes—
66C2×C3⋊(C3⋊Dic3)—21no—
67C2×C3⋊(C3⋊Dic3)—21no—
68C2×C3⋊(C3⋊Dic3)—21no—
69C2×C3×C3⋊Dic3—21no—
70C2×C3×C3⋊Dic3—21no—
71C2×C3×C3⋊Dic3—21no—
72C2×C3×C3⋊Dic3—21no—
73C2×C3×C3⋊Dic3—21no—
74C2×C3×C3⋊Dic3D412yescomplemented
75C2×C32×Dic3—21no—
76C2×C32×Dic3—21no—
77C2×C32×Dic3C2×C412yes—
78C2×C32×Dic3D412yes—
79C2×C32×Dic3D412yes—
80C2×C32×Dic3D412yescomplemented
81C3×#626—28no—
82#5221—91no—
83#4957—91no—
84#4939—91no—
85C24×C32—31no—
86C23×C3⋊D3C2×D311yescharacteristic
87C23×C3×D3—21no—
88C23×C3×D3—31no—
89C23×C3×D3—31no—
90C23×C3×D3—61no—
91C23×C3×D3C2×D311yescharacteristic
92C23×C3×D3C2×D311yescharacteristic
93C22×C32×C4—31no—
94C22×C32×C4—31no—
95C22×C3⋊Dic3—31no—
96C22×C3⋊Dic3—31no—
97C22×C3⋊Dic3—31no—
98C22×C3⋊Dic3—61no—
99C22×C3⋊Dic3—61no—
100C22×C3⋊Dic3—61no—
101C22×C3⋊Dic3—121no—
102C22×C3⋊Dic3C2×D311yescharacteristic
103C22×C3⋊Dic3C2×D311yescharacteristic
104C2×C3×#67—34no—
105C2×C3×#67—62no—
106C2×C3×#67—62no—
107C22×C3×Dic3—21no—
108C22×C3×Dic3—21no—
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—61no—
114C22×C3×Dic3—61no—
115C22×C3×Dic3C2×D311yescharacteristic
116C22×C3×Dic3C2×D311yescharacteristic
117C22×C3×Dic3C2×D311yescharacteristic
118C22×C3×Dic3C2×D311yescharacteristic
119C2×C3×D12—34no—
120C2×C3×D12—62no—
121C2×C3×D12—62no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626Dic314yescomplemented
125#3757—62no—
126#3752—62no—
127C4⋊(C3⋊Dic3)—62no—
128C3×#217—62no—
129C3×(C2×D3)⋊C4—62no—
130C3×C4×Dic3—62no—
131C3×C4×Dic3—62no—
132Dic3⋊Dic3—64no—
133Dic3⋊Dic3—62no—
134Dic3⋊Dic3—62no—
135#3722—62no—
136(C2×D3)⋊Dic3—22no—
137(C2×D3)⋊Dic3—64no—
138(C2×D3)⋊Dic3—62no—
139(C2×D3)⋊Dic3—62no—
140(C2×D3)⋊Dic3—62no—
141(C2×D3)⋊Dic3—64no—
142(C2×D3)⋊Dic3—62no—
143(C2×D3)⋊Dic3—62no—
144(C2×D3)⋊Dic3—62no—
145Dic32—22no—
146C22×C33C22×C411yescharacteristic
147C22×C33C2×D411yescharacteristic
148C22×C33C2×D411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33#4111yescharacteristic
152C22×C33#4111yescharacteristic
153C2×C3×C3⋊D3—22no—
154C2×C3×C3⋊D3—22no—
155C2×C3×C3⋊D3—22no—
156C2×C3×C3⋊D3—41no—
157C2×C3×C3⋊D3—41no—
158C2×C3×C3⋊D3—41no—
159C2×C3×C3⋊D3—41no—
160C2×C32×D3—22no—
161C2×C32×D3—22no—
162C2×C32×D3—22no—
163C2×C32×D3—41no—
164C2×C32×D3—41no—
165C2×C32×D3—41no—
166C2×C32×D3—41no—
167C3⋊(C3⋊Dic3)—41no—
168C3×C3⋊Dic3—22no—
169C3×C3⋊Dic3—41no—
170C32×Dic3—22no—
171C32×Dic3C22⋊C414yescomplemented
172C22×C3×D4—91no—
173C22×#67—31no—
174C22×D12—31no—
175C2×C3×C22⋊C4—91no—
176C2×C3×C42—91no—
177C2×#217—31no—
178C2×#217—91no—
179C2×#217—91no—
180C2×#217—91no—
181C2×#217—91no—
182C2×#217—181no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—91no—
185C2×(C2×D3)⋊C4—91no—
186C2×(C2×D3)⋊C4—91no—
187C2×(C2×D3)⋊C4—91no—
188C2×(C2×D3)⋊C4—91no—
189C2×(C2×D3)⋊C4—181no—
190C2×C4⋊Dic3—91no—
191C2×C4⋊Dic3—91no—
192C2×C4⋊Dic3—181no—
193C2×Dic3⋊C4—91no—
194C2×C4×Dic3—31no—
195C2×C4×Dic3—31no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—32no—
200C23×C32—41no—
201C23×C32—61no—
202C23×C32—61no—
203C23×C32—61no—
204C23×C32—61no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32C22×D311yescharacteristic
208C23×C32C22×D311yescharacteristic
209C23×C32C22×D311yescharacteristic
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3—21no—
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3C2×Dic312yes—
217C22×C3×D3—22no—
218C22×C3×D3—22no—
219C22×C3×D3—21no—
220C22×C3×D3—21no—
221C22×C3×D3—21no—
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—22no—
232C22×C3×D3—32no—
233C22×C3×D3—32no—
234C22×C3×D3—41no—
235C22×C3×D3—41no—
236C22×C3×D3—41no—
237C22×C3×D3—41no—
238C22×C3×D3—62no—
239C22×C3×D3—62no—
240C22×C3×D3—62no—
241C22×C3×D3—61no—
242C22×C3×D3—61no—
243C22×C3×D3—61no—
244C22×C3×D3—61no—
245C22×C3×D3—61no—
246C22×C3×D3—61no—
247C22×C3×D3—61no—
248C22×C3×D3—61no—
249C22×C3×D3—61no—
250C22×C3×D3—61no—
251C22×C3×D3—61no—
252C22×C3×D3—61no—
253C22×C3×D3—121no—
254C22×C3×D3—121no—
255C22×C3×D3—121no—
256C22×C3×D3—121no—
257C22×C3×D3C4×D312yes—
258C22×C3×D3C2×Dic312yes—
259C2×C32×C4—32no—
260C2×C32×C4—32no—
261C2×C32×C4—32no—
262C2×C32×C4—32no—
263C2×C32×C4—61no—
264C2×C32×C4—61no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—21no—
270C2×C3⋊Dic3—61no—
271C2×C3⋊Dic3—61no—
272C2×C3⋊Dic3—61no—
273C2×C3⋊Dic3—62no—
274C2×C3⋊Dic3—62no—
275C2×C3⋊Dic3—62no—
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—121no—
283C2×C3⋊Dic3—121no—
284C2×C3⋊Dic3—121no—
285C2×C3⋊Dic3—121no—
286C2×C3⋊Dic3—121no—
287C2×C3⋊Dic3—121no—
288C2×C3⋊Dic3—122no—
289C2×C3⋊Dic3—122no—
290C2×C3⋊Dic3—122no—
291C2×C3⋊Dic3D1212yescomplemented
292C3×#67—68no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—22no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3—22no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—41no—
304C2×C3×Dic3—41no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—61no—
307C2×C3×Dic3—61no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—62no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—61no—
317C2×C3×Dic3—121no—
318C2×C3×Dic3—121no—
319C2×C3×Dic3—121no—
320C2×C3×Dic3—121no—
321C2×C3×Dic3C4×D312yes—
322C2×C3×Dic3D1212yes—
323C2×C3×Dic3D1212yescomplemented
324C2×C3×Dic3C2×Dic312yes—
325C2×C3×Dic3#6712yes—
326C2×C3×Dic3#6712yes—
327C2×C3×Dic3#6712yes—
328C2×C3×Dic3#6712yescomplemented
329C3×D12—68no—
330#626—28no—
331#390—271noSylow
332C2×C33C2×C22⋊C411yescharacteristic
333C2×C33C4×D411yescharacteristic
334C2×C33C4×D411yescharacteristic
335C2×C33#12111yescharacteristic
336C2×C33#12111yescharacteristic
337C2×C33#12411yescharacteristic
338C2×C33#12711yescharacteristic
339C3×C3⋊D3—42no—
340C32×D3—42no—
341C24×C3—31no—
342C24×C3—31no—
343C24×C3—61no—
344C24×C3—91no—
345C23×D3—31no—
346C23×D3—31no—
347C23×D3—61no—
348C23×D3D3211yescharacteristic
349C2×C3×D4—94no—
350C2×C3×D4—182no—
351C2×C3×D4—182no—
352C22×C3×C4—31no—
353C22×C3×C4—31no—
354C22×C3×C4—31no—
355C22×C3×C4—31no—
356C22×C3×C4—61no—
357C22×C3×C4—61no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C2×#67—34no—
361C2×#67—62no—
362C2×#67—62no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—61no—
368C22×Dic3—61no—
369C22×Dic3—91no—
370C22×Dic3—91no—
371C22×Dic3—91no—
372C22×Dic3—181no—
373C22×Dic3—181no—
374C22×Dic3—181no—
375C22×Dic3—361no—
376C22×Dic3D3211yescharacteristic
377C22×Dic3D3211yescharacteristic
378C2×D12—34no—
379C2×D12—62no—
380C2×D12—62no—
381C3×C22⋊C4—182no—
382C3×C42—182no—
383#217—62no—
384#217—182no—
385#217—182no—
386#217—182no—
387#217—184no—
388#217—182no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—182no—
391(C2×D3)⋊C4—182no—
392(C2×D3)⋊C4—182no—
393(C2×D3)⋊C4—182no—
394(C2×D3)⋊C4—184no—
395(C2×D3)⋊C4—182no—
396C4⋊Dic3—182no—
397C4⋊Dic3—182no—
398C4⋊Dic3—184no—
399Dic3⋊C4—182no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—62no—
431C22×C32—62no—
432C22×C32—62no—
433C22×C32—121no—
434C22×C32—121no—
435C22×C32—121no—
436C22×C32—121no—
437C22×C32C2×C4×D311yescharacteristic
438C22×C32C2×C4×D311yescharacteristic
439C22×C32C2×D1211yescharacteristic
440C22×C32C2×D1211yescharacteristic
441C22×C32C2×D1211yescharacteristic
442C22×C32#23511yescharacteristic
443C22×C32#23511yescharacteristic
444C22×C32#23511yescharacteristic
445C22×C32D3×D411yescharacteristic
446C22×C32D3×D411yescharacteristic
447C22×C32D3×D411yescharacteristic
448C22×C32D3×D411yescharacteristic
449C22×C32D3×D411yescharacteristic
450C22×C32#23711yescharacteristic
451C22×C32#23711yescharacteristic
452C22×C32#23711yescharacteristic
453C22×C32C22×Dic311yescharacteristic
454C22×C32C2×#6711yescharacteristic
455C22×C32C2×#6711yescharacteristic
456C22×C32C2×#6711yescharacteristic
457C22×C32C2×#6711yescharacteristic
458C2×C3⋊D3—22no—
459C2×C3⋊D3—22no—
460C2×C3⋊D3—22no—
461C2×C3⋊D3—41no—
462C2×C3⋊D3—41no—
463C2×C3⋊D3—41no—
464C2×C3⋊D3—41no—
465C2×C3×D3—24no—
466C2×C3×D3—22no—
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
471C2×C3×D3—22no—
472C2×C3×D3—42no—
473C2×C3×D3—42no—
474C2×C3×D3—42no—
475C2×C3×D3—42no—
476C2×C3×D3—42no—
477C2×C3×D3—42no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—41no—
483C2×C3×D3—41no—
484C2×C3×D3—41no—
485C2×C3×D3—41no—
486C2×C3×D3—64no—
487C2×C3×D3—62no—
488C2×C3×D3—62no—
489C2×C3×D3—62no—
490C2×C3×D3—62no—
491C2×C3×D3—62no—
492C2×C3×D3—62no—
493C2×C3×D3—122no—
494C2×C3×D3—122no—
495C2×C3×D3—122no—
496C2×C3×D3—122no—
497C2×C3×D3—122no—
498C2×C3×D3—122no—
499C2×C3×D3—121no—
500C2×C3×D3—121no—
501C2×C3×D3—121no—
502C2×C3×D3—121no—
503C2×C3×D3—121no—
504C2×C3×D3—121no—
505C2×C3×D3—121no—
506C2×C3×D3—121no—
507C32×C4—34no—
508C32×C4—62no—
509C3⋊Dic3—22no—
510C3⋊Dic3—41no—
511C3⋊Dic3—122no—
512C3⋊Dic3—122no—
513C3⋊Dic3—122no—
514C3⋊Dic3—124no—
515C3⋊Dic3—121no—
516C3⋊Dic3—121no—
517C3⋊Dic3—121no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—24no—
521C3×Dic3—42no—
522C3×Dic3—62no—
523C3×Dic3—62no—
524C3×Dic3—122no—
525C3×Dic3—122no—
526C3×Dic3—121no—
527C3×Dic3—121no—
528C3×Dic3(C2×D3)⋊C414yescomplemented
529C3×Dic3#21714yescomplemented
530C22×D4—91no—
531C2×C4⋊C4—271no—
532C2×C22⋊C4—91no—
533C2×C22⋊C4—271no—
534C2×C22⋊C4—271no—
535C2×C22⋊C4—271no—
536C2×C42—91no—
537C33#39011yescharacteristic, complemented, Sylow
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—32no—
542C23×C3—32no—
543C23×C3—41no—
544C23×C3—62no—
545C23×C3—62no—
546C23×C3—62no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3—61no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—61no—
557C23×C3—61no—
558C23×C3—61no—
559C23×C3—92no—
560C23×C3—121no—
561C23×C3—121no—
562C23×C3—121no—
563C23×C3—121no—
564C23×C3—181no—
565C23×C3—181no—
566C23×C3—181no—
567C23×C3—181no—
568C23×C3—181no—
569C23×C3—181no—
570C23×C3C2×D3211yescharacteristic
571C23×C3C2×D3211yescharacteristic
572C23×C3C2×D3211yescharacteristic
573C22×D3—21no—
574C22×D3—21no—
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—21no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—62no—
582C22×D3—62no—
583C22×D3—62no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—61no—
588C22×D3—61no—
589C22×D3—61no—
590C22×D3—61no—
591C22×D3—61no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—121no—
597C22×D3—121no—
598C22×D3—121no—
599C22×D3—121no—
600C22×D3D3×Dic312yes—
601C3×D4—188no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—62no—
611C2×C3×C4—62no—
612C2×C3×C4—62no—
613C2×C3×C4—62no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—92no—
619C2×C3×C4—121no—
620C2×C3×C4—121no—
621C2×C3×C4—181no—
622C2×C3×C4—181no—
623C2×C3×C4—181no—
624C2×C3×C4—181no—
625C2×C3×C4—181no—
626#67—68no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—62no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—62no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—121no—
644C2×Dic3—121no—
645C2×Dic3—121no—
646C2×Dic3—121no—
647C2×Dic3—182no—
648C2×Dic3—182no—
649C2×Dic3—182no—
650C2×Dic3—181no—
651C2×Dic3—181no—
652C2×Dic3—181no—
653C2×Dic3—181no—
654C2×Dic3—181no—
655C2×Dic3—181no—
656C2×Dic3—181no—
657C2×Dic3—181no—
658C2×Dic3—181no—
659C2×Dic3—361no—
660C2×Dic3—361no—
661C2×Dic3—361no—
662C2×Dic3—361no—
663C2×Dic3—361no—
664C2×Dic3—361no—
665C2×Dic3—362no—
666C2×Dic3—362no—
667C2×Dic3—362no—
668C2×Dic3D3×Dic312yes—
669C2×Dic3#62512yes—
670C2×Dic3#62612yes—
671C2×Dic3#62612yescomplemented
672D12—68no—
673C2×C32—21no—
674C2×C32—21no—
675C2×C32—21no—
676C2×C32—21no—
677C2×C32—21no—
678C2×C32—21no—
679C2×C32—21no—
680C2×C32—21no—
681C2×C32—21no—
682C2×C32—21no—
683C2×C32—21no—
684C2×C32—21no—
685C2×C32—21no—
686C2×C32—21no—
687C2×C32—21no—
688C2×C32—21no—
689C2×C32—21no—
690C2×C32—21no—
691C2×C32—21no—
692C2×C32—21no—
693C2×C32—21no—
694C2×C32—41no—
695C2×C32—41no—
696C2×C32—41no—
697C2×C32—41no—
698C2×C32—41no—
699C2×C32—41no—
700C2×C32—41no—
701C2×C32—122no—
702C2×C32C4×D1211yescharacteristic
703C2×C32C4×D1211yescharacteristic
704C2×C32#87411yescharacteristic
705C2×C32#87511yescharacteristic
706C2×C32D3×C22⋊C411yescharacteristic
707C2×C32#67⋊C411yescharacteristic
708C2×C32#88411yescharacteristic
709C2×C32#88511yescharacteristic
710C2×C32C2×(C2×D3)⋊C411yescharacteristic
711C2×C32C4×#6711yescharacteristic
712C2×C32#93011yescharacteristic
713C2×C32#93011yescharacteristic
714C2×C32D4×Dic311yescharacteristic
715C2×C32D4×Dic311yescharacteristic
716C2×C32#93611yescharacteristic
717C2×C32#93811yescharacteristic
718C2×C32#93811yescharacteristic
719C2×C32#93911yescharacteristic
720C2×C32#94011yescharacteristic
721C2×C32#94011yescharacteristic
722C2×C32C2×#21711yescharacteristic
723C3⋊D3—42no—
724C3×D3—44no—
725C3×D3—42no—
726C3×D3—42no—
727C3×D3—124no—
728C3×D3—122no—
729C3×D3—122no—
730C24—31no—
731C24—91no—
732C2×D4—94no—
733C2×D4—182no—
734C2×D4—182no—
735C22×C4—31no—
736C22×C4—31no—
737C22×C4—91no—
738C22×C4—91no—
739C22×C4—271no—
740C4⋊C4—542no—
741C22⋊C4—182no—
742C22⋊C4—542no—
743C22⋊C4—542no—
744C22⋊C4—542no—
745C42—182no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—21no—
750C22×C3—21no—
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—21no—
754C22×C3—21no—
755C22×C3—21no—
756C22×C3—21no—
757C22×C3—21no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—21no—
767C22×C3—41no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—41no—
773C22×C3—41no—
774C22×C3—64no—
775C22×C3—62no—
776C22×C3—62no—
777C22×C3—62no—
778C22×C3—62no—
779C22×C3—62no—
780C22×C3—62no—
781C22×C3—122no—
782C22×C3—122no—
783C22×C3—122no—
784C22×C3—122no—
785C22×C3—122no—
786C22×C3—122no—
787C22×C3—121no—
788C22×C3—121no—
789C22×C3—121no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—182no—
796C22×C3—182no—
797C22×C3—182no—
798C22×C3—361no—
799C22×C3—361no—
800C22×C3—361no—
801C22×C3—361no—
802C22×C3#379511yescharacteristic
803C22×C3#379511yescharacteristic
804C22×C3#379811yescharacteristic
805C22×C3C4×D3211yescharacteristic
806C22×C3D3×D1211yescharacteristic
807C22×C3D3×D1211yescharacteristic
808C22×C3D3×D1211yescharacteristic
809C22×C3D3×D1211yescharacteristic
810C22×C3C2×D3×Dic311yescharacteristic
811C22×C3C2×D3×Dic311yescharacteristic
812C22×C3#380411yescharacteristic
813C22×C3#380411yescharacteristic
814C22×C3#380511yescharacteristic
815C22×C3C2×#62511yescharacteristic
816C22×C3C2×#62611yescharacteristic
817C22×C3C2×#62611yescharacteristic
818C22×C3D3×#6711yescharacteristic
819C22×C3D3×#6711yescharacteristic
820C22×C3D3×#6711yescharacteristic
821C22×C3D3×#6711yescharacteristic
822C22×C3#381111yescharacteristic
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—64no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—62no—
835C2×D3—62no—
836C2×D3—62no—
837C2×D3—122no—
838C2×D3—122no—
839C2×D3—122no—
840C2×D3—122no—
841C2×D3—122no—
842C2×D3—122no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C3×C4—34no—
852C3×C4—34no—
853C3×C4—64no—
854C3×C4—62no—
855C3×C4—62no—
856C3×C4—122no—
857C3×C4—182no—
858C3×C4—361no—
859Dic3—22no—
860Dic3—62no—
861Dic3—62no—
862Dic3—122no—
863Dic3—122no—
864Dic3—121no—
865Dic3—121no—
866Dic3—362no—
867Dic3—362no—
868Dic3—362no—
869Dic3—364no—
870Dic3—361no—
871Dic3—361no—
872Dic3—361no—
873Dic3(C2×D3)⋊Dic314yescomplemented
874C32—21no—
875C32—21no—
876C32—21no—
877C32—41no—
878C32#493911yescharacteristic, complemented
879C32#495711yescharacteristic, complemented
880C32#522111yescharacteristic, complemented
881C23—32no—
882C23—61no—
883C23—61no—
884C23—61no—
885C23—61no—
886C23—61no—
887C23—61no—
888C23—92no—
889C23—181no—
890C23—181no—
891C23—181no—
892C23—181no—
893C23—181no—
894C23—181no—
895C23D3311yescharacteristic
896D4—188no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—92no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—181no—
908C2×C4—181no—
909C2×C4—541no—
910C2×C4—541no—
911C2×C4—541no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—21no—
924C2×C3—21no—
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—41no—
934C2×C3—41no—
935C2×C3—41no—
936C2×C3—41no—
937C2×C3—41no—
938C2×C3—41no—
939C2×C3—41no—
940C2×C3—124no—
941C2×C3—122no—
942C2×C3—122no—
943C2×C3—362no—
944C2×C3#6385211yescharacteristic
945C2×C3#6386011yescharacteristic
946C2×C3#6388011yescharacteristic
947C2×C3Dic3×D1211yescharacteristic
948C2×C3Dic3×D1211yescharacteristic
949C2×C3C4×#62611yescharacteristic
950C2×C3#6390611yescharacteristic
951C2×C3#6390811yescharacteristic
952C2×C3#6390811yescharacteristic
953C2×C3#6391111yescharacteristic
954C2×C3#6391111yescharacteristic
955C2×C3D3×(C2×D3)⋊C411yescharacteristic
956C2×C3#6395811yescharacteristic
957C2×C3#6395911yescharacteristic
958C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
959C2×C3D3×#21711yescharacteristic
960C2×C3#6397011yescharacteristic
961C2×C3Dic3×#6711yescharacteristic
962C2×C3#67⋊Dic311yescharacteristic
963C2×C3#6397811yescharacteristic
964C2×C3#6397911yescharacteristic
965D3—42no—
966D3—124no—
967D3—122no—
968D3—122no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—121no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—182no—
977C22—182no—
978C22—182no—
979C22—361no—
980C22—361no—
981C22—361no—
982C22—361no—
983C22D32×Dic311yescharacteristic
984C22D3×#62511yescharacteristic
985C22D3×#62611yescharacteristic
986C22D3×#62611yescharacteristic
987C22#8895511yescharacteristic
988C22#8896011yescharacteristic
989C22#8896111yescharacteristic
990C4—34no—
991C4—62no—
992C4—182no—
993C4—361no—
994C4—1081no—
995C3—21no—
996C3—21no—
997C3—21no—
998C3—41no—
999C3#1059131811yescharacteristic, complemented
1000C3#1059138311yescharacteristic, complemented
1001C3#1059170711yescharacteristic, complemented
1002C2—122no—
1003C2—362no—
1004C2D3×(C2×D3)⋊Dic311yescharacteristic
1005C2Dic3×#62611yescharacteristic
1006C2#1172292811yescharacteristic
1007C2#1172295611yescharacteristic
1008C2#1172295711yescharacteristic
1009C2#1172300211yescharacteristic
1010C2#1172303011yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×C3×#626C2
hypocenterC33#390
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×#88814C2semidirect
3. C2×Dic3⋊(C3⋊Dic3)C2semidirect
4. C2×#88803C2semidirect
5. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C2×C3×Dic32C2semidirect
20. C2×C3×#626C4semidirect
49. C2×(C2×D3)⋊Dic3D3semidirect
50. C2×Dic32D3semidirect
74. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
124. C2×#626Dic3semidirect
171. C32×Dic3C22⋊C4semidirect
291. C2×C3⋊Dic3D12semidirect
323. C2×C3×Dic3D12semidirect
328. C2×C3×Dic3#67semidirect
528. C3×Dic3(C2×D3)⋊C4semidirect
529. C3×Dic3#217semidirect
537. C33#390semidirect
671. C2×Dic3#626semidirect
873. Dic3(C2×D3)⋊Dic3semidirect
878. C32#4939semidirect
879. C32#4957semidirect
880. C32#5221semidirect
999. C3#10591318semidirect
1000. C3#10591383semidirect
1001. C3#10591707semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6262
C2×#888142
C2×Dic3⋊(C3⋊Dic3)2
C2×#888032
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×(C2×D3)⋊Dic32
C2×C3×Dic322
#105917073
#105913833
#105913183