Finite Group Databasebeta

← #13156761

Subgroups — #13156761

Order 1728.

1538 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#625C211yesmaximal, characteristic
2C22×C3×D3×Dic3C211yesmaximal, characteristic, complemented
3C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
4C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
6#11722082C211yesmaximal, characteristic, complemented
7#11722061C211yesmaximal, characteristic, complemented
8#10591721—31nomaximal
9#10591710—31nomaximal
10#10591381—31nomaximal
11C23×C32×D3C2211yescharacteristic
12C23×C32×D3C2211yescharacteristic
13C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C22×C3×C3⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊Dic3C2211yescharacteristic
17C22×C32×Dic3C2211yescharacteristic
18C2×C3×#625—22no—
19C2×C3×#625—22no—
20C2×C3×#625C414yescomplemented
21C2×C3×D3×Dic3—22no—
22C2×C3×D3×Dic3—22no—
23C2×C3×D3×Dic3—22no—
24(C2×D3)⋊(C3⋊Dic3)—22no—
25(C2×D3)⋊(C3⋊Dic3)—22no—
26C3×(C2×D3)⋊Dic3—22no—
27C22×C3×#67—31no—
28C22×C3×#67—31no—
29C23×C3×Dic3—31no—
30C22×C3×C4×D3—31no—
31C22×#625D311yescharacteristic
32C22×D3×Dic3D311yescharacteristic, complemented
33C2×#3757—31no—
34C2×#3757—31no—
35C2×C3×#217—31no—
36C2×C3×(C2×D3)⋊C4—31no—
37C2×(C2×D3)⋊Dic3—31no—
38C2×(C2×D3)⋊Dic3—31no—
39C2×(C2×D3)⋊Dic3—31no—
40C2×(C2×D3)⋊Dic3—31no—
41C2×(C2×D3)⋊Dic3—61no—
42C2×(C2×D3)⋊Dic3—61no—
43C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
44#63658—31no—
45#63579—31no—
46#63579—31no—
47#63579—31no—
48#63579—31no—
49#63579—31no—
50#63579—61no—
51C23×C33C2311yescharacteristic
52C22×C32×D3—21no—
53C22×C32×D3—21no—
54C22×C32×D3—21no—
55C22×C32×D3—21no—
56C22×C32×D3—21no—
57C22×C32×D3—21no—
58C22×C32×D3—21no—
59C22×C32×D3—21no—
60C22×C32×D3—21no—
61C22×C32×D3—21no—
62C22×C32×D3C2×C412yes—
63C22×C32×D3C2×C412yescomplemented
64C22×C32×D3D412yes—
65C22×C32×D3D412yes—
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⋊Dic3—21no—
75C2×C3×C3⋊Dic3—21no—
76C2×C3×C3⋊Dic3C2×C412yescomplemented
77C2×C3×C3⋊Dic3D412yescomplemented
78C2×C32×Dic3—21no—
79C2×C32×Dic3—21no—
80C2×C32×Dic3D412yescomplemented
81C3×#625—28no—
82C3×D3×Dic3—28no—
83#5220—91no—
84#5213—91no—
85#4956—91no—
86C24×C32—31no—
87C24×C32—31no—
88C23×C3×D3—21no—
89C23×C3×D3—21no—
90C23×C3×D3C2×D311yescharacteristic
91C23×C3×D3C2×D311yescharacteristic
92C23×C3×D3C2×D311yescharacteristic
93C23×C3×D3C2×D311yescharacteristic
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
104C22×C3⋊Dic3C2×D311yescharacteristic
105C2×C3×#67—34no—
106C2×C3×#67—34no—
107C2×C3×#67—62no—
108C2×C3×#67—62no—
109C2×C3×#67—62no—
110C2×C3×#67—62no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—31no—
113C22×C3×Dic3—31no—
114C22×C3×Dic3—31no—
115C22×C3×Dic3—31no—
116C22×C3×Dic3—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—62no—
119C22×C3×Dic3—62no—
120C22×C3×Dic3—62no—
121C22×C3×Dic3—61no—
122C22×C3×Dic3—61no—
123C22×C3×Dic3—61no—
124C22×C3×Dic3C2×D311yescharacteristic
125C22×C3×Dic3C2×D311yescharacteristic
126C2×C3×C4×D3—62no—
127C2×C3×C4×D3—62no—
128C2×C3×C4×D3—62no—
129C2×#625—22no—
130C2×#625—22no—
131C2×#625Dic314yescomplemented
132C2×D3×Dic3—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135#3757—62no—
136#3757—62no—
137C3×#217—62no—
138C3×(C2×D3)⋊C4—62no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—62no—
141(C2×D3)⋊Dic3—62no—
142(C2×D3)⋊Dic3—64no—
143(C2×D3)⋊Dic3—64no—
144(C2×D3)⋊Dic3—62no—
145(C2×D3)⋊Dic3—62no—
146C22×C33C22×C411yescharacteristic
147C22×C33C2×D411yescharacteristic
148C22×C33C2×D411yescharacteristic
149C22×C33C2×D411yescharacteristic
150C22×C33C2×D411yescharacteristic
151C22×C33#4111yescharacteristic
152C22×C33#4111yescharacteristic
153C2×C32×D3—22no—
154C2×C32×D3—22no—
155C2×C32×D3—22no—
156C2×C32×D3—22no—
157C2×C32×D3—22no—
158C2×C32×D3—22no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C2×C32×D3—22no—
162C2×C32×D3—41no—
163C2×C32×D3—41no—
164C2×C32×D3—41no—
165C2×C32×D3—41no—
166C2×C32×D3C22⋊C414yescomplemented
167C3⋊(C3⋊Dic3)—41no—
168C3×C3⋊Dic3—22no—
169C3×C3⋊Dic3—22no—
170C3×C3⋊Dic3—41no—
171C32×Dic3—22no—
172C22×C3×D4—91no—
173C23×C3×C4—91no—
174C22×#67—31no—
175C22×#67—31no—
176C23×Dic3—31no—
177C22×C4×D3—31no—
178C2×C3×C22⋊C4—91no—
179C2×#217—31no—
180C2×#217—91no—
181C2×#217—91no—
182C2×#217—91no—
183C2×#217—91no—
184C2×#217—181no—
185C2×#217—181no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—91no—
188C2×(C2×D3)⋊C4—91no—
189C3⋊#95—91no—
190C3⋊#95—91no—
191C3⋊#95—91no—
192C3⋊#95—91no—
193C3⋊#95—91no—
194C3⋊#95—91no—
195C3⋊#95—181no—
196C23×C32—21no—
197C23×C32—21no—
198C23×C32—21no—
199C23×C32—32no—
200C23×C32—32no—
201C23×C32—32no—
202C23×C32—32no—
203C23×C32—41no—
204C23×C32—61no—
205C23×C32—61no—
206C23×C32—61no—
207C23×C32—61no—
208C23×C32—61no—
209C23×C32—61no—
210C23×C32—61no—
211C23×C32—61no—
212C23×C32—61no—
213C23×C32—61no—
214C23×C32C22×D311yescharacteristic
215C23×C32C22×D311yescharacteristic
216C23×C32C22×D311yescharacteristic
217C22×C3×D3—21no—
218C22×C3×D3—21no—
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—22no—
226C22×C3×D3—22no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3—21no—
233C22×C3×D3—21no—
234C22×C3×D3—21no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—22no—
240C22×C3×D3—22no—
241C22×C3×D3—22no—
242C22×C3×D3—22no—
243C22×C3×D3—41no—
244C22×C3×D3—41no—
245C22×C3×D3—41no—
246C22×C3×D3—41no—
247C22×C3×D3—41no—
248C22×C3×D3—41no—
249C22×C3×D3—41no—
250C22×C3×D3—41no—
251C22×C3×D3C4×D312yes—
252C22×C3×D3C4×D312yescomplemented
253C22×C3×D3D1212yes—
254C22×C3×D3C2×Dic312yes—
255C22×C3×D3C2×Dic312yescomplemented
256C22×C3×D3#6712yes—
257C22×C3×D3#6712yes—
258C22×C3×D3#6712yes—
259C2×C32×C4—32no—
260C2×C32×C4—61no—
261C2×C32×C4—61no—
262C2×C3⋊Dic3—21no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—21no—
266C2×C3⋊Dic3—21no—
267C2×C3⋊Dic3—21no—
268C2×C3⋊Dic3—21no—
269C2×C3⋊Dic3—61no—
270C2×C3⋊Dic3—61no—
271C2×C3⋊Dic3—61no—
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—121no—
282C2×C3⋊Dic3—121no—
283C2×C3⋊Dic3—121no—
284C2×C3⋊Dic3—121no—
285C2×C3⋊Dic3—121no—
286C2×C3⋊Dic3—121no—
287C2×C3⋊Dic3—122no—
288C2×C3⋊Dic3—122no—
289C2×C3⋊Dic3—122no—
290C2×C3⋊Dic3C2×Dic312yescomplemented
291C2×C3⋊Dic3#6712yescomplemented
292C3×#67—68no—
293C3×#67—68no—
294C2×C3×Dic3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—22no—
299C2×C3×Dic3—32no—
300C2×C3×Dic3—32no—
301C2×C3×Dic3—32no—
302C2×C3×Dic3—32no—
303C2×C3×Dic3—41no—
304C2×C3×Dic3—41no—
305C2×C3×Dic3—62no—
306C2×C3×Dic3—62no—
307C2×C3×Dic3—68no—
308C2×C3×Dic3—61no—
309C2×C3×Dic3—61no—
310C2×C3×Dic3—61no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—61no—
314C2×C3×Dic3—61no—
315C2×C3×Dic3—61no—
316C2×C3×Dic3—62no—
317C2×C3×Dic3—61no—
318C2×C3×Dic3—61no—
319C2×C3×Dic3—61no—
320C2×C3×Dic3—61no—
321C2×C3×Dic3—61no—
322C2×C3×Dic3—61no—
323C2×C3×Dic3—121no—
324C2×C3×Dic3—121no—
325C2×C3×Dic3—121no—
326C2×C3×Dic3—121no—
327C2×C3×Dic3—121no—
328C2×C3×Dic3—121no—
329C2×C3×Dic3#6712yescomplemented
330C2×C3×Dic3#6712yescomplemented
331C3×C4×D3—68no—
332#625—28no—
333D3×Dic3—28no—
334#386—271noSylow
335C2×C33C2×C22⋊C411yescharacteristic
336C2×C33C4×D411yescharacteristic
337C2×C33C4×D411yescharacteristic
338C2×C33#12011yescharacteristic
339C2×C33#12111yescharacteristic
340C2×C33#12111yescharacteristic
341C2×C33#12311yescharacteristic
342C32×D3—24no—
343C32×D3—42no—
344C24×C3—31no—
345C24×C3—31no—
346C24×C3—31no—
347C24×C3—31no—
348C24×C3—61no—
349C24×C3—61no—
350C23×D3D3211yescharacteristic
351C23×D3D3211yescharacteristic
352C2×C3×D4—94no—
353C2×C3×D4—182no—
354C2×C3×D4—182no—
355C22×C3×C4—31no—
356C22×C3×C4—31no—
357C22×C3×C4—61no—
358C22×C3×C4—91no—
359C22×C3×C4—91no—
360C22×C3×C4—91no—
361C22×C3×C4—182no—
362C22×C3×C4—182no—
363C22×C3×C4—182no—
364C2×#67—34no—
365C2×#67—34no—
366C2×#67—62no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—62no—
370C22×Dic3—31no—
371C22×Dic3—31no—
372C22×Dic3—31no—
373C22×Dic3—31no—
374C22×Dic3—31no—
375C22×Dic3—31no—
376C22×Dic3—61no—
377C22×Dic3—61no—
378C22×Dic3—61no—
379C22×Dic3—62no—
380C22×Dic3—62no—
381C22×Dic3—62no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385C22×Dic3—181no—
386C22×Dic3—181no—
387C22×Dic3—181no—
388C22×Dic3—361no—
389C22×Dic3D3211yescharacteristic
390C2×C4×D3—62no—
391C2×C4×D3—62no—
392C2×C4×D3—62no—
393C3×C22⋊C4—182no—
394#217—62no—
395#217—182no—
396#217—182no—
397#217—182no—
398#217—182no—
399#217—184no—
400#217—184no—
401(C2×D3)⋊C4—62no—
402(C2×D3)⋊C4—182no—
403(C2×D3)⋊C4—182no—
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—21no—
424C22×C32—21no—
425C22×C32—34no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—41no—
432C22×C32—41no—
433C22×C32—62no—
434C22×C32—62no—
435C22×C32—62no—
436C22×C32—62no—
437C22×C32—62no—
438C22×C32—62no—
439C22×C32—62no—
440C22×C32—62no—
441C22×C32—62no—
442C22×C32—121no—
443C22×C32—121no—
444C22×C32—121no—
445C22×C32—121no—
446C22×C32C2×C4×D311yescharacteristic
447C22×C32C2×C4×D311yescharacteristic
448C22×C32C2×D1211yescharacteristic
449C22×C32#23511yescharacteristic
450C22×C32#23511yescharacteristic
451C22×C32#23511yescharacteristic
452C22×C32D3×D411yescharacteristic
453C22×C32D3×D411yescharacteristic
454C22×C32D3×D411yescharacteristic
455C22×C32D3×D411yescharacteristic
456C22×C32D3×D411yescharacteristic
457C22×C32#23711yescharacteristic
458C22×C32#23711yescharacteristic
459C22×C32#23711yescharacteristic
460C22×C32C22×Dic311yescharacteristic
461C22×C32C2×#6711yescharacteristic
462C22×C32C2×#6711yescharacteristic
463C22×C32C2×#6711yescharacteristic
464C22×C32C2×#6711yescharacteristic
465C22×C32C2×#6711yescharacteristic
466C22×C32C2×#6711yescharacteristic
467C2×C3×D3—22no—
468C2×C3×D3—22no—
469C2×C3×D3—22no—
470C2×C3×D3—22no—
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—22no—
481C2×C3×D3—22no—
482C2×C3×D3—22no—
483C2×C3×D3—22no—
484C2×C3×D3—22no—
485C2×C3×D3—22no—
486C2×C3×D3—24no—
487C2×C3×D3—42no—
488C2×C3×D3—42no—
489C2×C3×D3—42no—
490C2×C3×D3—42no—
491C2×C3×D3—42no—
492C2×C3×D3—42no—
493C2×C3×D3—42no—
494C2×C3×D3—42no—
495C2×C3×D3—42no—
496C2×C3×D3—42no—
497C2×C3×D3—42no—
498C2×C3×D3—42no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3(C2×D3)⋊C414yescomplemented
508C2×C3×D3#21714yescomplemented
509C32×C4—62no—
510C3⋊Dic3—22no—
511C3⋊Dic3—22no—
512C3⋊Dic3—41no—
513C3⋊Dic3—122no—
514C3⋊Dic3—122no—
515C3⋊Dic3—122no—
516C3⋊Dic3—124no—
517C3⋊Dic3—121no—
518C3⋊Dic3—121no—
519C3⋊Dic3—121no—
520C3×Dic3—22no—
521C3×Dic3—22no—
522C3×Dic3—42no—
523C3×Dic3—62no—
524C3×Dic3—62no—
525C3×Dic3—62no—
526C3×Dic3—62no—
527C3×Dic3—122no—
528C3×Dic3—122no—
529C3×Dic3—122no—
530C3×Dic3—121no—
531C3×Dic3—121no—
532C22×D4—91no—
533C23×C4—91no—
534C2×C22⋊C4—91no—
535C2×C22⋊C4—271no—
536C2×C22⋊C4—271no—
537#95—271no—
538#95—271no—
539C33#38611yescharacteristic, complemented, Sylow
540C23×C3—21no—
541C23×C3—21no—
542C23×C3—21no—
543C23×C3—32no—
544C23×C3—32no—
545C23×C3—32no—
546C23×C3—32no—
547C23×C3—32no—
548C23×C3—32no—
549C23×C3—32no—
550C23×C3—32no—
551C23×C3—41no—
552C23×C3—62no—
553C23×C3—62no—
554C23×C3—62no—
555C23×C3—62no—
556C23×C3—62no—
557C23×C3—62no—
558C23×C3—61no—
559C23×C3—61no—
560C23×C3—61no—
561C23×C3—61no—
562C23×C3—61no—
563C23×C3—61no—
564C23×C3—61no—
565C23×C3—61no—
566C23×C3—61no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—61no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—61no—
574C23×C3—61no—
575C23×C3—61no—
576C23×C3—61no—
577C23×C3—61no—
578C23×C3—121no—
579C23×C3—121no—
580C23×C3—121no—
581C23×C3—121no—
582C23×C3—121no—
583C23×C3—121no—
584C23×C3—121no—
585C23×C3—121no—
586C23×C3C2×D3211yescharacteristic
587C23×C3C2×D3211yescharacteristic
588C23×C3C2×D3211yescharacteristic
589C22×D3—21no—
590C22×D3—21no—
591C22×D3—21no—
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3D3×Dic312yes—
600C22×D3D3×Dic312yescomplemented
601C22×D3#62512yes—
602C22×D3#62612yes—
603C3×D4—188no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—62no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—92no—
612C2×C3×C4—92no—
613C2×C3×C4—121no—
614C2×C3×C4—121no—
615C2×C3×C4—188no—
616C2×C3×C4—181no—
617C2×C3×C4—181no—
618C2×C3×C4—181no—
619C2×C3×C4—181no—
620C2×C3×C4—181no—
621C2×C3×C4—181no—
622C2×C3×C4—181no—
623#67—68no—
624#67—68no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—32no—
630C2×Dic3—32no—
631C2×Dic3—62no—
632C2×Dic3—62no—
633C2×Dic3—68no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—62no—
643C2×Dic3—61no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—182no—
656C2×Dic3—182no—
657C2×Dic3—182no—
658C2×Dic3—181no—
659C2×Dic3—181no—
660C2×Dic3—181no—
661C2×Dic3—181no—
662C2×Dic3—181no—
663C2×Dic3—181no—
664C2×Dic3—181no—
665C2×Dic3—181no—
666C2×Dic3—181no—
667C2×Dic3—361no—
668C2×Dic3—361no—
669C2×Dic3—361no—
670C2×Dic3—361no—
671C2×Dic3—361no—
672C2×Dic3—361no—
673C2×Dic3—362no—
674C2×Dic3—362no—
675C2×Dic3—362no—
676C2×Dic3#62512yescomplemented
677C4×D3—68no—
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—21no—
695C2×C32—21no—
696C2×C32—21no—
697C2×C32—21no—
698C2×C32—21no—
699C2×C32—41no—
700C2×C32—41no—
701C2×C32—41no—
702C2×C32—41no—
703C2×C32—41no—
704C2×C32—41no—
705C2×C32—41no—
706C2×C32—64no—
707C2×C32—122no—
708C2×C32D3×C22⋊C411yescharacteristic
709C2×C32#67⋊C411yescharacteristic
710C2×C32#88311yescharacteristic
711C2×C32#88411yescharacteristic
712C2×C32C2×(C2×D3)⋊C411yescharacteristic
713C2×C32C4×#6711yescharacteristic
714C2×C32C4×#6711yescharacteristic
715C2×C32C4×#6711yescharacteristic
716C2×C32#92911yescharacteristic
717C2×C32#93011yescharacteristic
718C2×C32#93011yescharacteristic
719C2×C32D4×Dic311yescharacteristic
720C2×C32D4×Dic311yescharacteristic
721C2×C32#93511yescharacteristic
722C2×C32#93711yescharacteristic
723C2×C32#93711yescharacteristic
724C2×C32#93811yescharacteristic
725C2×C32#93911yescharacteristic
726C2×C32#93911yescharacteristic
727C2×C32C2×#21711yescharacteristic
728C2×C32#95311yescharacteristic
729C3×D3—24no—
730C3×D3—24no—
731C3×D3—44no—
732C3×D3—44no—
733C3×D3—42no—
734C3×D3—42no—
735C24—31no—
736C24—31no—
737C2×D4—94no—
738C2×D4—182no—
739C2×D4—182no—
740C22×C4—31no—
741C22×C4—91no—
742C22×C4—91no—
743C22×C4—91no—
744C22×C4—182no—
745C22×C4—182no—
746C22×C4—182no—
747C22×C4—271no—
748C22⋊C4—182no—
749C22⋊C4—542no—
750C22⋊C4—542no—
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—21no—
768C22×C3—21no—
769C22×C3—21no—
770C22×C3—21no—
771C22×C3—21no—
772C22×C3—34no—
773C22×C3—34no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—64no—
782C22×C3—64no—
783C22×C3—62no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—62no—
788C22×C3—62no—
789C22×C3—62no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—62no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3—62no—
801C22×C3—122no—
802C22×C3—122no—
803C22×C3—122no—
804C22×C3—122no—
805C22×C3—122no—
806C22×C3—122no—
807C22×C3—122no—
808C22×C3—122no—
809C22×C3—122no—
810C22×C3—122no—
811C22×C3—122no—
812C22×C3—122no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—121no—
819C22×C3—121no—
820C22×C3—121no—
821C22×C3#379511yescharacteristic
822C22×C3#379811yescharacteristic
823C22×C3C4×D3211yescharacteristic
824C22×C3D3×D1211yescharacteristic
825C22×C3C2×D3×Dic311yescharacteristic
826C22×C3C2×D3×Dic311yescharacteristic
827C22×C3#380411yescharacteristic
828C22×C3#380411yescharacteristic
829C22×C3#380411yescharacteristic
830C22×C3#380511yescharacteristic
831C22×C3C2×#62511yescharacteristic
832C22×C3C2×#62511yescharacteristic
833C22×C3C2×#62611yescharacteristic
834C22×C3D3×#6711yescharacteristic
835C22×C3D3×#6711yescharacteristic
836C22×C3D3×#6711yescharacteristic
837C22×C3D3×#6711yescharacteristic
838C22×C3D3×#6711yescharacteristic
839C22×C3D3×#6711yescharacteristic
840C22×C3D3×#6711yescharacteristic
841C22×C3#381111yescharacteristic
842C2×D3—22no—
843C2×D3—22no—
844C2×D3—22no—
845C2×D3—22no—
846C2×D3—22no—
847C2×D3—22no—
848C2×D3—22no—
849C2×D3—22no—
850C2×D3—22no—
851C2×D3—41no—
852C2×D3—41no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3(C2×D3)⋊Dic314yescomplemented
856C3×C4—62no—
857C3×C4—62no—
858C3×C4—122no—
859C3×C4—182no—
860C3×C4—182no—
861C3×C4—361no—
862Dic3—22no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—122no—
868Dic3—122no—
869Dic3—122no—
870Dic3—121no—
871Dic3—121no—
872Dic3—362no—
873Dic3—362no—
874Dic3—362no—
875Dic3—364no—
876Dic3—361no—
877Dic3—361no—
878Dic3—361no—
879C32—21no—
880C32—21no—
881C32—21no—
882C32—41no—
883C32#495611yescharacteristic, complemented
884C32#521311yescharacteristic, complemented
885C32#522011yescharacteristic, complemented
886C23—32no—
887C23—32no—
888C23—32no—
889C23—32no—
890C23—61no—
891C23—61no—
892C23—61no—
893C23—61no—
894C23—61no—
895C23—61no—
896C23—61no—
897C23—61no—
898C23—61no—
899C23—61no—
900C23D3311yescharacteristic
901D4—188no—
902C2×C4—32no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—92no—
906C2×C4—92no—
907C2×C4—188no—
908C2×C4—181no—
909C2×C4—181no—
910C2×C4—181no—
911C2×C4—181no—
912C2×C4—181no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—541no—
916C2×C4—541no—
917C2×C4—541no—
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—21no—
934C2×C3—21no—
935C2×C3—21no—
936C2×C3—21no—
937C2×C3—21no—
938C2×C3—21no—
939C2×C3—41no—
940C2×C3—41no—
941C2×C3—41no—
942C2×C3—41no—
943C2×C3—41no—
944C2×C3—41no—
945C2×C3—41no—
946C2×C3—64no—
947C2×C3—64no—
948C2×C3—124no—
949C2×C3—124no—
950C2×C3—122no—
951C2×C3—122no—
952C2×C3#6387911yescharacteristic
953C2×C3C4×#62511yescharacteristic
954C2×C3#6390511yescharacteristic
955C2×C3#6390611yescharacteristic
956C2×C3#6390811yescharacteristic
957C2×C3D3×(C2×D3)⋊C411yescharacteristic
958C2×C3C2×(C2×D3)⋊Dic311yescharacteristic
959C2×C3#6396111yescharacteristic
960C2×C3D3×#21711yescharacteristic
961C2×C3#6396911yescharacteristic
962C2×C3#6397011yescharacteristic
963C2×C3#6397111yescharacteristic
964C2×C3Dic3×#6711yescharacteristic
965C2×C3Dic3×#6711yescharacteristic
966C2×C3Dic3×#6711yescharacteristic
967C2×C3#67⋊Dic311yescharacteristic
968C2×C3#6397611yescharacteristic
969C2×C3#6397611yescharacteristic
970C2×C3#6397811yescharacteristic
971C2×C3#6397811yescharacteristic
972C2×C3#6398311yescharacteristic
973D3—24no—
974D3—42no—
975C22—34no—
976C22—62no—
977C22—62no—
978C22—62no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—121no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22D32×Dic311yescharacteristic
990C22D3×#62511yescharacteristic
991C22D3×#62511yescharacteristic
992C22D3×#62611yescharacteristic
993C22#8895211yescharacteristic
994C22#8895911yescharacteristic
995C22#8896111yescharacteristic
996C4—62no—
997C4—182no—
998C4—182no—
999C4—361no—
1000C4—1081no—
1001C3—21no—
1002C3—21no—
1003C3—21no—
1004C3—41no—
1005C3#1059138111yescharacteristic, complemented
1006C3#1059171011yescharacteristic, complemented
1007C3#1059172111yescharacteristic, complemented
1008C2—64no—
1009C2—122no—
1010C2D3×(C2×D3)⋊Dic311yescharacteristic
1011C2Dic3×#62511yescharacteristic
1012C2#1172292411yescharacteristic
1013C2#1172294611yescharacteristic
1014C2#1172295611yescharacteristic
1015C2#1172295811yescharacteristic
1016C2#1172298511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC23D33
commutatorC22×C33C22×C4
Fitting, socle, cosocleC23×C33C23
prime radicalC22×C3×#625C2
hypocenterC33#386
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×C3×D3×Dic3C2semidirect
3. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
4. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
5. C2×C3×(C2×D3)⋊Dic3C2semidirect
6. #11722082C2semidirect
7. #11722061C2semidirect
20. C2×C3×#625C4semidirect
32. C22×D3×Dic3D3semidirect
43. C2×(C2×D3)⋊Dic3D3semidirect
63. C22×C32×D3C2×C4semidirect
76. C2×C3×C3⋊Dic3C2×C4semidirect
77. C2×C3×C3⋊Dic3D4semidirect
80. C2×C32×Dic3D4semidirect
131. C2×#625Dic3semidirect
166. C2×C32×D3C22⋊C4semidirect
252. C22×C3×D3C4×D3semidirect
255. C22×C3×D3C2×Dic3semidirect
290. C2×C3⋊Dic3C2×Dic3semidirect
291. C2×C3⋊Dic3#67semidirect
329. C2×C3×Dic3#67semidirect
330. C2×C3×Dic3#67semidirect
507. C2×C3×D3(C2×D3)⋊C4semidirect
508. C2×C3×D3#217semidirect
539. C33#386semidirect
600. C22×D3D3×Dic3semidirect
676. C2×Dic3#625semidirect
855. C2×D3(C2×D3)⋊Dic3semidirect
883. C32#4956semidirect
884. C32#5213semidirect
885. C32#5220semidirect
1005. C3#10591381semidirect
1006. C3#10591710semidirect
1007. C3#10591721semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6252
C22×C3×D3×Dic32
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×C3×(C2×D3)⋊Dic32
#117220822
#117220612
#105917213
#105917103
#105913813