Finite Group Databasebeta

← C3×#10594380 #13173937

Subgroups — C3×#10594380 #13173937

Order 1728.

1330 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3798C211yesmaximal, characteristic
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64106C211yesmaximal, characteristic, complemented
4C32×#897C211yesmaximal, characteristic, complemented
5C32×#892C211yesmaximal, characteristic, complemented
6C3×#63918C212yesmaximal, complemented
7C3×#63891C212yesmaximal, complemented
8C3×#63890C212yesmaximal, complemented
9C3×#63871C211yesmaximal, characteristic, complemented
10C3×#63857C211yesmaximal, characteristic, complemented
11C3×#63852C212yesmaximal, complemented
12C3×#5628—31nomaximal
13C3×#5526—31nomaximal
14#10594380C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#627C2212yes—
21C2×C3×#627C2211yescharacteristic
22C2×C3×#626C2211yescharacteristic
23C2×C3×#626C2211yescharacteristic
24C2×C3×#625C2211yescharacteristic
25C2×C3×D3×Dic3C2212yes—
26C3×#3798—24no—
27C3×D3×Dic6—24no—
28C33×C4⋊C4C2211yescharacteristic
29C3×#3752C2212yes—
30C3×C4⋊(C3⋊Dic3)C2212yes—
31C32×(C2×D3)⋊C4C2212yes—
32C32×(C2×D3)⋊C4C2212yes—
33C32×C4⋊Dic3C2211yescharacteristic
34C32×C4⋊Dic3C2212yes—
35C32×C4×Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2212yes—
38C3×#3722C2212yes—
39C3×(C2×D3)⋊Dic3C2212yes—
40C2×C3×D3×Q8—31no—
41C2×C3×#235—31no—
42C2×C3×#235—31no—
43C22×C3×Dic6—31no—
44C2×#3798C2×C311yescharacteristic
45C2×D3×Dic6C2×C311yescharacteristic, complemented
46C32×C22⋊Q8—31no—
47C32×#117—31no—
48#64106C2×C311yescharacteristic, complemented
49C3×#946—31no—
50C3×#924—31no—
51C3×#897—21no—
52C3×#897—31no—
53C3×#897—31no—
54C3×#897—31no—
55C3×#897—31no—
56C3×#897—61no—
57C3×#897D311yescharacteristic, complemented
58C3×#897C2×C311yescharacteristic, complemented
59C3×#894—32no—
60C3×#892—21no—
61C3×#892D311yescharacteristic, complemented
62C3×#892C2×C311yescharacteristic, complemented
63C3×#888—32no—
64C3×#886—32no—
65C3×#886—32no—
66C3×#885—32no—
67C3×#883—32no—
68C3×#875—32no—
69C3×#869—32no—
70#63918C2×C312yescomplemented
71#63891C2×C312yescomplemented
72#63890C2×C312yescomplemented
73#63871C2×C311yescharacteristic, complemented
74#63857C2×C311yescharacteristic, complemented
75#63852C2×C312yescomplemented
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C2×C33×C4C2312yes—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C3×C4×C3⋊D3—22no—
84C3×#634—22no—
85C2×C32×Dic3C2312yes—
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C32×C4×D3—22no—
90C32×C4×D3D414yes—
91C32×Dic6—22no—
92C3×#627—24no—
93C3×#627—22no—
94C3×#626—22no—
95C3×#626—22no—
96C3×#625—22no—
97C3×D3×Dic3—24no—
98C3×#536—91no—
99#5628—31no—
100#5526—31no—
101C2×C32×Q8—31no—
102C22×C32×C4—31no—
103C22×C32×C4—31no—
104C2×C4×C3⋊D3C22×C311yescharacteristic
105C2×#634C22×C311yescharacteristic
106C2×C3×#67—31no—
107C2×C3×#67—31no—
108C2×C3×#67—31no—
109C2×C3×#67—31no—
110C22×C3×Dic3—32no—
111C3×D3×Q8—64no—
112C3×#235—64no—
113C3×#235—64no—
114C2×C3×D12—31no—
115C2×C3×D12—31no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—32no—
119C2×C3×C4×D3—31no—
120C2×C3×C4×D3—31no—
121C2×C3×C4×D3—61no—
122C2×C3×C4×D3C2×D311yescharacteristic
123C2×C3×C4×D3C2×D311yescharacteristic
124C2×C3×C4×D3C22×C311yescharacteristic
125C2×C3×C4×D3C22×C311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6—31no—
128C2×C3×Dic6—31no—
129C2×C3×Dic6—32no—
130C2×C3×Dic6—31no—
131C2×C3×Dic6—32no—
132C2×C3×Dic6—31no—
133C2×C3×Dic6—64no—
134C2×C3×Dic6—61no—
135C2×C3×Dic6C2×D311yescharacteristic
136C2×C3×Dic6C22×C311yescharacteristic
137C2×#627C22×C312yes—
138C2×#627C22×C311yescharacteristic
139C2×#626C22×C311yescharacteristic
140C2×#626C22×C311yescharacteristic
141C2×#625C22×C311yescharacteristic
142C2×D3×Dic3C22×C312yes—
143#3798—24no—
144D3×Dic6—24no—
145C32×C4⋊C4—21no—
146C32×C4⋊C4—21no—
147C32×C4⋊C4—21no—
148C32×C4⋊C4—32no—
149C32×C4⋊C4—31no—
150C32×C4⋊C4—41no—
151C32×C4⋊C4C2×D311yescharacteristic
152C32×C4⋊C4C2×D311yescharacteristic
153C32×C4⋊C4C22×C311yescharacteristic
154C32×C22⋊C4—32no—
155C32×C22⋊C4—32no—
156C32×C42—32no—
157#3752C22×C312yes—
158C4⋊(C3⋊Dic3)C22×C312yes—
159C3×#217—32no—
160C3×(C2×D3)⋊C4—22no—
161C3×(C2×D3)⋊C4—22no—
162C3×(C2×D3)⋊C4—32no—
163C3×(C2×D3)⋊C4—32no—
164C3×(C2×D3)⋊C4—32no—
165C3×(C2×D3)⋊C4—32no—
166C3×(C2×D3)⋊C4—32no—
167C3×(C2×D3)⋊C4—62no—
168C3×(C2×D3)⋊C4C2×D312yes—
169C3×(C2×D3)⋊C4C2×D312yes—
170C3×(C2×D3)⋊C4C22×C312yes—
171C3×(C2×D3)⋊C4C22×C312yes—
172C3×C4⋊Dic3—21no—
173C3×C4⋊Dic3—22no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3—32no—
176C3×C4⋊Dic3—32no—
177C3×C4⋊Dic3—32no—
178C3×C4⋊Dic3—62no—
179C3×C4⋊Dic3C2×D312yes—
180C3×C4⋊Dic3C2×D311yescharacteristic
181C3×C4⋊Dic3C22×C311yescharacteristic
182C3×C4⋊Dic3C22×C312yes—
183C3×Dic3⋊C4—32no—
184C3×Dic3⋊C4—32no—
185C3×C4×Dic3—22no—
186C3×C4×Dic3C2×D312yes—
187C3×C4×Dic3C22×C312yes—
188Dic3⋊Dic3C22×C312yes—
189Dic3⋊Dic3C22×C312yes—
190#3722C22×C312yes—
191(C2×D3)⋊Dic3C22×C312yes—
192C22×C33C2411yescharacteristic
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3—21no—
195C2×C3×C3⋊D3—21no—
196C2×C32×D3—21no—
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3C2×D412yes—
202C33×C4—22no—
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—22no—
205C3×C3⋊Dic3—21no—
206C32×Dic3—22no—
207C32×Dic3—21no—
208C32×Dic3—22no—
209C32×Dic3C2×D412yes—
210C2×C3×#41—91no—
211C22×C3×Q8—91no—
212C2×D3×Q8—31no—
213C2×#235—31no—
214C2×#235—31no—
215C22×Dic6—31no—
216C3×C4⋊Q8—92no—
217C3×#124—92no—
218C3×#123—92no—
219C3×#123—92no—
220C3×C22⋊Q8—31no—
221C3×C22⋊Q8—31no—
222C3×C22⋊Q8—61no—
223C3×C22⋊Q8—91no—
224C3×C22⋊Q8—91no—
225C3×C22⋊Q8—91no—
226C3×#117—31no—
227C3×#117—31no—
228C3×#117—61no—
229#946—31no—
230#924—31no—
231#897—31no—
232#897—31no—
233#897—31no—
234#897—31no—
235#897—61no—
236#897C3×D311yescharacteristic, complemented
237#894—32no—
238#892C3×D311yescharacteristic, complemented
239#888—32no—
240#886—32no—
241#886—32no—
242#885—32no—
243#883—32no—
244#875—32no—
245#869—32no—
246C23×C32—31no—
247C23×C32—31no—
248C22×C3⋊D3C23×C311yescharacteristic
249C22×C3×D3—21no—
250C22×C3×D3—21no—
251C22×C3×D3—31no—
252C22×C3×D3—31no—
253C22×C3×D3—61no—
254C22×C3×D3C22×D311yescharacteristic
255C22×C3×D3C22×D311yescharacteristic
256C22×C3×D3C23×C311yescharacteristic
257C22×C3×D3C23×C311yescharacteristic
258C32×Q8—62no—
259C2×C32×C4—21no—
260C2×C32×C4—22no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—22no—
264C2×C32×C4—22no—
265C2×C32×C4—31no—
266C2×C32×C4—34no—
267C2×C32×C4—31no—
268C2×C32×C4—32no—
269C2×C32×C4—32no—
270C2×C32×C4—41no—
271C2×C32×C4—42no—
272C2×C32×C4—62no—
273C2×C32×C4C22×D312yes—
274C2×C32×C4C22×D312yes—
275C2×C32×C4C22×D311yescharacteristic
276C2×C32×C4C22×D311yescharacteristic
277C2×C32×C4C23×C312yes—
278C2×C32×C4C23×C311yescharacteristic
279C2×C3⋊Dic3C23×C312yes—
280C2×C3⋊Dic3C23×C311yescharacteristic
281C4×C3⋊D3—22no—
282#634—22no—
283C3×#67—62no—
284C3×#67—62no—
285C3×#67—62no—
286C3×#67—62no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—22no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—32no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—32no—
295C2×C3×Dic3—61no—
296C2×C3×Dic3—62no—
297C2×C3×Dic3—64no—
298C2×C3×Dic3C22×D312yes—
299C2×C3×Dic3C22×D311yescharacteristic
300C2×C3×Dic3C22×D312yes—
301C2×C3×Dic3C22×D311yescharacteristic
302C2×C3×Dic3C23×C312yes—
303C2×C3×Dic3C23×C312yes—
304C2×C3×Dic3C23×C311yescharacteristic
305C2×C3×Dic3C23×C311yescharacteristic
306C3×D12—62no—
307C3×D12—62no—
308C3×C4×D3—22no—
309C3×C4×D3—22no—
310C3×C4×D3—24no—
311C3×C4×D3—42no—
312C3×C4×D3—64no—
313C3×C4×D3—62no—
314C3×C4×D3—62no—
315C3×C4×D3—122no—
316C3×C4×D3D1214yes—
317C3×C4×D3C3×D414yes—
318C3×Dic6—22no—
319C3×Dic6—22no—
320C3×Dic6—42no—
321C3×Dic6—64no—
322C3×Dic6—62no—
323C3×Dic6—62no—
324C3×Dic6—62no—
325C3×Dic6—62no—
326C3×Dic6—64no—
327C3×Dic6—122no—
328#627—24no—
329#627—22no—
330#626—22no—
331#626—22no—
332#625—22no—
333D3×Dic3—24no—
334#536—91noSylow
335C2×C33C22×D411yescharacteristic
336C2×C332−1+411yescharacteristic
337C2×C332−1+411yescharacteristic
338C3×C3⋊D3—41no—
339C32×D3—22no—
340C32×D3—41no—
341C3×#41—184no—
342C2×C3×Q8—31no—
343C2×C3×Q8—31no—
344C2×C3×Q8—61no—
345C2×C3×Q8—92no—
346C2×C3×Q8—91no—
347C2×C3×Q8—91no—
348C2×C3×Q8—184no—
349C2×C3×D4—91no—
350C2×C3×D4—91no—
351C2×C3×D4—91no—
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—92no—
359C22×C3×C4—91no—
360C2×#67—31no—
361C2×#67—31no—
362C2×#67—31no—
363C2×#67—31no—
364C22×Dic3—32no—
365D3×Q8—64no—
366#235—64no—
367#235—64no—
368C2×D12—31no—
369C2×D12—31no—
370C2×C4×D3—32no—
371C2×C4×D3—31no—
372C2×C4×D3—31no—
373C2×C4×D3—61no—
374C2×C4×D3C2×C3×D311yescharacteristic
375C2×C4×D3C2×C3×D311yescharacteristic
376C2×Dic6—31no—
377C2×Dic6—31no—
378C2×Dic6—31no—
379C2×Dic6—32no—
380C2×Dic6—32no—
381C2×Dic6—31no—
382C2×Dic6—61no—
383C2×Dic6—64no—
384C2×Dic6C2×C3×D311yescharacteristic
385C3×C4⋊C4—21no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—31no—
389C3×C4⋊C4—32no—
390C3×C4⋊C4—32no—
391C3×C4⋊C4—31no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—61no—
394C3×C4⋊C4—62no—
395C3×C4⋊C4—92no—
396C3×C4⋊C4—92no—
397C3×C4⋊C4—92no—
398C3×C4⋊C4D3211yescharacteristic
399C3×C4⋊C4C2×C3×D311yescharacteristic
400C3×C4⋊C4C2×C3×D311yescharacteristic
401C3×C22⋊C4—32no—
402C3×C22⋊C4—32no—
403C3×C22⋊C4—32no—
404C3×C22⋊C4—32no—
405C3×C22⋊C4—62no—
406C3×C22⋊C4—62no—
407C3×C22⋊C4—92no—
408C3×C22⋊C4—92no—
409C3×C22⋊C4—92no—
410C3×C42—32no—
411C3×C42—32no—
412C3×C42—62no—
413#217—32no—
414(C2×D3)⋊C4—32no—
415(C2×D3)⋊C4—32no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—32no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4C2×C3×D312yes—
421(C2×D3)⋊C4C2×C3×D312yes—
422C4⋊Dic3—32no—
423C4⋊Dic3—32no—
424C4⋊Dic3—32no—
425C4⋊Dic3—32no—
426C4⋊Dic3—62no—
427C4⋊Dic3C2×C3×D312yes—
428C4⋊Dic3C2×C3×D311yescharacteristic
429Dic3⋊C4—32no—
430Dic3⋊C4—32no—
431C4×Dic3C2×C3×D312yes—
432C22×C32—21no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32—32no—
436C22×C32—41no—
437C22×C32—61no—
438C22×C32—61no—
439C22×C32—61no—
440C22×C32—61no—
441C22×C32—61no—
442C22×C32C23×D311yescharacteristic
443C22×C32C23×D311yescharacteristic
444C22×C32C24×C311yescharacteristic
445C2×C3⋊D3—21no—
446C2×C3⋊D3—21no—
447C2×C3⋊D3—21no—
448C2×C3×D3—21no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—22no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—62no—
465C2×C3×D3—61no—
466C2×C3×D3—61no—
467C2×C3×D3—61no—
468C2×C3×D3—61no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3—121no—
472C2×C3×D3—121no—
473C2×C3×D3C2×D1212yes—
474C2×C3×D3C2×C3×D412yes—
475C32×C4—22no—
476C32×C4—22no—
477C32×C4—22no—
478C32×C4—22no—
479C32×C4—22no—
480C32×C4—22no—
481C32×C4—32no—
482C32×C4—42no—
483C32×C4—42no—
484C32×C4—42no—
485C32×C4—42no—
486C32×C4—62no—
487C32×C4—61no—
488C32×C4—62no—
489C32×C4—82no—
490C32×C4C2×D1212yes—
491C32×C4D3×D412yes—
492C32×C4C2×C3×D412yes—
493C3⋊Dic3—22no—
494C3⋊Dic3—21no—
495C3×Dic3—22no—
496C3×Dic3—21no—
497C3×Dic3—22no—
498C3×Dic3—22no—
499C3×Dic3—21no—
500C3×Dic3—22no—
501C3×Dic3—22no—
502C3×Dic3—42no—
503C3×Dic3—41no—
504C3×Dic3—42no—
505C3×Dic3—62no—
506C3×Dic3—61no—
507C3×Dic3—62no—
508C3×Dic3—61no—
509C3×Dic3—122no—
510C3×Dic3—121no—
511C3×Dic3C2×D1212yes—
512C3×Dic3C2×C3×D412yes—
513C2×#41—91no—
514C22×Q8—91no—
515C4⋊Q8—92no—
516#124—92no—
517#123—92no—
518#123—92no—
519C22⋊Q8—31no—
520C22⋊Q8—91no—
521C22⋊Q8—91no—
522C22⋊Q8—91no—
523#117—31no—
524C33#53611yescharacteristic, complemented, Sylow
525C23×C3—31no—
526C23×C3—31no—
527C23×C3—31no—
528C23×C3—31no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—91no—
532C22×D3—31no—
533C22×D3—31no—
534C22×D3—61no—
535C22×D3C22×C3×D311yescharacteristic
536C22×D3C22×C3×D311yescharacteristic
537C3×Q8—62no—
538C3×Q8—62no—
539C3×Q8—122no—
540C3×Q8—184no—
541C3×Q8—182no—
542C3×Q8—182no—
543C3×D4—182no—
544C3×D4—182no—
545C3×D4—182no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—22no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—34no—
555C2×C3×C4—34no—
556C2×C3×C4—32no—
557C2×C3×C4—32no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—32no—
561C2×C3×C4—32no—
562C2×C3×C4—41no—
563C2×C3×C4—42no—
564C2×C3×C4—64no—
565C2×C3×C4—61no—
566C2×C3×C4—62no—
567C2×C3×C4—62no—
568C2×C3×C4—61no—
569C2×C3×C4—62no—
570C2×C3×C4—62no—
571C2×C3×C4—92no—
572C2×C3×C4—91no—
573C2×C3×C4—122no—
574C2×C3×C4—184no—
575C2×C3×C4—182no—
576C2×C3×C4C2×D3212yes—
577C2×C3×C4C2×D3211yescharacteristic
578C2×C3×C4C22×C3×D312yes—
579C2×C3×C4C22×C3×D312yes—
580C2×C3×C4C22×C3×D311yescharacteristic
581C2×C3×C4C22×C3×D311yescharacteristic
582#67—62no—
583#67—62no—
584#67—62no—
585#67—62no—
586C2×Dic3—31no—
587C2×Dic3—32no—
588C2×Dic3—31no—
589C2×Dic3—32no—
590C2×Dic3—61no—
591C2×Dic3—62no—
592C2×Dic3—64no—
593C2×Dic3C22×C3×D312yes—
594C2×Dic3C22×C3×D311yescharacteristic
595C2×Dic3C22×C3×D312yes—
596C2×Dic3C22×C3×D311yescharacteristic
597D12—62no—
598D12—62no—
599C4×D3—22no—
600C4×D3—64no—
601C4×D3—62no—
602C4×D3—62no—
603C4×D3—122no—
604C4×D3C3×D1214yes—
605Dic6—22no—
606Dic6—64no—
607Dic6—62no—
608Dic6—62no—
609Dic6—62no—
610Dic6—62no—
611Dic6—64no—
612Dic6—122no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—21no—
616C2×C32—21no—
617C2×C32—21no—
618C2×C32—21no—
619C2×C32—21no—
620C2×C32—21no—
621C2×C32—21no—
622C2×C32—41no—
623C2×C32—41no—
624C2×C32—41no—
625C2×C32—62no—
626C2×C32—121no—
627C2×C32C22×D1211yescharacteristic
628C2×C32C2×D3×D411yescharacteristic
629C2×C32#100711yescharacteristic
630C2×C32#101011yescharacteristic
631C2×C32#101011yescharacteristic
632C2×C32#101011yescharacteristic
633C2×C32C22×C3×D411yescharacteristic
634C2×C32C3×2−1+411yescharacteristic
635C2×C32C3×2−1+411yescharacteristic
636C3⋊D3—41no—
637C3×D3—22no—
638C3×D3—22no—
639C3×D3—42no—
640C3×D3—42no—
641C3×D3—41no—
642C3×D3—41no—
643C3×D3—122no—
644C3×D3—121no—
645C3×D3—121no—
646#41—184no—
647C2×Q8—31no—
648C2×Q8—92no—
649C2×Q8—91no—
650C2×Q8—91no—
651C2×Q8—184no—
652C2×D4—91no—
653C2×D4—91no—
654C2×D4—91no—
655C22×C4—31no—
656C22×C4—31no—
657C22×C4—92no—
658C22×C4—91no—
659C4⋊C4—31no—
660C4⋊C4—32no—
661C4⋊C4—92no—
662C4⋊C4—92no—
663C4⋊C4—92no—
664C4⋊C4C3×D3211yescharacteristic
665C22⋊C4—32no—
666C22⋊C4—32no—
667C22⋊C4—92no—
668C22⋊C4—92no—
669C22⋊C4—92no—
670C42—32no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—32no—
675C22×C3—32no—
676C22×C3—41no—
677C22×C3—62no—
678C22×C3—62no—
679C22×C3—61no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—61no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—121no—
690C22×C3—121no—
691C22×C3—121no—
692C22×C3—121no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3—181no—
696C22×C3C22×D3211yescharacteristic
697C22×C3C23×C3×D311yescharacteristic
698C22×C3C23×C3×D311yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—62no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—61no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—121no—
712C2×D3—121no—
713C2×D3C2×C3×D1212yes—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—32no—
721C3×C4—32no—
722C3×C4—42no—
723C3×C4—42no—
724C3×C4—42no—
725C3×C4—42no—
726C3×C4—62no—
727C3×C4—61no—
728C3×C4—62no—
729C3×C4—62no—
730C3×C4—62no—
731C3×C4—61no—
732C3×C4—62no—
733C3×C4—82no—
734C3×C4—121no—
735C3×C4—122no—
736C3×C4—122no—
737C3×C4—181no—
738C3×C4—182no—
739C3×C4D3×D1212yes—
740C3×C4C2×C3×D1212yes—
741C3×C4C3×D3×D412yes—
742Dic3—22no—
743Dic3—21no—
744Dic3—22no—
745Dic3—62no—
746Dic3—61no—
747Dic3—62no—
748Dic3—61no—
749Dic3—122no—
750Dic3—121no—
751Dic3C2×C3×D1212yes—
752C32—21no—
753C32—21no—
754C32—21no—
755C32—41no—
756C32#552611yescharacteristic, complemented
757C32#562811yescharacteristic, complemented
758C32C3×#53611yescharacteristic, complemented
759C23—31no—
760C23—31no—
761C23—91no—
762Q8—62no—
763Q8—184no—
764Q8—182no—
765Q8—182no—
766D4—182no—
767D4—182no—
768D4—182no—
769C2×C4—31no—
770C2×C4—34no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—31no—
774C2×C4—62no—
775C2×C4—92no—
776C2×C4—91no—
777C2×C4—184no—
778C2×C4—182no—
779C2×C4C2×C3×D3212yes—
780C2×C4C2×C3×D3211yescharacteristic
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—21no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—41no—
791C2×C3—41no—
792C2×C3—41no—
793C2×C3—62no—
794C2×C3—62no—
795C2×C3—122no—
796C2×C3—122no—
797C2×C3—121no—
798C2×C3—121no—
799C2×C3—361no—
800C2×C3C2×D3×D1211yescharacteristic
801C2×C3#6430911yescharacteristic
802C2×C3#6431511yescharacteristic
803C2×C3C22×C3×D1211yescharacteristic
804C2×C3C2×C3×D3×D411yescharacteristic
805C2×C3C3×#100711yescharacteristic
806C2×C3C3×#101011yescharacteristic
807C2×C3C3×#101011yescharacteristic
808C2×C3C3×#101011yescharacteristic
809D3—22no—
810D3—41no—
811D3—122no—
812D3—121no—
813D3—121no—
814C22—32no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—181no—
821C22—181no—
822C22—181no—
823C22C22×C3×D3211yescharacteristic
824C4—22no—
825C4—32no—
826C4—61no—
827C4—62no—
828C4—62no—
829C4—181no—
830C4—182no—
831C4C3×D3×D1212yes—
832C3—21no—
833C3—21no—
834C3—21no—
835C3—41no—
836C3#1059438011yescharacteristic, direct product factor
837C3C3×#552611yescharacteristic, complemented
838C3C3×#562811yescharacteristic, complemented
839C2—62no—
840C2—121no—
841C2—361no—
842C2C2×C3×D3×D1211yescharacteristic
843C2C3×#6430911yescharacteristic
844C2C3×#6431511yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#3798C2
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#536
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64106C2semidirect
4. C32×#897C2semidirect
5. C32×#892C2semidirect
6. C3×#63918C2semidirect
7. C3×#63891C2semidirect
8. C3×#63890C2semidirect
9. C3×#63871C2semidirect
10. C3×#63857C2semidirect
11. C3×#63852C2semidirect
14. #10594380C3direct (N × H)
45. C2×D3×Dic6C2×C3semidirect
48. #64106C2×C3semidirect
57. C3×#897D3semidirect
58. C3×#897C2×C3semidirect
61. C3×#892D3semidirect
62. C3×#892C2×C3semidirect
70. #63918C2×C3semidirect
71. #63891C2×C3semidirect
72. #63890C2×C3semidirect
73. #63871C2×C3semidirect
74. #63857C2×C3semidirect
75. #63852C2×C3semidirect
236. #897C3×D3semidirect
238. #892C3×D3semidirect
524. C33#536semidirect
756. C32#5526semidirect
757. C32#5628semidirect
758. C32C3×#536semidirect
836. C3#10594380direct (N × H)
837. C3C3×#5526semidirect
838. C3C3×#5628semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37982
C2×C3×D3×Dic62
C3×#641062
C32×#8972
C32×#8922
C3×#639182
C3×#638912
C3×#638902
C3×#638712
C3×#638572
C3×#638522
C3×#56283
C3×#55263
#105943803