Finite Group Databasebeta

← C3×#10594383 #13173940

Subgroups — C3×#10594383 #13173940

Order 1728.

1364 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3797C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64106C211yesmaximal, characteristic, complemented
4C32×#897C211yesmaximal, characteristic, complemented
5C32×#887C211yesmaximal, characteristic, complemented
6C3×#63918C212yesmaximal, complemented
7C3×C4×#626C211yesmaximal, characteristic
8C3×#63895C212yesmaximal, complemented
9C3×#63893C212yesmaximal, complemented
10C3×#63880C212yesmaximal
11C3×#63866C211yesmaximal, characteristic, complemented
12C3×#5632—31nomaximal
13C3×Q8×D12—31nomaximal
14#10594383C311yesmaximal, characteristic, direct product factor
15C2×C3×C4×C3⋊D3C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×C4×D3C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×C3×#627C2212yes—
21C2×C3×#627C2212yes—
22C2×C3×#626C2211yescharacteristic
23C2×C3×#624C2212yes—
24C2×C3×D3×Dic3C2212yes—
25C3×#3797—24no—
26C3×D3×Dic6—24no—
27C33×C4⋊C4C2211yescharacteristic
28C3×#3752C2212yes—
29C3×C4⋊(C3⋊Dic3)C2212yes—
30C32×(C2×D3)⋊C4C2212yes—
31C32×C4⋊Dic3C2212yes—
32C32×Dic3⋊C4C2212yes—
33C32×C4×Dic3C2211yescharacteristic
34C32×C4×Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×Dic3⋊Dic3C2212yes—
37C3×Dic3⋊Dic3C2211yescharacteristic
38C3×#3722C2211yescharacteristic
39C3×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×C3×D3×Q8—31no—
41C2×C3×D3×Q8—31no—
42C2×C3×D3×Q8—31no—
43C22×C3×Dic6—31no—
44C2×#3797C2×C311yescharacteristic, complemented
45C2×D3×Dic6C2×C311yescharacteristic, complemented
46C32×C22⋊Q8—31no—
47C32×C4×Q8—31no—
48#64106C2×C311yescharacteristic, complemented
49C3×#944—31no—
50C3×C4×#67—31no—
51C3×#897—21no—
52C3×#897—31no—
53C3×#897—31no—
54C3×#897—32no—
55C3×#897—32no—
56C3×#897—61no—
57C3×#897D311yescharacteristic, complemented
58C3×#897C2×C311yescharacteristic, complemented
59C3×#896—32no—
60C3×#888—32no—
61C3×#887—21no—
62C3×#887D311yescharacteristic, complemented
63C3×#887C2×C311yescharacteristic, complemented
64C3×#67⋊C4—32no—
65C3×#878—32no—
66C3×C4×D12—31no—
67C3×C4×D12—32no—
68C3×#869—31no—
69C3×#869—32no—
70#63918C2×C312yescomplemented
71C4×#626C2×C311yescharacteristic
72#63895C2×C312yescomplemented
73#63893C2×C312yescomplemented
74#63880C2×C312yes—
75#63866C2×C311yescharacteristic, complemented
76C22×C3×C3⋊D3C2311yescharacteristic
77C22×C32×D3C2311yescharacteristic
78C2×C33×C4C2312yes—
79C2×C33×C4C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2312yes—
82C3×C4×C3⋊D3—22no—
83C3×#634—22no—
84C2×C32×Dic3C2312yes—
85C2×C32×Dic3C2311yescharacteristic
86C2×C32×Dic3C2311yescharacteristic
87C2×C32×Dic3C2312yes—
88C2×C32×Dic3C2311yescharacteristic
89C32×C4×D3—22no—
90C32×Dic6—22no—
91C32×Dic6D414yescomplemented
92C3×#627—24no—
93C3×#627—24no—
94C3×#626Q814yescomplemented
95C3×#624—24no—
96C3×D3×Dic3—24no—
97C3×D4×Q8—91no—
98#5632—31no—
99Q8×D12—31no—
100C2×C32×Q8—31no—
101C2×C32×Q8—31no—
102C22×C32×C4—31no—
103C2×C4×C3⋊D3C22×C311yescharacteristic
104C2×#634C22×C311yescharacteristic
105C2×C3×#67—31no—
106C22×C3×Dic3—32no—
107C3×D3×Q8—64no—
108C3×D3×Q8—64no—
109C3×D3×Q8—64no—
110C2×C3×D12—31no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—31no—
114C2×C3×C4×D3—31no—
115C2×C3×C4×D3—32no—
116C2×C3×C4×D3—32no—
117C2×C3×C4×D3—61no—
118C2×C3×C4×D3C2×D311yescharacteristic
119C2×C3×C4×D3C22×C311yescharacteristic
120C2×C3×Dic6—21no—
121C2×C3×Dic6—21no—
122C2×C3×Dic6—31no—
123C2×C3×Dic6—31no—
124C2×C3×Dic6—32no—
125C2×C3×Dic6—32no—
126C2×C3×Dic6—32no—
127C2×C3×Dic6—32no—
128C2×C3×Dic6—64no—
129C2×C3×Dic6—61no—
130C2×C3×Dic6C2×D311yescharacteristic
131C2×C3×Dic6C2×D311yescharacteristic
132C2×C3×Dic6C22×C311yescharacteristic
133C2×C3×Dic6C22×C311yescharacteristic
134C2×#627C22×C312yes—
135C2×#627C22×C312yes—
136C2×#626C22×C311yescharacteristic
137C2×#624C22×C312yes—
138C2×D3×Dic3C22×C312yes—
139#3797—24no—
140D3×Dic6—24no—
141C32×C4⋊C4—21no—
142C32×C4⋊C4—21no—
143C32×C4⋊C4—21no—
144C32×C4⋊C4—32no—
145C32×C4⋊C4—32no—
146C32×C4⋊C4—41no—
147C32×C4⋊C4C2×D311yescharacteristic
148C32×C4⋊C4C2×D311yescharacteristic
149C32×C4⋊C4C22×C311yescharacteristic
150C32×C22⋊C4—32no—
151C32×C42—32no—
152C32×C42—31no—
153#3752C22×C312yes—
154C4⋊(C3⋊Dic3)C22×C312yes—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—22no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—32no—
159C3×(C2×D3)⋊C4—32no—
160C3×(C2×D3)⋊C4—31no—
161C3×(C2×D3)⋊C4—31no—
162C3×(C2×D3)⋊C4—62no—
163C3×(C2×D3)⋊C4C2×D312yes—
164C3×(C2×D3)⋊C4C22×C312yes—
165C3×C4⋊Dic3—22no—
166C3×C4⋊Dic3—32no—
167C3×C4⋊Dic3—32no—
168C3×C4⋊Dic3—32no—
169C3×C4⋊Dic3—32no—
170C3×C4⋊Dic3—31no—
171C3×C4⋊Dic3—62no—
172C3×C4⋊Dic3C2×D312yes—
173C3×C4⋊Dic3C22×C312yes—
174C3×Dic3⋊C4—22no—
175C3×Dic3⋊C4—32no—
176C3×Dic3⋊C4—32no—
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4C2×D312yes—
179C3×Dic3⋊C4C22×C312yes—
180C3×C4×Dic3—22no—
181C3×C4×Dic3—21no—
182C3×C4×Dic3C2×D312yes—
183C3×C4×Dic3C2×D311yescharacteristic
184C3×C4×Dic3C22×C311yescharacteristic
185C3×C4×Dic3C22×C312yes—
186Dic3⋊Dic3C22×C312yes—
187Dic3⋊Dic3C22×C312yes—
188Dic3⋊Dic3C22×C311yescharacteristic
189#3722C22×C311yescharacteristic
190(C2×D3)⋊Dic3C22×C311yescharacteristic
191C22×C33C2411yescharacteristic
192C2×C3×C3⋊D3—21no—
193C2×C3×C3⋊D3—21no—
194C2×C3×C3⋊D3C2×Q812yescomplemented
195C2×C32×D3—21no—
196C2×C32×D3—21no—
197C2×C32×D3C2×Q812yescomplemented
198C33×C4—22no—
199C33×C4C2×D412yes—
200C3×C3⋊Dic3—22no—
201C3×C3⋊Dic3—21no—
202C32×Dic3—22no—
203C32×Dic3—21no—
204C32×Dic3—21no—
205C32×Dic3C2×D414yes—
206C32×Dic3C2×Q812yescomplemented
207C22×C3×Q8—91no—
208C22×C3×Q8—91no—
209C2×D3×Q8—31no—
210C2×D3×Q8—31no—
211C2×D3×Q8—31no—
212C22×Dic6—31no—
213C3×C4⋊Q8—92no—
214C3×C4⋊Q8—91no—
215C3×C22⋊Q8—31no—
216C3×C22⋊Q8—31no—
217C3×C22⋊Q8—61no—
218C3×C22⋊Q8—92no—
219C3×C22⋊Q8—92no—
220C3×C22⋊Q8—91no—
221C3×C4×Q8—31no—
222C3×C4×Q8—31no—
223C3×C4×Q8—61no—
224C3×C4×D4—92no—
225C3×C4×D4—91no—
226#944—31no—
227C4×#67—31no—
228#897—31no—
229#897—31no—
230#897—32no—
231#897—32no—
232#897—61no—
233#897C3×D311yescharacteristic, complemented
234#896—32no—
235#888—32no—
236#887C3×D311yescharacteristic, complemented
237#67⋊C4—32no—
238#878—32no—
239C4×D12—31no—
240C4×D12—32no—
241#869—31no—
242#869—32no—
243C23×C32—31no—
244C22×C3⋊D3C23×C311yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3—61no—
249C22×C3×D3C22×D311yescharacteristic
250C22×C3×D3C23×C311yescharacteristic
251C32×Q8—34no—
252C32×Q8—62no—
253C2×C32×C4—21no—
254C2×C32×C4—22no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—22no—
258C2×C32×C4—22no—
259C2×C32×C4—31no—
260C2×C32×C4—32no—
261C2×C32×C4—32no—
262C2×C32×C4—31no—
263C2×C32×C4—31no—
264C2×C32×C4—41no—
265C2×C32×C4—42no—
266C2×C32×C4—62no—
267C2×C32×C4C22×D312yes—
268C2×C32×C4C22×D312yes—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C23×C312yes—
272C2×C32×C4C23×C311yescharacteristic
273C2×C3⋊Dic3C23×C311yescharacteristic
274C2×C3⋊Dic3C23×C312yes—
275C4×C3⋊D3—22no—
276#634—22no—
277C3×#67—34no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—22no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—22no—
283C2×C3×Dic3—32no—
284C2×C3×Dic3—31no—
285C2×C3×Dic3—31no—
286C2×C3×Dic3—32no—
287C2×C3×Dic3—61no—
288C2×C3×Dic3—62no—
289C2×C3×Dic3—64no—
290C2×C3×Dic3C22×D311yescharacteristic
291C2×C3×Dic3C22×D312yes—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D312yes—
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C23×C311yescharacteristic
296C2×C3×Dic3C23×C311yescharacteristic
297C2×C3×Dic3C23×C312yes—
298C2×C3×Dic3C23×C312yes—
299C2×C3×Dic3C23×C311yescharacteristic
300C3×D12—34no—
301C3×C4×D3—22no—
302C3×C4×D3—22no—
303C3×C4×D3—42no—
304C3×C4×D3—64no—
305C3×C4×D3—64no—
306C3×C4×D3—62no—
307C3×C4×D3—62no—
308C3×C4×D3—64no—
309C3×C4×D3—122no—
310C3×Dic6—22no—
311C3×Dic6—22no—
312C3×Dic6—24no—
313C3×Dic6—42no—
314C3×Dic6—64no—
315C3×Dic6—64no—
316C3×Dic6—62no—
317C3×Dic6—62no—
318C3×Dic6—64no—
319C3×Dic6—64no—
320C3×Dic6—122no—
321C3×Dic6D1214yescomplemented
322C3×Dic6C3×D414yescomplemented
323#627—24no—
324#627—24no—
325#626C3×Q814yescomplemented
326#624—24no—
327D3×Dic3—24no—
328D4×Q8—91noSylow
329C2×C33C22×D411yescharacteristic
330C2×C33C22×Q811yescharacteristic
331C2×C332−1+411yescharacteristic
332C3×C3⋊D3—22no—
333C32×D3—22no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×Q8—31no—
337C2×C3×Q8—31no—
338C2×C3×Q8—61no—
339C2×C3×Q8—61no—
340C2×C3×Q8—92no—
341C2×C3×Q8—92no—
342C2×C3×Q8—91no—
343C2×C3×Q8—184no—
344C2×C3×Q8—184no—
345C2×C3×D4—91no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—92no—
350C22×C3×C4—92no—
351C22×C3×C4—91no—
352C2×#67—31no—
353C22×Dic3—32no—
354D3×Q8—64no—
355D3×Q8—64no—
356D3×Q8—64no—
357C2×D12—31no—
358C2×C4×D3—32no—
359C2×C4×D3—31no—
360C2×C4×D3—31no—
361C2×C4×D3—32no—
362C2×C4×D3—32no—
363C2×C4×D3—61no—
364C2×C4×D3C2×C3×D311yescharacteristic
365C2×Dic6—31no—
366C2×Dic6—31no—
367C2×Dic6—32no—
368C2×Dic6—32no—
369C2×Dic6—32no—
370C2×Dic6—32no—
371C2×Dic6—61no—
372C2×Dic6—64no—
373C2×Dic6C2×C3×D311yescharacteristic
374C2×Dic6C2×C3×D311yescharacteristic
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—32no—
379C3×C4⋊C4—32no—
380C3×C4⋊C4—32no—
381C3×C4⋊C4—32no—
382C3×C4⋊C4—41no—
383C3×C4⋊C4—62no—
384C3×C4⋊C4—62no—
385C3×C4⋊C4—92no—
386C3×C4⋊C4—91no—
387C3×C4⋊C4—92no—
388C3×C4⋊C4—92no—
389C3×C4⋊C4D3211yescharacteristic
390C3×C4⋊C4C2×C3×D311yescharacteristic
391C3×C4⋊C4C2×C3×D311yescharacteristic
392C3×C22⋊C4—32no—
393C3×C22⋊C4—32no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4—92no—
398C3×C42—32no—
399C3×C42—31no—
400C3×C42—32no—
401C3×C42—31no—
402C3×C42—61no—
403C3×C42—62no—
404#217—31no—
405(C2×D3)⋊C4—31no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—31no—
409(C2×D3)⋊C4—31no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4C2×C3×D312yes—
412C4⋊Dic3—32no—
413C4⋊Dic3—32no—
414C4⋊Dic3—32no—
415C4⋊Dic3—31no—
416C4⋊Dic3—32no—
417C4⋊Dic3—62no—
418C4⋊Dic3C2×C3×D312yes—
419Dic3⋊C4—32no—
420Dic3⋊C4—32no—
421Dic3⋊C4—31no—
422Dic3⋊C4C2×C3×D312yes—
423C4×Dic3C2×C3×D312yes—
424C4×Dic3C2×C3×D311yescharacteristic
425C22×C32—21no—
426C22×C32—21no—
427C22×C32—21no—
428C22×C32—32no—
429C22×C32—41no—
430C22×C32—61no—
431C22×C32—61no—
432C22×C32C23×D311yescharacteristic
433C22×C32C23×D311yescharacteristic
434C22×C32C24×C311yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3C2×C3×Q812yescomplemented
438C2×C3×D3—21no—
439C2×C3×D3—21no—
440C2×C3×D3—21no—
441C2×C3×D3—21no—
442C2×C3×D3—22no—
443C2×C3×D3—32no—
444C2×C3×D3—32no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—62no—
448C2×C3×D3—61no—
449C2×C3×D3—61no—
450C2×C3×D3—61no—
451C2×C3×D3—61no—
452C2×C3×D3—121no—
453C2×C3×D3—121no—
454C2×C3×D3D3×Q812yescomplemented
455C2×C3×D3C2×C3×Q812yescomplemented
456C32×C4—22no—
457C32×C4—22no—
458C32×C4—22no—
459C32×C4—22no—
460C32×C4—22no—
461C32×C4—22no—
462C32×C4—34no—
463C32×C4—32no—
464C32×C4—42no—
465C32×C4—42no—
466C32×C4—42no—
467C32×C4—42no—
468C32×C4—61no—
469C32×C4—62no—
470C32×C4—61no—
471C32×C4—82no—
472C32×C4C2×D1212yes—
473C32×C4D3×D412yes—
474C32×C4C2×C3×D412yes—
475C3⋊Dic3—22no—
476C3⋊Dic3—21no—
477C3×Dic3—22no—
478C3×Dic3—21no—
479C3×Dic3—21no—
480C3×Dic3—22no—
481C3×Dic3—21no—
482C3×Dic3—21no—
483C3×Dic3—24no—
484C3×Dic3—22no—
485C3×Dic3—42no—
486C3×Dic3—41no—
487C3×Dic3—41no—
488C3×Dic3—61no—
489C3×Dic3—62no—
490C3×Dic3—62no—
491C3×Dic3—61no—
492C3×Dic3—122no—
493C3×Dic3—121no—
494C3×Dic3C2×D1214yes—
495C3×Dic3D3×Q812yescomplemented
496C3×Dic3C2×C3×D414yes—
497C3×Dic3C2×C3×Q812yescomplemented
498C22×Q8—91no—
499C22×Q8—91no—
500C4⋊Q8—92no—
501C4⋊Q8—91no—
502C22⋊Q8—31no—
503C22⋊Q8—92no—
504C22⋊Q8—92no—
505C22⋊Q8—91no—
506C4×Q8—31no—
507C4×D4—92no—
508C4×D4—91no—
509C33D4×Q811yescharacteristic, complemented, Sylow
510C23×C3—31no—
511C23×C3—31no—
512C23×C3—61no—
513C23×C3—91no—
514C22×D3—31no—
515C22×D3—31no—
516C22×D3—61no—
517C22×D3C22×C3×D311yescharacteristic
518C3×Q8—34no—
519C3×Q8—34no—
520C3×Q8—64no—
521C3×Q8—62no—
522C3×Q8—62no—
523C3×Q8—122no—
524C3×Q8—184no—
525C3×Q8—184no—
526C3×Q8—182no—
527C3×D4—94no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—31no—
535C2×C3×C4—32no—
536C2×C3×C4—31no—
537C2×C3×C4—32no—
538C2×C3×C4—31no—
539C2×C3×C4—32no—
540C2×C3×C4—31no—
541C2×C3×C4—32no—
542C2×C3×C4—31no—
543C2×C3×C4—31no—
544C2×C3×C4—41no—
545C2×C3×C4—42no—
546C2×C3×C4—61no—
547C2×C3×C4—62no—
548C2×C3×C4—61no—
549C2×C3×C4—62no—
550C2×C3×C4—61no—
551C2×C3×C4—62no—
552C2×C3×C4—62no—
553C2×C3×C4—92no—
554C2×C3×C4—91no—
555C2×C3×C4—122no—
556C2×C3×C4—184no—
557C2×C3×C4—184no—
558C2×C3×C4—182no—
559C2×C3×C4C2×D3212yes—
560C2×C3×C4C2×D3211yescharacteristic
561C2×C3×C4C22×C3×D312yes—
562C2×C3×C4C22×C3×D312yes—
563C2×C3×C4C22×C3×D311yescharacteristic
564C2×C3×C4C22×C3×D311yescharacteristic
565#67—34no—
566C2×Dic3—32no—
567C2×Dic3—31no—
568C2×Dic3—31no—
569C2×Dic3—32no—
570C2×Dic3—61no—
571C2×Dic3—62no—
572C2×Dic3—64no—
573C2×Dic3C22×C3×D311yescharacteristic
574C2×Dic3C22×C3×D312yes—
575C2×Dic3C22×C3×D311yescharacteristic
576C2×Dic3C22×C3×D312yes—
577C2×Dic3C22×C3×D311yescharacteristic
578D12—34no—
579C4×D3—22no—
580C4×D3—64no—
581C4×D3—64no—
582C4×D3—62no—
583C4×D3—62no—
584C4×D3—64no—
585C4×D3—122no—
586Dic6—22no—
587Dic6—64no—
588Dic6—64no—
589Dic6—62no—
590Dic6—62no—
591Dic6—64no—
592Dic6—64no—
593Dic6—122no—
594Dic6C3×D1214yescomplemented
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—41no—
605C2×C32—41no—
606C2×C32—41no—
607C2×C32—62no—
608C2×C32C22×D1211yescharacteristic
609C2×C32C2×D3×D411yescharacteristic
610C2×C32C2×D3×Q811yescharacteristic
611C2×C32C2×D3×Q811yescharacteristic
612C2×C32#101011yescharacteristic
613C2×C32#101011yescharacteristic
614C2×C32C22×C3×D411yescharacteristic
615C2×C32C22×C3×Q811yescharacteristic
616C2×C32C3×2−1+411yescharacteristic
617C3⋊D3—22no—
618C3×D3—22no—
619C3×D3—22no—
620C3×D3—42no—
621C3×D3—62no—
622C3×D3—62no—
623C3×D3—122no—
624C2×Q8—31no—
625C2×Q8—31no—
626C2×Q8—92no—
627C2×Q8—92no—
628C2×Q8—91no—
629C2×Q8—184no—
630C2×Q8—184no—
631C2×D4—91no—
632C22×C4—31no—
633C22×C4—92no—
634C22×C4—92no—
635C22×C4—91no—
636C4⋊C4—32no—
637C4⋊C4—32no—
638C4⋊C4—92no—
639C4⋊C4—91no—
640C4⋊C4—92no—
641C4⋊C4—92no—
642C4⋊C4C3×D3211yescharacteristic
643C22⋊C4—32no—
644C22⋊C4—91no—
645C22⋊C4—91no—
646C22⋊C4—92no—
647C42—32no—
648C42—31no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—32no—
654C22×C3—41no—
655C22×C3—62no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—61no—
660C22×C3—92no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—181no—
664C22×C3—181no—
665C22×C3C22×D3211yescharacteristic
666C22×C3C23×C3×D311yescharacteristic
667C22×C3C23×C3×D311yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—32no—
671C2×D3—32no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3C3×D3×Q812yescomplemented
680C3×C4—22no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—34no—
687C3×C4—32no—
688C3×C4—34no—
689C3×C4—32no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4—42no—
694C3×C4—64no—
695C3×C4—62no—
696C3×C4—61no—
697C3×C4—62no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—62no—
701C3×C4—61no—
702C3×C4—82no—
703C3×C4—121no—
704C3×C4—122no—
705C3×C4—121no—
706C3×C4—182no—
707C3×C4—181no—
708C3×C4D3×D1212yes—
709C3×C4C2×C3×D1212yes—
710C3×C4C3×D3×D412yes—
711Dic3—22no—
712Dic3—21no—
713Dic3—21no—
714Dic3—61no—
715Dic3—62no—
716Dic3—61no—
717Dic3—62no—
718Dic3—122no—
719Dic3—121no—
720Dic3C2×C3×D1214yes—
721Dic3C3×D3×Q812yescomplemented
722C32—21no—
723C32—21no—
724C32—21no—
725C32—41no—
726C32Q8×D1211yescharacteristic, complemented
727C32#563211yescharacteristic, complemented
728C32C3×D4×Q811yescharacteristic, complemented
729C23—31no—
730C23—91no—
731Q8—34no—
732Q8—62no—
733Q8—184no—
734Q8—184no—
735Q8—182no—
736D4—94no—
737C2×C4—31no—
738C2×C4—32no—
739C2×C4—31no—
740C2×C4—32no—
741C2×C4—31no—
742C2×C4—62no—
743C2×C4—91no—
744C2×C4—92no—
745C2×C4—184no—
746C2×C4—184no—
747C2×C4—182no—
748C2×C4C2×C3×D3212yes—
749C2×C4C2×C3×D3211yescharacteristic
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—62no—
763C2×C3—62no—
764C2×C3—122no—
765C2×C3—182no—
766C2×C3C2×D3×D1211yescharacteristic
767C2×C3#6430911yescharacteristic
768C2×C3D32×Q811yescharacteristic
769C2×C3C22×C3×D1211yescharacteristic
770C2×C3C2×C3×D3×D411yescharacteristic
771C2×C3C2×C3×D3×Q811yescharacteristic
772C2×C3C2×C3×D3×Q811yescharacteristic
773C2×C3C3×#101011yescharacteristic
774C2×C3C3×#101011yescharacteristic
775D3—22no—
776D3—62no—
777D3—62no—
778D3—122no—
779C22—32no—
780C22—61no—
781C22—61no—
782C22—92no—
783C22—181no—
784C22—181no—
785C22C22×C3×D3211yescharacteristic
786C4—22no—
787C4—32no—
788C4—34no—
789C4—61no—
790C4—62no—
791C4—61no—
792C4—182no—
793C4—181no—
794C4C3×D3×D1212yes—
795C3—21no—
796C3—21no—
797C3—21no—
798C3—41no—
799C3#1059438311yescharacteristic, direct product factor
800C3C3×Q8×D1211yescharacteristic, complemented
801C3C3×#563211yescharacteristic, complemented
802C2—62no—
803C2—182no—
804C2C2×C3×D3×D1211yescharacteristic
805C2C3×#6430911yescharacteristic
806C2C3×D32×Q811yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
prime radicalC2×C3×#626C22
hypercenterC3×C4⋊C4D32
hypocenterC32C3×D4×Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3797C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64106C2semidirect
4. C32×#897C2semidirect
5. C32×#887C2semidirect
6. C3×#63918C2semidirect
8. C3×#63895C2semidirect
9. C3×#63893C2semidirect
11. C3×#63866C2semidirect
14. #10594383C3direct (N × H)
44. C2×#3797C2×C3semidirect
45. C2×D3×Dic6C2×C3semidirect
48. #64106C2×C3semidirect
57. C3×#897D3semidirect
58. C3×#897C2×C3semidirect
62. C3×#887D3semidirect
63. C3×#887C2×C3semidirect
70. #63918C2×C3semidirect
72. #63895C2×C3semidirect
73. #63893C2×C3semidirect
75. #63866C2×C3semidirect
91. C32×Dic6D4semidirect
94. C3×#626Q8semidirect
194. C2×C3×C3⋊D3C2×Q8semidirect
197. C2×C32×D3C2×Q8semidirect
206. C32×Dic3C2×Q8semidirect
233. #897C3×D3semidirect
236. #887C3×D3semidirect
321. C3×Dic6D12semidirect
322. C3×Dic6C3×D4semidirect
325. #626C3×Q8semidirect
437. C2×C3⋊D3C2×C3×Q8semidirect
454. C2×C3×D3D3×Q8semidirect
455. C2×C3×D3C2×C3×Q8semidirect
495. C3×Dic3D3×Q8semidirect
497. C3×Dic3C2×C3×Q8semidirect
509. C33D4×Q8semidirect
594. Dic6C3×D12semidirect
679. C2×D3C3×D3×Q8semidirect
721. Dic3C3×D3×Q8semidirect
726. C32Q8×D12semidirect
727. C32#5632semidirect
728. C32C3×D4×Q8semidirect
799. C3#10594383direct (N × H)
800. C3C3×Q8×D12semidirect
801. C3C3×#5632semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37972
C2×C3×D3×Dic62
C3×#641062
C32×#8972
C32×#8872
C3×#639182
C3×C4×#6262
C3×#638952
C3×#638932
C3×#638802
C3×#638662
C3×#56323
C3×Q8×D123
#105943833