Finite Group Databasebeta

← C3×#74378 #11801810

Subgroups — C3×#74378 #11801810

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×Dic3C211yesmaximal, characteristic
2C2×C3×#877C211yesmaximal, characteristic
3C2×C3×#877C211yesmaximal, characteristic
4C32×#385C211yesmaximal, characteristic
5C3×#5210C211yesmaximal, characteristic
6C3×#4976C212yesmaximal, complemented
7C3×Dic3×C4⋊C4C212yesmaximal, complemented
8C3×#4950C211yesmaximal, characteristic
9C3×#4946C211yesmaximal, characteristic
10C3×#4649C212yesmaximal, complemented
11C3×#4647C212yesmaximal, complemented
12C3×#2296—31nomaximal
13#74378C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C2×C32×C4⋊C4C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2212yes—
28C2×C3×C4×Dic3—24no—
29C2×C3×C4×Dic3C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2212yes—
34C3×#877—24no—
35C3×#877C418yescomplemented
36C32×#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×#117—31no—
41C2×C3×#117—31no—
42C22×C3×C42—31no—
43C22×C4×Dic3C2×C311yescharacteristic
44C2×#877C2×C311yescharacteristic
45C2×#877C2×C311yescharacteristic
46C3×#389—32no—
47C3×#389—32no—
48C3×#385—21no—
49C3×#385—31no—
50C3×#385—31no—
51C3×#385—31no—
52C3×#385D311yescharacteristic
53C3×#385C2×C311yescharacteristic
54C3×C4×C4⋊C4—32no—
55C3×C4×C4⋊C4—32no—
56#5210C2×C311yescharacteristic
57#4976C2×C312yescomplemented
58Dic3×C4⋊C4C2×C312yescomplemented
59#4950C2×C311yescharacteristic
60#4946C2×C311yescharacteristic
61#4649C2×C312yescomplemented
62#4647C2×C312yescomplemented
63C24×C32C2311yescharacteristic
64C22×C32×C4—22no—
65C22×C32×C4—24no—
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C3×Dic3—22no—
71C22×C3×Dic3—24no—
72C22×C3×Dic3C2×C414yes—
73C22×C3×Dic3D414yes—
74C22×C3×Dic3Q814yes—
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C32×C4⋊C4—24no—
82C32×C22⋊C4—22no—
83C32×C22⋊C4C2×C414yes—
84C3×#217—22no—
85C3×#217C2×C414yes—
86C3×C4⋊Dic3—24no—
87C3×Dic3⋊C4—24no—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—24no—
91C3×Dic3⋊C4C2×C418yescomplemented
92C3×C4×Dic3—22no—
93C3×C4×Dic3—22no—
94C3×C4×Dic3—24no—
95C3×C4×Dic3—24no—
96C3×C4×Dic3C2×C418yescomplemented
97#2296—31noSylow
98C23×C3×C4—21no—
99C23×C3×C4—31no—
100C23×C3×C4—31no—
101C23×C3×C4C2×D311yescharacteristic
102C23×C3×C4C22×C311yescharacteristic
103C23×Dic3C22×C311yescharacteristic
104C23×Dic3C22×C311yescharacteristic
105C3×#117—38no—
106C3×#117—64no—
107C2×C3×C4⋊C4—22no—
108C2×C3×C4⋊C4—32no—
109C2×C3×C4⋊C4—32no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4C2×D312yes—
115C2×C3×C4⋊C4C22×C312yes—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4C2×D311yescharacteristic
122C2×C3×C22⋊C4C22×C311yescharacteristic
123C2×C3×C22⋊C4C22×C311yescharacteristic
124C2×C3×C42—32no—
125C2×C3×C42—32no—
126C2×C3×C42—31no—
127C2×C3×C42—31no—
128C2×C3×C42—32no—
129C2×C3×C42—64no—
130C2×#217C22×C311yescharacteristic
131C2×#217C22×C311yescharacteristic
132C2×C4⋊Dic3C22×C312yes—
133C2×Dic3⋊C4C22×C311yescharacteristic
134C2×Dic3⋊C4C22×C312yes—
135C2×Dic3⋊C4C22×C312yes—
136C2×Dic3⋊C4C22×C311yescharacteristic
137C2×Dic3⋊C4C22×C312yes—
138C2×C4×Dic3—24no—
139C2×C4×Dic3C22×C312yes—
140C2×C4×Dic3C22×C311yescharacteristic
141C2×C4×Dic3C22×C312yes—
142C2×C4×Dic3C22×C311yescharacteristic
143C2×C4×Dic3C22×C312yes—
144#877—24no—
145#877C3×C418yescomplemented
146C3×#95—22no—
147C3×#95—32no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95C2×D312yes—
151C3×#95C22×C312yes—
152C3⋊#95C22×C312yes—
153C3⋊#95C22×C312yes—
154C3⋊#95C22×C312yes—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32C22×C412yes—
158C23×C32C2×D412yes—
159C23×C32C2×Q812yes—
160C23×C32C2411yescharacteristic
161C2×C32×C4—28no—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4C22×C414yes—
171C2×C32×C4#4114yes—
172C2×C3×Dic3—28no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3C4⋊C4116yescomplemented
182C2×C3×Dic3C22×C414yes—
183C2×C3×Dic3C22×C412yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C2×D412yes—
186C2×C3×Dic3C2×D412yes—
187C2×C3×Dic3C2×Q812yes—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3#4114yes—
190C2×#117—31no—
191C2×#117—31no—
192C22×C42—31no—
193#389—32no—
194#389—32no—
195#385—31no—
196#385—31no—
197#385—31no—
198#385C3×D311yescharacteristic
199C4×C4⋊C4—32no—
200C4×C4⋊C4—32no—
201C24×C3—21no—
202C24×C3C22×D311yescharacteristic
203C24×C3C23×C311yescharacteristic
204C22×C3×C4—22no—
205C22×C3×C4—22no—
206C22×C3×C4—24no—
207C22×C3×C4—24no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—34no—
213C22×C3×C4—34no—
214C22×C3×C4—34no—
215C22×C3×C4—31no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—44no—
222C22×C3×C4—42no—
223C22×C3×C4—64no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C23×C311yescharacteristic
230C22×C3×C4C23×C311yescharacteristic
231C22×C3×C4C23×C312yes—
232C22×C3×C4C23×C312yes—
233C22×Dic3—22no—
234C22×Dic3—24no—
235C22×Dic3C2×C3×C414yes—
236C22×Dic3C3×D414yes—
237C22×Dic3C3×Q814yes—
238C22×Dic3C23×C311yescharacteristic
239C22×Dic3C23×C311yescharacteristic
240C22×Dic3C23×C312yes—
241C22×Dic3C23×C312yes—
242C22×Dic3C23×C311yescharacteristic
243C22×Dic3C23×C311yescharacteristic
244C3×C4⋊C4—24no—
245C3×C4⋊C4—24no—
246C3×C4⋊C4—38no—
247C3×C4⋊C4—44no—
248C3×C4⋊C4—64no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—62no—
251C3×C4⋊C4—64no—
252C3×C4⋊C4—64no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—22no—
255C3×C22⋊C4—24no—
256C3×C22⋊C4—34no—
257C3×C22⋊C4—42no—
258C3×C22⋊C4—62no—
259C3×C22⋊C4C4×D314yes—
260C3×C22⋊C4C2×C3×C414yes—
261C3×C42—38no—
262C3×C42—64no—
263C3×C42—64no—
264C3×C42—62no—
265C3×C42—62no—
266#217—22no—
267#217C2×C3×C414yes—
268C4⋊Dic3—24no—
269Dic3⋊C4—24no—
270Dic3⋊C4—22no—
271Dic3⋊C4—22no—
272Dic3⋊C4—24no—
273Dic3⋊C4C2×C3×C418yescomplemented
274C4×Dic3—22no—
275C4×Dic3—22no—
276C4×Dic3—24no—
277C4×Dic3—24no—
278C4×Dic3C2×C3×C418yescomplemented
279C22×C32—24no—
280C22×C32—22no—
281C22×C32—22no—
282C22×C32—24no—
283C22×C32C2×C4⋊C414yes—
284C22×C32C23×C411yescharacteristic
285C22×C32C22×D411yescharacteristic
286C22×C32C22×Q811yescharacteristic
287C22×C32C2×#4112yes—
288C22×C32C2×#4112yes—
289C32×C4—24no—
290C32×C4—24no—
291C32×C4—41no—
292C32×C4—41no—
293C3×Dic3—24no—
294C3×Dic3—24no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3C2×C4⋊C414yes—
298C3×Dic3C2×C4⋊C414yes—
299C23×C4—31no—
300C23×C4—31no—
301C23×C4C2×C3×D311yescharacteristic
302#117—38no—
303#117—64no—
304C2×C4⋊C4—32no—
305C2×C4⋊C4—31no—
306C2×C4⋊C4—31no—
307C2×C4⋊C4—32no—
308C2×C4⋊C4—32no—
309C2×C4⋊C4—32no—
310C2×C4⋊C4C2×C3×D312yes—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4C2×C3×D311yescharacteristic
314C2×C22⋊C4C2×C3×D311yescharacteristic
315C2×C42—32no—
316C2×C42—31no—
317C2×C42—31no—
318C2×C42—32no—
319C2×C42—32no—
320C2×C42—64no—
321#95—32no—
322#95—32no—
323#95—32no—
324#95C2×C3×D312yes—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3C2×C4×D312yes—
336C23×C3D3×D412yes—
337C23×C3D3×Q812yes—
338C23×C3C22×C3×C412yes—
339C23×C3C2×C3×D412yes—
340C23×C3C2×C3×Q812yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C24×C311yescharacteristic
343C2×C3×C4—28no—
344C2×C3×C4—28no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—24no—
362C2×C3×C4—24no—
363C2×C3×C4—316no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—34no—
371C2×C3×C4—34no—
372C2×C3×C4—42no—
373C2×C3×C4—42no—
374C2×C3×C4—42no—
375C2×C3×C4—42no—
376C2×C3×C4—48no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—68no—
382C2×C3×C4—62no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4C2×C4×D314yes—
391C2×C3×C4#23714yes—
392C2×C3×C4C22×C3×C414yes—
393C2×C3×C4C3×#4114yes—
394C2×Dic3—28no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3C3×C4⋊C4116yescomplemented
404C2×Dic3C22×C3×C414yes—
405C2×Dic3C22×C3×C412yes—
406C2×Dic3C22×C3×C412yes—
407C2×Dic3C2×C3×D412yes—
408C2×Dic3C2×C3×D412yes—
409C2×Dic3C2×C3×Q812yes—
410C2×Dic3C2×C3×Q812yes—
411C2×Dic3C3×#4114yes—
412C2×C32—24no—
413C2×C32C22×C4⋊C411yescharacteristic
414C2×C32C4×#4112yes—
415C2×C32#52511yescharacteristic
416C2×C32#52511yescharacteristic
417C2×C32#53312yes—
418C24C22×C3×D311yescharacteristic
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—31no—
422C22×C4—31no—
423C22×C4—34no—
424C22×C4—34no—
425C22×C4—34no—
426C22×C4—32no—
427C22×C4—32no—
428C22×C4—31no—
429C22×C4—31no—
430C22×C4—64no—
431C22×C4—62no—
432C22×C4C22×C3×D311yescharacteristic
433C22×C4C22×C3×D311yescharacteristic
434C22×C4C22×C3×D312yes—
435C22×C4C22×C3×D312yes—
436C4⋊C4—24no—
437C4⋊C4—38no—
438C4⋊C4—62no—
439C4⋊C4—62no—
440C4⋊C4—64no—
441C4⋊C4—64no—
442C4⋊C4—64no—
443C22⋊C4—22no—
444C22⋊C4—34no—
445C22⋊C4—62no—
446C22⋊C4C3×C4×D314yes—
447C42—38no—
448C42—64no—
449C42—64no—
450C42—62no—
451C42—62no—
452C22×C3—22no—
453C22×C3—24no—
454C22×C3—22no—
455C22×C3—24no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—42no—
467C22×C3—44no—
468C22×C3—44no—
469C22×C3—42no—
470C22×C3D3×C4⋊C414yes—
471C22×C3C2×C3×C4⋊C414yes—
472C22×C3C22×C4×D311yescharacteristic
473C22×C3C2×D3×D411yescharacteristic
474C22×C3C2×#23712yes—
475C22×C3C2×D3×Q811yescharacteristic
476C22×C3D3×#4112yes—
477C22×C3C23×C3×C411yescharacteristic
478C22×C3C22×C3×D411yescharacteristic
479C22×C3C22×C3×Q811yescharacteristic
480C22×C3C2×C3×#4112yes—
481C22×C3C2×C3×#4112yes—
482C3×C4—24no—
483C3×C4—24no—
484C3×C4—24no—
485C3×C4—24no—
486C3×C4—34no—
487C3×C4—34no—
488C3×C4—44no—
489C3×C4—44no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4—41no—
493C3×C4—41no—
494C3×C4—64no—
495C3×C4—64no—
496C3×C4—81no—
497C3×C4—81no—
498C3×C4—121no—
499C3×C4—121no—
500Dic3—24no—
501Dic3—24no—
502Dic3—41no—
503Dic3—41no—
504Dic3C2×C3×C4⋊C414yes—
505Dic3C2×C3×C4⋊C414yes—
506C32#229611yescharacteristic, complemented, Sylow
507C23—22no—
508C23—22no—
509C23C2×C3×C4×D312yes—
510C23C3×D3×D412yes—
511C23C3×D3×Q812yes—
512C23C23×C3×D311yescharacteristic
513C2×C4—28no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—316no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—32no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—68no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—61no—
537C2×C4—61no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4C2×C3×C4×D314yes—
541C2×C4C3×#23714yes—
542C2×C3—24no—
543C2×C3—24no—
544C2×C3—21no—
545C2×C3—22no—
546C2×C3—21no—
547C2×C3—22no—
548C2×C3—21no—
549C2×C3—44no—
550C2×C3C2×D3×C4⋊C411yescharacteristic
551C2×C3C4×#23712yes—
552C2×C3#558611yescharacteristic
553C2×C3#562212yes—
554C2×C3#565611yescharacteristic
555C2×C3C22×C3×C4⋊C411yescharacteristic
556C2×C3C3×C4×#4112yes—
557C2×C3C3×#52511yescharacteristic
558C2×C3C3×#52511yescharacteristic
559C2×C3C3×#53312yes—
560C22—24no—
561C22—22no—
562C22—24no—
563C22—22no—
564C22C3×D3×C4⋊C414yes—
565C22C22×C3×C4×D311yescharacteristic
566C22C2×C3×D3×D411yescharacteristic
567C22C2×C3×#23712yes—
568C22C2×C3×D3×Q811yescharacteristic
569C22C3×D3×#4112yes—
570C4—24no—
571C4—24no—
572C4—34no—
573C4—34no—
574C4—41no—
575C4—41no—
576C4—64no—
577C4—64no—
578C4—121no—
579C4—121no—
580C3—21no—
581C3#7437811yescharacteristic, direct product factor
582C3C3×#229611yescharacteristic, complemented
583C2—24no—
584C2C2×C3×D3×C4⋊C411yescharacteristic
585C2C3×C4×#23712yes—
586C2C3×#558611yescharacteristic
587C2C3×#562212yes—
588C2C3×#565611yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#385C2
socleC23×C32C24
prime radicalC24×C32C23
cosocleC23×C3C24×C3
hypercenterC3×#385D3
hypocenterC3C3×#2296
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
6. C3×#4976C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
10. C3×#4649C2semidirect
11. C3×#4647C2semidirect
13. #74378C3direct (N × H)
35. C3×#877C4semidirect
57. #4976C2×C3semidirect
58. Dic3×C4⋊C4C2×C3semidirect
61. #4649C2×C3semidirect
62. #4647C2×C3semidirect
91. C3×Dic3⋊C4C2×C4semidirect
96. C3×C4×Dic3C2×C4semidirect
145. #877C3×C4semidirect
181. C2×C3×Dic3C4⋊C4semidirect
273. Dic3⋊C4C2×C3×C4semidirect
278. C4×Dic3C2×C3×C4semidirect
403. C2×Dic3C3×C4⋊C4semidirect
506. C32#2296semidirect
581. C3#74378direct (N × H)
582. C3C3×#2296semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×Dic32
C2×C3×#8772
C32×#3852
C3×#52102
C3×#49762
C3×Dic3×C4⋊C42
C3×#49502
C3×#49462
C3×#46492
C3×#46472
C3×#22963
#743783