Finite Group Databasebeta

← C3×#77682 #11824529

Subgroups — C3×#77682 #11824529

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 699 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×C3×#884C212yesmaximal, complemented
3C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
4C32×#397C211yesmaximal, characteristic, complemented
5C3×#4983C211yesmaximal, characteristic, complemented
6C3×#4960C211yesmaximal, characteristic, complemented
7C3×#4958C212yesmaximal, complemented
8C3×#4672C211yesmaximal, characteristic, complemented
9C3×#4669C212yesmaximal, complemented
10C3×#4665C212yesmaximal, complemented
11C3×D3×#95C211yesmaximal, characteristic, complemented
12C3×#2543—31nomaximal
13#77682C311yesmaximal, characteristic, direct product factor
14C22×C3×#67C2212yes—
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C22×C3×D12C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2212yes—
23C2×C32×C22⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#895—24no—
33C3×#884—28no—
34C3×#67⋊C4—24no—
35C32×#95C2211yescharacteristic
36C32×#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2212yes—
40C2×C3×#121—31no—
41C2×C3×#121—32no—
42C2×C3×C4×D4—31no—
43C2×#895C2×C311yescharacteristic, complemented
44C2×#884C2×C312yescomplemented
45C2×#67⋊C4C2×C311yescharacteristic, complemented
46C3×#398—31no—
47C3×#397—21no—
48C3×#397D311yescharacteristic, complemented
49C3×#397C2×C311yescharacteristic, complemented
50C3×#394—31no—
51C3×#392—31no—
52C3×#388—32no—
53C3×#386—32no—
54C3×#386—32no—
55C2×C3×#95—31no—
56#4983C2×C311yescharacteristic, complemented
57#4960C2×C311yescharacteristic, complemented
58#4958C2×C312yescomplemented
59#4672C2×C311yescharacteristic, complemented
60#4669C2×C312yescomplemented
61#4665C2×C312yescomplemented
62D3×#95C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C32×C4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×C3×#67—22no—
71C2×C3×#67—22no—
72C2×C3×#67—24no—
73C2×C3×#67—24no—
74C2×C3×#67—42no—
75C2×C3×#67D414yescomplemented
76C22×C3×Dic3—22no—
77C22×C3×Dic3—42no—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2312yes—
82C2×C3×D12—24no—
83C2×C3×D12—24no—
84C2×C3×D12—24no—
85C2×C3×D12—22no—
86C2×C3×D12—42no—
87C2×C3×C4×D3—24no—
88C2×C3×C4×D3—24no—
89C2×C3×C4×D3—42no—
90C2×C3×C4×D3—42no—
91C2×C3×C4×D3D414yescomplemented
92C32×C4⋊C4—22no—
93C32×C22⋊C4—24no—
94C32×C22⋊C4—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×(C2×D3)⋊C4—24no—
97C3×(C2×D3)⋊C4—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—42no—
100C3×Dic3⋊C4—22no—
101C3×Dic3⋊C4—24no—
102C3×C4×Dic3—22no—
103#2543—31noSylow
104C22×C3×D4—31no—
105C22×C3×D4—32no—
106C22×C3×D4—32no—
107C22×C3×D4—31no—
108C23×C3×C4—31no—
109C23×C3×C4—31no—
110C23×C3×C4—32no—
111C22×#67C22×C312yes—
112C22×#67C22×C311yescharacteristic
113C23×Dic3C22×C311yescharacteristic
114C22×D12C22×C312yes—
115C22×D12C22×C311yescharacteristic
116C22×C4×D3C22×C312yes—
117C22×C4×D3C22×C311yescharacteristic
118C3×#121—68no—
119C3×#121—64no—
120C3×C4×D4—64no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C4⋊C4C22×C311yescharacteristic
126C2×C3×C22⋊C4—21no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C22⋊C4C2×D312yes—
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C22×C312yes—
136C2×C3×C22⋊C4C22×C311yescharacteristic
137C2×C3×C42—31no—
138C2×(C2×D3)⋊C4C22×C311yescharacteristic
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×(C2×D3)⋊C4C22×C312yes—
141C2×(C2×D3)⋊C4C22×C312yes—
142C2×(C2×D3)⋊C4C22×C312yes—
143C2×Dic3⋊C4C22×C312yes—
144C2×Dic3⋊C4C22×C311yescharacteristic
145C2×C4×Dic3C22×C311yescharacteristic
146#895—24no—
147#884—28no—
148#67⋊C4—24no—
149C3×#95—21no—
150C3×#95—22no—
151C3×#95—32no—
152C3×#95—31no—
153C3×#95—32no—
154C3×#95C2×D311yescharacteristic
155C3×#95C2×D312yes—
156C3×#95C22×C311yescharacteristic
157C3×#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C3⋊#95C22×C311yescharacteristic
160C3⋊#95C22×C312yes—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—22no—
164C23×C32—22no—
165C23×C32C2×D412yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3—22no—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3#4112yes—
179C2×C32×C4—22no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4—22no—
187C2×C32×C4—22no—
188C2×C32×C4C2×D412yes—
189C3×#67—28no—
190C3×#67—48no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—44no—
199C2×C3×Dic3C2×D412yes—
200C2×C3×Dic3C2×D412yes—
201C2×C3×Dic3#4114yes—
202C3×D12—44no—
203C3×D12—48no—
204C3×C4×D3—44no—
205C3×C4×D3—48no—
206C2×#121—31no—
207C2×#121—32no—
208C2×C4×D4—31no—
209#398—31no—
210#397C3×D311yescharacteristic, complemented
211#394—31no—
212#392—31no—
213#388—32no—
214#386—32no—
215#386—32no—
216C2×#95—31no—
217C24×C3—21no—
218C24×C3—31no—
219C24×C3—32no—
220C24×C3C22×D311yescharacteristic
221C24×C3C23×C311yescharacteristic
222C23×D3C23×C312yes—
223C23×D3C23×C311yescharacteristic
224C2×C3×D4—34no—
225C2×C3×D4—64no—
226C2×C3×D4—64no—
227C2×C3×D4—64no—
228C2×C3×D4—64no—
229C2×C3×D4—62no—
230C2×C3×D4—62no—
231C2×C3×D4—64no—
232C2×C3×D4—62no—
233C2×C3×D4—122no—
234C2×C3×D4—122no—
235C22×C3×C4—21no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—32no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—34no—
243C22×C3×C4—31no—
244C22×C3×C4—64no—
245C22×C3×C4—64no—
246C22×C3×C4—62no—
247C22×C3×C4—122no—
248C22×C3×C4—122no—
249C22×C3×C4—122no—
250C22×C3×C4C22×D312yes—
251C22×C3×C4C22×D312yes—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C23×C312yes—
255C22×C3×C4C23×C312yes—
256C22×C3×C4C23×C311yescharacteristic
257C22×C3×C4C23×C311yescharacteristic
258C2×#67—22no—
259C2×#67—22no—
260C2×#67—24no—
261C2×#67—24no—
262C2×#67—42no—
263C2×#67C3×D414yescomplemented
264C22×Dic3—22no—
265C22×Dic3—42no—
266C22×Dic3C23×C311yescharacteristic
267C22×Dic3C23×C311yescharacteristic
268C22×Dic3C23×C311yescharacteristic
269C22×Dic3C23×C312yes—
270C2×D12—24no—
271C2×D12—24no—
272C2×D12—24no—
273C2×D12—22no—
274C2×D12—42no—
275C2×C4×D3—24no—
276C2×C4×D3—24no—
277C2×C4×D3—42no—
278C2×C4×D3—42no—
279C2×C4×D3C3×D414yescomplemented
280C3×C4⋊C4—22no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—42no—
283C3×C4⋊C4—64no—
284C3×C4⋊C4—62no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—24no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4—42no—
290C3×C22⋊C4—44no—
291C3×C22⋊C4—64no—
292C3×C22⋊C4—64no—
293C3×C22⋊C4—64no—
294C3×C22⋊C4—62no—
295C3×C22⋊C4—122no—
296C3×C42—62no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—24no—
300(C2×D3)⋊C4—24no—
301(C2×D3)⋊C4—42no—
302Dic3⋊C4—22no—
303Dic3⋊C4—24no—
304C4×Dic3—22no—
305C22×C32—22no—
306C22×C32—24no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32—42no—
310C22×C32C22×D411yescharacteristic
311C22×C32C22×D411yescharacteristic
312C22×C32C2×#4111yescharacteristic
313C22×C32C2×#4112yes—
314C22×C32H(5,𝔽2)12yes—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—24no—
318C2×C3×D3—24no—
319C2×C3×D3—42no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3#12114yes—
327C32×C4—22no—
328C32×C4—42no—
329C32×C4—41no—
330C32×C4—42no—
331C3×Dic3—22no—
332C3×Dic3—22no—
333C3×Dic3—24no—
334C3×Dic3—41no—
335C22×D4—31no—
336C22×D4—32no—
337C22×D4—32no—
338C22×D4—31no—
339C23×C4—31no—
340C23×C4—31no—
341C23×C4—32no—
342#121—68no—
343#121—64no—
344C4×D4—64no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4C2×C3×D311yescharacteristic
348C2×C22⋊C4—31no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C22⋊C4—32no—
353C2×C22⋊C4C2×C3×D311yescharacteristic
354C2×C22⋊C4C2×C3×D312yes—
355C2×C42—31no—
356#95—32no—
357#95—31no—
358#95—32no—
359#95C2×C3×D311yescharacteristic
360#95C2×C3×D312yes—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—22no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—21no—
370C23×C3—22no—
371C23×C3—32no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—41no—
375C23×C3—41no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—62no—
379C23×C3—62no—
380C23×C3—62no—
381C23×C3—62no—
382C23×C3—62no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3D3×D412yes—
388C23×C3C2×C3×D412yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C24×C311yescharacteristic
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3C2×C3×D412yes—
401C22×D3C2×C3×D412yes—
402C22×D3C3×#4112yes—
403C3×D4—68no—
404C3×D4—124no—
405C3×D4—128no—
406C3×D4—128no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—21no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—32no—
427C2×C3×C4—32no—
428C2×C3×C4—34no—
429C2×C3×C4—42no—
430C2×C3×C4—41no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—42no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—61no—
439C2×C3×C4—62no—
440C2×C3×C4—61no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—62no—
445C2×C3×C4—124no—
446C2×C3×C4—128no—
447C2×C3×C4—124no—
448C2×C3×C4D3×D412yes—
449C2×C3×C4C2×C3×D412yes—
450#67—28no—
451#67—48no—
452C2×Dic3—21no—
453C2×Dic3—22no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—44no—
460C2×Dic3C2×C3×D412yes—
461C2×Dic3C2×C3×D412yes—
462C2×Dic3C3×#4114yes—
463D12—44no—
464D12—48no—
465C4×D3—44no—
466C4×D3—48no—
467C2×C32—42no—
468C2×C32C2×#12111yescharacteristic
469C2×C32#53211yescharacteristic
470C2×C32#53411yescharacteristic
471C2×C32#54612yes—
472C2×C32#55312yes—
473C3×D3—24no—
474C3×D3—82no—
475C24—31no—
476C24—32no—
477C24C22×C3×D311yescharacteristic
478C2×D4—34no—
479C2×D4—64no—
480C2×D4—64no—
481C2×D4—64no—
482C2×D4—64no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—64no—
486C2×D4—62no—
487C2×D4—122no—
488C2×D4—122no—
489C22×C4—32no—
490C22×C4—31no—
491C22×C4—31no—
492C22×C4—34no—
493C22×C4—31no—
494C22×C4—64no—
495C22×C4—64no—
496C22×C4—62no—
497C22×C4—122no—
498C22×C4—122no—
499C22×C4—122no—
500C22×C4C22×C3×D312yes—
501C22×C4C22×C3×D312yes—
502C22×C4C22×C3×D311yescharacteristic
503C22×C4C22×C3×D311yescharacteristic
504C4⋊C4—22no—
505C4⋊C4—64no—
506C4⋊C4—62no—
507C22⋊C4—24no—
508C22⋊C4—22no—
509C22⋊C4—64no—
510C22⋊C4—64no—
511C22⋊C4—64no—
512C22⋊C4—62no—
513C22⋊C4—122no—
514C42—62no—
515C22×C3—24no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—24no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—34no—
525C22×C3—42no—
526C22×C3—44no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—42no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—42no—
533C22×C3—62no—
534C22×C3—64no—
535C22×C3—62no—
536C22×C3—64no—
537C22×C3—81no—
538C22×C3—81no—
539C22×C3—82no—
540C22×C3—122no—
541C22×C3—122no—
542C22×C3—122no—
543C22×C3—122no—
544C22×C3—122no—
545C22×C3—122no—
546C22×C3—122no—
547C22×C3C2×D3×D411yescharacteristic
548C22×C3C2×D3×D411yescharacteristic
549C22×C3D3×#4112yes—
550C22×C3D3×#4111yescharacteristic
551C22×C3#100912yes—
552C22×C3C22×C3×D411yescharacteristic
553C22×C3C22×C3×D411yescharacteristic
554C22×C3C2×C3×#4111yescharacteristic
555C22×C3C2×C3×#4112yes—
556C22×C3C3×H(5,𝔽2)12yes—
557C2×D3—22no—
558C2×D3—22no—
559C2×D3—24no—
560C2×D3—24no—
561C2×D3—42no—
562C2×D3—42no—
563C2×D3—42no—
564C2×D3—42no—
565C2×D3—42no—
566C2×D3—42no—
567C2×D3—42no—
568C2×D3C3×#12114yes—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—42no—
572C3×C4—42no—
573C3×C4—41no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—41no—
577C3×C4—42no—
578C3×C4—62no—
579C3×C4—64no—
580C3×C4—62no—
581C3×C4—82no—
582C3×C4—82no—
583C3×C4—81no—
584C3×C4—121no—
585Dic3—22no—
586Dic3—22no—
587Dic3—24no—
588Dic3—41no—
589C32#254311yescharacteristic, complemented, Sylow
590C23—21no—
591C23—21no—
592C23—22no—
593C23—22no—
594C23—32no—
595C23—32no—
596C23—32no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23—62no—
602C23—62no—
603C23—62no—
604C23—62no—
605C23—62no—
606C23C3×D3×D412yes—
607C23C23×C3×D311yescharacteristic
608D4—68no—
609D4—124no—
610D4—128no—
611D4—128no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—32no—
622C2×C4—32no—
623C2×C4—34no—
624C2×C4—61no—
625C2×C4—62no—
626C2×C4—61no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—61no—
630C2×C4—62no—
631C2×C4—124no—
632C2×C4—128no—
633C2×C4—124no—
634C2×C4C3×D3×D412yes—
635C2×C3—21no—
636C2×C3—21no—
637C2×C3—22no—
638C2×C3—21no—
639C2×C3—22no—
640C2×C3—42no—
641C2×C3—42no—
642C2×C3—64no—
643C2×C3—82no—
644C2×C3—242no—
645C2×C3D3×#12111yescharacteristic
646C2×C3#565311yescharacteristic
647C2×C3#565412yes—
648C2×C3#566811yescharacteristic
649C2×C3#570912yes—
650C2×C3C2×C3×#12111yescharacteristic
651C2×C3C3×#53211yescharacteristic
652C2×C3C3×#53411yescharacteristic
653C2×C3C3×#54612yes—
654C2×C3C3×#55312yes—
655D3—24no—
656D3—82no—
657C22—22no—
658C22—24no—
659C22—34no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—62no—
664C22—64no—
665C22—62no—
666C22—64no—
667C22—122no—
668C22—122no—
669C22—122no—
670C22—122no—
671C22—122no—
672C22—122no—
673C22—122no—
674C22C2×C3×D3×D411yescharacteristic
675C22C2×C3×D3×D411yescharacteristic
676C22C3×D3×#4111yescharacteristic
677C22C3×D3×#4112yes—
678C22C3×#100912yes—
679C4—22no—
680C4—42no—
681C4—42no—
682C4—41no—
683C4—62no—
684C4—62no—
685C4—64no—
686C4—121no—
687C3—21no—
688C3#7768211yescharacteristic, direct product factor
689C3C3×#254311yescharacteristic, complemented
690C2—42no—
691C2—64no—
692C2—242no—
693C2C3×D3×#12111yescharacteristic
694C2C3×#565311yescharacteristic
695C2C3×#565412yes—
696C2C3×#566811yescharacteristic
697C2C3×#570912yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC23×C3C24×C3
FrattiniC23C23×C3×D3
FittingC32×#397C2
socleC23×C32C24
hypercenterC3×#397D3
hypocenterC3C3×#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#397

Complements

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

NH ≅ G/Ntype
1. C2×C3×#895C2semidirect
2. C2×C3×#884C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C32×#397C2semidirect
5. C3×#4983C2semidirect
6. C3×#4960C2semidirect
7. C3×#4958C2semidirect
8. C3×#4672C2semidirect
9. C3×#4669C2semidirect
10. C3×#4665C2semidirect
11. C3×D3×#95C2semidirect
13. #77682C3direct (N × H)
43. C2×#895C2×C3semidirect
44. C2×#884C2×C3semidirect
45. C2×#67⋊C4C2×C3semidirect
48. C3×#397D3semidirect
49. C3×#397C2×C3semidirect
56. #4983C2×C3semidirect
57. #4960C2×C3semidirect
58. #4958C2×C3semidirect
59. #4672C2×C3semidirect
60. #4669C2×C3semidirect
61. #4665C2×C3semidirect
62. D3×#95C2×C3semidirect
75. C2×C3×#67D4semidirect
91. C2×C3×C4×D3D4semidirect
210. #397C3×D3semidirect
263. C2×#67C3×D4semidirect
279. C2×C4×D3C3×D4semidirect
589. C32#2543semidirect
688. C3#77682direct (N × H)
689. C3C3×#2543semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×C3×#8842
C2×C3×#67⋊C42
C32×#3972
C3×#49832
C3×#49602
C3×#49582
C3×#46722
C3×#46692
C3×#46652
C3×D3×#952
C3×#25433
#776823