Finite Group Databasebeta

← C3×#68970 #11788230

Subgroups — C3×#68970 #11788230

Order 1152.

1267 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#882C211yesmaximal, characteristic
2C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
3C3×#4955C211yesmaximal, characteristic, complemented
4C2×C3×#806C211yesmaximal, characteristic, complemented
5C2×C3×#806C211yesmaximal, characteristic, complemented
6C32×#342C211yesmaximal, characteristic, complemented
7C3×#4526C211yesmaximal, characteristic, complemented
8C3×#1898—31nomaximal
9#68970C311yesmaximal, characteristic, direct product factor
10C24×C3×D3C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C22×C3×D12C412yescomplemented
13C22×C3×C4×D3—21no—
14C2×C32×C22⋊C4C2211yescharacteristic
15C2×C32×C22⋊C4C2211yescharacteristic
16C2×C32×C22⋊C4C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—22no—
21C2×C3×(C2×D3)⋊C4C412yescomplemented
22C3×#882—21no—
23C3×#882—22no—
24C3×#882—21no—
25C3×D3×C22⋊C4—22no—
26C3×D3×C22⋊C4—22no—
27C3×#806—22no—
28C3×#806—22no—
29C2×C3×#120—31no—
30C22×C3×C22⋊C4—31no—
31C2×#882C2×C311yescharacteristic
32C2×D3×C22⋊C4C2×C311yescharacteristic, complemented
33C2×C3×#99—31no—
34C2×C3×#99—31no—
35C3×#379—31no—
36#4955C2×C311yescharacteristic, complemented
37C2×#806C2×C311yescharacteristic, complemented
38C2×#806C2×C311yescharacteristic, complemented
39C3×#342—21no—
40C3×#342—31no—
41C3×#342D311yescharacteristic, complemented
42C3×#342C2×C311yescharacteristic, complemented
43#4526C2×C311yescharacteristic, complemented
44C24×C32C2311yescharacteristic
45C23×C3×D3—21no—
46C23×C3×D3—21no—
47C23×C3×D3—21no—
48C23×C3×D3—21no—
49C23×C3×D3—44no—
50C23×C3×D3C2×C412yes—
51C23×C3×D3C2×C411yescharacteristic, complemented
52C23×C3×D3D411yescharacteristic
53C23×C3×D3D412yes—
54C23×C3×D3D411yescharacteristic
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4C2×C412yescomplemented
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C2×C3×#67—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3C2×C411yescharacteristic, complemented
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—44no—
70C2×C3×C4×D3—24no—
71C2×C3×C4×D3—44no—
72C32×C22⋊C4—21no—
73C32×C22⋊C4—21no—
74C32×C22⋊C4—21no—
75C32×C22⋊C4—21no—
76C32×C22⋊C4—21no—
77C32×C22⋊C4D412yescomplemented
78C3×#217—21no—
79C3×#217—21no—
80C3×#217—21no—
81C3×#217D412yescomplemented
82C3×(C2×D3)⋊C4—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×(C2×D3)⋊C4—22no—
85C3×(C2×D3)⋊C4—44no—
86#1898—31noSylow
87C25×C3—31no—
88C24×D3C22×C311yescharacteristic
89C22×C3×D4—31no—
90C22×C3×D4—32no—
91C23×C3×C4—61no—
92C22×#67C22×C311yescharacteristic
93C22×D12C3×C412yescomplemented
94C22×C4×D3—21no—
95C3×#120—61no—
96C3×#120—62no—
97C3×#120—61no—
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—62no—
105C2×C3×C22⋊C4—61no—
106C2×C3×C22⋊C4—62no—
107C2×C3×C22⋊C4—62no—
108C2×C3×C22⋊C4C2×D311yescharacteristic
109C2×C3×C22⋊C4C2×D311yescharacteristic
110C2×C3×C22⋊C4C2×D311yescharacteristic
111C2×C3×C22⋊C4C22×C311yescharacteristic
112C2×C3×C22⋊C4C22×C311yescharacteristic
113C2×C3×C22⋊C4C22×C311yescharacteristic
114C2×#217C22×C311yescharacteristic
115C2×#217C22×C311yescharacteristic
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—22no—
118C2×(C2×D3)⋊C4C3×C412yescomplemented
119#882—21no—
120#882—22no—
121#882—21no—
122D3×C22⋊C4—22no—
123D3×C22⋊C4—22no—
124C3×#99—62no—
125C3×#99—62no—
126#806—22no—
127#806—22no—
128C23×C32—42no—
129C23×C32C22×C411yescharacteristic
130C23×C32C2×D411yescharacteristic
131C23×C32C2×D411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32#4111yescharacteristic
135C23×C32#4111yescharacteristic
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—24no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3—21no—
142C22×C3×D3—22no—
143C22×C3×D3—22no—
144C22×C3×D3—21no—
145C22×C3×D3—24no—
146C22×C3×D3—24no—
147C22×C3×D3—21no—
148C22×C3×D3—21no—
149C22×C3×D3—21no—
150C22×C3×D3—42no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3—44no—
154C22×C3×D3—44no—
155C22×C3×D3—44no—
156C22×C3×D3—44no—
157C22×C3×D3—42no—
158C22×C3×D3C22⋊C412yes—
159C22×C3×D3C22⋊C412yes—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—41no—
163C2×C32×C4—42no—
164C2×C32×C4—42no—
165C2×C32×C4—42no—
166C3×#67—41no—
167C3×#67—41no—
168C3×#67—41no—
169C3×#67—41no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—42no—
175C2×C3×Dic3—42no—
176C2×C3×Dic3—41no—
177C3×D12—44no—
178C3×D12—44no—
179C3×C4×D3—48no—
180C2×#120—31no—
181C22×C22⋊C4—31no—
182C2×#99—31no—
183C2×#99—31no—
184#379—31no—
185#342—31no—
186#342C3×D311yescharacteristic, complemented
187C24×C3—21no—
188C24×C3—31no—
189C24×C3—32no—
190C24×C3—32no—
191C24×C3—31no—
192C24×C3—31no—
193C24×C3—61no—
194C24×C3—61no—
195C24×C3—61no—
196C24×C3—61no—
197C24×C3—124no—
198C24×C3C22×D311yescharacteristic
199C24×C3C23×C311yescharacteristic
200C23×D3—21no—
201C23×D3—21no—
202C23×D3—21no—
203C23×D3—21no—
204C23×D3—44no—
205C23×D3C2×C3×C412yes—
206C23×D3C2×C3×C411yescharacteristic, complemented
207C23×D3C3×D411yescharacteristic
208C23×D3C3×D412yes—
209C23×D3C3×D411yescharacteristic
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—124no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—31no—
225C22×C3×C4—41no—
226C22×C3×C4—41no—
227C22×C3×C4—64no—
228C22×C3×C4—61no—
229C22×C3×C4—61no—
230C22×C3×C4—124no—
231C22×C3×C4C4×D312yescomplemented
232C22×C3×C4C2×C3×C412yescomplemented
233C2×#67—21no—
234C2×#67—21no—
235C2×#67—21no—
236C2×#67—21no—
237C2×#67—21no—
238C2×#67—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×C3×C411yescharacteristic, complemented
242C2×D12—22no—
243C2×D12—22no—
244C2×D12—44no—
245C2×C4×D3—24no—
246C2×C4×D3—44no—
247C3×C22⋊C4—21no—
248C3×C22⋊C4—21no—
249C3×C22⋊C4—21no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—21no—
253C3×C22⋊C4—22no—
254C3×C22⋊C4—21no—
255C3×C22⋊C4—21no—
256C3×C22⋊C4—21no—
257C3×C22⋊C4—21no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—32no—
260C3×C22⋊C4—41no—
261C3×C22⋊C4—41no—
262C3×C22⋊C4—41no—
263C3×C22⋊C4—41no—
264C3×C22⋊C4—62no—
265C3×C22⋊C4—62no—
266C3×C22⋊C4—64no—
267C3×C22⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—124no—
271C3×C22⋊C4D1212yescomplemented
272C3×C22⋊C4C3×D412yescomplemented
273#217—21no—
274#217—21no—
275#217—21no—
276#217C3×D412yescomplemented
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—44no—
281C22×C32—22no—
282C22×C32—22no—
283C22×C32—22no—
284C22×C32—41no—
285C22×C32—41no—
286C22×C32—41no—
287C22×C32—41no—
288C22×C32C2×C22⋊C411yescharacteristic
289C22×C32C4×D411yescharacteristic
290C22×C32C4×D411yescharacteristic
291C22×C32#12011yescharacteristic
292C22×C32#12111yescharacteristic
293C22×C32#12111yescharacteristic
294C22×C32#12311yescharacteristic
295C2×C3×D3—24no—
296C2×C3×D3—24no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—22no—
300C2×C3×D3—22no—
301C2×C3×D3—22no—
302C2×C3×D3—44no—
303C2×C3×D3—44no—
304C2×C3×D3—44no—
305C2×C3×D3—44no—
306C2×C3×D3—42no—
307C2×C3×D3—42no—
308C2×C3×D3—41no—
309C2×C3×D3—42no—
310C2×C3×D3—81no—
311C2×C3×D3—81no—
312C2×C3×D3#9914yescomplemented
313C32×C4—42no—
314C32×C4—42no—
315C32×C4—81no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3—81no—
319C25—31no—
320C22×D4—31no—
321C22×D4—32no—
322C23×C4—61no—
323#120—61no—
324#120—62no—
325#120—61no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—32no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—62no—
330C2×C22⋊C4—61no—
331C2×C22⋊C4—62no—
332C2×C22⋊C4—62no—
333C2×C22⋊C4C2×C3×D311yescharacteristic
334C2×C22⋊C4C2×C3×D311yescharacteristic
335C2×C22⋊C4C2×C3×D311yescharacteristic
336#99—62no—
337#99—62no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—32no—
346C23×C3—32no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3—61no—
353C23×C3—61no—
354C23×C3—62no—
355C23×C3—61no—
356C23×C3—62no—
357C23×C3—62no—
358C23×C3—61no—
359C23×C3—62no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—82no—
364C23×C3—122no—
365C23×C3—122no—
366C23×C3—122no—
367C23×C3—122no—
368C23×C3—124no—
369C23×C3—124no—
370C23×C3—124no—
371C23×C3—124no—
372C23×C3C2×C4×D311yescharacteristic
373C23×C3C2×D1211yescharacteristic
374C23×C3#23511yescharacteristic
375C23×C3D3×D411yescharacteristic
376C23×C3D3×D411yescharacteristic
377C23×C3D3×D411yescharacteristic
378C23×C3#23911yescharacteristic
379C23×C3C22×C3×C411yescharacteristic
380C23×C3C2×C3×D411yescharacteristic
381C23×C3C2×C3×D411yescharacteristic
382C23×C3C2×C3×D411yescharacteristic
383C23×C3C2×C3×D411yescharacteristic
384C23×C3C3×#4111yescharacteristic
385C23×C3C3×#4111yescharacteristic
386C22×D3—21no—
387C22×D3—21no—
388C22×D3—24no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—21no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3—21no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—44no—
404C22×D3—44no—
405C22×D3—44no—
406C22×D3—44no—
407C22×D3—42no—
408C22×D3C3×C22⋊C412yes—
409C22×D3C3×C22⋊C412yes—
410C3×D4—124no—
411C3×D4—124no—
412C3×D4—121no—
413C3×D4—121no—
414C3×D4—121no—
415C3×D4—121no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—62no—
434C2×C3×C4—61no—
435C2×C3×C4—82no—
436C2×C3×C4—82no—
437C2×C3×C4—82no—
438C2×C3×C4—128no—
439C2×C3×C4—122no—
440C2×C3×C4—122no—
441C2×C3×C4—121no—
442#67—41no—
443#67—41no—
444#67—41no—
445#67—41no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—42no—
451C2×Dic3—42no—
452C2×Dic3—41no—
453D12—44no—
454D12—44no—
455C4×D3—48no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32#38611yescharacteristic
463C2×C32C2×#9912yes—
464C3×D3—24no—
465C3×D3—42no—
466C3×D3—81no—
467C24—31no—
468C24—32no—
469C24—32no—
470C24—31no—
471C24—31no—
472C24—61no—
473C24—61no—
474C24—61no—
475C24—61no—
476C24—124no—
477C24C22×C3×D311yescharacteristic
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—124no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—31no—
490C22×C4—64no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—124no—
494C22×C4C3×C4×D312yescomplemented
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—32no—
501C22⋊C4—62no—
502C22⋊C4—62no—
503C22⋊C4—64no—
504C22⋊C4—61no—
505C22⋊C4—61no—
506C22⋊C4—61no—
507C22⋊C4—124no—
508C22⋊C4C3×D1212yescomplemented
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—21no—
522C22×C3—34no—
523C22×C3—42no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—41no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—64no—
535C22×C3—64no—
536C22×C3—62no—
537C22×C3—62no—
538C22×C3—62no—
539C22×C3—62no—
540C22×C3—62no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—124no—
546C22×C3—124no—
547C22×C3—124no—
548C22×C3—124no—
549C22×C3—122no—
550C22×C3—122no—
551C22×C3—121no—
552C22×C3—122no—
553C22×C3—241no—
554C22×C3—241no—
555C22×C3C4×D1211yescharacteristic
556C22×C3D3×C22⋊C411yescharacteristic
557C22×C3#88211yescharacteristic
558C22×C3#88411yescharacteristic
559C22×C3#89311yescharacteristic
560C22×C3#89411yescharacteristic
561C22×C3#89511yescharacteristic
562C22×C3C2×C3×C22⋊C411yescharacteristic
563C22×C3C3×C4×D411yescharacteristic
564C22×C3C3×C4×D411yescharacteristic
565C22×C3C3×#12011yescharacteristic
566C22×C3C3×#12111yescharacteristic
567C22×C3C3×#12111yescharacteristic
568C22×C3C3×#12311yescharacteristic
569C2×D3—24no—
570C2×D3—24no—
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—44no—
577C2×D3—44no—
578C2×D3—44no—
579C2×D3—44no—
580C2×D3—42no—
581C2×D3—42no—
582C2×D3—41no—
583C2×D3—42no—
584C2×D3—81no—
585C2×D3—81no—
586C2×D3C3×#9914yescomplemented
587C3×C4—42no—
588C3×C4—42no—
589C3×C4—42no—
590C3×C4—42no—
591C3×C4—82no—
592C3×C4—82no—
593C3×C4—81no—
594C3×C4—81no—
595C3×C4—82no—
596C3×C4—122no—
597C3×C4—121no—
598C3×C4—241no—
599Dic3—42no—
600Dic3—41no—
601Dic3—81no—
602C32#189811yescharacteristic, complemented, Sylow
603C23—32no—
604C23—32no—
605C23—42no—
606C23—64no—
607C23—64no—
608C23—64no—
609C23—61no—
610C23—61no—
611C23—61no—
612C23—62no—
613C23—62no—
614C23—61no—
615C23—62no—
616C23—62no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—122no—
621C23—122no—
622C23—122no—
623C23—122no—
624C23—124no—
625C23—124no—
626C23—124no—
627C23—124no—
628C23C2×C3×C4×D311yescharacteristic
629C23C2×C3×D1211yescharacteristic
630C23C3×#23511yescharacteristic
631C23C3×D3×D411yescharacteristic
632C23C3×D3×D411yescharacteristic
633C23C3×D3×D411yescharacteristic
634C23C3×#23911yescharacteristic
635D4—124no—
636D4—124no—
637D4—121no—
638D4—121no—
639D4—121no—
640D4—121no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—41no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—128no—
652C2×C4—122no—
653C2×C4—122no—
654C2×C4—121no—
655C2×C3—21no—
656C2×C3—21no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—22no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—41no—
673C2×C3—41no—
674C2×C3—41no—
675C2×C3—64no—
676C2×C3—122no—
677C2×C3—241no—
678C2×C3#466511yescharacteristic
679C2×C3D3×#9912yes—
680C2×C3C3×#38611yescharacteristic
681C2×C3C2×C3×#9912yes—
682D3—24no—
683D3—42no—
684D3—81no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—34no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—64no—
694C22—64no—
695C22—62no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—124no—
701C22—124no—
702C22—124no—
703C22—124no—
704C22—122no—
705C22—122no—
706C22—121no—
707C22—122no—
708C22—241no—
709C22—241no—
710C22C3×C4×D1211yescharacteristic
711C22C3×D3×C22⋊C411yescharacteristic
712C22C3×#88211yescharacteristic
713C22C3×#88411yescharacteristic
714C22C3×#89311yescharacteristic
715C22C3×#89411yescharacteristic
716C22C3×#89511yescharacteristic
717C4—42no—
718C4—42no—
719C4—81no—
720C4—122no—
721C4—121no—
722C4—241no—
723C3—21no—
724C3#6897011yescharacteristic, direct product factor
725C3C3×#189811yescharacteristic, complemented
726C2—21no—
727C2—21no—
728C2—21no—
729C2—21no—
730C2—21no—
731C2—21no—
732C2—64no—
733C2—122no—
734C2—241no—
735C2C3×#466511yescharacteristic
736C2C3×D3×#9912yes—
subgroupG/H
centerC22×C3D3×C22⋊C4
commutatorC23×C3C22×C3×C4
FrattiniC24C22×C3×D3
FittingC32×#342C2
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#882C2
cosocleC24×C3C23×C3
hypercenterC3×#342D3
hypocenterC3C3×#1898
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C24×C3 ◁ C3×#342

Complements

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

NH ≅ G/Ntype
2. C2×C3×D3×C22⋊C4C2semidirect
3. C3×#4955C2semidirect
4. C2×C3×#806C2semidirect
5. C2×C3×#806C2semidirect
6. C32×#342C2semidirect
7. C3×#4526C2semidirect
9. #68970C3direct (N × H)
12. C22×C3×D12C4semidirect
21. C2×C3×(C2×D3)⋊C4C4semidirect
32. C2×D3×C22⋊C4C2×C3semidirect
36. #4955C2×C3semidirect
37. C2×#806C2×C3semidirect
38. C2×#806C2×C3semidirect
41. C3×#342D3semidirect
42. C3×#342C2×C3semidirect
43. #4526C2×C3semidirect
51. C23×C3×D3C2×C4semidirect
57. C22×C32×C4C2×C4semidirect
66. C22×C3×Dic3C2×C4semidirect
77. C32×C22⋊C4D4semidirect
81. C3×#217D4semidirect
93. C22×D12C3×C4semidirect
118. C2×(C2×D3)⋊C4C3×C4semidirect
186. #342C3×D3semidirect
206. C23×D3C2×C3×C4semidirect
231. C22×C3×C4C4×D3semidirect
232. C22×C3×C4C2×C3×C4semidirect
241. C22×Dic3C2×C3×C4semidirect
271. C3×C22⋊C4D12semidirect
272. C3×C22⋊C4C3×D4semidirect
276. #217C3×D4semidirect
312. C2×C3×D3#99semidirect
494. C22×C4C3×C4×D3semidirect
508. C22⋊C4C3×D12semidirect
586. C2×D3C3×#99semidirect
602. C32#1898semidirect
724. C3#68970direct (N × H)
725. C3C3×#1898semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8822
C2×C3×D3×C22⋊C42
C3×#49552
C2×C3×#8062
C32×#3422
C3×#45262
C3×#18983
#689703