Finite Group Databasebeta

← #11803588

Subgroups — #11803588

Order 1152.

1453 conjugacy classes of subgroups.

The subgroup lattice has 717 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#930C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4#10592911C211yesmaximal, characteristic, complemented
5#10591721C212yesmaximal, complemented
6#10591707C212yesmaximal, complemented
7#10591377C212yesmaximal, complemented
8#10591352C211yesmaximal, characteristic, complemented
9#10591318C211yesmaximal, characteristic, complemented
10#10591307C212yesmaximal, complemented
11Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#82633—31nomaximal
13#82236—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×D12C2211yescharacteristic
17C22×D3×Dic3C2212yes—
18C2×#3757C2212yes—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C3×#930C418yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C3×#926—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×(C2×D3)⋊Dic3C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×Dic32C2212yes—
36Dic3×D12—24no—
37#63658C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C2×C3×#121—31no—
41C2×C3×#117—31no—
42C2×D4×Dic3—31no—
43C2×#930D311yescharacteristic
44C2×#926D311yescharacteristic, complemented
45C2×C4×D12—31no—
46#5221—32no—
47#5221—31no—
48#5220—32no—
49#5212—31no—
50#5212—31no—
51#5212—61no—
52#4990—32no—
53#4989—32no—
54#4984—31no—
55Dic3×C4⋊C4—31no—
56#4957—32no—
57#4956—32no—
58#4951—32no—
59#4950—32no—
60#4939—31no—
61C4×C4⋊Dic3—31no—
62#4928—31no—
63C24×C32C2311yescharacteristic
64C23×C3×D3C2312yes—
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2312yes—
72C2×C3×#67—42no—
73C2×C3×#67—42no—
74C2×C3×#67C2×C418yescomplemented
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C2×C3×D12—22no—
81C2×C3×D12—22no—
82C2×C3×D12C2×C414yes—
83C2×D3×Dic3—24no—
84C2×D3×Dic3—42no—
85C2×D3×Dic3—42no—
86#3757—42no—
87C4⋊(C3⋊Dic3)—22no—
88C4⋊(C3⋊Dic3)—22no—
89C3×#217—22no—
90C3×#217—22no—
91C3×(C2×D3)⋊C4C2×C418yescomplemented
92C3×C4⋊Dic3—22no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3C2×C414yescomplemented
95C3×C4×Dic3—22no—
96C3×C4×Dic3D414yescomplemented
97Dic3⋊Dic3—42no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—42no—
100(C2×D3)⋊Dic3—42no—
101Dic32—42no—
102#2324—91noSylow
103C22×C3×D4—32no—
104C22×C3×D4—31no—
105C23×C3×C4—21no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67C2×D312yes—
109C23×Dic3—32no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—32no—
112C3×#121—38no—
113C3×#117—64no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C42—31no—
121C2×C3×C42—31no—
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—32no—
127C2×#217—62no—
128C2×#217C2×D311yescharacteristic
129C2×#217C2×D311yescharacteristic
130D4×Dic3—64no—
131#930Dic318yescomplemented
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—32no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4C2×D312yes—
136#926—24no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—61no—
143C2×C4⋊Dic3—61no—
144C2×C4⋊Dic3C2×D311yescharacteristic
145C2×C4⋊Dic3C2×D311yescharacteristic
146C2×C4⋊Dic3C2×D311yescharacteristic
147C2×Dic3⋊C4—32no—
148C2×C4×Dic3—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3C2×D311yescharacteristic
151C2×C4×Dic3C2×D311yescharacteristic
152C4×D12—64no—
153C3⋊#95—32no—
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—32no—
159C3⋊#95—62no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32—21no—
165C23×C32—21no—
166C23×C32C22×C412yes—
167C23×C32C2411yescharacteristic
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×D3C22×C414yes—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—28no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4#4112yes—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—22no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—22no—
188C3×#67—48no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3C22×C414yes—
202C2×C3×Dic3C2×D412yes—
203C2×C3×Dic3C2×D412yes—
204C3×D12—28no—
205D3×Dic3—48no—
206C2×#121—31no—
207C2×C4×D4—91no—
208C2×#117—31no—
209#390—91no—
210#390—92no—
211#389—91no—
212#388—92no—
213#386—92no—
214#385—92no—
215#380—91no—
216C4×C4⋊C4—91no—
217C24×C3—21no—
218C24×C3—32no—
219C24×C3C22×D311yescharacteristic
220C24×C3C22×D311yescharacteristic
221C23×D3C22×D312yes—
222C2×C3×D4—38no—
223C2×C3×D4—34no—
224C2×C3×D4—62no—
225C2×C3×D4—62no—
226C2×C3×D4—122no—
227C2×C3×D4—122no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—24no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—32no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—42no—
241C22×C3×C4—42no—
242C22×C3×C4C4×D314yescomplemented
243C22×C3×C4C2×Dic314yescomplemented
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—42no—
249C2×#67—42no—
250C2×#67C2×Dic318yescomplemented
251C22×Dic3—32no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—32no—
255C22×Dic3—62no—
256C22×Dic3—62no—
257C22×Dic3—64no—
258C22×Dic3—122no—
259C22×Dic3—122no—
260C22×Dic3C22×D311yescharacteristic
261C22×Dic3C22×D311yescharacteristic
262C22×Dic3C22×D312yes—
263C22×Dic3C22×D311yescharacteristic
264C22×Dic3C22×D311yescharacteristic
265C2×D12—22no—
266C2×D12—22no—
267C2×D12C2×Dic314yes—
268C2×C4×D3—64no—
269C2×C4×D3—122no—
270C2×C4×D3—122no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—62no—
273C3×C4⋊C4—62no—
274C3×C22⋊C4—38no—
275C3×C22⋊C4—62no—
276C3×C22⋊C4—62no—
277C3×C42—34no—
278C3×C42—62no—
279#217—22no—
280#217—22no—
281#217—64no—
282#217—122no—
283#217—122no—
284#217—122no—
285#217—122no—
286#217—124no—
287(C2×D3)⋊C4—64no—
288(C2×D3)⋊C4—122no—
289(C2×D3)⋊C4—122no—
290(C2×D3)⋊C4C2×Dic318yescomplemented
291C4⋊Dic3—22no—
292C4⋊Dic3—22no—
293C4⋊Dic3—62no—
294C4⋊Dic3—62no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—122no—
298C4⋊Dic3—122no—
299C4⋊Dic3—122no—
300C4⋊Dic3C2×Dic314yescomplemented
301Dic3⋊C4—122no—
302C4×Dic3—22no—
303C4×Dic3—122no—
304C4×Dic3—122no—
305C4×Dic3#6714yescomplemented
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32—41no—
313C22×C32C23×C411yescharacteristic
314C22×C32C22×D411yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32H(5,𝔽2)11yescharacteristic
317C22×C32H(5,𝔽2)11yescharacteristic
318C22×C32H(5,𝔽2)11yescharacteristic
319C22×C322−1+411yescharacteristic
320C2×C3×D3—24no—
321C2×C3×D3—24no—
322C2×C3×D3—24no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3—42no—
327C32×C4—22no—
328C32×C4C4×D414yes—
329C3⋊Dic3—42no—
330C3⋊Dic3—42no—
331C3×Dic3—24no—
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C22×D4—32no—
337C22×D4—31no—
338C23×C4—92no—
339C23×C4D3211yescharacteristic
340#121—38no—
341C4×D4—184no—
342#117—64no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—91no—
347C2×C4⋊C4—91no—
348C2×C4⋊C4—92no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—31no—
352C2×C22⋊C4—92no—
353C2×C22⋊C4—92no—
354C2×C22⋊C4—92no—
355C2×C22⋊C4—92no—
356C2×C42—31no—
357C2×C42—31no—
358C2×C42—92no—
359#95—92no—
360#95—92no—
361#95—92no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—22no—
378C23×C3—34no—
379C23×C3—41no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—62no—
384C23×C3—62no—
385C23×C3—62no—
386C23×C3—62no—
387C23×C3—62no—
388C23×C3—62no—
389C23×C3C2×C4×D312yes—
390C23×C3C22×Dic312yes—
391C23×C3C23×D311yescharacteristic
392C23×C3C23×D311yescharacteristic
393C22×D3—22no—
394C22×D3—22no—
395C22×D3—22no—
396C22×D3—22no—
397C22×D3—22no—
398C22×D3—22no—
399C22×D3C22×Dic314yes—
400C3×D4—68no—
401C3×D4—128no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—28no—
407C2×C3×C4—28no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—34no—
413C2×C3×C4—32no—
414C2×C3×C4—32no—
415C2×C3×C4—48no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—61no—
419C2×C3×C4—61no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—61no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—61no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4C2×C4×D312yes—
431C2×C3×C4C2×C4×D312yes—
432C2×C3×C4#23512yes—
433C2×C3×C4D3×D412yes—
434C2×C3×C4#23712yes—
435C2×C3×C4C22×Dic312yes—
436C2×C3×C4C22×Dic312yes—
437C2×C3×C4C2×#6712yes—
438#67—48no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—62no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—62no—
456C2×Dic3—62no—
457C2×Dic3—62no—
458C2×Dic3—62no—
459C2×Dic3—62no—
460C2×Dic3—62no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—122no—
466C2×Dic3—122no—
467C2×Dic3—122no—
468C2×Dic3—122no—
469C2×Dic3—128no—
470C2×Dic3C22×Dic314yes—
471C2×Dic3C2×#6712yes—
472C2×Dic3C2×#6712yes—
473D12—28no—
474C4×D3—128no—
475C2×C32—42no—
476C2×C32C2×C4×D411yescharacteristic
477C2×C32#51811yescharacteristic
478C2×C32#52011yescharacteristic
479C2×C32#53511yescharacteristic
480C2×C32#53711yescharacteristic
481C2×C32#54011yescharacteristic
482C2×C32#54211yescharacteristic
483C3×D3—44no—
484C24—32no—
485C24C2×D3211yescharacteristic
486C2×D4—38no—
487C2×D4—34no—
488C2×D4—62no—
489C2×D4—62no—
490C2×D4—122no—
491C2×D4—122no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—31no—
495C22×C4—32no—
496C22×C4—31no—
497C22×C4—31no—
498C22×C4—31no—
499C22×C4—92no—
500C22×C4—92no—
501C22×C4—184no—
502C22×C4—362no—
503C22×C4—362no—
504C22×C4D3×Dic314yescomplemented
505C22×C4C2×D3211yescharacteristic
506C22×C4C2×D3211yescharacteristic
507C4⋊C4—34no—
508C4⋊C4—62no—
509C4⋊C4—62no—
510C4⋊C4—182no—
511C4⋊C4—182no—
512C4⋊C4—362no—
513C22⋊C4—38no—
514C22⋊C4—62no—
515C22⋊C4—62no—
516C22⋊C4—184no—
517C22⋊C4—362no—
518C22⋊C4—362no—
519C22⋊C4—362no—
520C42—34no—
521C42—62no—
522C42—362no—
523C22×C3—24no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—21no—
531C22×C3—21no—
532C22×C3—21no—
533C22×C3—21no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—41no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—41no—
547C22×C3—41no—
548C22×C3—41no—
549C22×C3—41no—
550C22×C3—41no—
551C22×C3—64no—
552C22×C3—64no—
553C22×C3—64no—
554C22×C3—122no—
555C22×C3—122no—
556C22×C3—122no—
557C22×C3—122no—
558C22×C3C22×C4×D311yescharacteristic
559C22×C3C2×#23511yescharacteristic
560C22×C3C2×D3×D411yescharacteristic
561C22×C3C2×#23711yescharacteristic
562C22×C3#100411yescharacteristic
563C22×C3#100411yescharacteristic
564C22×C3#100911yescharacteristic
565C22×C3#100911yescharacteristic
566C22×C3#100911yescharacteristic
567C22×C3#100911yescharacteristic
568C22×C3#101011yescharacteristic
569C22×C3#101011yescharacteristic
570C22×C3C23×Dic311yescharacteristic
571C22×C3C22×#6711yescharacteristic
572C2×D3—24no—
573C2×D3—24no—
574C2×D3—24no—
575C2×D3—42no—
576C2×D3—42no—
577C2×D3—42no—
578C2×D3—42no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—24no—
582C3×C4—42no—
583C3×C4—64no—
584C3×C4—62no—
585C3×C4—62no—
586C3×C4—121no—
587C3×C4—121no—
588C3×C4C4×#6714yes—
589C3×C4D4×Dic314yes—
590Dic3—24no—
591Dic3—22no—
592Dic3—22no—
593Dic3—41no—
594Dic3—41no—
595Dic3—122no—
596Dic3—122no—
597Dic3—122no—
598Dic3—122no—
599Dic3—242no—
600Dic3—242no—
601C32#232411yescharacteristic, complemented, Sylow
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—34no—
609C23—62no—
610C23—62no—
611C23—62no—
612C23—62no—
613C23—62no—
614C23—62no—
615C23C2×D3×Dic312yes—
616C23C22×D3211yescharacteristic
617D4—68no—
618D4—128no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—28no—
622C2×C4—34no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—61no—
637C2×C4—182no—
638C2×C4—182no—
639C2×C4—182no—
640C2×C4—182no—
641C2×C4—182no—
642C2×C4—182no—
643C2×C4—368no—
644C2×C4C2×D3×Dic312yes—
645C2×C4C2×D3×Dic312yes—
646C2×C4#380412yes—
647C2×C4D3×#6712yes—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—44no—
656C2×C3—42no—
657C2×C3—42no—
658C2×C3—124no—
659C2×C3#552111yescharacteristic
660C2×C3#552311yescharacteristic
661C2×C3#553411yescharacteristic
662C2×C3#553511yescharacteristic
663C2×C3#560311yescharacteristic
664C2×C3#560711yescharacteristic
665C2×C3#560811yescharacteristic
666C2×C3#561911yescharacteristic
667C2×C3C2×C4×#6711yescharacteristic
668C2×C3C2×D4×Dic311yescharacteristic
669C2×C3#579811yescharacteristic
670C2×C3#582711yescharacteristic
671C2×C3#583011yescharacteristic
672C2×C3#583311yescharacteristic
673D3—44no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—64no—
682C22—64no—
683C22—64no—
684C22—122no—
685C22—122no—
686C22—122no—
687C22—122no—
688C22#6429811yescharacteristic
689C22#6430711yescharacteristic
690C22#6430711yescharacteristic
691C22#6430811yescharacteristic
692C22C22×D3×Dic311yescharacteristic
693C22C2×#380411yescharacteristic
694C22C2×D3×#6711yescharacteristic
695C4—22no—
696C4—64no—
697C4—62no—
698C4—62no—
699C4—121no—
700C4—121no—
701C4—362no—
702C4—362no—
703C4Dic3×#6714yes—
704C3—21no—
705C3#8223611yescharacteristic, complemented
706C3#8263311yescharacteristic, complemented
707C2—42no—
708C2—124no—
709C2#1059498211yescharacteristic
710C2#1059498311yescharacteristic
711C2#1059498511yescharacteristic
712C2#1059499211yescharacteristic
713C2#1059500411yescharacteristic
714C2#1059506411yescharacteristic
715C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#930C2
hypercenterC23×C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×Dic3×D12C2semidirect
4. #10592911C2semidirect
5. #10591721C2semidirect
6. #10591707C2semidirect
7. #10591377C2semidirect
8. #10591352C2semidirect
9. #10591318C2semidirect
10. #10591307C2semidirect
11. Dic3×C4⋊Dic3C2semidirect
23. C3×#930C4semidirect
44. C2×#926D3semidirect
67. C22×C32×C4C2×C4semidirect
74. C2×C3×#67C2×C4semidirect
91. C3×(C2×D3)⋊C4C2×C4semidirect
94. C3×C4⋊Dic3C2×C4semidirect
96. C3×C4×Dic3D4semidirect
131. #930Dic3semidirect
242. C22×C3×C4C4×D3semidirect
243. C22×C3×C4C2×Dic3semidirect
250. C2×#67C2×Dic3semidirect
290. (C2×D3)⋊C4C2×Dic3semidirect
300. C4⋊Dic3C2×Dic3semidirect
305. C4×Dic3#67semidirect
504. C22×C4D3×Dic3semidirect
601. C32#2324semidirect
705. C3#82236semidirect
706. C3#82633semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9302
C2×C3×#9262
C2×Dic3×D122
#105929112
#105917212
#105917072
#105913772
#105913522
#105913182
#105913072
Dic3×C4⋊Dic32
#826333
#822363