Finite Group Databasebeta

← Dic3×#894 #11802186

Subgroups — Dic3×#894 #11802186

Order 1152.

1453 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#894C211yesmaximal, characteristic
2C2×Dic3×D12C211yesmaximal, characteristic
3C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
4#10592679C211yesmaximal, characteristic, complemented
5C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
6#10591377C211yesmaximal, characteristic, complemented
7#10591376C211yesmaximal, characteristic
8Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
9Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#10591307C211yesmaximal, characteristic, complemented
12#10591294C211yesmaximal, characteristic, complemented
13#10591286C211yesmaximal, characteristic, complemented
14#10591272C211yesmaximal, characteristic, complemented
15Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
16Dic3×#123—31nomaximal
17C4×#894—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C2×C32×C4⋊C4C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#894C418yescomplemented
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×(C2×D3)⋊Dic3C2211yescharacteristic
39C2×(C2×D3)⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
42C2×Dic32C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44Dic3×D12—24no—
45C4×D3×Dic3—24no—
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48#63658C2211yescharacteristic
49#63658C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×C3×#123—31no—
57C2×D4×Dic3—31no—
58C22×C4×Dic3—31no—
59C2×#894D311yescharacteristic
60C2×C4×D12—31no—
61C2×C42×D3—31no—
62C3×C4×C4⋊C4—31no—
63#5220—31no—
64#5211—31no—
65#4990—31no—
66#4989—31no—
67#4980—31no—
68#4980—31no—
69#4980—31no—
70#4980—61no—
71Dic3×C4⋊C4—31no—
72Dic3×C4⋊C4D311yescharacteristic, complemented
73#4951—31no—
74#4951—31no—
75#4950—31no—
76Dic3×C22⋊C4—31no—
77Dic3×C22⋊C4—31no—
78Dic3×C22⋊C4—31no—
79C4×(C2×D3)⋊C4—31no—
80C4×(C2×D3)⋊C4—31no—
81C4×(C2×D3)⋊C4—31no—
82C4×Dic3⋊C4—31no—
83#4669—31no—
84#4665—31no—
85#4664—31no—
86#4655—31no—
87C23×C3×D3C2311yescharacteristic
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×C3×D12—22no—
103C2×C3×D12—22no—
104C2×C3×D12C2×C414yes—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3C2×C414yescomplemented
108C2×D3×Dic3—22no—
109C2×D3×Dic3—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3D414yes—
117C32×C4⋊C4C2×C414yescomplemented
118C4⋊(C3⋊Dic3)—22no—
119C4×C3⋊Dic3—22no—
120C3×(C2×D3)⋊C4C2×C414yescomplemented
121C3×(C2×D3)⋊C4C2×C414yescomplemented
122C3×(C2×D3)⋊C4C2×C414yescomplemented
123C3×C4⋊Dic3—22no—
124C3×Dic3⋊C4C2×C414yescomplemented
125C3×C4×Dic3—22no—
126C3×C4×Dic3—22no—
127C3×C4×Dic3—22no—
128Dic3⋊Dic3—22no—
129(C2×D3)⋊Dic3—22no—
130(C2×D3)⋊Dic3—22no—
131(C2×D3)⋊Dic3—22no—
132(C2×D3)⋊Dic3—22no—
133(C2×D3)⋊Dic3—22no—
134Dic32—22no—
135Dic32—22no—
136Dic32—22no—
137C4×#123—91noSylow
138C22×C3×D4—31no—
139C23×C3×C4—31no—
140C23×Dic3—31no—
141C23×Dic3—31no—
142C23×Dic3—31no—
143C22×D12C2×D311yescharacteristic
144C22×C4×D3—31no—
145C22×C4×D3—31no—
146C22×C4×D3—31no—
147C22×C4×D3C2×D311yescharacteristic
148C3×#123—38no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4—31no—
151C2×C3×C4⋊C4—31no—
152C2×C3×C4⋊C4C2×D311yescharacteristic
153C2×C3×C4⋊C4C2×D311yescharacteristic
154C2×C3×C22⋊C4—31no—
155C2×C3×C22⋊C4—31no—
156C2×C3×C22⋊C4—31no—
157C2×C3×C42—31no—
158C2×C3×C42—31no—
159C2×C3×C42—31no—
160C2×#217—31no—
161C2×#217—31no—
162C2×#217—31no—
163C2×#217—31no—
164C2×#217—31no—
165D4×Dic3—64no—
166C2×(C2×D3)⋊C4—31no—
167C2×(C2×D3)⋊C4—31no—
168C2×(C2×D3)⋊C4—31no—
169C2×(C2×D3)⋊C4—31no—
170C2×(C2×D3)⋊C4—31no—
171C2×(C2×D3)⋊C4C2×D311yescharacteristic
172C2×(C2×D3)⋊C4C2×D311yescharacteristic
173C2×(C2×D3)⋊C4C2×D311yescharacteristic
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3—61no—
178C2×C4⋊Dic3C2×D311yescharacteristic
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×C4×Dic3—31no—
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—61no—
190C2×C4×Dic3—64no—
191C2×C4×Dic3C2×D311yescharacteristic
192C2×C4×Dic3C2×D311yescharacteristic
193C2×C4×Dic3C2×D311yescharacteristic
194#894Dic318yesdirect product factor
195C4×D12—64no—
196C42×D3—64no—
197C3×#95—31no—
198C3×#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—61no—
216C3⋊#95—61no—
217C3⋊#95—61no—
218C3⋊#95—61no—
219C3⋊#95C2×D311yescharacteristic
220C3⋊#95C2×D311yescharacteristic
221C23×C32C2411yescharacteristic
222C22×C3×D3—21no—
223C22×C3×D3—21no—
224C22×C3×D3—21no—
225C22×C3×D3—21no—
226C22×C3×D3—21no—
227C22×C3×D3—21no—
228C22×C3×D3—21no—
229C22×C3×D3—21no—
230C22×C3×D3—21no—
231C22×C3×D3—21no—
232C22×C3×D3C22×C412yes—
233C22×C3×D3C22×C412yes—
234C22×C3×D3C2×D412yes—
235C22×C3×D3#4112yes—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C22×C412yes—
243C2×C32×C4C22×C412yes—
244C2×C32×C4C22×C412yes—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3C2×D412yes—
256C2×C3⋊Dic3#4112yes—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3C22×C412yes—
270C2×C3×Dic3C22×C412yes—
271C2×C3×Dic3C2×D412yes—
272C2×C3×Dic3#4112yes—
273C2×C3×Dic3#4112yes—
274C2×C3×Dic3#4112yes—
275C3×D12—28no—
276C3×C4×D3—28no—
277D3×Dic3—28no—
278D3×Dic3—28no—
279D3×Dic3—44no—
280C2×#123—31no—
281C2×C4×D4—91no—
282C22×C42—91no—
283#388—91no—
284#388—91no—
285#387—91no—
286#387—91no—
287#386—91no—
288#385—91no—
289#381—91no—
290C4×C4⋊C4—31no—
291C4×C4⋊C4—91no—
292C4×C22⋊C4—91no—
293C4×C22⋊C4—91no—
294C4×C22⋊C4—91no—
295C24×C3—31no—
296C24×C3—31no—
297C23×D3C22×D311yescharacteristic
298C23×D3C22×D311yescharacteristic
299C2×C3×D4—34no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—31no—
309C22×C3×C4—34no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C22×C3×C4C22×D311yescharacteristic
320C22×Dic3—31no—
321C22×Dic3—31no—
322C22×Dic3—31no—
323C22×Dic3—31no—
324C22×Dic3—34no—
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—62no—
334C22×Dic3—62no—
335C22×Dic3—62no—
336C22×Dic3—62no—
337C22×Dic3—62no—
338C22×Dic3—62no—
339C22×Dic3—62no—
340C22×Dic3—62no—
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D311yescharacteristic
343C22×Dic3C22×D311yescharacteristic
344C22×Dic3C22×D311yescharacteristic
345C22×Dic3C22×D311yescharacteristic
346C22×Dic3C22×D311yescharacteristic
347C2×D12—22no—
348C2×D12—22no—
349C2×D12C2×Dic314yes—
350C2×C4×D3—22no—
351C2×C4×D3—22no—
352C2×C4×D3—34no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—62no—
356C2×C4×D3—62no—
357C2×C4×D3—62no—
358C2×C4×D3—62no—
359C2×C4×D3—62no—
360C2×C4×D3—62no—
361C2×C4×D3C2×Dic314yescomplemented
362C3×C4⋊C4—24no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—62no—
365C3×C4⋊C4C4×D314yescomplemented
366C3×C4⋊C4C2×Dic314yescomplemented
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C42—62no—
371C3×C42—62no—
372C3×C42—62no—
373#217—62no—
374#217—62no—
375#217—62no—
376#217—62no—
377#217—62no—
378(C2×D3)⋊C4—62no—
379(C2×D3)⋊C4—62no—
380(C2×D3)⋊C4—62no—
381(C2×D3)⋊C4—62no—
382(C2×D3)⋊C4—62no—
383(C2×D3)⋊C4C2×Dic314yescomplemented
384(C2×D3)⋊C4C2×Dic314yescomplemented
385(C2×D3)⋊C4C2×Dic314yescomplemented
386C4⋊Dic3—22no—
387C4⋊Dic3—62no—
388C4⋊Dic3—62no—
389C4⋊Dic3—62no—
390C4⋊Dic3—122no—
391Dic3⋊C4—62no—
392Dic3⋊C4C2×Dic314yescomplemented
393C4×Dic3—22no—
394C4×Dic3—22no—
395C4×Dic3—22no—
396C4×Dic3—62no—
397C4×Dic3—62no—
398C4×Dic3—62no—
399C4×Dic3—62no—
400C4×Dic3—62no—
401C4×Dic3—62no—
402C4×Dic3—62no—
403C4×Dic3—62no—
404C4×Dic3—122no—
405C22×C32C23×C411yescharacteristic
406C22×C32C22×D411yescharacteristic
407C22×C32C2×#4111yescharacteristic
408C22×C32C2×#4111yescharacteristic
409C22×C32C2×#4111yescharacteristic
410C22×C32C2×#4111yescharacteristic
411C22×C32C2×#4111yescharacteristic
412C2×C3×D3—22no—
413C2×C3×D3—22no—
414C2×C3×D3—22no—
415C2×C3×D3—22no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—22no—
419C2×C3×D3—22no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C4×D414yes—
426C32×C4—22no—
427C32×C4—22no—
428C32×C4—22no—
429C3⋊Dic3—22no—
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—22no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3#12314yescomplemented
439C22×D4—31no—
440C23×C4—31no—
441C23×C4—91no—
442C23×C4—91no—
443C23×C4—91no—
444#123—38no—
445C4×D4—184no—
446C2×C4⋊C4—31no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C4⋊C4D3211yescharacteristic
451C2×C22⋊C4—31no—
452C2×C22⋊C4—31no—
453C2×C22⋊C4—31no—
454C2×C22⋊C4—91no—
455C2×C22⋊C4—91no—
456C2×C22⋊C4—91no—
457C2×C22⋊C4—91no—
458C2×C22⋊C4—91no—
459C2×C42—31no—
460C2×C42—31no—
461C2×C42—31no—
462C2×C42—91no—
463C2×C42—91no—
464C2×C42—91no—
465C2×C42—91no—
466C2×C42—184no—
467#95—31no—
468#95—31no—
469#95—91no—
470#95—91no—
471#95—91no—
472#95—91no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477C23×C3—21no—
478C23×C3—32no—
479C23×C3—32no—
480C23×C3—32no—
481C23×C3—32no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—61no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—61no—
491C23×C3—61no—
492C23×C3C23×D311yescharacteristic
493C23×C3C23×D311yescharacteristic
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—21no—
504C22×D3D3×D412yes—
505C22×D3#23712yes—
506C22×D3C22×Dic312yes—
507C22×D3C22×Dic312yes—
508C3×D4—68no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—22no—
522C2×C3×C4—22no—
523C2×C3×C4—22no—
524C2×C3×C4—32no—
525C2×C3×C4—32no—
526C2×C3×C4—32no—
527C2×C3×C4—32no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—41no—
535C2×C3×C4—41no—
536C2×C3×C4—68no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—61no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4C2×C4×D312yes—
550C2×C3×C4C2×C4×D312yes—
551C2×C3×C4C2×C4×D312yes—
552C2×C3×C4C22×Dic312yes—
553C2×C3×C4C22×Dic312yes—
554C2×C3×C4C22×Dic312yes—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—62no—
572C2×Dic3—62no—
573C2×Dic3—68no—
574C2×Dic3—61no—
575C2×Dic3—61no—
576C2×Dic3—61no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—68no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—121no—
605C2×Dic3—124no—
606C2×Dic3#23512yes—
607C2×Dic3#23512yes—
608C2×Dic3D3×D412yes—
609C2×Dic3#23912yes—
610C2×Dic3C22×Dic312yes—
611C2×Dic3C22×Dic312yes—
612D12—28no—
613C4×D3—28no—
614C4×D3—68no—
615C4×D3—68no—
616C4×D3—124no—
617C2×C32C2×C4×D411yescharacteristic
618C2×C32C4×#4111yescharacteristic
619C2×C32C4×#4111yescharacteristic
620C2×C32C2×#12311yescharacteristic
621C2×C32#52511yescharacteristic
622C2×C32#52911yescharacteristic
623C2×C32#52911yescharacteristic
624C3×D3—24no—
625C3×D3—42no—
626C24—31no—
627C24—31no—
628C2×D4—34no—
629C2×D4—62no—
630C2×D4—62no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—31no—
634C22×C4—31no—
635C22×C4—34no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—94no—
641C22×C4—91no—
642C22×C4—91no—
643C22×C4—91no—
644C22×C4—91no—
645C22×C4—182no—
646C22×C4—182no—
647C22×C4—182no—
648C22×C4—182no—
649C22×C4—182no—
650C22×C4—182no—
651C22×C4—182no—
652C22×C4—182no—
653C22×C4C2×D3211yescharacteristic
654C22×C4C2×D3211yescharacteristic
655C22×C4C2×D3211yescharacteristic
656C4⋊C4—34no—
657C4⋊C4—62no—
658C4⋊C4—182no—
659C4⋊C4—182no—
660C4⋊C4D3×Dic314yescomplemented
661C22⋊C4—34no—
662C22⋊C4—34no—
663C22⋊C4—34no—
664C22⋊C4—182no—
665C22⋊C4—182no—
666C22⋊C4—182no—
667C22⋊C4—182no—
668C22⋊C4—182no—
669C42—62no—
670C42—62no—
671C42—62no—
672C42—182no—
673C42—182no—
674C42—182no—
675C42—182no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—34no—
684C22×C3—62no—
685C22×C3—62no—
686C22×C3—62no—
687C22×C3—62no—
688C22×C3—62no—
689C22×C3—62no—
690C22×C3—62no—
691C22×C3—62no—
692C22×C3—62no—
693C22×C3—121no—
694C22×C3—121no—
695C22×C3—121no—
696C22×C3—121no—
697C22×C3C22×C4×D311yescharacteristic
698C22×C3C2×#23511yescharacteristic
699C22×C3C2×#23511yescharacteristic
700C22×C3C2×D3×D411yescharacteristic
701C22×C3C2×D3×D411yescharacteristic
702C22×C3C2×#23711yescharacteristic
703C22×C3C2×#23911yescharacteristic
704C22×C3D3×#4111yescharacteristic
705C22×C3D3×#4111yescharacteristic
706C22×C3D3×#4111yescharacteristic
707C22×C3D3×#4111yescharacteristic
708C22×C3D3×#4111yescharacteristic
709C22×C3D3×#4111yescharacteristic
710C22×C3C23×Dic311yescharacteristic
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—22no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—41no—
723C2×D3—41no—
724C2×D3D4×Dic314yes—
725C3×C4—22no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—22no—
729C3×C4—22no—
730C3×C4—22no—
731C3×C4—34no—
732C3×C4—42no—
733C3×C4—42no—
734C3×C4—42no—
735C3×C4—62no—
736C3×C4—62no—
737C3×C4—62no—
738C3×C4—121no—
739C3×C4—121no—
740Dic3—22no—
741Dic3—22no—
742Dic3—22no—
743Dic3—41no—
744Dic3—41no—
745Dic3—62no—
746Dic3—62no—
747Dic3—62no—
748Dic3—62no—
749Dic3—122no—
750Dic3—122no—
751Dic3—121no—
752Dic3—121no—
753Dic3—121no—
754Dic3—121no—
755Dic3—241no—
756Dic3—241no—
757Dic3#89414yesdirect product factor
758C32C4×#12311yescharacteristic, complemented, Sylow
759C23—32no—
760C23—32no—
761C23—32no—
762C23—32no—
763C23—61no—
764C23—61no—
765C23—61no—
766C23—61no—
767C23—61no—
768C23—61no—
769C23—61no—
770C23—61no—
771C23—61no—
772C23—61no—
773C23C22×D3211yescharacteristic
774D4—68no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—32no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—68no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—61no—
791C2×C4—61no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—92no—
801C2×C4—92no—
802C2×C4—188no—
803C2×C4—188no—
804C2×C4—181no—
805C2×C4—181no—
806C2×C4—181no—
807C2×C4—181no—
808C2×C4—181no—
809C2×C4—181no—
810C2×C4—181no—
811C2×C4—181no—
812C2×C4—181no—
813C2×C4—181no—
814C2×C4—364no—
815C2×C4C2×D3×Dic312yes—
816C2×C4C2×D3×Dic312yes—
817C2×C4C2×D3×Dic312yes—
818C2×C3—21no—
819C2×C3—21no—
820C2×C3—21no—
821C2×C3—21no—
822C2×C3—21no—
823C2×C3—21no—
824C2×C3—21no—
825C2×C3—64no—
826C2×C3—122no—
827C2×C3C4×#23511yescharacteristic
828C2×C3C2×#89411yescharacteristic
829C2×C3#552811yescharacteristic
830C2×C3C4×D3×D411yescharacteristic
831C2×C3#554711yescharacteristic
832C2×C3C4×#23911yescharacteristic
833C2×C3#558011yescharacteristic
834C2×C3#564911yescharacteristic
835C2×C3#564911yescharacteristic
836C2×C3D3×#12311yescharacteristic
837C2×C3#565611yescharacteristic
838C2×C3C2×D4×Dic311yescharacteristic
839C2×C3Dic3×#4111yescharacteristic
840C2×C3Dic3×#4111yescharacteristic
841D3—24no—
842D3—42no—
843C22—34no—
844C22—62no—
845C22—62no—
846C22—62no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—62no—
853C22—121no—
854C22—121no—
855C22—121no—
856C22—121no—
857C22D3×#23511yescharacteristic
858C22D3×#23511yescharacteristic
859C22D32×D411yescharacteristic
860C22D3×#23711yescharacteristic
861C22D3×#23911yescharacteristic
862C22#6431911yescharacteristic
863C22C22×D3×Dic311yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—34no—
868C4—62no—
869C4—62no—
870C4—62no—
871C4—121no—
872C4—121no—
873C4—182no—
874C4—182no—
875C4—361no—
876C4—361no—
877C3—21no—
878C3C4×#89411yescharacteristic, complemented
879C3Dic3×#12311yescharacteristic, complemented
880C2—64no—
881C2—122no—
882C2#1059440411yescharacteristic
883C2#1059441611yescharacteristic
884C2D3×#89411yescharacteristic
885C2#1059461411yescharacteristic
886C2Dic3×#23511yescharacteristic
887C2D3×D4×Dic311yescharacteristic
888C2Dic3×#23911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×D3×Dic3C2semidirect
4. #10592679C2semidirect
5. C3×Dic3×C4⋊C4C2semidirect
6. #10591377C2semidirect
8. Dic3×(C2×D3)⋊C4C2semidirect
9. Dic3×(C2×D3)⋊C4C2semidirect
10. Dic3×(C2×D3)⋊C4C2semidirect
11. #10591307C2semidirect
12. #10591294C2semidirect
13. #10591286C2semidirect
14. #10591272C2semidirect
15. Dic3×Dic3⋊C4C2semidirect
34. C3×#894C4semidirect
72. Dic3×C4⋊C4D3semidirect
107. C2×C3×C4×D3C2×C4semidirect
117. C32×C4⋊C4C2×C4semidirect
120. C3×(C2×D3)⋊C4C2×C4semidirect
121. C3×(C2×D3)⋊C4C2×C4semidirect
122. C3×(C2×D3)⋊C4C2×C4semidirect
124. C3×Dic3⋊C4C2×C4semidirect
194. #894Dic3direct (N × H)
361. C2×C4×D3C2×Dic3semidirect
365. C3×C4⋊C4C4×D3semidirect
366. C3×C4⋊C4C2×Dic3semidirect
383. (C2×D3)⋊C4C2×Dic3semidirect
384. (C2×D3)⋊C4C2×Dic3semidirect
385. (C2×D3)⋊C4C2×Dic3semidirect
392. Dic3⋊C4C2×Dic3semidirect
438. C3×Dic3#123semidirect
660. C4⋊C4D3×Dic3semidirect
757. Dic3#894direct (N × H)
758. C32C4×#123semidirect
878. C3C4×#894semidirect
879. C3Dic3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8942
C2×Dic3×D122
C2×C4×D3×Dic32
#105926792
C3×Dic3×C4⋊C42
#105913772
#105913762
Dic3×(C2×D3)⋊C42
#105913072
#105912942
#105912862
#105912722
Dic3×Dic3⋊C42
Dic3×#1233
C4×#8943