Finite Group Databasebeta

← C4×#89039 #13177295

Subgroups — C4×#89039 #13177295

Order 1728.

3500 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#89039C211yesmaximal, characteristic
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×C4×#638C211yesmaximal, characteristic, complemented
5C32×C4×#67C211yesmaximal, characteristic, complemented
6#11723627C211yesmaximal, characteristic, complemented
7#11723626C211yesmaximal, characteristic, complemented
8#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10C4×#6292C211yesmaximal, characteristic, complemented
11C4×#6291C211yesmaximal, characteristic, complemented
12#11723472C211yesmaximal, characteristic, complemented
13#11723470C211yesmaximal, characteristic, complemented
14C4×#6289C211yesmaximal, characteristic, complemented
15#11723462C211yesmaximal, characteristic, complemented
16C4×D4×C3⋊D3—31nomaximal
17C4×#3811—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C22×C33×C4C2211yescharacteristic, complemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)—24no—
23C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
24C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
25C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
26C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
27C2×C3×#638C2211yescharacteristic
28C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
29C2×C32×#67C2211yescharacteristic
30C2×C32×C4×D3C2211yescharacteristic, complemented
31#89039C418yesdirect product factor
32C2×#6292C2211yescharacteristic
33C2×#6291C2211yescharacteristic
34C2×#6289C2211yescharacteristic
35C2×#6289C2211yescharacteristic
36C2×#6289C2211yescharacteristic
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
39C4×D3×C3⋊D3—24no—
40C3×#3757C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
44C32×#217C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47C32×C4×Dic3C2211yescharacteristic, complemented
48#88807C2211yescharacteristic, complemented
49Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
50#88804C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54Dic3×C3⋊Dic3C2211yescharacteristic, complemented
55Dic3×C3⋊Dic3C2211yescharacteristic, complemented
56C2×D4×C3⋊D3—31no—
57C22×C4×C3⋊D3—31no—
58C22×C4×C3⋊D3—31no—
59C22×C4×C3⋊D3—34no—
60C22×C4×C3⋊D3—64no—
61C2×#3811—34no—
62C2×C4×D32—34no—
63C32×C4×D4—31no—
64D4×C3⋊Dic3—31no—
65C4×#638—31no—
66C4×#638D311yescharacteristic, complemented
67#64102—31no—
68C4⋊C4×C3⋊D3—31no—
69#64090—31no—
70#64090—31no—
71C22⋊C4×C3⋊D3—31no—
72C22⋊C4×C3⋊D3—31no—
73C4×C4⋊(C3⋊D3)—31no—
74C42×C3⋊D3—31no—
75C3×C4×#67—34no—
76C3×C4×#67D314yescomplemented
77#63974—34no—
78#67⋊Dic3—34no—
79#67⋊Dic3—34no—
80#63921—34no—
81C4×#626—34no—
82C4×#626—34no—
83#63883—34no—
84C4×#624—34no—
85#63881—34no—
86#63881—34no—
87C23×C33C2311yescharacteristic
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)C2×C414yescomplemented
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3⋊(C3⋊D3)C2311yescharacteristic
93C22×C3×C3⋊D3C2311yescharacteristic
94C22×C32×D3C2311yescharacteristic
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3—22no—
97C2×D3×C3⋊D3C2×C414yescomplemented
98C2×C33×C4—22no—
99C2×C33×C4C2311yescharacteristic
100C2×C33×C4C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)—22no—
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
104C4×C3⋊(C3⋊D3)—22no—
105C4×C3⋊(C3⋊D3)—22no—
106C4×C3⋊(C3⋊D3)—22no—
107C4×C3⋊(C3⋊D3)D414yescomplemented
108C3×#638C2×C414yescomplemented
109C2×C3×C3⋊Dic3C2311yescharacteristic
110C2×C3×C3⋊Dic3C2311yescharacteristic
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C3×C4×C3⋊D3—22no—
113C32×#67C2×C414yescomplemented
114C2×C32×Dic3C2311yescharacteristic
115C2×C32×Dic3C2311yescharacteristic
116C2×C32×Dic3C2311yescharacteristic
117C32×C4×D3—22no—
118#6292C2×C414yescomplemented
119#6291C2×C414yescomplemented
120#6289—22no—
121#6289—22no—
122#6289C2×C414yescomplemented
123Dic3×C3⋊D3—22no—
124D3×C3⋊Dic3—22no—
125C4×D3×D4—94no—
126C4×D3×D4—91no—
127C23×C3⋊D3—31no—
128C23×C3⋊D3—34no—
129C23×C3⋊D3—31no—
130C23×C3⋊D3—64no—
131C22×D32—34no—
132C2×C32×D4—31no—
133C22×C32×C4—24no—
134C22×C32×C4—31no—
135C22×C32×C4C2×D314yescomplemented
136C22×C32×C4C2×D311yescharacteristic, complemented
137C2×#638—31no—
138C2×#638C2×D311yescharacteristic
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—34no—
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—64no—
143D4×C3⋊D3—38no—
144C2×C4⋊(C3⋊D3)—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—34no—
147C2×C4×C3⋊D3—31no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—31no—
152C2×C4×C3⋊D3—34no—
153C2×C4×C3⋊D3—34no—
154C2×C4×C3⋊D3—34no—
155C2×C4×C3⋊D3—31no—
156C2×C4×C3⋊D3—31no—
157C2×C4×C3⋊D3—64no—
158C2×C4×C3⋊D3—64no—
159C2×C4×C3⋊D3—616no—
160C2×C4×C3⋊D3—64no—
161C2×C4×C3⋊D3—64no—
162C2×C4×C3⋊D3—64no—
163C2×C4×C3⋊D3—64no—
164C2×C4×C3⋊D3—632no—
165C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
166C2×C3×#67—34no—
167C2×C3×#67C2×D314yes—
168C2×C3×C4×D3—34no—
169C2×C3×C4×D3C2×D314yescomplemented
170#3811—332no—
171C2×#626—34no—
172C2×#626—34no—
173C2×#624—34no—
174C2×#624—34no—
175C2×#624—34no—
176C2×D3×Dic3—34no—
177C2×D3×Dic3—34no—
178C4×D32—616no—
179C32×C4⋊C4—31no—
180C32×C22⋊C4—31no—
181C32×C22⋊C4—31no—
182C32×C42—31no—
183#3757—31no—
184#3757C2×D311yescharacteristic, complemented
185#3752—31no—
186#3752—31no—
187#3752—31no—
188#3752C2×D311yescharacteristic, complemented
189C4⋊(C3⋊Dic3)—31no—
190#3750—31no—
191#3750C2×D311yescharacteristic, complemented
192C4×C3⋊Dic3—31no—
193C4×C3⋊Dic3—31no—
194C4×C3⋊Dic3C2×D311yescharacteristic, complemented
195C3×#217—34no—
196C3×#217C2×D314yescomplemented
197C3×(C2×D3)⋊C4—34no—
198C3×(C2×D3)⋊C4C2×D314yescomplemented
199C3×Dic3⋊C4—34no—
200C3×Dic3⋊C4C2×D314yescomplemented
201C3×C4×Dic3—34no—
202C3×C4×Dic3C2×D314yescomplemented
203Dic3⋊Dic3—34no—
204Dic3⋊Dic3—34no—
205#3722—34no—
206#3722—34no—
207(C2×D3)⋊Dic3—34no—
208(C2×D3)⋊Dic3—34no—
209Dic32—34no—
210Dic32—34no—
211C22×C33—21no—
212C22×C33—21no—
213C22×C33C22×C412yescomplemented
214C22×C33C2411yescharacteristic
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—21no—
217C2×C3⋊(C3⋊D3)—28no—
218C2×C3⋊(C3⋊D3)C22×C412yes—
219C2×C3⋊(C3⋊D3)C22×C412yescomplemented
220C2×C3⋊(C3⋊D3)C2×D412yes—
221C2×C3⋊(C3⋊D3)#4112yes—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3—21no—
224C2×C3×C3⋊D3C22×C412yescomplemented
225C2×C32×D3—21no—
226C2×C32×D3—21no—
227C2×C32×D3C22×C412yescomplemented
228D3×C3⋊D3—28no—
229C33×C4—21no—
230C33×C4C2×D412yescomplemented
231C3⋊(C3⋊Dic3)—21no—
232C3⋊(C3⋊Dic3)C2×D412yescomplemented
233C3×C3⋊Dic3—21no—
234C3×C3⋊Dic3—21no—
235C3×C3⋊Dic3C22×C412yescomplemented
236C32×Dic3—21no—
237C32×Dic3—21no—
238C32×Dic3C22×C412yescomplemented
239C2×D3×D4—94no—
240C2×D3×D4—91no—
241C22×C4×D3—94no—
242C22×C4×D3—94no—
243C22×C4×D3—91no—
244C22×C4×D3—91no—
245C22×C4×D3—184no—
246C3×C4×D4—34no—
247C3×C4×D4—91no—
248D4×Dic3—94no—
249D4×Dic3—91no—
250C4×#67—34no—
251C4×#67—94no—
252C4×#67—91no—
253C4×#67C3⋊D311yescharacteristic, complemented
254#893—94no—
255#893—91no—
256D3×C4⋊C4—94no—
257D3×C4⋊C4—91no—
258#67⋊C4—94no—
259#67⋊C4—94no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262D3×C22⋊C4—94no—
263D3×C22⋊C4—94no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266C4×D12—94no—
267C4×D12—91no—
268C42×D3—94no—
269C42×D3—91no—
270C23×C32—24no—
271C23×C32—31no—
272C23×C32C22×D314yes—
273C23×C32C22×D311yescharacteristic
274C22×C3⋊D3—31no—
275C22×C3⋊D3—34no—
276C22×C3⋊D3—31no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—34no—
279C22×C3⋊D3—316no—
280C22×C3⋊D3—34no—
281C22×C3⋊D3—616no—
282C22×C3⋊D3—64no—
283C22×C3⋊D3—64no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—62no—
289C22×C3⋊D3—68no—
290C22×C3⋊D3—616no—
291C22×C3⋊D3—616no—
292C22×C3⋊D3C22×D311yescharacteristic
293C22×C3×D3—34no—
294C22×C3×D3C22×D314yes—
295C2×D32—316no—
296C2×D32—68no—
297C2×D32—68no—
298C32×D4—34no—
299C2×C32×C4—216no—
300C2×C32×C4—28no—
301C2×C32×C4—22no—
302C2×C32×C4—24no—
303C2×C32×C4—24no—
304C2×C32×C4—31no—
305C2×C32×C4—31no—
306C2×C32×C4—31no—
307C2×C32×C4—62no—
308C2×C32×C4C22×D314yes—
309C2×C32×C4C22×D314yes—
310C2×C32×C4C22×D311yescharacteristic
311C2×C32×C4C22×D311yescharacteristic
312#638—34no—
313#638C4×D314yescomplemented
314C2×C3⋊Dic3—31no—
315C2×C3⋊Dic3—31no—
316C2×C3⋊Dic3—34no—
317C2×C3⋊Dic3—34no—
318C2×C3⋊Dic3—64no—
319C2×C3⋊Dic3—64no—
320C2×C3⋊Dic3—62no—
321C2×C3⋊Dic3—62no—
322C2×C3⋊Dic3—68no—
323C2×C3⋊Dic3—616no—
324C2×C3⋊Dic3C22×D311yescharacteristic
325C2×C3⋊Dic3C22×D311yescharacteristic
326C2×C3⋊Dic3C22×D311yescharacteristic
327C4⋊(C3⋊D3)—34no—
328C4×C3⋊D3—22no—
329C4×C3⋊D3—34no—
330C4×C3⋊D3—34no—
331C4×C3⋊D3—316no—
332C4×C3⋊D3—616no—
333C4×C3⋊D3—62no—
334C4×C3⋊D3—62no—
335C4×C3⋊D3—62no—
336C4×C3⋊D3—68no—
337C4×C3⋊D3—62no—
338C4×C3⋊D3—62no—
339C4×C3⋊D3—68no—
340C4×C3⋊D3—616no—
341C4×C3⋊D3—616no—
342C4×C3⋊D3—616no—
343C4×C3⋊D3—68no—
344C4×C3⋊D3—62no—
345C3×#67—316no—
346C3×#67C4×D3116yescomplemented
347C2×C3×Dic3—34no—
348C2×C3×Dic3—34no—
349C2×C3×Dic3—34no—
350C2×C3×Dic3C22×D314yes—
351C2×C3×Dic3C22×D314yes—
352C2×C3×Dic3C22×D314yes—
353C3×C4×D3—28no—
354C3×C4×D3—68no—
355#626—316no—
356#626—316no—
357#624—316no—
358#624—68no—
359#624—68no—
360D3×Dic3—68no—
361D3×Dic3—68no—
362C2×C4×D4—271noSylow
363C2×C33—22no—
364C2×C33C23×C411yescharacteristic
365C2×C33C22×D411yescharacteristic
366C2×C33C2×#4111yescharacteristic
367C3⋊(C3⋊D3)—22no—
368C3⋊(C3⋊D3)C4×D414yescomplemented
369C3×C3⋊D3—22no—
370C32×D3—22no—
371C23×D3—94no—
372C23×D3—94no—
373C23×D3—91no—
374C23×D3—91no—
375C23×D3—184no—
376C2×C3×D4—34no—
377C2×C3×D4—91no—
378C22×C3×C4—24no—
379C22×C3×C4—34no—
380C22×C3×C4—91no—
381C22×C3×C4D3214yescomplemented
382C22×C3×C4C2×C3⋊D311yescharacteristic, complemented
383C2×#67—34no—
384C2×#67—94no—
385C2×#67—91no—
386C2×#67C2×C3⋊D311yescharacteristic
387C22×Dic3—94no—
388C22×Dic3—94no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—184no—
392D3×D4—932no—
393D3×D4—98no—
394C2×D12—94no—
395C2×D12—91no—
396C2×C4×D3—34no—
397C2×C4×D3—94no—
398C2×C4×D3—94no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—94no—
402C2×C4×D3—94no—
403C2×C4×D3—94no—
404C2×C4×D3—91no—
405C2×C4×D3—94no—
406C2×C4×D3—94no—
407C2×C4×D3—94no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—184no—
414C2×C4×D3—184no—
415C2×C4×D3—184no—
416C2×C4×D3—184no—
417C2×C4×D3—184no—
418C2×C4×D3—1816no—
419C2×C4×D3—1816no—
420C2×C4×D3—184no—
421C2×C4×D3—1832no—
422C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
423C3×C4⋊C4—34no—
424C3×C4⋊C4—91no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C42—34no—
430C3×C42—91no—
431#217—34no—
432#217—94no—
433#217—91no—
434#217C2×C3⋊D311yescharacteristic, complemented
435(C2×D3)⋊C4—34no—
436(C2×D3)⋊C4—94no—
437(C2×D3)⋊C4—94no—
438(C2×D3)⋊C4—94no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
443C4⋊Dic3—94no—
444C4⋊Dic3—91no—
445Dic3⋊C4—34no—
446Dic3⋊C4—94no—
447Dic3⋊C4—91no—
448Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
449C4×Dic3—34no—
450C4×Dic3—94no—
451C4×Dic3—94no—
452C4×Dic3—91no—
453C4×Dic3—91no—
454C4×Dic3C2×C3⋊D311yescharacteristic, complemented
455C22×C32—28no—
456C22×C32—28no—
457C22×C32—24no—
458C22×C32—21no—
459C22×C32—24no—
460C22×C32—21no—
461C22×C32—24no—
462C22×C32—28no—
463C22×C32—32no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32C2×C4×D318yescomplemented
467C22×C32C2×C4×D312yescomplemented
468C22×C32C23×D314yes—
469C22×C32C23×D311yescharacteristic
470C2×C3⋊D3—21no—
471C2×C3⋊D3—21no—
472C2×C3⋊D3—32no—
473C2×C3⋊D3—32no—
474C2×C3⋊D3—32no—
475C2×C3⋊D3—32no—
476C2×C3⋊D3—38no—
477C2×C3⋊D3—38no—
478C2×C3⋊D3—38no—
479C2×C3⋊D3—38no—
480C2×C3⋊D3—68no—
481C2×C3⋊D3—68no—
482C2×C3⋊D3—68no—
483C2×C3⋊D3—68no—
484C2×C3⋊D3—68no—
485C2×C3⋊D3—68no—
486C2×C3⋊D3—632no—
487C2×C3⋊D3—68no—
488C2×C3⋊D3—664no—
489C2×C3⋊D3—68no—
490C2×C3⋊D3—64no—
491C2×C3⋊D3—61no—
492C2×C3⋊D3—64no—
493C2×C3⋊D3—61no—
494C2×C3⋊D3C2×C4×D312yescomplemented
495C2×C3×D3—24no—
496C2×C3×D3—24no—
497C2×C3×D3—38no—
498C2×C3×D3—64no—
499C2×C3×D3—64no—
500C2×C3×D3C2×C4×D318yescomplemented
501D32—632no—
502C32×C4—28no—
503C32×C4—24no—
504C32×C4—21no—
505C32×C4—28no—
506C32×C4—32no—
507C32×C4—61no—
508C32×C4—61no—
509C32×C4D3×D418yescomplemented
510C32×C4D3×D412yescomplemented
511C3⋊Dic3—21no—
512C3⋊Dic3—21no—
513C3⋊Dic3—32no—
514C3⋊Dic3—38no—
515C3⋊Dic3—68no—
516C3⋊Dic3—68no—
517C3⋊Dic3—64no—
518C3⋊Dic3—61no—
519C3⋊Dic3C2×C4×D312yescomplemented
520C3×Dic3—24no—
521C3×Dic3—24no—
522C3×Dic3—38no—
523C3×Dic3—64no—
524C3×Dic3—64no—
525C3×Dic3C2×C4×D318yescomplemented
526C22×D4—271no—
527C23×C4—271no—
528C23×C4—271no—
529C4×D4—31no—
530C4×D4—91no—
531C4×D4—271no—
532C4×D4—271no—
533C4×D4—271no—
534C4×D4—271no—
535C4×D4—271no—
536C4×D4—271no—
537C2×C4⋊C4—271no—
538C2×C22⋊C4—271no—
539C2×C22⋊C4—271no—
540C2×C42—271no—
541C33C2×C4×D411yescharacteristic, complemented, Sylow
542C23×C3—24no—
543C23×C3—34no—
544C23×C3—91no—
545C23×C3C2×D3214yes—
546C23×C3C22×C3⋊D311yescharacteristic
547C22×D3—34no—
548C22×D3—916no—
549C22×D3—94no—
550C22×D3—91no—
551C22×D3—94no—
552C22×D3—91no—
553C22×D3—916no—
554C22×D3—94no—
555C22×D3—94no—
556C22×D3—184no—
557C22×D3—184no—
558C22×D3—1816no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—188no—
562C22×D3—188no—
563C22×D3—188no—
564C22×D3—182no—
565C22×D3—188no—
566C22×D3—182no—
567C22×D3—1816no—
568C22×D3—1816no—
569C22×D3C22×C3⋊D311yescharacteristic
570C3×D4—316no—
571C3×D4—94no—
572C2×C3×C4—216no—
573C2×C3×C4—28no—
574C2×C3×C4—22no—
575C2×C3×C4—24no—
576C2×C3×C4—24no—
577C2×C3×C4—34no—
578C2×C3×C4—34no—
579C2×C3×C4—34no—
580C2×C3×C4—68no—
581C2×C3×C4—91no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—182no—
585C2×C3×C4C2×D3214yes—
586C2×C3×C4C2×D3214yes—
587C2×C3×C4C22×C3⋊D311yescharacteristic
588C2×C3×C4C22×C3⋊D311yescharacteristic
589#67—316no—
590#67—916no—
591#67—94no—
592#67C4×C3⋊D314yescomplemented
593C2×Dic3—34no—
594C2×Dic3—34no—
595C2×Dic3—34no—
596C2×Dic3—94no—
597C2×Dic3—91no—
598C2×Dic3—94no—
599C2×Dic3—91no—
600C2×Dic3—184no—
601C2×Dic3—184no—
602C2×Dic3—182no—
603C2×Dic3—188no—
604C2×Dic3—188no—
605C2×Dic3—182no—
606C2×Dic3—1816no—
607C2×Dic3C22×C3⋊D311yescharacteristic
608C2×Dic3C22×C3⋊D311yescharacteristic
609C2×Dic3C22×C3⋊D311yescharacteristic
610D12—916no—
611D12—94no—
612C4×D3—22no—
613C4×D3—68no—
614C4×D3—916no—
615C4×D3—916no—
616C4×D3—94no—
617C4×D3—94no—
618C4×D3—1816no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—188no—
622C4×D3—188no—
623C4×D3—188no—
624C4×D3—182no—
625C4×D3—188no—
626C4×D3—182no—
627C4×D3—188no—
628C4×D3—182no—
629C4×D3—1816no—
630C4×D3—1816no—
631C4×D3—1816no—
632C4×D3—188no—
633C4×D3—182no—
634C2×C32—216no—
635C2×C32—28no—
636C2×C32—22no—
637C2×C32—24no—
638C2×C32—24no—
639C2×C32—24no—
640C2×C32—62no—
641C2×C32C22×C4×D314yes—
642C2×C32C22×C4×D311yescharacteristic
643C2×C32C2×D3×D414yes—
644C2×C32C2×D3×D411yescharacteristic
645C2×C32D3×#4114yes—
646C2×C32D3×#4111yescharacteristic
647C3⋊D3—22no—
648C3⋊D3—34no—
649C3⋊D3—316no—
650C3⋊D3—616no—
651C3⋊D3—616no—
652C3⋊D3—68no—
653C3⋊D3—62no—
654C3×D3—28no—
655C3×D3—68no—
656C24—271no—
657C24—271no—
658C2×D4—31no—
659C2×D4—91no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—278no—
663C22×C4—31no—
664C22×C4—91no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C22×C4—271no—
671C22×C4—271no—
672C22×C4—271no—
673C22×C4—271no—
674C22×C4—271no—
675C22×C4—544no—
676C22×C4—544no—
677C22×C4D3×C3⋊D311yescharacteristic, complemented
678C4⋊C4—31no—
679C4⋊C4—91no—
680C4⋊C4—271no—
681C4⋊C4—271no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—271no—
687C22⋊C4—271no—
688C22⋊C4—271no—
689C22⋊C4—271no—
690C42—31no—
691C42—91no—
692C42—271no—
693C42—271no—
694C22×C3—28no—
695C22×C3—28no—
696C22×C3—24no—
697C22×C3—24no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—24no—
701C22×C3—28no—
702C22×C3—38no—
703C22×C3—64no—
704C22×C3—64no—
705C22×C3—92no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3C4×D3218yescomplemented
709C22×C3C2×C4×C3⋊D312yescomplemented
710C22×C3C22×D3214yes—
711C22×C3C23×C3⋊D311yescharacteristic
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—38no—
715C2×D3—64no—
716C2×D3—64no—
717C2×D3—98no—
718C2×D3—98no—
719C2×D3—98no—
720C2×D3—92no—
721C2×D3—92no—
722C2×D3—92no—
723C2×D3—98no—
724C2×D3—92no—
725C2×D3—188no—
726C2×D3—188no—
727C2×D3—188no—
728C2×D3—188no—
729C2×D3—188no—
730C2×D3—1832no—
731C2×D3—188no—
732C2×D3—1832no—
733C2×D3—188no—
734C2×D3—1864no—
735C2×D3—188no—
736C2×D3—184no—
737C2×D3—184no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3C2×C4×C3⋊D312yescomplemented
741C3×C4—28no—
742C3×C4—24no—
743C3×C4—21no—
744C3×C4—28no—
745C3×C4—38no—
746C3×C4—64no—
747C3×C4—64no—
748C3×C4—92no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4#381118yescomplemented
752C3×C4D4×C3⋊D312yescomplemented
753Dic3—21no—
754Dic3—21no—
755Dic3—38no—
756Dic3—64no—
757Dic3—64no—
758Dic3—98no—
759Dic3—92no—
760Dic3—188no—
761Dic3—188no—
762Dic3—184no—
763Dic3—181no—
764Dic3C2×C4×C3⋊D312yescomplemented
765C32—24no—
766C32C4×D3×D414yescomplemented
767C32C4×D3×D411yescharacteristic, complemented
768C23—31no—
769C23—91no—
770C23—274no—
771C23—271no—
772C23—271no—
773C23—274no—
774C23—542no—
775C23—542no—
776C23—542no—
777C23—542no—
778C23C2×D3×C3⋊D311yescharacteristic
779D4—34no—
780D4—94no—
781D4—274no—
782D4—274no—
783C2×C4—22no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—62no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—182no—
792C2×C4—274no—
793C2×C4—271no—
794C2×C4—274no—
795C2×C4—271no—
796C2×C4—542no—
797C2×C4—542no—
798C2×C4—542no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4—542no—
803C2×C4—542no—
804C2×C4C2×D3×C3⋊D311yescharacteristic
805C2×C4C2×D3×C3⋊D311yescharacteristic
806C2×C3—216no—
807C2×C3—22no—
808C2×C3—28no—
809C2×C3—24no—
810C2×C3—24no—
811C2×C3—24no—
812C2×C3—68no—
813C2×C3—182no—
814C2×C3C2×C4×D3214yes—
815C2×C3#6430614yes—
816C2×C3C2×#381114yes—
817C2×C3C22×C4×C3⋊D311yescharacteristic
818C2×C3C2×D4×C3⋊D311yescharacteristic
819C2×C3#41×C3⋊D311yescharacteristic
820D3—22no—
821D3—68no—
822D3—94no—
823D3—916no—
824D3—1816no—
825D3—1816no—
826D3—182no—
827D3—188no—
828C22—21no—
829C22—21no—
830C22—32no—
831C22—61no—
832C22—61no—
833C22—92no—
834C22—181no—
835C22—181no—
836C22—272no—
837C22—272no—
838C22—272no—
839C22—272no—
840C22—548no—
841C22—548no—
842C22—541no—
843C22—541no—
844C22C4×D3×C3⋊D312yescomplemented
845C22C22×D3×C3⋊D311yescharacteristic
846C4—21no—
847C4—32no—
848C4—61no—
849C4—61no—
850C4—92no—
851C4—181no—
852C4—181no—
853C4—272no—
854C4—541no—
855C4#8903912yesdirect product factor
856C3—24no—
857C3C4×#381114yescomplemented
858C3C4×D4×C3⋊D311yescharacteristic, complemented
859C2—22no—
860C2—62no—
861C2—182no—
862C2—274no—
863C2—542no—
864C2C2×C4×D3×C3⋊D311yescharacteristic
865C2#1172457811yescharacteristic
866C2C2×#8903911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×C3⋊D3
commutatorC2×C33C23×C4
FrattiniC22C22×D3×C3⋊D3
FittingC22×C33×C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89039C2
hypercenterC22×C4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊(C3⋊D3)C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. C3×C4×#638C2semidirect
5. C32×C4×#67C2semidirect
6. #11723627C2semidirect
7. #11723626C2semidirect
8. #67⋊(C3⋊Dic3)C2semidirect
9. #11723539C2semidirect
10. C4×#6292C2semidirect
11. C4×#6291C2semidirect
12. #11723472C2semidirect
13. #11723470C2semidirect
14. C4×#6289C2semidirect
15. #11723462C2semidirect
20. C22×C33×C4C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
25. C2×C4×C3⋊(C3⋊D3)C22semidirect
26. C2×C4×C3⋊(C3⋊D3)C22semidirect
28. C2×C3×C4×C3⋊D3C22semidirect
30. C2×C32×C4×D3C22semidirect
31. #89039C4direct (N × H)
37. C2×Dic3×C3⋊D3C22semidirect
38. C2×D3×C3⋊Dic3C22semidirect
40. C3×#3757C22semidirect
41. C3×#3752C22semidirect
42. C3×#3750C22semidirect
43. C3×C4×C3⋊Dic3C22semidirect
44. C32×#217C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. C32×C4×Dic3C22semidirect
48. #88807C22semidirect
49. Dic3⋊(C3⋊Dic3)C22semidirect
50. #88804C22semidirect
51. #88804C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. Dic3×C3⋊Dic3C22semidirect
66. C4×#638D3semidirect
76. C3×C4×#67D3semidirect
90. C22×C3⋊(C3⋊D3)C2×C4semidirect
97. C2×D3×C3⋊D3C2×C4semidirect
107. C4×C3⋊(C3⋊D3)D4semidirect
108. C3×#638C2×C4semidirect
113. C32×#67C2×C4semidirect
118. #6292C2×C4semidirect
119. #6291C2×C4semidirect
122. #6289C2×C4semidirect
135. C22×C32×C4C2×D3semidirect
136. C22×C32×C4C2×D3semidirect
165. C2×C4×C3⋊D3C2×D3semidirect
169. C2×C3×C4×D3C2×D3semidirect
184. #3757C2×D3semidirect
188. #3752C2×D3semidirect
191. #3750C2×D3semidirect
194. C4×C3⋊Dic3C2×D3semidirect
196. C3×#217C2×D3semidirect
198. C3×(C2×D3)⋊C4C2×D3semidirect
200. C3×Dic3⋊C4C2×D3semidirect
202. C3×C4×Dic3C2×D3semidirect
213. C22×C33C22×C4semidirect
219. C2×C3⋊(C3⋊D3)C22×C4semidirect
224. C2×C3×C3⋊D3C22×C4semidirect
227. C2×C32×D3C22×C4semidirect
230. C33×C4C2×D4semidirect
232. C3⋊(C3⋊Dic3)C2×D4semidirect
235. C3×C3⋊Dic3C22×C4semidirect
238. C32×Dic3C22×C4semidirect
253. C4×#67C3⋊D3semidirect
313. #638C4×D3semidirect
346. C3×#67C4×D3semidirect
368. C3⋊(C3⋊D3)C4×D4semidirect
381. C22×C3×C4D32semidirect
382. C22×C3×C4C2×C3⋊D3semidirect
422. C2×C4×D3C2×C3⋊D3semidirect
434. #217C2×C3⋊D3semidirect
442. (C2×D3)⋊C4C2×C3⋊D3semidirect
448. Dic3⋊C4C2×C3⋊D3semidirect
454. C4×Dic3C2×C3⋊D3semidirect
466. C22×C32C2×C4×D3semidirect
467. C22×C32C2×C4×D3semidirect
494. C2×C3⋊D3C2×C4×D3semidirect
500. C2×C3×D3C2×C4×D3semidirect
509. C32×C4D3×D4semidirect
510. C32×C4D3×D4semidirect
519. C3⋊Dic3C2×C4×D3semidirect
525. C3×Dic3C2×C4×D3semidirect
541. C33C2×C4×D4semidirect
592. #67C4×C3⋊D3semidirect
677. C22×C4D3×C3⋊D3semidirect
708. C22×C3C4×D32semidirect
709. C22×C3C2×C4×C3⋊D3semidirect
740. C2×D3C2×C4×C3⋊D3semidirect
751. C3×C4#3811semidirect
752. C3×C4D4×C3⋊D3semidirect
764. Dic3C2×C4×C3⋊D3semidirect
766. C32C4×D3×D4semidirect
767. C32C4×D3×D4semidirect
844. C22C4×D3×C3⋊D3semidirect
855. C4#89039direct (N × H)
857. C3C4×#3811semidirect
858. C3C4×D4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊(C3⋊D3)2
C2×#890392
C2×C4×D3×C3⋊D32
C3×C4×#6382
C32×C4×#672
#117236272
#117236262
#67⋊(C3⋊Dic3)2
#117235392
C4×#62922
C4×#62912
#117234722
#117234702
C4×#62892
#117234622
C4×D4×C3⋊D33
C4×#38113