Finite Group Databasebeta

← #13175912

Subgroups — #13175912

Order 1728.

3084 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic
2C22×#6289C211yesmaximal, characteristic, complemented
3C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
4C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
5C3×#64090C211yesmaximal, characteristic, complemented
6C32×#67⋊C4C211yesmaximal, characteristic, complemented
7#67×C3⋊Dic3C211yesmaximal, characteristic, complemented
8Dic3×#638C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723512C211yesmaximal, characteristic, complemented
11#11723510C211yesmaximal, characteristic, complemented
12#11723471C211yesmaximal, characteristic, complemented
13#11723470C211yesmaximal, characteristic, complemented
14C4×#6289C211yesmaximal, characteristic, complemented
15#11723461C211yesmaximal, characteristic, complemented
16C4×D4×C3⋊D3—31nomaximal
17#10594255—34nomaximal
18C23×C3⋊(C3⋊D3)C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×#638C2211yescharacteristic
23C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×C32×C4×D3C2211yescharacteristic, complemented
28#89039C418yescomplemented
29C2×#6292C2211yescharacteristic
30C2×#6291C2211yescharacteristic
31C2×#6289—24no—
32C2×#6289C2211yescharacteristic
33C2×#6289C2211yescharacteristic
34C2×#6289C2211yescharacteristic
35C2×#6289C2211yescharacteristic, complemented
36C2×#6289C2211yescharacteristic, complemented
37C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
38C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
39C4×D3×C3⋊D3—24no—
40C33×C22⋊C4C2211yescharacteristic, complemented
41#88864C2211yescharacteristic, complemented
42#88859C2211yescharacteristic, complemented
43#88859C2211yescharacteristic, complemented
44C3×#3752C2211yescharacteristic, complemented
45C3×#3750C2211yescharacteristic, complemented
46C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
47C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C32×Dic3⋊C4C2211yescharacteristic, complemented
49C32×C4×Dic3C2211yescharacteristic, complemented
50#88807C2211yescharacteristic, complemented
51Dic3⋊(C3⋊Dic3)C2211yescharacteristic, 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—
59C2×#3811—34no—
60C22×#624—34no—
61C2×C4×D32—34no—
62C32×C4×D4—31no—
63D4×C3⋊Dic3—31no—
64C4×#638—31no—
65C4×#638—31no—
66#64102—31no—
67C4⋊C4×C3⋊D3—31no—
68#64090—31no—
69#64090D311yescharacteristic, complemented
70C22⋊C4×C3⋊D3—31no—
71C22⋊C4×C3⋊D3—31no—
72C22⋊C4×C3⋊D3—34no—
73C22⋊C4×C3⋊D3—64no—
74C4×C4⋊(C3⋊D3)—31no—
75C42×C3⋊D3—31no—
76C3×#67⋊C4—34no—
77C3×#67⋊C4D314yescomplemented
78Dic3×#67—34no—
79Dic3×#67—34no—
80#63921—34no—
81#63904—34no—
82#63904—34no—
83#63883—34no—
84C4×#624—34no—
85#63880—34no—
86#63880—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×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C4×C3⋊(C3⋊D3)—22no—
103C4×C3⋊(C3⋊D3)—22no—
104C3×#638C2×C414yescomplemented
105C2×C3×C3⋊Dic3—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C2×C3×C3⋊Dic3C2311yescharacteristic
109C3×C4×C3⋊D3—22no—
110C32×#67C2×C414yescomplemented
111C2×C32×Dic3—22no—
112C2×C32×Dic3C2311yescharacteristic
113C2×C32×Dic3C2311yescharacteristic
114C2×C32×Dic3C2311yescharacteristic
115C32×C4×D3—22no—
116#6292C2×C414yescomplemented
117#6291C2×C414yescomplemented
118#6289—22no—
119#6289—22no—
120#6289—22no—
121#6289C2×C414yescomplemented
122#6289D414yescomplemented
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—31no—
134C22×C32×C4—31no—
135C2×#638—31no—
136C2×#638C2×D311yescharacteristic
137C22×C3⋊Dic3—31no—
138C22×C3⋊Dic3C2×D311yescharacteristic, complemented
139D4×C3⋊D3—38no—
140C2×C4⋊(C3⋊D3)—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—31no—
143C2×C4×C3⋊D3—31no—
144C2×C4×C3⋊D3—31no—
145C2×C4×C3⋊D3—31no—
146C2×C4×C3⋊D3—34no—
147C2×C4×C3⋊D3—34no—
148C2×C4×C3⋊D3—31no—
149C2×C4×C3⋊D3—31no—
150C2×C4×C3⋊D3—31no—
151C2×C4×C3⋊D3—64no—
152C2×C4×C3⋊D3—64no—
153C2×C4×C3⋊D3—64no—
154C2×C4×C3⋊D3—64no—
155C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
156C2×C3×#67—34no—
157C2×C3×#67C2×D314yes—
158C22×C3×Dic3—34no—
159C22×C3×Dic3C2×D314yescomplemented
160C2×C3×C4×D3—34no—
161C2×C3×C4×D3C2×D314yescomplemented
162#3811—332no—
163C2×#626—34no—
164C2×#626—34no—
165C2×#624—34no—
166C2×#624—34no—
167C2×#624—34no—
168C2×#624—34no—
169C2×#624—34no—
170C2×#624—616no—
171C2×D3×Dic3—34no—
172C2×D3×Dic3—34no—
173C4×D32—616no—
174C32×C4⋊C4—31no—
175C32×C22⋊C4—24no—
176C32×C22⋊C4—31no—
177C32×C22⋊C4C2×D314yescomplemented
178C32×C22⋊C4C2×D311yescharacteristic, complemented
179C32×C42—31no—
180#3757—31no—
181#3757—34no—
182#3757—31no—
183#3757—64no—
184#3752—31no—
185#3752—31no—
186#3752—31no—
187#3752—34no—
188#3752—34no—
189#3752—64no—
190#3752—64no—
191#3752C2×D311yescharacteristic, complemented
192C4⋊(C3⋊Dic3)—31no—
193#3750—31no—
194#3750C2×D311yescharacteristic, complemented
195C4×C3⋊Dic3—31no—
196C4×C3⋊Dic3—31no—
197C4×C3⋊Dic3C2×D311yescharacteristic, complemented
198C3×(C2×D3)⋊C4—34no—
199C3×(C2×D3)⋊C4C2×D314yescomplemented
200C3×Dic3⋊C4—34no—
201C3×Dic3⋊C4C2×D314yescomplemented
202C3×C4×Dic3—34no—
203C3×C4×Dic3C2×D314yescomplemented
204Dic3⋊Dic3—34no—
205Dic3⋊Dic3—34no—
206(C2×D3)⋊Dic3—34no—
207(C2×D3)⋊Dic3—34no—
208Dic32—34no—
209Dic32—34no—
210C22×C33—21no—
211C22×C33—21no—
212C22×C33C22×C412yescomplemented
213C22×C33C2411yescharacteristic
214C2×C3⋊(C3⋊D3)—21no—
215C2×C3⋊(C3⋊D3)—21no—
216C2×C3⋊(C3⋊D3)—28no—
217C2×C3⋊(C3⋊D3)C22×C412yes—
218C2×C3⋊(C3⋊D3)C22×C412yescomplemented
219C2×C3⋊(C3⋊D3)C2×D412yes—
220C2×C3⋊(C3⋊D3)#4112yes—
221C2×C3×C3⋊D3—21no—
222C2×C3×C3⋊D3—21no—
223C2×C3×C3⋊D3C22×C412yescomplemented
224C2×C32×D3—21no—
225C2×C32×D3—21no—
226C2×C32×D3C22×C412yescomplemented
227D3×C3⋊D3—28no—
228C33×C4—21no—
229C33×C4—21no—
230C3⋊(C3⋊Dic3)—21no—
231C3⋊(C3⋊Dic3)—21no—
232C3×C3⋊Dic3—21no—
233C3×C3⋊Dic3C22×C412yescomplemented
234C3×C3⋊Dic3C2×D412yescomplemented
235C32×Dic3—21no—
236C32×Dic3C22×C412yescomplemented
237C32×Dic3C2×D412yescomplemented
238C2×D3×D4—94no—
239C2×D3×D4—91no—
240C22×C4×D3—94no—
241C22×C4×D3—94no—
242C22×C4×D3—91no—
243C22×C4×D3—91no—
244C3×C4×D4—34no—
245C3×C4×D4—91no—
246D4×Dic3—94no—
247D4×Dic3—91no—
248C4×#67—94no—
249C4×#67—94no—
250C4×#67—91no—
251C4×#67—91no—
252#893—94no—
253#893—91no—
254D3×C4⋊C4—94no—
255D3×C4⋊C4—91no—
256#67⋊C4—34no—
257#67⋊C4—94no—
258#67⋊C4—91no—
259#67⋊C4C3⋊D311yescharacteristic, complemented
260D3×C22⋊C4—94no—
261D3×C22⋊C4—94no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—184no—
265C4×D12—94no—
266C4×D12—91no—
267C42×D3—94no—
268C42×D3—91no—
269C23×C32—24no—
270C23×C32—31no—
271C23×C32C22×D314yes—
272C23×C32C22×D311yescharacteristic
273C22×C3⋊D3—31no—
274C22×C3⋊D3—34no—
275C22×C3⋊D3—31no—
276C22×C3⋊D3—34no—
277C22×C3⋊D3—34no—
278C22×C3⋊D3—316no—
279C22×C3⋊D3—34no—
280C22×C3⋊D3—64no—
281C22×C3⋊D3—64no—
282C22×C3⋊D3—616no—
283C22×C3⋊D3—62no—
284C22×C3⋊D3—62no—
285C22×C3⋊D3—62no—
286C22×C3⋊D3—62no—
287C22×C3⋊D3—68no—
288C22×C3⋊D3—68no—
289C22×C3⋊D3—128no—
290C22×C3⋊D3—128no—
291C22×C3⋊D3C22×D311yescharacteristic
292C22×C3×D3—34no—
293C22×C3×D3C22×D314yes—
294C2×D32—316no—
295C2×D32—68no—
296C2×D32—68no—
297C32×D4—34no—
298C2×C32×C4—24no—
299C2×C32×C4—24no—
300C2×C32×C4—31no—
301C2×C32×C4—31no—
302C2×C32×C4—31no—
303C2×C32×C4—62no—
304C2×C32×C4—62no—
305C2×C32×C4C22×D314yes—
306C2×C32×C4C22×D314yes—
307C2×C32×C4C22×D311yescharacteristic
308C2×C32×C4C22×D311yescharacteristic
309#638—34no—
310#638C4×D314yescomplemented
311C2×C3⋊Dic3—22no—
312C2×C3⋊Dic3—31no—
313C2×C3⋊Dic3—31no—
314C2×C3⋊Dic3—34no—
315C2×C3⋊Dic3—34no—
316C2×C3⋊Dic3—64no—
317C2×C3⋊Dic3—64no—
318C2×C3⋊Dic3—62no—
319C2×C3⋊Dic3C22×D311yescharacteristic
320C2×C3⋊Dic3C22×D311yescharacteristic
321C2×C3⋊Dic3C22×D311yescharacteristic
322C4⋊(C3⋊D3)—34no—
323C4×C3⋊D3—22no—
324C4×C3⋊D3—34no—
325C4×C3⋊D3—34no—
326C4×C3⋊D3—62no—
327C4×C3⋊D3—62no—
328C4×C3⋊D3—62no—
329C4×C3⋊D3—62no—
330C4×C3⋊D3—62no—
331C4×C3⋊D3—62no—
332C4×C3⋊D3—68no—
333C4×C3⋊D3—68no—
334C4×C3⋊D3—128no—
335C4×C3⋊D3—128no—
336C3×#67—316no—
337C3×#67C4×D3116yescomplemented
338C2×C3×Dic3—28no—
339C2×C3×Dic3—34no—
340C2×C3×Dic3—34no—
341C2×C3×Dic3—34no—
342C2×C3×Dic3—68no—
343C2×C3×Dic3C22×D314yes—
344C2×C3×Dic3C22×D314yes—
345C2×C3×Dic3C22×D314yes—
346C3×C4×D3—28no—
347C3×C4×D3—68no—
348#626—316no—
349#626—316no—
350#624—316no—
351#624—316no—
352#624—68no—
353#624—68no—
354#624—68no—
355D3×Dic3—68no—
356D3×Dic3—68no—
357C2×C4×D4—271noSylow
358C2×C33—22no—
359C2×C33C23×C411yescharacteristic
360C2×C33C22×D411yescharacteristic
361C2×C33C2×#4111yescharacteristic
362C3⋊(C3⋊D3)—22no—
363C3⋊(C3⋊D3)C4×D414yescomplemented
364C3×C3⋊D3—22no—
365C32×D3—22no—
366C23×D3—94no—
367C23×D3—94no—
368C23×D3—91no—
369C23×D3—91no—
370C23×D3—184no—
371C2×C3×D4—34no—
372C2×C3×D4—91no—
373C22×C3×C4—34no—
374C22×C3×C4—34no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C2×#67—34no—
378C2×#67—94no—
379C2×#67—91no—
380C2×#67C2×C3⋊D311yescharacteristic
381C22×Dic3—34no—
382C22×Dic3—94no—
383C22×Dic3—91no—
384C22×Dic3C2×C3⋊D311yescharacteristic, complemented
385D3×D4—932no—
386D3×D4—98no—
387C2×D12—94no—
388C2×D12—91no—
389C2×C4×D3—34no—
390C2×C4×D3—94no—
391C2×C4×D3—94no—
392C2×C4×D3—91no—
393C2×C4×D3—91no—
394C2×C4×D3—94no—
395C2×C4×D3—94no—
396C2×C4×D3—94no—
397C2×C4×D3—94no—
398C2×C4×D3—91no—
399C2×C4×D3—94no—
400C2×C4×D3—94no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—184no—
407C2×C4×D3—184no—
408C2×C4×D3—184no—
409C2×C4×D3—1816no—
410C2×C4×D3—184no—
411C2×C4×D3—1816no—
412C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
413C3×C4⋊C4—34no—
414C3×C4⋊C4—91no—
415C3×C22⋊C4—24no—
416C3×C22⋊C4—34no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4D3214yescomplemented
419C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
420C3×C42—34no—
421C3×C42—91no—
422#217—94no—
423#217—94no—
424#217—91no—
425#217—91no—
426#217—184no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—94no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—94no—
431(C2×D3)⋊C4—94no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—184no—
435(C2×D3)⋊C4—184no—
436(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
437C4⋊Dic3—94no—
438C4⋊Dic3—91no—
439Dic3⋊C4—34no—
440Dic3⋊C4—94no—
441Dic3⋊C4—91no—
442Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
443C4×Dic3—34no—
444C4×Dic3—94no—
445C4×Dic3—94no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C4×Dic3C2×C3⋊D311yescharacteristic, complemented
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—24no—
452C22×C32—28no—
453C22×C32—24no—
454C22×C32—24no—
455C22×C32—32no—
456C22×C32—44no—
457C22×C32—44no—
458C22×C32—61no—
459C22×C32—61no—
460C22×C32C2×C4×D318yescomplemented
461C22×C32C2×C4×D312yescomplemented
462C22×C32C23×D314yes—
463C22×C32C23×D311yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—32no—
467C2×C3⋊D3—32no—
468C2×C3⋊D3—32no—
469C2×C3⋊D3—32no—
470C2×C3⋊D3—38no—
471C2×C3⋊D3—38no—
472C2×C3⋊D3—38no—
473C2×C3⋊D3—38no—
474C2×C3⋊D3—68no—
475C2×C3⋊D3—68no—
476C2×C3⋊D3—68no—
477C2×C3⋊D3—68no—
478C2×C3⋊D3—68no—
479C2×C3⋊D3—68no—
480C2×C3⋊D3—61no—
481C2×C3⋊D3—61no—
482C2×C3⋊D3—632no—
483C2×C3⋊D3—64no—
484C2×C3⋊D3—64no—
485C2×C3⋊D3—1232no—
486C2×C3⋊D3—124no—
487C2×C3⋊D3—124no—
488C2×C3⋊D3C2×C4×D312yescomplemented
489C2×C3×D3—24no—
490C2×C3×D3—24no—
491C2×C3×D3—38no—
492C2×C3×D3—64no—
493C2×C3×D3—64no—
494C2×C3×D3C2×C4×D318yescomplemented
495D32—632no—
496C32×C4—21no—
497C32×C4—21no—
498C32×C4—24no—
499C32×C4—24no—
500C32×C4—32no—
501C32×C4—32no—
502C32×C4—44no—
503C32×C4—44no—
504C32×C4—61no—
505C3⋊Dic3—21no—
506C3⋊Dic3—61no—
507C3⋊Dic3—61no—
508C3⋊Dic3—64no—
509C3⋊Dic3—64no—
510C3⋊Dic3—124no—
511C3⋊Dic3—124no—
512C3⋊Dic3C2×C4×D312yescomplemented
513C3⋊Dic3D3×D412yescomplemented
514C3×Dic3—24no—
515C3×Dic3—38no—
516C3×Dic3—38no—
517C3×Dic3—64no—
518C3×Dic3C2×C4×D318yescomplemented
519C3×Dic3D3×D418yescomplemented
520C22×D4—271no—
521C23×C4—271no—
522C23×C4—271no—
523C4×D4—31no—
524C4×D4—91no—
525C4×D4—271no—
526C4×D4—271no—
527C4×D4—271no—
528C4×D4—271no—
529C4×D4—271no—
530C4×D4—271no—
531C2×C4⋊C4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C2×C42—271no—
535C33C2×C4×D411yescharacteristic, complemented, Sylow
536C23×C3—24no—
537C23×C3—34no—
538C23×C3—91no—
539C23×C3C2×D3214yes—
540C23×C3C22×C3⋊D311yescharacteristic
541C22×D3—34no—
542C22×D3—916no—
543C22×D3—94no—
544C22×D3—91no—
545C22×D3—94no—
546C22×D3—91no—
547C22×D3—916no—
548C22×D3—94no—
549C22×D3—94no—
550C22×D3—184no—
551C22×D3—184no—
552C22×D3—1816no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—188no—
556C22×D3—188no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—188no—
560C22×D3—188no—
561C22×D3—368no—
562C22×D3—368no—
563C22×D3C22×C3⋊D311yescharacteristic
564C3×D4—316no—
565C3×D4—94no—
566C2×C3×C4—24no—
567C2×C3×C4—24no—
568C2×C3×C4—34no—
569C2×C3×C4—34no—
570C2×C3×C4—34no—
571C2×C3×C4—68no—
572C2×C3×C4—68no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—182no—
577C2×C3×C4—182no—
578C2×C3×C4C2×D3214yes—
579C2×C3×C4C2×D3214yes—
580C2×C3×C4C22×C3⋊D311yescharacteristic
581C2×C3×C4C22×C3⋊D311yescharacteristic
582#67—316no—
583#67—916no—
584#67—94no—
585#67C4×C3⋊D314yescomplemented
586C2×Dic3—22no—
587C2×Dic3—34no—
588C2×Dic3—34no—
589C2×Dic3—34no—
590C2×Dic3—68no—
591C2×Dic3—94no—
592C2×Dic3—94no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—184no—
596C2×Dic3—184no—
597C2×Dic3—188no—
598C2×Dic3—182no—
599C2×Dic3C22×C3⋊D311yescharacteristic
600C2×Dic3C22×C3⋊D311yescharacteristic
601C2×Dic3C22×C3⋊D311yescharacteristic
602D12—916no—
603D12—94no—
604C4×D3—22no—
605C4×D3—68no—
606C4×D3—916no—
607C4×D3—916no—
608C4×D3—94no—
609C4×D3—94no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—188no—
613C4×D3—188no—
614C4×D3—188no—
615C4×D3—182no—
616C4×D3—182no—
617C4×D3—188no—
618C4×D3—188no—
619C4×D3—188no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—368no—
623C4×D3—368no—
624C2×C32—22no—
625C2×C32—24no—
626C2×C32—24no—
627C2×C32—24no—
628C2×C32—28no—
629C2×C32—48no—
630C2×C32—62no—
631C2×C32C22×C4×D314yes—
632C2×C32C22×C4×D311yescharacteristic
633C2×C32C2×D3×D414yes—
634C2×C32C2×D3×D411yescharacteristic
635C2×C32D3×#4114yes—
636C2×C32D3×#4111yescharacteristic
637C3⋊D3—22no—
638C3⋊D3—34no—
639C3⋊D3—316no—
640C3⋊D3—616no—
641C3⋊D3—62no—
642C3⋊D3—68no—
643C3⋊D3—128no—
644C3×D3—28no—
645C3×D3—68no—
646C24—271no—
647C24—271no—
648C2×D4—31no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—278no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—271no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C22×C4—271no—
666C22×C4—544no—
667C22×C4—544no—
668C4⋊C4—31no—
669C4⋊C4—91no—
670C4⋊C4—271no—
671C4⋊C4—271no—
672C22⋊C4—31no—
673C22⋊C4—91no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4D3×C3⋊D311yescharacteristic, complemented
680C42—31no—
681C42—91no—
682C42—271no—
683C42—271no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—24no—
689C22×C3—28no—
690C22×C3—38no—
691C22×C3—44no—
692C22×C3—44no—
693C22×C3—64no—
694C22×C3—64no—
695C22×C3—92no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C4×D3218yescomplemented
699C22×C3C2×C4×C3⋊D312yescomplemented
700C22×C3C22×D3214yes—
701C22×C3C23×C3⋊D311yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—38no—
705C2×D3—64no—
706C2×D3—64no—
707C2×D3—98no—
708C2×D3—98no—
709C2×D3—98no—
710C2×D3—92no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—98no—
714C2×D3—92no—
715C2×D3—188no—
716C2×D3—188no—
717C2×D3—188no—
718C2×D3—188no—
719C2×D3—188no—
720C2×D3—1832no—
721C2×D3—188no—
722C2×D3—1832no—
723C2×D3—184no—
724C2×D3—184no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—3632no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3C2×C4×C3⋊D312yescomplemented
731C3×C4—24no—
732C3×C4—24no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—38no—
736C3×C4—38no—
737C3×C4—44no—
738C3×C4—44no—
739C3×C4—64no—
740C3×C4—92no—
741C3×C4—92no—
742C3×C4—181no—
743Dic3—21no—
744Dic3—38no—
745Dic3—38no—
746Dic3—64no—
747Dic3—184no—
748Dic3—184no—
749Dic3—181no—
750Dic3—181no—
751Dic3—364no—
752Dic3—364no—
753Dic3C2×C4×C3⋊D312yescomplemented
754Dic3D4×C3⋊D312yescomplemented
755C32—24no—
756C32C4×D3×D414yescomplemented
757C32C4×D3×D411yescharacteristic, complemented
758C23—31no—
759C23—91no—
760C23—274no—
761C23—271no—
762C23—271no—
763C23—274no—
764C23—542no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23C2×D3×C3⋊D311yescharacteristic
769D4—34no—
770D4—94no—
771D4—274no—
772D4—274no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—91no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—182no—
782C2×C4—182no—
783C2×C4—274no—
784C2×C4—274no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—542no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4C2×D3×C3⋊D311yescharacteristic
795C2×C4C2×D3×C3⋊D311yescharacteristic
796C2×C3—22no—
797C2×C3—28no—
798C2×C3—24no—
799C2×C3—24no—
800C2×C3—24no—
801C2×C3—48no—
802C2×C3—68no—
803C2×C3—182no—
804C2×C3C2×C4×D3214yes—
805C2×C3D32×D414yes—
806C2×C3#6431214yes—
807C2×C3C22×C4×C3⋊D311yescharacteristic
808C2×C3C2×D4×C3⋊D311yescharacteristic
809C2×C3#41×C3⋊D311yescharacteristic
810D3—22no—
811D3—68no—
812D3—94no—
813D3—916no—
814D3—1816no—
815D3—182no—
816D3—188no—
817D3—368no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—272no—
827C22—272no—
828C22—272no—
829C22—272no—
830C22—548no—
831C22—548no—
832C22—541no—
833C22—541no—
834C22C4×D3×C3⋊D312yescomplemented
835C22C22×D3×C3⋊D311yescharacteristic
836C4—21no—
837C4—21no—
838C4—32no—
839C4—32no—
840C4—61no—
841C4—92no—
842C4—92no—
843C4—181no—
844C4—541no—
845C4—541no—
846C3—24no—
847C3#1059425514yescomplemented
848C3C4×D4×C3⋊D311yescharacteristic, complemented
849C2—22no—
850C2—62no—
851C2—182no—
852C2—274no—
853C2—542no—
854C2C2×C4×D3×C3⋊D311yescharacteristic
855C2D3×D4×C3⋊D311yescharacteristic
856C2#1172458611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutatorC2×C33C23×C4
FittingC33×C22⋊C4C22
socle, cosocleC22×C33C24
prime radicalC2×#89039C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×C4×D4
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#6289C2semidirect
3. C2×C4×D3×C3⋊D3C2semidirect
4. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
5. C3×#64090C2semidirect
6. C32×#67⋊C4C2semidirect
7. #67×C3⋊Dic3C2semidirect
8. Dic3×#638C2semidirect
9. #11723539C2semidirect
10. #11723512C2semidirect
11. #11723510C2semidirect
12. #11723471C2semidirect
13. #11723470C2semidirect
14. C4×#6289C2semidirect
15. #11723461C2semidirect
23. C22×C3×C3⋊Dic3C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C22×C32×Dic3C22semidirect
27. C2×C32×C4×D3C22semidirect
28. #89039C4semidirect
35. C2×#6289C22semidirect
36. C2×#6289C22semidirect
37. C2×Dic3×C3⋊D3C22semidirect
38. C2×D3×C3⋊Dic3C22semidirect
40. C33×C22⋊C4C22semidirect
41. #88864C22semidirect
42. #88859C22semidirect
43. #88859C22semidirect
44. C3×#3752C22semidirect
45. C3×#3750C22semidirect
46. C3×C4×C3⋊Dic3C22semidirect
47. C32×(C2×D3)⋊C4C22semidirect
48. C32×Dic3⋊C4C22semidirect
49. C32×C4×Dic3C22semidirect
50. #88807C22semidirect
51. Dic3⋊(C3⋊Dic3)C22semidirect
52. #88803C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. Dic3×C3⋊Dic3C22semidirect
55. Dic3×C3⋊Dic3C22semidirect
69. #64090D3semidirect
77. C3×#67⋊C4D3semidirect
90. C22×C3⋊(C3⋊D3)C2×C4semidirect
97. C2×D3×C3⋊D3C2×C4semidirect
104. C3×#638C2×C4semidirect
110. C32×#67C2×C4semidirect
116. #6292C2×C4semidirect
117. #6291C2×C4semidirect
121. #6289C2×C4semidirect
122. #6289D4semidirect
138. C22×C3⋊Dic3C2×D3semidirect
155. C2×C4×C3⋊D3C2×D3semidirect
159. C22×C3×Dic3C2×D3semidirect
161. C2×C3×C4×D3C2×D3semidirect
177. C32×C22⋊C4C2×D3semidirect
178. C32×C22⋊C4C2×D3semidirect
191. #3752C2×D3semidirect
194. #3750C2×D3semidirect
197. C4×C3⋊Dic3C2×D3semidirect
199. C3×(C2×D3)⋊C4C2×D3semidirect
201. C3×Dic3⋊C4C2×D3semidirect
203. C3×C4×Dic3C2×D3semidirect
212. C22×C33C22×C4semidirect
218. C2×C3⋊(C3⋊D3)C22×C4semidirect
223. C2×C3×C3⋊D3C22×C4semidirect
226. C2×C32×D3C22×C4semidirect
233. C3×C3⋊Dic3C22×C4semidirect
234. C3×C3⋊Dic3C2×D4semidirect
236. C32×Dic3C22×C4semidirect
237. C32×Dic3C2×D4semidirect
259. #67⋊C4C3⋊D3semidirect
310. #638C4×D3semidirect
337. C3×#67C4×D3semidirect
363. C3⋊(C3⋊D3)C4×D4semidirect
384. C22×Dic3C2×C3⋊D3semidirect
412. C2×C4×D3C2×C3⋊D3semidirect
418. C3×C22⋊C4D32semidirect
419. C3×C22⋊C4C2×C3⋊D3semidirect
436. (C2×D3)⋊C4C2×C3⋊D3semidirect
442. Dic3⋊C4C2×C3⋊D3semidirect
448. C4×Dic3C2×C3⋊D3semidirect
460. C22×C32C2×C4×D3semidirect
461. C22×C32C2×C4×D3semidirect
488. C2×C3⋊D3C2×C4×D3semidirect
494. C2×C3×D3C2×C4×D3semidirect
512. C3⋊Dic3C2×C4×D3semidirect
513. C3⋊Dic3D3×D4semidirect
518. C3×Dic3C2×C4×D3semidirect
519. C3×Dic3D3×D4semidirect
535. C33C2×C4×D4semidirect
585. #67C4×C3⋊D3semidirect
679. C22⋊C4D3×C3⋊D3semidirect
698. C22×C3C4×D32semidirect
699. C22×C3C2×C4×C3⋊D3semidirect
730. C2×D3C2×C4×C3⋊D3semidirect
753. Dic3C2×C4×C3⋊D3semidirect
754. Dic3D4×C3⋊D3semidirect
756. C32C4×D3×D4semidirect
757. C32C4×D3×D4semidirect
834. C22C4×D3×C3⋊D3semidirect
847. C3#10594255semidirect
848. C3C4×D4×C3⋊D3semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C22×#62892
C2×C4×D3×C3⋊D32
C22⋊C4×C3⋊(C3⋊D3)2
C3×#640902
C32×#67⋊C42
#67×C3⋊Dic32
Dic3×#6382
#117235392
#117235122
#117235102
#117234712
#117234702
C4×#62892
#117234612
C4×D4×C3⋊D33
#105942553