Finite Group Databasebeta

← #13175919

Subgroups — #13175919

Order 1728.

2580 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89039C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C22⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#64092C211yesmaximal, characteristic, complemented
5C32×#883C211yesmaximal, characteristic, complemented
6#11723627C211yesmaximal, characteristic, complemented
7#11723621C211yesmaximal, characteristic, complemented
8#11723614C211yesmaximal, characteristic, complemented
9#11723539C211yesmaximal, characteristic, complemented
10#11723503C211yesmaximal, characteristic, complemented
11#11723493C211yesmaximal, characteristic, complemented
12#11723479C211yesmaximal, characteristic, complemented
13#11723470C211yesmaximal, characteristic, complemented
14#11723417C211yesmaximal, characteristic, complemented
15#11723414C211yesmaximal, characteristic, complemented
16C3⋊D3×#123—31nomaximal
17#10594260—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
23C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C32×#67C2211yescharacteristic
25C2×C32×C4×D3C2211yescharacteristic, complemented
26#89039—24no—
27C2×#6292C2211yescharacteristic
28C2×#6291C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C2×#6289C2211yescharacteristic
32C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
33C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
34C4×D3×C3⋊D3—24no—
35C33×C22⋊C4C2211yescharacteristic, complemented
36#88864C2211yescharacteristic, complemented
37#88859C2211yescharacteristic, complemented
38#88859C2211yescharacteristic, complemented
39C3×#3757C2211yescharacteristic, complemented
40C3×#3752C2211yescharacteristic, complemented
41C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C32×#217C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×C4⋊Dic3C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88806C2211yescharacteristic, complemented
50Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51#88804C2211yescharacteristic, complemented
52#88804C2211yescharacteristic, complemented
53#88803C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C22×C4×C3⋊D3—31no—
57C2×#3811—34no—
58C2×C4×D32—34no—
59C32×#123—31no—
60#64144—31no—
61#64138—31no—
62#64103—31no—
63#64103—31no—
64C4⋊C4×C3⋊D3—31no—
65C4⋊C4×C3⋊D3—31no—
66#64095—31no—
67#64092—31no—
68#64092D311yescharacteristic, complemented
69C22⋊C4×C3⋊D3—31no—
70C22⋊C4×C3⋊D3—31no—
71C22⋊C4×C3⋊D3—31no—
72C22⋊C4×C3⋊D3—34no—
73C22⋊C4×C3⋊D3—64no—
74C3×#883—34no—
75C3×#883D314yescomplemented
76#63974—34no—
77#63969—34no—
78#63969—34no—
79#63921—34no—
80#63900—34no—
81#63890—34no—
82#63890—34no—
83#63883—34no—
84#63850—34no—
85#63850—34no—
86C23×C33C2311yescharacteristic
87C22×C3⋊(C3⋊D3)—22no—
88C22×C3⋊(C3⋊D3)—22no—
89C22×C3⋊(C3⋊D3)—22no—
90C22×C3⋊(C3⋊D3)C2311yescharacteristic
91C22×C3⋊(C3⋊D3)C2311yescharacteristic
92C22×C3×C3⋊D3C2311yescharacteristic
93C22×C32×D3C2311yescharacteristic
94C2×D3×C3⋊D3—22no—
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3D414yes—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C4×C3⋊(C3⋊D3)—22no—
102C4×C3⋊(C3⋊D3)—22no—
103C3×#638—22no—
104C2×C3×C3⋊Dic3C2311yescharacteristic
105C2×C3×C3⋊Dic3C2311yescharacteristic
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C3×C4×C3⋊D3—22no—
108C32×#67—22no—
109C2×C32×Dic3C2311yescharacteristic
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×C4×D3—22no—
113#6292—22no—
114#6291—22no—
115#6289—22no—
116#6289—22no—
117#6289—22no—
118Dic3×C3⋊D3—22no—
119D3×C3⋊Dic3—22no—
120D3×#123—94no—
121D3×#123—91no—
122C23×C3⋊D3—31no—
123C23×C3⋊D3—31no—
124C23×C3⋊D3—34no—
125C23×C3⋊D3—64no—
126C22×D32—34no—
127C2×C32×D4—31no—
128C22×C32×C4—31no—
129C2×#638—31no—
130C2×#638C2×D311yescharacteristic
131C22×C3⋊Dic3—31no—
132D4×C3⋊D3—64no—
133C2×C4⋊(C3⋊D3)—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—34no—
138C2×C4×C3⋊D3—34no—
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—31no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—64no—
143C2×C4×C3⋊D3—64no—
144C2×C4×C3⋊D3—64no—
145C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
146C2×C3×#67—34no—
147C2×C3×#67C2×D314yes—
148C2×C3×C4×D3—34no—
149C2×C3×C4×D3C2×D314yescomplemented
150#3811—616no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#624—34no—
154C2×#624—34no—
155C2×#624—34no—
156C2×D3×Dic3—34no—
157C2×D3×Dic3—34no—
158C4×D32—616no—
159C32×C4⋊C4—31no—
160C32×C4⋊C4—31no—
161C32×C22⋊C4—24no—
162C32×C22⋊C4—31no—
163C32×C22⋊C4—31no—
164C32×C22⋊C4C2×D314yescomplemented
165C32×C22⋊C4C2×D311yescharacteristic, complemented
166#3757—31no—
167#3757—34no—
168#3757—31no—
169#3757—64no—
170#3757C2×D311yescharacteristic, complemented
171#3752—31no—
172#3752—31no—
173#3752—31no—
174#3752—34no—
175#3752—34no—
176#3752—31no—
177#3752—31no—
178#3752—64no—
179#3752—64no—
180#3752C2×D311yescharacteristic, complemented
181C4⋊(C3⋊Dic3)—31no—
182C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
183#3750—31no—
184#3750—31no—
185#3750—31no—
186#3750C2×D311yescharacteristic, complemented
187C3×#217—34no—
188C3×#217C2×D314yescomplemented
189C3×(C2×D3)⋊C4—34no—
190C3×(C2×D3)⋊C4C2×D314yescomplemented
191C3×C4⋊Dic3—34no—
192C3×C4⋊Dic3C2×D314yescomplemented
193C3×Dic3⋊C4—34no—
194C3×Dic3⋊C4C2×D314yescomplemented
195#3724—34no—
196#3724—34no—
197Dic3⋊Dic3—34no—
198Dic3⋊Dic3—34no—
199#3722—34no—
200#3722—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33—21no—
204C22×C33—21no—
205C22×C33—21no—
206C22×C33C2411yescharacteristic
207C2×C3⋊(C3⋊D3)—21no—
208C2×C3⋊(C3⋊D3)—21no—
209C2×C3⋊(C3⋊D3)—21no—
210C2×C3⋊(C3⋊D3)—44no—
211C2×C3⋊(C3⋊D3)C2×D412yes—
212C2×C3⋊(C3⋊D3)#4112yes—
213C2×C3⋊(C3⋊D3)#4112yes—
214C2×C3×C3⋊D3—21no—
215C2×C3×C3⋊D3—21no—
216C2×C3×C3⋊D3C2×D412yes—
217C2×C32×D3—21no—
218C2×C32×D3—21no—
219C2×C32×D3C2×D412yes—
220D3×C3⋊D3—28no—
221C33×C4—21no—
222C33×C4—21no—
223C3⋊(C3⋊Dic3)—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3×C3⋊Dic3—21no—
226C3×C3⋊Dic3—21no—
227C3×C3⋊Dic3—21no—
228C32×Dic3—21no—
229C32×Dic3—21no—
230C32×Dic3—21no—
231C2×D3×D4—94no—
232C2×D3×D4—91no—
233C22×C4×D3—94no—
234C22×C4×D3—91no—
235C3×#123—34no—
236C3×#123—91no—
237#935—94no—
238#935—91no—
239#929—94no—
240#929—91no—
241#894—94no—
242#894—94no—
243#894—91no—
244#894—91no—
245D3×C4⋊C4—94no—
246D3×C4⋊C4—94no—
247D3×C4⋊C4—91no—
248D3×C4⋊C4—91no—
249#886—94no—
250#886—91no—
251#883—34no—
252#883—94no—
253#883—91no—
254#883C3⋊D311yescharacteristic, complemented
255D3×C22⋊C4—94no—
256D3×C22⋊C4—94no—
257D3×C22⋊C4—94no—
258D3×C22⋊C4—91no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—184no—
262C23×C32—24no—
263C23×C32—31no—
264C23×C32C22×D314yes—
265C23×C32C22×D311yescharacteristic
266C22×C3⋊D3—31no—
267C22×C3⋊D3—34no—
268C22×C3⋊D3—31no—
269C22×C3⋊D3—34no—
270C22×C3⋊D3—34no—
271C22×C3⋊D3—64no—
272C22×C3⋊D3—64no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3⋊D3—68no—
277C22×C3⋊D3—62no—
278C22×C3⋊D3—62no—
279C22×C3⋊D3—616no—
280C22×C3⋊D3—68no—
281C22×C3⋊D3—68no—
282C22×C3⋊D3—128no—
283C22×C3⋊D3—128no—
284C22×C3⋊D3C22×D311yescharacteristic
285C22×C3×D3—34no—
286C22×C3×D3C22×D314yes—
287C2×D32—316no—
288C2×D32—68no—
289C2×D32—68no—
290C32×D4—62no—
291C2×C32×C4—24no—
292C2×C32×C4—24no—
293C2×C32×C4—31no—
294C2×C32×C4—31no—
295C2×C32×C4—31no—
296C2×C32×C4—62no—
297C2×C32×C4C22×D314yes—
298C2×C32×C4C22×D314yes—
299C2×C32×C4C22×D311yescharacteristic
300C2×C32×C4C22×D311yescharacteristic
301#638—22no—
302#638—62no—
303C2×C3⋊Dic3—31no—
304C2×C3⋊Dic3—31no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—34no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—62no—
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C2×C3⋊Dic3C22×D311yescharacteristic
313C4⋊(C3⋊D3)—62no—
314C4×C3⋊D3—22no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—62no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—62no—
321C4×C3⋊D3—68no—
322C4×C3⋊D3—68no—
323C4×C3⋊D3—128no—
324C4×C3⋊D3—128no—
325C3×#67—28no—
326C3×#67—68no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3—34no—
329C2×C3×Dic3—34no—
330C2×C3×Dic3C22×D314yes—
331C2×C3×Dic3C22×D314yes—
332C2×C3×Dic3C22×D314yes—
333C3×C4×D3—28no—
334C3×C4×D3—68no—
335#626—68no—
336#626—68no—
337#624—68no—
338#624—68no—
339#624—68no—
340D3×Dic3—68no—
341D3×Dic3—68no—
342C2×#123—271noSylow
343C2×C33—41no—
344C2×C33C22×D411yescharacteristic
345C2×C33C2×#4111yescharacteristic
346C2×C33C2×#4111yescharacteristic
347C3⋊(C3⋊D3)—41no—
348C3⋊(C3⋊D3)#12314yescomplemented
349C3×C3⋊D3—22no—
350C32×D3—22no—
351C23×D3—94no—
352C23×D3—91no—
353C23×D3—94no—
354C23×D3—91no—
355C23×D3—184no—
356C2×C3×D4—34no—
357C2×C3×D4—91no—
358C22×C3×C4—34no—
359C22×C3×C4—91no—
360C2×#67—34no—
361C2×#67—94no—
362C2×#67—91no—
363C2×#67C2×C3⋊D311yescharacteristic
364C22×Dic3—94no—
365C22×Dic3—91no—
366D3×D4—184no—
367D3×D4—1816no—
368C2×D12—94no—
369C2×D12—91no—
370C2×C4×D3—34no—
371C2×C4×D3—94no—
372C2×C4×D3—94no—
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—94no—
377C2×C4×D3—94no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—91no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—184no—
384C2×C4×D3—184no—
385C2×C4×D3—184no—
386C2×C4×D3—1816no—
387C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—91no—
391C3×C4⋊C4—91no—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397C3×C22⋊C4D3214yescomplemented
398C3×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
399#217—34no—
400#217—94no—
401#217—94no—
402#217—91no—
403#217—91no—
404#217—184no—
405#217C2×C3⋊D311yescharacteristic, complemented
406(C2×D3)⋊C4—34no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—94no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—94no—
412(C2×D3)⋊C4—94no—
413(C2×D3)⋊C4—91no—
414(C2×D3)⋊C4—91no—
415(C2×D3)⋊C4—91no—
416(C2×D3)⋊C4—91no—
417(C2×D3)⋊C4—184no—
418(C2×D3)⋊C4—184no—
419(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
420C4⋊Dic3—34no—
421C4⋊Dic3—94no—
422C4⋊Dic3—91no—
423C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
424Dic3⋊C4—34no—
425Dic3⋊C4—94no—
426Dic3⋊C4—94no—
427Dic3⋊C4—94no—
428Dic3⋊C4—91no—
429Dic3⋊C4—91no—
430Dic3⋊C4—91no—
431Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
432C22×C32—28no—
433C22×C32—21no—
434C22×C32—24no—
435C22×C32—21no—
436C22×C32—21no—
437C22×C32—24no—
438C22×C32—24no—
439C22×C32—24no—
440C22×C32—32no—
441C22×C32—44no—
442C22×C32—44no—
443C22×C32—61no—
444C22×C32—61no—
445C22×C32C23×D314yes—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—21no—
448C2×C3⋊D3—21no—
449C2×C3⋊D3—32no—
450C2×C3⋊D3—32no—
451C2×C3⋊D3—32no—
452C2×C3⋊D3—38no—
453C2×C3⋊D3—38no—
454C2×C3⋊D3—38no—
455C2×C3⋊D3—68no—
456C2×C3⋊D3—68no—
457C2×C3⋊D3—68no—
458C2×C3⋊D3—68no—
459C2×C3⋊D3—68no—
460C2×C3⋊D3—61no—
461C2×C3⋊D3—64no—
462C2×C3⋊D3—61no—
463C2×C3⋊D3—61no—
464C2×C3⋊D3—64no—
465C2×C3⋊D3—64no—
466C2×C3⋊D3—124no—
467C2×C3⋊D3—124no—
468C2×C3⋊D3—124no—
469C2×C3⋊D3—1216no—
470C2×C3⋊D3—1232no—
471C2×C3⋊D3D3×D412yes—
472C2×C3×D3—24no—
473C2×C3×D3—24no—
474C2×C3×D3—38no—
475C2×C3×D3—64no—
476C2×C3×D3—64no—
477C2×C3×D3D3×D418yes—
478D32—632no—
479C32×C4—21no—
480C32×C4—21no—
481C32×C4—24no—
482C32×C4—24no—
483C32×C4—44no—
484C32×C4—44no—
485C32×C4—61no—
486C32×C4—61no—
487C32×C4—61no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3⋊Dic3—21no—
491C3⋊Dic3—61no—
492C3⋊Dic3—61no—
493C3⋊Dic3—64no—
494C3⋊Dic3—64no—
495C3⋊Dic3—124no—
496C3⋊Dic3—124no—
497C3×Dic3—24no—
498C3×Dic3—24no—
499C3×Dic3—24no—
500C3×Dic3—64no—
501C3×Dic3—64no—
502C3×Dic3—64no—
503C22×D4—271no—
504C23×C4—271no—
505#123—31no—
506#123—91no—
507#123—271no—
508#123—271no—
509#123—271no—
510#123—271no—
511#123—271no—
512#123—271no—
513C2×C4⋊C4—271no—
514C2×C4⋊C4—271no—
515C2×C22⋊C4—271no—
516C2×C22⋊C4—271no—
517C2×C22⋊C4—271no—
518C33C2×#12311yescharacteristic, complemented, Sylow
519C23×C3—24no—
520C23×C3—34no—
521C23×C3—91no—
522C23×C3C2×D3214yes—
523C23×C3C22×C3⋊D311yescharacteristic
524C22×D3—34no—
525C22×D3—916no—
526C22×D3—94no—
527C22×D3—91no—
528C22×D3—94no—
529C22×D3—94no—
530C22×D3—91no—
531C22×D3—184no—
532C22×D3—184no—
533C22×D3—182no—
534C22×D3—182no—
535C22×D3—188no—
536C22×D3—188no—
537C22×D3—182no—
538C22×D3—188no—
539C22×D3—182no—
540C22×D3—182no—
541C22×D3—188no—
542C22×D3—188no—
543C22×D3—1816no—
544C22×D3—368no—
545C22×D3—368no—
546C22×D3C22×C3⋊D311yescharacteristic
547C3×D4—68no—
548C3×D4—182no—
549C2×C3×C4—24no—
550C2×C3×C4—24no—
551C2×C3×C4—34no—
552C2×C3×C4—34no—
553C2×C3×C4—34no—
554C2×C3×C4—68no—
555C2×C3×C4—91no—
556C2×C3×C4—91no—
557C2×C3×C4—91no—
558C2×C3×C4—182no—
559C2×C3×C4C2×D3214yes—
560C2×C3×C4C2×D3214yes—
561C2×C3×C4C22×C3⋊D311yescharacteristic
562C2×C3×C4C22×C3⋊D311yescharacteristic
563#67—22no—
564#67—68no—
565#67—182no—
566#67—188no—
567C2×Dic3—34no—
568C2×Dic3—34no—
569C2×Dic3—34no—
570C2×Dic3—94no—
571C2×Dic3—94no—
572C2×Dic3—91no—
573C2×Dic3—91no—
574C2×Dic3—184no—
575C2×Dic3—184no—
576C2×Dic3—182no—
577C2×Dic3—188no—
578C2×Dic3C22×C3⋊D311yescharacteristic
579C2×Dic3C22×C3⋊D311yescharacteristic
580C2×Dic3C22×C3⋊D311yescharacteristic
581D12—188no—
582D12—182no—
583C4×D3—22no—
584C4×D3—68no—
585C4×D3—182no—
586C4×D3—182no—
587C4×D3—182no—
588C4×D3—188no—
589C4×D3—188no—
590C4×D3—188no—
591C4×D3—182no—
592C4×D3—182no—
593C4×D3—188no—
594C4×D3—188no—
595C4×D3—188no—
596C4×D3—182no—
597C4×D3—368no—
598C4×D3—368no—
599C2×C32—24no—
600C2×C32—24no—
601C2×C32—24no—
602C2×C32—48no—
603C2×C32—44no—
604C2×C32—41no—
605C2×C32—62no—
606C2×C32C2×D3×D414yes—
607C2×C32C2×D3×D411yescharacteristic
608C2×C32D3×#4114yes—
609C2×C32D3×#4114yes—
610C2×C32D3×#4111yescharacteristic
611C2×C32D3×#4111yescharacteristic
612C3⋊D3—22no—
613C3⋊D3—34no—
614C3⋊D3—316no—
615C3⋊D3—616no—
616C3⋊D3—128no—
617C3⋊D3—124no—
618C3⋊D3—121no—
619C3×D3—28no—
620C3×D3—68no—
621C24—271no—
622C24—271no—
623C2×D4—31no—
624C2×D4—91no—
625C2×D4—271no—
626C2×D4—271no—
627C2×D4—544no—
628C22×C4—31no—
629C22×C4—91no—
630C22×C4—271no—
631C22×C4—271no—
632C22×C4—271no—
633C22×C4—271no—
634C22×C4—271no—
635C22×C4—271no—
636C22×C4—271no—
637C22×C4—544no—
638C4⋊C4—31no—
639C4⋊C4—31no—
640C4⋊C4—91no—
641C4⋊C4—91no—
642C4⋊C4—271no—
643C4⋊C4—271no—
644C4⋊C4—271no—
645C4⋊C4—271no—
646C22⋊C4—31no—
647C22⋊C4—31no—
648C22⋊C4—91no—
649C22⋊C4—91no—
650C22⋊C4—271no—
651C22⋊C4—271no—
652C22⋊C4—271no—
653C22⋊C4—271no—
654C22⋊C4—271no—
655C22⋊C4—271no—
656C22⋊C4—271no—
657C22⋊C4D3×C3⋊D311yescharacteristic, complemented
658C22×C3—28no—
659C22×C3—24no—
660C22×C3—24no—
661C22×C3—24no—
662C22×C3—21no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—24no—
666C22×C3—38no—
667C22×C3—44no—
668C22×C3—44no—
669C22×C3—64no—
670C22×C3—64no—
671C22×C3—92no—
672C22×C3—181no—
673C22×C3—181no—
674C22×C3C22×D3214yes—
675C22×C3C23×C3⋊D311yescharacteristic
676C2×D3—21no—
677C2×D3—21no—
678C2×D3—38no—
679C2×D3—64no—
680C2×D3—64no—
681C2×D3—98no—
682C2×D3—98no—
683C2×D3—98no—
684C2×D3—92no—
685C2×D3—92no—
686C2×D3—92no—
687C2×D3—188no—
688C2×D3—188no—
689C2×D3—188no—
690C2×D3—188no—
691C2×D3—1832no—
692C2×D3—188no—
693C2×D3—184no—
694C2×D3—184no—
695C2×D3—184no—
696C2×D3—181no—
697C2×D3—181no—
698C2×D3—181no—
699C2×D3—364no—
700C2×D3—364no—
701C2×D3—364no—
702C2×D3—3616no—
703C2×D3—3632no—
704C2×D3D4×C3⋊D312yes—
705C3×C4—24no—
706C3×C4—24no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—44no—
710C3×C4—44no—
711C3×C4—64no—
712C3×C4—64no—
713C3×C4—64no—
714C3×C4—181no—
715C3×C4—181no—
716C3×C4—181no—
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—64no—
721Dic3—64no—
722Dic3—64no—
723Dic3—184no—
724Dic3—184no—
725Dic3—181no—
726Dic3—181no—
727Dic3—364no—
728Dic3—364no—
729C32—24no—
730C32D3×#12314yescomplemented
731C32D3×#12311yescharacteristic, complemented
732C23—31no—
733C23—91no—
734C23—274no—
735C23—271no—
736C23—271no—
737C23—542no—
738C23—542no—
739C23—542no—
740C23—542no—
741C23—542no—
742C23C2×D3×C3⋊D311yescharacteristic
743D4—62no—
744D4—182no—
745D4—542no—
746D4—542no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—31no—
750C2×C4—62no—
751C2×C4—91no—
752C2×C4—91no—
753C2×C4—91no—
754C2×C4—182no—
755C2×C4—271no—
756C2×C4—271no—
757C2×C4—542no—
758C2×C4—542no—
759C2×C4—542no—
760C2×C4—542no—
761C2×C4—542no—
762C2×C4—542no—
763C2×C4—542no—
764C2×C4C2×D3×C3⋊D311yescharacteristic
765C2×C4C2×D3×C3⋊D311yescharacteristic
766C2×C3—24no—
767C2×C3—24no—
768C2×C3—24no—
769C2×C3—48no—
770C2×C3—41no—
771C2×C3—44no—
772C2×C3—68no—
773C2×C3—182no—
774C2×C3#6430614yes—
775C2×C3D32×D414yes—
776C2×C3#6431214yes—
777C2×C3C2×D4×C3⋊D311yescharacteristic
778C2×C3#41×C3⋊D311yescharacteristic
779C2×C3#41×C3⋊D311yescharacteristic
780D3—22no—
781D3—68no—
782D3—94no—
783D3—916no—
784D3—1816no—
785D3—368no—
786D3—361no—
787D3—364no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—32no—
792C22—61no—
793C22—61no—
794C22—92no—
795C22—181no—
796C22—181no—
797C22—272no—
798C22—272no—
799C22—272no—
800C22—548no—
801C22—541no—
802C22—541no—
803C22—541no—
804C22—1084no—
805C22C22×D3×C3⋊D311yescharacteristic
806C4—21no—
807C4—21no—
808C4—61no—
809C4—61no—
810C4—61no—
811C4—181no—
812C4—181no—
813C4—181no—
814C4—541no—
815C4—541no—
816C3—24no—
817C3#1059426014yescomplemented
818C3C3⋊D3×#12311yescharacteristic, complemented
819C2—41no—
820C2—62no—
821C2—182no—
822C2—274no—
823C2—1081no—
824C2#1172457811yescharacteristic
825C2D3×D4×C3⋊D311yescharacteristic
826C2#1172458611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C22⋊C4C22
prime radicalC2×#89039C2
hypercenterC22⋊C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×C3⋊D3C2semidirect
3. C22⋊C4×C3⋊(C3⋊D3)C2semidirect
4. C3×#64092C2semidirect
5. C32×#883C2semidirect
6. #11723627C2semidirect
7. #11723621C2semidirect
8. #11723614C2semidirect
9. #11723539C2semidirect
10. #11723503C2semidirect
11. #11723493C2semidirect
12. #11723479C2semidirect
13. #11723470C2semidirect
14. #11723417C2semidirect
15. #11723414C2semidirect
23. C2×C3×C4×C3⋊D3C22semidirect
25. C2×C32×C4×D3C22semidirect
32. C2×Dic3×C3⋊D3C22semidirect
33. C2×D3×C3⋊Dic3C22semidirect
35. C33×C22⋊C4C22semidirect
36. #88864C22semidirect
37. #88859C22semidirect
38. #88859C22semidirect
39. C3×#3757C22semidirect
40. C3×#3752C22semidirect
41. C3×C4⋊(C3⋊Dic3)C22semidirect
42. C3×#3750C22semidirect
43. C32×#217C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×C4⋊Dic3C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
49. #88806C22semidirect
50. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88804C22semidirect
52. #88804C22semidirect
53. #88803C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
68. #64092D3semidirect
75. C3×#883D3semidirect
145. C2×C4×C3⋊D3C2×D3semidirect
149. C2×C3×C4×D3C2×D3semidirect
164. C32×C22⋊C4C2×D3semidirect
165. C32×C22⋊C4C2×D3semidirect
170. #3757C2×D3semidirect
180. #3752C2×D3semidirect
182. C4⋊(C3⋊Dic3)C2×D3semidirect
186. #3750C2×D3semidirect
188. C3×#217C2×D3semidirect
190. C3×(C2×D3)⋊C4C2×D3semidirect
192. C3×C4⋊Dic3C2×D3semidirect
194. C3×Dic3⋊C4C2×D3semidirect
254. #883C3⋊D3semidirect
348. C3⋊(C3⋊D3)#123semidirect
387. C2×C4×D3C2×C3⋊D3semidirect
397. C3×C22⋊C4D32semidirect
398. C3×C22⋊C4C2×C3⋊D3semidirect
405. #217C2×C3⋊D3semidirect
419. (C2×D3)⋊C4C2×C3⋊D3semidirect
423. C4⋊Dic3C2×C3⋊D3semidirect
431. Dic3⋊C4C2×C3⋊D3semidirect
518. C33C2×#123semidirect
657. C22⋊C4D3×C3⋊D3semidirect
730. C32D3×#123semidirect
731. C32D3×#123semidirect
817. C3#10594260semidirect
818. C3C3⋊D3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#890392
C2×C4×D3×C3⋊D32
C22⋊C4×C3⋊(C3⋊D3)2
C3×#640922
C32×#8832
#117236272
#117236212
#117236142
#117235392
#117235032
#117234932
#117234792
#117234702
#117234172
#117234142
C3⋊D3×#1233
#105942603