Finite Group Databasebeta

← #13176532

Subgroups — #13176532

Order 1728.

2420 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89026C211yesmaximal, characteristic
2C2×C4×D3×C3⋊D3C211yesmaximal, characteristic, complemented
3C4⋊C4×C3⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#64103C211yesmaximal, characteristic, complemented
5C32×#894C211yesmaximal, characteristic, complemented
6#11723539C211yesmaximal, characteristic, complemented
7#11723539C211yesmaximal, characteristic, complemented
8#11723539C211yesmaximal, characteristic, complemented
9#11723523C211yesmaximal, characteristic, complemented
10#11723518C211yesmaximal, characteristic, complemented
11#11723513C211yesmaximal, characteristic, complemented
12#11723488C211yesmaximal, characteristic, complemented
13#11723480C211yesmaximal, characteristic, complemented
14#11723473C211yesmaximal, characteristic, complemented
15#11723470C211yesmaximal, characteristic, complemented
16C3⋊D3×#123—31nomaximal
17#10594608—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
21C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×C32×D12C2211yescharacteristic
26C2×C32×C4×D3C2211yescharacteristic, complemented
27C2×#6290C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6289C2211yescharacteristic
30C2×#6289C2211yescharacteristic
31C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
32C2×D3×C3⋊Dic3C2211yescharacteristic, complemented
33#89026—24no—
34C4×D3×C3⋊D3—24no—
35C33×C4⋊C4C2211yescharacteristic, complemented
36C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
37#88857C2211yescharacteristic, complemented
38#88857C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic, complemented
40C3×#3752C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic, complemented
42C3×#3750C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88803C2211yescharacteristic, complemented
50#88803C2211yescharacteristic, complemented
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
53(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
54(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
55C2×D4×C3⋊D3—31no—
56C22×C4×C3⋊D3—31no—
57C2×#3802—34no—
58C2×C4×D32—34no—
59C32×#123—31no—
60#64144—31no—
61#64138—31no—
62#64103—31no—
63#64103D311yescharacteristic, complemented
64C4⋊C4×C3⋊D3—31no—
65C4⋊C4×C3⋊D3—31no—
66C4⋊C4×C3⋊D3—34no—
67C4⋊C4×C3⋊D3—64no—
68#64095—31no—
69#64092—31no—
70#64092—31no—
71C22⋊C4×C3⋊D3—31no—
72C22⋊C4×C3⋊D3—31no—
73C22⋊C4×C3⋊D3—31no—
74C3×#894—34no—
75C3×#894D314yescomplemented
76#63921—34no—
77#63921—34no—
78#63921—34no—
79#63905—34no—
80#63905—34no—
81#63891—34no—
82#63891—34no—
83#63884—34no—
84#63884—34no—
85#63883—34no—
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C22×C32×D3C2311yescharacteristic
91C2×D3×C3⋊D3—22no—
92C2×D3×C3⋊D3—22no—
93C2×D3×C3⋊D3—22no—
94C2×D3×C3⋊D3—22no—
95C2×D3×C3⋊D3—22no—
96C2×D3×C3⋊D3D414yes—
97C2×C33×C4C2311yescharacteristic
98C2×C33×C4C2311yescharacteristic
99C2×C33×C4C2311yescharacteristic
100C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
101C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
102C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
103C4×C3⋊(C3⋊D3)—22no—
104C4×C3⋊(C3⋊D3)—22no—
105C4×C3⋊(C3⋊D3)—22no—
106C2×C3×C3⋊Dic3C2311yescharacteristic
107C2×C3×C3⋊Dic3C2311yescharacteristic
108C3×C4⋊(C3⋊D3)—22no—
109C3×C4×C3⋊D3—22no—
110C2×C32×Dic3C2311yescharacteristic
111C2×C32×Dic3C2311yescharacteristic
112C32×D12—22no—
113C32×C4×D3—22no—
114#6290—22no—
115#6290—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—
124C22×D32—34no—
125C22×D32—34no—
126C2×C32×D4—31no—
127C22×C32×C4—31no—
128C2×#638—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131D4×C3⋊D3—64no—
132C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
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—34no—
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⋊D3—64no—
146C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
147C2×C3×D12—34no—
148C2×C3×D12C2×D314yes—
149C2×C3×C4×D3—34no—
150C2×C3×C4×D3C2×D314yescomplemented
151C2×#625—34no—
152C2×#625—34no—
153C2×#624—34no—
154C2×#624—34no—
155C2×D3×Dic3—34no—
156C2×D3×Dic3—34no—
157#3802—616no—
158C4×D32—616no—
159C32×C4⋊C4—24no—
160C32×C4⋊C4—31no—
161C32×C4⋊C4C2×D314yescomplemented
162C32×C4⋊C4C2×D311yescharacteristic, complemented
163C32×C22⋊C4—31no—
164C32×C22⋊C4—31no—
165C32×C22⋊C4—31no—
166#3757—31no—
167#3757—31no—
168#3757—31no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752C2×D311yescharacteristic, complemented
173#3752C2×D311yescharacteristic, complemented
174#3752C2×D311yescharacteristic, complemented
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)—34no—
177C4⋊(C3⋊Dic3)—31no—
178C4⋊(C3⋊Dic3)—64no—
179#3750—31no—
180#3750—31no—
181#3750—34no—
182#3750—34no—
183#3750—31no—
184#3750—64no—
185#3750—64no—
186#3750C2×D311yescharacteristic, complemented
187C3×(C2×D3)⋊C4—34no—
188C3×(C2×D3)⋊C4—34no—
189C3×(C2×D3)⋊C4—34no—
190C3×(C2×D3)⋊C4C2×D314yescomplemented
191C3×(C2×D3)⋊C4C2×D314yescomplemented
192C3×(C2×D3)⋊C4C2×D314yescomplemented
193C3×Dic3⋊C4—34no—
194C3×Dic3⋊C4C2×D314yescomplemented
195Dic3⋊Dic3—34no—
196Dic3⋊Dic3—34no—
197(C2×D3)⋊Dic3—34no—
198(C2×D3)⋊Dic3—34no—
199(C2×D3)⋊Dic3—34no—
200(C2×D3)⋊Dic3—34no—
201(C2×D3)⋊Dic3—34no—
202(C2×D3)⋊Dic3—34no—
203C22×C33C2411yescharacteristic
204C2×C3⋊(C3⋊D3)C2×D412yes—
205C2×C3⋊(C3⋊D3)#4112yes—
206C2×C3⋊(C3⋊D3)#4112yes—
207C2×C3×C3⋊D3—21no—
208C2×C3×C3⋊D3—21no—
209C2×C3×C3⋊D3—21no—
210C2×C3×C3⋊D3—21no—
211C2×C3×C3⋊D3—21no—
212C2×C3×C3⋊D3C2×D412yes—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215C2×C32×D3—21no—
216C2×C32×D3—21no—
217C2×C32×D3—21no—
218C2×C32×D3C2×D412yes—
219D3×C3⋊D3—28no—
220D3×C3⋊D3—44no—
221C33×C4—21no—
222C33×C4—21no—
223C33×C4—21no—
224C3⋊(C3⋊Dic3)—21no—
225C3⋊(C3⋊Dic3)—21no—
226C3⋊(C3⋊Dic3)—21no—
227C3×C3⋊Dic3—21no—
228C3×C3⋊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—34no—
242#894—94no—
243#894—91no—
244#894C3⋊D311yescharacteristic, complemented
245D3×C4⋊C4—94no—
246D3×C4⋊C4—94no—
247D3×C4⋊C4—91no—
248D3×C4⋊C4—91no—
249D3×C4⋊C4—184no—
250#886—94no—
251#886—91no—
252#883—94no—
253#883—94no—
254#883—91no—
255#883—91no—
256D3×C22⋊C4—94no—
257D3×C22⋊C4—94no—
258D3×C22⋊C4—94no—
259D3×C22⋊C4—91no—
260D3×C22⋊C4—91no—
261D3×C22⋊C4—91no—
262C23×C32—31no—
263C23×C32—31no—
264C22×C3⋊D3—31no—
265C22×C3⋊D3—34no—
266C22×C3⋊D3—34no—
267C22×C3⋊D3—64no—
268C22×C3⋊D3—62no—
269C22×C3⋊D3—62no—
270C22×C3⋊D3—62no—
271C22×C3⋊D3—62no—
272C22×C3⋊D3—62no—
273C22×C3⋊D3C22×D311yescharacteristic
274C22×C3⋊D3C22×D311yescharacteristic
275C22×C3×D3—34no—
276C22×C3×D3—34no—
277C22×C3×D3C22×D314yes—
278C22×C3×D3C22×D314yes—
279C2×D32—316no—
280C2×D32—68no—
281C2×D32—68no—
282C2×D32—68no—
283C2×D32—68no—
284C2×D32—68no—
285C32×D4—62no—
286C2×C32×C4—24no—
287C2×C32×C4—24no—
288C2×C32×C4—24no—
289C2×C32×C4—31no—
290C2×C32×C4—31no—
291C2×C32×C4—62no—
292C2×C32×C4C22×D314yes—
293C2×C32×C4C22×D314yes—
294C2×C32×C4C22×D314yes—
295C2×C32×C4C22×D311yescharacteristic
296C2×C32×C4C22×D311yescharacteristic
297C2×C32×C4C22×D311yescharacteristic
298#638—62no—
299#638—62no—
300C2×C3⋊Dic3—31no—
301C2×C3⋊Dic3—31no—
302C2×C3⋊Dic3—31no—
303C2×C3⋊Dic3—34no—
304C2×C3⋊Dic3—34no—
305C2×C3⋊Dic3—34no—
306C2×C3⋊Dic3—64no—
307C2×C3⋊Dic3—64no—
308C2×C3⋊Dic3—64no—
309C2×C3⋊Dic3—62no—
310C2×C3⋊Dic3C22×D311yescharacteristic
311C2×C3⋊Dic3C22×D311yescharacteristic
312C4⋊(C3⋊D3)—22no—
313C4×C3⋊D3—22no—
314C4×C3⋊D3—62no—
315C4×C3⋊D3—62no—
316C4×C3⋊D3—62no—
317C4×C3⋊D3—68no—
318C4×C3⋊D3—62no—
319C4×C3⋊D3—62no—
320C4×C3⋊D3—616no—
321C4×C3⋊D3—62no—
322C4×C3⋊D3—68no—
323C4×C3⋊D3—68no—
324C4×C3⋊D3—128no—
325C4×C3⋊D3—128no—
326C2×C3×Dic3—34no—
327C2×C3×Dic3—34no—
328C2×C3×Dic3C22×D314yes—
329C2×C3×Dic3C22×D314yes—
330C3×D12—28no—
331C3×D12—68no—
332C3×C4×D3—28no—
333C3×C4×D3—68no—
334#625—68no—
335#625—68no—
336#624—68no—
337#624—68no—
338D3×Dic3—68no—
339D3×Dic3—68no—
340C2×#123—271noSylow
341C2×C33C22×D411yescharacteristic
342C2×C33C2×#4111yescharacteristic
343C2×C33C2×#4111yescharacteristic
344C3⋊(C3⋊D3)#12314yescomplemented
345C3×C3⋊D3—22no—
346C3×C3⋊D3—41no—
347C32×D3—22no—
348C32×D3—41no—
349C23×D3—94no—
350C23×D3—94no—
351C23×D3—91no—
352C23×D3—91no—
353C2×C3×D4—34no—
354C2×C3×D4—91no—
355C22×C3×C4—34no—
356C22×C3×C4—91no—
357C2×#67—94no—
358C2×#67—94no—
359C2×#67—91no—
360C2×#67—91no—
361C22×Dic3—94no—
362C22×Dic3—91no—
363D3×D4—184no—
364D3×D4—1816no—
365C2×D12—34no—
366C2×D12C2×C3⋊D311yescharacteristic
367C2×C4×D3—34no—
368C2×C4×D3—94no—
369C2×C4×D3—94no—
370C2×C4×D3—94no—
371C2×C4×D3—91no—
372C2×C4×D3—94no—
373C2×C4×D3—94no—
374C2×C4×D3—94no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—91no—
380C2×C4×D3—184no—
381C2×C4×D3—184no—
382C2×C4×D3—184no—
383C2×C4×D3—184no—
384C2×C4×D3—1816no—
385C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
386C3×C4⋊C4—24no—
387C3×C4⋊C4—34no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4D3214yescomplemented
390C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
391C3×C22⋊C4—34no—
392C3×C22⋊C4—34no—
393C3×C22⋊C4—34no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C22⋊C4—91no—
397#217—94no—
398#217—94no—
399#217—94no—
400#217—91no—
401#217—91no—
402#217—91no—
403(C2×D3)⋊C4—34no—
404(C2×D3)⋊C4—34no—
405(C2×D3)⋊C4—34no—
406(C2×D3)⋊C4—94no—
407(C2×D3)⋊C4—94no—
408(C2×D3)⋊C4—94no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—91no—
411(C2×D3)⋊C4—91no—
412(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
413(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
414(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
415C4⋊Dic3—94no—
416C4⋊Dic3—94no—
417C4⋊Dic3—91no—
418C4⋊Dic3—91no—
419C4⋊Dic3—184no—
420Dic3⋊C4—34no—
421Dic3⋊C4—94no—
422Dic3⋊C4—94no—
423Dic3⋊C4—94no—
424Dic3⋊C4—91no—
425Dic3⋊C4—91no—
426Dic3⋊C4—91no—
427Dic3⋊C4—184no—
428Dic3⋊C4—184no—
429Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
430C22×C32—24no—
431C22×C32—32no—
432C22×C32—61no—
433C22×C32—61no—
434C22×C32—61no—
435C22×C32—61no—
436C22×C32—61no—
437C22×C32C23×D314yes—
438C22×C32C23×D311yescharacteristic
439C2×C3⋊D3—21no—
440C2×C3⋊D3—21no—
441C2×C3⋊D3—21no—
442C2×C3⋊D3—21no—
443C2×C3⋊D3—21no—
444C2×C3⋊D3—32no—
445C2×C3⋊D3—32no—
446C2×C3⋊D3—32no—
447C2×C3⋊D3—38no—
448C2×C3⋊D3—38no—
449C2×C3⋊D3—38no—
450C2×C3⋊D3—68no—
451C2×C3⋊D3—68no—
452C2×C3⋊D3—68no—
453C2×C3⋊D3—68no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3D3×D412yes—
456C2×C3×D3—24no—
457C2×C3×D3—24no—
458C2×C3×D3—24no—
459C2×C3×D3—24no—
460C2×C3×D3—24no—
461C2×C3×D3—38no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3D3×D418yes—
468D32—632no—
469D32—1216no—
470C32×C4—28no—
471C32×C4—21no—
472C32×C4—21no—
473C32×C4—24no—
474C32×C4—21no—
475C32×C4—24no—
476C32×C4—24no—
477C32×C4—44no—
478C32×C4—44no—
479C32×C4—61no—
480C32×C4—61no—
481C3⋊Dic3—21no—
482C3⋊Dic3—21no—
483C3⋊Dic3—68no—
484C3⋊Dic3—61no—
485C3⋊Dic3—61no—
486C3⋊Dic3—64no—
487C3⋊Dic3—61no—
488C3⋊Dic3—64no—
489C3⋊Dic3—64no—
490C3⋊Dic3—124no—
491C3⋊Dic3—124no—
492C3×Dic3—24no—
493C3×Dic3—24no—
494C3×Dic3—64no—
495C3×Dic3—64no—
496C22×D4—271no—
497C23×C4—271no—
498#123—31no—
499#123—91no—
500#123—271no—
501#123—271no—
502#123—271no—
503#123—271no—
504#123—271no—
505#123—271no—
506C2×C4⋊C4—271no—
507C2×C4⋊C4—271no—
508C2×C22⋊C4—271no—
509C2×C22⋊C4—271no—
510C2×C22⋊C4—271no—
511C33C2×#12311yescharacteristic, complemented, Sylow
512C23×C3—34no—
513C23×C3—34no—
514C23×C3—91no—
515C23×C3—91no—
516C22×D3—34no—
517C22×D3—34no—
518C22×D3—916no—
519C22×D3—94no—
520C22×D3—91no—
521C22×D3—94no—
522C22×D3—184no—
523C22×D3—182no—
524C22×D3—182no—
525C22×D3—182no—
526C22×D3—182no—
527C22×D3—182no—
528C22×D3—188no—
529C22×D3—188no—
530C22×D3—188no—
531C22×D3—188no—
532C22×D3—188no—
533C22×D3C22×C3⋊D311yescharacteristic
534C22×D3C22×C3⋊D311yescharacteristic
535C3×D4—68no—
536C3×D4—182no—
537C2×C3×C4—24no—
538C2×C3×C4—24no—
539C2×C3×C4—24no—
540C2×C3×C4—34no—
541C2×C3×C4—34no—
542C2×C3×C4—68no—
543C2×C3×C4—91no—
544C2×C3×C4—91no—
545C2×C3×C4—182no—
546C2×C3×C4C2×D3214yes—
547C2×C3×C4C2×D3214yes—
548C2×C3×C4C2×D3214yes—
549C2×C3×C4C22×C3⋊D311yescharacteristic
550C2×C3×C4C22×C3⋊D311yescharacteristic
551C2×C3×C4C22×C3⋊D311yescharacteristic
552#67—182no—
553#67—188no—
554#67—188no—
555#67—182no—
556C2×Dic3—34no—
557C2×Dic3—34no—
558C2×Dic3—94no—
559C2×Dic3—94no—
560C2×Dic3—94no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—184no—
565C2×Dic3—184no—
566C2×Dic3—184no—
567C2×Dic3—182no—
568C2×Dic3—188no—
569C2×Dic3C22×C3⋊D311yescharacteristic
570C2×Dic3C22×C3⋊D311yescharacteristic
571D12—22no—
572D12—68no—
573C4×D3—22no—
574C4×D3—68no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—188no—
578C4×D3—188no—
579C4×D3—188no—
580C4×D3—182no—
581C4×D3—182no—
582C4×D3—182no—
583C4×D3—188no—
584C4×D3—188no—
585C4×D3—1816no—
586C4×D3—188no—
587C4×D3—182no—
588C4×D3—368no—
589C4×D3—368no—
590C2×C32—24no—
591C2×C32—24no—
592C2×C32—24no—
593C2×C32—62no—
594C2×C32—121no—
595C2×C32C2×D3×D414yes—
596C2×C32C2×D3×D411yescharacteristic
597C2×C32D3×#4114yes—
598C2×C32D3×#4114yes—
599C2×C32D3×#4111yescharacteristic
600C2×C32D3×#4111yescharacteristic
601C3⋊D3—22no—
602C3⋊D3—34no—
603C3⋊D3—316no—
604C3⋊D3—41no—
605C3⋊D3—616no—
606C3×D3—28no—
607C3×D3—44no—
608C3×D3—68no—
609C3×D3—124no—
610C24—271no—
611C24—271no—
612C2×D4—31no—
613C2×D4—91no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—544no—
617C22×C4—31no—
618C22×C4—91no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C22×C4—271no—
625C22×C4—271no—
626C22×C4—544no—
627C4⋊C4—31no—
628C4⋊C4—91no—
629C4⋊C4—271no—
630C4⋊C4—271no—
631C4⋊C4—271no—
632C4⋊C4—271no—
633C4⋊C4—271no—
634C4⋊C4D3×C3⋊D311yescharacteristic, complemented
635C22⋊C4—31no—
636C22⋊C4—31no—
637C22⋊C4—31no—
638C22⋊C4—91no—
639C22⋊C4—91no—
640C22⋊C4—91no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C22⋊C4—271no—
644C22⋊C4—271no—
645C22⋊C4—271no—
646C22⋊C4—271no—
647C22×C3—24no—
648C22×C3—38no—
649C22×C3—64no—
650C22×C3—64no—
651C22×C3—64no—
652C22×C3—64no—
653C22×C3—64no—
654C22×C3—92no—
655C22×C3—181no—
656C22×C3—181no—
657C22×C3—181no—
658C22×C3—181no—
659C22×C3—181no—
660C22×C3C22×D3214yes—
661C22×C3C23×C3⋊D311yescharacteristic
662C2×D3—21no—
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—21no—
667C2×D3—38no—
668C2×D3—64no—
669C2×D3—64no—
670C2×D3—64no—
671C2×D3—64no—
672C2×D3—64no—
673C2×D3—98no—
674C2×D3—98no—
675C2×D3—98no—
676C2×D3—92no—
677C2×D3—92no—
678C2×D3—92no—
679C2×D3—188no—
680C2×D3—188no—
681C2×D3—188no—
682C2×D3—188no—
683C2×D3—1832no—
684C2×D3—364no—
685C2×D3—3616no—
686C2×D3D4×C3⋊D312yes—
687C3×C4—28no—
688C3×C4—24no—
689C3×C4—24no—
690C3×C4—24no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—44no—
695C3×C4—44no—
696C3×C4—64no—
697C3×C4—64no—
698C3×C4—181no—
699C3×C4—181no—
700Dic3—21no—
701Dic3—21no—
702Dic3—64no—
703Dic3—64no—
704Dic3—188no—
705Dic3—184no—
706Dic3—184no—
707Dic3—184no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—364no—
712Dic3—364no—
713C32—24no—
714C32D3×#12314yescomplemented
715C32D3×#12311yescharacteristic, complemented
716C23—31no—
717C23—31no—
718C23—91no—
719C23—91no—
720C23—274no—
721C23—271no—
722C23—542no—
723C23—542no—
724C23—542no—
725C23—542no—
726C23—542no—
727D4—62no—
728D4—182no—
729D4—542no—
730D4—542no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—62no—
734C2×C4—91no—
735C2×C4—91no—
736C2×C4—182no—
737C2×C4—271no—
738C2×C4—271no—
739C2×C4—271no—
740C2×C4—542no—
741C2×C4—542no—
742C2×C4—542no—
743C2×C4—542no—
744C2×C4—542no—
745C2×C4—542no—
746C2×C4—542no—
747C2×C4C2×D3×C3⋊D311yescharacteristic
748C2×C4C2×D3×C3⋊D311yescharacteristic
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C3—24no—
751C2×C3—24no—
752C2×C3—24no—
753C2×C3—68no—
754C2×C3—124no—
755C2×C3—182no—
756C2×C3—361no—
757C2×C3#6430614yes—
758C2×C3D32×D414yes—
759C2×C3#6431914yes—
760C2×C3C2×D4×C3⋊D311yescharacteristic
761C2×C3#41×C3⋊D311yescharacteristic
762C2×C3#41×C3⋊D311yescharacteristic
763D3—22no—
764D3—41no—
765D3—68no—
766D3—94no—
767D3—916no—
768D3—124no—
769D3—1816no—
770C22—32no—
771C22—61no—
772C22—61no—
773C22—61no—
774C22—61no—
775C22—61no—
776C22—92no—
777C22—181no—
778C22—181no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—272no—
783C22—272no—
784C22—272no—
785C22—548no—
786C22—1084no—
787C22C22×D3×C3⋊D311yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—61no—
792C4—61no—
793C4—181no—
794C4—181no—
795C4—541no—
796C4—541no—
797C4—541no—
798C3—24no—
799C3#1059460814yescomplemented
800C3C3⋊D3×#12311yescharacteristic, complemented
801C2—62no—
802C2—121no—
803C2—182no—
804C2—274no—
805C2—361no—
806C2#1172457811yescharacteristic
807C2D3×D4×C3⋊D311yescharacteristic
808C2#1172459611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
prime radicalC2×#89026C2
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33C2×#123
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×C3⋊D3C2semidirect
3. C4⋊C4×C3⋊(C3⋊D3)C2semidirect
4. C3×#64103C2semidirect
5. C32×#894C2semidirect
6. #11723539C2semidirect
7. #11723539C2semidirect
8. #11723539C2semidirect
9. #11723523C2semidirect
10. #11723518C2semidirect
11. #11723513C2semidirect
12. #11723488C2semidirect
13. #11723480C2semidirect
14. #11723473C2semidirect
15. #11723470C2semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
26. C2×C32×C4×D3C22semidirect
31. C2×Dic3×C3⋊D3C22semidirect
32. C2×D3×C3⋊Dic3C22semidirect
35. C33×C4⋊C4C22semidirect
36. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
37. #88857C22semidirect
38. #88857C22semidirect
39. C3×#3752C22semidirect
40. C3×#3752C22semidirect
41. C3×#3752C22semidirect
42. C3×#3750C22semidirect
43. C32×(C2×D3)⋊C4C22semidirect
44. C32×(C2×D3)⋊C4C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
49. #88803C22semidirect
50. #88803C22semidirect
51. #88803C22semidirect
52. (C2×D3)⋊(C3⋊Dic3)C22semidirect
53. (C2×D3)⋊(C3⋊Dic3)C22semidirect
54. (C2×D3)⋊(C3⋊Dic3)C22semidirect
63. #64103D3semidirect
75. C3×#894D3semidirect
146. C2×C4×C3⋊D3C2×D3semidirect
150. C2×C3×C4×D3C2×D3semidirect
161. C32×C4⋊C4C2×D3semidirect
162. C32×C4⋊C4C2×D3semidirect
172. #3752C2×D3semidirect
173. #3752C2×D3semidirect
174. #3752C2×D3semidirect
186. #3750C2×D3semidirect
190. C3×(C2×D3)⋊C4C2×D3semidirect
191. C3×(C2×D3)⋊C4C2×D3semidirect
192. C3×(C2×D3)⋊C4C2×D3semidirect
194. C3×Dic3⋊C4C2×D3semidirect
244. #894C3⋊D3semidirect
344. C3⋊(C3⋊D3)#123semidirect
385. C2×C4×D3C2×C3⋊D3semidirect
389. C3×C4⋊C4D32semidirect
390. C3×C4⋊C4C2×C3⋊D3semidirect
412. (C2×D3)⋊C4C2×C3⋊D3semidirect
413. (C2×D3)⋊C4C2×C3⋊D3semidirect
414. (C2×D3)⋊C4C2×C3⋊D3semidirect
429. Dic3⋊C4C2×C3⋊D3semidirect
511. C33C2×#123semidirect
634. C4⋊C4D3×C3⋊D3semidirect
714. C32D3×#123semidirect
715. C32D3×#123semidirect
799. C3#10594608semidirect
800. C3C3⋊D3×#123semidirect

Maximal subgroups

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

subgroupindex
C2×#890262
C2×C4×D3×C3⋊D32
C4⋊C4×C3⋊(C3⋊D3)2
C3×#641032
C32×#8942
#117235392
#117235232
#117235182
#117235132
#117234882
#117234802
#117234732
#117234702
C3⋊D3×#1233
#105946083