Finite Group Databasebeta

← #13176608

Subgroups — #13176608

Order 1728.

1888 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723936C211yesmaximal, characteristic, complemented
2C3×#64103C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723542C211yesmaximal, characteristic, complemented
6#11723541C211yesmaximal, characteristic, complemented
7#11723527C211yesmaximal, characteristic, complemented
8#11723526C211yesmaximal, characteristic, complemented
9#11723525C211yesmaximal, characteristic, complemented
10#11723520C211yesmaximal, characteristic, complemented
11#11723517C211yesmaximal, characteristic, complemented
12#11723504C211yesmaximal, characteristic, complemented
13#11723486C211yesmaximal, characteristic, complemented
14#11723453C211yesmaximal, characteristic, complemented
15#11723421C211yesmaximal, characteristic, complemented
16#10596182—31nomaximal
17#10594663—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
21C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic, complemented
22C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6291C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×#6289C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic
38C3×#3752C2211yescharacteristic
39C3×#3752C2211yescharacteristic, complemented
40C3×#3750C2211yescharacteristic, complemented
41C32×(C2×D3)⋊C4C2211yescharacteristic
42C32×(C2×D3)⋊C4C2211yescharacteristic
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×C4⋊Dic3C2211yescharacteristic, complemented
45C32×Dic3⋊C4C2211yescharacteristic, complemented
46C32×C4×Dic3C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48#88806C2211yescharacteristic, complemented
49#88804C2211yescharacteristic
50#88804C2211yescharacteristic
51#88804C2211yescharacteristic, complemented
52#88803C2211yescharacteristic
53C32×#126—31no—
54#64104—31no—
55#64104—31no—
56#64104—31no—
57#64104—34no—
58#64104—64no—
59#64103—31no—
60#64103—31no—
61#64103D311yescharacteristic, complemented
62#64093—31no—
63#64093—31no—
64#64093—31no—
65#64091—31no—
66#64091—31no—
67#64091—31no—
68#64085—31no—
69#64083—31no—
70C3×#898D314yescomplemented
71C3×#894—34no—
72#63923—34no—
73#63923—34no—
74#63922—34no—
75#63912—34no—
76#63911—34no—
77#63910—34no—
78#63910—34no—
79#63909—34no—
80#63906—34no—
81#63868—34no—
82#63854—34no—
83#63853—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3⋊(C3⋊D3)C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C3×C3⋊D3C2311yescharacteristic
89C22×C32×D3C2311yescharacteristic
90C2×D3×C3⋊D3—41no—
91C2×D3×C3⋊D3—41no—
92C2×D3×C3⋊D3—41no—
93C2×C33×C4C2311yescharacteristic
94C2×C33×C4C2311yescharacteristic
95C2×C33×C4C2311yescharacteristic
96C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
97C4⋊(C3⋊(C3⋊D3))—41no—
98C4⋊(C3⋊(C3⋊D3))—41no—
99C4⋊(C3⋊(C3⋊D3))—41no—
100C4×C3⋊(C3⋊D3)—41no—
101C2×C3×C3⋊Dic3C2311yescharacteristic
102C2×C3×C3⋊Dic3C2311yescharacteristic
103C3×C4⋊(C3⋊D3)—41no—
104C3×C4×C3⋊D3—41no—
105C2×C32×Dic3C2311yescharacteristic
106C2×C32×Dic3C2311yescharacteristic
107C2×C32×Dic3C2311yescharacteristic
108#6292—41no—
109#6292—41no—
110#6292—41no—
111#6292—41no—
112#6292—41no—
113#6291—41no—
114#6291—41no—
115#6290—41no—
116#6289—41no—
117#5711—94no—
118#5666—91no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×#638—31no—
122C2×#638—31no—
123C2×#638—31no—
124C2×C4⋊(C3⋊D3)—31no—
125C2×C4⋊(C3⋊D3)—31no—
126C2×C4⋊(C3⋊D3)—31no—
127C2×C4⋊(C3⋊D3)—31no—
128C2×C4⋊(C3⋊D3)—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)—31no—
132C2×C4⋊(C3⋊D3)—34no—
133C2×C4⋊(C3⋊D3)—34no—
134C2×C4⋊(C3⋊D3)—34no—
135C2×C4⋊(C3⋊D3)—64no—
136C2×C4⋊(C3⋊D3)—64no—
137C2×C4⋊(C3⋊D3)—64no—
138C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
139C2×C4×C3⋊D3—31no—
140C2×C4×C3⋊D3—34no—
141C2×C4×C3⋊D3—31no—
142C2×C4×C3⋊D3—64no—
143C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
144C2×C3×D12—34no—
145C2×C3×C4×D3—34no—
146C2×#626—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#626—34no—
151C2×#626—34no—
152C2×#626—34no—
153C2×#625—34no—
154C2×#624—34no—
155C32×C4⋊C4—24no—
156C32×C4⋊C4—31no—
157C32×C4⋊C4—31no—
158C32×C4⋊C4C2×D314yescomplemented
159C32×C4⋊C4C2×D311yescharacteristic, complemented
160C32×C22⋊C4—31no—
161C32×C22⋊C4—31no—
162C32×C22⋊C4—31no—
163C32×C42—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—34no—
168#3752—34no—
169#3752—31no—
170#3752—31no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752C2×D311yescharacteristic
175#3752C2×D311yescharacteristic
176#3752C2×D311yescharacteristic, complemented
177#3750—31no—
178#3750—31no—
179#3750C2×D311yescharacteristic, complemented
180C3×(C2×D3)⋊C4—34no—
181C3×(C2×D3)⋊C4—34no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4C2×D314yes—
184C3×(C2×D3)⋊C4C2×D314yes—
185C3×(C2×D3)⋊C4C2×D314yes—
186C3×C4⋊Dic3C2×D314yescomplemented
187C3×Dic3⋊C4—34no—
188C3×Dic3⋊C4C2×D314yescomplemented
189C3×C4×Dic3C2×D314yescomplemented
190#3724—34no—
191Dic3⋊Dic3—34no—
192#3722—34no—
193#3722—34no—
194#3722—34no—
195(C2×D3)⋊Dic3—34no—
196C22×C33C2411yescharacteristic
197C2×C3⋊(C3⋊D3)—21no—
198C2×C3⋊(C3⋊D3)—21no—
199C2×C3⋊(C3⋊D3)—21no—
200C2×C3⋊(C3⋊D3)—21no—
201C2×C3⋊(C3⋊D3)—21no—
202C2×C3⋊(C3⋊D3)—21no—
203C2×C3⋊(C3⋊D3)—21no—
204C2×C3⋊(C3⋊D3)—21no—
205C2×C3⋊(C3⋊D3)—21no—
206C2×C3×C3⋊D3—21no—
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×C32×D3—21no—
213C2×C32×D3—21no—
214C2×C32×D3—21no—
215D3×C3⋊D3—44no—
216C33×C4—21no—
217C33×C4—21no—
218C33×C4—21no—
219C3⋊(C3⋊Dic3)—21no—
220C3×C3⋊Dic3—21no—
221C3×C3⋊Dic3—21no—
222C32×Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#126—34no—
226C3×#123—91no—
227#940—91no—
228#937—91no—
229#930—91no—
230#930—91no—
231#898—91no—
232#898C3⋊D311yescharacteristic, complemented
233#895—94no—
234#895—94no—
235#895—94no—
236#895—91no—
237#895—91no—
238#895—184no—
239#894—34no—
240#894—94no—
241#894—94no—
242#884—94no—
243#884—94no—
244#884—94no—
245#884—91no—
246#884—91no—
247#883—91no—
248#883—91no—
249#882—94no—
250#882—94no—
251#882—94no—
252#882—91no—
253#882—91no—
254#876—94no—
255#874—94no—
256C23×C32—31no—
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—31no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—34no—
262C22×C3⋊D3—34no—
263C22×C3⋊D3—64no—
264C22×C3⋊D3—64no—
265C22×C3⋊D3—64no—
266C22×C3⋊D3—121no—
267C22×C3⋊D3—121no—
268C22×C3⋊D3—121no—
269C22×C3⋊D3C22×D311yescharacteristic
270C22×C3⋊D3C22×D311yescharacteristic
271C22×C3×D3—34no—
272C22×C3×D3—34no—
273C22×C3×D3C22×D314yes—
274C2×D32—124no—
275C2×D32—124no—
276C2×D32—124no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—24no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
282C2×C32×C4—31no—
283C2×C32×C4C22×D314yes—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D314yes—
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288C2×C32×C4C22×D311yescharacteristic
289#638—121no—
290#638—121no—
291#638—121no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—64no—
295C2×C3⋊Dic3C22×D311yescharacteristic
296C2×C3⋊Dic3C22×D311yescharacteristic
297C4⋊(C3⋊D3)—41no—
298C4⋊(C3⋊D3)—121no—
299C4⋊(C3⋊D3)—121no—
300C4⋊(C3⋊D3)—121no—
301C4⋊(C3⋊D3)—124no—
302C4⋊(C3⋊D3)—124no—
303C4⋊(C3⋊D3)—124no—
304C4⋊(C3⋊D3)—128no—
305C4⋊(C3⋊D3)—128no—
306C4⋊(C3⋊D3)—128no—
307C4⋊(C3⋊D3)—121no—
308C4⋊(C3⋊D3)—121no—
309C4⋊(C3⋊D3)—121no—
310C4⋊(C3⋊D3)—121no—
311C4⋊(C3⋊D3)—121no—
312C4×C3⋊D3—41no—
313C4×C3⋊D3—121no—
314C4×C3⋊D3—121no—
315C4×C3⋊D3—124no—
316C4×C3⋊D3—128no—
317C2×C3×Dic3—34no—
318C2×C3×Dic3—34no—
319C2×C3×Dic3C22×D314yes—
320C2×C3×Dic3C22×D314yes—
321C2×C3×Dic3C22×D314yes—
322C3×D12—124no—
323C3×C4×D3—124no—
324#626—124no—
325#626—124no—
326#626—124no—
327#626—124no—
328#626—124no—
329#626—124no—
330#626—124no—
331#625—124no—
332#624—124no—
333#560—271noSylow
334C2×C33H(5,𝔽2)11yescharacteristic
335C2×C33H(5,𝔽2)11yescharacteristic
336C2×C33H(5,𝔽2)11yescharacteristic
337C3⋊(C3⋊D3)—41no—
338C3⋊(C3⋊D3)—41no—
339C3⋊(C3⋊D3)—41no—
340C3×C3⋊D3—41no—
341C3×C3⋊D3—41no—
342C32×D3—41no—
343C23×D3—94no—
344C23×D3—91no—
345C2×C3×D4—91no—
346C22×C3×C4—91no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—94no—
350C2×#67—91no—
351C2×#67—91no—
352C2×#67—91no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×D12—34no—
357C2×D12—94no—
358C2×D12—94no—
359C2×D12—94no—
360C2×D12—94no—
361C2×D12—94no—
362C2×D12—91no—
363C2×D12—91no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—94no—
367C2×D12—91no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12—184no—
371C2×D12—184no—
372C2×D12—184no—
373C2×C4×D3—34no—
374C2×C4×D3—94no—
375C2×C4×D3—94no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—184no—
379C3×C4⋊C4—24no—
380C3×C4⋊C4—34no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4—91no—
383C3×C4⋊C4D3214yescomplemented
384C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
385C3×C22⋊C4—34no—
386C3×C22⋊C4—34no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4—91no—
389C3×C22⋊C4—91no—
390C3×C22⋊C4—91no—
391C3×C42—34no—
392#217—91no—
393(C2×D3)⋊C4—34no—
394(C2×D3)⋊C4—34no—
395(C2×D3)⋊C4—34no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—94no—
399(C2×D3)⋊C4—94no—
400(C2×D3)⋊C4—94no—
401(C2×D3)⋊C4—94no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—184no—
408(C2×D3)⋊C4—184no—
409(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
410(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
411(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
412C4⋊Dic3—91no—
413C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
414Dic3⋊C4—34no—
415Dic3⋊C4—94no—
416Dic3⋊C4—94no—
417Dic3⋊C4—91no—
418Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
419C4×Dic3C2×C3⋊D311yescharacteristic, complemented
420C22×C32—24no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32—61no—
424C22×C32C23×D314yes—
425C22×C32C23×D311yescharacteristic
426C2×C3⋊D3—21no—
427C2×C3⋊D3—21no—
428C2×C3⋊D3—21no—
429C2×C3⋊D3—21no—
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3—68no—
433C2×C3⋊D3—61no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—61no—
438C2×C3⋊D3—64no—
439C2×C3⋊D3—61no—
440C2×C3⋊D3—61no—
441C2×C3⋊D3—61no—
442C2×C3⋊D3—61no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—64no—
447C2×C3⋊D3—64no—
448C2×C3⋊D3—64no—
449C2×C3⋊D3—64no—
450C2×C3⋊D3—64no—
451C2×C3⋊D3—124no—
452C2×C3⋊D3—124no—
453C2×C3⋊D3—124no—
454C2×C3⋊D3—124no—
455C2×C3⋊D3—124no—
456C2×C3⋊D3—124no—
457C2×C3⋊D3—124no—
458C2×C3⋊D3—124no—
459C2×C3⋊D3—124no—
460C2×C3×D3—24no—
461C2×C3×D3—24no—
462C2×C3×D3—24no—
463C2×C3×D3—64no—
464C2×C3×D3—64no—
465C2×C3×D3—64no—
466C2×C3×D3—64no—
467C2×C3×D3—64no—
468C2×C3×D3—64no—
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—
481C32×C4—61no—
482C3⋊Dic3—21no—
483C3⋊Dic3—21no—
484C3⋊Dic3—61no—
485C3⋊Dic3—64no—
486C3⋊Dic3—124no—
487C3×Dic3—24no—
488C3×Dic3—24no—
489C3×Dic3—24no—
490C3×Dic3—64no—
491C3×Dic3—64no—
492#127—271no—
493#126—31no—
494#126—271no—
495#123—91no—
496#123—271no—
497#123—271no—
498#121—271no—
499#121—271no—
500#121—271no—
501#121—271no—
502#121—271no—
503#121—271no—
504#120—271no—
505#120—271no—
506#120—271no—
507C33#56011yescharacteristic, complemented, Sylow
508C23×C3—34no—
509C23×C3—91no—
510C23×C3—91no—
511C22×D3—34no—
512C22×D3—34no—
513C22×D3—94no—
514C22×D3—94no—
515C22×D3—94no—
516C22×D3—91no—
517C22×D3—91no—
518C22×D3—91no—
519C22×D3—184no—
520C22×D3—184no—
521C22×D3—184no—
522C22×D3—361no—
523C22×D3—361no—
524C22×D3—361no—
525C22×D3—364no—
526C22×D3—364no—
527C22×D3—364no—
528C22×D3C22×C3⋊D311yescharacteristic
529C3×D4—361no—
530C2×C3×C4—24no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—34no—
534C2×C3×C4—34no—
535C2×C3×C4—34no—
536C2×C3×C4—91no—
537C2×C3×C4—91no—
538C2×C3×C4—361no—
539C2×C3×C4C2×D3214yes—
540C2×C3×C4C2×D3214yes—
541C2×C3×C4C2×D3214yes—
542C2×C3×C4C22×C3⋊D311yescharacteristic
543C2×C3×C4C22×C3⋊D311yescharacteristic
544C2×C3×C4C22×C3⋊D311yescharacteristic
545#67—361no—
546#67—361no—
547#67—361no—
548#67—361no—
549#67—361no—
550#67—364no—
551#67—364no—
552#67—361no—
553#67—364no—
554C2×Dic3—34no—
555C2×Dic3—34no—
556C2×Dic3—94no—
557C2×Dic3—91no—
558C2×Dic3—184no—
559C2×Dic3C22×C3⋊D311yescharacteristic
560C2×Dic3C22×C3⋊D311yescharacteristic
561C2×Dic3C22×C3⋊D311yescharacteristic
562D12—124no—
563D12—364no—
564D12—364no—
565D12—364no—
566D12—361no—
567D12—361no—
568D12—361no—
569D12—368no—
570D12—368no—
571D12—368no—
572D12—364no—
573D12—364no—
574D12—364no—
575D12—364no—
576D12—364no—
577D12—361no—
578D12—361no—
579C4×D3—124no—
580C4×D3—361no—
581C4×D3—364no—
582C4×D3—364no—
583C4×D3—361no—
584C4×D3—368no—
585C2×C32—24no—
586C2×C32—24no—
587C2×C32—24no—
588C2×C32—121no—
589C2×C32#100411yescharacteristic
590C2×C32#100914yes—
591C2×C32#100914yes—
592C2×C32#100914yes—
593C2×C32#100911yescharacteristic
594C2×C32#100911yescharacteristic
595C3⋊D3—41no—
596C3⋊D3—41no—
597C3⋊D3—128no—
598C3⋊D3—121no—
599C3⋊D3—121no—
600C3⋊D3—121no—
601C3⋊D3—124no—
602C3⋊D3—124no—
603C3⋊D3—124no—
604C3⋊D3—244no—
605C3⋊D3—244no—
606C3×D3—44no—
607C3×D3—124no—
608C3×D3—124no—
609C24—271no—
610C2×D4—91no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C2×D4—271no—
616C2×D4—271no—
617C2×D4—271no—
618C2×D4—271no—
619C2×D4—271no—
620C2×D4—271no—
621C2×D4—271no—
622C22×C4—91no—
623C22×C4—271no—
624C22×C4—271no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—91no—
628C4⋊C4—271no—
629C4⋊C4—271no—
630C4⋊C4D3×C3⋊D311yescharacteristic, complemented
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—91no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C22⋊C4—271no—
641C22⋊C4—271no—
642C22⋊C4—271no—
643C42—31no—
644C22×C3—24no—
645C22×C3—64no—
646C22×C3—64no—
647C22×C3—64no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3C22×D3214yes—
655C22×C3C23×C3⋊D311yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—64no—
664C2×D3—64no—
665C2×D3—188no—
666C2×D3—184no—
667C2×D3—184no—
668C2×D3—184no—
669C2×D3—184no—
670C2×D3—184no—
671C2×D3—184no—
672C2×D3—184no—
673C2×D3—184no—
674C2×D3—184no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—181no—
682C2×D3—181no—
683C2×D3—181no—
684C2×D3—364no—
685C2×D3—364no—
686C2×D3—364no—
687C2×D3—364no—
688C2×D3—364no—
689C2×D3—364no—
690C2×D3—364no—
691C2×D3—364no—
692C2×D3—364no—
693C2×D3—3616no—
694C3×C4—28no—
695C3×C4—24no—
696C3×C4—24no—
697C3×C4—24no—
698C3×C4—21no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—44no—
702C3×C4—44no—
703C3×C4—64no—
704C3×C4—64no—
705C3×C4—64no—
706C3×C4—181no—
707C3×C4—181no—
708Dic3—21no—
709Dic3—21no—
710Dic3—21no—
711Dic3—64no—
712Dic3—64no—
713Dic3—184no—
714Dic3—181no—
715Dic3—364no—
716C32—24no—
717C32#566611yescharacteristic, complemented
718C32#571114yescomplemented
719C23—31no—
720C23—91no—
721C23—91no—
722C23—271no—
723C23—271no—
724C23—271no—
725C23—1081no—
726C23—1081no—
727C23—1081no—
728D4—361no—
729D4—1081no—
730D4—1081no—
731D4—1081no—
732D4—1081no—
733D4—1081no—
734D4—1081no—
735D4—1081no—
736D4—1081no—
737D4—1081no—
738D4—1081no—
739D4—1081no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—91no—
744C2×C4—91no—
745C2×C4—271no—
746C2×C4—361no—
747C2×C4—1081no—
748C2×C4—1081no—
749C2×C4C2×D3×C3⋊D311yescharacteristic
750C2×C4C2×D3×C3⋊D311yescharacteristic
751C2×C4C2×D3×C3⋊D311yescharacteristic
752C2×C3—24no—
753C2×C3—24no—
754C2×C3—24no—
755C2×C3—124no—
756C2×C3—361no—
757C2×C3—361no—
758C2×C3#6430814yes—
759C2×C3#6431414yes—
760C2×C3#6432014yes—
761C2×C3#6436611yescharacteristic
762C2×C3#6436611yescharacteristic
763C2×C3#6436611yescharacteristic
764D3—41no—
765D3—124no—
766D3—124no—
767D3—368no—
768D3—361no—
769D3—361no—
770D3—361no—
771D3—364no—
772D3—364no—
773D3—364no—
774D3—724no—
775D3—724no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—181no—
780C22—181no—
781C22—181no—
782C22—181no—
783C22—181no—
784C22—181no—
785C22—541no—
786C22—541no—
787C22—541no—
788C22—541no—
789C22—541no—
790C22—541no—
791C22—541no—
792C22—541no—
793C22—541no—
794C22—1084no—
795C22C22×D3×C3⋊D311yescharacteristic
796C4—21no—
797C4—21no—
798C4—21no—
799C4—61no—
800C4—61no—
801C4—61no—
802C4—181no—
803C4—181no—
804C4—541no—
805C3—24no—
806C3#1059466314yescomplemented
807C3#1059618211yescharacteristic, complemented
808C2—121no—
809C2—361no—
810C2—361no—
811C2—1081no—
812C2—1081no—
813C2—1081no—
814C2#1172458111yescharacteristic
815C2#1172458911yescharacteristic
816C2#1172459711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×C3⋊D3
commutator, socle, cosocleC22×C33C24
FittingC33×C4⋊C4C22
hypercenterC4⋊C4D3×C3⋊D3
hypocenterC33#560
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #11723936C2semidirect
2. C3×#64103C2semidirect
3. C32×#898C2semidirect
4. #11723542C2semidirect
5. #11723542C2semidirect
6. #11723541C2semidirect
7. #11723527C2semidirect
8. #11723526C2semidirect
9. #11723525C2semidirect
10. #11723520C2semidirect
11. #11723517C2semidirect
12. #11723504C2semidirect
13. #11723486C2semidirect
14. #11723453C2semidirect
15. #11723421C2semidirect
21. C2×C4⋊(C3⋊(C3⋊D3))C22semidirect
22. C2×C4×C3⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
28. C2×#6292C22semidirect
29. C2×#6292C22semidirect
33. C2×#6289C22semidirect
34. C33×C4⋊C4C22semidirect
36. #88859C22semidirect
39. C3×#3752C22semidirect
40. C3×#3750C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×C4×Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
51. #88804C22semidirect
61. #64103D3semidirect
70. C3×#898D3semidirect
143. C2×C4×C3⋊D3C2×D3semidirect
158. C32×C4⋊C4C2×D3semidirect
159. C32×C4⋊C4C2×D3semidirect
176. #3752C2×D3semidirect
179. #3750C2×D3semidirect
186. C3×C4⋊Dic3C2×D3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
189. C3×C4×Dic3C2×D3semidirect
232. #898C3⋊D3semidirect
383. C3×C4⋊C4D32semidirect
384. C3×C4⋊C4C2×C3⋊D3semidirect
413. C4⋊Dic3C2×C3⋊D3semidirect
418. Dic3⋊C4C2×C3⋊D3semidirect
419. C4×Dic3C2×C3⋊D3semidirect
507. C33#560semidirect
630. C4⋊C4D3×C3⋊D3semidirect
717. C32#5666semidirect
718. C32#5711semidirect
806. C3#10594663semidirect
807. C3#10596182semidirect

Maximal subgroups

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

subgroupindex
#117239362
C3×#641032
C32×#8982
#117235422
#117235412
#117235272
#117235262
#117235252
#117235202
#117235172
#117235042
#117234862
#117234532
#117234212
#105961823
#105946633