Finite Group Databasebeta

← #13176606

Subgroups — #13176606

Order 1728.

1752 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723939C211yesmaximal, characteristic, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C32×#894C211yesmaximal, characteristic, complemented
4#11723541C211yesmaximal, characteristic, complemented
5#11723541C211yesmaximal, characteristic, complemented
6#11723540C211yesmaximal, characteristic, complemented
7#11723529C211yesmaximal, characteristic, complemented
8#11723523C211yesmaximal, characteristic, complemented
9#11723520C211yesmaximal, characteristic, complemented
10#11723519C211yesmaximal, characteristic, complemented
11#11723518C211yesmaximal, characteristic, complemented
12#11723515C211yesmaximal, characteristic, complemented
13#11723514C211yesmaximal, characteristic, complemented
14#11723482C211yesmaximal, characteristic, complemented
15#11723433C211yesmaximal, characteristic, complemented
16#10596137—31nomaximal
17#10594662—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
20C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
22C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
23C2×C32×D12C2211yescharacteristic
24C2×C32×C4×D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6291C2211yescharacteristic
28C2×#6290C2211yescharacteristic
29C2×#6290C2211yescharacteristic
30C2×#6290C2211yescharacteristic
31C2×#6290C2211yescharacteristic, complemented
32C2×#6290C2211yescharacteristic, complemented
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37#88859C2211yescharacteristic
38C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
39#88857C2211yescharacteristic, complemented
40C4×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41C3×#3752C2211yescharacteristic
42C3×#3752C2211yescharacteristic, complemented
43C32×(C2×D3)⋊C4C2211yescharacteristic
44C32×(C2×D3)⋊C4C2211yescharacteristic
45C32×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C32×Dic3⋊C4C2211yescharacteristic, complemented
47#88807C2211yescharacteristic, complemented
48Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
49#88803C2211yescharacteristic
50#88803C2211yescharacteristic
51#88803C2211yescharacteristic, complemented
52(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
53C32×#123—31no—
54#64149—31no—
55#64146—31no—
56#64139—31no—
57#64139—31no—
58#64107—31no—
59#64107—31no—
60#64107—34no—
61#64107—64no—
62#64104—31no—
63#64104D311yescharacteristic, complemented
64#64093—31no—
65#64093—31no—
66#64092—31no—
67#64092—31no—
68#64091—31no—
69#64091—31no—
70C3×#895—34no—
71C3×#894D314yescomplemented
72#63922—34no—
73#63922—34no—
74#63922—34no—
75#63914—34no—
76#63908—34no—
77#63906—34no—
78#63906—34no—
79#63905—34no—
80#63891—34no—
81#63886—34no—
82#63885—34no—
83#63862—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3×C3⋊D3C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
87C22×C3×C3⋊D3C2311yescharacteristic
88C22×C32×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
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
99C2×C3×C3⋊Dic3C2311yescharacteristic
100C3×C4⋊(C3⋊D3)—41no—
101C3×C4⋊(C3⋊D3)—41no—
102C3×C4⋊(C3⋊D3)—41no—
103C3×C4×C3⋊D3—41no—
104C2×C32×Dic3C2311yescharacteristic
105C2×C32×Dic3C2311yescharacteristic
106C32×D12—41no—
107C32×C4×D3—41no—
108#6292—41no—
109#6292—41no—
110#6291—41no—
111#6290—41no—
112#6290—41no—
113#6290—41no—
114#6290—41no—
115#6290—41no—
116Dic3×C3⋊D3—41no—
117#5666—94no—
118#5620—91no—
119C23×C3⋊D3—31no—
120C22×D32—34no—
121C2×C32×D4—31no—
122C22×C32×C4—31no—
123C2×#638—31no—
124C2×#638—31no—
125C2×#638—31no—
126C2×#638—31no—
127C2×#638—31no—
128C2×#638—31no—
129C2×C4⋊(C3⋊D3)—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
132C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
133C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
136C2×C3×D12—34no—
137C2×C3×D12—34no—
138C2×C3×D12—34no—
139C2×C3×D12C2×D314yes—
140C2×C3×C4×D3—34no—
141C2×C3×C4×D3C2×D314yescomplemented
142C2×#626—34no—
143C2×#626—34no—
144C2×#626—34no—
145C2×#625—34no—
146C2×#625—34no—
147C2×#625—34no—
148C2×#625—34no—
149C2×#625—34no—
150C2×D3×Dic3—34no—
151C32×C4⋊C4—24no—
152C32×C4⋊C4—31no—
153C32×C4⋊C4C2×D314yescomplemented
154C32×C4⋊C4C2×D311yescharacteristic, complemented
155C32×C22⋊C4—31no—
156C32×C22⋊C4—31no—
157C32×C22⋊C4—31no—
158#3757—31no—
159#3752—31no—
160#3752—31no—
161#3752—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—34no—
166#3752—34no—
167#3752—34no—
168#3752—64no—
169#3752—64no—
170#3752—64no—
171#3752C2×D311yescharacteristic
172#3752C2×D311yescharacteristic, complemented
173C4⋊(C3⋊Dic3)—31no—
174C4⋊(C3⋊Dic3)—34no—
175C4⋊(C3⋊Dic3)—31no—
176C4⋊(C3⋊Dic3)—64no—
177#3750—31no—
178#3750—34no—
179#3750—31no—
180#3750—64no—
181C4×C3⋊Dic3—31no—
182C4×C3⋊Dic3—34no—
183C4×C3⋊Dic3—64no—
184C3×(C2×D3)⋊C4—34no—
185C3×(C2×D3)⋊C4—34no—
186C3×(C2×D3)⋊C4C2×D314yes—
187C3×(C2×D3)⋊C4C2×D314yes—
188C3×(C2×D3)⋊C4C2×D314yescomplemented
189C3×Dic3⋊C4C2×D314yescomplemented
190Dic3⋊Dic3—34no—
191Dic3⋊Dic3—34no—
192(C2×D3)⋊Dic3—34no—
193(C2×D3)⋊Dic3—34no—
194(C2×D3)⋊Dic3—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×C32×D3—21no—
210C2×C32×D3—21no—
211C2×C32×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—
222C3×C3⋊Dic3—21no—
223C32×Dic3—21no—
224C32×Dic3—21no—
225C3×#123—34no—
226C3×#121—91no—
227#940—94no—
228#940—91no—
229#939—91no—
230#939—91no—
231#938—91no—
232#937—94no—
233#937—91no—
234#937—91no—
235#930—94no—
236#930—94no—
237#930—91no—
238#929—91no—
239#898—94no—
240#898—94no—
241#898—91no—
242#898—184no—
243#895—34no—
244#895—94no—
245#894C3⋊D311yescharacteristic, complemented
246#886—91no—
247#884—94no—
248#884—94no—
249#884—91no—
250#883—94no—
251#883—94no—
252#882—94no—
253#882—94no—
254#882—91no—
255#879—91no—
256C23×C32—31no—
257C23×C32—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—64no—
261C22×C3⋊D3—121no—
262C22×C3⋊D3—121no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3C22×D311yescharacteristic
265C22×C3⋊D3C22×D311yescharacteristic
266C22×C3⋊D3C22×D311yescharacteristic
267C22×C3×D3—34no—
268C22×C3×D3—34no—
269C22×C3×D3—34no—
270C22×C3×D3C22×D314yes—
271C22×C3×D3C22×D314yes—
272C2×D32—124no—
273C2×D32—124no—
274C2×D32—124no—
275C32×D4—121no—
276C2×C32×C4—24no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—121no—
282C2×C32×C4C22×D314yes—
283C2×C32×C4C22×D314yes—
284C2×C32×C4C22×D314yes—
285C2×C32×C4C22×D311yescharacteristic
286C2×C32×C4C22×D311yescharacteristic
287C2×C32×C4C22×D311yescharacteristic
288#638—121no—
289#638—121no—
290#638—121no—
291#638—121no—
292#638—121no—
293#638—121no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—31no—
297C2×C3⋊Dic3—34no—
298C2×C3⋊Dic3—34no—
299C2×C3⋊Dic3—34no—
300C2×C3⋊Dic3—64no—
301C2×C3⋊Dic3—64no—
302C2×C3⋊Dic3—64no—
303C2×C3⋊Dic3C22×D311yescharacteristic
304C4⋊(C3⋊D3)—41no—
305C4⋊(C3⋊D3)—41no—
306C4⋊(C3⋊D3)—41no—
307C4⋊(C3⋊D3)—121no—
308C4⋊(C3⋊D3)—121no—
309C4×C3⋊D3—41no—
310C4×C3⋊D3—121no—
311C2×C3×Dic3—34no—
312C2×C3×Dic3C22×D314yes—
313C2×C3×Dic3C22×D314yes—
314C3×D12—44no—
315C3×D12—124no—
316C3×D12—124no—
317C3×D12—124no—
318C3×C4×D3—44no—
319C3×C4×D3—124no—
320#626—124no—
321#626—124no—
322#626—124no—
323#625—124no—
324#625—124no—
325#625—124no—
326#625—124no—
327#625—124no—
328D3×Dic3—124no—
329#560—271noSylow
330C2×C33H(5,𝔽2)11yescharacteristic
331C2×C33H(5,𝔽2)11yescharacteristic
332C2×C33H(5,𝔽2)11yescharacteristic
333C3⋊(C3⋊D3)—41no—
334C3×C3⋊D3—41no—
335C3×C3⋊D3—41no—
336C3×C3⋊D3—41no—
337C32×D3—41no—
338C32×D3—41no—
339C23×D3—94no—
340C23×D3—91no—
341C2×C3×D4—34no—
342C2×C3×D4—91no—
343C2×C3×D4—91no—
344C2×C3×D4—91no—
345C22×C3×C4—34no—
346C22×C3×C4—91no—
347C2×#67—94no—
348C2×#67—94no—
349C2×#67—94no—
350C2×#67—94no—
351C2×#67—94no—
352C2×#67—94no—
353C2×#67—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C22×Dic3—91no—
361C2×D12—34no—
362C2×D12—34no—
363C2×D12—34no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—91no—
367C2×D12C2×C3⋊D311yescharacteristic
368C2×C4×D3—34no—
369C2×C4×D3—94no—
370C2×C4×D3C2×C3⋊D311yescharacteristic, complemented
371C3×C4⋊C4—24no—
372C3×C4⋊C4—34no—
373C3×C4⋊C4D3214yescomplemented
374C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
375C3×C22⋊C4—34no—
376C3×C22⋊C4—34no—
377C3×C22⋊C4—34no—
378C3×C22⋊C4—91no—
379C3×C22⋊C4—91no—
380#217—94no—
381#217—91no—
382#217—91no—
383#217—91no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—94no—
387(C2×D3)⋊C4—94no—
388(C2×D3)⋊C4—94no—
389(C2×D3)⋊C4—91no—
390(C2×D3)⋊C4—94no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—94no—
393(C2×D3)⋊C4—91no—
394(C2×D3)⋊C4—91no—
395(C2×D3)⋊C4—91no—
396(C2×D3)⋊C4—184no—
397(C2×D3)⋊C4—184no—
398(C2×D3)⋊C4—184no—
399(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
400(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
401(C2×D3)⋊C4C2×C3⋊D311yescharacteristic, complemented
402C4⋊Dic3—94no—
403C4⋊Dic3—94no—
404C4⋊Dic3—91no—
405C4⋊Dic3—91no—
406C4⋊Dic3—184no—
407Dic3⋊C4—94no—
408Dic3⋊C4—94no—
409Dic3⋊C4—91no—
410Dic3⋊C4—91no—
411Dic3⋊C4—184no—
412Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
413C4×Dic3—94no—
414C4×Dic3—91no—
415C4×Dic3—184no—
416C22×C32—24no—
417C22×C32—61no—
418C22×C32—61no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32—61no—
423C22×C32C23×D314yes—
424C22×C32C23×D311yescharacteristic
425C2×C3⋊D3—21no—
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—21no—
433C2×C3⋊D3—21no—
434C2×C3⋊D3—61no—
435C2×C3⋊D3—61no—
436C2×C3⋊D3—61no—
437C2×C3⋊D3—64no—
438C2×C3⋊D3—64no—
439C2×C3⋊D3—64no—
440C2×C3⋊D3—124no—
441C2×C3⋊D3—124no—
442C2×C3⋊D3—124no—
443C2×C3⋊D3—124no—
444C2×C3×D3—24no—
445C2×C3×D3—24no—
446C2×C3×D3—24no—
447C2×C3×D3—24no—
448C2×C3×D3—24no—
449C2×C3×D3—24no—
450C2×C3×D3—64no—
451C2×C3×D3—64no—
452C2×C3×D3—64no—
453C2×C3×D3—64no—
454C2×C3×D3—64no—
455C2×C3×D3—64no—
456C2×C3×D3—64no—
457C2×C3×D3—64no—
458C2×C3×D3—64no—
459D32—1216no—
460C32×C4—21no—
461C32×C4—21no—
462C32×C4—21no—
463C32×C4—24no—
464C32×C4—24no—
465C32×C4—24no—
466C32×C4—44no—
467C32×C4—44no—
468C32×C4—44no—
469C32×C4—61no—
470C32×C4—61no—
471C3⋊Dic3—21no—
472C3⋊Dic3—61no—
473C3⋊Dic3—61no—
474C3⋊Dic3—61no—
475C3⋊Dic3—64no—
476C3⋊Dic3—64no—
477C3⋊Dic3—64no—
478C3⋊Dic3—124no—
479C3⋊Dic3—124no—
480C3⋊Dic3—124no—
481C3×Dic3—24no—
482C3×Dic3—24no—
483C3×Dic3—64no—
484#127—271no—
485#126—271no—
486#126—271no—
487#123—31no—
488#123—271no—
489#123—271no—
490#121—91no—
491#121—271no—
492#121—271no—
493#121—271no—
494#121—271no—
495#121—271no—
496#120—271no—
497#120—271no—
498#120—271no—
499C33#56011yescharacteristic, complemented, Sylow
500C23×C3—34no—
501C23×C3—34no—
502C23×C3—91no—
503C23×C3—91no—
504C23×C3—91no—
505C22×D3—34no—
506C22×D3—34no—
507C22×D3—34no—
508C22×D3—94no—
509C22×D3—91no—
510C22×D3—184no—
511C22×D3—361no—
512C22×D3—361no—
513C22×D3—361no—
514C22×D3—364no—
515C22×D3—364no—
516C22×D3—364no—
517C22×D3C22×C3⋊D311yescharacteristic
518C22×D3C22×C3⋊D311yescharacteristic
519C3×D4—124no—
520C3×D4—361no—
521C3×D4—361no—
522C3×D4—361no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—24no—
526C2×C3×C4—34no—
527C2×C3×C4—34no—
528C2×C3×C4—91no—
529C2×C3×C4—124no—
530C2×C3×C4—361no—
531C2×C3×C4C2×D3214yes—
532C2×C3×C4C2×D3214yes—
533C2×C3×C4C2×D3214yes—
534C2×C3×C4C22×C3⋊D311yescharacteristic
535C2×C3×C4C22×C3⋊D311yescharacteristic
536C2×C3×C4C22×C3⋊D311yescharacteristic
537#67—361no—
538#67—361no—
539#67—364no—
540#67—361no—
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545#67—364no—
546#67—364no—
547#67—364no—
548#67—364no—
549#67—364no—
550C2×Dic3—34no—
551C2×Dic3—94no—
552C2×Dic3—94no—
553C2×Dic3—94no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—91no—
557C2×Dic3—184no—
558C2×Dic3—184no—
559C2×Dic3—184no—
560C2×Dic3—361no—
561C2×Dic3C22×C3⋊D311yescharacteristic
562C2×Dic3C22×C3⋊D311yescharacteristic
563D12—41no—
564D12—124no—
565D12—124no—
566D12—124no—
567D12—364no—
568D12—364no—
569D12—361no—
570C4×D3—41no—
571C4×D3—124no—
572C4×D3—364no—
573C2×C32—24no—
574C2×C32—24no—
575C2×C32—24no—
576C2×C32—121no—
577C2×C32—121no—
578C2×C32#100414yes—
579C2×C32#100411yescharacteristic
580C2×C32#100411yescharacteristic
581C2×C32#100914yes—
582C2×C32#100914yes—
583C2×C32#100911yescharacteristic
584C3⋊D3—41no—
585C3⋊D3—41no—
586C3⋊D3—41no—
587C3⋊D3—121no—
588C3⋊D3—124no—
589C3⋊D3—244no—
590C3×D3—44no—
591C3×D3—44no—
592C3×D3—124no—
593C3×D3—124no—
594C3×D3—124no—
595C24—271no—
596C2×D4—31no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—271no—
601C2×D4—271no—
602C2×D4—271no—
603C2×D4—271no—
604C2×D4—271no—
605C2×D4—271no—
606C2×D4—271no—
607C2×D4—271no—
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—271no—
611C4⋊C4—31no—
612C4⋊C4—271no—
613C4⋊C4—271no—
614C4⋊C4—271no—
615C4⋊C4—271no—
616C4⋊C4D3×C3⋊D311yescharacteristic, complemented
617C22⋊C4—31no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—271no—
623C22⋊C4—271no—
624C22⋊C4—271no—
625C22⋊C4—271no—
626C22⋊C4—271no—
627C22⋊C4—271no—
628C22⋊C4—271no—
629C42—271no—
630C22×C3—24no—
631C22×C3—64no—
632C22×C3—64no—
633C22×C3—64no—
634C22×C3—64no—
635C22×C3—64no—
636C22×C3—64no—
637C22×C3—181no—
638C22×C3—181no—
639C22×C3—181no—
640C22×C3—181no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3C22×D3214yes—
647C22×C3C23×C3⋊D311yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—64no—
655C2×D3—64no—
656C2×D3—64no—
657C2×D3—64no—
658C2×D3—64no—
659C2×D3—64no—
660C2×D3—64no—
661C2×D3—64no—
662C2×D3—64no—
663C2×D3—184no—
664C2×D3—184no—
665C2×D3—184no—
666C2×D3—181no—
667C2×D3—181no—
668C2×D3—181no—
669C2×D3—364no—
670C2×D3—364no—
671C2×D3—364no—
672C2×D3—364no—
673C2×D3—3616no—
674C3×C4—24no—
675C3×C4—24no—
676C3×C4—24no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—44no—
681C3×C4—44no—
682C3×C4—44no—
683C3×C4—64no—
684C3×C4—64no—
685C3×C4—181no—
686Dic3—21no—
687Dic3—21no—
688Dic3—64no—
689Dic3—184no—
690Dic3—184no—
691Dic3—184no—
692Dic3—181no—
693Dic3—181no—
694Dic3—181no—
695Dic3—364no—
696Dic3—364no—
697Dic3—364no—
698C32—24no—
699C32#562011yescharacteristic, complemented
700C32#566614yescomplemented
701C23—31no—
702C23—31no—
703C23—91no—
704C23—91no—
705C23—91no—
706C23—271no—
707C23—1081no—
708C23—1081no—
709C23—1081no—
710D4—121no—
711D4—361no—
712D4—361no—
713D4—361no—
714D4—1081no—
715D4—1081no—
716D4—1081no—
717D4—1081no—
718D4—1081no—
719D4—1081no—
720D4—1081no—
721D4—1081no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—91no—
725C2×C4—121no—
726C2×C4—271no—
727C2×C4—271no—
728C2×C4—271no—
729C2×C4—361no—
730C2×C4—1081no—
731C2×C4C2×D3×C3⋊D311yescharacteristic
732C2×C4C2×D3×C3⋊D311yescharacteristic
733C2×C4C2×D3×C3⋊D311yescharacteristic
734C2×C3—24no—
735C2×C3—24no—
736C2×C3—24no—
737C2×C3—124no—
738C2×C3—124no—
739C2×C3—361no—
740C2×C3—361no—
741C2×C3—361no—
742C2×C3#6430714yes—
743C2×C3#6431314yes—
744C2×C3#6432014yes—
745C2×C3#6436111yescharacteristic
746C2×C3#6436611yescharacteristic
747C2×C3#6436611yescharacteristic
748D3—41no—
749D3—41no—
750D3—124no—
751D3—124no—
752D3—124no—
753D3—361no—
754D3—364no—
755D3—724no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—181no—
763C22—181no—
764C22—181no—
765C22—181no—
766C22—181no—
767C22—181no—
768C22—181no—
769C22—181no—
770C22—181no—
771C22—541no—
772C22—541no—
773C22—541no—
774C22—1084no—
775C22C22×D3×C3⋊D311yescharacteristic
776C4—21no—
777C4—21no—
778C4—21no—
779C4—61no—
780C4—61no—
781C4—181no—
782C4—541no—
783C4—541no—
784C4—541no—
785C3—24no—
786C3#1059466214yescomplemented
787C3#1059613711yescharacteristic, complemented
788C2—121no—
789C2—121no—
790C2—361no—
791C2—361no—
792C2—361no—
793C2—1081no—
794C2#1172458011yescharacteristic
795C2#1172458711yescharacteristic
796C2#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. #11723939C2semidirect
2. C3×#64104C2semidirect
3. C32×#894C2semidirect
4. #11723541C2semidirect
5. #11723541C2semidirect
6. #11723540C2semidirect
7. #11723529C2semidirect
8. #11723523C2semidirect
9. #11723520C2semidirect
10. #11723519C2semidirect
11. #11723518C2semidirect
12. #11723515C2semidirect
13. #11723514C2semidirect
14. #11723482C2semidirect
15. #11723433C2semidirect
21. C2×C3×C4⋊(C3⋊D3)C22semidirect
22. C2×C3×C4×C3⋊D3C22semidirect
24. C2×C32×C4×D3C22semidirect
31. C2×#6290C22semidirect
32. C2×#6290C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C33×C4⋊C4C22semidirect
38. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
39. #88857C22semidirect
40. C4×C3⋊(C3⋊Dic3)C22semidirect
42. C3×#3752C22semidirect
45. C32×(C2×D3)⋊C4C22semidirect
46. C32×Dic3⋊C4C22semidirect
47. #88807C22semidirect
48. Dic3⋊(C3⋊Dic3)C22semidirect
51. #88803C22semidirect
63. #64104D3semidirect
71. C3×#894D3semidirect
133. C2×C4⋊(C3⋊D3)C2×D3semidirect
135. C2×C4×C3⋊D3C2×D3semidirect
141. C2×C3×C4×D3C2×D3semidirect
153. C32×C4⋊C4C2×D3semidirect
154. C32×C4⋊C4C2×D3semidirect
172. #3752C2×D3semidirect
188. C3×(C2×D3)⋊C4C2×D3semidirect
189. C3×Dic3⋊C4C2×D3semidirect
245. #894C3⋊D3semidirect
370. C2×C4×D3C2×C3⋊D3semidirect
373. C3×C4⋊C4D32semidirect
374. C3×C4⋊C4C2×C3⋊D3semidirect
401. (C2×D3)⋊C4C2×C3⋊D3semidirect
412. Dic3⋊C4C2×C3⋊D3semidirect
499. C33#560semidirect
616. C4⋊C4D3×C3⋊D3semidirect
699. C32#5620semidirect
700. C32#5666semidirect
786. C3#10594662semidirect
787. C3#10596137semidirect

Maximal subgroups

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

subgroupindex
#117239392
C3×#641042
C32×#8942
#117235412
#117235402
#117235292
#117235232
#117235202
#117235192
#117235182
#117235152
#117235142
#117234822
#117234332
#105961373
#105946623