Finite Group Databasebeta

← #13176605

Subgroups — #13176605

Order 1728.

1824 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723935C211yesmaximal, characteristic, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C32×#898C211yesmaximal, characteristic, complemented
4#11723542C211yesmaximal, characteristic, complemented
5#11723541C211yesmaximal, characteristic, complemented
6#11723541C211yesmaximal, characteristic, complemented
7#11723532C211yesmaximal, characteristic, complemented
8#11723527C211yesmaximal, characteristic, complemented
9#11723520C211yesmaximal, characteristic, complemented
10#11723519C211yesmaximal, characteristic, complemented
11#11723517C211yesmaximal, characteristic, complemented
12#11723493C211yesmaximal, characteristic, complemented
13#11723482C211yesmaximal, characteristic, complemented
14#11723438C211yesmaximal, characteristic, complemented
15#11723417C211yesmaximal, characteristic, complemented
16#10596182—31nomaximal
17#10594661—34nomaximal
18C22×D3×C3⋊D3C2211yescharacteristic
19C2×C4⋊(C3⋊(C3⋊D3))C2211yescharacteristic
20C2×C4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
22C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
24C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
25C2×#6292C2211yescharacteristic
26C2×#6292C2211yescharacteristic
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic, complemented
29C2×#6292C2211yescharacteristic, complemented
30C2×#6291C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×#6290C2211yescharacteristic
33C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
34C33×C4⋊C4C2211yescharacteristic, complemented
35#88859C2211yescharacteristic
36#88859C2211yescharacteristic
37#88859C2211yescharacteristic, complemented
38#88857C2211yescharacteristic, complemented
39C3×#3752C2211yescharacteristic
40C3×#3752C2211yescharacteristic, 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#88803C2211yescharacteristic
51#88803C2211yescharacteristic
52#88803C2211yescharacteristic, complemented
53C32×#126—31no—
54#64104—31no—
55#64104—31no—
56#64104D311yescharacteristic, complemented
57#64103—31no—
58#64103—31no—
59#64103—31no—
60#64103—34no—
61#64103—64no—
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×#895—34no—
72#63923—34no—
73#63922—34no—
74#63922—34no—
75#63916—34no—
76#63912—34no—
77#63911—34no—
78#63906—34no—
79#63890—34no—
80#63886—34no—
81#63885—34no—
82#63859—34no—
83#63850—34no—
84C22×C3⋊(C3⋊D3)C2311yescharacteristic
85C22×C3⋊(C3⋊D3)C2311yescharacteristic
86C22×C3×C3⋊D3C2311yescharacteristic
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
97C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
98C4⋊(C3⋊(C3⋊D3))—41no—
99C4×C3⋊(C3⋊D3)—41no—
100C2×C3×C3⋊Dic3C2311yescharacteristic
101C3×C4⋊(C3⋊D3)—41no—
102C3×C4⋊(C3⋊D3)—41no—
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#6290—41no—
115#6290—41no—
116Dic3×C3⋊D3—41no—
117#5711—94no—
118#5620—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)—34no—
131C2×C4⋊(C3⋊D3)—64no—
132C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
133C2×C4⋊(C3⋊D3)C2×D311yescharacteristic
134C2×C4⋊(C3⋊D3)C2×D311yescharacteristic, complemented
135C2×C4×C3⋊D3—31no—
136C2×C4×C3⋊D3—31no—
137C2×C4×C3⋊D3—34no—
138C2×C4×C3⋊D3—64no—
139C2×C4×C3⋊D3C2×D311yescharacteristic, complemented
140C2×C3×D12—34no—
141C2×C3×D12—34no—
142C2×C3×D12—34no—
143C2×C3×C4×D3—34no—
144C2×#626—34no—
145C2×#626—34no—
146C2×#626—34no—
147C2×#626—34no—
148C2×#626—34no—
149C2×#626—34no—
150C2×#625—34no—
151C2×#625—34no—
152C2×D3×Dic3—34no—
153C32×C4⋊C4—24no—
154C32×C4⋊C4—31no—
155C32×C4⋊C4—31no—
156C32×C4⋊C4C2×D314yescomplemented
157C32×C4⋊C4C2×D311yescharacteristic, complemented
158C32×C22⋊C4—31no—
159C32×C22⋊C4—31no—
160C32×C22⋊C4—31no—
161C32×C42—31no—
162#3752—31no—
163#3752—31no—
164#3752—31no—
165#3752—31no—
166#3752—31no—
167#3752—31no—
168#3752—34no—
169#3752—34no—
170#3752—34no—
171#3752—31no—
172#3752—64no—
173#3752—64no—
174#3752—64no—
175#3752C2×D311yescharacteristic
176#3752C2×D311yescharacteristic, complemented
177#3750—31no—
178#3750—34no—
179#3750—31no—
180#3750—31no—
181#3750—64no—
182C3×(C2×D3)⋊C4—34no—
183C3×(C2×D3)⋊C4—34no—
184C3×(C2×D3)⋊C4C2×D314yes—
185C3×(C2×D3)⋊C4C2×D314yes—
186C3×(C2×D3)⋊C4C2×D314yes—
187C3×C4⋊Dic3C2×D314yescomplemented
188C3×Dic3⋊C4C2×D314yescomplemented
189C3×C4×Dic3C2×D314yescomplemented
190#3724—34no—
191Dic3⋊Dic3—34no—
192#3722—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×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×#121—91no—
227#940—91no—
228#939—91no—
229#939—91no—
230#938—91no—
231#937—91no—
232#937—91no—
233#930—91no—
234#929—91no—
235#898C3⋊D311yescharacteristic, complemented
236#895—34no—
237#895—94no—
238#895—94no—
239#894—94no—
240#894—94no—
241#894—94no—
242#894—91no—
243#894—184no—
244#886—91no—
245#884—94no—
246#884—94no—
247#884—94no—
248#884—91no—
249#882—94no—
250#882—94no—
251#882—94no—
252#882—91no—
253#879—91no—
254#876—94no—
255#874—94no—
256C23×C32—31no—
257C22×C3⋊D3—31no—
258C22×C3⋊D3—31no—
259C22×C3⋊D3—34no—
260C22×C3⋊D3—34no—
261C22×C3⋊D3—64no—
262C22×C3⋊D3—64no—
263C22×C3⋊D3—121no—
264C22×C3⋊D3—121no—
265C22×C3⋊D3—121no—
266C22×C3⋊D3C22×D311yescharacteristic
267C22×C3⋊D3C22×D311yescharacteristic
268C22×C3⋊D3C22×D311yescharacteristic
269C22×C3×D3—34no—
270C22×C3×D3—34no—
271C22×C3×D3—34no—
272C22×C3×D3C22×D314yes—
273C2×D32—124no—
274C2×D32—124no—
275C2×D32—124no—
276C2×C32×C4—24no—
277C2×C32×C4—24no—
278C2×C32×C4—24no—
279C2×C32×C4—31no—
280C2×C32×C4—31no—
281C2×C32×C4—31no—
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—
291C2×C3⋊Dic3—31no—
292C2×C3⋊Dic3—31no—
293C2×C3⋊Dic3—34no—
294C2×C3⋊Dic3—34no—
295C2×C3⋊Dic3—64no—
296C2×C3⋊Dic3—64no—
297C2×C3⋊Dic3C22×D311yescharacteristic
298C4⋊(C3⋊D3)—41no—
299C4⋊(C3⋊D3)—41no—
300C4⋊(C3⋊D3)—41no—
301C4⋊(C3⋊D3)—121no—
302C4⋊(C3⋊D3)—124no—
303C4⋊(C3⋊D3)—128no—
304C4⋊(C3⋊D3)—121no—
305C4⋊(C3⋊D3)—121no—
306C4⋊(C3⋊D3)—121no—
307C4⋊(C3⋊D3)—121no—
308C4⋊(C3⋊D3)—121no—
309C4×C3⋊D3—41no—
310C4×C3⋊D3—121no—
311C4×C3⋊D3—124no—
312C4×C3⋊D3—121no—
313C4×C3⋊D3—128no—
314C2×C3×Dic3—34no—
315C2×C3×Dic3C22×D314yes—
316C2×C3×Dic3C22×D314yes—
317C2×C3×Dic3C22×D314yes—
318C3×D12—124no—
319C3×D12—124no—
320C3×D12—124no—
321C3×C4×D3—124no—
322#626—124no—
323#626—124no—
324#626—124no—
325#626—124no—
326#626—124no—
327#626—124no—
328#625—124no—
329#625—124no—
330D3×Dic3—124no—
331#560—271noSylow
332C2×C33H(5,𝔽2)11yescharacteristic
333C2×C33H(5,𝔽2)11yescharacteristic
334C2×C33H(5,𝔽2)11yescharacteristic
335C3⋊(C3⋊D3)—41no—
336C3⋊(C3⋊D3)—41no—
337C3×C3⋊D3—41no—
338C3×C3⋊D3—41no—
339C3×C3⋊D3—41no—
340C32×D3—41no—
341C23×D3—94no—
342C23×D3—91no—
343C2×C3×D4—91no—
344C2×C3×D4—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×#67—91no—
357C22×Dic3—91no—
358C2×D12—34no—
359C2×D12—34no—
360C2×D12—34no—
361C2×D12—94no—
362C2×D12—94no—
363C2×D12—94no—
364C2×D12—94no—
365C2×D12—94no—
366C2×D12—91no—
367C2×D12—94no—
368C2×D12—91no—
369C2×D12—184no—
370C2×C4×D3—34no—
371C2×C4×D3—94no—
372C2×C4×D3—94no—
373C2×C4×D3—91no—
374C2×C4×D3—184no—
375C3×C4⋊C4—24no—
376C3×C4⋊C4—34no—
377C3×C4⋊C4—34no—
378C3×C4⋊C4D3214yescomplemented
379C3×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
380C3×C22⋊C4—34no—
381C3×C22⋊C4—34no—
382C3×C22⋊C4—34no—
383C3×C22⋊C4—91no—
384C3×C22⋊C4—91no—
385C3×C42—34no—
386#217—91no—
387#217—91no—
388#217—91no—
389(C2×D3)⋊C4—34no—
390(C2×D3)⋊C4—34no—
391(C2×D3)⋊C4—94no—
392(C2×D3)⋊C4—94no—
393(C2×D3)⋊C4—94no—
394(C2×D3)⋊C4—94no—
395(C2×D3)⋊C4—94no—
396(C2×D3)⋊C4—94no—
397(C2×D3)⋊C4—94no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—184no—
403(C2×D3)⋊C4—184no—
404(C2×D3)⋊C4—184no—
405(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
406(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
407(C2×D3)⋊C4C2×C3⋊D311yescharacteristic
408C4⋊Dic3—91no—
409C4⋊Dic3C2×C3⋊D311yescharacteristic, complemented
410Dic3⋊C4—94no—
411Dic3⋊C4—94no—
412Dic3⋊C4—94no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—184no—
416Dic3⋊C4C2×C3⋊D311yescharacteristic, complemented
417C4×Dic3C2×C3⋊D311yescharacteristic, complemented
418C22×C32—24no—
419C22×C32—61no—
420C22×C32—61no—
421C22×C32—61no—
422C22×C32C23×D314yes—
423C22×C32C23×D311yescharacteristic
424C2×C3⋊D3—21no—
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—68no—
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—64no—
442C2×C3⋊D3—64no—
443C2×C3⋊D3—64no—
444C2×C3⋊D3—64no—
445C2×C3⋊D3—64no—
446C2×C3⋊D3—124no—
447C2×C3⋊D3—124no—
448C2×C3⋊D3—124no—
449C2×C3⋊D3—124no—
450C2×C3⋊D3—124no—
451C2×C3⋊D3—124no—
452C2×C3×D3—24no—
453C2×C3×D3—24no—
454C2×C3×D3—24no—
455C2×C3×D3—64no—
456C2×C3×D3—64no—
457C2×C3×D3—64no—
458C2×C3×D3—64no—
459C2×C3×D3—64no—
460C2×C3×D3—64no—
461C2×C3×D3—64no—
462C2×C3×D3—64no—
463C2×C3×D3—64no—
464D32—1216no—
465C32×C4—21no—
466C32×C4—21no—
467C32×C4—21no—
468C32×C4—24no—
469C32×C4—24no—
470C32×C4—24no—
471C32×C4—44no—
472C32×C4—44no—
473C32×C4—44no—
474C32×C4—61no—
475C32×C4—61no—
476C32×C4—61no—
477C3⋊Dic3—21no—
478C3⋊Dic3—61no—
479C3⋊Dic3—61no—
480C3⋊Dic3—64no—
481C3⋊Dic3—64no—
482C3⋊Dic3—124no—
483C3⋊Dic3—124no—
484C3×Dic3—24no—
485C3×Dic3—24no—
486C3×Dic3—24no—
487C3×Dic3—64no—
488#127—271no—
489#126—31no—
490#126—271no—
491#123—271no—
492#123—271no—
493#123—271no—
494#121—91no—
495#121—271no—
496#121—271no—
497#121—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502#120—271no—
503C33#56011yescharacteristic, complemented, Sylow
504C23×C3—34no—
505C23×C3—91no—
506C23×C3—91no—
507C23×C3—91no—
508C22×D3—34no—
509C22×D3—34no—
510C22×D3—34no—
511C22×D3—94no—
512C22×D3—94no—
513C22×D3—91no—
514C22×D3—91no—
515C22×D3—184no—
516C22×D3—184no—
517C22×D3—361no—
518C22×D3—361no—
519C22×D3—361no—
520C22×D3—364no—
521C22×D3—364no—
522C22×D3—364no—
523C22×D3C22×C3⋊D311yescharacteristic
524C3×D4—361no—
525C3×D4—361no—
526C3×D4—361no—
527C2×C3×C4—24no—
528C2×C3×C4—24no—
529C2×C3×C4—24no—
530C2×C3×C4—34no—
531C2×C3×C4—34no—
532C2×C3×C4—34no—
533C2×C3×C4—91no—
534C2×C3×C4—361no—
535C2×C3×C4C2×D3214yes—
536C2×C3×C4C2×D3214yes—
537C2×C3×C4C2×D3214yes—
538C2×C3×C4C22×C3⋊D311yescharacteristic
539C2×C3×C4C22×C3⋊D311yescharacteristic
540C2×C3×C4C22×C3⋊D311yescharacteristic
541#67—361no—
542#67—361no—
543#67—361no—
544#67—361no—
545#67—361no—
546#67—364no—
547#67—361no—
548#67—361no—
549#67—364no—
550#67—364no—
551C2×Dic3—34no—
552C2×Dic3—94no—
553C2×Dic3—94no—
554C2×Dic3—91no—
555C2×Dic3—91no—
556C2×Dic3—184no—
557C2×Dic3—184no—
558C2×Dic3—361no—
559C2×Dic3C22×C3⋊D311yescharacteristic
560C2×Dic3C22×C3⋊D311yescharacteristic
561C2×Dic3C22×C3⋊D311yescharacteristic
562D12—124no—
563D12—124no—
564D12—124no—
565D12—364no—
566D12—361no—
567D12—368no—
568D12—364no—
569D12—364no—
570D12—364no—
571D12—364no—
572D12—364no—
573D12—361no—
574C4×D3—124no—
575C4×D3—364no—
576C4×D3—361no—
577C4×D3—364no—
578C4×D3—368no—
579C2×C32—24no—
580C2×C32—24no—
581C2×C32—24no—
582C2×C32—121no—
583C2×C32#100411yescharacteristic
584C2×C32#100411yescharacteristic
585C2×C32#100914yes—
586C2×C32#100914yes—
587C2×C32#100914yes—
588C2×C32#100911yescharacteristic
589C3⋊D3—41no—
590C3⋊D3—41no—
591C3⋊D3—41no—
592C3⋊D3—128no—
593C3⋊D3—124no—
594C3⋊D3—121no—
595C3⋊D3—121no—
596C3⋊D3—124no—
597C3⋊D3—244no—
598C3×D3—44no—
599C3×D3—124no—
600C3×D3—124no—
601C3×D3—124no—
602C24—271no—
603C2×D4—91no—
604C2×D4—91no—
605C2×D4—91no—
606C2×D4—271no—
607C2×D4—271no—
608C2×D4—271no—
609C2×D4—271no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—91no—
616C22×C4—271no—
617C22×C4—271no—
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—271no—
621C4⋊C4—271no—
622C4⋊C4—271no—
623C4⋊C4D3×C3⋊D311yescharacteristic, complemented
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—31no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—271no—
630C22⋊C4—271no—
631C22⋊C4—271no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C42—31no—
637C22×C3—24no—
638C22×C3—64no—
639C22×C3—64no—
640C22×C3—64no—
641C22×C3—181no—
642C22×C3—181no—
643C22×C3—181no—
644C22×C3—181no—
645C22×C3—181no—
646C22×C3—181no—
647C22×C3—181no—
648C22×C3—181no—
649C22×C3—181no—
650C22×C3C22×D3214yes—
651C22×C3C23×C3⋊D311yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
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—64no—
664C2×D3—188no—
665C2×D3—184no—
666C2×D3—184no—
667C2×D3—184no—
668C2×D3—184no—
669C2×D3—184no—
670C2×D3—184no—
671C2×D3—181no—
672C2×D3—181no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—364no—
678C2×D3—364no—
679C2×D3—364no—
680C2×D3—364no—
681C2×D3—364no—
682C2×D3—364no—
683C2×D3—3616no—
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—24no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—44no—
691C3×C4—44no—
692C3×C4—44no—
693C3×C4—64no—
694C3×C4—64no—
695C3×C4—64no—
696C3×C4—181no—
697Dic3—21no—
698Dic3—21no—
699Dic3—21no—
700Dic3—64no—
701Dic3—184no—
702Dic3—184no—
703Dic3—181no—
704Dic3—181no—
705Dic3—364no—
706Dic3—364no—
707C32—24no—
708C32#562011yescharacteristic, complemented
709C32#571114yescomplemented
710C23—31no—
711C23—91no—
712C23—91no—
713C23—91no—
714C23—271no—
715C23—271no—
716C23—1081no—
717C23—1081no—
718C23—1081no—
719D4—361no—
720D4—361no—
721D4—361no—
722D4—1081no—
723D4—1081no—
724D4—1081no—
725D4—1081no—
726D4—1081no—
727D4—1081no—
728D4—1081no—
729D4—1081no—
730D4—1081no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—91no—
735C2×C4—271no—
736C2×C4—271no—
737C2×C4—361no—
738C2×C4—1081no—
739C2×C4—1081no—
740C2×C4C2×D3×C3⋊D311yescharacteristic
741C2×C4C2×D3×C3⋊D311yescharacteristic
742C2×C4C2×D3×C3⋊D311yescharacteristic
743C2×C3—24no—
744C2×C3—24no—
745C2×C3—24no—
746C2×C3—124no—
747C2×C3—361no—
748C2×C3—361no—
749C2×C3—361no—
750C2×C3#6430714yes—
751C2×C3#6431414yes—
752C2×C3#6432014yes—
753C2×C3#6436611yescharacteristic
754C2×C3#6436611yescharacteristic
755C2×C3#6436611yescharacteristic
756D3—41no—
757D3—124no—
758D3—124no—
759D3—124no—
760D3—368no—
761D3—361no—
762D3—361no—
763D3—364no—
764D3—364no—
765D3—724no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—181no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—181no—
776C22—181no—
777C22—181no—
778C22—541no—
779C22—541no—
780C22—541no—
781C22—541no—
782C22—541no—
783C22—541no—
784C22—1084no—
785C22C22×D3×C3⋊D311yescharacteristic
786C4—21no—
787C4—21no—
788C4—21no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—181no—
793C4—541no—
794C4—541no—
795C3—24no—
796C3#1059466114yescomplemented
797C3#1059618211yescharacteristic, complemented
798C2—121no—
799C2—361no—
800C2—361no—
801C2—361no—
802C2—1081no—
803C2—1081no—
804C2#1172458011yescharacteristic
805C2#1172458911yescharacteristic
806C2#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. #11723935C2semidirect
2. C3×#64104C2semidirect
3. C32×#898C2semidirect
4. #11723542C2semidirect
5. #11723541C2semidirect
6. #11723541C2semidirect
7. #11723532C2semidirect
8. #11723527C2semidirect
9. #11723520C2semidirect
10. #11723519C2semidirect
11. #11723517C2semidirect
12. #11723493C2semidirect
13. #11723482C2semidirect
14. #11723438C2semidirect
15. #11723417C2semidirect
20. C2×C4×C3⋊(C3⋊D3)C22semidirect
23. C2×C3×C4⋊(C3⋊D3)C22semidirect
24. C2×C3×C4×C3⋊D3C22semidirect
28. C2×#6292C22semidirect
29. C2×#6292C22semidirect
33. C2×Dic3×C3⋊D3C22semidirect
34. C33×C4⋊C4C22semidirect
37. #88859C22semidirect
38. #88857C22semidirect
40. C3×#3752C22semidirect
44. C32×C4⋊Dic3C22semidirect
45. C32×Dic3⋊C4C22semidirect
46. C32×C4×Dic3C22semidirect
47. #88807C22semidirect
48. #88806C22semidirect
52. #88803C22semidirect
56. #64104D3semidirect
70. C3×#898D3semidirect
134. C2×C4⋊(C3⋊D3)C2×D3semidirect
139. C2×C4×C3⋊D3C2×D3semidirect
156. C32×C4⋊C4C2×D3semidirect
157. C32×C4⋊C4C2×D3semidirect
176. #3752C2×D3semidirect
187. C3×C4⋊Dic3C2×D3semidirect
188. C3×Dic3⋊C4C2×D3semidirect
189. C3×C4×Dic3C2×D3semidirect
235. #898C3⋊D3semidirect
378. C3×C4⋊C4D32semidirect
379. C3×C4⋊C4C2×C3⋊D3semidirect
409. C4⋊Dic3C2×C3⋊D3semidirect
416. Dic3⋊C4C2×C3⋊D3semidirect
417. C4×Dic3C2×C3⋊D3semidirect
503. C33#560semidirect
623. C4⋊C4D3×C3⋊D3semidirect
708. C32#5620semidirect
709. C32#5711semidirect
796. C3#10594661semidirect
797. C3#10596182semidirect

Maximal subgroups

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

subgroupindex
#117239352
C3×#641042
C32×#8982
#117235422
#117235412
#117235322
#117235272
#117235202
#117235192
#117235172
#117234932
#117234822
#117234382
#117234172
#105961823
#105946613