Finite Group Databasebeta

← C2×#10588712⋊C3 #72268933

Subgroups — C2×#10588712⋊C3 #72268933

Order 3456.

3385 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63710⋊C3C211yesmaximal, characteristic, complemented
2C2×3−1+2×#120C211yesmaximal, characteristic, complemented
3C2×#11721704C212yesmaximal, complemented
4C2×#63393⋊C3C211yesmaximal, characteristic, complemented
5#10588712⋊C3C218yesmaximal, direct product factor
6C2×#63365⋊C3C212yesmaximal, complemented
7C2×C3×#5032—31nomaximal
8C2×#10588712C311yesmaximal, characteristic, complemented
9C25×3−1+2C2211yescharacteristic, complemented
10C22×D4×3−1+2—21no—
11C22×D4×3−1+2C2211yescharacteristic
12C22×#611⋊C3—21no—
13C22×#611⋊C3—22no—
14C22×#611⋊C3C2212yes—
15#63710⋊C3—22no—
16#63710⋊C3—24no—
17#63710⋊C3C2214yescomplemented
18C2×#3699⋊C3—22no—
19C2×D4×AGL(1,ℤ/9)—22no—
20C2×#3697⋊C3—21no—
213−1+2×#120—22no—
223−1+2×#120C2214yescomplemented
23C2×C22⋊C4×3−1+2—21no—
24C2×C22⋊C4×3−1+2C2211yescharacteristic, complemented
25#11721704—24no—
26#11721704C2218yescomplemented
27C2×#3676⋊C3—22no—
28C2×#3676⋊C3C2212yescomplemented
29#63393⋊C3C2214yescomplemented
30#63365⋊C3C2218yescomplemented
31C2×C3×#1004—31no—
32C2×C32×#120D311yescharacteristic
33C2×C3×#953—32no—
34C2×#63710C2×C311yescharacteristic, complemented
35C2×C3×#834—31no—
36C3×#5032—38no—
37C2×C3×#806—32no—
38C2×C9×#120—21no—
39C2×C9×#120C2×C311yescharacteristic, complemented
40C2×#63515C2×C312yescomplemented
41C2×#63393C2×C311yescharacteristic, complemented
42#10588712C2×C318yescomplemented
43C2×#63365C2×C312yescomplemented
44C24×3−1+2—21no—
45C24×3−1+2—22no—
46C24×3−1+2—21no—
47C24×3−1+2—22no—
48C24×3−1+2—44no—
49C24×3−1+2D411yescharacteristic, complemented
50C24×3−1+2C2311yescharacteristic
51C24×3−1+2C2312yescomplemented
52C23×AGL(1,ℤ/9)—21no—
53C23×AGL(1,ℤ/9)D412yescomplemented
54C2×D4×3−1+2—22no—
55C2×D4×3−1+2—22no—
56C2×D4×3−1+2—24no—
57C2×D4×3−1+2—44no—
58C2×D4×3−1+2D412yescomplemented
59C2×D4×3−1+2C2312yes—
60C22×C4×3−1+2—21no—
61C22×C4×3−1+2D411yescharacteristic, complemented
62C2×#611⋊C3—22no—
63C2×#611⋊C3—24no—
64C2×#611⋊C3—22no—
65C2×#611⋊C3—22no—
66C2×#611⋊C3—22no—
67C2×#611⋊C3—22no—
68C2×#611⋊C3—24no—
69C2×#611⋊C3—28no—
70C2×#611⋊C3—48no—
71C2×#611⋊C3D414yescomplemented
72C2×#611⋊C3C2314yes—
73C22×3−1+2⋊C4—21no—
74C22×3−1+2⋊C4—22no—
75C22×3−1+2⋊C4D412yescomplemented
76#3699⋊C3—28no—
77#3699⋊C3—28no—
78D4×AGL(1,ℤ/9)—28no—
79D4×AGL(1,ℤ/9)—28no—
80#3697⋊C3—24no—
81#3697⋊C3—24no—
82C2×C4⋊AGL(1,ℤ/9)—21no—
83C2×C4×AGL(1,ℤ/9)—22no—
84C2×3−1+2⋊Q8—21no—
85C22⋊C4×3−1+2—21no—
86C22⋊C4×3−1+2—24no—
87C22⋊C4×3−1+2C2312yescomplemented
88#3676⋊C3—22no—
89#3676⋊C3—28no—
90#3676⋊C3C2314yescomplemented
91C2×C3×B(4,𝔽2)—91no—
92C2×#5032—31no—
93C25×C32C2×D311yescharacteristic
94C22×C32×D4—21no—
95C22×C32×D4C2×D311yescharacteristic
96C22×C3×#67—32no—
97C22×C3×#67—62no—
98C22×C3×#67—61no—
99C3×#1004—34no—
100C3×#1004—64no—
101C3×#1004—62no—
102C2×C3×#237—62no—
103C2×C3×D3×D4—62no—
104C2×C3×#235—61no—
105C25×C9—21no—
106C25×C9C22×C311yescharacteristic, complemented
107C32×#120—22no—
108C32×#120C2×D314yes—
109C2×C32×C22⋊C4—21no—
110C2×C32×C22⋊C4C2×D311yescharacteristic
111C3×#953—38no—
112C3×#953—64no—
113C2×C3×#217—32no—
114C2×C3×#217—62no—
115C22×D4×C9—22no—
116C22×D4×C9—21no—
117C22×D4×C9—21no—
118C22×D4×C9C22×C311yescharacteristic
119C22×#611—21no—
120C22×#611—22no—
121C22×#611C22×C312yes—
122#63710—22no—
123#63710—24no—
124#63710C22×C314yescomplemented
125C2×#3699—22no—
126C2×D4×D9—22no—
127C2×#3697—21no—
128C3×#834—34no—
129C3×#806—38no—
130C9×#120—24no—
131C9×#120—24no—
132C9×#120—22no—
133C9×#120C22×C314yescomplemented
134C2×C9×C22⋊C4—22no—
135C2×C9×C22⋊C4—21no—
136C2×C9×C22⋊C4—21no—
137C2×C9×C22⋊C4C22×C311yescharacteristic, complemented
138#63515—24no—
139#63515C22×C318yescomplemented
140C2×#3676—22no—
141C2×#3676C22×C312yescomplemented
142#63393C22×C314yescomplemented
143#63365C22×C318yescomplemented
144C23×3−1+2—24no—
145C23×3−1+2—28no—
146C23×3−1+2—21no—
147C23×3−1+2—22no—
148C23×3−1+2—24no—
149C23×3−1+2—21no—
150C23×3−1+2—42no—
151C23×3−1+2—44no—
152C23×3−1+2—42no—
153C23×3−1+2—44no—
154C23×3−1+2—44no—
155C23×3−1+2—48no—
156C23×3−1+2—42no—
157C23×3−1+2—42no—
158C23×3−1+2—41no—
159C23×3−1+2—41no—
160C23×3−1+2C2×D412yes—
161C23×3−1+2C2×D411yescharacteristic
162C23×3−1+2C2×D412yes—
163C23×3−1+2C2×D411yescharacteristic
164C23×3−1+2C2×D412yescomplemented
165C23×3−1+2C2411yescharacteristic
166C22×AGL(1,ℤ/9)—22no—
167C22×AGL(1,ℤ/9)—24no—
168C22×AGL(1,ℤ/9)—22no—
169C22×AGL(1,ℤ/9)—44no—
170C22×AGL(1,ℤ/9)—82no—
171C22×AGL(1,ℤ/9)C2×D414yescomplemented
172D4×3−1+2—24no—
173D4×3−1+2—24no—
174D4×3−1+2—48no—
175C2×C4×3−1+2—21no—
176C2×C4×3−1+2—21no—
177C2×C4×3−1+2—22no—
178C2×C4×3−1+2—42no—
179C2×C4×3−1+2C2×D412yescomplemented
180#611⋊C3—28no—
181#611⋊C3—24no—
182#611⋊C3—24no—
183#611⋊C3—24no—
184#611⋊C3—24no—
185#611⋊C3—416no—
186C2×3−1+2⋊C4—24no—
187C2×3−1+2⋊C4—22no—
188C2×3−1+2⋊C4—22no—
189C2×3−1+2⋊C4—24no—
190C2×3−1+2⋊C4—44no—
191C2×3−1+2⋊C4C2×D414yescomplemented
192C4⋊AGL(1,ℤ/9)—24no—
193C4×AGL(1,ℤ/9)—28no—
1943−1+2⋊Q8—24no—
195C2×C3×H(5,𝔽2)—91no—
196C2×#1004—31no—
197C2×C3×#120—31no—
198C2×C3×#120—92no—
199C2×C3×#120C3×D311yescharacteristic
200C2×#953—32no—
201C3×B(4,𝔽2)—98no—
202C2×C3×#99—92no—
203C2×C3×#99—91no—
204C2×#834—31no—
205#5032—38no—
206C2×#806—32no—
207C24×C32—22no—
208C24×C32—21no—
209C24×C32—22no—
210C24×C32—21no—
211C24×C32—44no—
212C24×C32#6711yescharacteristic
213C24×C32C22×D312yes—
214C24×C32C22×D311yescharacteristic
215C23×C3×D3—32no—
216C23×C3×D3—61no—
217C2×C32×D4—22no—
218C2×C32×D4—22no—
219C2×C32×D4—24no—
220C2×C32×D4—44no—
221C2×C32×D4#6712yes—
222C2×C32×D4C22×D312yes—
223C22×C32×C4—21no—
224C22×C32×C4#6711yescharacteristic
225C2×C3×#67—34no—
226C2×C3×#67—34no—
227C2×C3×#67—62no—
228C2×C3×#67—64no—
229C2×C3×#67—62no—
230C2×C3×#67—62no—
231C2×C3×#67—62no—
232C2×C3×#67—64no—
233C2×C3×#67—62no—
234C2×C3×#67—68no—
235C2×C3×#67—128no—
236C22×C3×Dic3—32no—
237C22×C3×Dic3—61no—
238C22×C3×Dic3—62no—
239C3×#237—68no—
240C3×#237—68no—
241C3×D3×D4—68no—
242C3×D3×D4—68no—
243C3×#235—64no—
244C3×#235—64no—
245C2×C3×D12—61no—
246C2×C3×C4×D3—62no—
247C2×C3×Dic6—61no—
248C24×C9—22no—
249C24×C9—21no—
250C24×C9—22no—
251C24×C9—21no—
252C24×C9—22no—
253C24×C9—21no—
254C24×C9—22no—
255C24×C9—22no—
256C24×C9—21no—
257C24×C9—44no—
258C24×C9—42no—
259C24×C9—42no—
260C24×C9—48no—
261C24×C9C3×D411yescharacteristic, complemented
262C24×C9C23×C311yescharacteristic
263C24×C9C23×C312yescomplemented
264C23×D9—21no—
265C23×D9C3×D412yescomplemented
266C32×C22⋊C4—21no—
267C32×C22⋊C4—24no—
268C32×C22⋊C4C22×D312yes—
269C3×#217—34no—
270C3×#217—68no—
271C3×#217—62no—
272C2×D4×C9—22no—
273C2×D4×C9—22no—
274C2×D4×C9—28no—
275C2×D4×C9—22no—
276C2×D4×C9—22no—
277C2×D4×C9—24no—
278C2×D4×C9—42no—
279C2×D4×C9—42no—
280C2×D4×C9—44no—
281C2×D4×C9—48no—
282C2×D4×C9C3×D412yescomplemented
283C2×D4×C9C23×C312yes—
284C22×C4×C9—22no—
285C22×C4×C9—21no—
286C22×C4×C9—21no—
287C22×C4×C9C3×D411yescharacteristic, complemented
288C2×#611—22no—
289C2×#611—24no—
290C2×#611—22no—
291C2×#611—22no—
292C2×#611—22no—
293C2×#611—22no—
294C2×#611—24no—
295C2×#611—28no—
296C2×#611—48no—
297C2×#611C3×D414yescomplemented
298C2×#611C23×C314yes—
299C22×Dic9—21no—
300C22×Dic9—22no—
301C22×Dic9C3×D412yescomplemented
302#3699—28no—
303#3699—28no—
304D4×D9—28no—
305D4×D9—28no—
306#3697—24no—
307#3697—24no—
308C2×D36—21no—
309C2×C4×D9—22no—
310C2×Dic18—21no—
311C9×C22⋊C4—22no—
312C9×C22⋊C4—28no—
313C9×C22⋊C4—22no—
314C9×C22⋊C4—21no—
315C9×C22⋊C4—24no—
316C9×C22⋊C4C23×C312yescomplemented
317#3676—22no—
318#3676—28no—
319#3676C23×C314yescomplemented
320C2×B(4,𝔽2)—91noSylow
321C22×3−1+2—22no—
322C22×3−1+2—24no—
323C22×3−1+2—24no—
324C22×3−1+2—28no—
325C22×3−1+2—22no—
326C22×3−1+2—41no—
327C22×3−1+2—42no—
328C22×3−1+2—41no—
329C22×3−1+2—42no—
330C22×3−1+2—44no—
331C22×3−1+2—44no—
332C22×3−1+2—48no—
333C22×3−1+2—42no—
334C22×3−1+2—42no—
335C22×3−1+2—44no—
336C22×3−1+2—42no—
337C22×3−1+2—81no—
338C22×3−1+2#12012yes—
339C22×3−1+2#12011yescharacteristic
340C22×3−1+2#12011yescharacteristic
341C22×3−1+2C22×D412yes—
342C22×3−1+2C22×D411yescharacteristic
343C2×AGL(1,ℤ/9)—24no—
344C2×AGL(1,ℤ/9)—44no—
345C2×AGL(1,ℤ/9)—44no—
346C2×AGL(1,ℤ/9)—82no—
347C2×AGL(1,ℤ/9)—84no—
348C4×3−1+2—22no—
349C4×3−1+2—42no—
3503−1+2⋊C4—24no—
3513−1+2⋊C4—44no—
352C25×C3—31no—
353C25×C3C2×C3×D311yescharacteristic
354C3×H(5,𝔽2)—94no—
355C3×H(5,𝔽2)—182no—
356C3×H(5,𝔽2)—184no—
357C2×C3×#41—181no—
358C2×C3×#41—182no—
359C22×C3×D4—21no—
360C22×C3×D4—31no—
361C22×C3×D4—61no—
362C22×C3×D4—92no—
363C22×C3×D4—182no—
364C22×C3×D4—181no—
365C22×C3×D4—182no—
366C22×C3×D4C2×C3×D311yescharacteristic
367C22×#67—32no—
368C22×#67—61no—
369C22×#67—62no—
370#1004—34no—
371#1004—64no—
372#1004—62no—
373C2×#237—62no—
374C2×D3×D4—62no—
375C2×#235—61no—
376C3×#120—22no—
377C3×#120—34no—
378C3×#120—62no—
379C3×#120—98no—
380C3×#120—184no—
381C3×#120C2×C3×D314yes—
382C2×C3×C22⋊C4—21no—
383C2×C3×C22⋊C4—31no—
384C2×C3×C22⋊C4—61no—
385C2×C3×C22⋊C4—92no—
386C2×C3×C22⋊C4—182no—
387C2×C3×C22⋊C4C2×C3×D311yescharacteristic
388#953—38no—
389#953—64no—
390C2×#217—32no—
391C2×#217—62no—
392C3×#99—98no—
393C3×#99—94no—
394#834—34no—
395#806—38no—
396C23×C32—28no—
397C23×C32—24no—
398C23×C32—21no—
399C23×C32—24no—
400C23×C32—22no—
401C23×C32—21no—
402C23×C32—42no—
403C23×C32—44no—
404C23×C32—44no—
405C23×C32—42no—
406C23×C32—48no—
407C23×C32—44no—
408C23×C32—42no—
409C23×C32—42no—
410C23×C32—41no—
411C23×C32—41no—
412C23×C32D3×D412yes—
413C23×C32D3×D412yes—
414C23×C32C2×#6711yescharacteristic
415C23×C32C2×#6712yes—
416C23×C32C2×#6711yescharacteristic
417C23×C32C23×D311yescharacteristic
418C22×C3×D3—34no—
419C22×C3×D3—62no—
420C22×C3×D3—64no—
421C22×C3×D3—62no—
422C22×C3×D3—124no—
423C22×C3×D3—242no—
424C32×D4—24no—
425C32×D4—24no—
426C32×D4—48no—
427C2×C32×C4—21no—
428C2×C32×C4—21no—
429C2×C32×C4—22no—
430C2×C32×C4—42no—
431C2×C32×C4C2×#6712yes—
432C3×#67—68no—
433C3×#67—64no—
434C3×#67—64no—
435C3×#67—64no—
436C3×#67—64no—
437C3×#67—1216no—
438C2×C3×Dic3—34no—
439C2×C3×Dic3—64no—
440C2×C3×Dic3—62no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3—64no—
443C2×C3×Dic3—124no—
444C3×D12—64no—
445C3×C4×D3—68no—
446C3×Dic6—64no—
447C23×C9—24no—
448C23×C9—28no—
449C23×C9—28no—
450C23×C9—24no—
451C23×C9—21no—
452C23×C9—24no—
453C23×C9—22no—
454C23×C9—21no—
455C23×C9—21no—
456C23×C9—22no—
457C23×C9—22no—
458C23×C9—21no—
459C23×C9—21no—
460C23×C9—22no—
461C23×C9—44no—
462C23×C9—41no—
463C23×C9—41no—
464C23×C9—48no—
465C23×C9—42no—
466C23×C9—44no—
467C23×C9—44no—
468C23×C9—48no—
469C23×C9—44no—
470C23×C9—44no—
471C23×C9—42no—
472C23×C9—48no—
473C23×C9—44no—
474C23×C9—48no—
475C23×C9—42no—
476C23×C9—42no—
477C23×C9—44no—
478C23×C9—42no—
479C23×C9—44no—
480C23×C9—48no—
481C23×C9—416no—
482C23×C9—42no—
483C23×C9—41no—
484C23×C9—41no—
485C23×C9C2×C3×D412yes—
486C23×C9C2×C3×D412yes—
487C23×C9C2×C3×D411yescharacteristic
488C23×C9C2×C3×D411yescharacteristic
489C23×C9C2×C3×D412yescomplemented
490C23×C9C24×C311yescharacteristic
491C22×D9—22no—
492C22×D9—24no—
493C22×D9—22no—
494C22×D9—44no—
495C22×D9—82no—
496C22×D9C2×C3×D414yescomplemented
497D4×C9—24no—
498D4×C9—24no—
499D4×C9—44no—
500D4×C9—44no—
501D4×C9—48no—
502D4×C9—416no—
503C2×C4×C9—21no—
504C2×C4×C9—21no—
505C2×C4×C9—24no—
506C2×C4×C9—22no—
507C2×C4×C9—22no—
508C2×C4×C9—41no—
509C2×C4×C9—41no—
510C2×C4×C9—44no—
511C2×C4×C9—42no—
512C2×C4×C9C2×C3×D412yescomplemented
513#611—28no—
514#611—24no—
515#611—24no—
516#611—24no—
517#611—24no—
518#611—416no—
519C2×Dic9—24no—
520C2×Dic9—22no—
521C2×Dic9—22no—
522C2×Dic9—24no—
523C2×Dic9—44no—
524C2×Dic9C2×C3×D414yescomplemented
525D36—24no—
526C4×D9—28no—
527Dic18—24no—
528C2×H(5,𝔽2)—91no—
529C2×#120—92no—
530C2×#120AGL(1,ℤ/9)11yescharacteristic, complemented
531B(4,𝔽2)—98no—
532C2×#99—91no—
533C2×#99—92no—
534C2×3−1+2—21no—
535C2×3−1+2—21no—
536C2×3−1+2—22no—
537C2×3−1+2—22no—
538C2×3−1+2—44no—
539C2×3−1+2—42no—
540C2×3−1+2B(4,𝔽2)12yescomplemented
541C2×3−1+2C2×#12011yescharacteristic
542AGL(1,ℤ/9)—44no—
543C24×C3—22no—
544C24×C3—21no—
545C24×C3—22no—
546C24×C3—21no—
547C24×C3—31no—
548C24×C3—31no—
549C24×C3—32no—
550C24×C3—44no—
551C24×C3—61no—
552C24×C3—62no—
553C24×C3—61no—
554C24×C3—62no—
555C24×C3—92no—
556C24×C3—124no—
557C24×C3—181no—
558C24×C3C3×#6711yescharacteristic
559C24×C3C22×C3×D311yescharacteristic
560C24×C3C22×C3×D312yes—
561C23×D3—32no—
562C23×D3—61no—
563C3×#41—184no—
564C3×#41—184no—
565C3×#41—188no—
566C3×#41—188no—
567C2×C3×Q8—181no—
568C2×C3×D4—22no—
569C2×C3×D4—22no—
570C2×C3×D4—24no—
571C2×C3×D4—32no—
572C2×C3×D4—32no—
573C2×C3×D4—44no—
574C2×C3×D4—62no—
575C2×C3×D4—62no—
576C2×C3×D4—64no—
577C2×C3×D4—94no—
578C2×C3×D4—94no—
579C2×C3×D4—124no—
580C2×C3×D4—181no—
581C2×C3×D4—188no—
582C2×C3×D4—188no—
583C2×C3×D4—182no—
584C2×C3×D4—182no—
585C2×C3×D4—182no—
586C2×C3×D4—182no—
587C2×C3×D4—184no—
588C2×C3×D4—182no—
589C2×C3×D4—184no—
590C2×C3×D4—188no—
591C2×C3×D4—368no—
592C2×C3×D4C3×#6712yes—
593C2×C3×D4C22×C3×D312yes—
594C22×C3×C4—21no—
595C22×C3×C4—31no—
596C22×C3×C4—61no—
597C22×C3×C4—92no—
598C22×C3×C4—182no—
599C22×C3×C4—181no—
600C22×C3×C4—182no—
601C22×C3×C4C3×#6711yescharacteristic
602C2×#67—34no—
603C2×#67—34no—
604C2×#67—62no—
605C2×#67—64no—
606C2×#67—62no—
607C2×#67—62no—
608C2×#67—62no—
609C2×#67—64no—
610C2×#67—62no—
611C2×#67—68no—
612C2×#67—128no—
613C22×Dic3—32no—
614C22×Dic3—61no—
615C22×Dic3—62no—
616#237—68no—
617#237—68no—
618D3×D4—68no—
619D3×D4—68no—
620#235—64no—
621#235—64no—
622C2×D12—61no—
623C2×C4×D3—62no—
624C2×Dic6—61no—
625C3×C22⋊C4—21no—
626C3×C22⋊C4—24no—
627C3×C22⋊C4—32no—
628C3×C22⋊C4—64no—
629C3×C22⋊C4—61no—
630C3×C22⋊C4—94no—
631C3×C22⋊C4—188no—
632C3×C22⋊C4—182no—
633C3×C22⋊C4C22×C3×D312yes—
634#217—34no—
635#217—68no—
636#217—62no—
637C22×C32—24no—
638C22×C32—22no—
639C22×C32—28no—
640C22×C32—24no—
641C22×C32—22no—
642C22×C32—42no—
643C22×C32—41no—
644C22×C32—41no—
645C22×C32—42no—
646C22×C32—44no—
647C22×C32—42no—
648C22×C32—48no—
649C22×C32—44no—
650C22×C32—42no—
651C22×C32—42no—
652C22×C32—44no—
653C22×C32—81no—
654C22×C32#93712yes—
655C22×C32#93711yescharacteristic
656C22×C32#93711yescharacteristic
657C22×C32C2×D3×D412yes—
658C22×C32C22×#6711yescharacteristic
659C2×C3×D3—64no—
660C2×C3×D3—124no—
661C2×C3×D3—124no—
662C2×C3×D3—242no—
663C2×C3×D3—244no—
664C32×C4—22no—
665C32×C4—42no—
666C3×Dic3—64no—
667C3×Dic3—124no—
668C22×C9—24no—
669C22×C9—24no—
670C22×C9—22no—
671C22×C9—28no—
672C22×C9—28no—
673C22×C9—24no—
674C22×C9—22no—
675C22×C9—21no—
676C22×C9—21no—
677C22×C9—22no—
678C22×C9—22no—
679C22×C9—21no—
680C22×C9—44no—
681C22×C9—42no—
682C22×C9—48no—
683C22×C9—42no—
684C22×C9—41no—
685C22×C9—41no—
686C22×C9—42no—
687C22×C9—42no—
688C22×C9—44no—
689C22×C9—42no—
690C22×C9—44no—
691C22×C9—48no—
692C22×C9—44no—
693C22×C9—42no—
694C22×C9—48no—
695C22×C9—44no—
696C22×C9—44no—
697C22×C9—48no—
698C22×C9—44no—
699C22×C9—48no—
700C22×C9—416no—
701C22×C9—42no—
702C22×C9—44no—
703C22×C9—42no—
704C22×C9—82no—
705C22×C9—81no—
706C22×C9—82no—
707C22×C9C3×#12012yes—
708C22×C9C3×#12011yescharacteristic
709C22×C9C3×#12011yescharacteristic
710C22×C9C22×C3×D412yes—
711C22×C9C22×C3×D411yescharacteristic
712C2×D9—24no—
713C2×D9—44no—
714C2×D9—44no—
715C2×D9—82no—
716C2×D9—84no—
717C4×C9—22no—
718C4×C9—42no—
719C4×C9—44no—
720C4×C9—42no—
721Dic9—24no—
722Dic9—44no—
723C25C2×AGL(1,ℤ/9)11yescharacteristic, complemented
724H(5,𝔽2)—94no—
725H(5,𝔽2)—184no—
726H(5,𝔽2)—182no—
727C2×#41—182no—
728C2×#41—181no—
729C22×D4—21no—
730C22×D4—92no—
731C22×D4—182no—
732C22×D4—181no—
733C22×D4—182no—
734C22×D4C2×AGL(1,ℤ/9)11yescharacteristic
735#120—22no—
736#120—98no—
737#120—184no—
738#120C2×AGL(1,ℤ/9)14yescomplemented
739C2×C22⋊C4—21no—
740C2×C22⋊C4—92no—
741C2×C22⋊C4—182no—
742C2×C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic, complemented
743#99—94no—
744#99—98no—
7453−1+2C2×B(4,𝔽2)11yescharacteristic, complemented, Sylow
746C23×C3—24no—
747C23×C3—28no—
748C23×C3—21no—
749C23×C3—24no—
750C23×C3—22no—
751C23×C3—21no—
752C23×C3—31no—
753C23×C3—32no—
754C23×C3—32no—
755C23×C3—31no—
756C23×C3—31no—
757C23×C3—32no—
758C23×C3—42no—
759C23×C3—44no—
760C23×C3—44no—
761C23×C3—42no—
762C23×C3—48no—
763C23×C3—44no—
764C23×C3—42no—
765C23×C3—42no—
766C23×C3—41no—
767C23×C3—41no—
768C23×C3—62no—
769C23×C3—64no—
770C23×C3—61no—
771C23×C3—61no—
772C23×C3—64no—
773C23×C3—68no—
774C23×C3—94no—
775C23×C3—121no—
776C23×C3—122no—
777C23×C3—121no—
778C23×C3—122no—
779C23×C3—124no—
780C23×C3—122no—
781C23×C3—124no—
782C23×C3—124no—
783C23×C3—128no—
784C23×C3—122no—
785C23×C3—182no—
786C23×C3—182no—
787C23×C3—184no—
788C23×C3—364no—
789C23×C3—722no—
790C23×C3C3×D3×D412yes—
791C23×C3C3×D3×D412yes—
792C23×C3C2×C3×#6711yescharacteristic
793C23×C3C2×C3×#6711yescharacteristic
794C23×C3C2×C3×#6712yes—
795C23×C3C23×C3×D311yescharacteristic
796C22×D3—34no—
797C22×D3—62no—
798C22×D3—64no—
799C22×D3—62no—
800C22×D3—124no—
801C22×D3—242no—
802C3×Q8—184no—
803C3×D4—24no—
804C3×D4—24no—
805C3×D4—48no—
806C3×D4—64no—
807C3×D4—64no—
808C3×D4—128no—
809C3×D4—184no—
810C3×D4—184no—
811C3×D4—184no—
812C3×D4—184no—
813C3×D4—184no—
814C3×D4—188no—
815C3×D4—3616no—
816C2×C3×C4—21no—
817C2×C3×C4—21no—
818C2×C3×C4—22no—
819C2×C3×C4—32no—
820C2×C3×C4—42no—
821C2×C3×C4—61no—
822C2×C3×C4—61no—
823C2×C3×C4—62no—
824C2×C3×C4—94no—
825C2×C3×C4—122no—
826C2×C3×C4—188no—
827C2×C3×C4—182no—
828C2×C3×C4—182no—
829C2×C3×C4—184no—
830C2×C3×C4—184no—
831C2×C3×C4—364no—
832C2×C3×C4C2×C3×#6712yes—
833#67—68no—
834#67—64no—
835#67—64no—
836#67—64no—
837#67—64no—
838#67—1216no—
839C2×Dic3—34no—
840C2×Dic3—64no—
841C2×Dic3—62no—
842C2×Dic3—62no—
843C2×Dic3—64no—
844C2×Dic3—124no—
845D12—64no—
846C4×D3—68no—
847Dic6—64no—
848C2×C32—22no—
849C2×C32—21no—
850C2×C32—22no—
851C2×C32—21no—
852C2×C32—42no—
853C2×C32—44no—
854C2×C32#503212yes—
855C2×C32C2×#93711yescharacteristic
856C3×D3—124no—
857C2×C9—22no—
858C2×C9—22no—
859C2×C9—22no—
860C2×C9—21no—
861C2×C9—22no—
862C2×C9—21no—
863C2×C9—21no—
864C2×C9—22no—
865C2×C9—42no—
866C2×C9—42no—
867C2×C9—48no—
868C2×C9—42no—
869C2×C9—44no—
870C2×C9—82no—
871C2×C9C3×B(4,𝔽2)12yescomplemented
872C2×C9C2×C3×#12011yescharacteristic
873D9—44no—
874C24—22no—
875C24—21no—
876C24—22no—
877C24—21no—
878C24—44no—
879C24—92no—
880C24—181no—
881C24#611⋊C311yescharacteristic, complemented
882C24C22×AGL(1,ℤ/9)11yescharacteristic
883C24C22×AGL(1,ℤ/9)12yescomplemented
884#41—184no—
885#41—188no—
886#41—188no—
887#41—184no—
888C2×Q8—181no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—24no—
892C2×D4—44no—
893C2×D4—94no—
894C2×D4—94no—
895C2×D4—181no—
896C2×D4—188no—
897C2×D4—188no—
898C2×D4—182no—
899C2×D4—184no—
900C2×D4—182no—
901C2×D4—182no—
902C2×D4—182no—
903C2×D4—182no—
904C2×D4—184no—
905C2×D4—188no—
906C2×D4—368no—
907C2×D4#611⋊C312yescomplemented
908C2×D4C22×AGL(1,ℤ/9)12yes—
909C22×C4—21no—
910C22×C4—92no—
911C22×C4—182no—
912C22×C4—181no—
913C22×C4—182no—
914C22×C4#611⋊C311yescharacteristic, complemented
915C22⋊C4—21no—
916C22⋊C4—24no—
917C22⋊C4—94no—
918C22⋊C4—188no—
919C22⋊C4—182no—
920C22⋊C4C22×AGL(1,ℤ/9)12yescomplemented
921C22×C3—24no—
922C22×C3—22no—
923C22×C3—28no—
924C22×C3—24no—
925C22×C3—22no—
926C22×C3—32no—
927C22×C3—31no—
928C22×C3—31no—
929C22×C3—32no—
930C22×C3—31no—
931C22×C3—41no—
932C22×C3—42no—
933C22×C3—41no—
934C22×C3—42no—
935C22×C3—44no—
936C22×C3—42no—
937C22×C3—48no—
938C22×C3—44no—
939C22×C3—42no—
940C22×C3—42no—
941C22×C3—44no—
942C22×C3—62no—
943C22×C3—64no—
944C22×C3—62no—
945C22×C3—64no—
946C22×C3—68no—
947C22×C3—81no—
948C22×C3—124no—
949C22×C3—122no—
950C22×C3—122no—
951C22×C3—121no—
952C22×C3—122no—
953C22×C3—121no—
954C22×C3—122no—
955C22×C3—122no—
956C22×C3—124no—
957C22×C3—124no—
958C22×C3—128no—
959C22×C3—184no—
960C22×C3—241no—
961C22×C3—364no—
962C22×C3—364no—
963C22×C3—722no—
964C22×C3—724no—
965C22×C3C3×#93712yes—
966C22×C3C3×#93711yescharacteristic
967C22×C3C3×#93711yescharacteristic
968C22×C3C2×C3×D3×D412yes—
969C22×C3C22×C3×#6711yescharacteristic
970C2×D3—64no—
971C2×D3—124no—
972C2×D3—124no—
973C2×D3—242no—
974C2×D3—244no—
975C3×C4—22no—
976C3×C4—42no—
977C3×C4—62no—
978C3×C4—122no—
979C3×C4—184no—
980C3×C4—364no—
981Dic3—64no—
982Dic3—124no—
983C32C2×#503211yescharacteristic
984C9—21no—
985C9C2×C3×B(4,𝔽2)11yescharacteristic, complemented
986C23—24no—
987C23—28no—
988C23—24no—
989C23—22no—
990C23—21no—
991C23—21no—
992C23—42no—
993C23—44no—
994C23—42no—
995C23—44no—
996C23—44no—
997C23—48no—
998C23—42no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—94no—
1003C23—184no—
1004C23—182no—
1005C23—182no—
1006C23—364no—
1007C23—722no—
1008C23D4×AGL(1,ℤ/9)12yes—
1009C23D4×AGL(1,ℤ/9)12yes—
1010C23C2×#611⋊C311yescharacteristic
1011C23C2×#611⋊C311yescharacteristic
1012C23C2×#611⋊C312yescomplemented
1013C23C23×AGL(1,ℤ/9)11yescharacteristic
1014Q8—184no—
1015D4—24no—
1016D4—24no—
1017D4—48no—
1018D4—184no—
1019D4—188no—
1020D4—184no—
1021D4—184no—
1022D4—184no—
1023D4—184no—
1024D4—3616no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—22no—
1028C2×C4—42no—
1029C2×C4—94no—
1030C2×C4—188no—
1031C2×C4—184no—
1032C2×C4—182no—
1033C2×C4—182no—
1034C2×C4—184no—
1035C2×C4—364no—
1036C2×C4C2×#611⋊C312yescomplemented
1037C2×C3—22no—
1038C2×C3—21no—
1039C2×C3—22no—
1040C2×C3—21no—
1041C2×C3—32no—
1042C2×C3—31no—
1043C2×C3—42no—
1044C2×C3—44no—
1045C2×C3—61no—
1046C2×C3—62no—
1047C2×C3—61no—
1048C2×C3—62no—
1049C2×C3—124no—
1050C2×C3—122no—
1051C2×C3—364no—
1052C2×C3C3×#503212yes—
1053C2×C3C2×C3×#93711yescharacteristic
1054D3—124no—
1055C22—22no—
1056C22—24no—
1057C22—24no—
1058C22—28no—
1059C22—22no—
1060C22—41no—
1061C22—42no—
1062C22—41no—
1063C22—42no—
1064C22—42no—
1065C22—44no—
1066C22—44no—
1067C22—48no—
1068C22—44no—
1069C22—42no—
1070C22—42no—
1071C22—81no—
1072C22—184no—
1073C22—364no—
1074C22—364no—
1075C22—722no—
1076C22—724no—
1077C22#63499⋊C311yescharacteristic
1078C22#63499⋊C312yes—
1079C22#63499⋊C311yescharacteristic
1080C22C2×D4×AGL(1,ℤ/9)12yes—
1081C22C22×#611⋊C311yescharacteristic
1082C4—22no—
1083C4—42no—
1084C4—184no—
1085C4—364no—
1086C3—31no—
1087C3C2×C3×#503211yescharacteristic
1088C2—21no—
1089C2—22no—
1090C2—21no—
1091C2—22no—
1092C2—44no—
1093C2—42no—
1094C2—364no—
1095C2#10588712⋊C312yesdirect product factor
1096C2C2×#63499⋊C311yescharacteristic
subgroupG/H
centerC22#63499⋊C3
commutator, cosocleC23×C9C24×C3
FrattiniC23×C3C23×C3×D3
FittingC2×3−1+2×#120C2
socleC22×C3C3×#937
hypercenterC2×#120AGL(1,ℤ/9)
hypocenterC9C2×C3×B(4,𝔽2)
LCSG ▷ C23×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C24 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#63710⋊C3C2semidirect
2. C2×3−1+2×#120C2semidirect
3. C2×#11721704C2semidirect
4. C2×#63393⋊C3C2semidirect
5. #10588712⋊C3C2direct (N × H)
6. C2×#63365⋊C3C2semidirect
8. C2×#10588712C3semidirect
9. C25×3−1+2C22semidirect
17. #63710⋊C3C22semidirect
22. 3−1+2×#120C22semidirect
24. C2×C22⋊C4×3−1+2C22semidirect
26. #11721704C22semidirect
28. C2×#3676⋊C3C22semidirect
29. #63393⋊C3C22semidirect
30. #63365⋊C3C22semidirect
34. C2×#63710C2×C3semidirect
39. C2×C9×#120C2×C3semidirect
40. C2×#63515C2×C3semidirect
41. C2×#63393C2×C3semidirect
42. #10588712C2×C3semidirect
43. C2×#63365C2×C3semidirect
49. C24×3−1+2D4semidirect
51. C24×3−1+2C23semidirect
53. C23×AGL(1,ℤ/9)D4semidirect
58. C2×D4×3−1+2D4semidirect
61. C22×C4×3−1+2D4semidirect
71. C2×#611⋊C3D4semidirect
75. C22×3−1+2⋊C4D4semidirect
87. C22⋊C4×3−1+2C23semidirect
90. #3676⋊C3C23semidirect
106. C25×C9C22×C3semidirect
124. #63710C22×C3semidirect
133. C9×#120C22×C3semidirect
137. C2×C9×C22⋊C4C22×C3semidirect
139. #63515C22×C3semidirect
141. C2×#3676C22×C3semidirect
142. #63393C22×C3semidirect
143. #63365C22×C3semidirect
164. C23×3−1+2C2×D4semidirect
171. C22×AGL(1,ℤ/9)C2×D4semidirect
179. C2×C4×3−1+2C2×D4semidirect
191. C2×3−1+2⋊C4C2×D4semidirect
261. C24×C9C3×D4semidirect
263. C24×C9C23×C3semidirect
265. C23×D9C3×D4semidirect
282. C2×D4×C9C3×D4semidirect
287. C22×C4×C9C3×D4semidirect
297. C2×#611C3×D4semidirect
301. C22×Dic9C3×D4semidirect
316. C9×C22⋊C4C23×C3semidirect
319. #3676C23×C3semidirect
489. C23×C9C2×C3×D4semidirect
496. C22×D9C2×C3×D4semidirect
512. C2×C4×C9C2×C3×D4semidirect
524. C2×Dic9C2×C3×D4semidirect
530. C2×#120AGL(1,ℤ/9)semidirect
540. C2×3−1+2B(4,𝔽2)semidirect
723. C25C2×AGL(1,ℤ/9)semidirect
738. #120C2×AGL(1,ℤ/9)semidirect
742. C2×C22⋊C4C2×AGL(1,ℤ/9)semidirect
745. 3−1+2C2×B(4,𝔽2)semidirect
871. C2×C9C3×B(4,𝔽2)semidirect
881. C24#611⋊C3semidirect
883. C24C22×AGL(1,ℤ/9)semidirect
907. C2×D4#611⋊C3semidirect
914. C22×C4#611⋊C3semidirect
920. C22⋊C4C22×AGL(1,ℤ/9)semidirect
985. C9C2×C3×B(4,𝔽2)semidirect
1012. C23C2×#611⋊C3semidirect
1036. C2×C4C2×#611⋊C3semidirect
1095. C2#10588712⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#63710⋊C32
C2×3−1+2×#1202
C2×#117217042
C2×#63393⋊C32
#10588712⋊C32
C2×#63365⋊C32
C2×C3×#50323
C2×#105887123