Finite Group Databasebeta

← #10589752⋊C3 #13153059

Subgroups — #10589752⋊C3 #13153059

Order 1728.

681 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
13−1+2×#123C211yesmaximal, characteristic
2#63497⋊C3C211yesmaximal, characteristic
3D4×3−1+2⋊C4C211yesmaximal, characteristic
4#63488⋊C3C211yesmaximal, characteristic, complemented
5C2×(3−1+2⋊C4)⋊C4C211yesmaximal, characteristic, complemented
6#63452⋊C3C211yesmaximal, characteristic, complemented
7#63451⋊C3C211yesmaximal, characteristic, complemented
8#63451⋊C3C211yesmaximal, characteristic, complemented
9#63449⋊C3C211yesmaximal, characteristic, complemented
10#63441⋊C3C211yesmaximal, characteristic, complemented
11#63441⋊C3C211yesmaximal, characteristic, complemented
12#63440⋊C3C211yesmaximal, characteristic, complemented
13#63440⋊C3C211yesmaximal, characteristic, complemented
14#63439⋊C3C211yesmaximal, characteristic, complemented
15#63439⋊C3C211yesmaximal, characteristic, complemented
16C3×#5650—31nomaximal
17#10589752C311yesmaximal, characteristic, complemented
18C2×D4×3−1+2C2211yescharacteristic
19C22×C4×3−1+2C2211yescharacteristic
20C22×3−1+2⋊C4C2211yescharacteristic
21C22×3−1+2⋊C4C2211yescharacteristic
22C22×3−1+2⋊C4C2211yescharacteristic
23C2×3−1+2⋊Q8C2211yescharacteristic
24C4⋊C4×3−1+2C2211yescharacteristic
25C4⋊C4×3−1+2C2211yescharacteristic
26C22⋊C4×3−1+2C2211yescharacteristic
27C22⋊C4×3−1+2C2211yescharacteristic
28C22⋊C4×3−1+2C2211yescharacteristic
29#3676⋊C3C2211yescharacteristic
30#3676⋊C3C2211yescharacteristic
31#3676⋊C3C2211yescharacteristic
32#3676⋊C3C2211yescharacteristic
33#3676⋊C3C2211yescharacteristic
34C4⋊(3−1+2⋊C4)C2211yescharacteristic
35C4⋊(3−1+2⋊C4)C2211yescharacteristic
36C4⋊(3−1+2⋊C4)C2211yescharacteristic
37C4⋊(3−1+2⋊C4)C2211yescharacteristic
38(3−1+2⋊C4)⋊C4C2211yescharacteristic
39(3−1+2⋊C4)⋊C4C2211yescharacteristic
40(3−1+2⋊C4)⋊C4C2211yescharacteristic
41(3−1+2⋊C4)⋊C4C2211yescharacteristic
42(3−1+2⋊C4)⋊C4C2211yescharacteristic
43(3−1+2⋊C4)⋊C4C2211yescharacteristic
44(3−1+2⋊C4)⋊C4C2211yescharacteristic
45(3−1+2⋊C4)⋊C4C2211yescharacteristic
46(3−1+2⋊C4)⋊C4C2211yescharacteristic
47(3−1+2⋊C4)⋊C4C2211yescharacteristic
48C4×3−1+2⋊C4C2211yescharacteristic
49C4×3−1+2⋊C4C2211yescharacteristic
50C4×3−1+2⋊C4C2211yescharacteristic
51C4×3−1+2⋊C4C2211yescharacteristic
52C4×3−1+2⋊C4C2211yescharacteristic
53C32×#123D311yescharacteristic
54C3×#935—31no—
55C3×D4×Dic3—31no—
56C3×#926—31no—
57C2×C3×Dic3⋊C4—31no—
58C3×#890—31no—
59C3×#889—31no—
60C3×#889—31no—
61C3×#887—31no—
62C3×#879—31no—
63C3×#879—31no—
64C3×#878—31no—
65C3×#878—31no—
66C3×#877—31no—
67C3×#877—31no—
68C9×#123—21no—
69C9×#123C2×C311yescharacteristic
70#63497C2×C311yescharacteristic
71D4×Dic9C2×C311yescharacteristic
72#63488C2×C311yescharacteristic, complemented
73C2×Dic9⋊C4C2×C311yescharacteristic, complemented
74#63452C2×C311yescharacteristic, complemented
75#63451C2×C311yescharacteristic, complemented
76#63451C2×C311yescharacteristic, complemented
77#63449C2×C311yescharacteristic, complemented
78#63441C2×C311yescharacteristic, complemented
79#63441C2×C311yescharacteristic, complemented
80#63440C2×C311yescharacteristic, complemented
81#63440C2×C311yescharacteristic, complemented
82#63439C2×C311yescharacteristic, complemented
83#63439C2×C311yescharacteristic, complemented
84C23×3−1+2C2311yescharacteristic
85C23×3−1+2C2311yescharacteristic
86D4×3−1+2—22no—
87C2×C4×3−1+2—22no—
88C2×C4×3−1+2C2311yescharacteristic
89C2×C4×3−1+2C2311yescharacteristic
90C2×C4×3−1+2C2311yescharacteristic
91C2×C4×3−1+2C2311yescharacteristic
92C2×C4×3−1+2C2311yescharacteristic
93C2×3−1+2⋊C4—22no—
94C2×3−1+2⋊C4—22no—
95C2×3−1+2⋊C4—22no—
96C2×3−1+2⋊C4C2311yescharacteristic
97C2×3−1+2⋊C4C2311yescharacteristic
98C2×3−1+2⋊C4C2311yescharacteristic
99C2×3−1+2⋊C4C2311yescharacteristic
100C2×3−1+2⋊C4C2311yescharacteristic
101C2×3−1+2⋊C4C2311yescharacteristic
102C2×3−1+2⋊C4C2311yescharacteristic
103C2×3−1+2⋊C4C2311yescharacteristic
1043−1+2⋊Q8—22no—
105C3×#552—91no—
106#5650—31no—
107C2×C32×D4C2×D311yescharacteristic
108C22×C32×C4C2×D311yescharacteristic
109C22×C3×Dic3—31no—
110C22×C3×Dic3—31no—
111C22×C3×Dic3—31no—
112C2×C3×Dic6—31no—
113C32×C4⋊C4C2×D311yescharacteristic
114C32×C4⋊C4C2×D311yescharacteristic
115C32×C22⋊C4C2×D311yescharacteristic
116C32×C22⋊C4C2×D311yescharacteristic
117C32×C22⋊C4C2×D311yescharacteristic
118C3×#217—31no—
119C3×#217—31no—
120C3×#217—31no—
121C3×#217—31no—
122C3×#217—31no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3—31no—
125C3×C4⋊Dic3—31no—
126C3×C4⋊Dic3—31no—
127C3×Dic3⋊C4—31no—
128C3×Dic3⋊C4—31no—
129C3×Dic3⋊C4—31no—
130C3×Dic3⋊C4—31no—
131C3×Dic3⋊C4—31no—
132C3×Dic3⋊C4—31no—
133C3×Dic3⋊C4—31no—
134C3×Dic3⋊C4—31no—
135C3×Dic3⋊C4—31no—
136C3×Dic3⋊C4—31no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—31no—
142C2×D4×C9—21no—
143C2×D4×C9C22×C311yescharacteristic
144C22×C4×C9—21no—
145C22×C4×C9C22×C311yescharacteristic
146C22×Dic9C22×C311yescharacteristic
147C22×Dic9C22×C311yescharacteristic
148C22×Dic9C22×C311yescharacteristic
149C2×Dic18C22×C311yescharacteristic
150C9×C4⋊C4—21no—
151C9×C4⋊C4—21no—
152C9×C4⋊C4C22×C311yescharacteristic
153C9×C4⋊C4C22×C311yescharacteristic
154C9×C22⋊C4—21no—
155C9×C22⋊C4—21no—
156C9×C22⋊C4—21no—
157C9×C22⋊C4C22×C311yescharacteristic
158C9×C22⋊C4C22×C311yescharacteristic
159C9×C22⋊C4C22×C311yescharacteristic
160#3676C22×C311yescharacteristic
161#3676C22×C311yescharacteristic
162#3676C22×C311yescharacteristic
163#3676C22×C311yescharacteristic
164#3676C22×C311yescharacteristic
165C4⋊Dic9C22×C311yescharacteristic
166C4⋊Dic9C22×C311yescharacteristic
167C4⋊Dic9C22×C311yescharacteristic
168C4⋊Dic9C22×C311yescharacteristic
169Dic9⋊C4C22×C311yescharacteristic
170Dic9⋊C4C22×C311yescharacteristic
171Dic9⋊C4C22×C311yescharacteristic
172Dic9⋊C4C22×C311yescharacteristic
173Dic9⋊C4C22×C311yescharacteristic
174Dic9⋊C4C22×C311yescharacteristic
175Dic9⋊C4C22×C311yescharacteristic
176Dic9⋊C4C22×C311yescharacteristic
177Dic9⋊C4C22×C311yescharacteristic
178Dic9⋊C4C22×C311yescharacteristic
179C4×Dic9C22×C311yescharacteristic
180C4×Dic9C22×C311yescharacteristic
181C4×Dic9C22×C311yescharacteristic
182C4×Dic9C22×C311yescharacteristic
183C4×Dic9C22×C311yescharacteristic
184C22×3−1+2—21no—
185C22×3−1+2—21no—
186C22×3−1+2—21no—
187C22×3−1+2—21no—
188C22×3−1+2—21no—
189C22×3−1+2#4112yes—
190C22×3−1+2C2411yescharacteristic
191C4×3−1+2—21no—
192C4×3−1+2—21no—
193C4×3−1+2—21no—
194C4×3−1+2—21no—
195C4×3−1+2—21no—
1963−1+2⋊C4—21no—
1973−1+2⋊C4—21no—
1983−1+2⋊C4—21no—
1993−1+2⋊C4—21no—
2003−1+2⋊C4—21no—
2013−1+2⋊C4—21no—
2023−1+2⋊C4—21no—
2033−1+2⋊C4#4112yes—
204C3×#126—91no—
205C3×#126—91no—
206C3×#125—91no—
207C3×#125—91no—
208C3×#125—91no—
209C3×#123—31no—
210C3×#123—91no—
211C3×#123C3×D311yescharacteristic
212C3×C22⋊Q8—91no—
213C3×C22⋊Q8—91no—
214C3×C4×Q8—91no—
215C3×C4×D4—91no—
216C3×#117—91no—
217C3×#117—91no—
218C3×#117—91no—
219C2×C3×C4⋊C4—91no—
220#935—31no—
221D4×Dic3—31no—
222#926—31no—
223C2×Dic3⋊C4—31no—
224#890—31no—
225#889—31no—
226#889—31no—
227#887—31no—
228#879—31no—
229#879—31no—
230#878—31no—
231#878—31no—
232#877—31no—
233#877—31no—
234C23×C32C22×D311yescharacteristic
235C23×C32C22×D311yescharacteristic
236C32×D4—22no—
237C2×C32×C4—22no—
238C2×C32×C4C22×D311yescharacteristic
239C2×C32×C4C22×D311yescharacteristic
240C2×C32×C4C22×D311yescharacteristic
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C3×Dic3—31no—
244C2×C3×Dic3—31no—
245C2×C3×Dic3—31no—
246C2×C3×Dic3—31no—
247C2×C3×Dic3—31no—
248C2×C3×Dic3—31no—
249C2×C3×Dic3—31no—
250C2×C3×Dic3—31no—
251C2×C3×Dic3—62no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—62no—
254C3×Dic6—62no—
255C23×C9—21no—
256C23×C9—21no—
257C23×C9C23×C311yescharacteristic
258C23×C9C23×C311yescharacteristic
259D4×C9—22no—
260D4×C9—42no—
261C2×C4×C9—22no—
262C2×C4×C9—21no—
263C2×C4×C9—21no—
264C2×C4×C9—21no—
265C2×C4×C9—21no—
266C2×C4×C9—21no—
267C2×C4×C9—42no—
268C2×C4×C9C23×C311yescharacteristic
269C2×C4×C9C23×C311yescharacteristic
270C2×C4×C9C23×C311yescharacteristic
271C2×C4×C9C23×C311yescharacteristic
272C2×C4×C9C23×C311yescharacteristic
273C2×Dic9—22no—
274C2×Dic9—22no—
275C2×Dic9—22no—
276C2×Dic9C23×C311yescharacteristic
277C2×Dic9C23×C311yescharacteristic
278C2×Dic9C23×C311yescharacteristic
279C2×Dic9C23×C311yescharacteristic
280C2×Dic9C23×C311yescharacteristic
281C2×Dic9C23×C311yescharacteristic
282C2×Dic9C23×C311yescharacteristic
283C2×Dic9C23×C311yescharacteristic
284Dic18—22no—
285#552—91noSylow
286C2×3−1+2—22no—
287C2×3−1+2—41no—
288C2×3−1+2C2×#4111yescharacteristic
289C2×3−1+2C2×#4111yescharacteristic
290C2×3−1+22−1+411yescharacteristic
291C2×C3×Q8—91no—
292C2×C3×D4—31no—
293C2×C3×D4C2×C3×D311yescharacteristic
294C22×C3×C4—31no—
295C22×C3×C4—91no—
296C22×C3×C4—91no—
297C22×C3×C4—91no—
298C22×C3×C4C2×C3×D311yescharacteristic
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C2×Dic6—31no—
303C3×C4⋊C4—31no—
304C3×C4⋊C4—31no—
305C3×C4⋊C4—91no—
306C3×C4⋊C4—91no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—91no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4—91no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4—91no—
313C3×C4⋊C4—91no—
314C3×C4⋊C4—91no—
315C3×C4⋊C4—91no—
316C3×C4⋊C4—91no—
317C3×C4⋊C4—91no—
318C3×C4⋊C4—91no—
319C3×C4⋊C4C2×C3×D311yescharacteristic
320C3×C4⋊C4C2×C3×D311yescharacteristic
321C3×C22⋊C4—31no—
322C3×C22⋊C4—31no—
323C3×C22⋊C4—31no—
324C3×C22⋊C4—91no—
325C3×C22⋊C4—91no—
326C3×C22⋊C4—91no—
327C3×C22⋊C4—91no—
328C3×C22⋊C4—91no—
329C3×C22⋊C4C2×C3×D311yescharacteristic
330C3×C22⋊C4C2×C3×D311yescharacteristic
331C3×C22⋊C4C2×C3×D311yescharacteristic
332C3×C42—91no—
333C3×C42—91no—
334C3×C42—91no—
335C3×C42—91no—
336C3×C42—91no—
337#217—31no—
338#217—31no—
339#217—31no—
340#217—31no—
341#217—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—31no—
344C4⋊Dic3—31no—
345C4⋊Dic3—31no—
346Dic3⋊C4—31no—
347Dic3⋊C4—31no—
348Dic3⋊C4—31no—
349Dic3⋊C4—31no—
350Dic3⋊C4—31no—
351Dic3⋊C4—31no—
352Dic3⋊C4—31no—
353Dic3⋊C4—31no—
354Dic3⋊C4—31no—
355Dic3⋊C4—31no—
356C4×Dic3—31no—
357C4×Dic3—31no—
358C4×Dic3—31no—
359C4×Dic3—31no—
360C4×Dic3—31no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—21no—
366C22×C32#23712yes—
367C22×C32C23×D311yescharacteristic
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—21no—
371C32×C4—21no—
372C32×C4—21no—
373C3×Dic3—32no—
374C3×Dic3—61no—
375C3×Dic3—61no—
376C3×Dic3—61no—
377C3×Dic3—61no—
378C3×Dic3—61no—
379C3×Dic3—61no—
380C3×Dic3—61no—
381C22×C9—21no—
382C22×C9—21no—
383C22×C9—21no—
384C22×C9—21no—
385C22×C9—21no—
386C22×C9—21no—
387C22×C9—22no—
388C22×C9—41no—
389C22×C9—41no—
390C22×C9—41no—
391C22×C9—41no—
392C22×C9—41no—
393C22×C9C3×#4112yes—
394C22×C9C24×C311yescharacteristic
395C4×C9—21no—
396C4×C9—21no—
397C4×C9—21no—
398C4×C9—21no—
399C4×C9—21no—
400C4×C9—41no—
401C4×C9—41no—
402C4×C9—41no—
403C4×C9—41no—
404C4×C9—41no—
405Dic9—21no—
406Dic9—21no—
407Dic9—21no—
408Dic9—21no—
409Dic9—21no—
410Dic9—21no—
411Dic9—21no—
412Dic9C3×#4112yes—
413#126—91no—
414#126—91no—
415#125—91no—
416#125—91no—
417#125—91no—
418#123—91no—
419#123AGL(1,ℤ/9)11yescharacteristic
420C22⋊Q8—91no—
421C22⋊Q8—91no—
422C4×Q8—91no—
423C4×D4—91no—
424#117—91no—
425#117—91no—
426#117—91no—
427C2×C4⋊C4—91no—
4283−1+2#55211yescharacteristic, complemented, Sylow
429C23×C3—31no—
430C23×C3—31no—
431C23×C3C22×C3×D311yescharacteristic
432C23×C3C22×C3×D311yescharacteristic
433C3×Q8—182no—
434C3×D4—22no—
435C3×D4—62no—
436C2×C3×C4—22no—
437C2×C3×C4—31no—
438C2×C3×C4—31no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—62no—
443C2×C3×C4—91no—
444C2×C3×C4—91no—
445C2×C3×C4—91no—
446C2×C3×C4—91no—
447C2×C3×C4—91no—
448C2×C3×C4—91no—
449C2×C3×C4—91no—
450C2×C3×C4—91no—
451C2×C3×C4—182no—
452C2×C3×C4—182no—
453C2×C3×C4—182no—
454C2×C3×C4C22×C3×D311yescharacteristic
455C2×C3×C4C22×C3×D311yescharacteristic
456C2×C3×C4C22×C3×D311yescharacteristic
457C2×C3×C4C22×C3×D311yescharacteristic
458C2×C3×C4C22×C3×D311yescharacteristic
459C2×Dic3—31no—
460C2×Dic3—31no—
461C2×Dic3—31no—
462C2×Dic3—31no—
463C2×Dic3—31no—
464C2×Dic3—31no—
465C2×Dic3—31no—
466C2×Dic3—31no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470Dic6—62no—
471C2×C32—22no—
472C2×C32—41no—
473C2×C32C2×#23711yescharacteristic
474C2×C32D3×#4111yescharacteristic
475C2×C32#101011yescharacteristic
476C2×C9—22no—
477C2×C9—21no—
478C2×C9—21no—
479C2×C9—21no—
480C2×C9—42no—
481C2×C9—41no—
482C2×C9—81no—
483C2×C9C2×C3×#4111yescharacteristic
484C2×C9C2×C3×#4111yescharacteristic
485C2×C9C3×2−1+411yescharacteristic
486C2×Q8—91no—
487C2×D4C2×AGL(1,ℤ/9)11yescharacteristic
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—91no—
491C22×C4C2×AGL(1,ℤ/9)11yescharacteristic
492C4⋊C4—91no—
493C4⋊C4—91no—
494C4⋊C4—91no—
495C4⋊C4—91no—
496C4⋊C4—91no—
497C4⋊C4—91no—
498C4⋊C4—91no—
499C4⋊C4—91no—
500C4⋊C4—91no—
501C4⋊C4—91no—
502C4⋊C4—91no—
503C4⋊C4—91no—
504C4⋊C4—91no—
505C4⋊C4—91no—
506C4⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
507C4⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
508C22⋊C4—91no—
509C22⋊C4—91no—
510C22⋊C4—91no—
511C22⋊C4—91no—
512C22⋊C4—91no—
513C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
514C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
515C22⋊C4C2×AGL(1,ℤ/9)11yescharacteristic
516C42—91no—
517C42—91no—
518C42—91no—
519C42—91no—
520C42—91no—
521C22×C3—21no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—31no—
527C22×C3—32no—
528C22×C3—61no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3C3×#23712yes—
534C22×C3C23×C3×D311yescharacteristic
535C3×C4—21no—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—61no—
541C3×C4—61no—
542C3×C4—61no—
543C3×C4—61no—
544C3×C4—61no—
545C3×C4—92no—
546C3×C4—181no—
547C3×C4—181no—
548C3×C4—181no—
549C3×C4—181no—
550C3×C4—181no—
551C3×C4—181no—
552C3×C4—181no—
553Dic3—32no—
554Dic3—61no—
555Dic3—61no—
556Dic3—61no—
557Dic3—61no—
558Dic3—61no—
559Dic3—61no—
560Dic3—61no—
561C32#565011yescharacteristic
562C9—21no—
563C9C3×#55211yescharacteristic, complemented
564C23C22×AGL(1,ℤ/9)11yescharacteristic
565C23C22×AGL(1,ℤ/9)11yescharacteristic
566Q8—182no—
567D4—22no—
568C2×C4—22no—
569C2×C4—91no—
570C2×C4—91no—
571C2×C4—91no—
572C2×C4—91no—
573C2×C4—91no—
574C2×C4—91no—
575C2×C4—91no—
576C2×C4—91no—
577C2×C4—182no—
578C2×C4—182no—
579C2×C4—182no—
580C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
581C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
582C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
583C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
584C2×C4C22×AGL(1,ℤ/9)11yescharacteristic
585C2×C3—22no—
586C2×C3—31no—
587C2×C3—31no—
588C2×C3—31no—
589C2×C3—41no—
590C2×C3—62no—
591C2×C3—121no—
592C2×C3C2×C3×#23711yescharacteristic
593C2×C3C3×D3×#4111yescharacteristic
594C2×C3C3×#101011yescharacteristic
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22#3699⋊C312yes—
601C22C23×AGL(1,ℤ/9)11yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—21no—
607C4—92no—
608C4—181no—
609C4—181no—
610C4—181no—
611C4—181no—
612C4—181no—
613C4—181no—
614C4—181no—
615C3—31no—
616C3C3×#565011yescharacteristic
617C2—22no—
618C2—41no—
619C2C2×#3699⋊C311yescharacteristic
620C2#41×AGL(1,ℤ/9)11yescharacteristic
621C2#1172264211yescharacteristic
subgroupG/H
centerC22C23×AGL(1,ℤ/9)
commutator, cosocleC22×C9C24×C3
Frattini, socleC22×C3C23×C3×D3
Fitting3−1+2×#123C2
prime radicalC2×C32×D4C2×D3
hypercenter#123AGL(1,ℤ/9)
hypocenterC9C3×#552
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
4. #63488⋊C3C2semidirect
5. C2×(3−1+2⋊C4)⋊C4C2semidirect
6. #63452⋊C3C2semidirect
7. #63451⋊C3C2semidirect
8. #63451⋊C3C2semidirect
9. #63449⋊C3C2semidirect
10. #63441⋊C3C2semidirect
11. #63441⋊C3C2semidirect
12. #63440⋊C3C2semidirect
13. #63440⋊C3C2semidirect
14. #63439⋊C3C2semidirect
15. #63439⋊C3C2semidirect
17. #10589752C3semidirect
72. #63488C2×C3semidirect
73. C2×Dic9⋊C4C2×C3semidirect
74. #63452C2×C3semidirect
75. #63451C2×C3semidirect
76. #63451C2×C3semidirect
77. #63449C2×C3semidirect
78. #63441C2×C3semidirect
79. #63441C2×C3semidirect
80. #63440C2×C3semidirect
81. #63440C2×C3semidirect
82. #63439C2×C3semidirect
83. #63439C2×C3semidirect
428. 3−1+2#552semidirect
563. C9C3×#552semidirect

Maximal subgroups

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

subgroupindex
3−1+2×#1232
#63497⋊C32
D4×3−1+2⋊C42
#63488⋊C32
C2×(3−1+2⋊C4)⋊C42
#63452⋊C32
#63451⋊C32
#63449⋊C32
#63441⋊C32
#63440⋊C32
#63439⋊C32
C3×#56503
#105897523