Finite Group Databasebeta

← D3×#92303 #72254063

Subgroups — D3×#92303 #72254063

Order 2916.

820 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 820 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊#92303C211yesmaximal, characteristic, complemented
2C3×#92303C211yesmaximal, characteristic, complemented
3D3×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
4D3×C3⋊(C3⋊D9)C311yesmaximal, characteristic, complemented
5D3×C3⋊AGL(1,ℤ/9)—31nomaximal
6D3×C3⋊((C3⋊D3)⋊C3)—31nomaximal
7C2×#92303—31nomaximal
8D3×#4169—32nomaximal
9C3×C9⋊H(3,𝔽3)C2211yescharacteristic, complemented, Sylow
10C3⋊(C3⋊(C3⋊D9))C2×C311yescharacteristic, complemented
11C3⋊(C3⋊AGL(1,ℤ/9))—31no—
12C3⋊(C3⋊((C3⋊D3)⋊C3))—31no—
13C3×C3⋊(C3⋊D9)C2×C311yescharacteristic, complemented
14C3×C3⋊AGL(1,ℤ/9)—31no—
15C3×C3⋊((C3⋊D3)⋊C3)—31no—
16C3×D3×3−1+2—21no—
17C3×D3×3−1+2D311yescharacteristic, complemented
18C3×D3×H(3,𝔽3)D311yescharacteristic
19C32×D3×C9C2×C311yescharacteristic, complemented
20C2×C9⋊H(3,𝔽3)—31no—
21#92303—21no—
22#92303—31no—
23#92303—62no—
24#92303—61no—
25#92303—61no—
26#92303D311yescharacteristic, direct product factor
27C3⋊#4169—32no—
28D3×C32⋊C9—21no—
29D3×C32⋊C9—22no—
30D3×C32⋊C9D312yescomplemented
31C3×#4169—32no—
32D3×C3⋊(C3⋊D3)—31no—
33C3×D3×C3⋊D3—91no—
34C2×C3⋊(C3⋊D9)—31no—
35C2×C3⋊AGL(1,ℤ/9)—91no—
36C2×C3⋊((C3⋊D3)⋊C3)—91no—
37D3×C3⋊D9—31no—
38D3×C3⋊D9—32no—
39D3×C3⋊D9—91no—
40D3×C3⋊D9—91no—
41D3×C3⋊D9—91no—
42D3×AGL(1,ℤ/9)—91no—
43D3×AGL(1,ℤ/9)—91no—
44D3×AGL(1,ℤ/9)—91no—
45D3×(C3⋊D3)⋊C3—91no—
46D3×(C3⋊D3)⋊C3—91no—
47D3×(C3⋊D3)⋊C3—91no—
48C2×#4169—92no—
49C32×3−1+2—21no—
50C32×3−1+2C2×D311yescharacteristic, complemented
51C32×H(3,𝔽3)C2×D311yescharacteristic
52C33×C9C22×C311yescharacteristic, complemented
53C9⋊H(3,𝔽3)—21no—
54C9⋊H(3,𝔽3)—21no—
55C9⋊H(3,𝔽3)—21no—
56C9⋊H(3,𝔽3)—22no—
57C9⋊H(3,𝔽3)—42no—
58C9⋊H(3,𝔽3)—41no—
59C9⋊H(3,𝔽3)—41no—
60C9⋊H(3,𝔽3)C2×D311yescharacteristic, complemented
61C3×C32⋊C9—21no—
62C3×C32⋊C9—22no—
63C3×C32⋊C9C2×D312yescomplemented
64C3⋊(C3⋊(C3⋊D3))—31no—
65C3×C3⋊(C3⋊D3)—31no—
66C3×C3⋊(C3⋊D3)—91no—
67C32×C3⋊D3—91no—
68C33×D3—21no—
69C33×D3C3×D311yescharacteristic
70C33×D3C3⋊D311yescharacteristic
71C2×C3×3−1+2—31no—
72C2×C3×3−1+2—61no—
73C2×C3×H(3,𝔽3)—31no—
74C2×C32×C9—31no—
75C3⋊(C3⋊D9)—31no—
76C3⋊(C3⋊D9)—31no—
77C3⋊(C3⋊D9)—32no—
78C3⋊(C3⋊D9)—61no—
79C3⋊(C3⋊D9)—62no—
80C3⋊(C3⋊D9)—61no—
81C3⋊(C3⋊D9)—91no—
82C3⋊(C3⋊D9)—91no—
83C3⋊(C3⋊D9)—91no—
84C3⋊(C3⋊D9)—181no—
85C3⋊(C3⋊D9)—181no—
86C3⋊(C3⋊D9)—181no—
87C3⋊(C3⋊D9)C3×D311yescharacteristic, complemented
88C3⋊AGL(1,ℤ/9)—31no—
89C3⋊AGL(1,ℤ/9)—61no—
90C3⋊AGL(1,ℤ/9)—91no—
91C3⋊AGL(1,ℤ/9)—91no—
92C3⋊AGL(1,ℤ/9)—91no—
93C3⋊AGL(1,ℤ/9)—91no—
94C3⋊AGL(1,ℤ/9)—181no—
95C3⋊AGL(1,ℤ/9)—181no—
96C3⋊AGL(1,ℤ/9)—181no—
97C3⋊AGL(1,ℤ/9)—181no—
98C3⋊((C3⋊D3)⋊C3)—31no—
99C3⋊((C3⋊D3)⋊C3)—61no—
100C3⋊((C3⋊D3)⋊C3)—91no—
101C3⋊((C3⋊D3)⋊C3)—91no—
102C3⋊((C3⋊D3)⋊C3)—91no—
103C3⋊((C3⋊D3)⋊C3)—91no—
104C3⋊((C3⋊D3)⋊C3)—181no—
105C3⋊((C3⋊D3)⋊C3)—181no—
106C3⋊((C3⋊D3)⋊C3)—181no—
107C3⋊((C3⋊D3)⋊C3)—181no—
108C3×C3⋊D9—31no—
109C3×C3⋊D9—32no—
110C3×C3⋊D9—91no—
111C3×C3⋊D9—91no—
112C3×C3⋊D9—91no—
113D3×3−1+2—31no—
114D3×3−1+2—61no—
115D3×3−1+2—61no—
116D3×3−1+2—61no—
117D3×3−1+2—61no—
118D3×3−1+2—61no—
119C3×AGL(1,ℤ/9)—91no—
120C3×AGL(1,ℤ/9)—91no—
121C3×AGL(1,ℤ/9)—91no—
122D3×H(3,𝔽3)—61no—
123D3×H(3,𝔽3)—61no—
124D3×H(3,𝔽3)—61no—
125C3×(C3⋊D3)⋊C3—91no—
126C3×(C3⋊D3)⋊C3—91no—
127C3×(C3⋊D3)⋊C3—91no—
128C3×D3×C9—21no—
129C3×D3×C9—22no—
130C3×D3×C9—31no—
131C3×D3×C9—31no—
132C3×D3×C9—31no—
133C3×D3×C9C3×D312yes—
134C3×D3×C9C3×D311yescharacteristic
135C2×C32⋊C9—32no—
136C2×C32⋊C9—62no—
137C2×C32⋊C9—61no—
138#4169—32no—
139#4169—62no—
140#4169—92no—
141#4169—182no—
142C2×C3⋊(C3⋊D3)—91no—
143C2×C3×C3⋊D3—271no—
144D3×C3⋊D3—91no—
145D3×C3⋊D3—91no—
146D3×C3⋊D3—91no—
147D3×C3⋊D3—91no—
148D3×C3⋊D3—271no—
149D3×C3⋊D3—271no—
150D3×C3⋊D3—271no—
151C3×D32—271no—
152C3×D32—271no—
153C3×D32—271no—
154C3×D32—271no—
155C2×C3⋊D9—91no—
156C2×C3⋊D9—92no—
157C2×C3⋊D9—271no—
158C2×C3⋊D9—271no—
159C2×C3⋊D9—271no—
160C2×AGL(1,ℤ/9)—271no—
161C2×AGL(1,ℤ/9)—271no—
162C2×AGL(1,ℤ/9)—271no—
163C2×(C3⋊D3)⋊C3—271no—
164C2×(C3⋊D3)⋊C3—271no—
165C2×(C3⋊D3)⋊C3—271no—
166D3×D9—91no—
167D3×D9—91no—
168D3×D9—91no—
169D3×D9—272no—
170C34—21no—
171C34C2×C3×D311yescharacteristic
172C34C2×C3⋊D311yescharacteristic
173C3×3−1+2—21no—
174C3×3−1+2—21no—
175C3×3−1+2—21no—
176C3×3−1+2—31no—
177C3×3−1+2—41no—
178C3×3−1+2—42no—
179C3×3−1+2—41no—
180C3×3−1+2—41no—
181C3×3−1+2—61no—
182C3×3−1+2—61no—
183C3×3−1+2—61no—
184C3×3−1+2—61no—
185C3×3−1+2—61no—
186C3×3−1+2—61no—
187C3×3−1+2—121no—
188C3×3−1+2—121no—
189C3×3−1+2—121no—
190C3×3−1+2—121no—
191C3×3−1+2—121no—
192C3×3−1+2D3211yescharacteristic, complemented
193C3×H(3,𝔽3)—21no—
194C3×H(3,𝔽3)—21no—
195C3×H(3,𝔽3)—41no—
196C3×H(3,𝔽3)—61no—
197C3×H(3,𝔽3)—61no—
198C3×H(3,𝔽3)—61no—
199C3×H(3,𝔽3)—61no—
200C3×H(3,𝔽3)—61no—
201C3×H(3,𝔽3)—121no—
202C3×H(3,𝔽3)D3211yescharacteristic
203C32×C9—21no—
204C32×C9—22no—
205C32×C9—21no—
206C32×C9—22no—
207C32×C9—21no—
208C32×C9—31no—
209C32×C9—31no—
210C32×C9—31no—
211C32×C9—61no—
212C32×C9—61no—
213C32×C9—61no—
214C32×C9C2×C3×D311yescharacteristic
215C32×C9C2×C3×D312yes—
216C32×C9C2×C3×D311yescharacteristic, complemented
217C32⋊C9—21no—
218C32⋊C9—22no—
219C32⋊C9—22no—
220C32⋊C9—22no—
221C32⋊C9—42no—
222C32⋊C9—42no—
223C32⋊C9—42no—
224C32⋊C9—42no—
225C32⋊C9—41no—
226C32⋊C9—42no—
227C32⋊C9—41no—
228C32⋊C9—42no—
229C32⋊C9D3212yescomplemented
230C2×C33—31no—
231C2×C33—31no—
232C2×C33—61no—
233C3⋊(C3⋊D3)—31no—
234C3⋊(C3⋊D3)—91no—
235C3⋊(C3⋊D3)—91no—
236C3⋊(C3⋊D3)—91no—
237C3⋊(C3⋊D3)—91no—
238C3⋊(C3⋊D3)—91no—
239C3⋊(C3⋊D3)—181no—
240C3⋊(C3⋊D3)—181no—
241C3⋊(C3⋊D3)—181no—
242C3⋊(C3⋊D3)—181no—
243C3⋊(C3⋊D3)—271no—
244C3⋊(C3⋊D3)—271no—
245C3⋊(C3⋊D3)—271no—
246C3⋊(C3⋊D3)—541no—
247C3⋊(C3⋊D3)—541no—
248C3⋊(C3⋊D3)—541no—
249C3×C3⋊D3—91no—
250C3×C3⋊D3—91no—
251C3×C3⋊D3—91no—
252C3×C3⋊D3—91no—
253C3×C3⋊D3—91no—
254C3×C3⋊D3—181no—
255C3×C3⋊D3—271no—
256C3×C3⋊D3—271no—
257C3×C3⋊D3—271no—
258C3×C3⋊D3—271no—
259C3×C3⋊D3—271no—
260C3×C3⋊D3—271no—
261C3×C3⋊D3—271no—
262C3×C3⋊D3—271no—
263C3×C3⋊D3—541no—
264C3×C3⋊D3—541no—
265C3×C3⋊D3—541no—
266C3×C3⋊D3—541no—
267C32×D3—31no—
268C32×D3—31no—
269C32×D3—31no—
270C32×D3—61no—
271C32×D3—61no—
272C32×D3—61no—
273C32×D3—61no—
274C32×D3—61no—
275C32×D3—61no—
276C32×D3—61no—
277C32×D3—61no—
278C32×D3—271no—
279C32×D3—271no—
280C32×D3—271no—
281C32×D3—271no—
282C32×D3AGL(1,ℤ/9)11yescharacteristic, complemented
283C32×D3AGL(1,ℤ/9)11yescharacteristic, complemented
284C32×D3AGL(1,ℤ/9)11yescharacteristic, complemented
285C32×D3C3×C3⋊D311yescharacteristic
286C2×3−1+2—181no—
287C2×3−1+2—181no—
288C2×3−1+2—181no—
289C2×3−1+2—181no—
290C2×3−1+2—181no—
291C2×3−1+2—181no—
292C2×H(3,𝔽3)—91no—
293C2×H(3,𝔽3)—181no—
294C2×H(3,𝔽3)—181no—
295C2×C3×C9—31no—
296C2×C3×C9—32no—
297C2×C3×C9—62no—
298C2×C3×C9—61no—
299C2×C3×C9—91no—
300C2×C3×C9—91no—
301C2×C3×C9—91no—
302C3⋊D9—31no—
303C3⋊D9—32no—
304C3⋊D9—91no—
305C3⋊D9—91no—
306C3⋊D9—91no—
307C3⋊D9—91no—
308C3⋊D9—91no—
309C3⋊D9—91no—
310C3⋊D9—91no—
311C3⋊D9—92no—
312C3⋊D9—181no—
313C3⋊D9—181no—
314C3⋊D9—181no—
315C3⋊D9—181no—
316C3⋊D9—182no—
317C3⋊D9—271no—
318C3⋊D9—271no—
319C3⋊D9—271no—
320C3⋊D9—272no—
321C3⋊D9—541no—
322C3⋊D9—541no—
323C3⋊D9—541no—
324C3⋊D9—542no—
325C3⋊D9—542no—
326C3⋊D9—542no—
327C3⋊D9—541no—
328C3⋊D9—541no—
329C3⋊D9—541no—
330C3⋊D9—542no—
331AGL(1,ℤ/9)—91no—
332AGL(1,ℤ/9)—91no—
333AGL(1,ℤ/9)—91no—
334AGL(1,ℤ/9)—181no—
335AGL(1,ℤ/9)—181no—
336AGL(1,ℤ/9)—181no—
337AGL(1,ℤ/9)—271no—
338AGL(1,ℤ/9)—271no—
339AGL(1,ℤ/9)—271no—
340AGL(1,ℤ/9)—541no—
341AGL(1,ℤ/9)—541no—
342AGL(1,ℤ/9)—541no—
343(C3⋊D3)⋊C3—91no—
344(C3⋊D3)⋊C3—91no—
345(C3⋊D3)⋊C3—91no—
346(C3⋊D3)⋊C3—181no—
347(C3⋊D3)⋊C3—181no—
348(C3⋊D3)⋊C3—181no—
349(C3⋊D3)⋊C3—271no—
350(C3⋊D3)⋊C3—271no—
351(C3⋊D3)⋊C3—271no—
352(C3⋊D3)⋊C3—541no—
353(C3⋊D3)⋊C3—541no—
354(C3⋊D3)⋊C3—541no—
355D3×C9—32no—
356D3×C9—61no—
357D3×C9—62no—
358D3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
359D3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
360D3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
361C3×D9—91no—
362C3×D9—91no—
363C3×D9—91no—
364C3×D9—272no—
365C2×C3⋊D3—271no—
366C2×C3⋊D3—271no—
367C2×C3⋊D3—271no—
368C2×C3⋊D3—271no—
369C2×C3⋊D3—811no—
370C2×C3⋊D3—811no—
371C2×C3⋊D3—811no—
372C2×C3×D3—811no—
373C2×C3×D3—811no—
374C2×C3×D3—811no—
375C2×C3×D3—811no—
376C2×C3×D3—811no—
377D32—271no—
378D32—271no—
379D32—271no—
380D32—271no—
381D32—811no—
382D32—811no—
383D32—811no—
384C2×D9—271no—
385C2×D9—271no—
386C2×D9—271no—
387C2×D9—812no—
388C33—21no—
389C33—21no—
390C33—21no—
391C33—21no—
392C33—21no—
393C33—21no—
394C33—31no—
395C33—31no—
396C33—31no—
397C33—41no—
398C33—61no—
399C33—61no—
400C33—61no—
401C33—61no—
402C33—61no—
403C33—61no—
404C33—61no—
405C33—61no—
406C33—61no—
407C33—61no—
408C33—61no—
409C33—61no—
410C33—121no—
411C33—121no—
412C33—121no—
413C33—121no—
414C33—121no—
415C33—121no—
416C33—121no—
417C33C2×AGL(1,ℤ/9)11yescharacteristic, complemented
418C33C2×AGL(1,ℤ/9)11yescharacteristic, complemented
419C33C2×AGL(1,ℤ/9)11yescharacteristic, complemented
420C33C3×D3211yescharacteristic
421C33D3×C3⋊D311yescharacteristic
422C33C2×C3×C3⋊D311yescharacteristic
4233−1+2—61no—
4243−1+2—61no—
4253−1+2—61no—
4263−1+2—61no—
4273−1+2—61no—
4283−1+2—61no—
4293−1+2—61no—
4303−1+2—61no—
4313−1+2—121no—
4323−1+2—121no—
4333−1+2—121no—
4343−1+2—122no—
4353−1+2—122no—
4363−1+2—122no—
4373−1+2—121no—
4383−1+2—121no—
4393−1+2—121no—
4403−1+2—121no—
4413−1+2—121no—
4423−1+2—121no—
4433−1+2—121no—
4443−1+2—121no—
4453−1+2—121no—
4463−1+2—121no—
447H(3,𝔽3)—31no—
448H(3,𝔽3)—61no—
449H(3,𝔽3)—61no—
450H(3,𝔽3)—61no—
451H(3,𝔽3)—61no—
452H(3,𝔽3)—61no—
453H(3,𝔽3)—121no—
454H(3,𝔽3)—121no—
455H(3,𝔽3)—121no—
456H(3,𝔽3)—121no—
457H(3,𝔽3)—121no—
458H(3,𝔽3)—121no—
459C3×C9—21no—
460C3×C9—21no—
461C3×C9—21no—
462C3×C9—21no—
463C3×C9—22no—
464C3×C9—21no—
465C3×C9—22no—
466C3×C9—31no—
467C3×C9—31no—
468C3×C9—31no—
469C3×C9—32no—
470C3×C9—42no—
471C3×C9—41no—
472C3×C9—62no—
473C3×C9—62no—
474C3×C9—62no—
475C3×C9—61no—
476C3×C9—61no—
477C3×C9—61no—
478C3×C9—62no—
479C3×C9—61no—
480C3×C9—61no—
481C3×C9—61no—
482C3×C9—61no—
483C3×C9—62no—
484C3×C9—121no—
485C3×C9—122no—
486C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
487C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
488C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
489C3×C9C3×D3212yes—
490C3×C9C3×D3211yescharacteristic
491C2×C32—31no—
492C2×C32—31no—
493C2×C32—31no—
494C2×C32—31no—
495C2×C32—91no—
496C2×C32—91no—
497C2×C32—91no—
498C2×C32—91no—
499C2×C32—91no—
500C2×C32—181no—
501C2×C32—181no—
502C2×C32—181no—
503C2×C32—181no—
504C2×C32—181no—
505C2×C32—181no—
506C2×C32—811no—
507C3⋊D3—91no—
508C3⋊D3—91no—
509C3⋊D3—91no—
510C3⋊D3—91no—
511C3⋊D3—271no—
512C3⋊D3—271no—
513C3⋊D3—271no—
514C3⋊D3—271no—
515C3⋊D3—271no—
516C3⋊D3—271no—
517C3⋊D3—271no—
518C3⋊D3—271no—
519C3⋊D3—271no—
520C3⋊D3—271no—
521C3⋊D3—271no—
522C3⋊D3—541no—
523C3⋊D3—541no—
524C3⋊D3—541no—
525C3⋊D3—541no—
526C3⋊D3—541no—
527C3⋊D3—541no—
528C3⋊D3—541no—
529C3⋊D3—811no—
530C3⋊D3—811no—
531C3⋊D3—811no—
532C3⋊D3—811no—
533C3⋊D3—811no—
534C3⋊D3—811no—
535C3⋊D3—1621no—
536C3⋊D3—1621no—
537C3⋊D3—1621no—
538C3⋊D3—1621no—
539C3⋊D3—1621no—
540C3⋊D3—1621no—
541C3⋊D3—1621no—
542C3⋊D3—1621no—
543C3⋊D3—1621no—
544C3⋊D3—1621no—
545C3⋊D3—1621no—
546C3⋊D3—1621no—
547C3⋊D3—1621no—
548C3⋊D3—1621no—
549C3⋊D3—1621no—
550C3×D3—31no—
551C3×D3—31no—
552C3×D3—31no—
553C3×D3—181no—
554C3×D3—181no—
555C3×D3—271no—
556C3×D3—271no—
557C3×D3—271no—
558C3×D3—271no—
559C3×D3—271no—
560C3×D3—271no—
561C3×D3—271no—
562C3×D3—271no—
563C3×D3—541no—
564C3×D3—541no—
565C3×D3—541no—
566C3×D3—541no—
567C3×D3—811no—
568C3×D3—811no—
569C3×D3—811no—
570C3×D3—811no—
571C3×D3—811no—
572C3×D3—811no—
573C3×D3—811no—
574C3×D3—811no—
575C3×D3—1621no—
576C3×D3—1621no—
577C3×D3—1621no—
578C3×D3—1621no—
579C3×D3C3⋊((C3⋊D3)⋊C3)11yescharacteristic
580C3×D3C3⋊AGL(1,ℤ/9)11yescharacteristic
581C3×D3#420711yescharacteristic
582C3×D3#420711yescharacteristic
583C2×C9—31no—
584C2×C9—31no—
585C2×C9—31no—
586C2×C9—92no—
587C2×C9—181no—
588C2×C9—182no—
589D9—91no—
590D9—91no—
591D9—91no—
592D9—272no—
593D9—271no—
594D9—271no—
595D9—271no—
596D9—541no—
597D9—541no—
598D9—541no—
599D9—812no—
600D9—1622no—
601C22×C3—2431no—
602C2×D3—811no—
603C2×D3—811no—
604C2×D3—811no—
605C2×D3—811no—
606C2×D3—811no—
607C2×D3—2431no—
608C2×D3—2431no—
609C2×D3—2431no—
610C32—21no—
611C32—21no—
612C32—21no—
613C32—21no—
614C32—21no—
615C32—21no—
616C32—21no—
617C32—31no—
618C32—31no—
619C32—31no—
620C32—31no—
621C32—31no—
622C32—31no—
623C32—31no—
624C32—31no—
625C32—61no—
626C32—61no—
627C32—61no—
628C32—61no—
629C32—61no—
630C32—61no—
631C32—61no—
632C32—61no—
633C32—61no—
634C32—61no—
635C32—61no—
636C32—61no—
637C32—61no—
638C32—61no—
639C32—61no—
640C32—61no—
641C32—61no—
642C32—61no—
643C32—61no—
644C32—61no—
645C32—61no—
646C32—61no—
647C32—121no—
648C32—121no—
649C32—121no—
650C32—121no—
651C32—121no—
652C32—121no—
653C32—121no—
654C32—181no—
655C32—181no—
656C32—361no—
657C32—361no—
658C32—361no—
659C32—361no—
660C32—361no—
661C32—361no—
662C32—361no—
663C32—361no—
664C32D3×AGL(1,ℤ/9)11yescharacteristic, complemented
665C32D3×AGL(1,ℤ/9)11yescharacteristic, complemented
666C32D3×AGL(1,ℤ/9)11yescharacteristic, complemented
667C32C2×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
668C32C2×C3⋊AGL(1,ℤ/9)11yescharacteristic
669C32C2×#420711yescharacteristic
670C32C2×#420711yescharacteristic
671C32C3×D3×C3⋊D311yescharacteristic
672C9—21no—
673C9—21no—
674C9—21no—
675C9—32no—
676C9—62no—
677C9—61no—
678C9—62no—
679C9—121no—
680C9—122no—
681C9D3×(C3⋊D3)⋊C311yescharacteristic, complemented
682C9D3×(C3⋊D3)⋊C311yescharacteristic, complemented
683C9D3×(C3⋊D3)⋊C311yescharacteristic, complemented
684C2×C3—31no—
685C2×C3—31no—
686C2×C3—31no—
687C2×C3—31no—
688C2×C3—91no—
689C2×C3—91no—
690C2×C3—91no—
691C2×C3—541no—
692C2×C3—541no—
693C2×C3—811no—
694C2×C3—811no—
695C2×C3—1621no—
696C2×C3—2431no—
697D3—271no—
698D3—271no—
699D3—271no—
700D3—271no—
701D3—811no—
702D3—811no—
703D3—811no—
704D3—811no—
705D3—811no—
706D3—811no—
707D3—811no—
708D3—811no—
709D3—1621no—
710D3—1621no—
711D3—1621no—
712D3—1621no—
713D3—4861no—
714D3—4861no—
715D3—4861no—
716D3—2431no—
717D3—2431no—
718D3—2431no—
719D3#9230311yescharacteristic, direct product factor
720C22—2431noSylow
721C3—21no—
722C3—21no—
723C3—21no—
724C3—21no—
725C3—31no—
726C3—31no—
727C3—31no—
728C3—61no—
729C3—61no—
730C3—61no—
731C3—181no—
732C3—181no—
733C3—181no—
734C3—361no—
735C3C2×#9230311yescharacteristic, complemented
736C3D3×C3⋊((C3⋊D3)⋊C3)11yescharacteristic
737C3D3×C3⋊AGL(1,ℤ/9)11yescharacteristic
738C3D3×#420711yescharacteristic
739C3D3×#420711yescharacteristic
740C2—31no—
741C2—811no—
742C2—2431no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC33×C9C22×C3
FrattiniC32C3×D3×C3⋊D3
FittingC3×C9⋊H(3,𝔽3)C22
socleC33C2×C3×C3⋊D3
LCSG ▷ C33×C9
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊#92303C2semidirect
2. C3×#92303C2semidirect
3. D3×C9⋊H(3,𝔽3)C2semidirect
4. D3×C3⋊(C3⋊D9)C3semidirect
9. C3×C9⋊H(3,𝔽3)C22semidirect
10. C3⋊(C3⋊(C3⋊D9))C2×C3semidirect
13. C3×C3⋊(C3⋊D9)C2×C3semidirect
17. C3×D3×3−1+2D3semidirect
19. C32×D3×C9C2×C3semidirect
26. #92303D3direct (N × H)
30. D3×C32⋊C9D3semidirect
50. C32×3−1+2C2×D3semidirect
52. C33×C9C22×C3semidirect
60. C9⋊H(3,𝔽3)C2×D3semidirect
63. C3×C32⋊C9C2×D3semidirect
87. C3⋊(C3⋊D9)C3×D3semidirect
192. C3×3−1+2D32semidirect
216. C32×C9C2×C3×D3semidirect
229. C32⋊C9D32semidirect
282. C32×D3AGL(1,ℤ/9)semidirect
283. C32×D3AGL(1,ℤ/9)semidirect
284. C32×D3AGL(1,ℤ/9)semidirect
358. D3×C9(C3⋊D3)⋊C3semidirect
359. D3×C9(C3⋊D3)⋊C3semidirect
360. D3×C9(C3⋊D3)⋊C3semidirect
417. C33C2×AGL(1,ℤ/9)semidirect
418. C33C2×AGL(1,ℤ/9)semidirect
419. C33C2×AGL(1,ℤ/9)semidirect
486. C3×C9C2×(C3⋊D3)⋊C3semidirect
487. C3×C9C2×(C3⋊D3)⋊C3semidirect
488. C3×C9C2×(C3⋊D3)⋊C3semidirect
664. C32D3×AGL(1,ℤ/9)semidirect
665. C32D3×AGL(1,ℤ/9)semidirect
666. C32D3×AGL(1,ℤ/9)semidirect
681. C9D3×(C3⋊D3)⋊C3semidirect
682. C9D3×(C3⋊D3)⋊C3semidirect
683. C9D3×(C3⋊D3)⋊C3semidirect
719. D3#92303direct (N × H)
735. C3C2×#92303semidirect

Maximal subgroups

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

subgroupindex
C3⋊#923032
C3×#923032
D3×C9⋊H(3,𝔽3)2
D3×C3⋊(C3⋊D9)3
D3×C3⋊AGL(1,ℤ/9)3
D3×C3⋊((C3⋊D3)⋊C3)3
C2×#923033
D3×#41693