Finite Group Databasebeta

← D3×#4184⋊C3 #72243808

Subgroups — D3×#4184⋊C3 #72243808

Order 2916.

696 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 59 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⋊(#4184⋊C3)C211yesmaximal, characteristic, complemented
2C3×#4184⋊C3C211yesmaximal, characteristic, complemented
3D3×#6910C211yesmaximal, characteristic, complemented
4C3×D3×AGL(1,ℤ/9)—31nomaximal
5C3×D3×AGL(1,ℤ/9)—31nomaximal
6C3×D3×AGL(1,ℤ/9)—31nomaximal
7C3×D3×(C3⋊D3)⋊C3—31nomaximal
8C2×#4184⋊C3—31nomaximal
9D3×#4184C311yesmaximal, characteristic, complemented
10C3×#6910C2211yescharacteristic, complemented, Sylow
11C3×C3⋊AGL(1,ℤ/9)—31no—
12C3×C3⋊AGL(1,ℤ/9)—31no—
13C3×C3⋊AGL(1,ℤ/9)—31no—
14C3×C3⋊((C3⋊D3)⋊C3)—31no—
15C3×D3×3−1+2D311yescharacteristic, complemented
16C3×D3×3−1+2D311yescharacteristic, complemented
17C3×D3×3−1+2D311yescharacteristic, complemented
18C32×AGL(1,ℤ/9)—31no—
19C32×AGL(1,ℤ/9)—31no—
20C32×AGL(1,ℤ/9)—31no—
21C3×D3×H(3,𝔽3)D311yescharacteristic
22C32×(C3⋊D3)⋊C3—31no—
23C2×#6910—31no—
24C3⋊#4184C2×C311yescharacteristic, complemented
25#4184⋊C3—21no—
26#4184⋊C3—31no—
27#4184⋊C3—61no—
28#4184⋊C3—61no—
29#4184⋊C3—61no—
30#4184⋊C3—61no—
31#4184⋊C3D311yescharacteristic, direct product factor
32C3×#4184C2×C311yescharacteristic, complemented
33D3×#731—21no—
34D3×#731—21no—
35D3×#731—21no—
36D3×#731—21no—
37D3×#731C2×C311yescharacteristic, complemented
38C3×D3×C3⋊D3—31no—
39C32×D32—91no—
40C2×C3×AGL(1,ℤ/9)—91no—
41C2×C3×AGL(1,ℤ/9)—91no—
42C2×C3×AGL(1,ℤ/9)—91no—
43C2×C3×(C3⋊D3)⋊C3—91no—
44D3×AGL(1,ℤ/9)—31no—
45D3×AGL(1,ℤ/9)—31no—
46D3×AGL(1,ℤ/9)—31no—
47D3×AGL(1,ℤ/9)—31no—
48D3×AGL(1,ℤ/9)—31no—
49D3×AGL(1,ℤ/9)—31no—
50D3×AGL(1,ℤ/9)—31no—
51D3×AGL(1,ℤ/9)—31no—
52D3×AGL(1,ℤ/9)—31no—
53D3×(C3⋊D3)⋊C3—31no—
54D3×(C3⋊D3)⋊C3—31no—
55D3×(C3⋊D3)⋊C3—31no—
56C3×D3×D9—31no—
57C3×D3×D9—31no—
58C3×D3×D9—31no—
59C2×#4184—31no—
60C32×3−1+2C2×D311yescharacteristic, complemented
61C32×3−1+2C2×D311yescharacteristic, complemented
62C32×3−1+2C2×D311yescharacteristic, complemented
63C32×H(3,𝔽3)C2×D311yescharacteristic
64#6910—21no—
65#6910—21no—
66#6910—21no—
67#6910—21no—
68#6910—21no—
69#6910—41no—
70#6910—41no—
71#6910—41no—
72#6910—41no—
73#6910C2×D311yescharacteristic, complemented
74C3×#731—21no—
75C3×#731—21no—
76C3×#731—21no—
77C3×#731—21no—
78C3×#731C22×C311yescharacteristic, complemented
79C3×C3⋊(C3⋊D3)—31no—
80C32×C3⋊D3—31no—
81C32×C3⋊D3—91no—
82C33×D3—31no—
83C33×D3—91no—
84C33×D3C3⋊D311yescharacteristic
85C2×C3×3−1+2—31no—
86C2×C3×3−1+2—31no—
87C2×C3×3−1+2—31no—
88C2×C3×H(3,𝔽3)—31no—
89C3⋊AGL(1,ℤ/9)—31no—
90C3⋊AGL(1,ℤ/9)—31no—
91C3⋊AGL(1,ℤ/9)—31no—
92C3⋊AGL(1,ℤ/9)—31no—
93C3⋊AGL(1,ℤ/9)—31no—
94C3⋊AGL(1,ℤ/9)—31no—
95C3⋊AGL(1,ℤ/9)—31no—
96C3⋊AGL(1,ℤ/9)—31no—
97C3⋊AGL(1,ℤ/9)—31no—
98C3⋊((C3⋊D3)⋊C3)—31no—
99C3⋊((C3⋊D3)⋊C3)—31no—
100C3⋊((C3⋊D3)⋊C3)—31no—
101C3×C3⋊D9—31no—
102C3×C3⋊D9—31no—
103C3×C3⋊D9—31no—
104D3×3−1+2—21no—
105D3×3−1+2—21no—
106D3×3−1+2—31no—
107D3×3−1+2—31no—
108D3×3−1+2—31no—
109D3×3−1+2—61no—
110D3×3−1+2—61no—
111D3×3−1+2—61no—
112D3×3−1+2—61no—
113D3×3−1+2C3×D311yescharacteristic, complemented
114D3×3−1+2C3×D311yescharacteristic, complemented
115C3×AGL(1,ℤ/9)—31no—
116C3×AGL(1,ℤ/9)—31no—
117C3×AGL(1,ℤ/9)—31no—
118C3×AGL(1,ℤ/9)—31no—
119C3×AGL(1,ℤ/9)—31no—
120C3×AGL(1,ℤ/9)—31no—
121C3×AGL(1,ℤ/9)—31no—
122C3×AGL(1,ℤ/9)—31no—
123C3×AGL(1,ℤ/9)—31no—
124C3×AGL(1,ℤ/9)—31no—
125C3×AGL(1,ℤ/9)—31no—
126C3×AGL(1,ℤ/9)—31no—
127C3×AGL(1,ℤ/9)—61no—
128C3×AGL(1,ℤ/9)—61no—
129C3×AGL(1,ℤ/9)—61no—
130C3×AGL(1,ℤ/9)—61no—
131C3×AGL(1,ℤ/9)—61no—
132C3×AGL(1,ℤ/9)—61no—
133C3×AGL(1,ℤ/9)—61no—
134C3×AGL(1,ℤ/9)—61no—
135C3×AGL(1,ℤ/9)—61no—
136C3×AGL(1,ℤ/9)—61no—
137C3×AGL(1,ℤ/9)—61no—
138C3×AGL(1,ℤ/9)—61no—
139C3×AGL(1,ℤ/9)—91no—
140C3×AGL(1,ℤ/9)—91no—
141C3×AGL(1,ℤ/9)—91no—
142C3×AGL(1,ℤ/9)—181no—
143C3×AGL(1,ℤ/9)—181no—
144C3×AGL(1,ℤ/9)—181no—
145D3×H(3,𝔽3)—21no—
146D3×H(3,𝔽3)—31no—
147D3×H(3,𝔽3)—61no—
148D3×H(3,𝔽3)C3×D311yescharacteristic
149C3×(C3⋊D3)⋊C3—31no—
150C3×(C3⋊D3)⋊C3—31no—
151C3×(C3⋊D3)⋊C3—31no—
152C3×(C3⋊D3)⋊C3—31no—
153C3×(C3⋊D3)⋊C3—61no—
154C3×(C3⋊D3)⋊C3—61no—
155C3×(C3⋊D3)⋊C3—61no—
156C3×(C3⋊D3)⋊C3—61no—
157C3×(C3⋊D3)⋊C3—91no—
158C3×(C3⋊D3)⋊C3—181no—
159C3×D3×C9—21no—
160C3×D3×C9—31no—
161C3×D3×C9—31no—
162C3×D3×C9C3×D311yescharacteristic, complemented
163C32×D9—31no—
164C32×D9—31no—
165C32×D9—31no—
166C2×#731—31no—
167C2×#731—61no—
168C2×#731—61no—
169C2×#731—61no—
170C2×#731—61no—
171#4184—31no—
172#4184—61no—
173#4184—61no—
174#4184—61no—
175#4184—61no—
176#4184C3×D311yescharacteristic, complemented
177C2×C3×C3⋊D3—91no—
178C2×C32×D3—271no—
179C2×C32×D3—271no—
180D3×C3⋊D3—31no—
181C3×D32—91no—
182C3×D32—91no—
183C3×D32—91no—
184C3×D32—91no—
185C3×D32—271no—
186C2×AGL(1,ℤ/9)—91no—
187C2×AGL(1,ℤ/9)—91no—
188C2×AGL(1,ℤ/9)—91no—
189C2×AGL(1,ℤ/9)—91no—
190C2×AGL(1,ℤ/9)—91no—
191C2×AGL(1,ℤ/9)—91no—
192C2×AGL(1,ℤ/9)—91no—
193C2×AGL(1,ℤ/9)—91no—
194C2×AGL(1,ℤ/9)—91no—
195C2×(C3⋊D3)⋊C3—91no—
196C2×(C3⋊D3)⋊C3—91no—
197C2×(C3⋊D3)⋊C3—91no—
198C2×C3×D9—91no—
199C2×C3×D9—91no—
200C2×C3×D9—91no—
201D3×D9—31no—
202D3×D9—31no—
203D3×D9—31no—
204C34—31no—
205C34C2×C3⋊D311yescharacteristic
206C3×3−1+2—21no—
207C3×3−1+2—21no—
208C3×3−1+2—21no—
209C3×3−1+2—21no—
210C3×3−1+2—21no—
211C3×3−1+2—21no—
212C3×3−1+2—21no—
213C3×3−1+2—21no—
214C3×3−1+2—31no—
215C3×3−1+2—31no—
216C3×3−1+2—31no—
217C3×3−1+2—41no—
218C3×3−1+2—41no—
219C3×3−1+2—41no—
220C3×3−1+2—61no—
221C3×3−1+2—61no—
222C3×3−1+2—61no—
223C3×3−1+2—61no—
224C3×3−1+2—61no—
225C3×3−1+2—61no—
226C3×3−1+2—121no—
227C3×3−1+2—121no—
228C3×3−1+2—121no—
229C3×3−1+2—121no—
230C3×3−1+2—121no—
231C3×3−1+2—121no—
232C3×3−1+2—121no—
233C3×3−1+2D3211yescharacteristic, complemented
234C3×3−1+2D3211yescharacteristic, complemented
235C3×3−1+2D3211yescharacteristic, complemented
236C3×3−1+2C2×C3×D311yescharacteristic, complemented
237C3×3−1+2C2×C3×D311yescharacteristic, complemented
238C3×H(3,𝔽3)—21no—
239C3×H(3,𝔽3)—21no—
240C3×H(3,𝔽3)—21no—
241C3×H(3,𝔽3)—31no—
242C3×H(3,𝔽3)—41no—
243C3×H(3,𝔽3)—61no—
244C3×H(3,𝔽3)—61no—
245C3×H(3,𝔽3)—121no—
246C3×H(3,𝔽3)—121no—
247C3×H(3,𝔽3)D3211yescharacteristic
248C3×H(3,𝔽3)C2×C3×D311yescharacteristic
249C32×C9—21no—
250C32×C9—31no—
251C32×C9—31no—
252C32×C9C2×C3×D311yescharacteristic, complemented
253#731—21no—
254#731—21no—
255#731—21no—
256#731—21no—
257#731—21no—
258#731—21no—
259#731—21no—
260#731—21no—
261#731—41no—
262#731—41no—
263#731—41no—
264#731—41no—
265#731—41no—
266#731—41no—
267#731—41no—
268#731—41no—
269#731—41no—
270#731—41no—
271#731—41no—
272#731—41no—
273#731—41no—
274#731—41no—
275#731—41no—
276#731—41no—
277#731C2×C3×D311yescharacteristic, complemented
278C2×C33—31no—
279C2×C33—181no—
280C2×C33—271no—
281C3⋊(C3⋊D3)—31no—
282C3×C3⋊D3—31no—
283C3×C3⋊D3—31no—
284C3×C3⋊D3—61no—
285C3×C3⋊D3—91no—
286C3×C3⋊D3—91no—
287C3×C3⋊D3—91no—
288C3×C3⋊D3—91no—
289C3×C3⋊D3—91no—
290C3×C3⋊D3—181no—
291C3×C3⋊D3—271no—
292C3×C3⋊D3—541no—
293C32×D3—31no—
294C32×D3—61no—
295C32×D3—91no—
296C32×D3—91no—
297C32×D3—91no—
298C32×D3—91no—
299C32×D3—91no—
300C32×D3—181no—
301C32×D3—181no—
302C32×D3—181no—
303C32×D3—181no—
304C32×D3—181no—
305C32×D3—181no—
306C32×D3—181no—
307C32×D3—271no—
308C32×D3—271no—
309C32×D3—271no—
310C32×D3—541no—
311C32×D3#27211yescharacteristic
312C32×D3#27211yescharacteristic
313C32×D3#27211yescharacteristic
314C32×D3C3×C3⋊D311yescharacteristic
315C2×3−1+2—31no—
316C2×3−1+2—31no—
317C2×3−1+2—61no—
318C2×3−1+2—61no—
319C2×3−1+2—91no—
320C2×3−1+2—181no—
321C2×3−1+2—181no—
322C2×3−1+2—181no—
323C2×3−1+2—181no—
324C2×3−1+2—181no—
325C2×3−1+2—181no—
326C2×H(3,𝔽3)—31no—
327C2×H(3,𝔽3)—61no—
328C2×H(3,𝔽3)—91no—
329C2×H(3,𝔽3)—181no—
330C2×C3×C9—31no—
331C2×C3×C9—61no—
332C2×C3×C9—91no—
333C2×C3×C9—181no—
334C3⋊D9—31no—
335C3⋊D9—31no—
336C3⋊D9—31no—
337AGL(1,ℤ/9)—31no—
338AGL(1,ℤ/9)—31no—
339AGL(1,ℤ/9)—31no—
340AGL(1,ℤ/9)—31no—
341AGL(1,ℤ/9)—31no—
342AGL(1,ℤ/9)—31no—
343AGL(1,ℤ/9)—31no—
344AGL(1,ℤ/9)—31no—
345AGL(1,ℤ/9)—31no—
346AGL(1,ℤ/9)—61no—
347AGL(1,ℤ/9)—61no—
348AGL(1,ℤ/9)—61no—
349AGL(1,ℤ/9)—61no—
350AGL(1,ℤ/9)—61no—
351AGL(1,ℤ/9)—61no—
352AGL(1,ℤ/9)—61no—
353AGL(1,ℤ/9)—61no—
354AGL(1,ℤ/9)—61no—
355AGL(1,ℤ/9)—91no—
356AGL(1,ℤ/9)—91no—
357AGL(1,ℤ/9)—91no—
358AGL(1,ℤ/9)—91no—
359AGL(1,ℤ/9)—91no—
360AGL(1,ℤ/9)—91no—
361AGL(1,ℤ/9)—91no—
362AGL(1,ℤ/9)—91no—
363AGL(1,ℤ/9)—91no—
364AGL(1,ℤ/9)—181no—
365AGL(1,ℤ/9)—181no—
366AGL(1,ℤ/9)—181no—
367AGL(1,ℤ/9)—181no—
368AGL(1,ℤ/9)—181no—
369AGL(1,ℤ/9)—181no—
370AGL(1,ℤ/9)—181no—
371AGL(1,ℤ/9)—181no—
372AGL(1,ℤ/9)—181no—
373(C3⋊D3)⋊C3—31no—
374(C3⋊D3)⋊C3—31no—
375(C3⋊D3)⋊C3—31no—
376(C3⋊D3)⋊C3—61no—
377(C3⋊D3)⋊C3—61no—
378(C3⋊D3)⋊C3—61no—
379(C3⋊D3)⋊C3—91no—
380(C3⋊D3)⋊C3—91no—
381(C3⋊D3)⋊C3—91no—
382(C3⋊D3)⋊C3—181no—
383(C3⋊D3)⋊C3—181no—
384(C3⋊D3)⋊C3—181no—
385D3×C9—31no—
386D3×C9—61no—
387D3×C9—61no—
388D3×C9—61no—
389D3×C9—61no—
390D3×C9—61no—
391C3×D9—31no—
392C3×D9—31no—
393C3×D9—31no—
394C3×D9—31no—
395C3×D9—31no—
396C3×D9—31no—
397C3×D9—61no—
398C3×D9—61no—
399C3×D9—61no—
400C3×D9—91no—
401C3×D9—91no—
402C3×D9—91no—
403C3×D9—181no—
404C3×D9—181no—
405C3×D9—181no—
406C22×C32—811no—
407C2×C3⋊D3—91no—
408C2×C3×D3—271no—
409C2×C3×D3—271no—
410C2×C3×D3—271no—
411C2×C3×D3—271no—
412C2×C3×D3—271no—
413C2×C3×D3—271no—
414C2×C3×D3—271no—
415C2×C3×D3—271no—
416C2×C3×D3—811no—
417D32—91no—
418D32—271no—
419C2×D9—91no—
420C2×D9—91no—
421C2×D9—91no—
422C33—21no—
423C33—21no—
424C33—21no—
425C33—21no—
426C33—31no—
427C33—61no—
428C33—61no—
429C33—61no—
430C33—121no—
431C33—121no—
432C33—181no—
433C33—181no—
434C33—181no—
435C33—361no—
436C33—361no—
437C33—361no—
438C33C2×#27211yescharacteristic
439C33C2×#27211yescharacteristic
440C33C2×#27211yescharacteristic
441C33D3×C3⋊D311yescharacteristic
442C33C2×C3×C3⋊D311yescharacteristic
4433−1+2—21no—
4443−1+2—21no—
4453−1+2—21no—
4463−1+2—21no—
4473−1+2—31no—
4483−1+2—41no—
4493−1+2—41no—
4503−1+2—61no—
4513−1+2—61no—
4523−1+2—61no—
4533−1+2—61no—
4543−1+2—61no—
4553−1+2—61no—
4563−1+2—61no—
4573−1+2—61no—
4583−1+2—61no—
4593−1+2—61no—
4603−1+2—121no—
4613−1+2—121no—
4623−1+2—121no—
4633−1+2—121no—
4643−1+2—121no—
4653−1+2—121no—
4663−1+2—121no—
4673−1+2—121no—
4683−1+2—121no—
4693−1+2—121no—
4703−1+2—121no—
4713−1+2—121no—
4723−1+2—121no—
4733−1+2—121no—
4743−1+2—121no—
4753−1+2—121no—
4763−1+2—121no—
4773−1+2—121no—
4783−1+2—121no—
4793−1+2—121no—
4803−1+2—121no—
4813−1+2C3×D3211yescharacteristic, complemented
4823−1+2C3×D3211yescharacteristic, complemented
483H(3,𝔽3)—21no—
484H(3,𝔽3)—21no—
485H(3,𝔽3)—31no—
486H(3,𝔽3)—41no—
487H(3,𝔽3)—61no—
488H(3,𝔽3)—61no—
489H(3,𝔽3)—121no—
490H(3,𝔽3)—121no—
491H(3,𝔽3)—121no—
492H(3,𝔽3)—121no—
493H(3,𝔽3)—121no—
494H(3,𝔽3)—121no—
495H(3,𝔽3)—121no—
496H(3,𝔽3)C3×D3211yescharacteristic
497C3×C9—21no—
498C3×C9—21no—
499C3×C9—31no—
500C3×C9—31no—
501C3×C9—41no—
502C3×C9—61no—
503C3×C9—61no—
504C3×C9—61no—
505C3×C9—61no—
506C3×C9—61no—
507C3×C9—61no—
508C3×C9—61no—
509C3×C9—121no—
510C3×C9—121no—
511C3×C9—121no—
512C3×C9—121no—
513C3×C9—121no—
514C3×C9—121no—
515C3×C9—121no—
516C3×C9C3×D3211yescharacteristic, complemented
517C2×C32—31no—
518C2×C32—31no—
519C2×C32—31no—
520C2×C32—31no—
521C2×C32—181no—
522C2×C32—181no—
523C2×C32—271no—
524C2×C32—271no—
525C2×C32—271no—
526C2×C32—271no—
527C2×C32—271no—
528C2×C32—541no—
529C2×C32—541no—
530C2×C32—541no—
531C2×C32—541no—
532C2×C32—541no—
533C2×C32—541no—
534C2×C32—541no—
535C2×C32—811no—
536C3⋊D3—31no—
537C3⋊D3—91no—
538C3⋊D3—91no—
539C3⋊D3—181no—
540C3⋊D3—271no—
541C3⋊D3—541no—
542C3×D3—31no—
543C3×D3—31no—
544C3×D3—31no—
545C3×D3—31no—
546C3×D3—91no—
547C3×D3—91no—
548C3×D3—91no—
549C3×D3—91no—
550C3×D3—91no—
551C3×D3—181no—
552C3×D3—181no—
553C3×D3—181no—
554C3×D3—181no—
555C3×D3—181no—
556C3×D3—181no—
557C3×D3—271no—
558C3×D3—271no—
559C3×D3—271no—
560C3×D3—271no—
561C3×D3—271no—
562C3×D3—271no—
563C3×D3—271no—
564C3×D3—271no—
565C3×D3—271no—
566C3×D3—271no—
567C3×D3—541no—
568C3×D3—541no—
569C3×D3—541no—
570C3×D3—541no—
571C3×D3—541no—
572C3×D3—811no—
573C3×D3—1621no—
574C3×D3C3×#27211yescharacteristic
575C2×C9—91no—
576C2×C9—181no—
577C2×C9—181no—
578C2×C9—181no—
579C2×C9—181no—
580C2×C9—181no—
581D9—31no—
582D9—31no—
583D9—31no—
584D9—91no—
585D9—91no—
586D9—91no—
587D9—181no—
588D9—181no—
589D9—181no—
590C22×C3—811no—
591C22×C3—811no—
592C22×C3—811no—
593C22×C3—811no—
594C2×D3—271no—
595C2×D3—271no—
596C2×D3—811no—
597C32—21no—
598C32—21no—
599C32—21no—
600C32—21no—
601C32—31no—
602C32—31no—
603C32—31no—
604C32—31no—
605C32—61no—
606C32—61no—
607C32—61no—
608C32—61no—
609C32—121no—
610C32—121no—
611C32—121no—
612C32—121no—
613C32—181no—
614C32—181no—
615C32—181no—
616C32—181no—
617C32—181no—
618C32—181no—
619C32—181no—
620C32—361no—
621C32—361no—
622C32—361no—
623C32—361no—
624C32—361no—
625C32—361no—
626C32—361no—
627C32—361no—
628C32—361no—
629C32—362no—
630C32D3×#27211yescharacteristic
631C32D3×#27211yescharacteristic
632C32D3×#27211yescharacteristic
633C32C2×C3×#27211yescharacteristic
634C32C3×D3×C3⋊D311yescharacteristic
635C9—31no—
636C9—61no—
637C9—61no—
638C9—61no—
639C9—61no—
640C9—61no—
641C9—61no—
642C9—121no—
643C9—121no—
644C9—121no—
645C9—121no—
646C9—121no—
647C2×C3—31no—
648C2×C3—91no—
649C2×C3—181no—
650C2×C3—181no—
651C2×C3—181no—
652C2×C3—271no—
653C2×C3—271no—
654C2×C3—271no—
655C2×C3—271no—
656C2×C3—271no—
657C2×C3—541no—
658C2×C3—541no—
659C2×C3—541no—
660C2×C3—541no—
661C2×C3—541no—
662C2×C3—541no—
663C2×C3—811no—
664C2×C3—811no—
665C2×C3—811no—
666C2×C3—811no—
667D3—91no—
668D3—271no—
669D3—271no—
670D3—271no—
671D3—541no—
672D3—811no—
673D3—1621no—
674D3#4184⋊C311yescharacteristic, direct product factor
675C22—811noSylow
676C3—21no—
677C3—31no—
678C3—61no—
679C3—61no—
680C3—61no—
681C3—61no—
682C3—121no—
683C3—121no—
684C3—121no—
685C3—181no—
686C3—181no—
687C3—361no—
688C3—361no—
689C3C2×#4184⋊C311yescharacteristic, complemented
690C3C3×D3×#27211yescharacteristic
691C2—31no—
692C2—271no—
693C2—811no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC3×#731C22×C3
FrattiniC32C3×D3×C3⋊D3
FittingC3×#6910C22
socleC32C2×C3×#272
LCSG ▷ C3×#731
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(#4184⋊C3)C2semidirect
2. C3×#4184⋊C3C2semidirect
3. D3×#6910C2semidirect
9. D3×#4184C3semidirect
10. C3×#6910C22semidirect
15. C3×D3×3−1+2D3semidirect
16. C3×D3×3−1+2D3semidirect
17. C3×D3×3−1+2D3semidirect
24. C3⋊#4184C2×C3semidirect
31. #4184⋊C3D3direct (N × H)
32. C3×#4184C2×C3semidirect
37. D3×#731C2×C3semidirect
60. C32×3−1+2C2×D3semidirect
61. C32×3−1+2C2×D3semidirect
62. C32×3−1+2C2×D3semidirect
73. #6910C2×D3semidirect
78. C3×#731C22×C3semidirect
113. D3×3−1+2C3×D3semidirect
114. D3×3−1+2C3×D3semidirect
162. C3×D3×C9C3×D3semidirect
176. #4184C3×D3semidirect
233. C3×3−1+2D32semidirect
234. C3×3−1+2D32semidirect
235. C3×3−1+2D32semidirect
236. C3×3−1+2C2×C3×D3semidirect
237. C3×3−1+2C2×C3×D3semidirect
252. C32×C9C2×C3×D3semidirect
277. #731C2×C3×D3semidirect
481. 3−1+2C3×D32semidirect
482. 3−1+2C3×D32semidirect
516. C3×C9C3×D32semidirect
674. D3#4184⋊C3direct (N × H)
689. C3C2×#4184⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊(#4184⋊C3)2
C3×#4184⋊C32
D3×#69102
C3×D3×AGL(1,ℤ/9)3
C3×D3×(C3⋊D3)⋊C33
C2×#4184⋊C33
D3×#41843