Finite Group Databasebeta

← D3×#92262 #72254048

Subgroups — D3×#92262 #72254048

Order 2916.

592 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 79 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⋊#92262C211yesmaximal, characteristic, complemented
2C3×#92262C211yesmaximal, characteristic, complemented
3D3×C9⋊H(3,𝔽3)C211yesmaximal, characteristic, complemented
4D3×C9×C3⋊D3C311yesmaximal, characteristic, complemented
5D32×3−1+2—31nomaximal
6C3×D3×(C3⋊D3)⋊C3C311yesmaximal, characteristic
7C2×#92262—31nomaximal
8D3×(C3⋊D3)⋊C9C311yesmaximal, characteristic, complemented
9D3×(C3⋊D3)⋊C9C311yesmaximal, characteristic, complemented
10C3×C9⋊H(3,𝔽3)C2211yescharacteristic, complemented, Sylow
11C9×C3⋊(C3⋊D3)C2×C311yescharacteristic, complemented
12C3⋊D3×3−1+2—31no—
13C3×C3⋊((C3⋊D3)⋊C3)C2×C311yescharacteristic
14C3×C9×C3⋊D3C2×C311yescharacteristic, complemented
15C3×D3×3−1+2—21no—
16C3×D3×3−1+2—31no—
17C3×D3×3−1+2D311yescharacteristic, complemented
18C3×D3×H(3,𝔽3)C2×C311yescharacteristic
19C32×(C3⋊D3)⋊C3C2×C311yescharacteristic
20C32×D3×C9C2×C311yescharacteristic, complemented
21C2×C9⋊H(3,𝔽3)—31no—
22C3⋊((C3⋊D3)⋊C9)C2×C311yescharacteristic, complemented
23C3⋊((C3⋊D3)⋊C9)C2×C311yescharacteristic, complemented
24#92262—21no—
25#92262—21no—
26#92262—21no—
27#92262—21no—
28#92262—31no—
29#92262—61no—
30#92262D311yescharacteristic, direct product factor
31D3×C32⋊C9—21no—
32D3×C32⋊C9—21no—
33D3×C32⋊C9—21no—
34D3×C32⋊C9C2×C311yescharacteristic, complemented
35D3×C32⋊C9C2×C311yescharacteristic, complemented
36C3×(C3⋊D3)⋊C9C2×C311yescharacteristic, complemented
37C3×(C3⋊D3)⋊C9C2×C311yescharacteristic, complemented
38C3×D3×C3⋊D3C3211yescharacteristic
39C32×D32—31no—
40C2×C9×C3⋊D3—31no—
41C2×D3×3−1+2—91no—
42C2×D3×3−1+2—91no—
43C2×C3×(C3⋊D3)⋊C3—31no—
44D3×(C3⋊D3)⋊C3—31no—
45D32×C9—31no—
46D32×C9—31no—
47D32×C9—31no—
48D32×C9—91no—
49C2×(C3⋊D3)⋊C9—31no—
50C2×(C3⋊D3)⋊C9—31no—
51C32×3−1+2—21no—
52C32×3−1+2C2×D311yescharacteristic, complemented
53C32×H(3,𝔽3)C22×C311yescharacteristic
54C33×C9C22×C311yescharacteristic, complemented
55C9⋊H(3,𝔽3)—21no—
56C9⋊H(3,𝔽3)—21no—
57C9⋊H(3,𝔽3)—21no—
58C9⋊H(3,𝔽3)—21no—
59C9⋊H(3,𝔽3)—21no—
60C9⋊H(3,𝔽3)—41no—
61C9⋊H(3,𝔽3)—41no—
62C9⋊H(3,𝔽3)—41no—
63C9⋊H(3,𝔽3)—41no—
64C9⋊H(3,𝔽3)C2×D311yescharacteristic, complemented
65C3×C32⋊C9—21no—
66C3×C32⋊C9—21no—
67C3×C32⋊C9—21no—
68C3×C32⋊C9C22×C311yescharacteristic, complemented
69C3×C32⋊C9C22×C311yescharacteristic, complemented
70C3×C3⋊(C3⋊D3)C2×C3211yescharacteristic
71C32×C3⋊D3—31no—
72C32×C3⋊D3C2×C3211yescharacteristic
73C33×D3—21no—
74C33×D3—31no—
75C33×D3C3×D311yescharacteristic
76C33×D3C2×C3211yescharacteristic
77C2×C3×3−1+2—31no—
78C2×C3×3−1+2—61no—
79C2×C3×3−1+2—91no—
80C2×C3×H(3,𝔽3)—31no—
81C2×C32×C9—31no—
82C3⋊((C3⋊D3)⋊C3)—31no—
83C9×C3⋊D3—21no—
84C9×C3⋊D3—31no—
85C9×C3⋊D3—31no—
86C9×C3⋊D3—31no—
87C9×C3⋊D3—31no—
88C9×C3⋊D3—61no—
89C9×C3⋊D3—91no—
90C9×C3⋊D3—181no—
91C9×C3⋊D3C3×D311yescharacteristic, complemented
92D3×3−1+2—31no—
93D3×3−1+2—62no—
94D3×3−1+2—61no—
95D3×3−1+2—61no—
96D3×3−1+2—61no—
97D3×3−1+2—61no—
98D3×3−1+2—61no—
99D3×3−1+2—61no—
100D3×3−1+2—61no—
101D3×3−1+2—91no—
102D3×3−1+2—91no—
103D3×3−1+2—181no—
104D3×H(3,𝔽3)—31no—
105D3×H(3,𝔽3)—61no—
106C3×(C3⋊D3)⋊C3—21no—
107C3×(C3⋊D3)⋊C3—31no—
108C3×(C3⋊D3)⋊C3—31no—
109C3×(C3⋊D3)⋊C3—61no—
110C3×(C3⋊D3)⋊C3—61no—
111C3×(C3⋊D3)⋊C3C3×D311yescharacteristic
112C3×D3×C9—21no—
113C3×D3×C9—21no—
114C3×D3×C9—21no—
115C3×D3×C9—31no—
116C3×D3×C9—31no—
117C3×D3×C9—31no—
118C3×D3×C9—31no—
119C3×D3×C9—61no—
120C3×D3×C9—91no—
121C3×D3×C9C3×D311yescharacteristic
122C3×D3×C9C3×D311yescharacteristic
123C3×D3×C9C3×D311yescharacteristic
124C2×C32⋊C9—31no—
125C2×C32⋊C9—31no—
126C2×C32⋊C9—61no—
127C2×C32⋊C9—61no—
128C2×C32⋊C9—61no—
129(C3⋊D3)⋊C9—21no—
130(C3⋊D3)⋊C9—21no—
131(C3⋊D3)⋊C9—31no—
132(C3⋊D3)⋊C9—31no—
133(C3⋊D3)⋊C9—61no—
134(C3⋊D3)⋊C9—61no—
135(C3⋊D3)⋊C9C3×D311yescharacteristic, complemented
136(C3⋊D3)⋊C9C3×D311yescharacteristic, complemented
137C2×C3×C3⋊D3—31no—
138C2×C32×D3—91no—
139C2×C32×D3—91no—
140D3×C3⋊D33−1+211yescharacteristic, complemented
141C3×D32—31no—
142C3×D32—91no—
143C3×D32—91no—
144C22×3−1+2—271no—
145C2×(C3⋊D3)⋊C3—91no—
146C2×D3×C9—91no—
147C2×D3×C9—91no—
148C2×D3×C9—91no—
149C2×D3×C9—91no—
150C2×D3×C9—91no—
151C2×D3×C9—91no—
152C2×D3×C9—271no—
153C34—21no—
154C34C2×C3×D311yescharacteristic
155C34C22×C3211yescharacteristic
156C3×3−1+2—21no—
157C3×3−1+2—21no—
158C3×3−1+2—21no—
159C3×3−1+2—21no—
160C3×3−1+2—21no—
161C3×3−1+2—41no—
162C3×3−1+2—41no—
163C3×3−1+2—41no—
164C3×3−1+2—41no—
165C3×3−1+2—62no—
166C3×3−1+2—61no—
167C3×3−1+2—61no—
168C3×3−1+2—61no—
169C3×3−1+2—121no—
170C3×3−1+2—121no—
171C3×3−1+2—121no—
172C3×3−1+2—122no—
173C3×3−1+2D3211yescharacteristic, complemented
174C3×H(3,𝔽3)—21no—
175C3×H(3,𝔽3)—21no—
176C3×H(3,𝔽3)—31no—
177C3×H(3,𝔽3)—41no—
178C3×H(3,𝔽3)—61no—
179C3×H(3,𝔽3)—61no—
180C3×H(3,𝔽3)—121no—
181C3×H(3,𝔽3)C2×C3×D311yescharacteristic
182C32×C9—21no—
183C32×C9—21no—
184C32×C9—21no—
185C32×C9—21no—
186C32×C9—21no—
187C32×C9—31no—
188C32×C9—41no—
189C32×C9—61no—
190C32×C9—61no—
191C32×C9—121no—
192C32×C9C2×C3×D311yescharacteristic
193C32×C9C2×C3×D311yescharacteristic
194C32×C9C2×C3×D311yescharacteristic
195C32×C9C2×C3×D311yescharacteristic, complemented
196C32⋊C9—21no—
197C32⋊C9—21no—
198C32⋊C9—21no—
199C32⋊C9—21no—
200C32⋊C9—21no—
201C32⋊C9—21no—
202C32⋊C9—21no—
203C32⋊C9—41no—
204C32⋊C9—41no—
205C32⋊C9—41no—
206C32⋊C9—41no—
207C32⋊C9—41no—
208C32⋊C9—41no—
209C32⋊C9—41no—
210C32⋊C9—41no—
211C32⋊C9—41no—
212C32⋊C9—41no—
213C32⋊C9—41no—
214C32⋊C9—41no—
215C32⋊C9—41no—
216C32⋊C9—41no—
217C32⋊C9C2×C3×D311yescharacteristic, complemented
218C32⋊C9C2×C3×D311yescharacteristic, complemented
219C2×C33—31no—
220C2×C33—31no—
221C2×C33—61no—
222C2×C33—91no—
223C3⋊(C3⋊D3)C2×3−1+211yescharacteristic, complemented
224C3×C3⋊D3—21no—
225C3×C3⋊D3—31no—
226C3×C3⋊D3—31no—
227C3×C3⋊D3—61no—
228C3×C3⋊D3—91no—
229C3×C3⋊D3—91no—
230C3×C3⋊D3—181no—
231C3×C3⋊D3C2×3−1+211yescharacteristic, complemented
232C3×C3⋊D3C32×D311yescharacteristic
233C32×D3—21no—
234C32×D3—31no—
235C32×D3—31no—
236C32×D3—31no—
237C32×D3—31no—
238C32×D3—61no—
239C32×D3—61no—
240C32×D3—62no—
241C32×D3—61no—
242C32×D3—61no—
243C32×D3—61no—
244C32×D3—61no—
245C32×D3—91no—
246C32×D3—91no—
247C32×D3—91no—
248C32×D3—91no—
249C32×D3—181no—
250C32×D3—181no—
251C32×D3C2×3−1+211yescharacteristic, complemented
252C32×D3C32×D311yescharacteristic
253C2×3−1+2—91no—
254C2×3−1+2—181no—
255C2×3−1+2—181no—
256C2×3−1+2—181no—
257C2×3−1+2—182no—
258C2×3−1+2—181no—
259C2×3−1+2—181no—
260C2×3−1+2—181no—
261C2×3−1+2—181no—
262C2×3−1+2—271no—
263C2×H(3,𝔽3)—91no—
264C2×H(3,𝔽3)—181no—
265C2×C3×C9—31no—
266C2×C3×C9—31no—
267C2×C3×C9—31no—
268C2×C3×C9—61no—
269C2×C3×C9—61no—
270C2×C3×C9—61no—
271C2×C3×C9—91no—
272C2×C3×C9—91no—
273C2×C3×C9—91no—
274C2×C3×C9—91no—
275C2×C3×C9—181no—
276(C3⋊D3)⋊C3—31no—
277(C3⋊D3)⋊C3—61no—
278(C3⋊D3)⋊C3—91no—
279(C3⋊D3)⋊C3—181no—
280D3×C9—21no—
281D3×C9—31no—
282D3×C9—31no—
283D3×C9—31no—
284D3×C9—61no—
285D3×C9—61no—
286D3×C9—61no—
287D3×C9—61no—
288D3×C9—61no—
289D3×C9—61no—
290D3×C9—61no—
291D3×C9—61no—
292D3×C9—91no—
293D3×C9—91no—
294D3×C9—91no—
295D3×C9—91no—
296D3×C9—91no—
297D3×C9—91no—
298D3×C9—91no—
299D3×C9—181no—
300D3×C9—181no—
301D3×C9—181no—
302D3×C9—181no—
303D3×C9—271no—
304D3×C9—541no—
305D3×C9(C3⋊D3)⋊C311yescharacteristic, complemented
306C22×C32—271no—
307C2×C3⋊D3—31no—
308C2×C3×D3—91no—
309C2×C3×D3—91no—
310C2×C3×D3—271no—
311C2×C3×D3—271no—
312C2×C3×D3—271no—
313D32—31no—
314D32—91no—
315C22×C9—271no—
316C22×C9—271no—
317C22×C9—271no—
318C33—21no—
319C33—21no—
320C33—21no—
321C33—21no—
322C33—21no—
323C33—31no—
324C33—31no—
325C33—41no—
326C33—41no—
327C33—61no—
328C33—61no—
329C33—61no—
330C33—61no—
331C33—62no—
332C33—61no—
333C33—61no—
334C33—61no—
335C33—121no—
336C33—121no—
337C33—121no—
338C33—121no—
339C33—122no—
340C33—121no—
341C33C22×3−1+211yescharacteristic, complemented
342C33C3×D3211yescharacteristic
343C33C2×C32×D311yescharacteristic
344C33C2×C32×D311yescharacteristic
3453−1+2—61no—
3463−1+2—62no—
3473−1+2—61no—
3483−1+2—61no—
3493−1+2—61no—
3503−1+2—121no—
3513−1+2—121no—
3523−1+2—121no—
3533−1+2—121no—
3543−1+2—121no—
3553−1+2—121no—
3563−1+2—122no—
3573−1+2—121no—
3583−1+2—121no—
3593−1+2—121no—
3603−1+2—122no—
3613−1+2—122no—
3623−1+2—122no—
3633−1+2—121no—
3643−1+2—121no—
365H(3,𝔽3)—31no—
366H(3,𝔽3)—61no—
367H(3,𝔽3)—61no—
368H(3,𝔽3)—61no—
369H(3,𝔽3)—121no—
370H(3,𝔽3)—121no—
371H(3,𝔽3)—121no—
372H(3,𝔽3)—122no—
373C3×C9—21no—
374C3×C9—21no—
375C3×C9—21no—
376C3×C9—21no—
377C3×C9—21no—
378C3×C9—21no—
379C3×C9—21no—
380C3×C9—21no—
381C3×C9—31no—
382C3×C9—41no—
383C3×C9—41no—
384C3×C9—41no—
385C3×C9—41no—
386C3×C9—61no—
387C3×C9—61no—
388C3×C9—61no—
389C3×C9—61no—
390C3×C9—61no—
391C3×C9—61no—
392C3×C9—61no—
393C3×C9—61no—
394C3×C9—61no—
395C3×C9—121no—
396C3×C9—121no—
397C3×C9—122no—
398C3×C9—121no—
399C3×C9—121no—
400C3×C9—121no—
401C3×C9—121no—
402C3×C9—121no—
403C3×C9C2×(C3⋊D3)⋊C311yescharacteristic, complemented
404C3×C9C3×D3211yescharacteristic
405C3×C9C3×D3211yescharacteristic
406C3×C9C3×D3211yescharacteristic
407C2×C32—31no—
408C2×C32—31no—
409C2×C32—61no—
410C2×C32—91no—
411C2×C32—91no—
412C2×C32—91no—
413C2×C32—91no—
414C2×C32—181no—
415C2×C32—181no—
416C2×C32—181no—
417C2×C32—181no—
418C2×C32—181no—
419C2×C32—182no—
420C2×C32—181no—
421C2×C32—271no—
422C2×C32—271no—
423C2×C32—541no—
424C3⋊D3—31no—
425C3⋊D3—31no—
426C3⋊D3—61no—
427C3⋊D3—91no—
428C3⋊D3—181no—
429C3⋊D3D3×3−1+211yescharacteristic, complemented
430C3×D3—21no—
431C3×D3—31no—
432C3×D3—31no—
433C3×D3—31no—
434C3×D3—61no—
435C3×D3—61no—
436C3×D3—91no—
437C3×D3—91no—
438C3×D3—91no—
439C3×D3—91no—
440C3×D3—91no—
441C3×D3—91no—
442C3×D3—181no—
443C3×D3—181no—
444C3×D3—181no—
445C3×D3—181no—
446C3×D3—271no—
447C3×D3—271no—
448C3×D3—271no—
449C3×D3—541no—
450C3×D3—541no—
451C3×D3C3×(C3⋊D3)⋊C311yescharacteristic
452C3×D3D3×3−1+211yescharacteristic
453C2×C9—31no—
454C2×C9—61no—
455C2×C9—91no—
456C2×C9—91no—
457C2×C9—91no—
458C2×C9—91no—
459C2×C9—181no—
460C2×C9—181no—
461C2×C9—181no—
462C2×C9—181no—
463C2×C9—181no—
464C2×C9—181no—
465C2×C9—181no—
466C2×C9—271no—
467C2×C9—271no—
468C2×C9—271no—
469C22×C3—271no—
470C22×C3—811no—
471C2×D3—91no—
472C2×D3—91no—
473C2×D3—271no—
474C32—21no—
475C32—21no—
476C32—21no—
477C32—21no—
478C32—21no—
479C32—31no—
480C32—31no—
481C32—31no—
482C32—41no—
483C32—41no—
484C32—61no—
485C32—61no—
486C32—61no—
487C32—61no—
488C32—62no—
489C32—61no—
490C32—61no—
491C32—61no—
492C32—61no—
493C32—61no—
494C32—61no—
495C32—91no—
496C32—121no—
497C32—121no—
498C32—121no—
499C32—121no—
500C32—122no—
501C32—121no—
502C32—122no—
503C32—121no—
504C32—121no—
505C32—121no—
506C32—181no—
507C32—361no—
508C32—361no—
509C32—361no—
510C32—361no—
511C32—361no—
512C32—362no—
513C32C2×C3×(C3⋊D3)⋊C311yescharacteristic
514C32C2×D3×3−1+211yescharacteristic
515C32C2×D3×3−1+211yescharacteristic, complemented
516C32C32×D3211yescharacteristic
517C9—21no—
518C9—21no—
519C9—31no—
520C9—41no—
521C9—61no—
522C9—61no—
523C9—61no—
524C9—61no—
525C9—61no—
526C9—121no—
527C9—121no—
528C9—121no—
529C9—121no—
530C9D3×(C3⋊D3)⋊C311yescharacteristic, complemented
531C2×C3—31no—
532C2×C3—31no—
533C2×C3—61no—
534C2×C3—91no—
535C2×C3—91no—
536C2×C3—91no—
537C2×C3—181no—
538C2×C3—181no—
539C2×C3—271no—
540C2×C3—271no—
541C2×C3—271no—
542C2×C3—541no—
543C2×C3—541no—
544C2×C3—811no—
545D3—31no—
546D3—91no—
547D3—91no—
548D3—91no—
549D3—181no—
550D3—271no—
551D3—541no—
552D3#9226211yescharacteristic, direct product factor
553C22—271noSylow
554C3—21no—
555C3—21no—
556C3—21no—
557C3—31no—
558C3—41no—
559C3—61no—
560C3—61no—
561C3—91no—
562C3—121no—
563C3—181no—
564C3—181no—
565C3—361no—
566C3C2×#9226211yescharacteristic, complemented
567C3C3×D3×(C3⋊D3)⋊C311yescharacteristic
568C3D32×3−1+211yescharacteristic
569C2—31no—
570C2—91no—
571C2—271no—
subgroupG/H
centerC3C3×D3×(C3⋊D3)⋊C3
commutator, cosocleC34C22×C32
FrattiniC32C32×D32
FittingC3×C9⋊H(3,𝔽3)C22
socleC33C2×C32×D3
prime radicalC3×D3×(C3⋊D3)⋊C3C3
hypercenterC9D3×(C3⋊D3)⋊C3
hypocenterC33C22×3−1+2
LCSG ▷ C34 ▷ C33
UCSC1 ◁ C3 ◁ C9

Complements

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

NH ≅ G/Ntype
1. C3⋊#92262C2semidirect
2. C3×#92262C2semidirect
3. D3×C9⋊H(3,𝔽3)C2semidirect
4. D3×C9×C3⋊D3C3semidirect
8. D3×(C3⋊D3)⋊C9C3semidirect
9. D3×(C3⋊D3)⋊C9C3semidirect
10. C3×C9⋊H(3,𝔽3)C22semidirect
11. C9×C3⋊(C3⋊D3)C2×C3semidirect
14. C3×C9×C3⋊D3C2×C3semidirect
17. C3×D3×3−1+2D3semidirect
20. C32×D3×C9C2×C3semidirect
22. C3⋊((C3⋊D3)⋊C9)C2×C3semidirect
23. C3⋊((C3⋊D3)⋊C9)C2×C3semidirect
30. #92262D3direct (N × H)
34. D3×C32⋊C9C2×C3semidirect
35. D3×C32⋊C9C2×C3semidirect
36. C3×(C3⋊D3)⋊C9C2×C3semidirect
37. C3×(C3⋊D3)⋊C9C2×C3semidirect
52. C32×3−1+2C2×D3semidirect
54. C33×C9C22×C3semidirect
64. C9⋊H(3,𝔽3)C2×D3semidirect
68. C3×C32⋊C9C22×C3semidirect
69. C3×C32⋊C9C22×C3semidirect
91. C9×C3⋊D3C3×D3semidirect
135. (C3⋊D3)⋊C9C3×D3semidirect
136. (C3⋊D3)⋊C9C3×D3semidirect
140. D3×C3⋊D33−1+2semidirect
173. C3×3−1+2D32semidirect
195. C32×C9C2×C3×D3semidirect
217. C32⋊C9C2×C3×D3semidirect
218. C32⋊C9C2×C3×D3semidirect
223. C3⋊(C3⋊D3)C2×3−1+2semidirect
231. C3×C3⋊D3C2×3−1+2semidirect
251. C32×D3C2×3−1+2semidirect
305. D3×C9(C3⋊D3)⋊C3semidirect
341. C33C22×3−1+2semidirect
403. C3×C9C2×(C3⋊D3)⋊C3semidirect
429. C3⋊D3D3×3−1+2semidirect
515. C32C2×D3×3−1+2semidirect
530. C9D3×(C3⋊D3)⋊C3semidirect
552. D3#92262direct (N × H)
566. C3C2×#92262semidirect

Maximal subgroups

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

subgroupindex
C3⋊#922622
C3×#922622
D3×C9⋊H(3,𝔽3)2
D3×C9×C3⋊D33
D32×3−1+23
C3×D3×(C3⋊D3)⋊C33
C2×#922623
D3×(C3⋊D3)⋊C93