Finite Group Databasebeta

← C3×#10593495 #13166893

Subgroups — C3×#10593495 #13166893

Order 1728.

496 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C3×#3792C211yesmaximal, characteristic, complemented
2C2×C3×#3775C211yesmaximal, characteristic, complemented
3C3×#63982C211yesmaximal, characteristic, complemented
4C3×#63980C211yesmaximal, characteristic
5C3×#63743C211yesmaximal, characteristic, complemented
6C3×#63740C211yesmaximal, characteristic, complemented
7C3×#63739C211yesmaximal, characteristic, complemented
8#10593495C311yesmaximal, characteristic, direct product factor
9C22×C3×C3⋊Dic3C2211yescharacteristic
10C2×C32×#67—21no—
11C2×C3×#627C2211yescharacteristic
12C2×C3×#625C2211yescharacteristic
13C3×#3792—22no—
14C2×C3×#622C2211yescharacteristic
15C2×C3×#622C2211yescharacteristic
16C3×#3775—22no—
17C32×#217—21no—
18C3×#3724C2211yescharacteristic
19C3×#3724C2211yescharacteristic
20C3×Dic3⋊Dic3—21no—
21C3×(C2×D3)⋊Dic3—21no—
22C2×#3792C2×C311yescharacteristic, complemented
23C2×#3775C2×C311yescharacteristic, complemented
24C3×#939—61no—
25C3×#878—61no—
26#63982C2×C311yescharacteristic, complemented
27#63980C2×C311yescharacteristic
28#63743C2×C311yescharacteristic, complemented
29#63740C2×C311yescharacteristic, complemented
30#63739C2×C311yescharacteristic, complemented
31C23×C33D411yescharacteristic
32C22×C32×D3—21no—
33C2×C3×C3⋊Dic3—21no—
34C2×C3×C3⋊Dic3—21no—
35C2×C3×C3⋊Dic3D411yescharacteristic
36C2×C3×C3⋊Dic3C2311yescharacteristic
37C32×#67—42no—
38C2×C32×Dic3—21no—
39C2×C32×Dic3—21no—
40C2×C32×Dic3—21no—
41C3×#627—21no—
42C3×#627—21no—
43C3×#625—21no—
44C3×#625—21no—
45C3×#622—21no—
46C3×#622D412yescomplemented
47C3×#468—91nomaximal
48C2×C32×D4—61no—
49C22×C3⋊Dic3C22×C311yescharacteristic
50C2×C3×#67—21no—
51C2×C3×#67—21no—
52C2×C3×#67—41no—
53C2×C3×#67—61no—
54C22×C3×Dic3—61no—
55C22×C3×Dic3—61no—
56C2×C3×Dic6—61no—
57C2×#627C22×C311yescharacteristic
58C2×#625C22×C311yescharacteristic
59#3792—22no—
60C2×#622C22×C311yescharacteristic
61C2×#622C22×C311yescharacteristic
62#3775—22no—
63C32×C22⋊C4—61no—
64C3×#217—21no—
65C3×#217—21no—
66C3×#217—41no—
67C3×#217—61no—
68C3×(C2×D3)⋊C4—61no—
69C3×C4⋊Dic3—61no—
70C3×Dic3⋊C4—61no—
71C3×Dic3⋊C4—61no—
72C3×Dic3⋊C4—61no—
73#3724C22×C311yescharacteristic
74#3724C22×C311yescharacteristic
75Dic3⋊Dic3—21no—
76(C2×D3)⋊Dic3—21no—
77C22×C33—21no—
78C22×C33—21no—
79C22×C33—21no—
80C22×C33C2×D411yescharacteristic
81C2×C32×D3—41no—
82C2×C32×D3—41no—
83C2×C32×D3—41no—
84C3×C3⋊Dic3—21no—
85C3×C3⋊Dic3C2×D411yescharacteristic
86C3×C3⋊Dic3#4111yescharacteristic
87C32×Dic3—41no—
88C32×Dic3—41no—
89C32×Dic3—41no—
90C2×C3×SD16—91no—
91C2×C3×M16—91no—
92C3×C22⋊Q8—91no—
93C3×#121—91no—
94#939—61no—
95#878—61no—
96C3×#107—91no—
97C3×#103—91no—
98C3×#102—91no—
99C23×C32—21no—
100C23×C32—21no—
101C23×C32—41no—
102C23×C32—41no—
103C23×C32—61no—
104C23×C32C3×D411yescharacteristic
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—41no—
108C32×D4—122no—
109C2×C32×C4—61no—
110C2×C32×C4—61no—
111C2×C32×C4—61no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3C3×D411yescharacteristic
115C2×C3⋊Dic3C23×C311yescharacteristic
116C3×#67—42no—
117C3×#67—42no—
118C3×#67—44no—
119C3×#67—121no—
120C3×#67—121no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—61no—
131C2×C3×Dic3—61no—
132C2×C3×Dic3—61no—
133C2×C3×Dic3—61no—
134C2×C3×Dic3—121no—
135C2×C3×Dic3—121no—
136C2×C3×Dic3—121no—
137C2×C3×Dic3—121no—
138C3×Dic6—121no—
139C3×Dic6—121no—
140#627—21no—
141#627—21no—
142#625—21no—
143#625—21no—
144#622—21no—
145#622C3×D412yescomplemented
146#468—91noSylow
147C2×C33—41no—
148C2×C33#12111yescharacteristic
149C2×C33AGL(1,ℤ/8)11yescharacteristic
150C2×C33#13711yescharacteristic
151C32×D3—81no—
152C2×C3×Q8—91no—
153C2×C3×D4—61no—
154C2×C3×D4—61no—
155C2×C3×D4—91no—
156C2×C3×D4—121no—
157C22×C3×C4—91no—
158C2×#67—21no—
159C2×#67—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C2×Dic6—61no—
163C3×SD16—182no—
164C3×M16—182no—
165C2×C3×C8—91no—
166C2×C3×C8—91no—
167C3×C4⋊C4—91no—
168C3×C4⋊C4—91no—
169C3×C4⋊C4—181no—
170C3×C22⋊C4—61no—
171C3×C22⋊C4—61no—
172C3×C22⋊C4—121no—
173C3×C22⋊C4—181no—
174#217—21no—
175#217—61no—
176(C2×D3)⋊C4—61no—
177C4⋊Dic3—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181C22×C32—22no—
182C22×C32—22no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—41no—
193C22×C32—41no—
194C22×C32—42no—
195C22×C32—42no—
196C22×C32—81no—
197C22×C32—81no—
198C22×C32—81no—
199C22×C32—81no—
200C22×C32—121no—
201C22×C32—121no—
202C22×C32—121no—
203C22×C32C2×C3×D411yescharacteristic
204C2×C3×D3—41no—
205C2×C3×D3—41no—
206C2×C3×D3—41no—
207C2×C3×D3—42no—
208C2×C3×D3—41no—
209C2×C3×D3—41no—
210C2×C3×D3—41no—
211C2×C3×D3—81no—
212C2×C3×D3—81no—
213C32×C4—121no—
214C32×C4—121no—
215C32×C4—121no—
216C3⋊Dic3—21no—
217C3⋊Dic3C2×C3×D411yescharacteristic
218C3⋊Dic3C3×#4111yescharacteristic
219C3×Dic3—41no—
220C3×Dic3—41no—
221C3×Dic3—41no—
222C3×Dic3—42no—
223C3×Dic3—41no—
224C3×Dic3—41no—
225C3×Dic3—41no—
226C3×Dic3—61no—
227C3×Dic3—61no—
228C3×Dic3—61no—
229C3×Dic3—61no—
230C3×Dic3—81no—
231C3×Dic3—81no—
232C3×Dic3—121no—
233C3×Dic3—121no—
234C2×SD16—91no—
235C2×M16—91no—
236C22⋊Q8—91no—
237#121—91no—
238#107—91no—
239#103—91no—
240#102—91no—
241C33#46811yescharacteristic, complemented, Sylow
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—41no—
245C23×C3—41no—
246C23×C3—61no—
247C23×C3—61no—
248C23×C3—121no—
249C23×C3GO+(4,𝔽2)11yescharacteristic
250C22×D3—21no—
251C3×Q8—181no—
252C3×Q8—181no—
253C3×D4—122no—
254C3×D4—122no—
255C3×D4—124no—
256C3×D4—181no—
257C3×D4—181no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—91no—
265C2×C3×C4—91no—
266C2×C3×C4—121no—
267C2×C3×C4—121no—
268C2×C3×C4—121no—
269C2×C3×C4—181no—
270C2×C3×C4—181no—
271#67—42no—
272#67—121no—
273#67—121no—
274C2×Dic3—21no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—61no—
280C2×Dic3—61no—
281C2×Dic3—121no—
282C2×Dic3—121no—
283C2×Dic3—121no—
284C2×Dic3—121no—
285Dic6—121no—
286Dic6—121no—
287C3×C8—92no—
288C3×C8—181no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—21no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—21no—
295C2×C32—41no—
296C2×C32—41no—
297C2×C32—41no—
298C2×C32—41no—
299C2×C32—41no—
300C2×C32—41no—
301C2×C32—41no—
302C2×C32—42no—
303C2×C32—42no—
304C2×C32—82no—
305C2×C32—82no—
306C2×C32—241no—
307C2×C32C3×#12111yescharacteristic
308C2×C32C3×AGL(1,ℤ/8)11yescharacteristic
309C2×C32C3×#13711yescharacteristic
310C3×D3—81no—
311C3×D3—82no—
312C3×D3—81no—
313C2×Q8—91no—
314C2×D4—61no—
315C2×D4—91no—
316C22×C4—91no—
317SD16—182no—
318M16—182no—
319C2×C8—91no—
320C2×C8—91no—
321C4⋊C4—91no—
322C4⋊C4—91no—
323C4⋊C4—181no—
324C22⋊C4—61no—
325C22⋊C4—181no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—41no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3—42no—
338C22×C3—42no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—81no—
342C22×C3—81no—
343C22×C3—81no—
344C22×C3—81no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3—121no—
348C22×C3—122no—
349C22×C3—121no—
350C22×C3—121no—
351C22×C3—121no—
352C22×C3—241no—
353C22×C3—241no—
354C22×C3C2×GO+(4,𝔽2)11yescharacteristic
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C3×C4—91no—
359C3×C4—91no—
360C3×C4—121no—
361C3×C4—121no—
362C3×C4—121no—
363C3×C4—122no—
364C3×C4—121no—
365C3×C4—121no—
366C3×C4—121no—
367C3×C4—181no—
368C3×C4—241no—
369C3×C4—241no—
370Dic3—41no—
371Dic3—41no—
372Dic3—41no—
373Dic3—61no—
374Dic3—61no—
375Dic3—61no—
376Dic3—61no—
377Dic3—121no—
378Dic3—121no—
379C32—21no—
380C32—21no—
381C32—41no—
382C32—41no—
383C32C3×#46811yescharacteristic, complemented
384C23—61no—
385C23C3×GO+(4,𝔽2)11yescharacteristic
386Q8—181no—
387Q8—181no—
388D4—122no—
389D4—181no—
390D4—181no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—91no—
395C2×C4—91no—
396C2×C4—181no—
397C2×C4—181no—
398C8—92no—
399C8—181no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—21no—
406C2×C3—42no—
407C2×C3—42no—
408C2×C3—41no—
409C2×C3—41no—
410C2×C3—41no—
411C2×C3—41no—
412C2×C3—41no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—82no—
416C2×C3—82no—
417C2×C3—241no—
418C2×C3—242no—
419C2×C3—241no—
420C2×C3#6423611yescharacteristic
421C2×C3#6423911yescharacteristic
422C2×C3#6424211yescharacteristic
423D3—81no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—121no—
428C22—121no—
429C22—121no—
430C22C2×C3×GO+(4,𝔽2)11yescharacteristic
431C4—91no—
432C4—91no—
433C4—121no—
434C4—121no—
435C4—121no—
436C4—181no—
437C3—21no—
438C3—21no—
439C3—41no—
440C3—41no—
441C3#1059349511yescharacteristic, direct product factor
442C2—41no—
443C2—241no—
444C2C3×#6423611yescharacteristic
445C2C3×#6423911yescharacteristic
446C2C3×#6424211yescharacteristic
subgroupG/H
centerC22×C3C2×GO+(4,𝔽2)
commutator, cosocleC2×C3⋊Dic3C23×C3
FrattiniC22C2×C3×GO+(4,𝔽2)
FittingC23×C33D4
socleC22×C33C2×D4
prime radicalC3×#63980C2
hypercenterC23×C3GO+(4,𝔽2)
hypocenterC32C3×#468
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C23×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3792C2semidirect
2. C2×C3×#3775C2semidirect
3. C3×#63982C2semidirect
5. C3×#63743C2semidirect
6. C3×#63740C2semidirect
7. C3×#63739C2semidirect
8. #10593495C3direct (N × H)
22. C2×#3792C2×C3semidirect
23. C2×#3775C2×C3semidirect
26. #63982C2×C3semidirect
28. #63743C2×C3semidirect
29. #63740C2×C3semidirect
30. #63739C2×C3semidirect
46. C3×#622D4semidirect
145. #622C3×D4semidirect
241. C33#468semidirect
383. C32C3×#468semidirect
441. C3#10593495direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#37922
C2×C3×#37752
C3×#639822
C3×#639802
C3×#637432
C3×#637402
C3×#637392
#105934953
C3×#4689