Finite Group Databasebeta

← C3×#10593401 #13166762

Subgroups — C3×#10593401 #13166762

Order 1728.

884 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3802C211yesmaximal, characteristic
2C2×C3×D32⋊C4C212yesmaximal, complemented
3C2×C3×D32⋊C4C212yesmaximal, complemented
4C3×#63883C211yesmaximal, characteristic, complemented
5C3×#63781C211yesmaximal, characteristic, complemented
6#10593401C311yesmaximal, characteristic, direct product factor
7C22×C3×D32C2212yes—
8C22×C3×#157C2212yes—
9C2×C3×C4×C3⋊D3C2211yescharacteristic
10C2×C32×D12—21no—
11C2×C3×#625—21no—
12C2×C3×#624C2211yescharacteristic
13C2×C3×#624C2211yescharacteristic
14C3×#3802—24no—
15C3×D32⋊C4—24no—
16C3×D32⋊C4—24no—
17C32×Dic3⋊C4—21no—
18C3×Dic3⋊Dic3—21no—
19C2×C3×D3×D4—61no—
20C2×#3802C2×C311yescharacteristic
21C2×D32⋊C4C2×C312yescomplemented
22C2×D32⋊C4C2×C312yescomplemented
23C3×D3×C4⋊C4—61no—
24#63883C2×C311yescharacteristic, complemented
25#63781C2×C311yescharacteristic, complemented
26C22×C3×C3⋊D3C2311yescharacteristic
27C22×C32×D3—22no—
28C2×C3×D32—22no—
29C2×C3×D32—22no—
30C2×C3×D32—22no—
31C2×C3×D32—22no—
32C2×C3×D32—22no—
33C2×C3×D32D414yes—
34C2×C3×#157—22no—
35C2×C3×#157—22no—
36C2×C3×#157—22no—
37C2×C33×C4D411yescharacteristic
38C2×C3×C3⋊Dic3D411yescharacteristic
39C3×C4×C3⋊D3—22no—
40C2×C32×Dic3—21no—
41C2×C32×Dic3—21no—
42C32×D12—24no—
43C3×#625—24no—
44C3×#624—21no—
45C3×#624—22no—
46C3×#624D412yescomplemented
47C3×#394—91nomaximal
48C23×C3×D3—62no—
49C22×D32C22×C312yes—
50C22×#157C22×C312yes—
51C2×C32×D4—61no—
52C2×C4×C3⋊D3C22×C311yescharacteristic
53C2×C3×#67—62no—
54C3×D3×D4—68no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—41no—
58C2×C3×C4×D3—61no—
59C2×C3×C4×D3—61no—
60C2×C3×C4×D3—61no—
61C2×C3×C4×D3—61no—
62C2×#625—21no—
63C2×#624C22×C311yescharacteristic
64C2×#624C22×C311yescharacteristic
65#3802—24no—
66D32⋊C4—24no—
67D32⋊C4—24no—
68C32×C4⋊C4—61no—
69C3×C4⋊Dic3—61no—
70C3×Dic3⋊C4—21no—
71C3×Dic3⋊C4—21no—
72C3×Dic3⋊C4—41no—
73C3×Dic3⋊C4—61no—
74Dic3⋊Dic3—21no—
75C22×C33C2×D411yescharacteristic
76C2×C3×C3⋊D3C2×D411yescharacteristic
77C2×C3×C3⋊D3C2×D412yes—
78C2×C3×C3⋊D3#4112yes—
79C2×C3×C3⋊D3#4111yescharacteristic
80C2×C32×D3—24no—
81C2×C32×D3—42no—
82C2×C32×D3—42no—
83C3×D32—24no—
84C3×D32—24no—
85C3×D32—42no—
86C3×D32—42no—
87C3×#157—42no—
88C33×C4—21no—
89C3×C3⋊Dic3—21no—
90C32×Dic3—22no—
91C32×Dic3—41no—
92C22×C3×D4—91no—
93C2×D3×D4—61no—
94C2×C3×C4⋊C4—91no—
95C2×C3×C22⋊C4—92no—
96C2×C3×C22⋊C4—92no—
97D3×C4⋊C4—61no—
98C3×#95—91no—
99C23×C32—62no—
100C22×C3⋊D3C23×C311yescharacteristic
101C22×C3×D3—22no—
102C22×C3×D3—22no—
103C22×C3×D3—42no—
104C22×C3×D3—64no—
105C22×C3×D3—61no—
106C22×C3×D3—61no—
107C22×C3×D3—64no—
108C22×C3×D3—122no—
109C22×C3×D3—122no—
110C22×C3×D3—122no—
111C22×C3×D3—122no—
112C2×D32—22no—
113C2×D32—22no—
114C2×D32—22no—
115C2×D32—22no—
116C2×D32—22no—
117C2×D32C3×D414yes—
118C2×#157—22no—
119C2×#157—22no—
120C2×#157—22no—
121C32×D4—64no—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—61no—
127C2×C32×C4—61no—
128C2×C32×C4C3×D411yescharacteristic
129C2×C3⋊Dic3C3×D411yescharacteristic
130C4×C3⋊D3—22no—
131C3×#67—68no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—61no—
139C2×C3×Dic3—61no—
140C3×D12—24no—
141C3×D12—24no—
142C3×D12—44no—
143C3×C4×D3—62no—
144C3×C4×D3—62no—
145C3×C4×D3—64no—
146C3×C4×D3—122no—
147C3×C4×D3—122no—
148#625—24no—
149#624—21no—
150#624—22no—
151#624C3×D412yescomplemented
152#394—91noSylow
153C2×C33#12011yescharacteristic
154C2×C33#12111yescharacteristic
155C2×C33#12411yescharacteristic
156C3×C3⋊D3#12112yes—
157C3×C3⋊D3#12312yes—
158C32×D3—44no—
159C24×C3—92no—
160C23×D3—62no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—121no—
164C2×C3×D4—181no—
165C2×C3×D4—184no—
166C22×C3×C4—91no—
167C22×C3×C4—91no—
168C22×C3×C4—91no—
169C22×C3×C4—92no—
170C2×#67—62no—
171D3×D4—68no—
172C2×D12—21no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—121no—
180C3×C4⋊C4—181no—
181C3×C22⋊C4—184no—
182C3×C22⋊C4—184no—
183C4⋊Dic3—61no—
184Dic3⋊C4—21no—
185Dic3⋊C4—61no—
186C22×C32—21no—
187C22×C32—21no—
188C22×C32—41no—
189C22×C32—41no—
190C22×C32—64no—
191C22×C32—122no—
192C22×C32—122no—
193C22×C32C2×C3×D411yescharacteristic
194C2×C3⋊D3C2×C3×D411yescharacteristic
195C2×C3⋊D3C2×C3×D412yes—
196C2×C3⋊D3C3×#4112yes—
197C2×C3⋊D3C3×#4111yescharacteristic
198C2×C3×D3—24no—
199C2×C3×D3—24no—
200C2×C3×D3—44no—
201C2×C3×D3—42no—
202C2×C3×D3—42no—
203C2×C3×D3—42no—
204C2×C3×D3—42no—
205C2×C3×D3—61no—
206C2×C3×D3—62no—
207C2×C3×D3—62no—
208C2×C3×D3—61no—
209C2×C3×D3—61no—
210C2×C3×D3—62no—
211C2×C3×D3—62no—
212C2×C3×D3—61no—
213C2×C3×D3—82no—
214C2×C3×D3—82no—
215C2×C3×D3—124no—
216C2×C3×D3—124no—
217C2×C3×D3—124no—
218C2×C3×D3—124no—
219D32—24no—
220D32—24no—
221D32—42no—
222D32—42no—
223#157—42no—
224C32×C4—22no—
225C32×C4—21no—
226C32×C4—41no—
227C32×C4—42no—
228C32×C4—62no—
229C32×C4—81no—
230C32×C4—121no—
231C3⋊Dic3—21no—
232C3×Dic3—22no—
233C3×Dic3—22no—
234C3×Dic3—42no—
235C3×Dic3—41no—
236C3×Dic3—41no—
237C3×Dic3—62no—
238C3×Dic3—81no—
239C3×Dic3—121no—
240C22×D4—91no—
241C2×C4⋊C4—91no—
242C2×C22⋊C4—92no—
243C2×C22⋊C4—92no—
244#95—91no—
245C33#39411yescharacteristic, complemented, Sylow
246C23×C3—62no—
247C23×C3—62no—
248C23×C3—94no—
249C23×C3—91no—
250C23×C3—122no—
251C23×C3—182no—
252C23×C3—182no—
253C23×C3—182no—
254C23×C3—182no—
255C23×C3—182no—
256C22×D3—22no—
257C22×D3—64no—
258C22×D3—61no—
259C22×D3—61no—
260C22×D3—64no—
261C22×D3—122no—
262C22×D3—122no—
263C22×D3—122no—
264C22×D3—122no—
265C3×D4—64no—
266C3×D4—64no—
267C3×D4—124no—
268C3×D4—184no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—92no—
278C2×C3×C4—91no—
279C2×C3×C4—121no—
280C2×C3×C4—121no—
281C2×C3×C4—182no—
282C2×C3×C4—181no—
283C2×C3×C4—182no—
284C2×C3×C4—182no—
285C2×C3×C4—182no—
286C2×C3×C4—182no—
287C2×C3×C4GO+(4,𝔽2)11yescharacteristic
288#67—68no—
289C2×Dic3—21no—
290C2×Dic3—21no—
291C2×Dic3—61no—
292C2×Dic3—61no—
293D12—24no—
294C4×D3—62no—
295C4×D3—62no—
296C4×D3—64no—
297C4×D3—122no—
298C4×D3—122no—
299C2×C32—21no—
300C2×C32—21no—
301C2×C32—21no—
302C2×C32—21no—
303C2×C32—21no—
304C2×C32—21no—
305C2×C32—41no—
306C2×C32—41no—
307C2×C32—41no—
308C2×C32—41no—
309C2×C32—41no—
310C2×C32—41no—
311C2×C32—124no—
312C2×C32C3×#12011yescharacteristic
313C2×C32C3×#12111yescharacteristic
314C2×C32C3×#12411yescharacteristic
315C3⋊D3C3×#12112yes—
316C3⋊D3C3×#12312yes—
317C3×D3—44no—
318C3×D3—44no—
319C3×D3—62no—
320C3×D3—62no—
321C3×D3—62no—
322C3×D3—62no—
323C3×D3—84no—
324C24—92no—
325C2×D4—61no—
326C2×D4—181no—
327C2×D4—184no—
328C22×C4—91no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—92no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C22⋊C4—184no—
335C22⋊C4—184no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—41no—
339C22×C3—41no—
340C22×C3—64no—
341C22×C3—64no—
342C22×C3—92no—
343C22×C3—91no—
344C22×C3—91no—
345C22×C3—92no—
346C22×C3—124no—
347C22×C3—122no—
348C22×C3—122no—
349C22×C3—122no—
350C22×C3—122no—
351C22×C3—184no—
352C22×C3—184no—
353C22×C3—242no—
354C22×C3—242no—
355C22×C3—362no—
356C22×C3—362no—
357C22×C3C2×GO+(4,𝔽2)11yescharacteristic
358C2×D3—24no—
359C2×D3—42no—
360C2×D3—42no—
361C2×D3—62no—
362C2×D3—61no—
363C2×D3—61no—
364C2×D3—62no—
365C2×D3—61no—
366C2×D3—62no—
367C2×D3—61no—
368C2×D3—62no—
369C2×D3—124no—
370C2×D3—124no—
371C2×D3—124no—
372C2×D3—124no—
373C3×C4—22no—
374C3×C4—21no—
375C3×C4—41no—
376C3×C4—42no—
377C3×C4—62no—
378C3×C4—62no—
379C3×C4—81no—
380C3×C4—122no—
381C3×C4—121no—
382C3×C4—121no—
383C3×C4—181no—
384C3×C4—241no—
385C3×C4—362no—
386Dic3—22no—
387Dic3—41no—
388Dic3—62no—
389Dic3—121no—
390C32—21no—
391C32—21no—
392C32—41no—
393C32—41no—
394C32C3×#39411yescharacteristic, complemented
395C23—62no—
396C23—94no—
397C23—91no—
398C23—182no—
399C23—182no—
400C23—182no—
401C23—182no—
402C23—182no—
403D4—64no—
404D4—184no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—92no—
408C2×C4—91no—
409C2×C4—182no—
410C2×C4—181no—
411C2×C4—182no—
412C2×C4—182no—
413C2×C4—182no—
414C2×C4—182no—
415C2×C4C3×GO+(4,𝔽2)11yescharacteristic
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—41no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—41no—
426C2×C3—41no—
427C2×C3—41no—
428C2×C3—92no—
429C2×C3—92no—
430C2×C3—124no—
431C2×C3—124no—
432C2×C3—244no—
433C2×C3#6422111yescharacteristic
434C2×C3#6423011yescharacteristic
435C2×C3#6424111yescharacteristic
436D3—44no—
437D3—62no—
438D3—62no—
439D3—62no—
440D3—62no—
441C22—64no—
442C22—92no—
443C22—92no—
444C22—91no—
445C22—91no—
446C22—122no—
447C22—122no—
448C22—184no—
449C22—184no—
450C22—362no—
451C22—362no—
452C22C2×C3×GO+(4,𝔽2)11yescharacteristic
453C4—21no—
454C4—62no—
455C4—121no—
456C4—181no—
457C4—362no—
458C3—21no—
459C3—21no—
460C3—41no—
461C3—41no—
462C3#1059340111yescharacteristic, direct product factor
463C2—92no—
464C2—92no—
465C2—124no—
466C2C3×#6422111yescharacteristic
467C2C3×#6423011yescharacteristic
468C2C3×#6424111yescharacteristic
subgroupG/H
centerC22×C3C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C23×C3
FrattiniC22C2×C3×GO+(4,𝔽2)
FittingC2×C33×C4D4
socleC22×C33C2×D4
prime radicalC2×C3×#3802C2
hypercenterC2×C3×C4GO+(4,𝔽2)
hypocenterC32C3×#394
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D32⋊C4C2semidirect
3. C2×C3×D32⋊C4C2semidirect
4. C3×#63883C2semidirect
5. C3×#63781C2semidirect
6. #10593401C3direct (N × H)
21. C2×D32⋊C4C2×C3semidirect
22. C2×D32⋊C4C2×C3semidirect
24. #63883C2×C3semidirect
25. #63781C2×C3semidirect
46. C3×#624D4semidirect
151. #624C3×D4semidirect
245. C33#394semidirect
394. C32C3×#394semidirect
462. C3#10593401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38022
C2×C3×D32⋊C42
C3×#638832
C3×#637812
#105934013
C3×#3949