Finite Group Databasebeta

← D3×#63786 #13166607

Subgroups — D3×#63786 #13166607

Order 1728.

1000 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 68 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×D3×#638C211yesmaximal, characteristic
2D3×C22⋊#157C212yesmaximal, complemented
3#11723111C211yesmaximal, characteristic, complemented
4C3×#63786C211yesmaximal, characteristic, complemented
5#11722727C212yesmaximal, complemented
6C2×#63786—31nomaximal
7C23×C32×D3C411yescharacteristic, complemented
8C22×D3×C3⋊D3C2211yescharacteristic
9C2×D3×#157—22no—
10C2×#6312C411yescharacteristic, complemented
11C2×C3×#638C2211yescharacteristic
12D3×#638—22no—
13D3×#638—22no—
14C2×#6291C411yescharacteristic, complemented
15C2×#6290C2211yescharacteristic
16C2×D3×C3⋊Dic3C411yescharacteristic, complemented
17#88994C2212yescomplemented
18C3×C22⋊#157C2212yescomplemented
19(C2×D3)⋊#157—22no—
20C22×#638—31no—
21C2×D3×#67—62no—
22C2×C22⋊#157—32no—
23#63786—31no—
24#63786—32no—
25#63786D311yescharacteristic, direct product factor
26C23×C33C2×C411yescharacteristic, complemented
27C22×C3⋊(C3⋊D3)C2×C411yescharacteristic
28C22×C3×C3⋊D3C2311yescharacteristic
29C22×C32×D3—21no—
30C22×C32×D3—21no—
31C22×C32×D3—42no—
32C22×C32×D3C2×C411yescharacteristic
33C22×C32×D3C2×C411yescharacteristic, complemented
34C2×D3×C3⋊D3—42no—
35C2×D3×C3⋊D3D412yes—
36C2×D3×C3⋊D3D412yes—
37C2×C3⋊#157—22no—
38C2×C3×#157—22no—
39D3×#157—44no—
40#6312—22no—
41C2×C3⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
42C3×#638—22no—
43C2×C3×C3⋊Dic3C2×C411yescharacteristic, complemented
44#6291—22no—
45#6290—22no—
46D3×C3⋊Dic3—21no—
47D3×C3⋊Dic3—21no—
48D3×#99—91nomaximal
49C24×C32—31no—
50C23×C3⋊D3—31no—
51C23×C3×D3—22no—
52C22×D32—62no—
53C22×#157—62no—
54C2×#638—31no—
55C2×#638—31no—
56C2×#638—31no—
57C2×#638—62no—
58C2×#638—62no—
59C2×#638—62no—
60C2×#638—122no—
61C2×#638C2×D311yescharacteristic
62C22×C3⋊Dic3—31no—
63C2×C3×#67—62no—
64D3×#67—68no—
65D3×#67—68no—
66C2×#626—62no—
67C2×#625—62no—
68C2×D3×Dic3—62no—
69C22⋊#157—32no—
70C22⋊#157—62no—
71C22⋊#157C2×D312yescomplemented
72C22×C33—21no—
73C22×C33—41no—
74C22×C33C22×C411yescharacteristic
75C2×C3⋊(C3⋊D3)—41no—
76C2×C3⋊(C3⋊D3)C22⋊C412yes—
77C2×C3×C3⋊D3—41no—
78C2×C3×C3⋊D3C2×D412yes—
79C2×C32×D3—22no—
80C2×C32×D3—21no—
81C2×C32×D3—42no—
82C2×C32×D3—42no—
83C2×C32×D3—41no—
84C2×C32×D3C22⋊C411yescharacteristic
85C2×C32×D3C22⋊C411yescharacteristic
86D3×C3⋊D3—24no—
87D3×C3⋊D3—42no—
88C3⋊#157—42no—
89C3×#157—42no—
90C3⋊(C3⋊Dic3)—21no—
91C3×C3⋊Dic3—21no—
92C22×#67—182no—
93C2×D3×D4—91no—
94D3×C22⋊C4—92no—
95C3×#99—91no—
96#834—91no—
97#806—92no—
98C23×C32—22no—
99C23×C32—31no—
100C23×C32—31no—
101C23×C32—42no—
102C23×C32—61no—
103C23×C32—61no—
104C23×C32—122no—
105C23×C32C4×D311yescharacteristic, complemented
106C22×C3⋊D3—31no—
107C22×C3⋊D3—32no—
108C22×C3⋊D3—32no—
109C22×C3⋊D3—62no—
110C22×C3⋊D3—122no—
111C22×C3⋊D3—122no—
112C22×C3⋊D3C22×D311yescharacteristic
113C22×C3×D3—24no—
114C22×C3×D3—24no—
115C22×C3×D3—22no—
116C22×C3×D3—22no—
117C22×C3×D3—48no—
118C22×C3×D3—62no—
119C2×D32—64no—
120C2×D32—64no—
121C2×D32—128no—
122C2×#157—22no—
123C2×#157—62no—
124C2×#157—124no—
125#638—22no—
126#638—62no—
127#638—62no—
128#638—62no—
129#638—68no—
130#638—128no—
131C2×C3⋊Dic3—31no—
132C2×C3⋊Dic3—62no—
133C2×C3⋊Dic3—61no—
134C2×C3⋊Dic3—61no—
135C2×C3⋊Dic3—122no—
136C2×C3⋊Dic3C4×D311yescharacteristic, complemented
137C3×#67—68no—
138C2×C3×Dic3—62no—
139#626—68no—
140#625—68no—
141D3×Dic3—64no—
142D3×Dic3—64no—
143C2×#99—271noSylow
144C2×C33—21no—
145C2×C33—41no—
146C2×C33C2×C22⋊C411yescharacteristic
147C3⋊(C3⋊D3)—22no—
148C3×C3⋊D3—22no—
149C32×D3—21no—
150C32×D3—41no—
151C32×D3#9912yescomplemented
152C24×C3—62no—
153C23×D3—91no—
154C23×D3—182no—
155C23×D3#15711yescharacteristic, complemented
156C2×C3×D4—91no—
157C2×#67—62no—
158C2×#67—91no—
159C2×#67—91no—
160C2×#67—182no—
161C2×#67—182no—
162C2×#67—182no—
163C2×#67—188no—
164C2×#67—188no—
165C2×#67—362no—
166C22×Dic3—182no—
167D3×D4—182no—
168D3×D4—182no—
169C2×D12—91no—
170C2×C4×D3—91no—
171C2×C4×D3—182no—
172C3×C22⋊C4—92no—
173#217—92no—
174(C2×D3)⋊C4—182no—
175C22×C32—21no—
176C22×C32—24no—
177C22×C32—22no—
178C22×C32—31no—
179C22×C32—31no—
180C22×C32—44no—
181C22×C32—42no—
182C22×C32—41no—
183C22×C32—44no—
184C22×C32—62no—
185C22×C32—61no—
186C22×C32—84no—
187C22×C32—121no—
188C22×C32—122no—
189C22×C32—122no—
190C22×C32C2×C4×D311yescharacteristic
191C2×C3⋊D3—32no—
192C2×C3⋊D3—41no—
193C2×C3⋊D3—64no—
194C2×C3⋊D3—64no—
195C2×C3⋊D3—124no—
196C2×C3⋊D3—122no—
197C2×C3⋊D3—121no—
198C2×C3⋊D3—124no—
199C2×C3⋊D3—244no—
200C2×C3⋊D3D3×D412yes—
201C2×C3×D3—28no—
202C2×C3×D3—24no—
203C2×C3×D3—22no—
204C2×C3×D3—22no—
205C2×C3×D3—48no—
206C2×C3×D3—48no—
207C2×C3×D3—44no—
208C2×C3×D3—64no—
209C2×C3×D3—124no—
210D32—128no—
211D32—128no—
212#157—42no—
213#157—122no—
214C3⋊Dic3—21no—
215C3⋊Dic3—61no—
216C3⋊Dic3—64no—
217C3⋊Dic3—124no—
218C3×Dic3—64no—
219C22×D4—271no—
220C2×C22⋊C4—272no—
221#99—91no—
222#99—272no—
223#99—271no—
224C33C2×#9911yescharacteristic, complemented, Sylow
225C23×C3—22no—
226C23×C3—42no—
227C23×C3—62no—
228C23×C3—62no—
229C23×C3—64no—
230C23×C3—64no—
231C23×C3—91no—
232C23×C3—128no—
233C23×C3C2×#15711yescharacteristic, complemented
234C22×D3—21no—
235C22×D3—21no—
236C22×D3—42no—
237C22×D3—62no—
238C22×D3—91no—
239C22×D3—92no—
240C22×D3—92no—
241C22×D3—184no—
242C22×D3—184no—
243C22×D3—182no—
244C22×D3—362no—
245C22×D3—362no—
246C22×D3—368no—
247C22×D3C2×#15711yescharacteristic
248C22×D3C2×#15711yescharacteristic, complemented
249C3×D4—182no—
250C2×C3×C4—91no—
251C2×C3×C4—182no—
252#67—68no—
253#67—188no—
254#67—182no—
255#67—188no—
256#67—182no—
257#67—188no—
258#67—368no—
259C2×Dic3—62no—
260C2×Dic3—91no—
261C2×Dic3—182no—
262C2×Dic3—184no—
263C2×Dic3—184no—
264C2×Dic3—182no—
265C2×Dic3—362no—
266D12—182no—
267C4×D3—181no—
268C4×D3—181no—
269C4×D3—364no—
270C2×C32—21no—
271C2×C32—24no—
272C2×C32—22no—
273C2×C32—32no—
274C2×C32—44no—
275C2×C32—42no—
276C2×C32—41no—
277C2×C32—44no—
278C2×C32—61no—
279C2×C32—84no—
280C2×C32—121no—
281C2×C32D3×C22⋊C411yescharacteristic
282C3⋊D3—22no—
283C3⋊D3—62no—
284C3⋊D3—124no—
285C3⋊D3—244no—
286C3×D3—24no—
287C3×D3—24no—
288C3×D3—44no—
289C3×D3—124no—
290C24—31no—
291C24—271no—
292C2×D4—91no—
293C2×D4—271no—
294C2×D4—271no—
295C2×D4—271no—
296C2×D4—542no—
297C2×D4—542no—
298C22×C4—271no—
299C22×C4—542no—
300C22⋊C4—92no—
301C22⋊C4—272no—
302C22⋊C4—542no—
303C22×C3—24no—
304C22×C3—21no—
305C22×C3—22no—
306C22×C3—44no—
307C22×C3—41no—
308C22×C3—44no—
309C22×C3—42no—
310C22×C3—62no—
311C22×C3—62no—
312C22×C3—68no—
313C22×C3—64no—
314C22×C3—84no—
315C22×C3—92no—
316C22×C3—124no—
317C22×C3—128no—
318C22×C3—128no—
319C22×C3—361no—
320C22×C3C22×#15711yescharacteristic
321C2×D3—22no—
322C2×D3—21no—
323C2×D3—42no—
324C2×D3—42no—
325C2×D3—41no—
326C2×D3—64no—
327C2×D3—92no—
328C2×D3—124no—
329C2×D3—184no—
330C2×D3—184no—
331C2×D3—364no—
332C2×D3—368no—
333C2×D3—362no—
334C2×D3—368no—
335C2×D3—361no—
336C2×D3—364no—
337C2×D3—724no—
338C2×D3C22⋊#15711yescharacteristic
339C2×D3C22⋊#15711yescharacteristic
340C3×C4—181no—
341C3×C4—362no—
342Dic3—64no—
343Dic3—184no—
344Dic3—181no—
345Dic3—364no—
346Dic3—362no—
347C32—22no—
348C32—42no—
349C32D3×#9911yescharacteristic, complemented
350C23—31no—
351C23—31no—
352C23—61no—
353C23—61no—
354C23—91no—
355C23—122no—
356C23—272no—
357C23—272no—
358C23—271no—
359C23—1082no—
360C23D3×#15711yescharacteristic, complemented
361D4—182no—
362D4—542no—
363D4—542no—
364D4—542no—
365C2×C4—91no—
366C2×C4—182no—
367C2×C4—271no—
368C2×C4—541no—
369C2×C4—541no—
370C2×C4—542no—
371C2×C4—1084no—
372C2×C3—24no—
373C2×C3—21no—
374C2×C3—22no—
375C2×C3—44no—
376C2×C3—44no—
377C2×C3—41no—
378C2×C3—42no—
379C2×C3—64no—
380C2×C3—64no—
381C2×C3—84no—
382C2×C3—124no—
383C2×C3—182no—
384C2×C3C2×C22⋊#15711yescharacteristic
385D3—21no—
386D3—41no—
387D3—124no—
388D3—182no—
389D3—364no—
390D3—724no—
391D3#6378612yesdirect product factor
392C22—21no—
393C22—31no—
394C22—31no—
395C22—41no—
396C22—62no—
397C22—61no—
398C22—92no—
399C22—121no—
400C22—122no—
401C22—122no—
402C22—272no—
403C22—361no—
404C22—544no—
405C22—1081no—
406C22—1082no—
407C22C2×D3×#15711yescharacteristic
408C4—181no—
409C4—362no—
410C4—541no—
411C4—1082no—
412C3—22no—
413C3—42no—
414C3C2×#6378611yescharacteristic, complemented
415C2—21no—
416C2—32no—
417C2—41no—
418C2—61no—
419C2—121no—
420C2—182no—
421C2—542no—
422C2D3×C22⋊#15711yescharacteristic
subgroupG/H
centerC2D3×C22⋊#157
commutatorC22×C33C22×C4
FrattiniC22C2×D3×#157
FittingC23×C33C2×C4
socleC2×C33C2×C22⋊C4
prime radicalC2×D3×#638C2
cosocleC22×C3×C3⋊D3C23
hypercenterC23D3×#157
hypocenterC33C2×#99
LCSG ▷ C22×C33 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. D3×C22⋊#157C2semidirect
3. #11723111C2semidirect
4. C3×#63786C2semidirect
5. #11722727C2semidirect
7. C23×C32×D3C4semidirect
10. C2×#6312C4semidirect
14. C2×#6291C4semidirect
16. C2×D3×C3⋊Dic3C4semidirect
17. #88994C22semidirect
18. C3×C22⋊#157C22semidirect
25. #63786D3direct (N × H)
26. C23×C33C2×C4semidirect
33. C22×C32×D3C2×C4semidirect
41. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
43. C2×C3×C3⋊Dic3C2×C4semidirect
71. C22⋊#157C2×D3semidirect
105. C23×C32C4×D3semidirect
136. C2×C3⋊Dic3C4×D3semidirect
151. C32×D3#99semidirect
155. C23×D3#157semidirect
224. C33C2×#99semidirect
233. C23×C3C2×#157semidirect
248. C22×D3C2×#157semidirect
349. C32D3×#99semidirect
360. C23D3×#157semidirect
391. D3#63786direct (N × H)
414. C3C2×#63786semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6382
D3×C22⋊#1572
#117231112
C3×#637862
#117227272
C2×#637863
D3×#999