Finite Group Databasebeta

← C2×D3×#869 #11900725

Subgroups — C2×D3×#869 #11900725

Order 1152.

3393 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C212yesmaximal
2C2×#64078C211yesmaximal, characteristic, complemented
3C2×C3×C42×D3C211yesmaximal, characteristic
4C2×C3×#869C211yesmaximal, characteristic, complemented
5C2×#63918C214yesmaximal, complemented
6C2×D3×C4⋊Dic3C214yesmaximal
7C2×#63866C212yesmaximal, complemented
8D3×#869C2116yesmaximal, direct product factor
9C2×D3×C4⋊Q8—31nomaximal
10C22×#869—31nomaximal
11C22×#634C2212yes—
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×C4×D3C2212yes—
14C22×C3×Dic6C2212yes—
15C22×#627C2214yes—
16C22×D3×Dic3C2214yes—
17C2×D3×Dic6—216no—
18C2×D3×Dic6C22116yes—
19C2×C32×C42C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2214yes—
21#64078C2218yescomplemented
22C2×C3×C4⋊Dic3C2214yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C3×C42×D3C2218yes—
26C3×#869C2218yescomplemented
27C2×Dic3⋊Dic3C2218yes—
28#63918C22132yescomplemented
29D3×C4⋊Dic3C22132yes—
30#63866C22116yescomplemented
31C22×D3×Q8—32no—
32C23×Dic6—32no—
33C2×C3×C4⋊Q8—31no—
34C22×C3×C42—31no—
35C2×#944—32no—
36C22×C4⋊Dic3—34no—
37D3×C4⋊Q8—316no—
38C2×D3×C4⋊C4—34no—
39C2×#888—34no—
40C2×C42×D3D311yescharacteristic
41C2×#869—32no—
42C2×#869—31no—
43C2×#869—31no—
44C2×#869—34no—
45C2×#869—316no—
46C2×#869—61no—
47C2×#869D311yescharacteristic, direct product factor
48C23×C3×D3C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2312yes—
51C22×C3⋊Dic3C2314yes—
52C2×#634—28no—
53C2×#634C2318yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C2×C3×C4×D3D418yes—
58C2×C3×C4×D3Q8116yescomplemented
59C2×C3×C4×D3C2314yes—
60C2×C3×C4×D3C2318yes—
61C2×C3×Dic6—28no—
62C2×C3×Dic6C2318yes—
63C2×#627—216no—
64C2×#627C23116yes—
65C2×D3×Dic3—216no—
66C2×D3×Dic3C23116yes—
67D3×Dic6—264no—
68C32×C42C2314yes—
69C4⋊(C3⋊Dic3)C23116yes—
70C3×C4⋊Dic3C23116yes—
71C3×C4×Dic3C2314yes—
72C3×C4×Dic3C2318yes—
73Dic3⋊Dic3C23132yes—
74C22×C4⋊Q8—91noSylow
75C22×C3×Q8—32no—
76C23×C3×C4—31no—
77C23×C3×C4—32no—
78C23×Dic3—34no—
79C2×D3×Q8—316no—
80C2×D3×Q8—616no—
81C22×C4×D3—34no—
82C22×C4×D3C2×D312yes—
83C22×C4×D3C2×D311yescharacteristic
84C22×Dic6—32no—
85C22×Dic6—32no—
86C22×Dic6—34no—
87C22×Dic6—34no—
88C22×Dic6—316no—
89C22×Dic6—62no—
90C22×Dic6—616no—
91C22×Dic6C2×D312yes—
92C3×C4⋊Q8—38no—
93C2×C3×C4⋊C4—34no—
94C2×C3×C42—21no—
95C2×C3×C42—31no—
96C2×C3×C42—32no—
97C2×C3×C42—38no—
98C2×C3×C42C2×D311yescharacteristic
99C2×C3×C42C2×D311yescharacteristic
100#944—316no—
101C2×C4⋊Dic3—34no—
102C2×C4⋊Dic3—34no—
103C2×C4⋊Dic3—38no—
104C2×C4⋊Dic3—332no—
105C2×C4⋊Dic3—64no—
106C2×C4⋊Dic3C2×D314yes—
107C2×Dic3⋊C4—38no—
108C2×C4×Dic3C2×D312yes—
109C2×C4×Dic3C2×D311yescharacteristic
110D3×C4⋊C4—332no—
111#888—332no—
112C42×D3C2×D318yes—
113#869—316no—
114#869—38no—
115#869—38no—
116#869—332no—
117#869—68no—
118#869C2×D318yesdirect product factor
119C23×C32C2411yescharacteristic
120C22×C3×D3C2×D414yes—
121C22×C3×D3C2×Q818yes—
122C22×C3×D3C2412yes—
123C2×C32×C4C2×D414yes—
124C2×C32×C4C2×Q818yescomplemented
125C2×C32×C4C2412yes—
126C2×C32×C4C2414yes—
127C2×C3⋊Dic3—28no—
128C2×C3⋊Dic3C2418yes—
129#634—216no—
130C2×C3×Dic3—28no—
131C2×C3×Dic3C2×D414yes—
132C2×C3×Dic3C2×Q818yescomplemented
133C2×C3×Dic3C2418yes—
134C2×C3×Dic3C2412yes—
135C2×C3×Dic3C2414yes—
136C3×C4×D3C2×D4116yes—
137C3×C4×D3C2×Q8132yescomplemented
138C3×Dic6—216no—
139#627—232no—
140D3×Dic3—232no—
141C23×Q8—92no—
142C2×C4⋊Q8—31no—
143C2×C4⋊Q8—94no—
144C2×C4⋊Q8—916no—
145C2×C4⋊Q8—92no—
146C2×C4⋊Q8—91no—
147C22×C4⋊C4—94no—
148C22×C42—31no—
149C24×C3—31no—
150C23×D3C22×D311yescharacteristic
151C2×C3×Q8—38no—
152C2×C3×Q8—68no—
153C22×C3×C4—22no—
154C22×C3×C4—21no—
155C22×C3×C4—32no—
156C22×C3×C4—31no—
157C22×C3×C4—38no—
158C22×C3×C4—316no—
159C22×C3×C4—38no—
160C22×C3×C4—34no—
161C22×C3×C4—34no—
162C22×C3×C4C22×D312yes—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D312yes—
166C22×Dic3—34no—
167C22×Dic3—34no—
168C22×Dic3—316no—
169C22×Dic3—64no—
170C22×Dic3—616no—
171C22×Dic3C22×D314yes—
172C22×Dic3C22×D312yes—
173C22×Dic3C22×D311yescharacteristic
174D3×Q8—664no—
175C2×C4×D3—316no—
176C2×C4×D3—616no—
177C2×C4×D3Dic6116yescomplemented
178C2×C4×D3D1218yes—
179C2×C4×D3C22×D318yes—
180C2×C4×D3C22×D314yes—
181C2×Dic6—28no—
182C2×Dic6—38no—
183C2×Dic6—38no—
184C2×Dic6—316no—
185C2×Dic6—316no—
186C2×Dic6—68no—
187C2×Dic6—664no—
188C2×Dic6—616no—
189C2×Dic6—68no—
190C2×Dic6—68no—
191C2×Dic6—616no—
192C2×Dic6—128no—
193C2×Dic6C22×D318yes—
194C3×C4⋊C4—316no—
195C3×C42—24no—
196C3×C42—34no—
197C3×C42—38no—
198C3×C42C22×D314yes—
199C3×C42C22×D314yes—
200C4⋊Dic3—316no—
201C4⋊Dic3—316no—
202C4⋊Dic3—332no—
203C4⋊Dic3—616no—
204C4⋊Dic3C22×D3116yes—
205Dic3⋊C4—332no—
206C4×Dic3C22×D318yes—
207C4×Dic3C22×D314yes—
208C22×C32C22×D412yes—
209C22×C32C22×Q814yes—
210C22×C32C2511yescharacteristic
211C2×C3×D3C4⋊Q8116yescomplemented
212C2×C3×D3C22×D414yes—
213C2×C3×D3C22×Q818yes—
214C32×C4C22×D414yes—
215C32×C4C22×Q818yescomplemented
216C3⋊Dic3—28no—
217C3×Dic3—28no—
218C3×Dic3C22×D414yes—
219C3×Dic3C22×Q818yescomplemented
220C22×Q8—32no—
221C22×Q8—94no—
222C22×Q8—916no—
223C22×Q8—92no—
224C22×Q8—1816no—
225C23×C4—32no—
226C23×C4—31no—
227C23×C4—94no—
228C4⋊Q8—38no—
229C4⋊Q8—932no—
230C4⋊Q8—916no—
231C4⋊Q8—98no—
232C2×C4⋊C4—34no—
233C2×C4⋊C4—932no—
234C2×C4⋊C4—98no—
235C2×C4⋊C4—94no—
236C2×C42—31no—
237C2×C42—32no—
238C2×C42—38no—
239C2×C42D3211yescharacteristic
240C23×C3—21no—
241C23×C3—34no—
242C23×C3—38no—
243C23×C3—32no—
244C23×C3C23×D311yescharacteristic
245C23×C3C23×D311yescharacteristic
246C22×D3C2×Dic618yes—
247C22×D3C2×D1214yes—
248C22×D3C23×D312yes—
249C3×Q8—616no—
250C2×C3×C4—24no—
251C2×C3×C4—22no—
252C2×C3×C4—28no—
253C2×C3×C4—24no—
254C2×C3×C4—34no—
255C2×C3×C4—38no—
256C2×C3×C4—34no—
257C2×C3×C4—32no—
258C2×C3×C4—316no—
259C2×C3×C4—332no—
260C2×C3×C4—38no—
261C2×C3×C4—68no—
262C2×C3×C4C2×Dic618yescomplemented
263C2×C3×C4C2×D1214yes—
264C2×C3×C4D3×D414yes—
265C2×C3×C4D3×Q818yescomplemented
266C2×C3×C4C23×D314yes—
267C2×C3×C4C23×D312yes—
268C2×C3×C4C23×D312yes—
269C2×C3×C4C23×D314yes—
270C2×Dic3—28no—
271C2×Dic3—38no—
272C2×Dic3—38no—
273C2×Dic3—68no—
274C2×Dic3—632no—
275C2×Dic3—68no—
276C2×Dic3—68no—
277C2×Dic3—128no—
278C2×Dic3C2×Dic618yescomplemented
279C2×Dic3C2×D1214yes—
280C2×Dic3C23×D318yes—
281C2×Dic3C23×D314yes—
282C2×Dic3C23×D312yes—
283C4×D3—632no—
284C4×D3C2×Dic6132yescomplemented
285C4×D3C2×D12116yes—
286Dic6—216no—
287Dic6—632no—
288Dic6—616no—
289Dic6—616no—
290Dic6—632no—
291Dic6—1216no—
292C2×C32C2×C4⋊Q814yescomplemented
293C2×C32C23×D411yescharacteristic
294C2×C32C23×Q812yes—
295C3×D3C2×C4⋊Q818yescomplemented
296C24—31no—
297C2×Q8—38no—
298C2×Q8—68no—
299C2×Q8—916no—
300C2×Q8—98no—
301C2×Q8—1816no—
302C2×Q8—1864no—
303C2×Q8—188no—
304C22×C4—32no—
305C22×C4—31no—
306C22×C4—38no—
307C22×C4—34no—
308C22×C4—316no—
309C22×C4—38no—
310C22×C4—34no—
311C22×C4—916no—
312C22×C4—94no—
313C22×C4—1816no—
314C22×C4C2×D3212yes—
315C22×C4C2×D3211yescharacteristic
316C4⋊C4—316no—
317C4⋊C4—932no—
318C4⋊C4—916no—
319C42—34no—
320C42—38no—
321C42C2×D3214yes—
322C22×C3—24no—
323C22×C3—22no—
324C22×C3—21no—
325C22×C3—34no—
326C22×C3—38no—
327C22×C3—316no—
328C22×C3C22×Dic614yes—
329C22×C3C22×D1212yes—
330C22×C3C2×D3×D412yes—
331C22×C3C2×D3×Q814yes—
332C22×C3C24×D311yescharacteristic
333C22×C3C24×D311yescharacteristic
334C2×D3#869116yesdirect product factor
335C2×D3C22×Dic618yes—
336C2×D3C22×D1214yes—
337C3×C4—28no—
338C3×C4—24no—
339C3×C4—34no—
340C3×C4—38no—
341C3×C4—68no—
342C3×C4C22×Dic618yescomplemented
343C3×C4C22×D1214yes—
344C3×C4C2×D3×D414yes—
345C3×C4C2×D3×Q818yescomplemented
346Dic3—28no—
347Dic3—68no—
348Dic3—68no—
349Dic3—128no—
350Dic3C22×Dic618yescomplemented
351Dic3C22×D1214yes—
352C32C22×C4⋊Q811yescharacteristic, complemented, Sylow
353C23—38no—
354C23—34no—
355C23—32no—
356C23C22×D3211yescharacteristic
357Q8—616no—
358Q8—1832no—
359Q8—1816no—
360C2×C4—38no—
361C2×C4—34no—
362C2×C4—34no—
363C2×C4—32no—
364C2×C4—332no—
365C2×C4—316no—
366C2×C4—38no—
367C2×C4—68no—
368C2×C4—98no—
369C2×C4—1832no—
370C2×C4—188no—
371C2×C4D3×Dic618yescomplemented
372C2×C4D3×D1214yes—
373C2×C4C22×D3214yes—
374C2×C4C22×D3212yes—
375C2×C3—22no—
376C2×C3—21no—
377C2×C3—24no—
378C2×C3—38no—
379C2×C3C2×#86914yescomplemented
380C2×C3D3×C4⋊Q814yescomplemented
381C2×C3C23×Dic612yes—
382C2×C3C23×D1211yescharacteristic
383C2×C3C22×D3×D411yescharacteristic
384C2×C3C22×D3×Q812yes—
385D3C2×#86918yesdirect product factor
386C22—38no—
387C22—34no—
388C22—316no—
389C22C2×D3×Dic614yes—
390C22C2×D3×D1212yes—
391C22C23×D3211yescharacteristic
392C4—38no—
393C4—34no—
394C4—68no—
395C4—188no—
396C4C2×D3×Dic618yescomplemented
397C4C2×D3×D1214yes—
398C3—21no—
399C3C22×#86911yescharacteristic, complemented
400C3C2×D3×C4⋊Q811yescharacteristic, complemented
401C2—38no—
402C2D3×#86914yesdirect product factor
403C2C22×D3×Dic612yes—
404C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C22×C4⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#64078C2semidirect
4. C2×C3×#869C2semidirect
5. C2×#63918C2semidirect
7. C2×#63866C2semidirect
8. D3×#869C2direct (N × H)
21. #64078C22semidirect
26. C3×#869C22semidirect
28. #63918C22semidirect
30. #63866C22semidirect
47. C2×#869D3direct (N × H)
58. C2×C3×C4×D3Q8semidirect
118. #869C2×D3direct (N × H)
124. C2×C32×C4C2×Q8semidirect
132. C2×C3×Dic3C2×Q8semidirect
137. C3×C4×D3C2×Q8semidirect
177. C2×C4×D3Dic6semidirect
211. C2×C3×D3C4⋊Q8semidirect
215. C32×C4C22×Q8semidirect
219. C3×Dic3C22×Q8semidirect
262. C2×C3×C4C2×Dic6semidirect
265. C2×C3×C4D3×Q8semidirect
278. C2×Dic3C2×Dic6semidirect
284. C4×D3C2×Dic6semidirect
292. C2×C32C2×C4⋊Q8semidirect
295. C3×D3C2×C4⋊Q8semidirect
334. C2×D3#869direct (N × H)
342. C3×C4C22×Dic6semidirect
345. C3×C4C2×D3×Q8semidirect
350. Dic3C22×Dic6semidirect
352. C32C22×C4⋊Q8semidirect
371. C2×C4D3×Dic6semidirect
379. C2×C3C2×#869semidirect
380. C2×C3D3×C4⋊Q8semidirect
385. D3C2×#869direct (N × H)
396. C4C2×D3×Dic6semidirect
399. C3C22×#869semidirect
400. C3C2×D3×C4⋊Q8semidirect
402. C2D3×#869direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×#640782
C2×C3×C42×D32
C2×C3×#8692
C2×#639182
C2×D3×C4⋊Dic32
C2×#638662
D3×#8692
C2×D3×C4⋊Q83
C22×#8693