Finite Group Databasebeta

← C2×C3×D3×C4⋊Q8 #11900710

Subgroups — C2×C3×D3×C4⋊Q8 #11900710

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×C3×D3×Q8C212yesmaximal
2C2×C32×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×#944C212yesmaximal, complemented
4C3×D3×C4⋊Q8C2116yesmaximal, direct product factor
5C2×C3×D3×C4⋊C4C214yesmaximal
6C2×C3×#888C214yesmaximal, complemented
7C2×C3×C42×D3C211yesmaximal, characteristic
8C2×C3×#869C211yesmaximal, characteristic, complemented
9C22×C3×C4⋊Q8—31nomaximal
10C2×D3×C4⋊Q8C311yesmaximal, characteristic, direct product factor
11C22×C32×Q8C2212yes—
12C2×C3×D3×Q8—216no—
13C2×C3×D3×Q8C22116yes—
14C22×C3×C4×D3C2214yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×Dic6C2214yes—
18C22×C3×Dic6C2212yes—
19C32×C4⋊Q8C2218yescomplemented
20C2×C32×C4⋊C4C2214yes—
21C2×C32×C42C2211yescharacteristic
22C3×#944C22116yescomplemented
23C2×C3×C4⋊Dic3C2214yes—
24C2×C3×Dic3⋊C4C2218yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C3×D3×C4⋊C4C22132yes—
28C3×#888C22132yescomplemented
29C3×C42×D3C2218yes—
30C3×#869C2218yescomplemented
31C23×C3×Q8—32no—
32C22×D3×Q8C2×C312yes—
33C2×C3×C4⋊Q8—21no—
34C2×C3×C4⋊Q8—32no—
35C2×C3×C4⋊Q8—316no—
36C2×C3×C4⋊Q8—34no—
37C2×C3×C4⋊Q8—31no—
38C2×C3×C4⋊Q8D311yescharacteristic, direct product factor
39C2×C3×C4⋊Q8C2×C311yescharacteristic, complemented
40C22×C3×C4⋊C4—34no—
41C22×C3×C42—31no—
42C2×#944C2×C312yescomplemented
43D3×C4⋊Q8C2×C3116yesdirect product factor
44C2×D3×C4⋊C4C2×C314yes—
45C2×#888C2×C314yescomplemented
46C2×C42×D3C2×C311yescharacteristic
47C2×#869C2×C311yescharacteristic, complemented
48C23×C3×D3C2311yescharacteristic
49C2×C32×Q8—28no—
50C2×C32×Q8C2318yes—
51C22×C32×C4C2314yes—
52C22×C32×C4C2311yescharacteristic
53C22×C32×C4C2312yes—
54C22×C3×Dic3C2314yes—
55C22×C3×Dic3C2311yescharacteristic
56C22×C3×Dic3C2312yes—
57C3×D3×Q8—264no—
58C2×C3×C4×D3—216no—
59C2×C3×C4×D3D418yes—
60C2×C3×C4×D3Q8116yescomplemented
61C2×C3×C4×D3C23116yes—
62C2×C3×C4×D3C2314yes—
63C2×C3×C4×D3C2318yes—
64C2×C3×Dic6—28no—
65C2×C3×Dic6—216no—
66C2×C3×Dic6C23116yes—
67C2×C3×Dic6C2318yes—
68C32×C4⋊C4C23116yes—
69C32×C42C2314yes—
70C3×C4⋊Dic3C23116yes—
71C3×Dic3⋊C4C23132yes—
72C3×C4×Dic3C2318yes—
73C3×C4×Dic3C2314yes—
74C22×C4⋊Q8—31noSylow
75C22×C3×Q8—22no—
76C22×C3×Q8—316no—
77C22×C3×Q8—34no—
78C22×C3×Q8—32no—
79C22×C3×Q8—616no—
80C22×C3×Q8C2×D312yes—
81C22×C3×Q8C22×C312yes—
82C23×C3×C4—31no—
83C23×C3×C4—32no—
84C23×C3×C4—34no—
85C2×D3×Q8—216no—
86C2×D3×Q8C22×C3116yes—
87C22×C4×D3C22×C314yes—
88C22×C4×D3C22×C311yescharacteristic
89C22×C4×D3C22×C312yes—
90C22×Dic6C22×C312yes—
91C22×Dic6C22×C314yes—
92C3×C4⋊Q8—28no—
93C3×C4⋊Q8—316no—
94C3×C4⋊Q8—332no—
95C3×C4⋊Q8—38no—
96C3×C4⋊Q8C2×D318yesdirect product factor
97C3×C4⋊Q8C22×C318yescomplemented
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4—38no—
100C2×C3×C4⋊C4—34no—
101C2×C3×C4⋊C4—332no—
102C2×C3×C4⋊C4C2×D314yes—
103C2×C3×C4⋊C4C22×C314yes—
104C2×C3×C42—21no—
105C2×C3×C42—31no—
106C2×C3×C42—32no—
107C2×C3×C42—38no—
108C2×C3×C42C2×D311yescharacteristic
109C2×C3×C42C22×C311yescharacteristic
110#944C22×C3116yescomplemented
111C2×C4⋊Dic3C22×C314yes—
112C2×Dic3⋊C4C22×C318yes—
113C2×C4×Dic3C22×C312yes—
114C2×C4×Dic3C22×C311yescharacteristic
115D3×C4⋊C4C22×C3132yes—
116#888C22×C3132yescomplemented
117C42×D3C22×C318yes—
118#869C22×C318yescomplemented
119C23×C32C2411yescharacteristic
120C22×C3×D3C2×D414yes—
121C22×C3×D3C2×Q818yes—
122C22×C3×D3C2412yes—
123C32×Q8—216no—
124C2×C32×C4—28no—
125C2×C32×C4C2×D414yes—
126C2×C32×C4C2×Q818yescomplemented
127C2×C32×C4C2418yes—
128C2×C32×C4C2412yes—
129C2×C32×C4C2414yes—
130C2×C3×Dic3—28no—
131C2×C3×Dic3C2×D414yes—
132C2×C3×Dic3C2×Q818yescomplemented
133C2×C3×Dic3C2418yes—
134C2×C3×Dic3C2412yes—
135C2×C3×Dic3C2414yes—
136C3×C4×D3—232no—
137C3×C4×D3C2×D4116yes—
138C3×C4×D3C2×Q8132yescomplemented
139C3×Dic6—216no—
140C3×Dic6—232no—
141C23×Q8—32no—
142C2×C4⋊Q8—32no—
143C2×C4⋊Q8—316no—
144C2×C4⋊Q8—34no—
145C2×C4⋊Q8—31no—
146C2×C4⋊Q8C3×D311yescharacteristic, direct product factor
147C22×C4⋊C4—34no—
148C22×C42—31no—
149C24×C3—31no—
150C23×D3C23×C311yescharacteristic
151C2×C3×Q8—28no—
152C2×C3×Q8—28no—
153C2×C3×Q8—28no—
154C2×C3×Q8—316no—
155C2×C3×Q8—38no—
156C2×C3×Q8—48no—
157C2×C3×Q8—616no—
158C2×C3×Q8—664no—
159C2×C3×Q8—68no—
160C2×C3×Q8C22×D318yes—
161C2×C3×Q8C23×C318yes—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—24no—
165C22×C3×C4—32no—
166C22×C3×C4—31no—
167C22×C3×C4—38no—
168C22×C3×C4—316no—
169C22×C3×C4—38no—
170C22×C3×C4—34no—
171C22×C3×C4—34no—
172C22×C3×C4—316no—
173C22×C3×C4—616no—
174C22×C3×C4C22×D314yes—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D312yes—
177C22×C3×C4C23×C314yes—
178C22×C3×C4C23×C311yescharacteristic
179C22×C3×C4C23×C312yes—
180C22×Dic3C23×C314yes—
181C22×Dic3C23×C311yescharacteristic
182C22×Dic3C23×C312yes—
183D3×Q8—264no—
184C2×C4×D3—216no—
185C2×C4×D3C3×D418yes—
186C2×C4×D3C3×Q8116yescomplemented
187C2×C4×D3C23×C3116yes—
188C2×C4×D3C23×C314yes—
189C2×C4×D3C23×C318yes—
190C2×Dic6—28no—
191C2×Dic6—216no—
192C2×Dic6C23×C318yes—
193C2×Dic6C23×C3116yes—
194C3×C4⋊C4—216no—
195C3×C4⋊C4—332no—
196C3×C4⋊C4—316no—
197C3×C4⋊C4C22×D3116yes—
198C3×C4⋊C4C23×C3116yes—
199C3×C42—24no—
200C3×C42—34no—
201C3×C42—38no—
202C3×C42C22×D314yes—
203C3×C42C23×C314yes—
204C4⋊Dic3C23×C3116yes—
205Dic3⋊C4C23×C3132yes—
206C4×Dic3C23×C318yes—
207C4×Dic3C23×C314yes—
208C22×C32C22×D412yes—
209C22×C32C22×Q814yes—
210C22×C32C2511yescharacteristic
211C2×C3×D3C4⋊Q8116yesdirect product factor
212C2×C3×D3C22×D414yes—
213C2×C3×D3C22×Q818yes—
214C32×C4—28no—
215C32×C4C22×D414yes—
216C32×C4C22×Q818yescomplemented
217C3×Dic3—28no—
218C3×Dic3C22×D414yes—
219C3×Dic3C22×Q818yescomplemented
220C22×Q8—316no—
221C22×Q8—34no—
222C22×Q8—32no—
223C22×Q8—616no—
224C22×Q8C2×C3×D312yes—
225C23×C4—32no—
226C23×C4—31no—
227C23×C4—34no—
228C4⋊Q8—316no—
229C4⋊Q8—332no—
230C4⋊Q8—38no—
231C4⋊Q8C2×C3×D318yesdirect product factor
232C2×C4⋊C4—38no—
233C2×C4⋊C4—34no—
234C2×C4⋊C4—332no—
235C2×C4⋊C4C2×C3×D314yes—
236C2×C42—31no—
237C2×C42—32no—
238C2×C42—38no—
239C2×C42C2×C3×D311yescharacteristic
240C23×C3—21no—
241C23×C3—34no—
242C23×C3—38no—
243C23×C3—32no—
244C23×C3C23×D311yescharacteristic
245C23×C3C24×C311yescharacteristic
246C22×D3C2×C3×D414yes—
247C22×D3C2×C3×Q818yes—
248C22×D3C24×C312yes—
249C3×Q8—216no—
250C3×Q8—216no—
251C3×Q8—416no—
252C3×Q8—632no—
253C3×Q8—616no—
254C2×C3×C4—28no—
255C2×C3×C4—28no—
256C2×C3×C4—24no—
257C2×C3×C4—22no—
258C2×C3×C4—28no—
259C2×C3×C4—24no—
260C2×C3×C4—28no—
261C2×C3×C4—34no—
262C2×C3×C4—38no—
263C2×C3×C4—34no—
264C2×C3×C4—32no—
265C2×C3×C4—316no—
266C2×C3×C4—332no—
267C2×C3×C4—38no—
268C2×C3×C4—48no—
269C2×C3×C4—632no—
270C2×C3×C4—68no—
271C2×C3×C4D3×D414yes—
272C2×C3×C4D3×Q818yescomplemented
273C2×C3×C4C2×C3×D414yes—
274C2×C3×C4C2×C3×Q818yescomplemented
275C2×C3×C4C23×D318yes—
276C2×C3×C4C23×D312yes—
277C2×C3×C4C23×D314yes—
278C2×C3×C4C24×C318yes—
279C2×C3×C4C24×C312yes—
280C2×C3×C4C24×C314yes—
281C2×Dic3—28no—
282C2×Dic3C2×C3×D414yes—
283C2×Dic3C2×C3×Q818yescomplemented
284C2×Dic3C24×C318yes—
285C2×Dic3C24×C312yes—
286C2×Dic3C24×C314yes—
287C4×D3—232no—
288C4×D3C2×C3×D4116yes—
289C4×D3C2×C3×Q8132yescomplemented
290Dic6—216no—
291Dic6—232no—
292C2×C32C2×C4⋊Q814yescomplemented
293C2×C32C23×D411yescharacteristic
294C2×C32C23×Q812yes—
295C3×D3C2×C4⋊Q818yesdirect product factor
296C24—31no—
297C2×Q8—28no—
298C2×Q8—316no—
299C2×Q8—38no—
300C2×Q8—616no—
301C2×Q8—664no—
302C2×Q8—68no—
303C2×Q8C22×C3×D318yes—
304C22×C4—32no—
305C22×C4—31no—
306C22×C4—38no—
307C22×C4—34no—
308C22×C4—38no—
309C22×C4—316no—
310C22×C4—34no—
311C22×C4—316no—
312C22×C4—616no—
313C22×C4C22×C3×D314yes—
314C22×C4C22×C3×D311yescharacteristic
315C22×C4C22×C3×D312yes—
316C4⋊C4—332no—
317C4⋊C4—316no—
318C4⋊C4C22×C3×D3116yes—
319C42—34no—
320C42—38no—
321C42C22×C3×D314yes—
322C22×C3—22no—
323C22×C3—24no—
324C22×C3—21no—
325C22×C3—34no—
326C22×C3—38no—
327C22×C3—316no—
328C22×C3C2×D3×D412yes—
329C22×C3C2×D3×Q814yes—
330C22×C3C22×C3×D412yes—
331C22×C3C22×C3×Q814yes—
332C22×C3C24×D311yescharacteristic
333C22×C3C25×C311yescharacteristic
334C2×D3C3×C4⋊Q8116yesdirect product factor
335C2×D3C22×C3×D414yes—
336C2×D3C22×C3×Q818yes—
337C3×C4—28no—
338C3×C4—28no—
339C3×C4—24no—
340C3×C4—28no—
341C3×C4—34no—
342C3×C4—38no—
343C3×C4—48no—
344C3×C4—68no—
345C3×C4C2×D3×D414yes—
346C3×C4C2×D3×Q818yescomplemented
347C3×C4C22×C3×D414yes—
348C3×C4C22×C3×Q818yescomplemented
349Dic3—28no—
350Dic3C22×C3×D414yes—
351Dic3C22×C3×Q818yescomplemented
352C32C22×C4⋊Q811yescharacteristic, complemented, Sylow
353C23—34no—
354C23—38no—
355C23—32no—
356C23C23×C3×D311yescharacteristic
357Q8—216no—
358Q8—632no—
359Q8—616no—
360C2×C4—28no—
361C2×C4—34no—
362C2×C4—38no—
363C2×C4—34no—
364C2×C4—32no—
365C2×C4—316no—
366C2×C4—332no—
367C2×C4—38no—
368C2×C4—632no—
369C2×C4—68no—
370C2×C4C3×D3×D414yes—
371C2×C4C3×D3×Q818yescomplemented
372C2×C4C23×C3×D318yes—
373C2×C4C23×C3×D312yes—
374C2×C4C23×C3×D314yes—
375C2×C3—21no—
376C2×C3—22no—
377C2×C3—24no—
378C2×C3—38no—
379C2×C3D3×C4⋊Q814yesdirect product factor
380C2×C3C2×C3×C4⋊Q814yescomplemented
381C2×C3C22×D3×D411yescharacteristic
382C2×C3C22×D3×Q812yes—
383C2×C3C23×C3×D411yescharacteristic
384C2×C3C23×C3×Q812yes—
385D3C2×C3×C4⋊Q818yesdirect product factor
386C22—34no—
387C22—38no—
388C22—316no—
389C22C2×C3×D3×D412yes—
390C22C2×C3×D3×Q814yes—
391C22C24×C3×D311yescharacteristic
392C4—28no—
393C4—34no—
394C4—38no—
395C4—68no—
396C4C2×C3×D3×D414yes—
397C4C2×C3×D3×Q818yescomplemented
398C3—21no—
399C3C2×D3×C4⋊Q811yescharacteristic, direct product factor
400C3C22×C3×C4⋊Q811yescharacteristic, complemented
401C2—38no—
402C2C3×D3×C4⋊Q814yesdirect product factor
403C2C22×C3×D3×D411yescharacteristic
404C2C22×C3×D3×Q812yes—
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4⋊Q8C2
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C3×C4⋊Q8D3
hypocenterC3C22×C3×C4⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×C32×C4⋊Q8C2semidirect
3. C2×C3×#944C2semidirect
4. C3×D3×C4⋊Q8C2direct (N × H)
6. C2×C3×#888C2semidirect
8. C2×C3×#869C2semidirect
10. C2×D3×C4⋊Q8C3direct (N × H)
19. C32×C4⋊Q8C22semidirect
22. C3×#944C22semidirect
28. C3×#888C22semidirect
30. C3×#869C22semidirect
38. C2×C3×C4⋊Q8D3direct (N × H)
39. C2×C3×C4⋊Q8C2×C3semidirect
42. C2×#944C2×C3semidirect
43. D3×C4⋊Q8C2×C3direct (N × H)
45. C2×#888C2×C3semidirect
47. C2×#869C2×C3semidirect
60. C2×C3×C4×D3Q8semidirect
96. C3×C4⋊Q8C2×D3direct (N × H)
97. C3×C4⋊Q8C22×C3semidirect
110. #944C22×C3semidirect
116. #888C22×C3semidirect
118. #869C22×C3semidirect
126. C2×C32×C4C2×Q8semidirect
132. C2×C3×Dic3C2×Q8semidirect
138. C3×C4×D3C2×Q8semidirect
146. C2×C4⋊Q8C3×D3direct (N × H)
186. C2×C4×D3C3×Q8semidirect
211. C2×C3×D3C4⋊Q8direct (N × H)
216. C32×C4C22×Q8semidirect
219. C3×Dic3C22×Q8semidirect
231. C4⋊Q8C2×C3×D3direct (N × H)
272. C2×C3×C4D3×Q8semidirect
274. C2×C3×C4C2×C3×Q8semidirect
283. C2×Dic3C2×C3×Q8semidirect
289. C4×D3C2×C3×Q8semidirect
292. C2×C32C2×C4⋊Q8semidirect
295. C3×D3C2×C4⋊Q8direct (N × H)
334. C2×D3C3×C4⋊Q8direct (N × H)
346. C3×C4C2×D3×Q8semidirect
348. C3×C4C22×C3×Q8semidirect
351. Dic3C22×C3×Q8semidirect
352. C32C22×C4⋊Q8semidirect
371. C2×C4C3×D3×Q8semidirect
379. C2×C3D3×C4⋊Q8direct (N × H)
380. C2×C3C2×C3×C4⋊Q8semidirect
385. D3C2×C3×C4⋊Q8direct (N × H)
397. C4C2×C3×D3×Q8semidirect
399. C3C2×D3×C4⋊Q8direct (N × H)
400. C3C22×C3×C4⋊Q8semidirect
402. C2C3×D3×C4⋊Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×C32×C4⋊Q82
C2×C3×#9442
C3×D3×C4⋊Q82
C2×C3×D3×C4⋊C42
C2×C3×#8882
C2×C3×C42×D32
C2×C3×#8692
C22×C3×C4⋊Q83
C2×D3×C4⋊Q83