Finite Group Databasebeta

← C2×#10593874 #11900859

Subgroups — C2×#10593874 #11900859

Order 1152.

2449 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64079C211yesmaximal, characteristic, complemented
2C2×C3×C42×D3C211yesmaximal, characteristic
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63918C212yesmaximal, complemented
5C2×#63851C214yesmaximal
6C2×#63841C212yesmaximal
7C2×#63837C214yesmaximal, complemented
8#10593874C2116yesmaximal, direct product factor
9C2×#5688—31nomaximal
10C2×#5470—31nomaximal
11C22×C3×C4×D3C2212yes—
12C22×C3×C4×D3C2211yescharacteristic
13C22×#627C2214yes—
14C2×C32×C42C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2212yes—
16C2×#3750C2214yes—
17#64079C2218yescomplemented
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×Dic3⋊C4C2214yes—
20C2×C3×C4×Dic3C2211yescharacteristic
21C2×C3×C4×Dic3C2212yes—
22C3×C42×D3C2218yes—
23C3×#870C2218yescomplemented
24C2×Dic3⋊Dic3C2214yes—
25C2×(C2×D3)⋊Dic3C2214yes—
26C2×Dic32C2214yes—
27#63918C22116yescomplemented
28#63851C22132yes—
29#63841C22116yes—
30#63837C22132yescomplemented
31C2×C3×#125—31no—
32C22×C3×C42—31no—
33C2×#926—32no—
34C2×#924—34no—
35#5688—316no—
36C2×#896—34no—
37C2×#892—32no—
38C2×#888—32no—
39C2×#887—34no—
40C2×C42×D3D311yescharacteristic
41#5470—316no—
42C2×#870—31no—
43C2×#870—31no—
44C2×#870—61no—
45C2×#870D311yescharacteristic, complemented
46C2×#869—32no—
47C2×C4×Dic6—34no—
48C23×C3×D3C2311yescharacteristic
49C22×C32×C4C2312yes—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3C2314yes—
52C22×C3×Dic3C2314yes—
53C22×C3×Dic3C2311yescharacteristic
54C22×C3×Dic3C2312yes—
55C2×C3×C4×D3—28no—
56C2×C3×C4×D3Q818yescomplemented
57C2×C3×C4×D3C2318yes—
58C2×C3×C4×D3C2314yes—
59C2×#627—216no—
60C2×#627C23116yes—
61C32×C42C2314yes—
62C4⋊(C3⋊Dic3)C2318yes—
63#3750C23116yes—
64C3×C4⋊Dic3C2318yes—
65C3×Dic3⋊C4C23116yes—
66C3×C4×Dic3C2318yes—
67C3×C4×Dic3C2314yes—
68Dic3⋊Dic3C23116yes—
69(C2×D3)⋊Dic3C23116yes—
70Dic32C23116yes—
71C2×#533—91noSylow
72C23×C3×C4—31no—
73C23×C3×C4—32no—
74C22×C4×D3C2×D312yes—
75C22×C4×D3C2×D311yescharacteristic
76C22×Dic6—34no—
77C22×Dic6—34no—
78C3×#125—38no—
79C2×C3×C4⋊C4—34no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C42—21no—
82C2×C3×C42—32no—
83C2×C3×C42—31no—
84C2×C3×C42—38no—
85C2×C3×C42C2×D311yescharacteristic
86C2×C3×C42C2×D311yescharacteristic
87C2×#217—34no—
88C2×(C2×D3)⋊C4—34no—
89#926—316no—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—32no—
92C2×C4⋊Dic3—34no—
93C2×C4⋊Dic3—62no—
94C2×C4⋊Dic3C2×D312yes—
95#924—332no—
96C2×Dic3⋊C4—34no—
97C2×Dic3⋊C4—34no—
98C2×Dic3⋊C4—34no—
99C2×Dic3⋊C4—64no—
100C2×Dic3⋊C4C2×D314yes—
101C2×C4×Dic3—34no—
102C2×C4×Dic3—34no—
103C2×C4×Dic3C2×D312yes—
104C2×C4×Dic3C2×D311yescharacteristic
105#896—332no—
106#892—316no—
107#888—316no—
108#887—332no—
109C42×D3C2×D318yes—
110#870—38no—
111#870—38no—
112#870—68no—
113#870C2×D318yescomplemented
114#869—316no—
115C4×Dic6—332no—
116C23×C32C2411yescharacteristic
117C22×C3×D3—24no—
118C22×C3×D3C2×Q814yes—
119C22×C3×D3C2412yes—
120C2×C32×C4—24no—
121C2×C32×C4C2×Q814yes—
122C2×C32×C4C2414yes—
123C2×C32×C4C2412yes—
124C2×C3⋊Dic3—28no—
125C2×C3⋊Dic3C2418yes—
126C2×C3×Dic3—28no—
127C2×C3×Dic3C2×Q814yes—
128C2×C3×Dic3#4118yes—
129C2×C3×Dic3C2418yes—
130C2×C3×Dic3C2412yes—
131C2×C3×Dic3C2414yes—
132C3×C4×D3—216no—
133C3×C4×D3C2×Q8116yescomplemented
134#627—232no—
135#533—916no—
136C2×C4⋊Q8—92no—
137C2×#125—31no—
138C2×#125—91no—
139C2×C22⋊Q8—94no—
140C2×C4×Q8—94no—
141C2×#117—92no—
142C22×C42—31no—
143C24×C3—31no—
144C23×D3C22×D311yescharacteristic
145C22×C3×C4—21no—
146C22×C3×C4—22no—
147C22×C3×C4—31no—
148C22×C3×C4—32no—
149C22×C3×C4—38no—
150C22×C3×C4—34no—
151C22×C3×C4—34no—
152C22×C3×C4—38no—
153C22×C3×C4—68no—
154C22×C3×C4C22×D312yes—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—34no—
159C22×Dic3—34no—
160C22×Dic3—64no—
161C22×Dic3C22×D314yes—
162C22×Dic3C22×D311yescharacteristic
163C22×Dic3C22×D312yes—
164C2×C4×D3—28no—
165C2×C4×D3Dic618yescomplemented
166C2×C4×D3C22×D318yes—
167C2×C4×D3C22×D314yes—
168C2×Dic6—316no—
169C2×Dic6—316no—
170C2×Dic6—616no—
171C2×Dic6—616no—
172C3×C4⋊C4—316no—
173C3×C4⋊C4—38no—
174C3×C42—24no—
175C3×C42—38no—
176C3×C42—34no—
177C3×C42C22×D314yes—
178C3×C42C22×D314yes—
179#217—316no—
180(C2×D3)⋊C4—316no—
181C4⋊Dic3—38no—
182C4⋊Dic3—38no—
183C4⋊Dic3—316no—
184C4⋊Dic3—68no—
185C4⋊Dic3C22×D318yes—
186Dic3⋊C4—316no—
187Dic3⋊C4—316no—
188Dic3⋊C4—316no—
189Dic3⋊C4—616no—
190Dic3⋊C4C22×D3116yes—
191C4×Dic3—316no—
192C4×Dic3—316no—
193C4×Dic3C22×D318yes—
194C4×Dic3C22×D314yes—
195C22×C32C22×Q812yes—
196C22×C32C2×#4114yes—
197C22×C32C2511yescharacteristic
198C2×C3×D3—28no—
199C2×C3×D3—24no—
200C2×C3×D3C22×Q814yes—
201C32×C4—24no—
202C32×C4C22×Q814yes—
203C3⋊Dic3—28no—
204C3×Dic3—28no—
205C3×Dic3C22×Q814yes—
206C3×Dic3C2×#4118yes—
207C22×Q8—94no—
208C23×C4—31no—
209C23×C4—32no—
210C4⋊Q8—916no—
211#125—38no—
212#125—98no—
213C22⋊Q8—932no—
214C4×Q8—932no—
215#117—916no—
216C2×C4⋊C4—32no—
217C2×C4⋊C4—34no—
218C2×C4⋊C4—94no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—94no—
221C2×C22⋊C4—94no—
222C2×C42—32no—
223C2×C42—31no—
224C2×C42—38no—
225C2×C42—94no—
226C2×C42D3211yescharacteristic
227C23×C3—21no—
228C23×C3—34no—
229C23×C3—32no—
230C23×C3—64no—
231C23×C3C23×D311yescharacteristic
232C23×C3C23×D311yescharacteristic
233C22×D3—24no—
234C22×D3C2×Dic614yes—
235C22×D3C23×D312yes—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—22no—
239C2×C3×C4—24no—
240C2×C3×C4—24no—
241C2×C3×C4—34no—
242C2×C3×C4—38no—
243C2×C3×C4—32no—
244C2×C3×C4—34no—
245C2×C3×C4—316no—
246C2×C3×C4—38no—
247C2×C3×C4—44no—
248C2×C3×C4—616no—
249C2×C3×C4—68no—
250C2×C3×C4C2×Dic614yes—
251C2×C3×C4D3×Q814yes—
252C2×C3×C4C23×D314yes—
253C2×C3×C4C23×D314yes—
254C2×C3×C4C23×D312yes—
255C2×C3×C4C23×D312yes—
256C2×Dic3—28no—
257C2×Dic3—38no—
258C2×Dic3—38no—
259C2×Dic3—68no—
260C2×Dic3—68no—
261C2×Dic3—68no—
262C2×Dic3—128no—
263C2×Dic3C2×Dic614yes—
264C2×Dic3#23518yes—
265C2×Dic3C23×D318yes—
266C2×Dic3C23×D312yes—
267C2×Dic3C23×D314yes—
268C4×D3—216no—
269C4×D3C2×Dic6116yescomplemented
270Dic6—632no—
271Dic6—632no—
272C2×C32#53314yescomplemented
273C2×C32C23×Q811yescharacteristic
274C2×C32C22×#4112yes—
275C3×D3—24no—
276C24—31no—
277C2×Q8—916no—
278C2×Q8—1816no—
279C22×C4—31no—
280C22×C4—32no—
281C22×C4—34no—
282C22×C4—38no—
283C22×C4—34no—
284C22×C4—38no—
285C22×C4—68no—
286C22×C4—94no—
287C22×C4C2×D3212yes—
288C22×C4C2×D3211yescharacteristic
289C4⋊C4—38no—
290C4⋊C4—316no—
291C4⋊C4—916no—
292C4⋊C4—98no—
293C4⋊C4—916no—
294C22⋊C4—916no—
295C42—38no—
296C42—34no—
297C42—916no—
298C42C2×D3214yes—
299C22×C3—22no—
300C22×C3—24no—
301C22×C3—21no—
302C22×C3—34no—
303C22×C3—68no—
304C22×C3—64no—
305C22×C3C22×Dic612yes—
306C22×C3C2×#23514yes—
307C22×C3C2×D3×Q812yes—
308C22×C3D3×#4114yes—
309C22×C3C24×D311yescharacteristic
310C22×C3C24×D311yescharacteristic
311C2×D3—24no—
312C2×D3—28no—
313C2×D3C22×Dic614yes—
314C3×C4—24no—
315C3×C4—24no—
316C3×C4—24no—
317C3×C4—34no—
318C3×C4—38no—
319C3×C4—44no—
320C3×C4—68no—
321C3×C4C22×Dic614yes—
322C3×C4C2×D3×Q814yes—
323Dic3—28no—
324Dic3—68no—
325Dic3—68no—
326Dic3—128no—
327Dic3C22×Dic614yes—
328Dic3C2×#23518yes—
329C32C2×#53311yescharacteristic, complemented, Sylow
330C23—34no—
331C23—32no—
332C23—64no—
333C23C22×D3211yescharacteristic
334Q8—1832no—
335C2×C4—24no—
336C2×C4—34no—
337C2×C4—38no—
338C2×C4—32no—
339C2×C4—34no—
340C2×C4—316no—
341C2×C4—38no—
342C2×C4—616no—
343C2×C4—68no—
344C2×C4—98no—
345C2×C4—188no—
346C2×C4D3×Dic614yes—
347C2×C4C22×D3214yes—
348C2×C4C22×D3212yes—
349C2×C3—21no—
350C2×C3—22no—
351C2×C3—24no—
352C2×C3—64no—
353C2×C3#547014yescomplemented
354C2×C3#568814yescomplemented
355C2×C3C23×Dic611yescharacteristic
356C2×C3C22×#23512yes—
357C2×C3C22×D3×Q811yescharacteristic
358C2×C3C2×D3×#4112yes—
359D3—24no—
360C22—34no—
361C22—64no—
362C22—68no—
363C22C2×D3×Dic612yes—
364C22D3×#23514yes—
365C22C23×D3211yescharacteristic
366C4—24no—
367C4—34no—
368C4—38no—
369C4—68no—
370C4—188no—
371C4C2×D3×Dic614yes—
372C3—21no—
373C3C2×#547011yescharacteristic, complemented
374C3C2×#568811yescharacteristic, complemented
375C2—64no—
376C2#1059387414yesdirect product factor
377C2C22×D3×Dic611yescharacteristic
378C2C2×D3×#23512yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32C2×#533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64079C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63918C2semidirect
7. C2×#63837C2semidirect
8. #10593874C2direct (N × H)
17. #64079C22semidirect
23. C3×#870C22semidirect
27. #63918C22semidirect
30. #63837C22semidirect
45. C2×#870D3semidirect
56. C2×C3×C4×D3Q8semidirect
113. #870C2×D3semidirect
133. C3×C4×D3C2×Q8semidirect
165. C2×C4×D3Dic6semidirect
269. C4×D3C2×Dic6semidirect
272. C2×C32#533semidirect
329. C32C2×#533semidirect
353. C2×C3#5470semidirect
354. C2×C3#5688semidirect
373. C3C2×#5470semidirect
374. C3C2×#5688semidirect
376. C2#10593874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640792
C2×C3×C42×D32
C2×C3×#8702
C2×#639182
C2×#638512
C2×#638412
C2×#638372
#105938742
C2×#56883
C2×#54703