Finite Group Databasebeta

← C2×#10590782 #11868367

Subgroups — C2×#10590782 #11868367

Order 1152.

965 conjugacy classes of subgroups.

The subgroup lattice has 455 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×#63641C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#817C211yesmaximal, characteristic, complemented
6C2×#63576C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590782C218yesmaximal, direct product factor
9C2×#4871—31nomaximal
10C2×#4763—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63898—22no—
23#63898C2214yes—
24#63872—22no—
25#63872C2214yescomplemented
26#63641C2214yescomplemented
27C3×#821C2214yes—
28C3×#817C2214yescomplemented
29#63576C2214yescomplemented
30#63562C2214yes—
31C2×D4×Dic3—31no—
32C2×#893—31no—
33C2×#890—31no—
34C2×#890—31no—
35C2×C3×#106—31no—
36C2×C3×#102—31no—
37C2×#832—31no—
38C2×#821D311yescharacteristic
39C2×#817D311yescharacteristic, complemented
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8—31no—
42C2×Dic3⋊C8—61no—
43C2×#809—31no—
44C2×#807—31no—
45C2×#807—31no—
46#4871—38no—
47#4763—38no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C2×C3×D12—21no—
56C2×C3×D12—22no—
57C2×C3×D12Q814yes—
58C2×C3×D12C2312yes—
59C2×D3×Dic3—24no—
60C2×D3×Dic3—44no—
61C2×C32×C8—22no—
62C2×C32×C8C2312yes—
63C4×C3⋊Dic3D412yes—
64C4×C3⋊Dic3C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2312yes—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—24no—
75(C2×D3)⋊Dic3—24no—
76C2×#478—91noSylow
77C22×C3×D4—31no—
78C23×Dic3—61no—
79C22×D12C2×D311yescharacteristic
80C22×C4×D3—61no—
81C22×C3×C8—21no—
82C22×C3×C8C2×D311yescharacteristic
83C22×C3×C8C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×#217—61no—
88D4×Dic3—34no—
89D4×Dic3—62no—
90C2×(C2×D3)⋊C4—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4—61no—
98C2×C4×Dic3—31no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—61no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—31no—
103C22×C3⋊C8—61no—
104#893—34no—
105#893—62no—
106#890—34no—
107#890—34no—
108#890—62no—
109#890—62no—
110C3×#106—34no—
111C3×#102—34no—
112#832—34no—
113#821C2×D314yes—
114#817C2×D314yescomplemented
115Dic3⋊C8—34no—
116Dic3⋊C8—34no—
117Dic3⋊C8—64no—
118#809—34no—
119#807—34no—
120#807—34no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q812yes—
128C2×C32×C4#4112yes—
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C3×D12—24no—
141C3×D12—22no—
142C3×D12C2×Q814yes—
143D3×Dic3—48no—
144C32×C8—22no—
145C3⋊(C3⋊C8)—22no—
146C2×#125—91no—
147C2×C4×D4—91no—
148#478—98no—
149C2×#107—91no—
150C2×#106—31no—
151C2×C4⋊C8—91no—
152C2×#102—31no—
153C2×#102—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—34no—
157C2×C3×D4—32no—
158C2×C3×D4—62no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—31no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—64no—
176C22×Dic3—124no—
177C2×D12—21no—
178C2×D12—22no—
179C2×D12Dic614yes—
180C2×D12C22×D312yes—
181C2×C4×D3—64no—
182C2×C4×D3—124no—
183C2×C3×C8—22no—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—42no—
187C2×C3×C8C22×D312yes—
188C2×C3×C8C22×D312yes—
189C3×C4⋊C4—32no—
190C3×C4⋊C4—32no—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194C3×C4⋊C4—61no—
195#217—64no—
196(C2×D3)⋊C4—64no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—64no—
201C4⋊Dic3—64no—
202C4⋊Dic3C22×D312yes—
203C4⋊Dic3C22×D312yes—
204C4⋊Dic3C22×D312yes—
205Dic3⋊C4—64no—
206Dic3⋊C4—64no—
207C4×Dic3—32no—
208C4×Dic3—32no—
209C4×Dic3—32no—
210C4×Dic3—32no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—62no—
218C2×C3⋊C8—122no—
219C22×C32C22⋊Q812yes—
220C22×C32#13512yes—
221C22×C32AGL(1,ℤ/8)12yes—
222C22×C32C22×D411yescharacteristic
223C2×C3×D3—24no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—48no—
227C32×C4C22⋊Q812yes—
228C32×C4C22×Q811yescharacteristic
229C32×C4C2×#4111yescharacteristic
230C3⋊Dic3—22no—
231C3⋊Dic3—22no—
232C3×Dic3—42no—
233C3×Dic3—42no—
234C3×Dic3—42no—
235C22×D4—31no—
236C23×C4—181no—
237C22×C8—91no—
238C22×C8D3211yescharacteristic
239#125—94no—
240#125—182no—
241C4×D4—94no—
242C4×D4—182no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—31no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C42—91no—
250#107—94no—
251#106—34no—
252C4⋊C8—94no—
253#102—34no—
254#102—94no—
255C23×C3—21no—
256C23×C3—64no—
257C23×C3—62no—
258C23×C3—122no—
259C23×C3—122no—
260C23×C3D3×D411yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—24no—
263C22×D3—22no—
264C22×D3—42no—
265C22×D3—42no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—62no—
269C2×C3×C4—21no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—122no—
277C2×C3×C4—122no—
278C2×C3×C4—122no—
279C2×C3×C4C2×Dic612yes—
280C2×C3×C4#23512yes—
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4#23712yes—
284C2×C3×C4D3×Q812yes—
285C2×C3×C4C23×D311yescharacteristic
286C2×C3×C4C23×D311yescharacteristic
287C2×Dic3—22no—
288C2×Dic3—22no—
289C2×Dic3—22no—
290C2×Dic3—32no—
291C2×Dic3—32no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—42no—
295C2×Dic3—42no—
296C2×Dic3—42no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—64no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—62no—
303C2×Dic3—62no—
304C2×Dic3—122no—
305C2×Dic3—128no—
306D12—24no—
307D12—22no—
308D12C2×Dic614yes—
309C4×D3—128no—
310C3×C8—22no—
311C3×C8—22no—
312C3×C8—42no—
313C3⋊C8—62no—
314C3⋊C8—62no—
315C3⋊C8—122no—
316C2×C32#47814yescomplemented
317C2×C32C2×C22⋊Q811yescharacteristic
318C2×C32C2×#13511yescharacteristic
319C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
320C3×D3—44no—
321C24—61no—
322C2×D4—32no—
323C2×D4—34no—
324C2×D4—61no—
325C2×D4—62no—
326C22×C4—61no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—184no—
332C22×C4—364no—
333C22×C4C2×D3211yescharacteristic
334C2×C8—22no—
335C2×C8—92no—
336C2×C8—182no—
337C2×C8C2×D3212yes—
338C4⋊C4—32no—
339C4⋊C4—32no—
340C4⋊C4—32no—
341C4⋊C4—61no—
342C4⋊C4—61no—
343C4⋊C4—61no—
344C4⋊C4—184no—
345C4⋊C4—184no—
346C22⋊C4—184no—
347C42—92no—
348C42—92no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—64no—
354C22×C3—128no—
355C22×C3—122no—
356C22×C3—122no—
357C22×C3#87812yes—
358C22×C3#89612yes—
359C22×C3#91112yes—
360C22×C3#91412yes—
361C22×C3#91612yes—
362C22×C3#91612yes—
363C22×C3C2×D3×D411yescharacteristic
364C22×C3C2×D3×D411yescharacteristic
365C2×D3—24no—
366C2×D3—42no—
367C2×D3—42no—
368C2×D3—48no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—122no—
373C3×C4—122no—
374C3×C4—122no—
375C3×C4#87812yes—
376C3×C4#89612yes—
377C3×C4C22×Dic611yescharacteristic
378C3×C4C2×#23511yescharacteristic
379C3×C4C2×#23711yescharacteristic
380C3×C4C2×D3×Q811yescharacteristic
381Dic3—42no—
382Dic3—42no—
383Dic3—42no—
384Dic3—64no—
385Dic3—62no—
386Dic3—62no—
387Dic3—62no—
388Dic3—62no—
389Dic3—122no—
390C32C2×#47811yescharacteristic, complemented, Sylow
391C23—62no—
392C23—64no—
393C23—122no—
394C23—122no—
395C23#380211yescharacteristic
396D4—34no—
397D4—62no—
398D4—64no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—92no—
403C2×C4—92no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—122no—
407C2×C4—182no—
408C2×C4—182no—
409C2×C4—368no—
410C2×C4D3×Dic612yes—
411C2×C4#380211yescharacteristic
412C2×C4#380412yes—
413C2×C4C22×D3211yescharacteristic
414C8—22no—
415C8—182no—
416C2×C3—24no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—124no—
421C2×C3#476314yescomplemented
422C2×C3#487114yescomplemented
423C2×C3C2×#87811yescharacteristic
424C2×C3C2×#89611yescharacteristic
425C2×C3C2×#91111yescharacteristic
426C2×C3C2×#91411yescharacteristic
427C2×C3C2×#91611yescharacteristic
428C2×C3C2×#91611yescharacteristic
429D3—44no—
430C22—64no—
431C22—128no—
432C22—122no—
433C22—122no—
434C22#6379812yes—
435C22#6380912yes—
436C22#6389912yes—
437C22C2×#380211yescharacteristic
438C4—122no—
439C4—122no—
440C4—122no—
441C4—182no—
442C4—182no—
443C4#6389912yes—
444C4C2×D3×Dic611yescharacteristic
445C4C2×#380411yescharacteristic
446C3—21no—
447C3C2×#476311yescharacteristic, complemented
448C3C2×#487111yescharacteristic, complemented
449C2—124no—
450C2#1059078214yesdirect product factor
451C2C2×#6379811yescharacteristic
452C2C2×#6380911yescharacteristic
453C2C2×#6389911yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63872C2semidirect
3. C2×#63641C2semidirect
5. C2×C3×#817C2semidirect
6. C2×#63576C2semidirect
8. #10590782C2direct (N × H)
25. #63872C22semidirect
26. #63641C22semidirect
28. C3×#817C22semidirect
29. #63576C22semidirect
39. C2×#817D3semidirect
114. #817C2×D3semidirect
316. C2×C32#478semidirect
390. C32C2×#478semidirect
421. C2×C3#4763semidirect
422. C2×C3#4871semidirect
447. C3C2×#4763semidirect
448. C3C2×#4871semidirect
450. C2#10590782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638982
C2×#638722
C2×#636412
C2×C3×#8212
C2×C3×#8172
C2×#635762
C2×#635622
#105907822
C2×#48713
C2×#47633