Finite Group Databasebeta

← C2×#10590772 #11868369

Subgroups — C2×#10590772 #11868369

Order 1152.

961 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C2×#63869C211yesmaximal, characteristic, complemented
3C2×#63644C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic
8#10590772C218yesmaximal, direct product factor
9C2×#4847—31nomaximal
10C2×#4763—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×D3×Dic3—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3724—21no—
20C2×Dic3⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22Dic3×D12—22no—
23Dic3×D12C2214yes—
24#63869—22no—
25#63869C2214yescomplemented
26#63644C2214yescomplemented
27C3×#821C2214yes—
28C3×Dic3⋊C8C2214yescomplemented
29#63575C2214yescomplemented
30#63563C2214yes—
31C2×D4×Dic3—31no—
32C2×#890—31no—
33C2×C4×D12—31no—
34C2×#870—31no—
35C2×C3×C4⋊C8—31no—
36C2×C3×#102—31no—
37C2×#832—31no—
38C2×#821—31no—
39C2×#821D311yescharacteristic
40C2×#818—31no—
41C2×#817—31no—
42C2×#817—31no—
43C2×#817—61no—
44C2×Dic3⋊C8D311yescharacteristic, complemented
45C2×#807—31no—
46#4847—38no—
47#4763—38no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C22×C3×Dic3D411yescharacteristic
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⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66C4⋊(C3⋊Dic3)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4×Dic3D412yes—
70C3×C4×Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73#3724—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×C8—31no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C42—31no—
87C2×#217—61no—
88D4×Dic3—34no—
89D4×Dic3—62no—
90C2×(C2×D3)⋊C4—61no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104#890—34no—
105#890—62no—
106C4×D12—34no—
107C4×D12—62no—
108#870—34no—
109#870—62no—
110C3×C4⋊C8—34no—
111C3×#102—34no—
112#832—34no—
113#821—34no—
114#821C2×D314yes—
115#818—34no—
116#817—34no—
117#817—34no—
118#817—64no—
119Dic3⋊C8C2×D314yescomplemented
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⋊Dic3—42no—
133C2×C3⋊Dic3—42no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—42no—
138C2×C3×Dic3C2×D412yes—
139C2×C3×Dic3C2×D412yes—
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—91no—
151C2×C4⋊C8—31no—
152C2×#102—31no—
153C2×#102—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—34no—
157C2×C3×D4—32no—
158C2×C3×D4—61no—
159C2×C3×D4—62no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—64no—
172C22×Dic3—121no—
173C22×Dic3—121no—
174C22×Dic3—124no—
175C22×Dic3D1211yescharacteristic
176C22×Dic3D1211yescharacteristic
177C2×D12—21no—
178C2×D12—22no—
179C2×D12Dic614yes—
180C2×D12C22×D312yes—
181C2×C4×D3—64no—
182C2×C4×D3—124no—
183C2×C3×C8—24no—
184C2×C3×C8—22no—
185C2×C3×C8—22no—
186C2×C3×C8—22no—
187C2×C3×C8—32no—
188C2×C3×C8—62no—
189C2×C3×C8C22×D312yes—
190C2×C3×C8C22×D312yes—
191C3×C4⋊C4—32no—
192C3×C4⋊C4—61no—
193C3×C42—32no—
194C3×C42—32no—
195#217—64no—
196(C2×D3)⋊C4—64no—
197C4⋊Dic3—21no—
198C4⋊Dic3—32no—
199C4⋊Dic3—32no—
200C4⋊Dic3—32no—
201C4⋊Dic3—32no—
202C4⋊Dic3—62no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—64no—
209C4⋊Dic3—121no—
210C4⋊Dic3—121no—
211C4⋊Dic3C22×D312yes—
212Dic3⋊C4—64no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215C4×Dic3D1212yes—
216C4×Dic3C22×D312yes—
217C2×C3⋊C8—22no—
218C2×C3⋊C8C22×D312yes—
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—42no—
231C3⋊Dic3—42no—
232C3×Dic3—22no—
233C3×Dic3—22no—
234C3×Dic3—42no—
235C22×D4—31no—
236C23×C4—181no—
237C22×C8—31no—
238C22×C8D3211yescharacteristic
239#125—94no—
240#125—182no—
241C4×D4—94no—
242C4×D4—182no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C22⋊C4—181no—
249C2×C42—31no—
250#107—94no—
251#106—94no—
252C4⋊C8—34no—
253#102—34no—
254#102—94no—
255C23×C3—21no—
256C23×C3—64no—
257C23×C3—62no—
258C23×C3—122no—
259C23×C3—122no—
260C23×C3C2×D1211yescharacteristic
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—32no—
274C2×C3×C4—32no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—122no—
279C2×C3×C4C2×Dic612yes—
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4#23712yes—
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—42no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297C2×Dic3—128no—
298C2×Dic3—122no—
299C2×Dic3—122no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—242no—
303C2×Dic3—242no—
304C2×Dic3C2×D1212yes—
305C2×Dic3C2×D1212yes—
306D12—24no—
307D12—22no—
308D12C2×Dic614yes—
309C4×D3—128no—
310C3×C8—24no—
311C3×C8—22no—
312C3×C8—22no—
313C3×C8—62no—
314C3⋊C8—22no—
315C2×C32#47814yescomplemented
316C2×C32C2×C22⋊Q811yescharacteristic
317C2×C32C2×#13511yescharacteristic
318C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
319C3×D3—44no—
320C24—61no—
321C2×D4—32no—
322C2×D4—34no—
323C2×D4—61no—
324C2×D4—62no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—61no—
328C22×C4—184no—
329C22×C4—181no—
330C22×C4—181no—
331C22×C4—364no—
332C22×C4C2×D3211yescharacteristic
333C2×C8—22no—
334C2×C8—32no—
335C2×C8—62no—
336C2×C8C2×D3212yes—
337C4⋊C4—32no—
338C4⋊C4—61no—
339C4⋊C4—92no—
340C4⋊C4—92no—
341C4⋊C4—184no—
342C4⋊C4—184no—
343C4⋊C4—181no—
344C4⋊C4—181no—
345C22⋊C4—184no—
346C42—32no—
347C42—32no—
348C22×C3—21no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—64no—
353C22×C3—122no—
354C22×C3—122no—
355C22×C3—128no—
356C22×C3#87812yes—
357C22×C3#89712yes—
358C22×C3#90412yes—
359C22×C3#90812yes—
360C22×C3#91112yes—
361C22×C3#91612yes—
362C22×C3C22×D1211yescharacteristic
363C22×C3C2×D3×D411yescharacteristic
364C2×D3—24no—
365C2×D3—42no—
366C2×D3—42no—
367C2×D3—48no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—22no—
371C3×C4—62no—
372C3×C4—62no—
373C3×C4—122no—
374C3×C4#87812yes—
375C3×C4#89712yes—
376C3×C4C22×Dic611yescharacteristic
377C3×C4C2×#23711yescharacteristic
378C3×C4C2×#23711yescharacteristic
379C3×C4C2×D3×Q811yescharacteristic
380Dic3—22no—
381Dic3—22no—
382Dic3—42no—
383Dic3—122no—
384Dic3—122no—
385Dic3—122no—
386Dic3—122no—
387Dic3—242no—
388Dic3—242no—
389C32C2×#47811yescharacteristic, complemented, Sylow
390C23—62no—
391C23—64no—
392C23—122no—
393C23—122no—
394C23D3×D1211yescharacteristic
395D4—34no—
396D4—62no—
397D4—64no—
398C2×C4—32no—
399C2×C4—32no—
400C2×C4—62no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—122no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4—368no—
407C2×C4—362no—
408C2×C4—362no—
409C2×C4D3×Dic612yes—
410C2×C4D3×D1211yescharacteristic
411C2×C4#380512yes—
412C2×C4C22×D3211yescharacteristic
413C8—22no—
414C8—62no—
415C2×C3—24no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—124no—
420C2×C3#476314yescomplemented
421C2×C3#484714yescomplemented
422C2×C3C2×#87811yescharacteristic
423C2×C3C2×#89711yescharacteristic
424C2×C3C2×#90411yescharacteristic
425C2×C3C2×#90811yescharacteristic
426C2×C3C2×#91111yescharacteristic
427C2×C3C2×#91611yescharacteristic
428D3—44no—
429C22—64no—
430C22—128no—
431C22—122no—
432C22—122no—
433C22#6379512yes—
434C22#6380612yes—
435C22#6389312yes—
436C22C2×D3×D1211yescharacteristic
437C4—62no—
438C4—62no—
439C4—122no—
440C4—362no—
441C4—362no—
442C4#6389312yes—
443C4C2×D3×Dic611yescharacteristic
444C4C2×#380511yescharacteristic
445C3—21no—
446C3C2×#476311yescharacteristic, complemented
447C3C2×#484711yescharacteristic, complemented
448C2—124no—
449C2#1059077214yesdirect product factor
450C2C2×#6379511yescharacteristic
451C2C2×#6380611yescharacteristic
452C2C2×#6389311yescharacteristic
subgroupG/H
centerC23D3×D12
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×#63869C2semidirect
3. C2×#63644C2semidirect
5. C2×C3×Dic3⋊C8C2semidirect
6. C2×#63575C2semidirect
8. #10590772C2direct (N × H)
25. #63869C22semidirect
26. #63644C22semidirect
28. C3×Dic3⋊C8C22semidirect
29. #63575C22semidirect
44. C2×Dic3⋊C8D3semidirect
119. Dic3⋊C8C2×D3semidirect
315. C2×C32#478semidirect
389. C32C2×#478semidirect
420. C2×C3#4763semidirect
421. C2×C3#4847semidirect
446. C3C2×#4763semidirect
447. C3C2×#4847semidirect
449. C2#10590772direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C2×#638692
C2×#636442
C2×C3×#8212
C2×C3×Dic3⋊C82
C2×#635752
C2×#635632
#105907722
C2×#48473
C2×#47633