Finite Group Databasebeta

← C2×#10590545 #11868366

Subgroups — C2×#10590545 #11868366

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×C3×#893C211yesmaximal, characteristic
2C2×#63869C211yesmaximal, characteristic, complemented
3C2×#63634C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C2×#63562C211yesmaximal, characteristic
8#10590545C218yesmaximal, direct product factor
9C2×#5009—31nomaximal
10C2×#4871—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#893—22no—
21C3×#893C2214yes—
22C2×#3724—21no—
23C2×Dic3⋊Dic3—21no—
24#63869—22no—
25#63869C2214yescomplemented
26#63634C2214yescomplemented
27C3×#808C2214yescomplemented
28Dic3⋊(C3⋊C8)C2214yescomplemented
29#63563C2214yes—
30#63562C2214yes—
31C2×C3×C4×D4—31no—
32C2×#893D311yescharacteristic
33C2×#890—31no—
34C2×#870—31no—
35C2×C3×#106—31no—
36C2×#832—31no—
37C2×#832—31no—
38C2×#821—31no—
39C2×Dic3⋊C8—31no—
40#5009—38no—
41C2×#809—31no—
42C2×#808D311yescharacteristic, complemented
43C2×#807—31no—
44C2×#807—31no—
45C2×#807—61no—
46C2×C4⋊(C3⋊C8)—31no—
47#4871—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
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×C3×C4×D3—24no—
60C2×C3×C4×D3—44no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C2×C3⋊(C3⋊C8)—22no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C3×(C2×D3)⋊C4—24no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3C2312yes—
70C3×C4×Dic3D412yes—
71C3×C4×Dic3C2312yes—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8C2312yes—
74#3724—24no—
75Dic3⋊Dic3—24no—
76C2×#478—91noSylow
77C22×C3×D4—31no—
78C23×C3×C4—61no—
79C22×D12C2×D311yescharacteristic
80C22×C4×D3—21no—
81C22×C3×C8—31no—
82C3×C4×D4—34no—
83C3×C4×D4—62no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×C3×C22⋊C4—61no—
89C2×C3×C42—31no—
90C2×(C2×D3)⋊C4—21no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—31no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×Dic3⋊C4—61no—
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104#893—22no—
105#893C2×D314yes—
106#890—34no—
107#890—62no—
108#870—34no—
109#870—62no—
110C3×#106—34no—
111#832—34no—
112#832—34no—
113#821—34no—
114Dic3⋊C8—34no—
115#809—34no—
116#808C2×D314yescomplemented
117#807—34no—
118#807—34no—
119#807—64no—
120C4⋊(C3⋊C8)—34no—
121C23×C32C2×D411yescharacteristic
122C22×C3×D3—24no—
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C2×C32×C4—22no—
127C2×C32×C4—42no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q812yes—
130C2×C32×C4#4112yes—
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—22no—
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—
143C3×C4×D3—48no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C2×#125—91no—
147C2×C4×D4—31no—
148#478—98no—
149C2×#107—91no—
150C2×#106—31no—
151C2×C4⋊C8—91no—
152C2×#102—91no—
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—21no—
162C22×C3×C4—21no—
163C22×C3×C4—31no—
164C22×C3×C4—31no—
165C22×C3×C4—41no—
166C22×C3×C4—64no—
167C22×C3×C4—61no—
168C22×C3×C4—124no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—61no—
173C22×Dic3—61no—
174C22×Dic3—121no—
175C22×Dic3#6711yescharacteristic
176C22×Dic3#6711yescharacteristic
177C2×D12—22no—
178C2×D12—21no—
179C2×D12Dic614yes—
180C2×D12C22×D312yes—
181C2×C4×D3—24no—
182C2×C4×D3—44no—
183C2×C3×C8—32no—
184C2×C3×C8—62no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—22no—
188C3×C4⋊C4—32no—
189C3×C4⋊C4—41no—
190C3×C4⋊C4—61no—
191C3×C4⋊C4C22×D312yes—
192C3×C4⋊C4C22×D312yes—
193C3×C22⋊C4—64no—
194C3×C42—32no—
195C3×C42—32no—
196(C2×D3)⋊C4—24no—
197C4⋊Dic3—21no—
198C4⋊Dic3—32no—
199C4⋊Dic3—32no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—64no—
204C4⋊Dic3—121no—
205C4⋊Dic3C22×D312yes—
206Dic3⋊C4—64no—
207Dic3⋊C4—64no—
208Dic3⋊C4—64no—
209C4×Dic3#6712yes—
210C4×Dic3C22×D312yes—
211C2×C3⋊C8—22no—
212C2×C3⋊C8—32no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—62no—
215C2×C3⋊C8—64no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—62no—
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×C4—42no—
228C32×C4C22⋊Q812yes—
229C32×C4C22×Q811yescharacteristic
230C32×C4C2×#4111yescharacteristic
231C3⋊Dic3—42no—
232C3×Dic3—22no—
233C3×Dic3—22no—
234C3×Dic3—42no—
235C22×D4—31no—
236C23×C4—61no—
237C22×C8—31no—
238C22×C8—91no—
239#125—94no—
240#125—182no—
241C4×D4—34no—
242C4×D4—62no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4D3211yescharacteristic
248C2×C22⋊C4—61no—
249C2×C42—31no—
250#107—94no—
251#106—34no—
252C4⋊C8—94no—
253#102—94no—
254#102—94no—
255C23×C3—21no—
256C23×C3—64no—
257C23×C3—62no—
258C23×C3—122no—
259C23×C3—122no—
260C23×C3D3×D411yescharacteristic
261C23×C3C2×#6711yescharacteristic
262C22×D3—24no—
263C22×D3—22no—
264C22×D3—42no—
265C22×D3—42no—
266C3×D4—34no—
267C3×D4—64no—
268C3×D4—62no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—21no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—21no—
275C2×C3×C4—32no—
276C2×C3×C4—32no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—42no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—82no—
284C2×C3×C4—128no—
285C2×C3×C4—122no—
286C2×C3×C4C2×Dic612yes—
287C2×C3×C4#23512yes—
288C2×C3×C4#23512yes—
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×Q812yes—
291C2×C3×C4C2×#6711yescharacteristic
292C2×C3×C4C23×D311yescharacteristic
293C2×C3×C4C23×D311yescharacteristic
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—42no—
298C2×Dic3—62no—
299C2×Dic3—62no—
300C2×Dic3—122no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3—242no—
304C2×Dic3C2×#6712yes—
305C2×Dic3C2×#6712yes—
306D12—24no—
307D12—22no—
308D12C2×Dic614yes—
309C4×D3—48no—
310C3×C8—62no—
311C3⋊C8—22no—
312C3⋊C8—64no—
313C3⋊C8—62no—
314C3⋊C8—62no—
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—62no—
324C2×D4—61no—
325C22×C4—21no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—64no—
329C22×C4—61no—
330C22×C4—124no—
331C22×C4—181no—
332C22×C4C2×D3211yescharacteristic
333C2×C8—32no—
334C2×C8—62no—
335C2×C8—92no—
336C2×C8—182no—
337C4⋊C4—21no—
338C4⋊C4—32no—
339C4⋊C4—61no—
340C4⋊C4—92no—
341C4⋊C4—184no—
342C4⋊C4—184no—
343C4⋊C4—181no—
344C4⋊C4C2×D3212yes—
345C22⋊C4—64no—
346C42—32no—
347C42—32no—
348C22×C3—21no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—64no—
353C22×C3—128no—
354C22×C3—122no—
355C22×C3—122no—
356C22×C3#89612yes—
357C22×C3#91412yes—
358C22×C3#91612yes—
359C22×C3#92412yes—
360C22×C3#93212yes—
361C22×C3#95012yes—
362C22×C3C2×D3×D411yescharacteristic
363C22×C3C22×#6711yescharacteristic
364C2×D3—24no—
365C2×D3—48no—
366C2×D3—42no—
367C2×D3—42no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—22no—
371C3×C4—42no—
372C3×C4—42no—
373C3×C4—62no—
374C3×C4—62no—
375C3×C4—82no—
376C3×C4—122no—
377C3×C4#89612yes—
378C3×C4#92412yes—
379C3×C4C22×Dic611yescharacteristic
380C3×C4C2×#23511yescharacteristic
381C3×C4C2×#23511yescharacteristic
382C3×C4C2×D3×Q811yescharacteristic
383Dic3—22no—
384Dic3—22no—
385Dic3—42no—
386Dic3—122no—
387Dic3—122no—
388Dic3—242no—
389C32C2×#47811yescharacteristic, complemented, Sylow
390C23—62no—
391C23—64no—
392C23—122no—
393C23—122no—
394C23D3×#6711yescharacteristic
395D4—34no—
396D4—62no—
397D4—64no—
398C2×C4—22no—
399C2×C4—32no—
400C2×C4—32no—
401C2×C4—42no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—128no—
406C2×C4—122no—
407C2×C4—182no—
408C2×C4—362no—
409C2×C4D3×Dic612yes—
410C2×C4#379812yes—
411C2×C4D3×#6711yescharacteristic
412C2×C4C22×D3211yescharacteristic
413C8—62no—
414C8—182no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—24no—
419C2×C3—124no—
420C2×C3#487114yescomplemented
421C2×C3#500914yescomplemented
422C2×C3C2×#89611yescharacteristic
423C2×C3C2×#91411yescharacteristic
424C2×C3C2×#91611yescharacteristic
425C2×C3C2×#92411yescharacteristic
426C2×C3C2×#93211yescharacteristic
427C2×C3C2×#95011yescharacteristic
428D3—44no—
429C22—64no—
430C22—122no—
431C22—122no—
432C22—128no—
433C22#6385112yes—
434C22#6393412yes—
435C22#6394712yes—
436C22C2×D3×#6711yescharacteristic
437C4—42no—
438C4—62no—
439C4—62no—
440C4—122no—
441C4—362no—
442C4#6385112yes—
443C4C2×D3×Dic611yescharacteristic
444C4C2×#379811yescharacteristic
445C3—21no—
446C3C2×#487111yescharacteristic, complemented
447C3C2×#500911yescharacteristic, complemented
448C2—124no—
449C2#1059054514yesdirect product factor
450C2C2×#6385111yescharacteristic
451C2C2×#6393411yescharacteristic
452C2C2×#6394711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63869C2semidirect
3. C2×#63634C2semidirect
4. C2×C3×#808C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590545C2direct (N × H)
25. #63869C22semidirect
26. #63634C22semidirect
27. C3×#808C22semidirect
28. Dic3⋊(C3⋊C8)C22semidirect
42. C2×#808D3semidirect
116. #808C2×D3semidirect
315. C2×C32#478semidirect
389. C32C2×#478semidirect
420. C2×C3#4871semidirect
421. C2×C3#5009semidirect
446. C3C2×#4871semidirect
447. C3C2×#5009semidirect
449. C2#10590545direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×#638692
C2×#636342
C2×C3×#8082
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#635622
#105905452
C2×#50093
C2×#48713