Finite Group Databasebeta

← C2×#10590590 #11860081

Subgroups — C2×#10590590 #11860081

Order 1152.

1169 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590590C218yesmaximal, direct product factor
9C2×#5018—31nomaximal
10C2×#4889—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
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×Dic32—21no—
24#63844—22no—
25#63844C2214yescomplemented
26C2×#3716C418yescomplemented
27C2×#3716C2214yes—
28#63637C2214yescomplemented
29C3×#807C2214yescomplemented
30#63562C2214yes—
31#63554C2214yescomplemented
32C2×C3×C4×D4—31no—
33C22×#214—31no—
34C22×#204—31no—
35C2×#893D311yescharacteristic
36C2×#887—31no—
37C2×C4×Dic6—31no—
38C2×C3×#107—31no—
39C2×#832—31no—
40C2×#815—31no—
41#5018—38no—
42C2×#810—31no—
43C2×#810—31no—
44C2×#810—61no—
45C2×#809—31no—
46C2×#807D311yescharacteristic, complemented
47C2×#803—31no—
48#4889—38no—
49C23×C3×D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×#634—21no—
54C2×#634—22no—
55C2×#634C2×C414yescomplemented
56C2×#634C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—44no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68C2×C3⋊(C3⋊C8)—22no—
69C2×C3⋊(C3⋊C8)C2312yes—
70C3×(C2×D3)⋊C4—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8C2×C414yescomplemented
76C2×C3×C3⋊C8C2312yes—
77#3724—24no—
78Dic32—24no—
79#3716C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×D4—31no—
82C23×C3×C4—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—21no—
85C22×Dic6—31no—
86C22×Dic6—31no—
87C22×Dic6—61no—
88C22×C3×C8—31no—
89C3×C4×D4—34no—
90C3×C4×D4—62no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4—61no—
96C2×C3×C42—31no—
97C2×#214—38no—
98C2×#214—34no—
99C2×(C2×D3)⋊C4—21no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3—61no—
105C2×C4×Dic3C2×D311yescharacteristic
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110C2×#204—38no—
111C2×#204—34no—
112#893—22no—
113#893C2×D314yes—
114#887—34no—
115#887—62no—
116C4×Dic6—34no—
117C4×Dic6—62no—
118C3×#107—34no—
119#832—34no—
120#815—34no—
121#810—34no—
122#810—34no—
123#810—64no—
124#809—34no—
125#807C2×D314yescomplemented
126#803—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—24no—
139C2×C3⋊Dic3—22no—
140#634—24no—
141#634—22no—
142#634C22×C414yescomplemented
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—42no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×D12—24no—
150C3×D12—22no—
151C3×D12C22×C414yes—
152C3×C4×D3—48no—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—91no—
157C2×C4×D4—31no—
158#440—98no—
159C2×#107—31no—
160C2×#103—91no—
161C2×#102—91no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×D4—34no—
166C2×C3×D4—32no—
167C2×C3×D4—61no—
168C2×C3×D4—62no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—64no—
176C22×C3×C4—61no—
177C22×C3×C4—124no—
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—21no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184C22×Dic3#6711yescharacteristic
185C22×Dic3#6711yescharacteristic
186C2×D12—22no—
187C2×D12—21no—
188C2×D12C4×D314yes—
189C2×D12C22×D312yes—
190C2×C4×D3—24no—
191C2×C4×D3—44no—
192C2×Dic6—34no—
193C2×Dic6—34no—
194C2×Dic6—32no—
195C2×Dic6—32no—
196C2×Dic6—62no—
197C2×Dic6—64no—
198C2×Dic6—62no—
199C2×Dic6—61no—
200C2×Dic6—62no—
201C2×Dic6—61no—
202C2×Dic6—122no—
203C2×Dic6—121no—
204C2×C3×C8—34no—
205C2×C3×C8—32no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—41no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4C22×D312yes—
213C3×C4⋊C4C22×D312yes—
214C3×C22⋊C4—64no—
215C3×C42—32no—
216C3×C42—32no—
217#214—316no—
218(C2×D3)⋊C4—24no—
219C4⋊Dic3—21no—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—64no—
222Dic3⋊C4—64no—
223C4×Dic3—64no—
224C4×Dic3—64no—
225C4×Dic3#6712yes—
226C4×Dic3C22×D312yes—
227C2×C3⋊C8—32no—
228C2×C3⋊C8—32no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—62no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—122no—
233C2×C3⋊C8C4×D314yescomplemented
234C2×C3⋊C8C22×D312yes—
235#204—316no—
236C22×C32C4×D412yes—
237C22×C32AGL(1,ℤ/8)12yes—
238C22×C32#13712yes—
239C22×C32C22×D411yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—48no—
244C32×C4—42no—
245C32×C4C4×D412yes—
246C32×C4C23×C411yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3⋊Dic3—24no—
249C3×Dic3—22no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C22×Q8—91no—
253C22×D4—31no—
254C23×C4—61no—
255C2×SD16—98no—
256C2×SD16—94no—
257C22×C8—31no—
258C22×C8—91no—
259C4×Q8—94no—
260C4×Q8—182no—
261C4×D4—34no—
262C4×D4—62no—
263C2×C4⋊C4—31no—
264C2×C4⋊C4—181no—
265C2×C4⋊C4D3211yescharacteristic
266C2×C22⋊C4—61no—
267C2×C42—31no—
268C2×C42—181no—
269#107—34no—
270#103—94no—
271#102—94no—
272#97—94no—
273C23×C3—21no—
274C23×C3—64no—
275C23×C3—62no—
276C23×C3—122no—
277C23×C3—122no—
278C23×C3D3×D411yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—24no—
281C22×D3—22no—
282C22×D3—42no—
283C22×D3—42no—
284C3×D4—34no—
285C3×D4—64no—
286C3×D4—62no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—32no—
294C2×C3×C4—32no—
295C2×C3×C4—42no—
296C2×C3×C4—42no—
297C2×C3×C4—42no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—82no—
302C2×C3×C4—128no—
303C2×C3×C4—122no—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D312yes—
306C2×C3×C4#23512yes—
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23912yes—
309C2×C3×C4C2×#6711yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—42no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3C2×#6712yes—
323C2×Dic3C2×#6712yes—
324D12—24no—
325D12—22no—
326D12C2×C4×D314yes—
327C4×D3—48no—
328Dic6—34no—
329Dic6—34no—
330Dic6—64no—
331Dic6—64no—
332Dic6—64no—
333Dic6—62no—
334Dic6—62no—
335Dic6—122no—
336Dic6—124no—
337C3×C8—34no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
341C3⋊C8C2×C4×D314yescomplemented
342C2×C32#44014yescomplemented
343C2×C32C2×C4×D411yescharacteristic
344C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3×D3—44no—
347C24—61no—
348C2×Q8—92no—
349C2×Q8—94no—
350C2×Q8—182no—
351C2×Q8—181no—
352C2×D4—32no—
353C2×D4—34no—
354C2×D4—62no—
355C2×D4—61no—
356C22×C4—21no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—64no—
360C22×C4—61no—
361C22×C4—124no—
362C22×C4—181no—
363C22×C4C2×D3211yescharacteristic
364SD16—916no—
365C2×C8—32no—
366C2×C8—34no—
367C2×C8—92no—
368C2×C8—182no—
369C4⋊C4—21no—
370C4⋊C4—32no—
371C4⋊C4—61no—
372C4⋊C4—184no—
373C4⋊C4C2×D3212yes—
374C22⋊C4—64no—
375C42—32no—
376C42—32no—
377C42—184no—
378C22×C3—21no—
379C22×C3—22no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—64no—
383C22×C3—128no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3#89312yes—
387C22×C3#91112yes—
388C22×C3#91812yes—
389C22×C3C4×#6712yes—
390C22×C3#93212yes—
391C22×C3#95112yes—
392C22×C3C2×D3×D411yescharacteristic
393C22×C3C22×#6711yescharacteristic
394C2×D3—24no—
395C2×D3—48no—
396C2×D3—42no—
397C2×D3—42no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—22no—
401C3×C4—42no—
402C3×C4—42no—
403C3×C4—62no—
404C3×C4—62no—
405C3×C4—82no—
406C3×C4—122no—
407C3×C4#89312yes—
408C3×C4C4×#6712yes—
409C3×C4C22×C4×D311yescharacteristic
410C3×C4C22×C4×D311yescharacteristic
411C3×C4C2×#23511yescharacteristic
412C3×C4C2×#23911yescharacteristic
413Dic3—22no—
414Dic3—22no—
415Dic3—42no—
416Dic3—64no—
417Dic3—64no—
418Dic3—124no—
419C32C2×#44011yescharacteristic, complemented, Sylow
420C23—62no—
421C23—64no—
422C23—122no—
423C23—122no—
424C23D3×#6711yescharacteristic
425Q8—94no—
426Q8—182no—
427Q8—184no—
428D4—34no—
429D4—62no—
430D4—64no—
431C2×C4—22no—
432C2×C4—32no—
433C2×C4—32no—
434C2×C4—42no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—128no—
439C2×C4—122no—
440C2×C4—182no—
441C2×C4—184no—
442C2×C4#379912yes—
443C2×C4C4×D3212yes—
444C2×C4D3×#6711yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—34no—
447C8—182no—
448C2×C3—21no—
449C2×C3—24no—
450C2×C3—21no—
451C2×C3—21no—
452C2×C3—124no—
453C2×C3#488914yescomplemented
454C2×C3#501814yescomplemented
455C2×C3C2×#89311yescharacteristic
456C2×C3C2×#91111yescharacteristic
457C2×C3C2×#91811yescharacteristic
458C2×C3C2×C4×#6711yescharacteristic
459C2×C3C2×#93211yescharacteristic
460C2×C3C2×#95111yescharacteristic
461D3—44no—
462C22—64no—
463C22—122no—
464C22—128no—
465C22—122no—
466C22#6390412yes—
467C22#6393212yes—
468C22#6394312yes—
469C22C2×D3×#6711yescharacteristic
470C4—42no—
471C4—62no—
472C4—62no—
473C4—122no—
474C4—184no—
475C4#6390412yes—
476C4C2×#379911yescharacteristic
477C4C2×C4×D3211yescharacteristic
478C3—21no—
479C3C2×#488911yescharacteristic, complemented
480C3C2×#501811yescharacteristic, complemented
481C2—124no—
482C2#1059059014yesdirect product factor
483C2C2×#6390411yescharacteristic
484C2C2×#6393211yescharacteristic
485C2C2×#6394311yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#440
LCSG ▷ 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×#63844C2semidirect
4. C2×#63637C2semidirect
5. C2×C3×#807C2semidirect
7. C2×#63554C2semidirect
8. #10590590C2direct (N × H)
25. #63844C22semidirect
26. C2×#3716C4semidirect
28. #63637C22semidirect
29. C3×#807C22semidirect
31. #63554C22semidirect
46. C2×#807D3semidirect
55. C2×#634C2×C4semidirect
75. C2×C3×C3⋊C8C2×C4semidirect
79. #3716C2×C4semidirect
125. #807C2×D3semidirect
142. #634C22×C4semidirect
154. C3×C3⋊C8C22×C4semidirect
233. C2×C3⋊C8C4×D3semidirect
341. C3⋊C8C2×C4×D3semidirect
342. C2×C32#440semidirect
419. C32C2×#440semidirect
453. C2×C3#4889semidirect
454. C2×C3#5018semidirect
479. C3C2×#4889semidirect
480. C3C2×#5018semidirect
482. C2#10590590direct (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×#638442
C22×#37162
C2×#636372
C2×C3×#8072
C2×#635622
C2×#635542
#105905902
C2×#50183
C2×#48893