Finite Group Databasebeta

← C2×#10590773 #11860082

Subgroups — C2×#10590773 #11860082

Order 1152.

1237 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#63894C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C2×C3×#818C211yesmaximal, characteristic, complemented
5C2×C3×#815C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590773C218yesmaximal, direct product factor
9C2×#4889—31nomaximal
10C2×#4710—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×#624—21no—
14C22×C32×C8C2211yescharacteristic
15C2×#3744C418yescomplemented
16C2×#3744C2214yes—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3724—21no—
22C2×#3722—21no—
23C2×Dic32—21no—
24#63894—22no—
25#63894C2214yes—
26#63844—22no—
27#63844C2214yescomplemented
28C3×#818C2214yescomplemented
29C3×#815C2214yescomplemented
30#63567C2214yescomplemented
31#63564C2214yes—
32C22×#204—31no—
33C22×#204—31no—
34C22×#204—61no—
35C2×#893—31no—
36C2×#887—31no—
37C2×C4×D12—31no—
38C2×C4×Dic6—31no—
39C2×C3×#107—31no—
40C2×C3×#97—31no—
41C2×#821—31no—
42C2×#818D311yescharacteristic, complemented
43C2×#816—31no—
44C2×#815D311yescharacteristic, complemented
45C2×#810—31no—
46C2×#809—31no—
47#4889—38no—
48#4710—38no—
49C23×C3⋊D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2×C414yes—
55C2×C4⋊(C3⋊D3)C2312yes—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634C2×C414yescomplemented
59C2×#634C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C22×C3×Dic3D411yescharacteristic
64C2×#624—24no—
65C2×#624—44no—
66C2×C32×C8C2×C414yescomplemented
67C2×C32×C8C2312yes—
68#3744C2×C4116yescomplemented
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73C3×C4×Dic3D412yes—
74C3×C4×Dic3C2312yes—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77#3724—24no—
78#3722—24no—
79Dic32—24no—
80C2×#440—91noSylow
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×C4×D3—61no—
85C22×C4×D3—61no—
86C22×Dic6—31no—
87C22×Dic6—31no—
88C22×Dic6—61no—
89C22×C3×C8—21no—
90C22×C3×C8—31no—
91C22×C3×C8C2×D311yescharacteristic
92C22×C3×C8C2×D311yescharacteristic
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—31no—
96C2×(C2×D3)⋊C4—61no—
97C2×(C2×D3)⋊C4—61no—
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3—61no—
104C2×C4×Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C2×#204—38no—
107C2×#204—38no—
108C2×#204—34no—
109C2×#204—34no—
110C2×#204—68no—
111C2×#204—64no—
112#893—34no—
113#893—62no—
114#887—34no—
115#887—62no—
116C4×D12—34no—
117C4×D12—62no—
118C4×Dic6—34no—
119C4×Dic6—62no—
120C3×#107—34no—
121C3×#97—34no—
122#821—34no—
123#818C2×D314yescomplemented
124#816—34no—
125#815C2×D314yescomplemented
126#810—34no—
127#809—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—24no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
133C2×C32×C4C22×C412yes—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4112yes—
136C2×C32×C4C2411yescharacteristic
137C2×C3⋊Dic3—24no—
138C2×C3⋊Dic3—22no—
139C4⋊(C3⋊D3)—24no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)C22×C414yes—
142#634—24no—
143#634—22no—
144#634C22×C414yescomplemented
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3C2×D412yes—
152C2×C3×Dic3C2×D412yes—
153#624—48no—
154C32×C8C22×C414yescomplemented
155C3×C3⋊C8—22no—
156C22×SD16—91no—
157C2×C4×Q8—91no—
158C2×C4×D4—91no—
159#440—98no—
160C2×#107—31no—
161C2×#103—91no—
162C2×#102—91no—
163C2×#97—31no—
164C23×D3—61no—
165C23×D3—61no—
166C23×D3—121no—
167C22×C3×C4—21no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—61no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C22×Dic3—121no—
179C22×Dic3D1211yescharacteristic
180C22×Dic3D1211yescharacteristic
181C2×D12—34no—
182C2×D12—34no—
183C2×D12—32no—
184C2×D12—32no—
185C2×D12—64no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—62no—
189C2×D12—61no—
190C2×D12—62no—
191C2×D12—122no—
192C2×D12—121no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—124no—
196C2×C4×D3—124no—
197C2×Dic6—34no—
198C2×Dic6—34no—
199C2×Dic6—32no—
200C2×Dic6—32no—
201C2×Dic6—64no—
202C2×Dic6—62no—
203C2×Dic6—61no—
204C2×Dic6—62no—
205C2×Dic6—61no—
206C2×Dic6—62no—
207C2×Dic6—122no—
208C2×Dic6—121no—
209C2×C3×C8—24no—
210C2×C3×C8—22no—
211C2×C3×C8—32no—
212C2×C3×C8—62no—
213C2×C3×C8C4×D314yescomplemented
214C2×C3×C8C4×D314yescomplemented
215C2×C3×C8C22×D312yes—
216C2×C3×C8C22×D312yes—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—32no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4—61no—
221C3×C42—32no—
222C3×C42—32no—
223(C2×D3)⋊C4—64no—
224(C2×D3)⋊C4—64no—
225C4⋊Dic3—21no—
226C4⋊Dic3—21no—
227C4⋊Dic3C22×D312yes—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—64no—
230Dic3⋊C4—64no—
231C4×Dic3—64no—
232C4×Dic3—64no—
233C4×Dic3D1212yes—
234C4×Dic3C22×D312yes—
235C2×C3⋊C8—22no—
236C2×C3⋊C8C22×D312yes—
237#204—316no—
238#204—316no—
239#204—616no—
240C22×C32C4×D412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32#13712yes—
243C22×C32C22×D411yescharacteristic
244C2×C3⋊D3—24no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—48no—
248C32×C4C4×D412yes—
249C32×C4C23×C411yescharacteristic
250C32×C4C2×#4111yescharacteristic
251C3⋊Dic3—24no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C22×Q8—91no—
257C22×D4—91no—
258C23×C4—181no—
259C2×SD16—98no—
260C2×SD16—94no—
261C22×C8—31no—
262C22×C8D3211yescharacteristic
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—94no—
266C4×D4—182no—
267C2×C4⋊C4—31no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—181no—
270C2×C22⋊C4—181no—
271C2×C42—31no—
272C2×C42—181no—
273#107—34no—
274#103—94no—
275#102—94no—
276#97—34no—
277C23×C3—21no—
278C23×C3C2×D1211yescharacteristic
279C23×C3D3×D411yescharacteristic
280C22×D3—64no—
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—122no—
285C22×D3—124no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—242no—
291C22×D3—242no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4—62no—
302C2×C3×C4—122no—
303C2×C3×C4—122no—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D312yes—
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23512yes—
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23912yes—
310C2×C3×C4C23×D311yescharacteristic
311C2×C3×C4C23×D311yescharacteristic
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—22no—
315C2×Dic3—22no—
316C2×Dic3—42no—
317C2×Dic3—42no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3—124no—
324C2×Dic3C2×D1212yes—
325C2×Dic3C2×D1212yes—
326D12—34no—
327D12—34no—
328D12—64no—
329D12—64no—
330D12—64no—
331D12—62no—
332D12—62no—
333D12—122no—
334D12—124no—
335C4×D3—128no—
336C4×D3—128no—
337Dic6—34no—
338Dic6—34no—
339Dic6—64no—
340Dic6—64no—
341Dic6—64no—
342Dic6—62no—
343Dic6—62no—
344Dic6—122no—
345Dic6—124no—
346C3×C8—24no—
347C3×C8—62no—
348C3×C8C2×C4×D314yescomplemented
349C3×C8C2×C4×D314yescomplemented
350C3⋊C8—22no—
351C2×C32#44014yescomplemented
352C2×C32C2×C4×D411yescharacteristic
353C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
354C2×C32C2×#13711yescharacteristic
355C3⋊D3—44no—
356C24—181no—
357C2×Q8—92no—
358C2×Q8—94no—
359C2×Q8—182no—
360C2×Q8—181no—
361C2×D4—92no—
362C2×D4—94no—
363C2×D4—182no—
364C2×D4—181no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—184no—
370C22×C4—181no—
371C22×C4—364no—
372C22×C4C2×D3211yescharacteristic
373SD16—916no—
374C2×C8—32no—
375C2×C8—62no—
376C2×C8#62414yescomplemented
377C2×C8C2×D3212yes—
378C4⋊C4—32no—
379C4⋊C4—32no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—184no—
383C22⋊C4—184no—
384C42—32no—
385C42—32no—
386C42—184no—
387C22×C3—21no—
388C22×C3—22no—
389C22×C3—22no—
390C22×C3—22no—
391C22×C3C4×D1212yes—
392C22×C3#89312yes—
393C22×C3#90812yes—
394C22×C3#90912yes—
395C22×C3#91112yes—
396C22×C3#91812yes—
397C22×C3C22×D1211yescharacteristic
398C22×C3C2×D3×D411yescharacteristic
399C2×D3—64no—
400C2×D3—64no—
401C2×D3—124no—
402C2×D3—128no—
403C2×D3—128no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—248no—
409C2×D3—242no—
410C2×D3—242no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—22no—
414C3×C4—62no—
415C3×C4—62no—
416C3×C4—122no—
417C3×C4—122no—
418C3×C4C4×D1212yes—
419C3×C4#89312yes—
420C3×C4C22×C4×D311yescharacteristic
421C3×C4C22×C4×D311yescharacteristic
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×#23911yescharacteristic
424Dic3—22no—
425Dic3—22no—
426Dic3—42no—
427Dic3—42no—
428Dic3—64no—
429Dic3—64no—
430Dic3—124no—
431C32C2×#44011yescharacteristic, complemented, Sylow
432C23—182no—
433C23—184no—
434C23—362no—
435C23—362no—
436C23D3×D1211yescharacteristic
437Q8—94no—
438Q8—182no—
439Q8—184no—
440D4—94no—
441D4—182no—
442D4—184no—
443C2×C4—32no—
444C2×C4—32no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—122no—
450C2×C4—122no—
451C2×C4—182no—
452C2×C4—184no—
453C2×C4—368no—
454C2×C4#379912yes—
455C2×C4D3×D1211yescharacteristic
456C2×C4C2×#62412yes—
457C2×C4C22×D3211yescharacteristic
458C8—62no—
459C8C2×#62414yescomplemented
460C2×C3—24no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3#471014yescomplemented
465C2×C3#488914yescomplemented
466C2×C3C2×C4×D1211yescharacteristic
467C2×C3C2×#89311yescharacteristic
468C2×C3C2×#90811yescharacteristic
469C2×C3C2×#90911yescharacteristic
470C2×C3C2×#91111yescharacteristic
471C2×C3C2×#91811yescharacteristic
472D3—124no—
473D3—124no—
474D3—244no—
475C22—184no—
476C22—368no—
477C22—362no—
478C22—362no—
479C22#6379512yes—
480C22#6380112yes—
481C22#6389412yes—
482C22C2×D3×D1211yescharacteristic
483C4—62no—
484C4—62no—
485C4—122no—
486C4—122no—
487C4—184no—
488C4#6389412yes—
489C4C2×#379911yescharacteristic
490C4C22×#62411yescharacteristic
491C3—21no—
492C3C2×#471011yescharacteristic, complemented
493C3C2×#488911yescharacteristic, complemented
494C2—364no—
495C2#1059077314yesdirect product factor
496C2C2×#6379511yescharacteristic
497C2C2×#6380111yescharacteristic
498C2C2×#6389411yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C2×#440
LCSG ▷ 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
3. C2×#63844C2semidirect
4. C2×C3×#818C2semidirect
5. C2×C3×#815C2semidirect
6. C2×#63567C2semidirect
8. #10590773C2direct (N × H)
15. C2×#3744C4semidirect
27. #63844C22semidirect
28. C3×#818C22semidirect
29. C3×#815C22semidirect
30. #63567C22semidirect
42. C2×#818D3semidirect
44. C2×#815D3semidirect
58. C2×#634C2×C4semidirect
66. C2×C32×C8C2×C4semidirect
68. #3744C2×C4semidirect
123. #818C2×D3semidirect
125. #815C2×D3semidirect
144. #634C22×C4semidirect
154. C32×C8C22×C4semidirect
213. C2×C3×C8C4×D3semidirect
214. C2×C3×C8C4×D3semidirect
348. C3×C8C2×C4×D3semidirect
349. C3×C8C2×C4×D3semidirect
351. C2×C32#440semidirect
376. C2×C8#624semidirect
431. C32C2×#440semidirect
459. C8C2×#624semidirect
464. C2×C3#4710semidirect
465. C2×C3#4889semidirect
492. C3C2×#4710semidirect
493. C3C2×#4889semidirect
495. C2#10590773direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638942
C2×#638442
C2×C3×#8182
C2×C3×#8152
C2×#635672
C2×#635642
#105907732
C2×#48893
C2×#47103