Finite Group Databasebeta

← C2×#10590589 #11860163

Subgroups — C2×#10590589 #11860163

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4C2×#63636C211yesmaximal, characteristic, complemented
5C2×C3×#808C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590589C218yesmaximal, direct product factor
9C2×#5014—31nomaximal
10C2×#4869—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×#624—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893—22no—
22C3×#893C2214yescomplemented
23C2×#3722—21no—
24#63894—22no—
25#63894C2214yescomplemented
26C2×#3714C418yescomplemented
27C2×#3714C2214yes—
28#63636C2214yescomplemented
29C3×#808C2214yescomplemented
30#63562C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×D4—31no—
33C22×#213—31no—
34C22×D24—31no—
35C2×#893—31no—
36C2×#893D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C3×#106—31no—
39C2×#832—31no—
40C2×#815—31no—
41#5014—38no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#809—31no—
45C2×#809—61no—
46C2×#808D311yescharacteristic, complemented
47C2×#803—31no—
48#4869—38no—
49C23×C3⋊D3—21no—
50C23×C3×D3—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)C2×C414yescomplemented
56C2×C4⋊(C3⋊D3)C2312yes—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C22×C3×Dic3D411yescharacteristic
60C2×C3×D12—21no—
61C2×C3×D12—22no—
62C2×C3×D12C2×C414yescomplemented
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—44no—
66C2×#624—24no—
67C2×#624—44no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C2×C3⋊(C3⋊C8)—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×(C2×D3)⋊C4—24no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79#3722—24no—
80#3714C2×C4116yescomplemented
81C2×#442—91noSylow
82C22×C3×D4—31no—
83C23×C3×C4—61no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—61no—
90C22×C4×D3—61no—
91C22×C3×C8—31no—
92C3×C4×D4—34no—
93C3×C4×D4—62no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C22⋊C4—61no—
99C2×C3×C42—31no—
100C2×#213—38no—
101C2×#213—34no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4×Dic3C2×D311yescharacteristic
107C22×C3⋊C8—31no—
108C22×C3⋊C8—31no—
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C2×D24—38no—
112C2×D24—34no—
113#893—22no—
114#893—34no—
115#893—62no—
116#893C2×D314yescomplemented
117C4×D12—34no—
118C4×D12—62no—
119C3×#106—34no—
120#832—34no—
121#815—34no—
122#809—34no—
123#809—34no—
124#809—34no—
125#809—64no—
126#808C2×D314yescomplemented
127#803—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3⋊D3—24no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—42no—
132C22×C3⋊D3—42no—
133C22×C3×D3—24no—
134C22×C3×D3—22no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C4⋊(C3⋊D3)—24no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)C22×C414yescomplemented
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3C2×D412yes—
151C2×C3×Dic3C2×D412yes—
152C3×D12—24no—
153C3×D12—22no—
154C3×D12C22×C414yescomplemented
155C3×C4×D3—48no—
156#624—48no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8C22×C414yescomplemented
159C22×D8—91no—
160C2×C4×D4—31no—
161C2×C4×D4—91no—
162#442—98no—
163C2×#106—31no—
164C2×#102—91no—
165C2×#102—91no—
166C2×#97—91no—
167C24×C3—61no—
168C23×D3—21no—
169C23×D3—61no—
170C23×D3—61no—
171C23×D3—121no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—61no—
175C2×C3×D4—62no—
176C22×C3×C4—21no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—41no—
182C22×C3×C4—64no—
183C22×C3×C4—61no—
184C22×C3×C4—124no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3#6711yescharacteristic
189C22×Dic3#6711yescharacteristic
190C2×D12—22no—
191C2×D12—21no—
192C2×D12—34no—
193C2×D12—34no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—62no—
197C2×D12—64no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—62no—
201C2×D12—61no—
202C2×D12—122no—
203C2×D12—121no—
204C2×D12C4×D314yescomplemented
205C2×D12C22×D312yes—
206C2×C4×D3—24no—
207C2×C4×D3—44no—
208C2×C4×D3—64no—
209C2×C4×D3—64no—
210C2×C4×D3—124no—
211C2×C4×D3—124no—
212C2×C3×C8—34no—
213C2×C3×C8—32no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—22no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—61no—
220C3×C4⋊C4C22×D312yes—
221C3×C4⋊C4C22×D312yes—
222C3×C22⋊C4—64no—
223C3×C42—32no—
224C3×C42—32no—
225#213—316no—
226(C2×D3)⋊C4—24no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3C22×D312yes—
231C4×Dic3#6712yes—
232C4×Dic3C22×D312yes—
233C2×C3⋊C8—32no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—62no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—122no—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241D24—316no—
242C22×C32C4×D412yes—
243C22×C32AGL(1,ℤ/8)12yes—
244C22×C32AGL(1,ℤ/8)12yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—24no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—48no—
250C2×C3×D3—24no—
251C2×C3×D3—42no—
252C2×C3×D3—42no—
253C2×C3×D3—48no—
254C32×C4—42no—
255C32×C4C4×D412yes—
256C32×C4C23×C411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3×Dic3—22no—
259C3×Dic3—22no—
260C3×Dic3—42no—
261C22×D4—31no—
262C22×D4—91no—
263C23×C4—61no—
264C23×C4—181no—
265C2×D8—98no—
266C2×D8—94no—
267C22×C8—31no—
268C22×C8—91no—
269C4×D4—34no—
270C4×D4—62no—
271C4×D4—94no—
272C4×D4—182no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4D3211yescharacteristic
275C2×C22⋊C4—61no—
276C2×C22⋊C4—181no—
277C2×C42—31no—
278#106—34no—
279#102—94no—
280#102—94no—
281#97—94no—
282C23×C3—21no—
283C23×C3—64no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3D3×D411yescharacteristic
288C23×C3C2×#6711yescharacteristic
289C22×D3—24no—
290C22×D3—22no—
291C22×D3—42no—
292C22×D3—42no—
293C22×D3—64no—
294C22×D3—64no—
295C22×D3—62no—
296C22×D3—62no—
297C22×D3—122no—
298C22×D3—124no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—122no—
302C22×D3—122no—
303C22×D3—242no—
304C22×D3—242no—
305C3×D4—34no—
306C3×D4—64no—
307C3×D4—62no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—21no—
314C2×C3×C4—32no—
315C2×C3×C4—32no—
316C2×C3×C4—42no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—62no—
322C2×C3×C4—82no—
323C2×C3×C4—128no—
324C2×C3×C4—122no—
325C2×C3×C4C2×C4×D312yes—
326C2×C3×C4C2×C4×D312yes—
327C2×C3×C4#23512yes—
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23912yes—
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C23×D311yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—22no—
334C2×Dic3—22no—
335C2×Dic3—22no—
336C2×Dic3—42no—
337C2×Dic3C2×#6712yes—
338C2×Dic3C2×#6712yes—
339D12—24no—
340D12—22no—
341D12—34no—
342D12—34no—
343D12—64no—
344D12—64no—
345D12—64no—
346D12—62no—
347D12—62no—
348D12—122no—
349D12—124no—
350D12C2×C4×D314yescomplemented
351C4×D3—48no—
352C4×D3—128no—
353C4×D3—128no—
354C3×C8—34no—
355C3⋊C8—62no—
356C3⋊C8—62no—
357C3⋊C8—122no—
358C3⋊C8C2×C4×D314yescomplemented
359C2×C32#44214yescomplemented
360C2×C32C2×C4×D411yescharacteristic
361C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
362C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
363C3⋊D3—44no—
364C3×D3—44no—
365C24—61no—
366C24—181no—
367C2×D4—32no—
368C2×D4—34no—
369C2×D4—62no—
370C2×D4—61no—
371C2×D4—92no—
372C2×D4—94no—
373C2×D4—182no—
374C2×D4—181no—
375C22×C4—21no—
376C22×C4—31no—
377C22×C4—31no—
378C22×C4—64no—
379C22×C4—61no—
380C22×C4—124no—
381C22×C4—184no—
382C22×C4—364no—
383C22×C4C2×D3211yescharacteristic
384D8—916no—
385C2×C8—32no—
386C2×C8—34no—
387C2×C8—92no—
388C2×C8—182no—
389C4⋊C4—21no—
390C4⋊C4—32no—
391C4⋊C4—61no—
392C4⋊C4C2×D3212yes—
393C22⋊C4—64no—
394C22⋊C4—184no—
395C42—32no—
396C42—32no—
397C22×C3—21no—
398C22×C3—22no—
399C22×C3—22no—
400C22×C3—22no—
401C22×C3—64no—
402C22×C3—128no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3#89312yes—
406C22×C3#91412yes—
407C22×C3#91412yes—
408C22×C3C4×#6712yes—
409C22×C3#93212yes—
410C22×C3#94912yes—
411C22×C3C2×D3×D411yescharacteristic
412C22×C3C22×#6711yescharacteristic
413C2×D3—24no—
414C2×D3—48no—
415C2×D3—42no—
416C2×D3—42no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—124no—
420C2×D3—128no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—128no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—242no—
427C2×D3—248no—
428C2×D3—242no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—42no—
433C3×C4—42no—
434C3×C4—62no—
435C3×C4—62no—
436C3×C4—82no—
437C3×C4—122no—
438C3×C4#89312yes—
439C3×C4C4×#6712yes—
440C3×C4C22×C4×D311yescharacteristic
441C3×C4C22×C4×D311yescharacteristic
442C3×C4C2×#23511yescharacteristic
443C3×C4C2×#23911yescharacteristic
444Dic3—22no—
445Dic3—22no—
446Dic3—42no—
447C32C2×#44211yescharacteristic, complemented, Sylow
448C23—62no—
449C23—64no—
450C23—122no—
451C23—122no—
452C23—182no—
453C23—184no—
454C23—362no—
455C23—362no—
456C23D3×#6711yescharacteristic
457D4—34no—
458D4—62no—
459D4—64no—
460D4—94no—
461D4—182no—
462D4—184no—
463C2×C4—22no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—42no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—128no—
471C2×C4—122no—
472C2×C4—368no—
473C2×C4#379912yes—
474C2×C4C4×D3212yes—
475C2×C4D3×#6711yescharacteristic
476C2×C4C22×D3211yescharacteristic
477C8—34no—
478C8—182no—
479C2×C3—21no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—124no—
484C2×C3#486914yescomplemented
485C2×C3#501414yescomplemented
486C2×C3C2×#89311yescharacteristic
487C2×C3C2×#91411yescharacteristic
488C2×C3C2×#91411yescharacteristic
489C2×C3C2×C4×#6711yescharacteristic
490C2×C3C2×#93211yescharacteristic
491C2×C3C2×#94911yescharacteristic
492D3—44no—
493D3—124no—
494D3—124no—
495D3—244no—
496C22—64no—
497C22—122no—
498C22—128no—
499C22—122no—
500C22—184no—
501C22—362no—
502C22—368no—
503C22—362no—
504C22#6390412yes—
505C22#6393412yes—
506C22#6393912yes—
507C22C2×D3×#6711yescharacteristic
508C4—42no—
509C4—62no—
510C4—62no—
511C4—122no—
512C4#6390412yes—
513C4C2×#379911yescharacteristic
514C4C2×C4×D3211yescharacteristic
515C3—21no—
516C3C2×#486911yescharacteristic, complemented
517C3C2×#501411yescharacteristic, complemented
518C2—124no—
519C2—364no—
520C2#1059058914yesdirect product factor
521C2C2×#6390411yescharacteristic
522C2C2×#6393411yescharacteristic
523C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#442
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
1. C2×C3×#893C2semidirect
2. C2×#63894C2semidirect
4. C2×#63636C2semidirect
5. C2×C3×#808C2semidirect
6. C2×#63562C2semidirect
7. C2×#63554C2semidirect
8. #10590589C2direct (N × H)
22. C3×#893C22semidirect
25. #63894C22semidirect
26. C2×#3714C4semidirect
28. #63636C22semidirect
29. C3×#808C22semidirect
30. #63562C22semidirect
31. #63554C22semidirect
36. C2×#893D3semidirect
46. C2×#808D3semidirect
55. C2×C4⋊(C3⋊D3)C2×C4semidirect
62. C2×C3×D12C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
80. #3714C2×C4semidirect
116. #893C2×D3semidirect
126. #808C2×D3semidirect
145. C4⋊(C3⋊D3)C22×C4semidirect
154. C3×D12C22×C4semidirect
158. C3×C3⋊C8C22×C4semidirect
204. C2×D12C4×D3semidirect
239. C2×C3⋊C8C4×D3semidirect
350. D12C2×C4×D3semidirect
358. C3⋊C8C2×C4×D3semidirect
359. C2×C32#442semidirect
447. C32C2×#442semidirect
484. C2×C3#4869semidirect
485. C2×C3#5014semidirect
516. C3C2×#4869semidirect
517. C3C2×#5014semidirect
520. C2#10590589direct (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×#638942
C22×#37142
C2×#636362
C2×C3×#8082
C2×#635622
C2×#635542
#105905892
C2×#50143
C2×#48693