Finite Group Databasebeta

← C2×#10590743 #11860074

Subgroups — C2×#10590743 #11860074

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic
4C2×#63642C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63576C211yesmaximal, characteristic, complemented
8#10590743C218yesmaximal, direct product factor
9C2×#4817—31nomaximal
10C2×#4757—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×D3×Dic3—21no—
14C22×C32×C8C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×Dic32—21no—
22#63898—22no—
23#63898C2214yes—
24#63843—22no—
25#63843C2214yescomplemented
26C2×#3715C418yescomplemented
27C2×#3715C2214yes—
28#63642C2214yescomplemented
29C3×#821C2214yes—
30C3×#816C2214yescomplemented
31#63576C2214yescomplemented
32C2×Q8×Dic3—31no—
33C22×#215—31no—
34C2×D4×Dic3—31no—
35C22×#214—31no—
36C2×#893—31no—
37C2×#887—31no—
38C2×C3×#103—31no—
39C2×C3×#102—31no—
40C2×#821D311yescharacteristic
41C2×#816D311yescharacteristic, complemented
42C2×#815—31no—
43C2×#815—31no—
44C2×#815—61no—
45C2×#807—31no—
46C2×#807—31no—
47#4817—38no—
48#4757—38no—
49C23×C3×D3—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—22no—
58C2×C3×D12C2×C414yes—
59C2×C3×D12C2312yes—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2×C414yescomplemented
63C2×C3×Dic6C2312yes—
64C2×D3×Dic3—24no—
65C2×D3×Dic3—44no—
66C2×C32×C8—22no—
67C2×C32×C8C2312yes—
68C4×C3⋊Dic3D412yes—
69C4×C3⋊Dic3C2312yes—
70C2×C3⋊(C3⋊C8)C2×C414yescomplemented
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4⋊Dic3C2312yes—
76Dic3⋊Dic3—24no—
77(C2×D3)⋊Dic3—24no—
78Dic32—24no—
79#3715C2×C4116yescomplemented
80C2×#440—91noSylow
81C22×C3×Q8—31no—
82C22×C3×D4—31no—
83C23×Dic3—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—61no—
86C22×Dic6C2×D311yescharacteristic
87C22×C3×C8—21no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×#217—61no—
93Q8×Dic3—34no—
94Q8×Dic3—62no—
95C2×#215—38no—
96C2×#215—34no—
97D4×Dic3—34no—
98D4×Dic3—62no—
99C2×#214—38no—
100C2×#214—34no—
101C2×(C2×D3)⋊C4—61no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—31no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114#893—34no—
115#893—62no—
116#887—34no—
117#887—62no—
118C3×#103—34no—
119C3×#102—34no—
120#821C2×D314yes—
121#816C2×D314yescomplemented
122#815—34no—
123#815—34no—
124#815—64no—
125#807—34no—
126#807—34no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3—42no—
131C22×C3×D3—42no—
132C2×C32×C4C22×C412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2×D412yes—
139C2×C3⋊Dic3C2×D412yes—
140C2×C3×Dic3—24no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C3×D12—24no—
147C3×D12—22no—
148C3×D12C22×C414yes—
149C3×Dic6—24no—
150C3×Dic6—22no—
151C3×Dic6C22×C414yescomplemented
152D3×Dic3—48no—
153C32×C8—22no—
154C3⋊(C3⋊C8)C22×C414yescomplemented
155C22×SD16—91no—
156C2×C4×Q8—91no—
157C2×C4×D4—91no—
158#440—98no—
159C2×#107—91no—
160C2×#103—31no—
161C2×#102—31no—
162C2×#97—91no—
163C24×C3—61no—
164C23×D3—21no—
165C2×C3×Q8—34no—
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—62no—
169C2×C3×D4—34no—
170C2×C3×D4—32no—
171C2×C3×D4—61no—
172C2×C3×D4—62no—
173C22×C3×C4—21no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—31no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—64no—
189C22×Dic3—124no—
190C2×D12—21no—
191C2×D12—22no—
192C2×D12C4×D314yes—
193C2×D12C22×D312yes—
194C2×C4×D3—64no—
195C2×C4×D3—124no—
196C2×Dic6—21no—
197C2×Dic6—22no—
198C2×Dic6C4×D314yescomplemented
199C2×Dic6C22×D312yes—
200C2×C3×C8—24no—
201C2×C3×C8—22no—
202C2×C3×C8—22no—
203C2×C3×C8—22no—
204C2×C3×C8C22×D312yes—
205C2×C3×C8C22×D312yes—
206C3×C4⋊C4—32no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210#217—64no—
211#215—316no—
212#214—316no—
213(C2×D3)⋊C4—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216C4⋊Dic3—64no—
217C4⋊Dic3C22×D312yes—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—64no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—62no—
225C4×Dic3—62no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C2×C3⋊C8—34no—
229C2×C3⋊C8—34no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—32no—
232C2×C3⋊C8—62no—
233C2×C3⋊C8—64no—
234C22×C32C4×D412yes—
235C22×C32AGL(1,ℤ/8)12yes—
236C22×C32#13712yes—
237C22×C32C22×D411yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—48no—
242C32×C4C4×D412yes—
243C32×C4C23×C411yescharacteristic
244C32×C4C2×#4111yescharacteristic
245C3⋊Dic3—22no—
246C3⋊Dic3—22no—
247C3×Dic3—24no—
248C3×Dic3—42no—
249C3×Dic3—42no—
250C22×Q8—31no—
251C22×D4—31no—
252C23×C4—181no—
253C2×SD16—98no—
254C2×SD16—94no—
255C22×C8—91no—
256C22×C8D3211yescharacteristic
257C4×Q8—94no—
258C4×Q8—182no—
259C4×D4—94no—
260C4×D4—182no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—181no—
264C2×C22⋊C4—181no—
265C2×C42—91no—
266C2×C42—181no—
267#107—94no—
268#103—34no—
269#102—34no—
270#97—94no—
271C23×C3—21no—
272C23×C3—64no—
273C23×C3—62no—
274C23×C3—122no—
275C23×C3—122no—
276C23×C3D3×D411yescharacteristic
277C23×C3D3×D411yescharacteristic
278C22×D3—24no—
279C22×D3—22no—
280C22×D3—42no—
281C22×D3—42no—
282C3×Q8—34no—
283C3×Q8—64no—
284C3×Q8—62no—
285C3×D4—34no—
286C3×D4—64no—
287C3×D4—62no—
288C2×C3×C4—21no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—22no—
292C2×C3×C4—64no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—122no—
297C2×C3×C4—122no—
298C2×C3×C4C2×C4×D312yes—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4#23712yes—
303C2×C3×C4#23712yes—
304C2×C3×C4C23×D311yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×Dic3—24no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—32no—
311C2×Dic3—32no—
312C2×Dic3—32no—
313C2×Dic3—32no—
314C2×Dic3—42no—
315C2×Dic3—42no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—62no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324C2×Dic3—128no—
325D12—24no—
326D12—22no—
327D12C2×C4×D314yes—
328C4×D3—128no—
329Dic6—24no—
330Dic6—22no—
331Dic6C2×C4×D314yescomplemented
332C3×C8—24no—
333C3×C8—22no—
334C3×C8—22no—
335C3⋊C8—34no—
336C3⋊C8—34no—
337C3⋊C8—64no—
338C2×C32#44014yescomplemented
339C2×C32C2×C4×D411yescharacteristic
340C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
341C2×C32C2×#13711yescharacteristic
342C3×D3—44no—
343C24—61no—
344C2×Q8—32no—
345C2×Q8—34no—
346C2×Q8—61no—
347C2×Q8—62no—
348C2×D4—32no—
349C2×D4—34no—
350C2×D4—61no—
351C2×D4—62no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4—184no—
358C22×C4—364no—
359C22×C4C2×D3211yescharacteristic
360SD16—916no—
361C2×C8—22no—
362C2×C8—92no—
363C2×C8—94no—
364C2×C8C2×D3212yes—
365C4⋊C4—32no—
366C4⋊C4—32no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—184no—
370C22⋊C4—184no—
371C42—92no—
372C42—92no—
373C42—184no—
374C22×C3—21no—
375C22×C3—22no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—64no—
379C22×C3—122no—
380C22×C3—122no—
381C22×C3—128no—
382C22×C3#67⋊C412yes—
383C22×C3#67⋊C412yes—
384C22×C3#91112yes—
385C22×C3#91412yes—
386C22×C3#91512yes—
387C22×C3#91812yes—
388C22×C3C2×D3×D411yescharacteristic
389C22×C3C2×D3×D411yescharacteristic
390C2×D3—24no—
391C2×D3—42no—
392C2×D3—42no—
393C2×D3—48no—
394C3×C4—21no—
395C3×C4—21no—
396C3×C4—22no—
397C3×C4—64no—
398C3×C4—122no—
399C3×C4—122no—
400C3×C4#67⋊C412yes—
401C3×C4#67⋊C412yes—
402C3×C4C22×C4×D311yescharacteristic
403C3×C4C22×C4×D311yescharacteristic
404C3×C4C2×#23711yescharacteristic
405C3×C4C2×#23711yescharacteristic
406Dic3—24no—
407Dic3—42no—
408Dic3—42no—
409Dic3—62no—
410Dic3—62no—
411Dic3—62no—
412Dic3—62no—
413Dic3—122no—
414Dic3—122no—
415C32C2×#44011yescharacteristic, complemented, Sylow
416C23—62no—
417C23—64no—
418C23—122no—
419C23—122no—
420C23#380211yescharacteristic
421Q8—34no—
422Q8—62no—
423Q8—64no—
424D4—34no—
425D4—62no—
426D4—64no—
427C2×C4—62no—
428C2×C4—64no—
429C2×C4—62no—
430C2×C4—62no—
431C2×C4—92no—
432C2×C4—92no—
433C2×C4—122no—
434C2×C4—122no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—368no—
438C2×C4C4×D3212yes—
439C2×C4#380211yescharacteristic
440C2×C4#380512yes—
441C2×C4C22×D3211yescharacteristic
442C8—22no—
443C8—94no—
444C2×C3—24no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—124no—
449C2×C3#475714yescomplemented
450C2×C3#481714yescomplemented
451C2×C3C2×#67⋊C411yescharacteristic
452C2×C3C2×#67⋊C411yescharacteristic
453C2×C3C2×#91111yescharacteristic
454C2×C3C2×#91411yescharacteristic
455C2×C3C2×#91511yescharacteristic
456C2×C3C2×#91811yescharacteristic
457D3—44no—
458C22—64no—
459C22—128no—
460C22—122no—
461C22—122no—
462C22#6379812yes—
463C22#6381112yes—
464C22#6390212yes—
465C22C2×#380211yescharacteristic
466C4—64no—
467C4—122no—
468C4—122no—
469C4—182no—
470C4—182no—
471C4#6390212yes—
472C4C2×C4×D3211yescharacteristic
473C4C2×#380511yescharacteristic
474C3—21no—
475C3C2×#475711yescharacteristic, complemented
476C3C2×#481711yescharacteristic, complemented
477C2—124no—
478C2#1059074314yesdirect product factor
479C2C2×#6379811yescharacteristic
480C2C2×#6381111yescharacteristic
481C2C2×#6390211yescharacteristic
subgroupG/H
centerC23#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
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
2. C2×#63843C2semidirect
4. C2×#63642C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63576C2semidirect
8. #10590743C2direct (N × H)
25. #63843C22semidirect
26. C2×#3715C4semidirect
28. #63642C22semidirect
30. C3×#816C22semidirect
31. #63576C22semidirect
41. C2×#816D3semidirect
62. C2×C3×Dic6C2×C4semidirect
70. C2×C3⋊(C3⋊C8)C2×C4semidirect
79. #3715C2×C4semidirect
121. #816C2×D3semidirect
151. C3×Dic6C22×C4semidirect
154. C3⋊(C3⋊C8)C22×C4semidirect
198. C2×Dic6C4×D3semidirect
331. Dic6C2×C4×D3semidirect
338. C2×C32#440semidirect
415. C32C2×#440semidirect
449. C2×C3#4757semidirect
450. C2×C3#4817semidirect
475. C3C2×#4757semidirect
476. C3C2×#4817semidirect
478. C2#10590743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638982
C2×#638432
C22×#37152
C2×#636422
C2×C3×#8212
C2×C3×#8162
C2×#635762
#105907432
C2×#48173
C2×#47573