Finite Group Databasebeta

← C2×#10590574 #11858434

Subgroups — C2×#10590574 #11858434

Order 1152.

1189 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63849C211yesmaximal, characteristic
3C22×#3710C211yesmaximal, characteristic
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×C3×#807C211yesmaximal, characteristic, complemented
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8#10590574C218yesmaximal, direct product factor
9C2×#4880—31nomaximal
10C2×#4860—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3752—21no—
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16#64101—22no—
17#64101C2214yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×#3722—21no—
23C2×Dic32—21no—
24#63849—22no—
25#63849C2214yes—
26C2×#3710C418yescomplemented
27C2×#3710C2214yes—
28C3×#808C2214yescomplemented
29C3×#807C2214yescomplemented
30#63575C2214yescomplemented
31#63573C2214yescomplemented
32C22×D3×C8—31no—
33C22×D3×C8—31no—
34C2×#892—31no—
35C2×#892—31no—
36C2×#892—31no—
37C2×#892—31no—
38C2×#892—61no—
39C2×C3×#107—31no—
40C2×C3×#106—31no—
41C2×#818—31no—
42C2×#817—31no—
43C2×#808—31no—
44C2×#808D311yescharacteristic, complemented
45C2×#807—31no—
46C2×#807D311yescharacteristic, complemented
47#4880—38no—
48#4860—38no—
49C23×C3⋊D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3⋊Dic3D411yescharacteristic
54C2×C4×C3⋊D3C2×C414yes—
55C2×C4×C3⋊D3D412yes—
56C2×C4×C3⋊D3Q814yes—
57C2×C4×C3⋊D3C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62#3752—24no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4×C3⋊Dic3—24no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C2×C3×C3⋊C8C2×C414yes—
71C2×C3×C3⋊C8C2×C414yes—
72C2×C3×C3⋊C8C2312yes—
73C2×C3×C3⋊C8C2312yes—
74#3722—24no—
75Dic32—24no—
76#3710C2×C4116yescomplemented
77C2×#427—91noSylow
78C22×C4×D3—31no—
79C22×C4×D3—31no—
80C22×C4×D3—61no—
81C22×C3×C8—31no—
82C22×C3×C8—31no—
83C2×C3×C4⋊C4—21no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×C3×C4⋊C4C2×D311yescharacteristic
88C2×(C2×D3)⋊C4—61no—
89C2×(C2×D3)⋊C4—61no—
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4×Dic3—61no—
99C2×C4×Dic3—61no—
100C2×C4×Dic3—61no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3—62no—
103C22×C3⋊C8C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C2×D3×C8—38no—
106C2×D3×C8—38no—
107C2×D3×C8—34no—
108C2×D3×C8—34no—
109#892—34no—
110#892—34no—
111#892—34no—
112#892—34no—
113#892—64no—
114#892—62no—
115#892—62no—
116#892—62no—
117#892—62no—
118#892—64no—
119C3×#107—34no—
120C3×#106—34no—
121#818—34no—
122#817—34no—
123#808—34no—
124#808C2×D314yescomplemented
125#807—34no—
126#807C2×D314yescomplemented
127C23×C32C2×D411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3C4⋊C414yes—
131C22×C3⋊D3C2×D412yes—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×Q812yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140C2×C3⋊Dic3C4⋊C414yes—
141C2×C3⋊Dic3C2×D412yes—
142C4×C3⋊D3C4⋊C418yes—
143C4×C3⋊D3C22×C414yes—
144C4×C3⋊D3C2×Q814yes—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—42no—
148C2×C3×Dic3—42no—
149C3×C3⋊C8C22×C414yes—
150C3×C3⋊C8C22×C414yes—
151C23×C8—91no—
152C2×#117—91no—
153C2×#117—91no—
154#427—98no—
155C2×#107—31no—
156C2×#107—91no—
157C2×#106—31no—
158C2×#106—91no—
159C23×D3—31no—
160C23×D3—31no—
161C23×D3—61no—
162C22×C3×C4—22no—
163C22×C3×C4—21no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—21no—
171C22×Dic3—21no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—61no—
175C22×Dic3—62no—
176C22×Dic3—61no—
177C22×Dic3—61no—
178C2×C4×D3—34no—
179C2×C4×D3—34no—
180C2×C4×D3—32no—
181C2×C4×D3—32no—
182C2×C4×D3—34no—
183C2×C4×D3—34no—
184C2×C4×D3—32no—
185C2×C4×D3—32no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C3×C8—34no—
191C2×C3×C8—34no—
192C2×C3×C8—32no—
193C2×C3×C8—32no—
194C3×C4⋊C4—22no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—32no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4C22×D312yes—
203C3×C4⋊C4C22×D312yes—
204(C2×D3)⋊C4—64no—
205(C2×D3)⋊C4—64no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—68no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—32no—
212C4⋊Dic3—32no—
213C4⋊Dic3—62no—
214C4⋊Dic3—62no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3C22×D312yes—
218C4⋊Dic3C22×D312yes—
219C4×Dic3—64no—
220C4×Dic3—64no—
221C4×Dic3—64no—
222C4×Dic3—64no—
223C4×Dic3—68no—
224C2×C3⋊C8C4×D314yes—
225C2×C3⋊C8C4×D314yes—
226C2×C3⋊C8C22×D312yes—
227C2×C3⋊C8C22×D312yes—
228D3×C8—316no—
229D3×C8—316no—
230C22×C32C2×C4⋊C412yes—
231C22×C32#13512yes—
232C22×C32#13512yes—
233C22×C32C22×D411yescharacteristic
234C2×C3⋊D3—22no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—28no—
237C2×C3⋊D3C2×C4⋊C414yes—
238C32×C4—42no—
239C32×C4C2×C4⋊C412yes—
240C32×C4C23×C411yescharacteristic
241C32×C4C22×Q811yescharacteristic
242C3⋊Dic3—42no—
243C3⋊Dic3C2×C4⋊C414yes—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C23×C4—91no—
247C22×C8—31no—
248C22×C8—31no—
249C22×C8—98no—
250C22×C8—94no—
251#117—94no—
252#117—94no—
253#117—182no—
254#117—182no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—181no—
260C2×C22⋊C4—181no—
261C2×C42—181no—
262C2×C42—181no—
263#107—34no—
264#107—94no—
265#106—34no—
266#106—94no—
267C23×C3—21no—
268C23×C3D3×D411yescharacteristic
269C23×C3D3×D411yescharacteristic
270C22×D3—34no—
271C22×D3—34no—
272C22×D3—32no—
273C22×D3—32no—
274C22×D3—64no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—122no—
281C22×D3—122no—
282C2×C3×C4—24no—
283C2×C3×C4—22no—
284C2×C3×C4—22no—
285C2×C3×C4—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—44no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—122no—
295C2×C3×C4—122no—
296C2×C3×C4C2×C4×D312yes—
297C2×C3×C4C2×C4×D312yes—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×Q812yes—
301C2×C3×C4D3×Q812yes—
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—22no—
306C2×Dic3—34no—
307C2×Dic3—34no—
308C2×Dic3—32no—
309C2×Dic3—32no—
310C2×Dic3—42no—
311C2×Dic3—42no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—64no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—124no—
318C2×Dic3—122no—
319C2×Dic3—122no—
320C4×D3—38no—
321C4×D3—38no—
322C4×D3—34no—
323C4×D3—34no—
324C4×D3—34no—
325C4×D3—34no—
326C4×D3—68no—
327C4×D3—64no—
328C4×D3—64no—
329C3×C8—34no—
330C3×C8—34no—
331C3⋊C8C2×C4×D314yes—
332C3⋊C8C2×C4×D314yes—
333C2×C32#42714yescomplemented
334C2×C32C22×C4⋊C411yescharacteristic
335C2×C32C2×#13511yescharacteristic
336C2×C32C2×#13511yescharacteristic
337C3⋊D3—24no—
338C24—91no—
339C22×C4—21no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—91no—
343C22×C4—92no—
344C22×C4—94no—
345C22×C4—94no—
346C22×C4—92no—
347C22×C4—181no—
348C22×C4C2×D3211yescharacteristic
349C2×C8—32no—
350C2×C8—32no—
351C2×C8—34no—
352C2×C8—34no—
353C2×C8—916no—
354C4⋊C4—21no—
355C4⋊C4—32no—
356C4⋊C4—32no—
357C4⋊C4—61no—
358C4⋊C4—61no—
359C4⋊C4—92no—
360C4⋊C4—181no—
361C4⋊C4C2×D3212yes—
362C22⋊C4—184no—
363C22⋊C4—184no—
364C42—184no—
365C42—184no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3D3×C4⋊C412yes—
371C22×C3D3×C4⋊C412yes—
372C22×C3#91212yes—
373C22×C3#91612yes—
374C22×C3#91612yes—
375C22×C3#91912yes—
376C22×C3C2×D3×D411yescharacteristic
377C22×C3C2×D3×D411yescharacteristic
378C2×D3—34no—
379C2×D3—34no—
380C2×D3—64no—
381C2×D3—68no—
382C2×D3—62no—
383C2×D3—62no—
384C2×D3—62no—
385C2×D3—62no—
386C2×D3—68no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—128no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—22no—
393C3×C4—44no—
394C3×C4—42no—
395C3×C4—42no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4D3×C4⋊C412yes—
399C3×C4D3×C4⋊C412yes—
400C3×C4C22×C4×D311yescharacteristic
401C3×C4C22×C4×D311yescharacteristic
402C3×C4C2×D3×Q811yescharacteristic
403C3×C4C2×D3×Q811yescharacteristic
404Dic3—34no—
405Dic3—34no—
406Dic3—42no—
407Dic3—42no—
408Dic3—64no—
409Dic3—124no—
410Dic3—122no—
411Dic3—122no—
412C32C2×#42711yescharacteristic, complemented, Sylow
413C23—92no—
414C23—94no—
415C23—182no—
416C23—182no—
417C23#381111yescharacteristic
418C2×C4—22no—
419C2×C4—42no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—92no—
423C2×C4—94no—
424C2×C4—94no—
425C2×C4—94no—
426C2×C4—98no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—182no—
430C2×C4—362no—
431C2×C4#379712yes—
432C2×C4C4×D3212yes—
433C2×C4#381111yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—34no—
436C8—34no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—24no—
441C2×C3#486014yescomplemented
442C2×C3#488014yescomplemented
443C2×C3C2×D3×C4⋊C411yescharacteristic
444C2×C3C2×D3×C4⋊C411yescharacteristic
445C2×C3C2×#91211yescharacteristic
446C2×C3C2×#91611yescharacteristic
447C2×C3C2×#91611yescharacteristic
448C2×C3C2×#91911yescharacteristic
449D3—64no—
450D3—64no—
451D3—124no—
452C22—94no—
453C22—182no—
454C22—182no—
455C22—188no—
456C22#6388312yes—
457C22#6393612yes—
458C22#6395012yes—
459C22C2×#381111yescharacteristic
460C4—42no—
461C4—94no—
462C4—122no—
463C4—122no—
464C4—362no—
465C4#6388312yes—
466C4C2×#379711yescharacteristic
467C4C2×C4×D3211yescharacteristic
468C3—21no—
469C3C2×#486011yescharacteristic, complemented
470C3C2×#488011yescharacteristic, complemented
471C2—184no—
472C2#1059057414yesdirect product factor
473C2C2×#6388311yescharacteristic
474C2C2×#6393611yescharacteristic
475C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#427
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
4. C2×C3×#808C2semidirect
5. C2×C3×#807C2semidirect
6. C2×#63575C2semidirect
7. C2×#63573C2semidirect
8. #10590574C2direct (N × H)
26. C2×#3710C4semidirect
28. C3×#808C22semidirect
29. C3×#807C22semidirect
30. #63575C22semidirect
31. #63573C22semidirect
44. C2×#808D3semidirect
46. C2×#807D3semidirect
76. #3710C2×C4semidirect
124. #808C2×D3semidirect
126. #807C2×D3semidirect
333. C2×C32#427semidirect
412. C32C2×#427semidirect
441. C2×C3#4860semidirect
442. C2×C3#4880semidirect
469. C3C2×#4860semidirect
470. C3C2×#4880semidirect
472. C2#10590574direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638492
C22×#37102
C2×C3×#8082
C2×C3×#8072
C2×#635752
C2×#635732
#105905742
C2×#48803
C2×#48603