Finite Group Databasebeta

← C2×#10590539 #11873450

Subgroups — C2×#10590539 #11873450

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64099C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590539C218yesmaximal, direct product factor
9C2×#4800—31nomaximal
10C2×#4768—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64099—22no—
19#64099C2214yescomplemented
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63863—22no—
25#63863C2214yes—
26C3×#810C2214yescomplemented
27C3×#809C2214yes—
28#63566C2214yescomplemented
29#63563C2214yes—
30#63553C2214yescomplemented
31C2×#947—31no—
32C2×#936—31no—
33C2×#890—31no—
34C2×#890—31no—
35C2×#890—61no—
36C2×C3×#103—31no—
37C2×C3×#102—31no—
38C2×#835—31no—
39C2×#832—31no—
40C2×#821—31no—
41C2×#816—31no—
42C2×C8×Dic3—31no—
43C2×C8×Dic3—31no—
44C2×#810D311yescharacteristic, complemented
45C2×#809D311yescharacteristic
46#4800—38no—
47#4768—38no—
48C23×C3×D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3×Dic3—21no—
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12—21no—
58C2×C3×D12C2312yes—
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C32×C4⋊C4—21no—
64C32×C4⋊C4C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—24no—
67C4⋊(C3⋊Dic3)C2312yes—
68#3750—24no—
69C4×C3⋊Dic3D412yes—
70C4×C3⋊Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8—22no—
73C2×C3×C3⋊C8C2312yes—
74C2×C3×C3⋊C8C2312yes—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77C2×#488—91noSylow
78C22×C3×Q8—31no—
79C22×C3×D4—31no—
80C22×D12C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C22×C3×C8—31no—
83C22×C3×C8—31no—
84C2×C3×C4⋊C4—21no—
85C2×C3×C4⋊C4C2×D311yescharacteristic
86C2×C3×C4⋊C4C2×D311yescharacteristic
87C2×#217—61no—
88C2×#217—61no—
89#947—34no—
90#947—62no—
91#936—34no—
92#936—62no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4⋊Dic3—61no—
99C2×C4⋊Dic3—61no—
100C2×C4⋊Dic3—62no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×Dic3⋊C4—62no—
104C2×C4×Dic3—31no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109#890—34no—
110#890—34no—
111#890—64no—
112#890—62no—
113#890—62no—
114#890—64no—
115C3×#103—34no—
116C3×#102—34no—
117#835—34no—
118#832—34no—
119#821—34no—
120#816—34no—
121C8×Dic3—34no—
122C8×Dic3—34no—
123#810C2×D314yescomplemented
124#809C2×D314yes—
125C23×C32C2×D411yescharacteristic
126C22×C3×D3—22no—
127C22×C3×D3—42no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C2×C32×C4—22no—
131C2×C32×C4—42no—
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4112yes—
134C2×C32×C4#4112yes—
135C2×C32×C4C2411yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140C2×C3⋊Dic3C2×D412yes—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—42no—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—42no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—42no—
150C3×C3⋊C8—22no—
151C3×C3⋊C8—22no—
152C2×#125—91no—
153C2×#124—91no—
154#488—98no—
155C2×#103—31no—
156C2×#103—91no—
157C2×#102—31no—
158C2×#102—91no—
159C2×C4×C8—91no—
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—62no—
165C2×C3×Q8—62no—
166C2×C3×D4—32no—
167C2×C3×D4—62no—
168C2×C3×D4—61no—
169C2×C3×D4—62no—
170C22×C3×C4—22no—
171C22×C3×C4—21no—
172C22×C3×C4—21no—
173C22×C3×C4—21no—
174C22×C3×C4—61no—
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C22×Dic3—21no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—61no—
183C22×Dic3—61no—
184C22×Dic3—62no—
185C22×Dic3—61no—
186C22×Dic3—61no—
187C2×D12—22no—
188C2×D12—22no—
189C2×D12—21no—
190C2×D12C22×D312yes—
191C2×Dic6—22no—
192C2×Dic6—22no—
193C2×Dic6—21no—
194C2×Dic6C22×D312yes—
195C2×C3×C8—32no—
196C2×C3×C8—32no—
197C2×C3×C8—62no—
198C2×C3×C8—62no—
199C3×C4⋊C4—22no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4C22×D312yes—
204C3×C4⋊C4C22×D312yes—
205#217—64no—
206#217—64no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209C4⋊Dic3—32no—
210C4⋊Dic3—32no—
211C4⋊Dic3—62no—
212C4⋊Dic3—64no—
213C4⋊Dic3—64no—
214C4⋊Dic3—68no—
215C4⋊Dic3—62no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218Dic3⋊C4—64no—
219Dic3⋊C4—64no—
220Dic3⋊C4—68no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—62no—
226C4×Dic3—62no—
227C2×C3⋊C8—22no—
228C2×C3⋊C8—22no—
229C2×C3⋊C8C22×D312yes—
230C2×C3⋊C8C22×D312yes—
231C22×C32#12412yes—
232C22×C32#13512yes—
233C22×C32#13512yes—
234C22×C32C22×D411yescharacteristic
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—84no—
239C32×C4—42no—
240C32×C4#12412yes—
241C32×C4C2×#4111yescharacteristic
242C32×C4C2×#4111yescharacteristic
243C3⋊Dic3—22no—
244C3⋊Dic3—22no—
245C3⋊Dic3—42no—
246C3×Dic3—42no—
247C22×Q8—31no—
248C22×D4—31no—
249C22×C8—31no—
250C22×C8—31no—
251#125—94no—
252#125—182no—
253#124—94no—
254#124—182no—
255C2×C4⋊C4—91no—
256C2×C4⋊C4—181no—
257C2×C4⋊C4—181no—
258C2×C4⋊C4D3211yescharacteristic
259C2×C22⋊C4—181no—
260C2×C22⋊C4—181no—
261C2×C42—91no—
262#103—34no—
263#103—94no—
264#102—34no—
265#102—94no—
266C4×C8—94no—
267C23×C3—21no—
268C23×C3—62no—
269C23×C3—122no—
270C23×C3—122no—
271C23×C3—122no—
272C23×C3D3×D411yescharacteristic
273C23×C3D3×D411yescharacteristic
274C22×D3—22no—
275C22×D3—42no—
276C22×D3—42no—
277C22×D3—42no—
278C3×Q8—62no—
279C3×Q8—62no—
280C3×Q8—122no—
281C3×D4—62no—
282C3×D4—62no—
283C3×D4—122no—
284C2×C3×C4—24no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—21no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—21no—
291C2×C3×C4—44no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—122no—
296C2×C3×C4#23512yes—
297C2×C3×C4#23512yes—
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23712yes—
301C2×C3×C4#23712yes—
302C2×C3×C4C23×D311yescharacteristic
303C2×C3×C4C23×D311yescharacteristic
304C2×Dic3—22no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—42no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—64no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—122no—
320C2×Dic3—122no—
321C2×Dic3—124no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324D12—22no—
325D12—22no—
326D12—42no—
327Dic6—22no—
328Dic6—22no—
329Dic6—42no—
330C3×C8—62no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C2×C32#48814yescomplemented
335C2×C32C2×#12411yescharacteristic
336C2×C32C2×#13511yescharacteristic
337C2×C32C2×#13511yescharacteristic
338C3×D3—82no—
339C24—61no—
340C2×Q8—32no—
341C2×Q8—61no—
342C2×Q8—62no—
343C2×Q8—62no—
344C2×D4—32no—
345C2×D4—62no—
346C2×D4—62no—
347C2×D4—61no—
348C22×C4—21no—
349C22×C4—61no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354C2×C8—32no—
355C2×C8—32no—
356C2×C8—62no—
357C2×C8—62no—
358C4⋊C4—21no—
359C4⋊C4—92no—
360C4⋊C4—184no—
361C4⋊C4—184no—
362C4⋊C4—181no—
363C4⋊C4C2×D3212yes—
364C22⋊C4—184no—
365C22⋊C4—184no—
366C42—92no—
367C42—92no—
368C22×C3—21no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3—22no—
372C22×C3—122no—
373C22×C3—122no—
374C22×C3—122no—
375C22×C3—244no—
376C22×C3#88512yes—
377C22×C3#88512yes—
378C22×C3#91212yes—
379C22×C3#91612yes—
380C22×C3#91612yes—
381C22×C3#91912yes—
382C22×C3C2×D3×D411yescharacteristic
383C22×C3C2×D3×D411yescharacteristic
384C2×D3—42no—
385C2×D3—42no—
386C2×D3—42no—
387C2×D3—84no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—22no—
391C3×C4—44no—
392C3×C4—42no—
393C3×C4—42no—
394C3×C4—122no—
395C3×C4#88512yes—
396C3×C4#88512yes—
397C3×C4C2×#23511yescharacteristic
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23711yescharacteristic
400C3×C4C2×#23711yescharacteristic
401Dic3—42no—
402Dic3—62no—
403Dic3—62no—
404Dic3—62no—
405Dic3—62no—
406Dic3—122no—
407Dic3—122no—
408Dic3—124no—
409Dic3—122no—
410Dic3—122no—
411C32C2×#48811yescharacteristic, complemented, Sylow
412C23—62no—
413C23—122no—
414C23—122no—
415C23—122no—
416C23#381111yescharacteristic
417Q8—62no—
418Q8—62no—
419Q8—122no—
420D4—62no—
421D4—62no—
422D4—122no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—62no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—122no—
429C2×C4—182no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—362no—
433C2×C4#379512yes—
434C2×C4#379512yes—
435C2×C4#381111yescharacteristic
436C2×C4C22×D3211yescharacteristic
437C8—62no—
438C8—62no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—24no—
442C2×C3—21no—
443C2×C3—242no—
444C2×C3#476814yescomplemented
445C2×C3#480014yescomplemented
446C2×C3C2×#88511yescharacteristic
447C2×C3C2×#88511yescharacteristic
448C2×C3C2×#91211yescharacteristic
449C2×C3C2×#91611yescharacteristic
450C2×C3C2×#91611yescharacteristic
451C2×C3C2×#91911yescharacteristic
452D3—82no—
453C22—122no—
454C22—122no—
455C22—122no—
456C22—244no—
457C22#6391312yes—
458C22#6393612yes—
459C22#6395012yes—
460C22C2×#381111yescharacteristic
461C4—42no—
462C4—122no—
463C4—182no—
464C4—182no—
465C4—362no—
466C4#6391312yes—
467C4C2×#379511yescharacteristic
468C4C2×#379511yescharacteristic
469C3—21no—
470C3C2×#476811yescharacteristic, complemented
471C3C2×#480011yescharacteristic, complemented
472C2—242no—
473C2#1059053914yesdirect product factor
474C2C2×#6391311yescharacteristic
475C2C2×#6393611yescharacteristic
476C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#488
LCSG ▷ C2×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×#64099C2semidirect
3. C2×C3×#810C2semidirect
5. C2×#63566C2semidirect
7. C2×#63553C2semidirect
8. #10590539C2direct (N × H)
19. #64099C22semidirect
26. C3×#810C22semidirect
28. #63566C22semidirect
30. #63553C22semidirect
44. C2×#810D3semidirect
123. #810C2×D3semidirect
334. C2×C32#488semidirect
411. C32C2×#488semidirect
444. C2×C3#4768semidirect
445. C2×C3#4800semidirect
470. C3C2×#4768semidirect
471. C3C2×#4800semidirect
473. C2#10590539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640992
C2×#638632
C2×C3×#8102
C2×C3×#8092
C2×#635662
C2×#635632
C2×#635532
#105905392
C2×#48003
C2×#47683