Finite Group Databasebeta

← C2×#10590868 #11873446

Subgroups — C2×#10590868 #11873446

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63872C211yesmaximal, characteristic, complemented
2C2×#63863C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic
8#10590868C218yesmaximal, direct product factor
9C2×#4800—31nomaximal
10C2×#4768—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×Dic3⋊Dic3—21no—
19C2×Dic3⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C2×(C2×D3)⋊Dic3—21no—
22#63872—22no—
23#63872C2214yescomplemented
24#63863—22no—
25#63863C2214yes—
26C8×C3⋊Dic3C2214yescomplemented
27C3×#821C2214yes—
28C3×#816C2214yescomplemented
29#63565C2214yescomplemented
30#63562C2214yes—
31C2×#947—31no—
32C2×#936—31no—
33C2×#890—31no—
34C2×#890—31no—
35C2×C3×#103—31no—
36C2×C3×#102—31no—
37C2×#835—31no—
38C2×#832—31no—
39C2×#821D311yescharacteristic
40C2×#816D311yescharacteristic, complemented
41C2×C8×Dic3—31no—
42C2×C8×Dic3—31no—
43C2×C8×Dic3—61no—
44C2×#810—31no—
45C2×#809—31no—
46#4800—38no—
47#4768—38no—
48C23×C3×D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
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—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C4×C3⋊Dic3D412yes—
66C4×C3⋊Dic3C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2312yes—
72C3×C4⋊Dic3C2312yes—
73Dic3⋊Dic3—24no—
74Dic3⋊Dic3—24no—
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—21no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
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—61no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—61no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107#890—34no—
108#890—34no—
109#890—62no—
110#890—62no—
111C3×#103—34no—
112C3×#102—34no—
113#835—34no—
114#832—34no—
115#821C2×D314yes—
116#816C2×D314yescomplemented
117C8×Dic3—34no—
118C8×Dic3—34no—
119C8×Dic3—64no—
120#810—34no—
121#809—34no—
122C23×C32C2×D411yescharacteristic
123C22×C3×D3—22no—
124C22×C3×D3—42no—
125C22×C3×D3—42no—
126C22×C3×D3—42no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4112yes—
129C2×C32×C4#4112yes—
130C2×C32×C4C2411yescharacteristic
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3C2×D412yes—
134C2×C3⋊Dic3C2×D412yes—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—42no—
139C2×C3×Dic3—42no—
140C2×C3×Dic3—42no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—42no—
144C3×Dic6—22no—
145C3×Dic6—22no—
146C3×Dic6—42no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149C2×#125—91no—
150C2×#124—91no—
151#488—98no—
152C2×#103—31no—
153C2×#103—91no—
154C2×#102—31no—
155C2×#102—91no—
156C2×C4×C8—91no—
157C24×C3—61no—
158C23×D3—21no—
159C2×C3×Q8—32no—
160C2×C3×Q8—61no—
161C2×C3×Q8—62no—
162C2×C3×Q8—62no—
163C2×C3×D4—32no—
164C2×C3×D4—62no—
165C2×C3×D4—61no—
166C2×C3×D4—62no—
167C22×C3×C4—21no—
168C22×C3×C4—61no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—31no—
177C22×Dic3—31no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C2×D12—22no—
183C2×D12—22no—
184C2×D12—21no—
185C2×D12C22×D312yes—
186C2×Dic6—22no—
187C2×Dic6—22no—
188C2×Dic6—21no—
189C2×Dic6C22×D312yes—
190C2×C3×C8—24no—
191C2×C3×C8—22no—
192C2×C3×C8—22no—
193C2×C3×C8—22no—
194C2×C3×C8C22×D312yes—
195C2×C3×C8C22×D312yes—
196C3×C4⋊C4—32no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200#217—64no—
201#217—64no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—64no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—64no—
207C4⋊Dic3—64no—
208C4⋊Dic3C22×D312yes—
209C4⋊Dic3C22×D312yes—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212C4×Dic3—32no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—62no—
217C4×Dic3—62no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—32no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—64no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—62no—
224C22×C32#12412yes—
225C22×C32#13512yes—
226C22×C32#13512yes—
227C22×C32C22×D411yescharacteristic
228C2×C3×D3—42no—
229C2×C3×D3—42no—
230C2×C3×D3—42no—
231C2×C3×D3—84no—
232C32×C4#12412yes—
233C32×C4C2×#4111yescharacteristic
234C32×C4C2×#4111yescharacteristic
235C3⋊Dic3—22no—
236C3⋊Dic3—22no—
237C3×Dic3—42no—
238C3×Dic3—42no—
239C3×Dic3—42no—
240C22×Q8—31no—
241C22×D4—31no—
242C22×C8—91no—
243C22×C8D3211yescharacteristic
244#125—94no—
245#125—182no—
246#124—94no—
247#124—182no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—181no—
251C2×C4⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C22⋊C4—181no—
254C2×C42—91no—
255#103—34no—
256#103—94no—
257#102—34no—
258#102—94no—
259C4×C8—94no—
260C23×C3—21no—
261C23×C3—62no—
262C23×C3—122no—
263C23×C3—122no—
264C23×C3—122no—
265C23×C3D3×D411yescharacteristic
266C23×C3D3×D411yescharacteristic
267C22×D3—22no—
268C22×D3—42no—
269C22×D3—42no—
270C22×D3—42no—
271C3×Q8—62no—
272C3×Q8—62no—
273C3×Q8—122no—
274C3×D4—62no—
275C3×D4—62no—
276C3×D4—122no—
277C2×C3×C4—21no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—62no—
282C2×C3×C4—62no—
283C2×C3×C4—62no—
284C2×C3×C4—122no—
285C2×C3×C4—122no—
286C2×C3×C4—122no—
287C2×C3×C4#23512yes—
288C2×C3×C4#23512yes—
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4#23712yes—
292C2×C3×C4#23712yes—
293C2×C3×C4C23×D311yescharacteristic
294C2×C3×C4C23×D311yescharacteristic
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—64no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313D12—22no—
314D12—22no—
315D12—42no—
316Dic6—22no—
317Dic6—22no—
318Dic6—42no—
319C3×C8—24no—
320C3×C8—22no—
321C3×C8—22no—
322C3⋊C8—64no—
323C3⋊C8—62no—
324C3⋊C8—62no—
325C2×C32#48814yescomplemented
326C2×C32C2×#12411yescharacteristic
327C2×C32C2×#13511yescharacteristic
328C2×C32C2×#13511yescharacteristic
329C3×D3—82no—
330C24—61no—
331C2×Q8—32no—
332C2×Q8—61no—
333C2×Q8—62no—
334C2×Q8—62no—
335C2×D4—32no—
336C2×D4—62no—
337C2×D4—61no—
338C2×D4—62no—
339C22×C4—61no—
340C22×C4—61no—
341C22×C4—61no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4C2×D3211yescharacteristic
345C2×C8—22no—
346C2×C8—92no—
347C2×C8—182no—
348C2×C8C2×D3212yes—
349C4⋊C4—32no—
350C4⋊C4—32no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—184no—
354C4⋊C4—184no—
355C22⋊C4—184no—
356C22⋊C4—184no—
357C42—92no—
358C42—92no—
359C22×C3—21no—
360C22×C3—22no—
361C22×C3—22no—
362C22×C3—22no—
363C22×C3—122no—
364C22×C3—122no—
365C22×C3—122no—
366C22×C3—244no—
367C22×C3#88512yes—
368C22×C3#88512yes—
369C22×C3#91212yes—
370C22×C3#91612yes—
371C22×C3#91612yes—
372C22×C3#91912yes—
373C22×C3C2×D3×D411yescharacteristic
374C22×C3C2×D3×D411yescharacteristic
375C2×D3—42no—
376C2×D3—42no—
377C2×D3—42no—
378C2×D3—84no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—122no—
383C3×C4—122no—
384C3×C4—122no—
385C3×C4#88512yes—
386C3×C4#88512yes—
387C3×C4C2×#23511yescharacteristic
388C3×C4C2×#23511yescharacteristic
389C3×C4C2×#23711yescharacteristic
390C3×C4C2×#23711yescharacteristic
391Dic3—42no—
392Dic3—42no—
393Dic3—42no—
394Dic3—64no—
395Dic3—64no—
396Dic3—62no—
397Dic3—62no—
398Dic3—62no—
399Dic3—62no—
400C32C2×#48811yescharacteristic, complemented, Sylow
401C23—62no—
402C23—122no—
403C23—122no—
404C23—122no—
405C23#380211yescharacteristic
406Q8—62no—
407Q8—62no—
408Q8—122no—
409D4—62no—
410D4—62no—
411D4—122no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—62no—
415C2×C4—92no—
416C2×C4—92no—
417C2×C4—122no—
418C2×C4—122no—
419C2×C4—122no—
420C2×C4—182no—
421C2×C4—182no—
422C2×C4#379812yes—
423C2×C4#380211yescharacteristic
424C2×C4#380512yes—
425C2×C4C22×D3211yescharacteristic
426C8—22no—
427C8—182no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—24no—
431C2×C3—21no—
432C2×C3—242no—
433C2×C3#476814yescomplemented
434C2×C3#480014yescomplemented
435C2×C3C2×#88511yescharacteristic
436C2×C3C2×#88511yescharacteristic
437C2×C3C2×#91211yescharacteristic
438C2×C3C2×#91611yescharacteristic
439C2×C3C2×#91611yescharacteristic
440C2×C3C2×#91911yescharacteristic
441D3—82no—
442C22—122no—
443C22—122no—
444C22—122no—
445C22—244no—
446C22#6380912yes—
447C22#6381012yes—
448C22#6391512yes—
449C22C2×#380211yescharacteristic
450C4—122no—
451C4—122no—
452C4—122no—
453C4—182no—
454C4—182no—
455C4#6391512yes—
456C4C2×#379811yescharacteristic
457C4C2×#380511yescharacteristic
458C3—21no—
459C3C2×#476811yescharacteristic, complemented
460C3C2×#480011yescharacteristic, complemented
461C2—242no—
462C2#1059086814yesdirect product factor
463C2C2×#6380911yescharacteristic
464C2C2×#6381011yescharacteristic
465C2C2×#6391511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32C2×#488
LCSG ▷ C2×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
1. C2×#63872C2semidirect
3. C2×C8×C3⋊Dic3C2semidirect
5. C2×C3×#816C2semidirect
6. C2×#63565C2semidirect
8. #10590868C2direct (N × H)
23. #63872C22semidirect
26. C8×C3⋊Dic3C22semidirect
28. C3×#816C22semidirect
29. #63565C22semidirect
40. C2×#816D3semidirect
116. #816C2×D3semidirect
325. C2×C32#488semidirect
400. C32C2×#488semidirect
433. C2×C3#4768semidirect
434. C2×C3#4800semidirect
459. C3C2×#4768semidirect
460. C3C2×#4800semidirect
462. C2#10590868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638722
C2×#638632
C2×C8×C3⋊Dic32
C2×C3×#8212
C2×C3×#8162
C2×#635652
C2×#635622
#105908682
C2×#48003
C2×#47683