Finite Group Databasebeta

← C2×#10590435 #11868365

Subgroups — C2×#10590435 #11868365

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×#63872C211yesmaximal, characteristic, complemented
3C2×C3×#808C211yesmaximal, characteristic, complemented
4C2×C3×#807C211yesmaximal, characteristic, complemented
5C2×#63572C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×#63564C211yesmaximal, characteristic
8#10590435C218yesmaximal, direct product factor
9C2×#4891—31nomaximal
10C2×#4871—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102—22no—
17#64102C2214yes—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic3⋊Dic3—21no—
24#63872—22no—
25#63872C2214yescomplemented
26C3×#808C2214yescomplemented
27C3×#807C2214yescomplemented
28#63572C2214yescomplemented
29#63564C2214yes—
30#63564C2214yes—
31C2×#893—31no—
32C2×#893—31no—
33C2×#893—61no—
34C2×#890—31no—
35C2×#890—31no—
36C2×C3×#107—31no—
37C2×C3×#106—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×Dic3⋊C8—31no—
41C2×Dic3⋊C8—31no—
42C2×#809—31no—
43C2×#809—31no—
44C2×#808D311yescharacteristic, complemented
45C2×#807D311yescharacteristic, complemented
46#4891—38no—
47#4871—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)Q814yes—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×C4×C3⋊D3—24no—
58C2×C4×C3⋊D3—44no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4C2312yes—
63#3752—24no—
64C4×C3⋊Dic3D412yes—
65C4×C3⋊Dic3C2312yes—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4⋊Dic3C2312yes—
70C2×C3×C3⋊C8—22no—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73C2×C3×C3⋊C8C2312yes—
74Dic3⋊Dic3—24no—
75Dic3⋊Dic3—24no—
76C2×#478—91noSylow
77C22×D12—31no—
78C22×D12—31no—
79C22×D12—61no—
80C22×C4×D3—61no—
81C22×C4×D3—61no—
82C22×C4×D3—62no—
83C22×C3×C8—31no—
84C22×C3×C8—31no—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4C2×D311yescharacteristic
89C2×C3×C4⋊C4C2×D311yescharacteristic
90C2×(C2×D3)⋊C4—61no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—62no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3—61no—
95C2×C4⋊Dic3C2×D311yescharacteristic
96C2×C4⋊Dic3C2×D311yescharacteristic
97C2×Dic3⋊C4—61no—
98C2×Dic3⋊C4—61no—
99C2×C4×Dic3—31no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—61no—
102C22×C3⋊C8C2×D311yescharacteristic
103C22×C3⋊C8C2×D311yescharacteristic
104#893—34no—
105#893—34no—
106#893—64no—
107#893—62no—
108#893—62no—
109#893—64no—
110#890—34no—
111#890—34no—
112#890—62no—
113#890—62no—
114C3×#107—34no—
115C3×#106—34no—
116#821—34no—
117#821—34no—
118Dic3⋊C8—34no—
119Dic3⋊C8—34no—
120#809—34no—
121#809—34no—
122#808C2×D314yescomplemented
123#807C2×D314yescomplemented
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—24no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—42no—
128C22×C3⋊D3—42no—
129C2×C32×C4—22no—
130C2×C32×C4—42no—
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×Q812yes—
133C2×C32×C4#4112yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3C2×D412yes—
138C2×C3⋊Dic3C2×D412yes—
139C4⋊(C3⋊D3)—24no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)C2×Q814yes—
142C4×C3⋊D3—48no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3—42no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—22no—
149C2×#125—91no—
150C2×C4×D4—91no—
151#478—98no—
152C2×#107—31no—
153C2×#106—31no—
154C2×C4⋊C8—91no—
155C2×#102—91no—
156C2×#102—91no—
157C23×D3—62no—
158C23×D3—61no—
159C23×D3—61no—
160C22×C3×C4—22no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—31no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C2×D12—34no—
177C2×D12—34no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—64no—
182C2×D12—62no—
183C2×D12—64no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—61no—
187C2×D12—61no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—68no—
191C2×C4×D3—128no—
192C2×C4×D3—124no—
193C2×C4×D3—124no—
194C2×C3×C8—32no—
195C2×C3×C8—32no—
196C2×C3×C8—62no—
197C2×C3×C8—62no—
198C3×C4⋊C4—22no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—22no—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4C22×D312yes—
207C3×C4⋊C4C22×D312yes—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—68no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213C4⋊Dic3—64no—
214C4⋊Dic3—64no—
215C4⋊Dic3C22×D312yes—
216C4⋊Dic3C22×D312yes—
217Dic3⋊C4—64no—
218Dic3⋊C4—64no—
219C4×Dic3—32no—
220C4×Dic3—32no—
221C4×Dic3—32no—
222C4×Dic3—32no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C2×C3⋊C8—22no—
226C2×C3⋊C8—22no—
227C2×C3⋊C8C22×D312yes—
228C2×C3⋊C8C22×D312yes—
229C22×C32C22⋊Q812yes—
230C22×C32#13512yes—
231C22×C32AGL(1,ℤ/8)12yes—
232C22×C32C22×D411yescharacteristic
233C2×C3⋊D3—24no—
234C2×C3⋊D3—42no—
235C2×C3⋊D3—42no—
236C2×C3⋊D3—48no—
237C32×C4—42no—
238C32×C4C22⋊Q812yes—
239C32×C4C22×Q811yescharacteristic
240C32×C4C2×#4111yescharacteristic
241C3⋊Dic3—22no—
242C3⋊Dic3—22no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C22×D4—91no—
246C23×C4—181no—
247C22×C8—31no—
248C22×C8—31no—
249#125—94no—
250#125—182no—
251C4×D4—94no—
252C4×D4—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—181no—
256C2×C4⋊C4—181no—
257C2×C4⋊C4D3211yescharacteristic
258C2×C22⋊C4—181no—
259C2×C42—91no—
260#107—34no—
261#106—34no—
262C4⋊C8—94no—
263#102—94no—
264#102—94no—
265C23×C3—21no—
266C23×C3D3×D411yescharacteristic
267C23×C3D3×D411yescharacteristic
268C22×D3—64no—
269C22×D3—68no—
270C22×D3—64no—
271C22×D3—64no—
272C22×D3—62no—
273C22×D3—62no—
274C22×D3—124no—
275C22×D3—124no—
276C22×D3—122no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—122no—
280C2×C3×C4—24no—
281C2×C3×C4—22no—
282C2×C3×C4—22no—
283C2×C3×C4—21no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—21no—
287C2×C3×C4—44no—
288C2×C3×C4—42no—
289C2×C3×C4—42no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4#23512yes—
295C2×C3×C4#23512yes—
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×Q812yes—
299C2×C3×C4D3×Q812yes—
300C2×C3×C4C23×D311yescharacteristic
301C2×C3×C4C23×D311yescharacteristic
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—32no—
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—42no—
309C2×Dic3—42no—
310C2×Dic3—62no—
311C2×Dic3—62no—
312C2×Dic3—64no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—122no—
318D12—34no—
319D12—34no—
320D12—64no—
321D12—64no—
322D12—68no—
323D12—64no—
324D12—64no—
325D12—62no—
326D12—62no—
327C4×D3—1216no—
328C4×D3—128no—
329C4×D3—128no—
330C3×C8—62no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—22no—
334C2×C32#47814yescomplemented
335C2×C32C2×C22⋊Q811yescharacteristic
336C2×C32C2×#13511yescharacteristic
337C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
338C3⋊D3—44no—
339C24—181no—
340C2×D4—92no—
341C2×D4—94no—
342C2×D4—182no—
343C2×D4—181no—
344C22×C4—21no—
345C22×C4—61no—
346C22×C4—61no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—184no—
350C22×C4—364no—
351C22×C4C2×D3211yescharacteristic
352C2×C8—32no—
353C2×C8—32no—
354C2×C8—62no—
355C2×C8—62no—
356C4⋊C4—21no—
357C4⋊C4—32no—
358C4⋊C4—32no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—184no—
362C4⋊C4—184no—
363C4⋊C4C2×D3212yes—
364C22⋊C4—184no—
365C42—92no—
366C42—92no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—22no—
370C22×C3—22no—
371C22×C3#89612yes—
372C22×C3#89612yes—
373C22×C3#91112yes—
374C22×C3#91412yes—
375C22×C3#91612yes—
376C22×C3#91912yes—
377C22×C3C2×D3×D411yescharacteristic
378C22×C3C2×D3×D411yescharacteristic
379C2×D3—68no—
380C2×D3—64no—
381C2×D3—64no—
382C2×D3—124no—
383C2×D3—124no—
384C2×D3—1216no—
385C2×D3—128no—
386C2×D3—128no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—122no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—22no—
394C3×C4—44no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—122no—
398C3×C4—122no—
399C3×C4#89612yes—
400C3×C4#89612yes—
401C3×C4C2×#23511yescharacteristic
402C3×C4C2×#23511yescharacteristic
403C3×C4C2×D3×Q811yescharacteristic
404C3×C4C2×D3×Q811yescharacteristic
405Dic3—42no—
406Dic3—42no—
407Dic3—64no—
408Dic3—62no—
409Dic3—62no—
410Dic3—62no—
411Dic3—62no—
412Dic3—122no—
413C32C2×#47811yescharacteristic, complemented, Sylow
414C23—182no—
415C23—184no—
416C23—362no—
417C23—362no—
418C23#381111yescharacteristic
419D4—94no—
420D4—182no—
421D4—184no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—92no—
427C2×C4—92no—
428C2×C4—122no—
429C2×C4—122no—
430C2×C4—182no—
431C2×C4—182no—
432C2×C4—368no—
433C2×C4#379712yes—
434C2×C4#379812yes—
435C2×C4#381111yescharacteristic
436C2×C4C22×D3211yescharacteristic
437C8—62no—
438C8—62no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—24no—
443C2×C3#487114yescomplemented
444C2×C3#489114yescomplemented
445C2×C3C2×#89611yescharacteristic
446C2×C3C2×#89611yescharacteristic
447C2×C3C2×#91111yescharacteristic
448C2×C3C2×#91411yescharacteristic
449C2×C3C2×#91611yescharacteristic
450C2×C3C2×#91911yescharacteristic
451D3—128no—
452D3—124no—
453D3—124no—
454C22—184no—
455C22—362no—
456C22—362no—
457C22—368no—
458C22#6386512yes—
459C22#6393712yes—
460C22#6395012yes—
461C22C2×#381111yescharacteristic
462C4—42no—
463C4—122no—
464C4—122no—
465C4—182no—
466C4—182no—
467C4#6386512yes—
468C4C2×#379711yescharacteristic
469C4C2×#379811yescharacteristic
470C3—21no—
471C3C2×#487111yescharacteristic, complemented
472C3C2×#489111yescharacteristic, complemented
473C2—364no—
474C2#1059043514yesdirect product factor
475C2C2×#6386511yescharacteristic
476C2C2×#6393711yescharacteristic
477C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#478
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
2. C2×#63872C2semidirect
3. C2×C3×#808C2semidirect
4. C2×C3×#807C2semidirect
5. C2×#63572C2semidirect
8. #10590435C2direct (N × H)
25. #63872C22semidirect
26. C3×#808C22semidirect
27. C3×#807C22semidirect
28. #63572C22semidirect
44. C2×#808D3semidirect
45. C2×#807D3semidirect
122. #808C2×D3semidirect
123. #807C2×D3semidirect
334. C2×C32#478semidirect
413. C32C2×#478semidirect
443. C2×C3#4871semidirect
444. C2×C3#4891semidirect
471. C3C2×#4871semidirect
472. C3C2×#4891semidirect
474. C2#10590435direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#638722
C2×C3×#8082
C2×C3×#8072
C2×#635722
C2×#635642
#105904352
C2×#48913
C2×#48713