Finite Group Databasebeta

← C2×#10590872 #11873445

Subgroups — C2×#10590872 #11873445

Order 1152.

925 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×#63869C211yesmaximal, characteristic, complemented
2C2×#63864C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590872C218yesmaximal, direct product factor
9C2×#4800—31nomaximal
10C2×#4697—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3724—21no—
19C2×Dic3⋊Dic3—21no—
20C2×#3722—21no—
21C2×#3722—21no—
22#63869—22no—
23#63869C2214yescomplemented
24#63864—22no—
25#63864C2214yes—
26#63648C2214yes—
27C3×#816C2214yescomplemented
28C3×C8×Dic3C2214yescomplemented
29#63566C2214yescomplemented
30#63564C2214yes—
31C2×#947—31no—
32C2×#890—31no—
33C2×#875—31no—
34C2×#870—31no—
35C2×C3×#103—31no—
36C2×C3×C4×C8—31no—
37C2×#835—31no—
38C2×#821—31no—
39C2×#821—31no—
40C2×#821—31no—
41C2×#821—61no—
42C2×#816—31no—
43C2×#816D311yescharacteristic, complemented
44C2×C8×Dic3D311yescharacteristic, complemented
45C2×#809—31no—
46#4800—38no—
47#4697—38no—
48C23×C3⋊D3—21no—
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C22×C3×Dic3D411yescharacteristic
58C22×C3×Dic3D411yescharacteristic
59C2×C3×Dic6—22no—
60C2×C3×Dic6—22no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6C2312yes—
63C2×C32×C8—22no—
64C2×C32×C8C2312yes—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)C2312yes—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3C2312yes—
69C3×C4×Dic3D412yes—
70C3×C4×Dic3C2312yes—
71C2×C3×C3⋊C8—22no—
72C2×C3×C3⋊C8C2312yes—
73#3724—24no—
74Dic3⋊Dic3—24no—
75#3722—24no—
76#3722—24no—
77C2×#488—91noSylow
78C22×C3×Q8—31no—
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C42—31no—
89#947—34no—
90#947—62no—
91C2×(C2×D3)⋊C4—61no—
92C2×(C2×D3)⋊C4—61no—
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⋊Dic3C2×D311yescharacteristic
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105#890—34no—
106#890—62no—
107#875—34no—
108#875—62no—
109#870—34no—
110#870—62no—
111C3×#103—34no—
112C3×C4×C8—34no—
113#835—34no—
114#821—34no—
115#821—34no—
116#821—34no—
117#821—64no—
118#816—34no—
119#816C2×D314yescomplemented
120C8×Dic3C2×D314yescomplemented
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—42no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—42no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3—42no—
141C2×C3×Dic3—42no—
142C2×C3×Dic3C2×D412yes—
143C2×C3×Dic3C2×D412yes—
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—91no—
155C2×#102—91no—
156C2×C4×C8—31no—
157C23×D3—61no—
158C23×D3—61no—
159C23×D3—121no—
160C2×C3×Q8—32no—
161C2×C3×Q8—61no—
162C2×C3×Q8—62no—
163C2×C3×Q8—62no—
164C22×C3×C4—21no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—21no—
172C22×Dic3—21no—
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C22×Dic3D1211yescharacteristic
177C22×Dic3D1211yescharacteristic
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—62no—
181C2×D12—64no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—121no—
189C2×D12—122no—
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—21no—
193C2×Dic6C22×D312yes—
194C2×C3×C8—22no—
195C2×C3×C8—22no—
196C2×C3×C8—22no—
197C2×C3×C8—32no—
198C2×C3×C8—42no—
199C2×C3×C8—62no—
200C2×C3×C8C22×D312yes—
201C2×C3×C8C22×D312yes—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C42—32no—
205C3×C42—32no—
206(C2×D3)⋊C4—64no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210C4⋊Dic3—21no—
211C4⋊Dic3—32no—
212C4⋊Dic3—32no—
213C4⋊Dic3—62no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—64no—
217C4⋊Dic3—121no—
218C4⋊Dic3C22×D312yes—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—64no—
222C4×Dic3D1212yes—
223C4×Dic3C22×D312yes—
224C2×C3⋊C8—22no—
225C2×C3⋊C8C22×D312yes—
226C22×C32#12412yes—
227C22×C32#13512yes—
228C22×C32#13512yes—
229C22×C32C22×D411yescharacteristic
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—42no—
233C2×C3⋊D3—84no—
234C32×C4#12412yes—
235C32×C4C2×#4111yescharacteristic
236C32×C4C2×#4111yescharacteristic
237C3⋊Dic3—42no—
238C3×Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—42no—
242C22×Q8—31no—
243C22×D4—91no—
244C22×C8—31no—
245C22×C8D3211yescharacteristic
246#125—94no—
247#125—182no—
248#124—94no—
249#124—182no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—91no—
252C2×C4⋊C4—181no—
253C2×C4⋊C4—181no—
254C2×C22⋊C4—181no—
255C2×C22⋊C4—181no—
256C2×C42—31no—
257#103—34no—
258#103—94no—
259#102—94no—
260#102—94no—
261C4×C8—34no—
262C23×C3—21no—
263C23×C3C2×D1211yescharacteristic
264C23×C3D3×D411yescharacteristic
265C22×D3—62no—
266C22×D3—62no—
267C22×D3—122no—
268C22×D3—124no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—122no—
272C22×D3—122no—
273C22×D3—122no—
274C22×D3—122no—
275C22×D3—242no—
276C22×D3—242no—
277C3×Q8—62no—
278C3×Q8—62no—
279C3×Q8—122no—
280C2×C3×C4—21no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—22no—
284C2×C3×C4—32no—
285C2×C3×C4—32no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—122no—
291C2×C3×C4—122no—
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23512yes—
294C2×C3×C4#23512yes—
295C2×C3×C4#23512yes—
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4#23712yes—
298C2×C3×C4C23×D311yescharacteristic
299C2×C3×C4C23×D311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—122no—
310C2×Dic3—122no—
311C2×Dic3—242no—
312C2×Dic3C2×D1212yes—
313C2×Dic3C2×D1212yes—
314D12—64no—
315D12—62no—
316D12—62no—
317D12—62no—
318D12—62no—
319D12—122no—
320D12—124no—
321D12—122no—
322D12—122no—
323Dic6—22no—
324Dic6—22no—
325Dic6—42no—
326C3×C8—22no—
327C3×C8—22no—
328C3×C8—42no—
329C3×C8—62no—
330C3⋊C8—22no—
331C2×C32#48814yescomplemented
332C2×C32C2×#12411yescharacteristic
333C2×C32C2×#13511yescharacteristic
334C2×C32C2×#13511yescharacteristic
335C3⋊D3—82no—
336C24—181no—
337C2×Q8—32no—
338C2×Q8—61no—
339C2×Q8—62no—
340C2×Q8—62no—
341C2×D4—92no—
342C2×D4—182no—
343C2×D4—181no—
344C2×D4—182no—
345C22×C4—31no—
346C22×C4—31no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—181no—
350C22×C4C2×D3211yescharacteristic
351C2×C8—22no—
352C2×C8—32no—
353C2×C8—62no—
354C2×C8C2×D3212yes—
355C4⋊C4—32no—
356C4⋊C4—61no—
357C4⋊C4—92no—
358C4⋊C4—184no—
359C4⋊C4—184no—
360C4⋊C4—181no—
361C22⋊C4—184no—
362C22⋊C4—184no—
363C42—32no—
364C42—32no—
365C22×C3—21no—
366C22×C3—22no—
367C22×C3—22no—
368C22×C3—22no—
369C22×C3#87512yes—
370C22×C3#88512yes—
371C22×C3#90412yes—
372C22×C3#90412yes—
373C22×C3#91612yes—
374C22×C3#91912yes—
375C22×C3C22×D1211yescharacteristic
376C22×C3C2×D3×D411yescharacteristic
377C2×D3—124no—
378C2×D3—122no—
379C2×D3—122no—
380C2×D3—122no—
381C2×D3—122no—
382C2×D3—122no—
383C2×D3—122no—
384C2×D3—242no—
385C2×D3—242no—
386C2×D3—248no—
387C2×D3—244no—
388C2×D3—244no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—22no—
392C3×C4—62no—
393C3×C4—62no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4#87512yes—
397C3×C4#88512yes—
398C3×C4C2×#23511yescharacteristic
399C3×C4C2×#23511yescharacteristic
400C3×C4C2×#23511yescharacteristic
401C3×C4C2×#23711yescharacteristic
402Dic3—22no—
403Dic3—22no—
404Dic3—42no—
405Dic3—42no—
406Dic3—122no—
407Dic3—122no—
408Dic3—242no—
409C32C2×#48811yescharacteristic, complemented, Sylow
410C23—182no—
411C23—362no—
412C23—362no—
413C23—362no—
414C23D3×D1211yescharacteristic
415Q8—62no—
416Q8—62no—
417Q8—122no—
418D4—182no—
419D4—182no—
420D4—362no—
421C2×C4—32no—
422C2×C4—32no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—122no—
428C2×C4—122no—
429C2×C4—182no—
430C2×C4—362no—
431C2×C4#379812yes—
432C2×C4D3×D1211yescharacteristic
433C2×C4#380412yes—
434C2×C4C22×D3211yescharacteristic
435C8—22no—
436C8—62no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—24no—
441C2×C3#469714yescomplemented
442C2×C3#480014yescomplemented
443C2×C3C2×#87511yescharacteristic
444C2×C3C2×#88511yescharacteristic
445C2×C3C2×#90411yescharacteristic
446C2×C3C2×#90411yescharacteristic
447C2×C3C2×#91611yescharacteristic
448C2×C3C2×#91911yescharacteristic
449D3—244no—
450D3—242no—
451D3—242no—
452C22—362no—
453C22—362no—
454C22—362no—
455C22—724no—
456C22#6380612yes—
457C22#6380812yes—
458C22#6385212yes—
459C22C2×D3×D1211yescharacteristic
460C4—62no—
461C4—62no—
462C4—122no—
463C4—122no—
464C4—362no—
465C4#6385212yes—
466C4C2×#379811yescharacteristic
467C4C2×#380411yescharacteristic
468C3—21no—
469C3C2×#469711yescharacteristic, complemented
470C3C2×#480011yescharacteristic, complemented
471C2—722no—
472C2#1059087214yesdirect product factor
473C2C2×#6380611yescharacteristic
474C2C2×#6380811yescharacteristic
475C2C2×#6385211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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×#63869C2semidirect
4. C2×C3×#816C2semidirect
5. C2×C3×C8×Dic3C2semidirect
6. C2×#63566C2semidirect
8. #10590872C2direct (N × H)
23. #63869C22semidirect
27. C3×#816C22semidirect
28. C3×C8×Dic3C22semidirect
29. #63566C22semidirect
43. C2×#816D3semidirect
44. C2×C8×Dic3D3semidirect
119. #816C2×D3semidirect
120. C8×Dic3C2×D3semidirect
331. C2×C32#488semidirect
409. C32C2×#488semidirect
441. C2×C3#4697semidirect
442. C2×C3#4800semidirect
469. C3C2×#4697semidirect
470. C3C2×#4800semidirect
472. C2#10590872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638692
C2×#638642
C2×#636482
C2×C3×#8162
C2×C3×C8×Dic32
C2×#635662
C2×#635642
#105908722
C2×#48003
C2×#46973