Finite Group Databasebeta

← C2×#10590483 #11859887

Subgroups — C2×#10590483 #11859887

Order 1152.

1317 conjugacy classes of subgroups.

The subgroup lattice has 507 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×C3×#808C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C2×#63553C211yesmaximal, characteristic, complemented
8#10590483C218yesmaximal, direct product factor
9C2×#4852—31nomaximal
10C2×#4788—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17#64102—22no—
18#64102C2214yes—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24#63843—22no—
25#63843C2214yescomplemented
26C2×#3717C418yescomplemented
27C2×#3717C2214yes—
28C3×#810C2214yescomplemented
29C3×#808C2214yescomplemented
30#63564C2214yes—
31#63553C2214yescomplemented
32C2×Q8×Dic3—31no—
33C22×#215—31no—
34C22×#204—31no—
35C2×#893—31no—
36C2×#893—31no—
37C2×#893—61no—
38C2×#887—31no—
39C2×C3×#106—31no—
40C2×C3×#103—31no—
41C2×#821—31no—
42C2×C8×Dic3—31no—
43C2×C8×Dic3—31no—
44C2×#810D311yescharacteristic, complemented
45C2×#809—31no—
46C2×#808D311yescharacteristic, complemented
47#4852—38no—
48#4788—38no—
49C23×C3⋊D3—21no—
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3D411yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)C2×C414yes—
57C2×C4⋊(C3⋊D3)C2312yes—
58C2×C4×C3⋊D3—24no—
59C2×C4×C3⋊D3—44no—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6C2×C414yescomplemented
65C2×C3×Dic6C2312yes—
66C32×C4⋊C4—21no—
67C32×C4⋊C4C2312yes—
68#3752—24no—
69C4×C3⋊Dic3D412yes—
70C4×C3⋊Dic3C2312yes—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C2×C3×C3⋊C8—22no—
74C2×C3×C3⋊C8C2×C414yescomplemented
75C2×C3×C3⋊C8C2312yes—
76C2×C3×C3⋊C8C2312yes—
77Dic3⋊Dic3—24no—
78Dic32—24no—
79#3717C2×C4116yescomplemented
80C2×C4×SD16—91noSylow
81C22×C3×Q8—31no—
82C22×D12—31no—
83C22×D12—31no—
84C22×D12—61no—
85C22×C4×D3—61no—
86C22×C4×D3—61no—
87C22×C4×D3—62no—
88C22×Dic6C2×D311yescharacteristic
89C22×C3×C8—31no—
90C22×C3×C8—31no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C4⋊C4C2×D311yescharacteristic
95Q8×Dic3—34no—
96Q8×Dic3—62no—
97C2×#215—38no—
98C2×#215—34no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—62no—
102C2×C4⋊Dic3—61no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—61no—
105C2×C4×Dic3—31no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C2×C4×Dic3—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C2×#204—38no—
113C2×#204—34no—
114#893—34no—
115#893—34no—
116#893—64no—
117#893—62no—
118#893—62no—
119#893—64no—
120#887—34no—
121#887—62no—
122C3×#106—34no—
123C3×#103—34no—
124#821—34no—
125C8×Dic3—34no—
126C8×Dic3—34no—
127#810C2×D314yescomplemented
128#809—34no—
129#808C2×D314yescomplemented
130C23×C32C2×D411yescharacteristic
131C22×C3⋊D3—24no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—42no—
134C22×C3⋊D3—42no—
135C2×C32×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C22×C412yes—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4112yes—
140C2×C32×C4C2411yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3SD1614yescomplemented
143C2×C3⋊Dic3C2×D412yes—
144C2×C3⋊Dic3C2×D412yes—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C4×C3⋊D3—48no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C3×Dic6—24no—
154C3×Dic6—22no—
155C3×Dic6C22×C414yescomplemented
156C3×C3⋊C8—22no—
157C3×C3⋊C8C22×C414yescomplemented
158C22×SD16—91no—
159C2×C4×Q8—91no—
160C2×C4×D4—91no—
161C4×SD16—98no—
162C2×#106—31no—
163C2×#103—31no—
164C2×#102—91no—
165C2×C4×C8—91no—
166C23×D3—62no—
167C23×D3—61no—
168C23×D3—61no—
169C2×C3×Q8—34no—
170C2×C3×Q8—32no—
171C2×C3×Q8—61no—
172C2×C3×Q8—62no—
173C22×C3×C4—22no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—31no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C2×D12—34no—
190C2×D12—34no—
191C2×D12—32no—
192C2×D12—32no—
193C2×D12—62no—
194C2×D12—64no—
195C2×D12—62no—
196C2×D12—64no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—62no—
200C2×D12—62no—
201C2×C4×D3—64no—
202C2×C4×D3—64no—
203C2×C4×D3—68no—
204C2×C4×D3—124no—
205C2×C4×D3—124no—
206C2×C4×D3—128no—
207C2×Dic6—21no—
208C2×Dic6—22no—
209C2×Dic6C4×D314yescomplemented
210C2×Dic6C22×D312yes—
211C2×C3×C8—34no—
212C2×C3×C8—32no—
213C2×C3×C8—32no—
214C2×C3×C8—62no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—61no—
221C3×C4⋊C4C22×D312yes—
222C3×C4⋊C4C22×D312yes—
223#215—316no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—68no—
227C4⋊Dic3—21no—
228C4⋊Dic3—64no—
229C4⋊Dic3C22×D312yes—
230Dic3⋊C4—64no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—62no—
236C4×Dic3—62no—
237C4×Dic3—64no—
238C4×Dic3—64no—
239C2×C3⋊C8—22no—
240C2×C3⋊C8C4×D314yescomplemented
241C2×C3⋊C8C22×D312yes—
242C2×C3⋊C8C22×D312yes—
243#204—316no—
244C22×C32C4×D412yes—
245C22×C32C2×SD1612yes—
246C22×C32#13512yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—48no—
252C32×C4—42no—
253C32×C4C4×D412yes—
254C32×C4C23×C411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—22no—
257C3⋊Dic3C2×SD1614yescomplemented
258C3×Dic3—24no—
259C3×Dic3—42no—
260C22×Q8—31no—
261C22×D4—91no—
262C23×C4—181no—
263C2×SD16—98no—
264C2×SD16—94no—
265C22×C8—31no—
266C22×C8—31no—
267C4×Q8—94no—
268C4×Q8—182no—
269C4×D4—94no—
270C4×D4—182no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—181no—
273C2×C4⋊C4D3211yescharacteristic
274C2×C22⋊C4—181no—
275C2×C42—91no—
276C2×C42—181no—
277#106—34no—
278#103—34no—
279#102—94no—
280C4×C8—94no—
281C23×C3—21no—
282C23×C3D3×D411yescharacteristic
283C23×C3D3×D411yescharacteristic
284C22×D3—64no—
285C22×D3—68no—
286C22×D3—64no—
287C22×D3—64no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—124no—
291C22×D3—124no—
292C22×D3—122no—
293C22×D3—122no—
294C22×D3—122no—
295C22×D3—122no—
296C3×Q8—34no—
297C3×Q8—64no—
298C3×Q8—62no—
299C2×C3×C4—24no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—22no—
304C2×C3×C4—22no—
305C2×C3×C4—21no—
306C2×C3×C4—44no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—64no—
310C2×C3×C4—62no—
311C2×C3×C4—62no—
312C2×C3×C4—122no—
313C2×C3×C4C2×C4×D312yes—
314C2×C3×C4C2×C4×D312yes—
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23712yes—
318C2×C3×C4#23912yes—
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321C2×Dic3—24no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—32no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—32no—
330C2×Dic3—42no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—62no—
335C2×Dic3—62no—
336C2×Dic3—122no—
337D12—34no—
338D12—34no—
339D12—64no—
340D12—64no—
341D12—68no—
342D12—64no—
343D12—64no—
344D12—62no—
345D12—62no—
346C4×D3—128no—
347C4×D3—128no—
348C4×D3—1216no—
349Dic6—24no—
350Dic6—22no—
351Dic6C2×C4×D314yescomplemented
352C3×C8—34no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8C2×C4×D314yescomplemented
356C2×C32C4×SD1614yescomplemented
357C2×C32C2×C4×D411yescharacteristic
358C2×C32C22×SD1611yescharacteristic
359C2×C32C2×#13511yescharacteristic
360C3⋊D3—44no—
361C24—181no—
362C2×Q8—32no—
363C2×Q8—34no—
364C2×Q8—62no—
365C2×Q8—61no—
366C2×D4—92no—
367C2×D4—94no—
368C2×D4—182no—
369C2×D4—181no—
370C22×C4—21no—
371C22×C4—61no—
372C22×C4—61no—
373C22×C4—91no—
374C22×C4—91no—
375C22×C4—184no—
376C22×C4—364no—
377C22×C4C2×D3211yescharacteristic
378SD16—916no—
379C2×C8—32no—
380C2×C8—34no—
381C2×C8—32no—
382C2×C8—62no—
383C4⋊C4—21no—
384C4⋊C4—32no—
385C4⋊C4—61no—
386C4⋊C4—184no—
387C4⋊C4C2×D3212yes—
388C22⋊C4—184no—
389C42—92no—
390C42—92no—
391C42—184no—
392C22×C3—21no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—22no—
396C22×C3#67⋊C412yes—
397C22×C3#89312yes—
398C22×C3D3×SD1612yes—
399C22×C3D3×SD1612yes—
400C22×C3#91612yes—
401C22×C3#91912yes—
402C22×C3C2×D3×D411yescharacteristic
403C22×C3C2×D3×D411yescharacteristic
404C2×D3—68no—
405C2×D3—64no—
406C2×D3—64no—
407C2×D3—124no—
408C2×D3—124no—
409C2×D3—1216no—
410C2×D3—122no—
411C2×D3—122no—
412C2×D3—122no—
413C2×D3—122no—
414C2×D3—128no—
415C2×D3—128no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—44no—
420C3×C4—42no—
421C3×C4—42no—
422C3×C4—64no—
423C3×C4—122no—
424C3×C4#67⋊C412yes—
425C3×C4#89312yes—
426C3×C4C22×C4×D311yescharacteristic
427C3×C4C22×C4×D311yescharacteristic
428C3×C4C2×#23711yescharacteristic
429C3×C4C2×#23911yescharacteristic
430Dic3—24no—
431Dic3—34no—
432Dic3—34no—
433Dic3—42no—
434Dic3—64no—
435Dic3—62no—
436Dic3—62no—
437Dic3—122no—
438C32C2×C4×SD1611yescharacteristic, complemented, Sylow
439C23—182no—
440C23—184no—
441C23—362no—
442C23—362no—
443C23#381111yescharacteristic
444Q8—34no—
445Q8—62no—
446Q8—64no—
447D4—94no—
448D4—182no—
449D4—184no—
450C2×C4—22no—
451C2×C4—42no—
452C2×C4—62no—
453C2×C4—64no—
454C2×C4—62no—
455C2×C4—92no—
456C2×C4—94no—
457C2×C4—92no—
458C2×C4—122no—
459C2×C4—182no—
460C2×C4—368no—
461C2×C4#379612yes—
462C2×C4C4×D3212yes—
463C2×C4#381111yescharacteristic
464C2×C4C22×D3211yescharacteristic
465C8—34no—
466C8—62no—
467C2×C3—21no—
468C2×C3—24no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3#478814yescomplemented
472C2×C3#485214yescomplemented
473C2×C3C2×#67⋊C411yescharacteristic
474C2×C3C2×#89311yescharacteristic
475C2×C3C2×D3×SD1611yescharacteristic
476C2×C3C2×D3×SD1611yescharacteristic
477C2×C3C2×#91611yescharacteristic
478C2×C3C2×#91911yescharacteristic
479D3—128no—
480D3—124no—
481D3—124no—
482C22—184no—
483C22—362no—
484C22—368no—
485C22—362no—
486C22#6388112yes—
487C22#6393012yes—
488C22#6395012yes—
489C22C2×#381111yescharacteristic
490C4—42no—
491C4—64no—
492C4—94no—
493C4—122no—
494C4—182no—
495C4#6388112yes—
496C4C2×#379611yescharacteristic
497C4C2×C4×D3211yescharacteristic
498C3—21no—
499C3C2×#478811yescharacteristic, complemented
500C3C2×#485211yescharacteristic, complemented
501C2—364no—
502C2#1059048314yesdirect product factor
503C2C2×#6388111yescharacteristic
504C2C2×#6393011yescharacteristic
505C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×C4×SD16
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
2. C2×#63843C2semidirect
4. C2×C3×#810C2semidirect
5. C2×C3×#808C2semidirect
7. C2×#63553C2semidirect
8. #10590483C2direct (N × H)
25. #63843C22semidirect
26. C2×#3717C4semidirect
28. C3×#810C22semidirect
29. C3×#808C22semidirect
31. #63553C22semidirect
44. C2×#810D3semidirect
46. C2×#808D3semidirect
64. C2×C3×Dic6C2×C4semidirect
74. C2×C3×C3⋊C8C2×C4semidirect
79. #3717C2×C4semidirect
127. #810C2×D3semidirect
129. #808C2×D3semidirect
142. C2×C3⋊Dic3SD16semidirect
155. C3×Dic6C22×C4semidirect
157. C3×C3⋊C8C22×C4semidirect
209. C2×Dic6C4×D3semidirect
240. C2×C3⋊C8C4×D3semidirect
257. C3⋊Dic3C2×SD16semidirect
351. Dic6C2×C4×D3semidirect
355. C3⋊C8C2×C4×D3semidirect
356. C2×C32C4×SD16semidirect
438. C32C2×C4×SD16semidirect
471. C2×C3#4788semidirect
472. C2×C3#4852semidirect
499. C3C2×#4788semidirect
500. C3C2×#4852semidirect
502. C2#10590483direct (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×#638432
C22×#37172
C2×C3×#8102
C2×C3×#8082
C2×#635642
C2×#635532
#105904832
C2×#48523
C2×#47883