Finite Group Databasebeta

← C2×#10590518 #11866801

Subgroups — C2×#10590518 #11866801

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#897C211yesmaximal, characteristic
2C2×#63856C211yesmaximal, characteristic
3C22×#3718C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic
5C2×#63634C211yesmaximal, characteristic, complemented
6C2×C3×#810C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590518C218yesmaximal, direct product factor
9C2×#5051—31nomaximal
10C2×#4813—31nomaximal
11C22×C3×C4×D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3—21no—
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#897—22no—
21C3×#897C2214yes—
22C2×#3724—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63856—22no—
25#63856C2214yes—
26C2×#3718—24no—
27C2×#3718C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yes—
30#63634C2214yescomplemented
31C3×#810C2214yescomplemented
32#63566C2214yescomplemented
33C2×C3×C22⋊Q8—31no—
34C2×#946—31no—
35C22×#216—31no—
36C22×#216—31no—
37C2×#924—31no—
38C23×C3⋊C8—31no—
39C22×D3×C8—31no—
40C2×#897D311yescharacteristic
41C2×C3×#103—31no—
42C2×#835—31no—
43C2×#816—31no—
44#5051—38no—
45C2×#810D311yescharacteristic, complemented
46C2×#807—31no—
47C2×#807—31no—
48C2×#807—61no—
49#4813—38no—
50C23×C3×D3D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3—21no—
56C22×C3×Dic3D411yescharacteristic
57C2×C3×C4×D3—22no—
58C2×C3×C4×D3—22no—
59C2×C3×C4×D3D412yes—
60C2×C3×C4×D3C2312yes—
61C2×C3×Dic6—22no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6—22no—
64C2×C3×Dic6—22no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6C2312yes—
68C2×C3×Dic6C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4C2312yes—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)D414yes—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—24no—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79#3724—24no—
80(C2×D3)⋊Dic3—24no—
81#3718—28no—
82D3×C3⋊C8—28no—
83C2×#467—91noSylow
84C22×C3×Q8—31no—
85C22×C3×Q8—31no—
86C23×C3×C4—31no—
87C22×C4×D3C2×D311yescharacteristic
88C22×Dic6C2×D311yescharacteristic
89C22×Dic6C2×D311yescharacteristic
90C22×C3×C8—31no—
91C3×C22⋊Q8—34no—
92C3×C22⋊Q8—62no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—61no—
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C22⋊C4—61no—
98C2×#217—61no—
99#946—34no—
100#946—62no—
101C2×#216—34no—
102C2×#216—34no—
103C2×#216—64no—
104C2×#216—64no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—21no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—31no—
110C2×C4⋊Dic3—61no—
111#924—34no—
112#924—62no—
113C2×Dic3⋊C4—61no—
114C2×Dic3⋊C4—61no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—34no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8—64no—
120C22×C3⋊C8C2×D311yescharacteristic
121C2×D3×C8—34no—
122C2×D3×C8—64no—
123#897—22no—
124#897C2×D314yes—
125C3×#103—34no—
126#835—34no—
127#816—34no—
128#810C2×D314yescomplemented
129#807—34no—
130#807—34no—
131#807—64no—
132C23×C32C2×D411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3Q1614yescomplemented
136C22×C3×D3C2×D412yes—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C2×D412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—42no—
149C2×C3×Dic3—42no—
150C2×C3×Dic3C2×D412yes—
151C3×C4×D3—24no—
152C3×C4×D3—22no—
153C3×C4×D3—22no—
154C3×Dic6—22no—
155C3×Dic6—22no—
156C3×Dic6—22no—
157C3×Dic6—22no—
158C3×Dic6—42no—
159C3×Dic6—42no—
160C3⋊(C3⋊C8)C2×D414yes—
161C3×C3⋊C8—22no—
162C22×Q16—91no—
163C23×C8—91no—
164C2×C22⋊Q8—31no—
165C2×C22⋊Q8—91no—
166#467—98no—
167C2×#107—91no—
168C2×#103—31no—
169C2×#103—91no—
170C24×C3—31no—
171C23×D3#6711yescharacteristic
172C2×C3×Q8—32no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—62no—
177C2×C3×Q8—62no—
178C2×C3×Q8—62no—
179C2×C3×Q8—62no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—31no—
184C22×C3×C4—32no—
185C22×C3×C4—32no—
186C22×C3×C4—41no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—61no—
196C22×Dic3—61no—
197C22×Dic3—121no—
198C22×Dic3#6711yescharacteristic
199C2×C4×D3—22no—
200C2×C4×D3—22no—
201C2×C4×D3#6712yes—
202C2×C4×D3C22×D312yes—
203C2×Dic6—22no—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—22no—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6C22×D312yes—
210C2×Dic6C22×D312yes—
211C2×C3×C8—32no—
212C2×C3×C8—62no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—22no—
216C3×C4⋊C4—41no—
217C3×C4⋊C4—64no—
218C3×C4⋊C4C22×D312yes—
219C3×C4⋊C4C22×D312yes—
220C3×C22⋊C4—64no—
221#217—64no—
222#216—68no—
223#216—68no—
224(C2×D3)⋊C4—24no—
225(C2×D3)⋊C4—64no—
226C4⋊Dic3—24no—
227C4⋊Dic3—32no—
228C4⋊Dic3—32no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—121no—
233Dic3⋊C4—64no—
234Dic3⋊C4—64no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—34no—
237C2×C3⋊C8—34no—
238C2×C3⋊C8—32no—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—62no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—68no—
243C2×C3⋊C8C22×D312yes—
244D3×C8—68no—
245C22×C32#12112yes—
246C22×C32C2×Q1612yes—
247C22×C32#13512yes—
248C22×C32C22×D411yescharacteristic
249C2×C3×D3—22no—
250C2×C3×D3—22no—
251C2×C3×D3—28no—
252C2×C3×D3C2×Q1614yescomplemented
253C32×C4—42no—
254C32×C4#12112yes—
255C32×C4C22×D411yescharacteristic
256C32×C4C2×#4111yescharacteristic
257C3⋊Dic3—42no—
258C3×Dic3—22no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C22×Q8—31no—
262C22×Q8—31no—
263C23×C4—31no—
264C2×Q16—94no—
265C2×Q16—184no—
266C22×C8—31no—
267C22×C8—94no—
268C22×C8—91no—
269C22×C8—184no—
270C22⋊Q8—34no—
271C22⋊Q8—62no—
272C22⋊Q8—94no—
273C22⋊Q8—182no—
274C2×C4⋊C4—61no—
275C2×C4⋊C4—91no—
276C2×C4⋊C4—181no—
277C2×C4⋊C4D3211yescharacteristic
278C2×C22⋊C4—61no—
279C2×C22⋊C4—181no—
280#107—94no—
281#103—34no—
282#103—94no—
283C23×C3—21no—
284C23×C3—34no—
285C23×C3—32no—
286C23×C3—62no—
287C23×C3—62no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—22no—
291C22×D3—22no—
292C22×D3#21614yescomplemented
293C22×D3C2×#6712yes—
294C3×Q8—62no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—62no—
298C3×Q8—122no—
299C3×Q8—122no—
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—32no—
307C2×C3×C4—42no—
308C2×C3×C4—42no—
309C2×C3×C4—42no—
310C2×C3×C4—62no—
311C2×C3×C4—64no—
312C2×C3×C4—62no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—82no—
317C2×C3×C4—122no—
318C2×C3×C4—122no—
319C2×C3×C4#23512yes—
320C2×C3×C4D3×D412yes—
321C2×C3×C4D3×D412yes—
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23712yes—
324C2×C3×C4C2×#6711yescharacteristic
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—42no—
331C2×Dic3—42no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—122no—
337C2×Dic3—242no—
338C2×Dic3C2×#6712yes—
339C4×D3—24no—
340C4×D3—22no—
341C4×D3—22no—
342Dic6—22no—
343Dic6—22no—
344Dic6—22no—
345Dic6—22no—
346Dic6—42no—
347Dic6—42no—
348C3×C8—62no—
349C3⋊C8—22no—
350C3⋊C8—34no—
351C3⋊C8—34no—
352C3⋊C8—64no—
353C2×C32#46714yescomplemented
354C2×C32C2×#12111yescharacteristic
355C2×C32C22×Q1611yescharacteristic
356C2×C32C2×#13511yescharacteristic
357C3×D3—24no—
358C24—31no—
359C2×Q8—32no—
360C2×Q8—32no—
361C2×Q8—61no—
362C2×Q8—61no—
363C2×Q8—62no—
364C2×Q8—62no—
365C2×Q8—62no—
366C2×Q8—62no—
367C22×C4—21no—
368C22×C4—31no—
369C22×C4—32no—
370C22×C4—32no—
371C22×C4—62no—
372C22×C4—62no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—181no—
376C22×C4C2×D3211yescharacteristic
377Q16—188no—
378C2×C8—32no—
379C2×C8—62no—
380C2×C8—92no—
381C2×C8—94no—
382C2×C8—188no—
383C4⋊C4—21no—
384C4⋊C4—64no—
385C4⋊C4—92no—
386C4⋊C4—184no—
387C4⋊C4—181no—
388C4⋊C4C2×D3212yes—
389C22⋊C4—64no—
390C22⋊C4—184no—
391C22×C3—21no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—22no—
395C22×C3—34no—
396C22×C3—62no—
397C22×C3—62no—
398C22×C3—68no—
399C22×C3#88412yes—
400C22×C3#91612yes—
401C22×C3D3×Q1612yes—
402C22×C3#93912yes—
403C22×C3C2×#21612yes—
404C22×C3#95012yes—
405C22×C3C2×D3×D411yescharacteristic
406C22×C3C22×#6711yescharacteristic
407C2×D3—22no—
408C2×D3—28no—
409C2×D3—22no—
410C2×D3C2×#21614yescomplemented
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—22no—
414C3×C4—42no—
415C3×C4—42no—
416C3×C4—62no—
417C3×C4—82no—
418C3×C4—122no—
419C3×C4—122no—
420C3×C4#88412yes—
421C3×C4#93912yes—
422C3×C4C2×#23511yescharacteristic
423C3×C4C2×D3×D411yescharacteristic
424C3×C4C2×D3×D411yescharacteristic
425C3×C4C2×#23711yescharacteristic
426Dic3—22no—
427Dic3—42no—
428Dic3—42no—
429Dic3—122no—
430Dic3—122no—
431Dic3—242no—
432C32C2×#46711yescharacteristic, complemented, Sylow
433C23—32no—
434C23—34no—
435C23—62no—
436C23—62no—
437C23D3×#6711yescharacteristic
438Q8—62no—
439Q8—62no—
440Q8—62no—
441Q8—62no—
442Q8—122no—
443Q8—122no—
444C2×C4—22no—
445C2×C4—32no—
446C2×C4—42no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—62no—
450C2×C4—64no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—122no—
454C2×C4—122no—
455C2×C4—182no—
456C2×C4—362no—
457C2×C4#379512yes—
458C2×C4#380212yes—
459C2×C4D3×#6711yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—62no—
462C8—94no—
463C2×C3—21no—
464C2×C3—24no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—64no—
468C2×C3#481314yescomplemented
469C2×C3#505114yescomplemented
470C2×C3C2×#88411yescharacteristic
471C2×C3C2×#91611yescharacteristic
472C2×C3C2×D3×Q1611yescharacteristic
473C2×C3C2×#93911yescharacteristic
474C2×C3C22×#21611yescharacteristic
475C2×C3C2×#95011yescharacteristic
476D3—24no—
477C22—34no—
478C22—62no—
479C22—68no—
480C22—62no—
481C22#6388512yes—
482C22#6393512yes—
483C22D3×#21612yes—
484C22C2×D3×#6711yescharacteristic
485C4—42no—
486C4—62no—
487C4—122no—
488C4—122no—
489C4—362no—
490C4#6388512yes—
491C4C2×#379511yescharacteristic
492C4C2×#380211yescharacteristic
493C3—21no—
494C3C2×#481311yescharacteristic, complemented
495C3C2×#505111yescharacteristic, complemented
496C2—64no—
497C2#1059051814yesdirect product factor
498C2C2×#6388511yescharacteristic
499C2C2×#6393511yescharacteristic
500C2C2×D3×#21611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#467
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
3. C22×#3718C2semidirect
5. C2×#63634C2semidirect
6. C2×C3×#810C2semidirect
7. C2×#63566C2semidirect
8. #10590518C2direct (N × H)
27. C2×#3718C22semidirect
30. #63634C22semidirect
31. C3×#810C22semidirect
32. #63566C22semidirect
45. C2×#810D3semidirect
128. #810C2×D3semidirect
135. C22×C3×D3Q16semidirect
252. C2×C3×D3C2×Q16semidirect
292. C22×D3#216semidirect
353. C2×C32#467semidirect
410. C2×D3C2×#216semidirect
432. C32C2×#467semidirect
468. C2×C3#4813semidirect
469. C2×C3#5051semidirect
494. C3C2×#4813semidirect
495. C3C2×#5051semidirect
497. C2#10590518direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8972
C2×#638562
C22×#37182
C22×D3×C3⋊C82
C2×#636342
C2×C3×#8102
C2×#635662
#105905182
C2×#50513
C2×#48133