Finite Group Databasebeta

← C2×#10590813 #11865709

Subgroups — C2×#10590813 #11865709

Order 1152.

1149 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#63864C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#816C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590813C218yesmaximal, direct product factor
9C2×#4845—31nomaximal
10C2×#4798—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3744—24no—
16C2×#3744C2214yes—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3724—21no—
21C2×#3722—21no—
22C2×#3722—21no—
23C2×Dic32—21no—
24#63864—22no—
25#63864C2214yes—
26#63844—22no—
27#63844C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C3×#816C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63564C2214yes—
33C2×#947—31no—
34C22×#216—31no—
35C22×Dic12—31no—
36C22×#204—31no—
37C22×#204—31no—
38C22×#204—61no—
39C2×#887—31no—
40C2×#875—31no—
41C2×C4×Dic6—31no—
42C2×C3×C4⋊C8—31no—
43C2×C3×#103—31no—
44C2×#821—31no—
45C2×#816D311yescharacteristic, complemented
46C2×Dic3⋊C8D311yescharacteristic, complemented
47C2×#809—31no—
48#4845—38no—
49#4798—38no—
50C23×C3⋊D3—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)C2312yes—
57C2×#634—21no—
58C2×#634—22no—
59C2×#634D414yes—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×C32×C8—22no—
70C2×C32×C8C2312yes—
71#3744—28no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3D412yes—
75C3×C4×Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2312yes—
78#3724—24no—
79#3722—24no—
80#3722—24no—
81Dic32—24no—
82#3719—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×C3×C8—21no—
93C22×C3×C8—31no—
94C22×C3×C8C2×D311yescharacteristic
95C22×C3×C8C2×D311yescharacteristic
96C2×C3×C4⋊C4—31no—
97C2×C3×C42—31no—
98#947—34no—
99#947—62no—
100C2×#216—34no—
101C2×#216—64no—
102C2×(C2×D3)⋊C4—61no—
103C2×(C2×D3)⋊C4—61no—
104C2×(C2×D3)⋊C4—61no—
105C2×(C2×D3)⋊C4—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×Dic3⋊C4—61no—
108C2×Dic3⋊C4—61no—
109C2×C4×Dic3—61no—
110C2×C4×Dic3—61no—
111C2×C4×Dic3C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113C2×Dic12—34no—
114C2×Dic12—64no—
115C2×#204—34no—
116C2×#204—34no—
117C2×#204—64no—
118C2×#204—64no—
119C2×#204—64no—
120C2×#204—68no—
121#887—34no—
122#887—62no—
123#875—34no—
124#875—62no—
125C4×Dic6—34no—
126C4×Dic6—62no—
127C3×C4⋊C8—34no—
128C3×#103—34no—
129#821—34no—
130#816C2×D314yescomplemented
131Dic3⋊C8C2×D314yescomplemented
132#809—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D412yes—
140C2×C32×C4#4112yes—
141C2×C32×C4C2411yescharacteristic
142C2×C3⋊Dic3—24no—
143C2×C3⋊Dic3—22no—
144C4⋊(C3⋊D3)—22no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—42no—
147#634—24no—
148#634—22no—
149#634C2×D414yes—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C2×C3×Dic3C2×D412yes—
158C3×Dic6—22no—
159C3×Dic6—22no—
160C3×Dic6—42no—
161C32×C8—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—91no—
165C2×#124—91no—
166C2×C4×Q8—91no—
167#464—98no—
168C2×C4⋊C8—31no—
169C2×#103—31no—
170C2×#102—91no—
171C23×D3—61no—
172C23×D3—61no—
173C23×D3—121no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
176C2×C3×Q8—62no—
177C2×C3×Q8—62no—
178C22×C3×C4—21no—
179C22×C3×C4—31no—
180C22×C3×C4—31no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4C22×D311yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3D1211yescharacteristic
191C22×Dic3D1211yescharacteristic
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—62no—
195C2×D12—64no—
196C2×D12—62no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—62no—
200C2×D12—61no—
201C2×D12—61no—
202C2×D12—122no—
203C2×D12—121no—
204C2×Dic6—22no—
205C2×Dic6—22no—
206C2×Dic6—21no—
207C2×Dic6—34no—
208C2×Dic6—34no—
209C2×Dic6—32no—
210C2×Dic6—32no—
211C2×Dic6—64no—
212C2×Dic6—62no—
213C2×Dic6—61no—
214C2×Dic6—62no—
215C2×Dic6—61no—
216C2×Dic6—62no—
217C2×Dic6—122no—
218C2×Dic6—121no—
219C2×Dic6C22×D312yes—
220C2×C3×C8—24no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—22no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C42—32no—
231C3×C42—32no—
232#216—68no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3C22×D312yes—
239Dic3⋊C4—64no—
240Dic3⋊C4—64no—
241C4×Dic3—64no—
242C4×Dic3—64no—
243C4×Dic3D1212yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—22no—
246C2×C3⋊C8C22×D312yes—
247Dic12—68no—
248#204—68no—
249#204—68no—
250#204—616no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32#13712yes—
254C22×C32C22×D411yescharacteristic
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—42no—
258C2×C3⋊D3—84no—
259C32×C4#12112yes—
260C32×C4C22×D411yescharacteristic
261C32×C4C2×#4111yescharacteristic
262C3⋊Dic3—24no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C22×Q8—91no—
269C22×D4—91no—
270C2×Q16—94no—
271C2×Q16—184no—
272C2×SD16—94no—
273C2×SD16—184no—
274C22×C8—31no—
275C22×C8D3211yescharacteristic
276#124—94no—
277#124—182no—
278C4×Q8—94no—
279C4×Q8—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—181no—
282C2×C22⋊C4—181no—
283C2×C22⋊C4—181no—
284C2×C42—31no—
285C2×C42—181no—
286C4⋊C8—34no—
287#103—34no—
288#102—94no—
289C23×C3—21no—
290C23×C3C2×D1211yescharacteristic
291C23×C3D3×D411yescharacteristic
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—122no—
295C22×D3—124no—
296C22×D3—122no—
297C22×D3—122no—
298C22×D3—122no—
299C22×D3—122no—
300C22×D3—122no—
301C22×D3—122no—
302C22×D3—242no—
303C22×D3—242no—
304C3×Q8—62no—
305C3×Q8—62no—
306C3×Q8—122no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—22no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—62no—
314C2×C3×C4—62no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—122no—
318C2×C3×C4—122no—
319C2×C3×C4C2×D1211yescharacteristic
320C2×C3×C4#23512yes—
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D412yes—
323C2×C3×C4D3×D412yes—
324C2×C3×C4#23912yes—
325C2×C3×C4C23×D311yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×Dic3—22no—
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—22no—
331C2×Dic3—42no—
332C2×Dic3—42no—
333C2×Dic3—64no—
334C2×Dic3—64no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—122no—
338C2×Dic3—124no—
339C2×Dic3C2×D1212yes—
340C2×Dic3C2×D1212yes—
341D12—64no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—122no—
347D12—124no—
348D12—122no—
349D12—122no—
350Dic6—22no—
351Dic6—22no—
352Dic6—34no—
353Dic6—34no—
354Dic6—42no—
355Dic6—64no—
356Dic6—64no—
357Dic6—64no—
358Dic6—62no—
359Dic6—62no—
360Dic6—122no—
361Dic6—124no—
362C3×C8—24no—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—62no—
366C3⋊C8—22no—
367C2×C32#46414yescomplemented
368C2×C32C2×#12111yescharacteristic
369C2×C32C2×#13511yescharacteristic
370C2×C32C2×#13711yescharacteristic
371C3⋊D3—82no—
372C24—181no—
373C2×Q8—32no—
374C2×Q8—61no—
375C2×Q8—62no—
376C2×Q8—62no—
377C2×Q8—92no—
378C2×Q8—94no—
379C2×Q8—182no—
380C2×Q8—181no—
381C2×D4—92no—
382C2×D4—182no—
383C2×D4—181no—
384C2×D4—182no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—181no—
390C22×C4C2×D3211yescharacteristic
391Q16—188no—
392SD16—188no—
393C2×C8—22no—
394C2×C8—32no—
395C2×C8—62no—
396C2×C8C2×D3212yes—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—184no—
400C22⋊C4—184no—
401C22⋊C4—184no—
402C42—32no—
403C42—32no—
404C42—184no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3#88412yes—
410C22×C3#89512yes—
411C22×C3#90412yes—
412C22×C3#90912yes—
413C22×C3#91612yes—
414C22×C3#91812yes—
415C22×C3C22×D1211yescharacteristic
416C22×C3C2×D3×D411yescharacteristic
417C2×D3—124no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—248no—
427C2×D3—244no—
428C2×D3—244no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—62no—
433C3×C4—62no—
434C3×C4—122no—
435C3×C4—122no—
436C3×C4#88412yes—
437C3×C4#89512yes—
438C3×C4C2×#23511yescharacteristic
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×D3×D411yescharacteristic
441C3×C4C2×#23911yescharacteristic
442Dic3—22no—
443Dic3—22no—
444Dic3—42no—
445Dic3—42no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—182no—
451C23—362no—
452C23—362no—
453C23—362no—
454C23D3×D1211yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—94no—
458Q8—122no—
459Q8—182no—
460Q8—184no—
461D4—182no—
462D4—182no—
463D4—362no—
464C2×C4—32no—
465C2×C4—32no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—122no—
471C2×C4—122no—
472C2×C4—182no—
473C2×C4—184no—
474C2×C4#379912yes—
475C2×C4D3×D1211yescharacteristic
476C2×C4#381112yes—
477C2×C4C22×D3211yescharacteristic
478C8—22no—
479C8—62no—
480C2×C3—24no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3#479814yescomplemented
485C2×C3#484514yescomplemented
486C2×C3C2×#88411yescharacteristic
487C2×C3C2×#89511yescharacteristic
488C2×C3C2×#90411yescharacteristic
489C2×C3C2×#90911yescharacteristic
490C2×C3C2×#91611yescharacteristic
491C2×C3C2×#91811yescharacteristic
492D3—244no—
493D3—242no—
494D3—242no—
495C22—362no—
496C22—362no—
497C22—362no—
498C22—724no—
499C22#6380112yes—
500C22#6380612yes—
501C22#6391012yes—
502C22C2×D3×D1211yescharacteristic
503C4—62no—
504C4—62no—
505C4—122no—
506C4—122no—
507C4—184no—
508C4#6391012yes—
509C4C2×#379911yescharacteristic
510C4C2×#381111yescharacteristic
511C3—21no—
512C3C2×#479811yescharacteristic, complemented
513C3C2×#484511yescharacteristic, complemented
514C2—722no—
515C2#1059081314yesdirect product factor
516C2C2×#6380111yescharacteristic
517C2C2×#6380611yescharacteristic
518C2C2×#6391011yescharacteristic
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×#464
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
3. C2×#63844C2semidirect
4. C22×#3719C2semidirect
5. C2×C3×#816C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
8. #10590813C2direct (N × H)
27. #63844C22semidirect
29. C2×#3719C22semidirect
30. C3×#816C22semidirect
31. C3×Dic3⋊C8C22semidirect
45. C2×#816D3semidirect
46. C2×Dic3⋊C8D3semidirect
130. #816C2×D3semidirect
131. Dic3⋊C8C2×D3semidirect
367. C2×C32#464semidirect
449. C32C2×#464semidirect
484. C2×C3#4798semidirect
485. C2×C3#4845semidirect
512. C3C2×#4798semidirect
513. C3C2×#4845semidirect
515. C2#10590813direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638642
C2×#638442
C22×#37192
C2×C3×#8162
C2×C3×Dic3⋊C82
C2×#635642
#105908132
C2×#48453
C2×#47983