Finite Group Databasebeta

← C2×#10591441 #11865697

Subgroups — C2×#10591441 #11865697

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×#3754C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic
3C2×#63844C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic
6#10591441C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5054—31nomaximal
10C2×#4767—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C2×#3754—24no—
15C2×#3754C2214yes—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—21no—
18C2×C3×#217—21no—
19C3×#936—22no—
20C3×#936C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×#3724—21no—
25C2×Dic32—21no—
26#63844—22no—
27#63844C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C3×#832C2214yes—
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63565C2214yescomplemented
33C2×C3×#124—31no—
34C22×#216—31no—
35C2×#936D311yescharacteristic
36C22×#214—31no—
37C22×#214—31no—
38C22×#214—61no—
39C22×Dic12—31no—
40C2×#887—31no—
41C2×C4×Dic6—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832D311yescharacteristic
45C2×Dic3⋊C8—31no—
46#5054—38no—
47C2×#810—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4767—38no—
50C24×C32—21no—
51C2×C32×D4—22no—
52C2×C32×D4—21no—
53C2×C32×D4—22no—
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
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—
69#3754—28no—
70C2×C3⋊(C3⋊C8)—22no—
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×#217—24no—
73C3×#217—24no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80#3724—24no—
81Dic32—24no—
82#3719—28no—
83C2×#464—91noSylow
84C22×C3×Q8—31no—
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C22×Dic6C2×D311yescharacteristic
92C22×C3×C8—31no—
93C3×#124—34no—
94C3×#124—62no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C22⋊C4—61no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—31no—
99C2×#217—21no—
100C2×#217—21no—
101C2×#216—34no—
102C2×#216—64no—
103#936—22no—
104#936C2×D314yes—
105C2×#214—34no—
106C2×#214—34no—
107C2×#214—64no—
108C2×#214—64no—
109C2×#214—64no—
110C2×#214—68no—
111C2×C4⋊Dic3C2×D311yescharacteristic
112C2×Dic3⋊C4—61no—
113C2×Dic3⋊C4—61no—
114C2×C4×Dic3—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3C2×D311yescharacteristic
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—61no—
120C22×C3⋊C8C2×D311yescharacteristic
121C2×Dic12—34no—
122C2×Dic12—64no—
123#887—34no—
124#887—62no—
125C4×Dic6—34no—
126C4×Dic6—62no—
127C3×#102—34no—
128#835—34no—
129#832C2×D314yes—
130Dic3⋊C8—34no—
131#810—34no—
132C4⋊(C3⋊C8)—34no—
133C23×C32—22no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32C2×D411yescharacteristic
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—42no—
141C2×C32×C4C2×D412yes—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4112yes—
144C2×C32×C4C2411yescharacteristic
145C2×C3⋊Dic3—24no—
146C2×C3⋊Dic3—22no—
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—
161C3⋊(C3⋊C8)—22no—
162C3×C3⋊C8—22no—
163C22×Q16—91no—
164C22×SD16—91no—
165C2×#124—31no—
166C2×C4×Q8—91no—
167#464—98no—
168C2×C4⋊C8—91no—
169C2×#103—91no—
170C2×#102—31no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—41no—
174C2×C3×Q8—32no—
175C2×C3×Q8—61no—
176C2×C3×Q8—62no—
177C2×C3×Q8—62no—
178C2×C3×D4—24no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—21no—
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—42no—
187C2×C3×D4—41no—
188C2×C3×D4C22×D312yes—
189C2×C3×D4C22×D312yes—
190C22×C3×C4—21no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C22×Dic3—121no—
202C22×Dic3#6711yescharacteristic
203C22×Dic3#6711yescharacteristic
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—62no—
214C2×Dic6—61no—
215C2×Dic6—62no—
216C2×Dic6—61no—
217C2×Dic6—122no—
218C2×Dic6—121no—
219C2×Dic6C22×D312yes—
220C2×C3×C8—32no—
221C2×C3×C8—62no—
222C3×C4⋊C4—32no—
223C3×C4⋊C4—61no—
224C3×C22⋊C4—64no—
225C3×C22⋊C4—64no—
226C3×C42—32no—
227C3×C42—32no—
228#217—24no—
229#217—24no—
230#216—68no—
231#214—68no—
232#214—68no—
233#214—616no—
234C4⋊Dic3—21no—
235C4⋊Dic3C22×D312yes—
236Dic3⋊C4—64no—
237Dic3⋊C4—64no—
238C4×Dic3—64no—
239C4×Dic3—64no—
240C4×Dic3#6712yes—
241C4×Dic3C22×D312yes—
242C2×C3⋊C8—22no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—64no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8C22×D312yes—
250Dic12—68no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—42no—
254C22×C32—84no—
255C22×C32#12112yes—
256C22×C32#13512yes—
257C22×C32#13712yes—
258C22×C32C22×D411yescharacteristic
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×D4D3211yescharacteristic
270C2×Q16—94no—
271C2×Q16—184no—
272C2×SD16—94no—
273C2×SD16—184no—
274C22×C8—31no—
275C22×C8—91no—
276#124—34no—
277#124—62no—
278C4×Q8—94no—
279C4×Q8—182no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—181no—
282C2×C22⋊C4—61no—
283C2×C22⋊C4—61no—
284C2×C42—31no—
285C2×C42—181no—
286C4⋊C8—94no—
287#103—94no—
288#102—34no—
289C23×C3—22no—
290C23×C3—22no—
291C23×C3—21no—
292C23×C3—42no—
293C23×C3—44no—
294C23×C3—42no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3—42no—
299C23×C3—42no—
300C23×C3—82no—
301C23×C3—82no—
302C23×C3D3×D411yescharacteristic
303C23×C3C2×#6711yescharacteristic
304C3×Q8—62no—
305C3×Q8—62no—
306C3×Q8—122no—
307C3×D4—24no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—22no—
312C3×D4—42no—
313C3×D4—44no—
314C3×D4—42no—
315C3×D4—42no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D412yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—42no—
341C2×Dic3—42no—
342C2×Dic3—64no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—124no—
348C2×Dic3C2×#6712yes—
349C2×Dic3C2×#6712yes—
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—62no—
363C3⋊C8—22no—
364C3⋊C8—64no—
365C3⋊C8—62no—
366C3⋊C8—62no—
367C2×C32—82no—
368C2×C32#46414yescomplemented
369C2×C32C2×#12111yescharacteristic
370C2×C32C2×#13511yescharacteristic
371C2×C32C2×#13711yescharacteristic
372C24—21no—
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—22no—
382C2×D4—21no—
383C2×D4—22no—
384C2×D4C2×D3212yes—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—61no—
388C22×C4—61no—
389C22×C4—181no—
390C22×C4C2×D3211yescharacteristic
391Q16—188no—
392SD16—188no—
393C2×C8—32no—
394C2×C8—62no—
395C2×C8—92no—
396C2×C8—182no—
397C4⋊C4—32no—
398C4⋊C4—61no—
399C4⋊C4—184no—
400C22⋊C4—64no—
401C22⋊C4—64no—
402C42—32no—
403C42—32no—
404C42—184no—
405C22×C3—21no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—22no—
409C22×C3—44no—
410C22×C3—42no—
411C22×C3—42no—
412C22×C3—42no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—82no—
417C22×C3—82no—
418C22×C3—88no—
419C22×C3—84no—
420C22×C3—84no—
421C22×C3#88412yes—
422C22×C3#91212yes—
423C22×C3#91512yes—
424C22×C3#93812yes—
425C22×C3#95012yes—
426C22×C3#95112yes—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C22×#6711yescharacteristic
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#93812yes—
438C3×C4C2×#23511yescharacteristic
439C3×C4C2×D3×D411yescharacteristic
440C3×C4C2×D3×D411yescharacteristic
441C3×C4C2×#23711yescharacteristic
442Dic3—22no—
443Dic3—22no—
444Dic3—42no—
445Dic3—42no—
446Dic3—64no—
447Dic3—64no—
448Dic3—124no—
449C32C2×#46411yescharacteristic, complemented, Sylow
450C23—22no—
451C23—42no—
452C23—42no—
453C23—42no—
454C23D3×#6711yescharacteristic
455Q8—62no—
456Q8—62no—
457Q8—94no—
458Q8—122no—
459Q8—182no—
460Q8—184no—
461D4—22no—
462D4—22no—
463D4—42no—
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#380412yes—
475C2×C4D3×#6711yescharacteristic
476C2×C4#381112yes—
477C2×C4C22×D3211yescharacteristic
478C8—62no—
479C8—182no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—24no—
484C2×C3—84no—
485C2×C3—82no—
486C2×C3—82no—
487C2×C3#476714yescomplemented
488C2×C3#505414yescomplemented
489C2×C3C2×#88411yescharacteristic
490C2×C3C2×#91211yescharacteristic
491C2×C3C2×#91511yescharacteristic
492C2×C3C2×#93811yescharacteristic
493C2×C3C2×#95011yescharacteristic
494C2×C3C2×#95111yescharacteristic
495C22—42no—
496C22—42no—
497C22—42no—
498C22—84no—
499C22#6392912yes—
500C22#6393312yes—
501C22#6395812yes—
502C22C2×D3×#6711yescharacteristic
503C4—62no—
504C4—62no—
505C4—122no—
506C4—122no—
507C4—184no—
508C4#6395812yes—
509C4C2×#380411yescharacteristic
510C4C2×#381111yescharacteristic
511C3—21no—
512C3C2×#476711yescharacteristic, complemented
513C3C2×#505411yescharacteristic, complemented
514C2—82no—
515C2#1059144114yesdirect product factor
516C2C2×#6392911yescharacteristic
517C2C2×#6393311yescharacteristic
518C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#464
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#63844C2semidirect
4. C22×#3719C2semidirect
6. #10591441C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63565C2semidirect
27. #63844C22semidirect
29. C2×#3719C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63565C22semidirect
368. C2×C32#464semidirect
449. C32C2×#464semidirect
487. C2×C3#4767semidirect
488. C2×C3#5054semidirect
512. C3C2×#4767semidirect
513. C3C2×#5054semidirect
515. C2#10591441direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×#9362
C2×#638442
C22×#37192
C2×C3×#8322
#105914412
C2×Dic3⋊(C3⋊C8)2
C2×#635652
C2×#50543
C2×#47673