Finite Group Databasebeta

← C2×#10591434 #11865542

Subgroups — C2×#10591434 #11865542

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64145C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591434C218yesmaximal, direct product factor
7C2×#63572C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#5153—31nomaximal
10C2×#4787—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×D3×Dic3—21no—
15C2×#3757—21no—
16C2×#3757—21no—
17#64145—22no—
18#64145C2214yescomplemented
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#213—24no—
21C2×C3×#213C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63898—22no—
27#63898C2214yescomplemented
28C2×#3716—24no—
29C2×#3716C2214yescomplemented
30C3×#832C2214yescomplemented
31#63572C2214yescomplemented
32#63567C2214yescomplemented
33C22×C3×D8—31no—
34C2×#936—31no—
35C2×#936—31no—
36C2×#936—61no—
37C2×D4×Dic3—31no—
38C22×#214—31no—
39C22×#213D311yescharacteristic
40C22×#204—31no—
41C2×#893—31no—
42C2×C3×#102—31no—
43C2×#832D311yescharacteristic, complemented
44#5153—38no—
45C2×#816—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—31no—
48C2×#810—31no—
49#4787—38no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C22×C3⋊Dic3D411yescharacteristic
59C22×C3⋊Dic3D411yescharacteristic
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12D414yes—
68C2×C3×D12C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71#3757—24no—
72#3757—24no—
73C4×C3⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C3×#213—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3716—28no—
84C2×#463—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C23×Dic3—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—61no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×D8—34no—
96C2×C3×D8—64no—
97C22×C3×C8—31no—
98C22×C3×C8—31no—
99C2×C3×C4⋊C4—31no—
100C2×#217—61no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#217—62no—
106C2×#217—62no—
107#936—34no—
108#936—34no—
109#936—64no—
110#936—62no—
111#936—62no—
112#936—64no—
113D4×Dic3—34no—
114D4×Dic3—62no—
115C2×#214—34no—
116C2×#214—64no—
117C2×#213—24no—
118C2×#213C2×D314yes—
119C2×(C2×D3)⋊C4—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C22×C3⋊C8C2×D311yescharacteristic
126C2×#204—34no—
127C2×#204—64no—
128#893—34no—
129#893—62no—
130C3×#102—34no—
131#832C2×D314yescomplemented
132#816—34no—
133Dic3⋊C8—34no—
134Dic3⋊C8—34no—
135#810—34no—
136C23×C32—22no—
137C23×C32—42no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—24no—
142C22×C3×D3—22no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C32×D4—22no—
146C32×D4—22no—
147C32×D4—42no—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—42no—
156C2×C3⋊Dic3C2×D412yes—
157C2×C3⋊Dic3C2×D412yes—
158#634—22no—
159#634—22no—
160#634—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12C2×D414yes—
166D3×Dic3—48no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C22×SD16—91no—
170C22×D8—31no—
171C2×#124—91no—
172C2×C4×D4—91no—
173#463—98no—
174C2×C4⋊C8—91no—
175C2×#103—91no—
176C2×#102—31no—
177C24×C3—22no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—34no—
191C2×C3×D4—32no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C2×C3×D4C22×D312yes—
197C2×C3×D4C22×D312yes—
198C22×C3×C4—21no—
199C22×C3×C4—61no—
200C22×C3×C4C22×D311yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—31no—
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—31no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—64no—
210C22×Dic3—62no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—124no—
214C2×D12—21no—
215C2×D12—22no—
216C2×D12#6714yes—
217C2×D12C22×D312yes—
218C2×C4×D3—64no—
219C2×C4×D3—124no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—122no—
231C2×Dic6—122no—
232C3×D8—68no—
233C2×C3×C8—32no—
234C2×C3×C8—32no—
235C2×C3×C8—62no—
236C2×C3×C8—62no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239#217—64no—
240#217—64no—
241#217—64no—
242#217—64no—
243#217—64no—
244#217—68no—
245#217—68no—
246#214—68no—
247#213—28no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3—21no—
250C4⋊Dic3C22×D312yes—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261#204—68no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32—42no—
265C22×C32—84no—
266C22×C32#12112yes—
267C22×C32#13512yes—
268C22×C32AGL(1,ℤ/8)12yes—
269C22×C32C22×D411yescharacteristic
270C2×C3×D3—24no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—48no—
274C32×C4#12112yes—
275C32×C4C22×D411yescharacteristic
276C32×C4C2×#4111yescharacteristic
277C3⋊Dic3—22no—
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C22×Q8—91no—
282C22×D4—31no—
283C22×D4D3211yescharacteristic
284C23×C4—181no—
285C2×SD16—94no—
286C2×SD16—184no—
287C2×D8—34no—
288C2×D8—64no—
289C22×C8—31no—
290C22×C8—31no—
291#124—94no—
292#124—182no—
293C4×D4—94no—
294C4×D4—182no—
295C2×C4⋊C4—31no—
296C2×C22⋊C4—181no—
297C2×C22⋊C4—181no—
298C2×C22⋊C4—181no—
299C2×C42—91no—
300C4⋊C8—94no—
301#103—94no—
302#102—34no—
303C23×C3—24no—
304C23×C3—22no—
305C23×C3—22no—
306C23×C3—21no—
307C23×C3—44no—
308C23×C3—44no—
309C23×C3—44no—
310C23×C3—42no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—42no—
316C23×C3—64no—
317C23×C3—62no—
318C23×C3—122no—
319C23×C3—122no—
320C23×C3D3×D411yescharacteristic
321C23×C3D3×D411yescharacteristic
322C22×D3—24no—
323C22×D3—22no—
324C22×D3—42no—
325C22×D3—42no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—22no—
330C3×D4—34no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—44no—
334C3×D4—42no—
335C3×D4—42no—
336C3×D4—64no—
337C3×D4—62no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—62no—
343C2×C3×C4—122no—
344C2×C3×C4#23512yes—
345C2×C3×C4D3×D412yes—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23712yes—
349C2×C3×C4C2×#6712yes—
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—32no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—42no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—64no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—128no—
370C2×Dic3—124no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373D12—24no—
374D12—22no—
375D12C2×#6714yes—
376C4×D3—128no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—124no—
384Dic6—122no—
385Dic6—122no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32—82no—
391C2×C32#46314yescomplemented
392C2×C32C2×#12111yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C3×D3—44no—
396C24—21no—
397C24—61no—
398C2×Q8—92no—
399C2×Q8—181no—
400C2×Q8—182no—
401C2×Q8—182no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—21no—
405C2×D4—32no—
406C2×D4—34no—
407C2×D4—62no—
408C2×D4—61no—
409C2×D4C2×D3212yes—
410C22×C4—61no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—184no—
414C22×C4—181no—
415C22×C4—364no—
416C22×C4C2×D3211yescharacteristic
417SD16—188no—
418D8—68no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—62no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C22⋊C4—184no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C42—92no—
429C42—92no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—64no—
444C22×C3—88no—
445C22×C3—84no—
446C22×C3—84no—
447C22×C3—122no—
448C22×C3—122no—
449C22×C3—128no—
450C22×C3#88412yes—
451C22×C3#91112yes—
452C22×C3#91112yes—
453C22×C3#91212yes—
454C22×C3#91612yes—
455C22×C3#93912yes—
456C22×C3C2×D3×D411yescharacteristic
457C22×C3C2×D3×D411yescharacteristic
458C2×D3—24no—
459C2×D3—48no—
460C2×D3—42no—
461C2×D3—42no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—122no—
466C3×C4#88412yes—
467C3×C4#93912yes—
468C3×C4C2×#23511yescharacteristic
469C3×C4C2×D3×D411yescharacteristic
470C3×C4C2×#23711yescharacteristic
471C3×C4C22×#6711yescharacteristic
472Dic3—42no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—122no—
478Dic3—122no—
479Dic3—124no—
480Dic3—122no—
481Dic3—122no—
482C32C2×#46311yescharacteristic, complemented, Sylow
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—62no—
488C23—64no—
489C23—122no—
490C23—122no—
491C23#381111yescharacteristic
492Q8—182no—
493Q8—182no—
494Q8—362no—
495D4—22no—
496D4—22no—
497D4—34no—
498D4—42no—
499D4—62no—
500D4—64no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—92no—
504C2×C4—122no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—368no—
509C2×C4—362no—
510C2×C4#380412yes—
511C2×C4D3×#6712yes—
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—62no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—24no—
520C2×C3—84no—
521C2×C3—82no—
522C2×C3—82no—
523C2×C3—124no—
524C2×C3#478714yescomplemented
525C2×C3#515314yescomplemented
526C2×C3C2×#88411yescharacteristic
527C2×C3C2×#91111yescharacteristic
528C2×C3C2×#91111yescharacteristic
529C2×C3C2×#91211yescharacteristic
530C2×C3C2×#91611yescharacteristic
531C2×C3C2×#93911yescharacteristic
532D3—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—64no—
537C22—84no—
538C22—122no—
539C22—122no—
540C22—128no—
541C22#6392712yes—
542C22#6393612yes—
543C22#6397112yes—
544C22C2×#381111yescharacteristic
545C4—122no—
546C4—182no—
547C4—182no—
548C4—362no—
549C4#6397112yes—
550C4C2×#380411yescharacteristic
551C4C2×D3×#6711yescharacteristic
552C3—21no—
553C3C2×#478711yescharacteristic, complemented
554C3C2×#515311yescharacteristic, complemented
555C2—82no—
556C2—124no—
557C2#1059143414yesdirect product factor
558C2C2×#6392711yescharacteristic
559C2C2×#6393611yescharacteristic
560C2C2×#6397111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
hypercenterC22×D4D32
hypocenterC32C2×#463
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
1. C2×#64145C2semidirect
3. C2×#63898C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#832C2semidirect
6. #10591434C2direct (N × H)
7. C2×#63572C2semidirect
8. C2×#63567C2semidirect
18. #64145C22semidirect
27. #63898C22semidirect
29. C2×#3716C22semidirect
30. C3×#832C22semidirect
31. #63572C22semidirect
32. #63567C22semidirect
43. C2×#832D3semidirect
131. #832C2×D3semidirect
391. C2×C32#463semidirect
482. C32C2×#463semidirect
524. C2×C3#4787semidirect
525. C2×C3#5153semidirect
553. C3C2×#4787semidirect
554. C3C2×#5153semidirect
557. C2#10591434direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641452
C22×C3×#2132
C2×#638982
C22×#37162
C2×C3×#8322
#105914342
C2×#635722
C2×#635672
C2×#51533
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