Finite Group Databasebeta

← C2×#10591178 #11866921

Subgroups — C2×#10591178 #11866921

Order 1152.

1301 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5#10591178C218yesmaximal, direct product factor
6C2×#63575C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5134—31nomaximal
10C2×#5049—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15#64139—22no—
16#64139C2214yes—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×#217—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C3×#924—22no—
22C3×#924C2214yescomplemented
23C2×C3×Dic3⋊C4—21no—
24C2×C3×#208—24no—
25C2×C3×#208C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30#63575C2214yescomplemented
31#63566C2214yescomplemented
32#63564C2214yescomplemented
33C22×C3×M16—31no—
34C2×C3×C22⋊Q8—31no—
35C22×#215—31no—
36C2×#930—31no—
37C2×#930—31no—
38C2×#930—61no—
39C2×#924D311yescharacteristic, complemented
40C22×#208D311yescharacteristic, complemented
41C22×#204—31no—
42C2×#835—31no—
43#5134—38no—
44C2×#821—31no—
45C2×#818—31no—
46C2×#816—31no—
47#5049—38no—
48C2×#809—31no—
49C2×#807—31no—
50C24×C32D411yescharacteristic
51C23×C3⋊D3—21no—
52C22×C32×C4—22no—
53C22×C32×C4—22no—
54C22×C32×C4D411yescharacteristic
55C22×C32×C4D412yes—
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C2×#638—24no—
59C2×#638—44no—
60C22×C3⋊Dic3—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—22no—
63C2×C4⋊(C3⋊D3)—21no—
64C2×C4⋊(C3⋊D3)C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71#3752—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C3×#217—24no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—24no—
78C3×#208—28no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8D414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82C2×C3×C3⋊C8C2312yes—
83#3717—28no—
84C2×#468—91noSylow
85C22×C3×Q8—31no—
86C23×C3×C4—21no—
87C23×C3×C4C2×D311yescharacteristic
88C23×C3×C4C2×D311yescharacteristic
89C22×#67—62no—
90C22×#67—61no—
91C22×#67—61no—
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×Dic6C2×D311yescharacteristic
96C2×C3×M16—34no—
97C2×C3×M16—64no—
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C3×C22⋊Q8—34no—
101C3×C22⋊Q8—62no—
102C2×C3×C4⋊C4—31no—
103C2×C3×C4⋊C4—61no—
104C2×C3×C22⋊C4—61no—
105C2×#217—21no—
106C2×#215—34no—
107C2×#215—64no—
108#930—34no—
109#930—34no—
110#930—64no—
111#930—64no—
112#930—62no—
113#930—62no—
114C2×(C2×D3)⋊C4—62no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—61no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121#924—22no—
122#924C2×D314yescomplemented
123C2×Dic3⋊C4—21no—
124C2×#208—24no—
125C2×#208C2×D314yescomplemented
126C22×C3⋊C8C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128C2×#204—34no—
129C2×#204—64no—
130#835—34no—
131#821—34no—
132#818—34no—
133#816—34no—
134#809—34no—
135#807—34no—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32—22no—
139C23×C32C2×D412yes—
140C23×C32C2×D411yescharacteristic
141C22×C3⋊D3—22no—
142C22×C3⋊D3—42no—
143C22×C3⋊D3—42no—
144C22×C3⋊D3—42no—
145C2×C32×C4—22no—
146C2×C32×C4—24no—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154#638—48no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—22no—
159C4⋊(C3⋊D3)—42no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C2×C3×Dic3—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D414yescomplemented
169C22×SD16—91no—
170C22×M16—31no—
171C2×C22⋊Q8—31no—
172C2×#121—91no—
173#468—98no—
174C2×#107—91no—
175C2×#103—91no—
176C2×#102—91no—
177C24×C3—21no—
178C24×C3D1211yescharacteristic
179C24×C3#6711yescharacteristic
180C23×D3—62no—
181C23×D3—61no—
182C23×D3—61no—
183C2×C3×Q8—32no—
184C2×C3×Q8—61no—
185C2×C3×Q8—62no—
186C2×C3×Q8—62no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—22no—
195C22×C3×C4—42no—
196C22×C3×C4—42no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4D1211yescharacteristic
200C22×C3×C4D1212yes—
201C22×C3×C4#6711yescharacteristic
202C22×C3×C4#6712yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C2×#67—68no—
208C2×#67—64no—
209C2×#67—64no—
210C2×#67—128no—
211C2×#67—124no—
212C2×#67—124no—
213C22×Dic3—21no—
214C22×Dic3—21no—
215C22×Dic3—62no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C2×D12—32no—
219C2×D12—32no—
220C2×D12—62no—
221C2×D12—62no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—61no—
228C2×D12—122no—
229C2×D12—122no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—21no—
233C2×Dic6C22×D312yes—
234C3×M16—68no—
235C2×C3×C8—34no—
236C2×C3×C8—32no—
237C2×C3×C8—32no—
238C2×C3×C8—62no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—64no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—64no—
243#217—24no—
244#215—68no—
245(C2×D3)⋊C4—68no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—21no—
249C4⋊Dic3—32no—
250C4⋊Dic3—32no—
251C4⋊Dic3—62no—
252C4⋊Dic3—62no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—24no—
257#208—28no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8#6714yescomplemented
260C2×C3⋊C8C22×D312yes—
261C2×C3⋊C8C22×D312yes—
262#204—68no—
263C22×C32—22no—
264C22×C32—22no—
265C22×C32—22no—
266C22×C32—44no—
267C22×C32#12112yes—
268C22×C32AGL(1,ℤ/8)12yes—
269C22×C32#13712yes—
270C22×C32C22×D411yescharacteristic
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—84no—
275C32×C4—22no—
276C32×C4#12112yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×Q8—31no—
283C22×D4—91no—
284C22×D4—181no—
285C23×C4D3211yescharacteristic
286C2×SD16—94no—
287C2×SD16—184no—
288C2×M16—34no—
289C2×M16—64no—
290C22×C8—31no—
291C22×C8—31no—
292C22⋊Q8—34no—
293C22⋊Q8—62no—
294#121—94no—
295#121—182no—
296C2×C4⋊C4—31no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—91no—
299C2×C22⋊C4—61no—
300C2×C22⋊C4—181no—
301#107—94no—
302#103—94no—
303#102—94no—
304C23×C3—24no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—22no—
312C23×C3—21no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3C2×D1212yes—
316C23×C3C2×D1211yescharacteristic
317C23×C3C2×#6712yes—
318C23×C3C2×#6711yescharacteristic
319C22×D3—64no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—124no—
323C22×D3—124no—
324C22×D3—124no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C3×Q8—62no—
332C3×Q8—62no—
333C3×Q8—122no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—24no—
337C2×C3×C4—24no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—44no—
350C2×C3×C4—42no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4—122no—
355C2×C3×C4C2×D1212yes—
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23512yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4#23712yes—
360C2×C3×C4C2×#6712yes—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6712yes—
363C2×C3×C4C23×D311yescharacteristic
364C2×C3×C4C23×D311yescharacteristic
365#67—1216no—
366#67—128no—
367#67—128no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—42no—
371C2×Dic3—42no—
372C2×Dic3—64no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—124no—
376C2×Dic3—122no—
377C2×Dic3—122no—
378D12—62no—
379D12—62no—
380D12—62no—
381D12—62no—
382D12—122no—
383D12—122no—
384D12—124no—
385D12—122no—
386D12—122no—
387Dic6—22no—
388Dic6—22no—
389Dic6—42no—
390C3×C8—34no—
391C3×C8—62no—
392C3⋊C8—22no—
393C3⋊C8C2×#6714yescomplemented
394C2×C32—42no—
395C2×C32#46814yescomplemented
396C2×C32C2×#12111yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32C2×#13711yescharacteristic
399C3⋊D3—82no—
400C24—181no—
401C24#62611yescharacteristic
402C2×Q8—32no—
403C2×Q8—61no—
404C2×Q8—62no—
405C2×Q8—62no—
406C2×D4—92no—
407C2×D4—184no—
408C2×D4—182no—
409C2×D4—181no—
410C2×D4—182no—
411C2×D4—364no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—61no—
415C22×C4—61no—
416C22×C4—181no—
417C22×C4#62612yes—
418C22×C4#62611yescharacteristic
419C22×C4C2×D3212yes—
420C22×C4C2×D3211yescharacteristic
421SD16—188no—
422M16—68no—
423C2×C8—32no—
424C2×C8—34no—
425C2×C8—32no—
426C2×C8—62no—
427C4⋊C4—32no—
428C4⋊C4—61no—
429C4⋊C4—64no—
430C4⋊C4—92no—
431C4⋊C4—181no—
432C22⋊C4—64no—
433C22⋊C4—184no—
434C22×C3—24no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—48no—
448C22×C3—44no—
449C22×C3—44no—
450C22×C3#90812yes—
451C22×C3#90912yes—
452C22×C3#93012yes—
453C22×C3#93912yes—
454C22×C3#94212yes—
455C22×C3#94912yes—
456C22×C3C22×D1211yescharacteristic
457C22×C3C22×#6711yescharacteristic
458C2×D3—124no—
459C2×D3—124no—
460C2×D3—124no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—122no—
466C2×D3—122no—
467C2×D3—248no—
468C2×D3—244no—
469C2×D3—244no—
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—42no—
476C3×C4—122no—
477C3×C4—122no—
478C3×C4#93012yes—
479C3×C4#93912yes—
480C3×C4C2×#23511yescharacteristic
481C3×C4C2×D3×D411yescharacteristic
482C3×C4C2×#23711yescharacteristic
483C3×C4C22×#6711yescharacteristic
484Dic3—42no—
485Dic3—42no—
486Dic3—124no—
487Dic3—122no—
488Dic3—122no—
489C32C2×#46811yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—182no—
494C23—362no—
495C23—362no—
496C23—362no—
497C23C2×#62612yes—
498C23C2×#62611yescharacteristic
499Q8—62no—
500Q8—62no—
501Q8—122no—
502D4—182no—
503D4—182no—
504D4—368no—
505D4—362no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—122no—
513C2×C4—122no—
514C2×C4—182no—
515C2×C4—362no—
516C2×C4#380412yes—
517C2×C4C2×#62612yes—
518C2×C4C2×#62611yescharacteristic
519C2×C4D3×#6712yes—
520C2×C4C22×D3211yescharacteristic
521C8—34no—
522C8—62no—
523C2×C3—21no—
524C2×C3—24no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—44no—
528C2×C3—42no—
529C2×C3—42no—
530C2×C3#504914yescomplemented
531C2×C3#513414yescomplemented
532C2×C3C2×#90811yescharacteristic
533C2×C3C2×#90911yescharacteristic
534C2×C3C2×#93011yescharacteristic
535C2×C3C2×#93911yescharacteristic
536C2×C3C2×#94211yescharacteristic
537C2×C3C2×#94911yescharacteristic
538D3—244no—
539D3—242no—
540D3—242no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—44no—
545C22—362no—
546C22—362no—
547C22—362no—
548C22—724no—
549C22#6382512yes—
550C22#6383312yes—
551C22#6397812yes—
552C22C22×#62611yescharacteristic
553C4—22no—
554C4—122no—
555C4—122no—
556C4—362no—
557C4#6397812yes—
558C4C2×#380411yescharacteristic
559C4C2×D3×#6711yescharacteristic
560C3—21no—
561C3C2×#504911yescharacteristic, complemented
562C3C2×#513411yescharacteristic, complemented
563C2—42no—
564C2—722no—
565C2#1059117814yesdirect product factor
566C2C2×#6382511yescharacteristic
567C2C2×#6383311yescharacteristic
568C2C2×#6397811yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32C2×#468
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C22×C3×#208C2semidirect
4. C22×#3717C2semidirect
5. #10591178C2direct (N × H)
6. C2×#63575C2semidirect
7. C2×#63566C2semidirect
8. C2×#63564C2semidirect
22. C3×#924C22semidirect
25. C2×C3×#208C22semidirect
29. C2×#3717C22semidirect
30. #63575C22semidirect
31. #63566C22semidirect
32. #63564C22semidirect
39. C2×#924D3semidirect
40. C22×#208D3semidirect
80. C2×C3×C3⋊C8D4semidirect
122. #924C2×D3semidirect
125. C2×#208C2×D3semidirect
168. C3×C3⋊C8C2×D4semidirect
259. C2×C3⋊C8#67semidirect
393. C3⋊C8C2×#67semidirect
395. C2×C32#468semidirect
489. C32C2×#468semidirect
530. C2×C3#5049semidirect
531. C2×C3#5134semidirect
561. C3C2×#5049semidirect
562. C3C2×#5134semidirect
565. C2#10591178direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641392
C2×C3×#9242
C22×C3×#2082
C22×#37172
#105911782
C2×#635752
C2×#635662
C2×#635642
C2×#51343
C2×#50493