Finite Group Databasebeta

← C2×#10591591 #11866702

Subgroups — C2×#10591591 #11866702

Order 1152.

1289 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×#64155C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63916C211yesmaximal, characteristic
4C22×#3710C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591591C218yesmaximal, direct product factor
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5171—31nomaximal
10C2×#4807—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#626—21no—
15#64155—22no—
16#64155C2214yescomplemented
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3750—21no—
20C2×C3×#215—24no—
21C2×C3×#215C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63916—22no—
27#63916C2214yes—
28C2×#3710—24no—
29C2×#3710C2214yescomplemented
30C3×#835C2214yescomplemented
31#63573C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#946—31no—
35C2×#946—31no—
36C2×#946—61no—
37C22×#215D311yescharacteristic, complemented
38C2×#938—31no—
39C22×D3×C8—31no—
40C22×D3×C8—31no—
41C2×#895—31no—
42C2×C3×#103—31no—
43C2×#835D311yescharacteristic, complemented
44C2×#832—31no—
45#5171—38no—
46C2×#821—31no—
47C2×#817—31no—
48C2×#808—31no—
49#4807—38no—
50C23×C3⋊D3D411yescharacteristic
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3⋊Dic3D411yescharacteristic
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×C4×C3⋊D3D412yes—
63C2×C4×C3⋊D3C2312yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×#626—24no—
70C2×#626—44no—
71#3752—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74#3750—24no—
75C3×#215—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8D414yescomplemented
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3710—28no—
84C2×#465—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×#67—61no—
90C22×D12—61no—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—61no—
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C22×C3×C8—31no—
98C22×C3×C8—31no—
99C2×C3×C4⋊C4—31no—
100C2×#217—61no—
101#946—34no—
102#946—34no—
103#946—64no—
104#946—62no—
105#946—62no—
106#946—64no—
107C2×#215—24no—
108C2×#215C2×D314yescomplemented
109#938—34no—
110#938—62no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—62no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—61no—
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×Dic3⋊C4—61no—
120C2×Dic3⋊C4—61no—
121C2×Dic3⋊C4—62no—
122C22×C3⋊C8C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124C2×D3×C8—34no—
125C2×D3×C8—34no—
126C2×D3×C8—64no—
127C2×D3×C8—64no—
128#895—34no—
129#895—62no—
130C3×#103—34no—
131#835C2×D314yescomplemented
132#832—34no—
133#821—34no—
134#817—34no—
135#808—34no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3SD1614yescomplemented
140C22×C3⋊D3C2×D412yes—
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C32×Q8—22no—
146C32×Q8—22no—
147C32×Q8—42no—
148C2×C32×C4—22no—
149C2×C32×C4—42no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D412yes—
152C2×C32×C4#4112yes—
153C2×C32×C4C2411yescharacteristic
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—42no—
157C2×C3⋊Dic3C2×D412yes—
158C4×C3⋊D3—24no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—22no—
164C3×D12—22no—
165C3×D12—42no—
166#626—48no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8C2×D414yescomplemented
169C22×SD16—31no—
170C23×C8—91no—
171C2×C22⋊Q8—91no—
172C2×#121—91no—
173#465—98no—
174C2×#106—91no—
175C2×#103—31no—
176C2×#102—91no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—31no—
180C23×D3—31no—
181C23×D3—61no—
182C2×C3×Q8—22no—
183C2×C3×Q8—21no—
184C2×C3×Q8—21no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C2×C3×Q8—22no—
190C2×C3×Q8—42no—
191C2×C3×Q8—42no—
192C2×C3×Q8C22×D312yes—
193C2×C3×Q8C22×D312yes—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—62no—
197C2×C3×D4—61no—
198C22×C3×C4—22no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—64no—
206C2×#67—124no—
207C22×Dic3—21no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—61no—
211C22×Dic3—62no—
212C22×Dic3—61no—
213C22×Dic3—61no—
214C2×D12—22no—
215C2×D12—22no—
216C2×D12—21no—
217C2×D12—64no—
218C2×D12—124no—
219C2×D12C22×D312yes—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—62no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C3×SD16—68no—
233C2×C3×C8—34no—
234C2×C3×C8—32no—
235C2×C3×C8—32no—
236C2×C3×C8—62no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239#217—64no—
240#215—28no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—68no—
245C4⋊Dic3—21no—
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3C22×D312yes—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—68no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8#6714yescomplemented
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260D3×C8—68no—
261D3×C8—68no—
262C22×C32#12112yes—
263C22×C32C2×SD1612yes—
264C22×C32#13512yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—22no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—28no—
269C2×C3⋊D3C2×SD1614yescomplemented
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—84no—
274C32×C4—42no—
275C32×C4#12112yes—
276C32×C4C22×D411yescharacteristic
277C32×C4C2×#4111yescharacteristic
278C3⋊Dic3—22no—
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C22×Q8D3211yescharacteristic
282C22×D4—31no—
283C22×D4—181no—
284C23×C4—91no—
285C2×SD16—34no—
286C2×SD16—64no—
287C22×C8—31no—
288C22×C8—31no—
289C22×C8—94no—
290C22×C8—184no—
291C22⋊Q8—94no—
292C22⋊Q8—182no—
293#121—94no—
294#121—182no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—181no—
298C2×C22⋊C4—181no—
299C2×C22⋊C4—181no—
300#106—94no—
301#103—34no—
302#102—94no—
303C23×C3—21no—
304C23×C3—62no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—22no—
311C22×D3—34no—
312C22×D3—34no—
313C22×D3—32no—
314C22×D3—32no—
315C22×D3—42no—
316C22×D3—42no—
317C22×D3—42no—
318C22×D3—64no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—122no—
325C22×D3—122no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—22no—
329C3×Q8—22no—
330C3×Q8—42no—
331C3×Q8—42no—
332C3×Q8—44no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—44no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—122no—
350C2×C3×C4#23512yes—
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4#23712yes—
355C2×C3×C4C2×#6712yes—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358#67—128no—
359C2×Dic3—22no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—42no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—64no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—122no—
370C2×Dic3—124no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373D12—22no—
374D12—22no—
375D12—42no—
376D12—128no—
377C4×D3—64no—
378C4×D3—64no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—62no—
382C4×D3—62no—
383C4×D3—122no—
384C4×D3—122no—
385C4×D3—124no—
386C3×C8—34no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8C2×#6714yescomplemented
390C2×C32#46514yescomplemented
391C2×C32C2×#12111yescharacteristic
392C2×C32C22×SD1611yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C3⋊D3—24no—
395C3×D3—82no—
396C24—61no—
397C24—91no—
398C2×Q8—21no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8C2×D3212yes—
402C2×D4—32no—
403C2×D4—62no—
404C2×D4—62no—
405C2×D4—61no—
406C2×D4—184no—
407C2×D4—364no—
408C22×C4—21no—
409C22×C4—61no—
410C22×C4—91no—
411C22×C4—92no—
412C22×C4—92no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417SD16—68no—
418C2×C8—32no—
419C2×C8—34no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—188no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C4⋊C4—92no—
426C4⋊C4—184no—
427C4⋊C4—181no—
428C22⋊C4—184no—
429C22⋊C4—184no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—122no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—244no—
438C22×C3#88412yes—
439C22×C3D3×SD1612yes—
440C22×C3D3×SD1612yes—
441C22×C3#91612yes—
442C22×C3#91912yes—
443C22×C3#93812yes—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C2×D3×D411yescharacteristic
446C2×D3—34no—
447C2×D3—34no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—64no—
452C2×D3—68no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—68no—
458C2×D3—84no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—128no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—22no—
465C3×C4—44no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4#88412yes—
470C3×C4#93812yes—
471C3×C4C2×#23511yescharacteristic
472C3×C4C2×D3×D411yescharacteristic
473C3×C4C2×#23711yescharacteristic
474C3×C4C22×#6711yescharacteristic
475Dic3—42no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—124no—
480Dic3—122no—
481Dic3—122no—
482C32C2×#46511yescharacteristic, complemented, Sylow
483C23—62no—
484C23—92no—
485C23—94no—
486C23—122no—
487C23—122no—
488C23—122no—
489C23—182no—
490C23—182no—
491C23#381111yescharacteristic
492Q8—22no—
493Q8—22no—
494Q8—42no—
495D4—62no—
496D4—62no—
497D4—122no—
498D4—368no—
499C2×C4—22no—
500C2×C4—42no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—122no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—184no—
508C2×C4—182no—
509C2×C4—362no—
510C2×C4#380412yes—
511C2×C4D3×#6712yes—
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—34no—
515C8—62no—
516C2×C3—21no—
517C2×C3—24no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—242no—
521C2×C3#480714yescomplemented
522C2×C3#517114yescomplemented
523C2×C3C2×#88411yescharacteristic
524C2×C3C2×D3×SD1611yescharacteristic
525C2×C3C2×D3×SD1611yescharacteristic
526C2×C3C2×#91611yescharacteristic
527C2×C3C2×#91911yescharacteristic
528C2×C3C2×#93811yescharacteristic
529D3—64no—
530D3—64no—
531D3—82no—
532D3—124no—
533C22—94no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—182no—
538C22—188no—
539C22—182no—
540C22—244no—
541C22#6394012yes—
542C22#6395012yes—
543C22#6395812yes—
544C22C2×#381111yescharacteristic
545C4—42no—
546C4—122no—
547C4—182no—
548C4—362no—
549C4#6395812yes—
550C4C2×#380411yescharacteristic
551C4C2×D3×#6711yescharacteristic
552C3—21no—
553C3C2×#480711yescharacteristic, complemented
554C3C2×#517111yescharacteristic, complemented
555C2—184no—
556C2—242no—
557C2#1059159114yesdirect product factor
558C2C2×#6394011yescharacteristic
559C2C2×#6395011yescharacteristic
560C2C2×#6395811yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
hypercenterC22×Q8D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C22×C3×#215C2semidirect
4. C22×#3710C2semidirect
5. C2×C3×#835C2semidirect
6. #10591591C2direct (N × H)
7. C2×#63573C2semidirect
8. C2×#63563C2semidirect
16. #64155C22semidirect
21. C2×C3×#215C22semidirect
29. C2×#3710C22semidirect
30. C3×#835C22semidirect
31. #63573C22semidirect
32. #63563C22semidirect
37. C22×#215D3semidirect
43. C2×#835D3semidirect
79. C2×C3×C3⋊C8D4semidirect
108. C2×#215C2×D3semidirect
131. #835C2×D3semidirect
139. C22×C3⋊D3SD16semidirect
168. C3×C3⋊C8C2×D4semidirect
257. C2×C3⋊C8#67semidirect
269. C2×C3⋊D3C2×SD16semidirect
389. C3⋊C8C2×#67semidirect
390. C2×C32#465semidirect
482. C32C2×#465semidirect
521. C2×C3#4807semidirect
522. C2×C3#5171semidirect
553. C3C2×#4807semidirect
554. C3C2×#5171semidirect
557. C2#10591591direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641552
C22×C3×#2152
C2×#639162
C22×#37102
C2×C3×#8352
#105915912
C2×#635732
C2×#635632
C2×#51713
C2×#48073