Finite Group Databasebeta

← #11864119

Subgroups — #11864119

Order 1152.

2418 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64158C211yesmaximal, characteristic, complemented
3C2×#64117C211yesmaximal, characteristic, complemented
4C2×#64104C211yesmaximal, characteristic, complemented
5C32×#417C211yesmaximal, characteristic, complemented
6#10592825C211yesmaximal, characteristic, complemented
7#10592665C211yesmaximal, characteristic, complemented
8#10592509C212yesmaximal, complemented
9#10592505C212yesmaximal, complemented
10#10592480C212yesmaximal, complemented
11#10592472C212yesmaximal, complemented
12#78884—34nomaximal
13C2×C32×#41C2211yescharacteristic
14#41×C3⋊D3—24no—
15#41×C3⋊D3—24no—
16C2×#3832C2211yescharacteristic, complemented
17C2×Q8×C3⋊D3C2211yescharacteristic, complemented
18C2×#3830—21no—
19C2×#3830C2211yescharacteristic, complemented
20C2×D4×C3⋊D3—21no—
21C2×D4×C3⋊D3C2211yescharacteristic, complemented
22C2×#3828—21no—
23C2×#3828C2211yescharacteristic
24C22×C4⋊(C3⋊D3)—21no—
25C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
26C22×C4×C3⋊D3—21no—
27C22×C4×C3⋊D3C2211yescharacteristic
28C2×C32×M16C2211yescharacteristic, complemented
29C2×C32×C4⋊C4C2211yescharacteristic, complemented
30#64158—24no—
31C2×#3755C2212yescomplemented
32C2×#3753C2212yescomplemented
33C2×#3752—21no—
34C2×#3748C2211yescharacteristic, complemented
35#64117—24no—
36C2×#3745C2212yescomplemented
37C2×#3744C2212yescomplemented
38#64104—21no—
39#64104—21no—
40#64104C2212yes—
41#64104C2212yescomplemented
42C32×#103C2212yescomplemented
43C32×#102C2212yescomplemented
44#63647C2212yescomplemented
45#63647C2212yescomplemented
46#63637C2212yescomplemented
47#63636C2212yescomplemented
48C2×D3×#41—34no—
49C2×#949—34no—
50C2×#908—34no—
51C2×#895—34no—
52C3×#417D314yescomplemented
53#5126—34no—
54#4966—34no—
55#4810—38no—
56#4806—38no—
57#4781—38no—
58#4773—38no—
59C23×C3⋊D3—21no—
60C23×C3⋊D3—21no—
61C23×C3⋊D3D411yescharacteristic
62C32×#41—22no—
63C32×#41D414yescomplemented
64C2×C32×Q8C2311yescharacteristic
65C2×C32×D4—21no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—21no—
71C2×#638—21no—
72C2×#638—21no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3D411yescharacteristic
75#3832—22no—
76#3832—22no—
77Q8×C3⋊D3—22no—
78Q8×C3⋊D3—22no—
79#3830—28no—
80#3830—22no—
81#3830—22no—
82D4×C3⋊D3—28no—
83D4×C3⋊D3—22no—
84D4×C3⋊D3—22no—
85#3828—28no—
86#3828—22no—
87#3828D414yescomplemented
88C2×C4⋊(C3⋊D3)—21no—
89C2×C4⋊(C3⋊D3)—22no—
90C2×C4⋊(C3⋊D3)—22no—
91C2×C4⋊(C3⋊D3)—22no—
92C2×C4⋊(C3⋊D3)—22no—
93C2×C4⋊(C3⋊D3)—21no—
94C2×C4⋊(C3⋊D3)—44no—
95C2×C4⋊(C3⋊D3)C2312yes—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—28no—
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3—21no—
100C2×C4×C3⋊D3—22no—
101C2×C4×C3⋊D3—22no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3D411yescharacteristic
104C2×C4×C3⋊D3D411yescharacteristic
105C2×C4×C3⋊D3C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×#634—21no—
108C2×#634C2311yescharacteristic
109C32×M16—22no—
110C2×C32×C8C2312yes—
111C32×C4⋊C4—21no—
112C32×C4⋊C4C2312yes—
113#3755—24no—
114#3753—24no—
115#3752—22no—
116#3752—22no—
117#3748—22no—
118C2×C3⋊(C3⋊C8)C2312yes—
119#3745—24no—
120#3744—24no—
121#3006—91noSylow
122C2×C3×#41C2×D314yes—
123D3×#41—616no—
124D3×#41—616no—
125C2×#239—34no—
126C2×D3×Q8—34no—
127C2×#237—34no—
128C2×#237—64no—
129C2×D3×D4—34no—
130C2×D3×D4—64no—
131C2×#235—34no—
132C2×#235—64no—
133C22×D12—34no—
134C22×D12—64no—
135C22×C4×D3—34no—
136C22×C4×D3—64no—
137C2×C3×M16C2×D314yescomplemented
138C2×C3×C4⋊C4C2×D314yescomplemented
139#949—616no—
140C2×#215—38no—
141C2×#213—38no—
142C2×(C2×D3)⋊C4—64no—
143C2×#208—34no—
144#908—616no—
145C2×D24—38no—
146C2×#204—38no—
147#895—38no—
148#895—38no—
149#895—64no—
150#895—64no—
151C3×#103C2×D318yescomplemented
152C3×#102C2×D318yescomplemented
153(C2×D3)⋊C8—38no—
154(C2×D3)⋊C8—38no—
155#810—38no—
156#809—38no—
157C23×C32—21no—
158C23×C32C2×D411yescharacteristic
159C22×C3⋊D3—24no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—41no—
165C22×C3⋊D3—42no—
166C22×C3⋊D3—42no—
167C22×C3⋊D3—42no—
168C22×C3⋊D3—42no—
169C22×C3⋊D3—42no—
170C22×C3⋊D3C2×D411yescharacteristic
171C22×C3⋊D3C2×D411yescharacteristic
172C32×Q8—21no—
173C32×Q8C2×D412yescomplemented
174C32×D4—24no—
175C32×D4—21no—
176C32×D4C2×D412yescomplemented
177C2×C32×C4—21no—
178C2×C32×C4—24no—
179C2×C32×C4—22no—
180C2×C32×C4—42no—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2411yescharacteristic
185#638—24no—
186#638—24no—
187#638—24no—
188C2×C3⋊Dic3—24no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—24no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—22no—
196C4⋊(C3⋊D3)—22no—
197C4⋊(C3⋊D3)—44no—
198C4⋊(C3⋊D3)—44no—
199C4⋊(C3⋊D3)—42no—
200C4⋊(C3⋊D3)C2×D412yescomplemented
201C4×C3⋊D3—24no—
202C4×C3⋊D3—24no—
203C4×C3⋊D3—22no—
204C4×C3⋊D3—24no—
205C4×C3⋊D3—22no—
206C4×C3⋊D3—21no—
207C4×C3⋊D3—21no—
208C4×C3⋊D3—21no—
209C4×C3⋊D3—21no—
210#634—24no—
211#634—21no—
212#634C2×D412yescomplemented
213C32×C8—22no—
214C3⋊(C3⋊C8)—22no—
215C22×#41—91no—
216C2×AGL(1,ℤ/8)—91no—
217C2×AGL(1,ℤ/8)—91no—
218C2×#121—91no—
219#449—92no—
220#449—92no—
221#448—92no—
222#447—92no—
223#417—91no—
224#417C3⋊D311yescharacteristic, complemented
225#407—91no—
226C23×D3—34no—
227C23×D3—64no—
228C23×D3—64no—
229C3×#41—28no—
230C3×#41D12116yescomplemented
231C2×C3×Q8C22×D314yes—
232C2×C3×D4—24no—
233C2×C3×D4C22×D314yes—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4C22×D314yes—
237C2×#67—64no—
238C2×#67—64no—
239C2×#67—64no—
240C22×Dic3—34no—
241C22×Dic3—64no—
242#239—68no—
243#239—68no—
244D3×Q8—68no—
245D3×Q8—68no—
246#237—68no—
247#237—632no—
248#237—68no—
249D3×D4—68no—
250D3×D4—632no—
251D3×D4—68no—
252#235—316no—
253#235—632no—
254#235—68no—
255C2×D12—34no—
256C2×D12—38no—
257C2×D12—64no—
258C2×D12—68no—
259C2×D12—68no—
260C2×D12—68no—
261C2×D12—68no—
262C2×D12—64no—
263C2×D12—1216no—
264C2×C4×D3—34no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—34no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—632no—
271C2×C4×D3—68no—
272C2×C4×D3—68no—
273C2×C4×D3—64no—
274C2×Dic6—34no—
275C2×Dic6—64no—
276C3×M16—28no—
277C2×C3×C8C22×D318yes—
278C3×C4⋊C4—24no—
279C3×C4⋊C4C22×D318yes—
280#215—616no—
281#213—616no—
282(C2×D3)⋊C4—68no—
283(C2×D3)⋊C4—68no—
284#208—68no—
285C2×C3⋊C8—38no—
286D24—616no—
287#204—616no—
288C22×C32—21no—
289C22×C32—21no—
290C22×C32—22no—
291C22×C32—41no—
292C22×C32—41no—
293C22×C32#12012yes—
294C22×C32C22×D411yescharacteristic
295C2×C3⋊D3—21no—
296C2×C3⋊D3—21no—
297C2×C3⋊D3—21no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3—21no—
300C2×C3⋊D3—21no—
301C2×C3⋊D3—44no—
302C2×C3⋊D3—48no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—84no—
309C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
310C32×C4—22no—
311C32×C4—42no—
312C32×C4#12012yes—
313C32×C4C22×D411yescharacteristic
314C32×C4C22×D411yescharacteristic
315C3⋊Dic3—21no—
316C3⋊Dic3—22no—
317C3⋊Dic3—21no—
318C2×#41—91no—
319C2×#41—91no—
320C2×#41—91no—
321C2×#41—181no—
322C2×#41—181no—
323C2×#41—184no—
324C2×#41—184no—
325C2×#41C2×C3⋊D311yescharacteristic
326C22×Q8—91no—
327C22×D4—91no—
328C22×D4—91no—
329C22×D4—181no—
330C22×D4—181no—
331C23×C4—91no—
332C23×C4—181no—
333AGL(1,ℤ/8)—184no—
334AGL(1,ℤ/8)—184no—
335C2×SD16—92no—
336C2×SD16—92no—
337C2×D8—92no—
338C2×D8—92no—
339C2×M16—91no—
340C2×M16C2×C3⋊D311yescharacteristic, complemented
341#121—92no—
342#121—92no—
343#121—181no—
344#121—181no—
345C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
346C2×C22⋊C4—181no—
347#103—92no—
348#103C2×C3⋊D312yescomplemented
349#102—92no—
350#102C2×C3⋊D312yescomplemented
351C22⋊C8—92no—
352C22⋊C8—92no—
353C23×C3—24no—
354C23×C3D3×D414yes—
355C22×D3—34no—
356C22×D3—34no—
357C22×D3—68no—
358C22×D3—616no—
359C22×D3—68no—
360C22×D3—64no—
361C22×D3—68no—
362C22×D3—128no—
363C22×D3—124no—
364C22×D3—128no—
365C22×D3—128no—
366C22×D3—128no—
367C22×D3—128no—
368C3×Q8—24no—
369C3×Q8C2×D1218yescomplemented
370C3×D4—216no—
371C3×D4—24no—
372C3×D4C2×D1218yescomplemented
373C2×C3×C4—24no—
374C2×C3×C4—216no—
375C2×C3×C4—28no—
376C2×C3×C4—48no—
377C2×C3×C4C2×D1218yes—
378C2×C3×C4D3×D414yes—
379C2×C3×C4D3×D418yes—
380C2×C3×C4C23×D314yes—
381#67—616no—
382#67—616no—
383#67—616no—
384C2×Dic3—34no—
385C2×Dic3—34no—
386C2×Dic3—616no—
387C2×Dic3—68no—
388C2×Dic3—64no—
389D12—38no—
390D12—616no—
391D12—64no—
392D12—68no—
393D12—68no—
394D12—1216no—
395D12—1216no—
396D12—128no—
397C4×D3—616no—
398C4×D3—616no—
399C4×D3—68no—
400C4×D3—68no—
401C4×D3—616no—
402C4×D3—64no—
403C4×D3—64no—
404C4×D3—64no—
405C4×D3—64no—
406Dic6—38no—
407Dic6—616no—
408Dic6—64no—
409C3×C8—28no—
410C3⋊C8—68no—
411C2×C32—22no—
412C2×C32—42no—
413C2×C32C2×#12011yescharacteristic
414C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
415C2×C32#57511yescharacteristic
416C3⋊D3—22no—
417C3⋊D3—41no—
418C3⋊D3—42no—
419C3⋊D3—82no—
420C24—91no—
421C24—181no—
422C24—181no—
423#41—22no—
424#41—94no—
425#41—188no—
426#41—182no—
427#41—188no—
428#41—182no—
429#41—182no—
430#41—182no—
431#41—182no—
432#41C4⋊(C3⋊D3)14yescomplemented
433C2×Q8—91no—
434C2×Q8—181no—
435C2×Q8—182no—
436C2×Q8—182no—
437C2×Q8C22×C3⋊D311yescharacteristic
438C2×D4—21no—
439C2×D4—91no—
440C2×D4—92no—
441C2×D4—181no—
442C2×D4—182no—
443C2×D4—182no—
444C2×D4—181no—
445C2×D4—182no—
446C2×D4—188no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—181no—
453C2×D4—364no—
454C2×D4C22×C3⋊D311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—181no—
463C22×C4—181no—
464C22×C4—188no—
465C22×C4—181no—
466C22×C4—182no—
467C22×C4—182no—
468C22×C4—181no—
469C22×C4C22×C3⋊D311yescharacteristic
470SD16—184no—
471SD16—184no—
472D8—184no—
473D8—184no—
474M16—22no—
475M16—182no—
476C2×C8—92no—
477C2×C8C22×C3⋊D312yes—
478C4⋊C4—21no—
479C4⋊C4C22×C3⋊D312yes—
480C22⋊C4—182no—
481C22⋊C4—182no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—28no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3#88218yes—
488C22×C3C2×D3×D414yes—
489C2×D3—38no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—68no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—64no—
496C2×D3—1216no—
497C2×D3—1232no—
498C2×D3—124no—
499C2×D3—124no—
500C2×D3—128no—
501C2×D3—128no—
502C2×D3—128no—
503C2×D3—2416no—
504C3×C4—28no—
505C3×C4—48no—
506C3×C4#88218yes—
507C3×C4C22×D1214yes—
508C3×C4C2×D3×D414yes—
509Dic3—68no—
510Dic3—64no—
511Dic3—64no—
512C32#300611yescharacteristic, complemented, Sylow
513C23—21no—
514C23—91no—
515C23—91no—
516C23—182no—
517C23—184no—
518C23—182no—
519C23—181no—
520C23—182no—
521C23—361no—
522C23—362no—
523C23—362no—
524C23—362no—
525C23—362no—
526C23—362no—
527C23D4×C3⋊D311yescharacteristic
528Q8—21no—
529Q8—92no—
530Q8—184no—
531Q8—181no—
532Q8C2×C4⋊(C3⋊D3)12yescomplemented
533D4—24no—
534D4—21no—
535D4—92no—
536D4—184no—
537D4—184no—
538D4—184no—
539D4—184no—
540D4—181no—
541D4—182no—
542D4—182no—
543D4—364no—
544D4—364no—
545D4—362no—
546D4C2×C4⋊(C3⋊D3)12yescomplemented
547C2×C4—21no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—42no—
551C2×C4—91no—
552C2×C4—91no—
553C2×C4—184no—
554C2×C4—184no—
555C2×C4—184no—
556C2×C4—182no—
557C2×C4—181no—
558C2×C4—182no—
559C2×C4—182no—
560C2×C4—184no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4C2×C4⋊(C3⋊D3)12yes—
566C2×C4D4×C3⋊D311yescharacteristic
567C2×C4D4×C3⋊D312yes—
568C2×C4C23×C3⋊D311yescharacteristic
569C8—22no—
570C8—182no—
571C2×C3—28no—
572C2×C3—48no—
573C2×C3C2×#88214yes—
574C2×C3D3×AGL(1,ℤ/8)14yes—
575C2×C3#577714yes—
576D3—68no—
577D3—124no—
578D3—128no—
579D3—248no—
580C22—21no—
581C22—21no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—92no—
586C22—181no—
587C22—181no—
588C22—182no—
589C22—181no—
590C22—181no—
591C22—181no—
592C22—364no—
593C22—368no—
594C22—361no—
595C22—361no—
596C22—362no—
597C22—362no—
598C22—362no—
599C22—724no—
600C22#6409112yes—
601C22C2×D4×C3⋊D311yescharacteristic
602C4—22no—
603C4—42no—
604C4—181no—
605C4—181no—
606C4—182no—
607C4#6409112yes—
608C4C22×C4⋊(C3⋊D3)11yescharacteristic
609C4C2×D4×C3⋊D311yescharacteristic
610C3#7888414yescomplemented
611C2—22no—
612C2—42no—
613C2—182no—
614C2—361no—
615C2—362no—
616C2—722no—
617C2C2×#6409111yescharacteristic
618C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
619C2#1059624811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#417C2
socleC22×C32C22×D4
hypercenter#417C3⋊D3
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. C2×#41×C3⋊D3C2semidirect
2. C2×#64158C2semidirect
3. C2×#64117C2semidirect
4. C2×#64104C2semidirect
5. C32×#417C2semidirect
6. #10592825C2semidirect
7. #10592665C2semidirect
8. #10592509C2semidirect
9. #10592505C2semidirect
10. #10592480C2semidirect
11. #10592472C2semidirect
16. C2×#3832C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
19. C2×#3830C22semidirect
21. C2×D4×C3⋊D3C22semidirect
25. C22×C4⋊(C3⋊D3)C22semidirect
28. C2×C32×M16C22semidirect
29. C2×C32×C4⋊C4C22semidirect
31. C2×#3755C22semidirect
32. C2×#3753C22semidirect
34. C2×#3748C22semidirect
36. C2×#3745C22semidirect
37. C2×#3744C22semidirect
41. #64104C22semidirect
42. C32×#103C22semidirect
43. C32×#102C22semidirect
44. #63647C22semidirect
45. #63647C22semidirect
46. #63637C22semidirect
47. #63636C22semidirect
52. C3×#417D3semidirect
63. C32×#41D4semidirect
87. #3828D4semidirect
137. C2×C3×M16C2×D3semidirect
138. C2×C3×C4⋊C4C2×D3semidirect
151. C3×#103C2×D3semidirect
152. C3×#102C2×D3semidirect
173. C32×Q8C2×D4semidirect
176. C32×D4C2×D4semidirect
200. C4⋊(C3⋊D3)C2×D4semidirect
212. #634C2×D4semidirect
224. #417C3⋊D3semidirect
230. C3×#41D12semidirect
309. C2×C3⋊D3AGL(1,ℤ/8)semidirect
340. C2×M16C2×C3⋊D3semidirect
345. C2×C4⋊C4C2×C3⋊D3semidirect
348. #103C2×C3⋊D3semidirect
350. #102C2×C3⋊D3semidirect
369. C3×Q8C2×D12semidirect
372. C3×D4C2×D12semidirect
432. #41C4⋊(C3⋊D3)semidirect
512. C32#3006semidirect
532. Q8C2×C4⋊(C3⋊D3)semidirect
546. D4C2×C4⋊(C3⋊D3)semidirect
610. C3#78884semidirect

Maximal subgroups

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

subgroupindex
C2×#41×C3⋊D32
C2×#641582
C2×#641172
C2×#641042
C32×#4172
#105928252
#105926652
#105925092
#105925052
#105924802
#105924722
#788843