Finite Group Databasebeta

← #11787602

Subgroups — #11787602

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic
4C2×#63567C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#68909—31nomaximal
9#68686—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×#3744—22no—
14C2×#3744—22no—
15C2×#3744C414yescomplemented
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×#3724—21no—
21C2×#3722—21no—
22C2×#3722—21no—
23C2×Dic32—21no—
24#63844—22no—
25#63844—22no—
26#63567—22no—
27#63564—22no—
28C22×#204—31no—
29C22×#204—31no—
30C22×#204—61no—
31C2×#887—31no—
32C2×C4×Dic6—31no—
33C2×#821—31no—
34C2×#816—31no—
35#4988—31no—
36C2×#810—31no—
37C2×#809—31no—
38#4939—31no—
39C3×#340—31no—
40C3×#336—31no—
41#4551D311yescharacteristic, complemented
42#4550D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634C2×C412yes—
56C2×#634D412yes—
57C2×#634D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C22×C3×Dic3D411yescharacteristic
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8C2×C412yes—
65#3744—28no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3D412yes—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#3724—24no—
76#3722—42no—
77#3722—42no—
78Dic32—24no—
79#1880—91noSylow
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×Dic6—31no—
84C22×Dic6—31no—
85C22×Dic6—61no—
86C22×C3×C8—21no—
87C22×C3×C8—31no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C42—31no—
93C2×(C2×D3)⋊C4—61no—
94C2×(C2×D3)⋊C4—61no—
95C2×(C2×D3)⋊C4—61no—
96C2×(C2×D3)⋊C4—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×Dic3⋊C4—61no—
101C2×C4×Dic3—61no—
102C2×C4×Dic3—61no—
103C2×C4×Dic3C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C2×#204—34no—
106C2×#204—34no—
107C2×#204—64no—
108C2×#204—62no—
109C2×#204—62no—
110C2×#204—62no—
111C2×#204—62no—
112C2×#204—64no—
113C2×#204—64no—
114#887—62no—
115#887—62no—
116C4×Dic6—62no—
117C4×Dic6—62no—
118#821—62no—
119#816—62no—
120#810—62no—
121#809—62no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C2×C32×C4C22×C411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—22no—
141C4⋊(C3⋊D3)—41no—
142C4⋊(C3⋊D3)—41no—
143#634—22no—
144#634—22no—
145#634—22no—
146#634C22⋊C414yescomplemented
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3SD1612yescomplemented
159C32×C8—22no—
160C3×C3⋊C8—41no—
161C22×SD16—91no—
162C2×C4×Q8—91no—
163C2×#103—91no—
164C2×#102—91no—
165#390—91no—
166#340—31no—
167#336—31no—
168C23×D3—61no—
169C23×D3—61no—
170C23×D3—121no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C22×Dic3—21no—
180C22×Dic3—61no—
181C22×Dic3—61no—
182C22×Dic3—121no—
183C22×Dic3D1211yescharacteristic
184C22×Dic3D1211yescharacteristic
185C2×D12—32no—
186C2×D12—32no—
187C2×D12—62no—
188C2×D12—62no—
189C2×D12—62no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—121no—
201C2×D12—121no—
202C2×D12—121no—
203C2×Dic6—32no—
204C2×Dic6—32no—
205C2×Dic6—32no—
206C2×Dic6—32no—
207C2×Dic6—32no—
208C2×Dic6—32no—
209C2×Dic6—62no—
210C2×Dic6—62no—
211C2×Dic6—62no—
212C2×Dic6—61no—
213C2×Dic6—61no—
214C2×Dic6—61no—
215C2×Dic6—61no—
216C2×Dic6—61no—
217C2×Dic6—61no—
218C2×Dic6—121no—
219C2×Dic6—121no—
220C2×Dic6—121no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—22no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8C4×D312yes—
232C2×C3×C8C4×D312yes—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4—61no—
236C3×C4⋊C4—61no—
237C3×C42—61no—
238C3×C42—61no—
239(C2×D3)⋊C4—122no—
240(C2×D3)⋊C4—122no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4—122no—
243C4⋊Dic3—21no—
244C4⋊Dic3—21no—
245C4⋊Dic3—21no—
246C4⋊Dic3D1212yes—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3—64no—
252C4×Dic3—64no—
253C2×C3⋊C8—21no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256#204—68no—
257#204—68no—
258#204—616no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12011yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32C2×SD1611yescharacteristic
263C22×C32#13511yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32#13711yescharacteristic
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—81no—
270C2×C3⋊D3—81no—
271C2×C3⋊D3—81no—
272C2×C3⋊D3—81no—
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12311yescharacteristic
277C3⋊Dic3—24no—
278C3×Dic3—22no—
279C3×Dic3—41no—
280C3×Dic3—42no—
281C3×Dic3—81no—
282C22×Q8—91no—
283C22×D4—91no—
284C2×SD16—94no—
285C2×SD16—182no—
286C2×SD16—182no—
287C22×C8—31no—
288C22×C8D3211yescharacteristic
289C4×Q8—182no—
290C4×Q8—182no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—31no—
293C2×C4⋊C4—181no—
294C2×C22⋊C4—181no—
295C2×C22⋊C4—181no—
296C2×C42—31no—
297C2×C42—181no—
298#103—182no—
299#102—182no—
300C23×C3—21no—
301C23×C3C2×D1211yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—122no—
306C22×D3—122no—
307C22×D3—122no—
308C22×D3—121no—
309C22×D3—121no—
310C22×D3—121no—
311C22×D3—121no—
312C22×D3—121no—
313C22×D3—121no—
314C22×D3—121no—
315C22×D3—121no—
316C22×D3—121no—
317C22×D3—121no—
318C22×D3—121no—
319C22×D3—121no—
320C22×D3—241no—
321C22×D3—241no—
322C22×D3—241no—
323C22×D3—241no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—32no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—61no—
335C2×C3×C4—61no—
336C2×C3×C4—61no—
337C2×C3×C4—121no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4—121no—
341C2×C3×C4—121no—
342C2×C3×C4C2×C4×D311yescharacteristic
343C2×C3×C4C2×C4×D311yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4#23511yescharacteristic
346C2×C3×C4#23511yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23911yescharacteristic
353C2×C3×C4#23911yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—21no—
357C2×Dic3—22no—
358C2×Dic3—21no—
359C2×Dic3—21no—
360C2×Dic3—41no—
361C2×Dic3—41no—
362C2×Dic3—41no—
363C2×Dic3—41no—
364C2×Dic3—41no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3#20412yescomplemented
375D12—64no—
376D12—62no—
377D12—62no—
378D12—62no—
379D12—62no—
380D12—122no—
381D12—122no—
382D12—122no—
383D12—121no—
384D12—121no—
385D12—121no—
386D12—121no—
387Dic6—34no—
388Dic6—34no—
389Dic6—64no—
390Dic6—62no—
391Dic6—62no—
392Dic6—62no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—122no—
397Dic6—122no—
398Dic6—122no—
399C3×C8—24no—
400C3×C8—22no—
401C3×C8—22no—
402C3×C8—121no—
403C3⋊C8—41no—
404C2×C32#38611yescharacteristic
405C2×C32C4×SD1611yescharacteristic
406C2×C32#44011yescharacteristic
407C2×C32#44811yescharacteristic
408C2×C32#44911yescharacteristic
409C2×C32#46011yescharacteristic
410C2×C32#46411yescharacteristic
411C3⋊D3—82no—
412C24—181no—
413C2×Q8—92no—
414C2×Q8—92no—
415C2×Q8—92no—
416C2×Q8—181no—
417C2×Q8—181no—
418C2×Q8—181no—
419C2×D4—92no—
420C2×D4—181no—
421C2×D4—181no—
422C2×D4—181no—
423C2×D4—181no—
424C2×D4—181no—
425C22×C4—31no—
426C22×C4—31no—
427C22×C4—61no—
428C22×C4—61no—
429C22×C4—181no—
430C22×C4C2×D3211yescharacteristic
431SD16—188no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—61no—
435C2×C8—61no—
436C2×C8—61no—
437C2×C8#62412yes—
438C4⋊C4—32no—
439C4⋊C4—61no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—184no—
443C22⋊C4—362no—
444C22⋊C4—362no—
445C42—61no—
446C42—61no—
447C42—184no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—21no—
453C22×C3—21no—
454C22×C3—21no—
455C22×C3C4×D1211yescharacteristic
456C22×C3#88211yescharacteristic
457C22×C3#88211yescharacteristic
458C22×C3#88411yescharacteristic
459C22×C3#89311yescharacteristic
460C22×C3#89511yescharacteristic
461C22×C3C2×#20411yescharacteristic
462C22×C3#90411yescharacteristic
463C22×C3#90811yescharacteristic
464C22×C3#90911yescharacteristic
465C22×C3#91111yescharacteristic
466C22×C3D3×SD1611yescharacteristic
467C22×C3#91611yescharacteristic
468C22×C3#91811yescharacteristic
469C2×D3—124no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—242no—
477C2×D3—242no—
478C2×D3—242no—
479C2×D3—242no—
480C2×D3—242no—
481C2×D3—242no—
482C2×D3—241no—
483C2×D3—241no—
484C2×D3—241no—
485C2×D3—241no—
486C2×D3—241no—
487C2×D3—241no—
488C2×D3—241no—
489C2×D3—241no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—62no—
495C3×C4—122no—
496C3×C4—121no—
497C3×C4—241no—
498C3×C4C4×D1211yescharacteristic
499C3×C4D3×C22⋊C411yescharacteristic
500C3×C4D3×C22⋊C411yescharacteristic
501C3×C4#88411yescharacteristic
502C3×C4#89311yescharacteristic
503C3×C4#89411yescharacteristic
504C3×C4#89411yescharacteristic
505C3×C4#89511yescharacteristic
506Dic3—22no—
507Dic3—41no—
508Dic3—42no—
509Dic3—64no—
510Dic3—64no—
511Dic3—81no—
512Dic3—124no—
513C32#188011yescharacteristic, complemented, Sylow
514C23—182no—
515C23—361no—
516C23—361no—
517C23—361no—
518C23—361no—
519C23—361no—
520C23—361no—
521C23D3×D1211yescharacteristic
522Q8—94no—
523Q8—182no—
524Q8—182no—
525Q8—182no—
526D4—182no—
527D4—182no—
528D4—361no—
529D4—361no—
530C2×C4—32no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—62no—
537C2×C4—121no—
538C2×C4—121no—
539C2×C4—121no—
540C2×C4—121no—
541C2×C4—121no—
542C2×C4—182no—
543C2×C4—182no—
544C2×C4—182no—
545C2×C4#379911yescharacteristic
546C2×C4#379911yescharacteristic
547C2×C4D3×D1211yescharacteristic
548C2×C4C2×#62411yescharacteristic
549C2×C4#381111yescharacteristic
550C2×C4#381111yescharacteristic
551C8—22no—
552C8—121no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3#466511yescharacteristic
561C2×C3#466511yescharacteristic
562C2×C3C4×#20411yescharacteristic
563C2×C3#471011yescharacteristic
564C2×C3#473411yescharacteristic
565C2×C3#473811yescharacteristic
566C2×C3#476211yescharacteristic
567C2×C3#478111yescharacteristic
568C2×C3#479811yescharacteristic
569C2×C3#480611yescharacteristic
570C2×C3#484511yescharacteristic
571C2×C3#484811yescharacteristic
572C2×C3#485211yescharacteristic
573C2×C3#488911yescharacteristic
574D3—244no—
575D3—242no—
576D3—242no—
577C22—362no—
578C22—362no—
579C22—362no—
580C22—721no—
581C22—721no—
582C22—721no—
583C22—721no—
584C22D3×#20411yescharacteristic
585C22#6379511yescharacteristic
586C22#6380111yescharacteristic
587C22#6380611yescharacteristic
588C22#6389411yescharacteristic
589C22#6391011yescharacteristic
590C22#6392311yescharacteristic
591C4—62no—
592C4—121no—
593C4—122no—
594C4—184no—
595C4—241no—
596C4#6389411yescharacteristic
597C4#6389711yescharacteristic
598C4#6391011yescharacteristic
599C4#6397411yescharacteristic
600C3—21no—
601C3#6868611yescharacteristic, complemented
602C3#6890911yescharacteristic, complemented
603C2—722no—
604C2#1059075811yescharacteristic
605C2#1059077311yescharacteristic
606C2#1059081311yescharacteristic
607C2#1059087911yescharacteristic
608C2#1059095111yescharacteristic
609C2#1059096811yescharacteristic
610C2#1059138011yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
4. C2×#63567C2semidirect
6. C3×#4551C2semidirect
7. C3×#4550C2semidirect
15. C2×#3744C4semidirect
41. #4551D3semidirect
42. #4550D3semidirect
146. #634C22⋊C4semidirect
158. C2×C3×Dic3SD16semidirect
374. C2×Dic3#204semidirect
513. C32#1880semidirect
601. C3#68686semidirect
602. C3#68909semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#638442
#105913202
C2×#635672
C2×#635642
C3×#45512
C3×#45502
#689093
#686863