Finite Group Databasebeta

← #11787283

Subgroups — #11787283

Order 1152.

777 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63856C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×C3×#816C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70269—31nomaximal
9#69931—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3724—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×Dic32—21no—
21#63856—22no—
22#63856C414yescomplemented
23#63841—22no—
24#63841—22no—
25C3×(C2×D3)⋊C8—22no—
26C3×#816—22no—
27#63566—22no—
28C2×#946—31no—
29C2×#926—31no—
30C2×#924—31no—
31C2×#892—31no—
32C2×C3×#103—31no—
33C2×C3×C22⋊C8—31no—
34C2×#835—31no—
35C2×(C2×D3)⋊C8D311yescharacteristic
36C2×#816—31no—
37C2×#816D311yescharacteristic, complemented
38#4551—31no—
39#4551—31no—
40#4551—31no—
41#4551—61no—
42#4529—31no—
43C23×C3×D3D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3⋊Dic3—21no—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3C2×C412yes—
55C2×C3×C4×D3D412yes—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yes—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)C2×C412yes—
68C4⋊(C3⋊Dic3)D412yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3724—24no—
75(C2×D3)⋊Dic3—24no—
76(C2×D3)⋊Dic3—24no—
77Dic32—24no—
78#1873—91noSylow
79C22×C3×Q8—31no—
80C23×C3×C4—31no—
81C22×C4×D3C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C22×C3×C8—21no—
84C22×C3×C8—31no—
85C22×C3×C8C2×D311yescharacteristic
86C22×C3×C8C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×#217—61no—
89C2×#217—61no—
90#946—34no—
91#946—62no—
92C2×(C2×D3)⋊C4—61no—
93C2×(C2×D3)⋊C4—61no—
94#926—62no—
95#926—62no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—31no—
100C2×C4⋊Dic3—61no—
101C2×C4⋊Dic3—61no—
102C2×C4⋊Dic3C2×D311yescharacteristic
103#924—34no—
104#924—62no—
105C2×Dic3⋊C4—61no—
106C2×Dic3⋊C4—61no—
107C2×C4×Dic3—61no—
108C2×C4×Dic3—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#892—62no—
111#892—62no—
112C3×#103—62no—
113C3×C22⋊C8—62no—
114#835—62no—
115(C2×D3)⋊C8—22no—
116#816—22no—
117#816—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3×D3—21no—
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—21no—
125C22×C3×D3C22⋊C412yes—
126C2×C32×C4C22×C411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C2×C3⋊Dic3—41no—
137C2×C3⋊Dic3—41no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3C22⋊C412yes—
147C3×C4×D3—22no—
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—22no—
152C3×Dic6—22no—
153C3×Dic6—41no—
154C3×Dic6—41no—
155C32×C8—41no—
156C3×C3⋊C8—41no—
157C2×C22⋊Q8—91no—
158C2×#117—91no—
159C2×#103—31no—
160C2×#103—91no—
161C2×C22⋊C8—31no—
162#340—91no—
163#340—91no—
164C24×C3—31no—
165C23×D3D1211yescharacteristic
166C2×C3×Q8—32no—
167C2×C3×Q8—61no—
168C2×C3×Q8—61no—
169C2×C3×Q8—61no—
170C2×C3×Q8—61no—
171C2×C3×Q8—61no—
172C22×C3×C4—21no—
173C22×C3×C4—31no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—121no—
191C22×Dic3—121no—
192C22×Dic3D1211yescharacteristic
193C2×C4×D3—21no—
194C2×C4×D3—21no—
195C2×C4×D3—21no—
196C2×C4×D3—21no—
197C2×C4×D3C4×D312yes—
198C2×C4×D3#6712yes—
199C2×Dic6—21no—
200C2×Dic6—21no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6C4×D312yes—
205C2×C3×C8—22no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—41no—
213C2×C3×C8—41no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—32no—
218C3×C4⋊C4—61no—
219#217—64no—
220#217—64no—
221(C2×D3)⋊C4—64no—
222(C2×D3)⋊C4—64no—
223C4⋊Dic3—21no—
224C4⋊Dic3—32no—
225C4⋊Dic3—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—32no—
228C4⋊Dic3—62no—
229C4⋊Dic3—62no—
230C4⋊Dic3—61no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4⋊Dic3—61no—
234C4⋊Dic3—121no—
235C4⋊Dic3—121no—
236C4⋊Dic3#6712yes—
237Dic3⋊C4—64no—
238Dic3⋊C4—64no—
239C4×Dic3—64no—
240C4×Dic3—64no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32#12011yescharacteristic
246C22×C32#12311yescharacteristic
247C22×C32#13511yescharacteristic
248C22×C32#13511yescharacteristic
249C22×C32#13711yescharacteristic
250C22×C32#13711yescharacteristic
251C2×C3×D3—22no—
252C2×C3×D3—22no—
253C2×C3×D3—22no—
254C2×C3×D3—41no—
255C2×C3×D3—41no—
256C2×C3×D3—41no—
257C2×C3×D3—41no—
258C32×C4C4×D411yescharacteristic
259C32×C4C4×D411yescharacteristic
260C32×C4#12111yescharacteristic
261C32×C4#12111yescharacteristic
262C3⋊Dic3—42no—
263C3⋊Dic3—42no—
264C3×Dic3—22no—
265C3×Dic3—42no—
266C3×Dic3—42no—
267C22×Q8—31no—
268C23×C4—31no—
269C22×C8—31no—
270C22×C8D3211yescharacteristic
271C22⋊Q8—94no—
272C22⋊Q8—182no—
273#117—182no—
274#117—182no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—91no—
277C2×C4⋊C4—91no—
278C2×C4⋊C4—181no—
279C2×C22⋊C4—181no—
280C2×C22⋊C4—181no—
281C2×C42—181no—
282#103—62no—
283#103—182no—
284C22⋊C8—62no—
285C23×C3—21no—
286C23×C3—32no—
287C23×C3—61no—
288C23×C3—61no—
289C23×C3—61no—
290C23×C3—61no—
291C23×C3—61no—
292C23×C3—61no—
293C23×C3C2×D1211yescharacteristic
294C23×C3D3×D411yescharacteristic
295C22×D3—21no—
296C22×D3—21no—
297C22×D3—21no—
298C22×D3—21no—
299C22×D3—21no—
300C22×D3—21no—
301C22×D3(C2×D3)⋊C412yes—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—121no—
305C3×Q8—121no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—32no—
313C2×C3×C4—61no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×C4×D311yescharacteristic
326C2×C3×C4C2×C4×D311yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—121no—
358C2×Dic3—121no—
359C2×Dic3—241no—
360C2×Dic3—241no—
361C2×Dic3—241no—
362C2×Dic3—241no—
363C2×Dic3(C2×D3)⋊C412yes—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—22no—
367C4×D3—22no—
368Dic6—22no—
369Dic6—22no—
370Dic6—41no—
371Dic6—41no—
372C3×C8—42no—
373C3×C8—41no—
374C3×C8—41no—
375C3×C8—121no—
376C3⋊C8—41no—
377C2×C32#38611yescharacteristic
378C2×C32#41611yescharacteristic
379C2×C32#41911yescharacteristic
380C2×C32#45211yescharacteristic
381C2×C32#45211yescharacteristic
382C2×C32#48511yescharacteristic
383C2×C32#48511yescharacteristic
384C3×D3—42no—
385C24—31no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×Q8—61no—
392C22×C4—31no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—61no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—61no—
399C22×C4—61no—
400C22×C4—61no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4C2×D3211yescharacteristic
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—21no—
407C2×C8—61no—
408C2×C8—61no—
409C2×C8—61no—
410C4⋊C4—32no—
411C4⋊C4—61no—
412C4⋊C4—92no—
413C4⋊C4—92no—
414C4⋊C4—184no—
415C4⋊C4—181no—
416C4⋊C4—181no—
417C22⋊C4—184no—
418C22⋊C4—184no—
419C42—184no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—62no—
428C22×C3—62no—
429C22×C3—62no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3—121no—
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3#88211yescharacteristic
436C22×C3#88311yescharacteristic
437C22×C3#88611yescharacteristic
438C22×C3#90411yescharacteristic
439C22×C3#90411yescharacteristic
440C22×C3#90911yescharacteristic
441C22×C3#90911yescharacteristic
442C22×C3#91511yescharacteristic
443C22×C3#91611yescharacteristic
444C22×C3#91811yescharacteristic
445C22×C3#91911yescharacteristic
446C22×C3C2×(C2×D3)⋊C411yescharacteristic
447C22×C3#93711yescharacteristic
448C2×D3—22no—
449C2×D3—22no—
450C2×D3—22no—
451C2×D3—41no—
452C2×D3—41no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—62no—
460C3×C4—122no—
461C3×C4—122no—
462C3×C4#67⋊C411yescharacteristic
463C3×C4#67⋊C411yescharacteristic
464C3×C4#67⋊C411yescharacteristic
465C3×C4#88411yescharacteristic
466C3×C4C4×#6711yescharacteristic
467C3×C4#93811yescharacteristic
468C3×C4#93911yescharacteristic
469C3×C4#93911yescharacteristic
470Dic3—22no—
471Dic3—42no—
472Dic3—42no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—242no—
478Dic3—242no—
479C32#187311yescharacteristic, complemented, Sylow
480C23—32no—
481C23—61no—
482C23—61no—
483C23—61no—
484C23—61no—
485C23—61no—
486C23—61no—
487C23D3×D1211yescharacteristic
488Q8—62no—
489Q8—62no—
490Q8—121no—
491Q8—121no—
492C2×C4—32no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—361no—
508C2×C4—361no—
509C2×C4—361no—
510C2×C4—361no—
511C2×C4#379511yescharacteristic
512C2×C4C4×D3211yescharacteristic
513C2×C4#380211yescharacteristic
514C2×C4#380511yescharacteristic
515C2×C4D3×#6711yescharacteristic
516C2×C4D3×#6711yescharacteristic
517C8—41no—
518C8—121no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—122no—
527C2×C3#472311yescharacteristic
528C2×C3#472311yescharacteristic
529C2×C3#473311yescharacteristic
530C2×C3#473311yescharacteristic
531C2×C3#480211yescharacteristic
532C2×C3#480411yescharacteristic
533C2×C3#481411yescharacteristic
534C2×C3#481511yescharacteristic
535C2×C3#495611yescharacteristic
536C2×C3#495811yescharacteristic
537C2×C3#511311yescharacteristic
538C2×C3#512011yescharacteristic
539C2×C3#517311yescharacteristic
540C2×C3#518711yescharacteristic
541D3—42no—
542C22—62no—
543C22—62no—
544C22—62no—
545C22—121no—
546C22—121no—
547C22—121no—
548C22—121no—
549C22#6380011yescharacteristic
550C22#6380111yescharacteristic
551C22#6380611yescharacteristic
552C22#6380811yescharacteristic
553C22#6389111yescharacteristic
554C22D3×(C2×D3)⋊C411yescharacteristic
555C22#6392211yescharacteristic
556C4—62no—
557C4—122no—
558C4—122no—
559C4—362no—
560C4—362no—
561C4#6387911yescharacteristic
562C4#6388511yescharacteristic
563C4#6390211yescharacteristic
564C4#6397011yescharacteristic
565C3—21no—
566C3#6993111yescharacteristic, complemented
567C3#7026911yescharacteristic, complemented
568C2—122no—
569C2#1059069011yescharacteristic
570C2#1059071011yescharacteristic
571C2#1059071111yescharacteristic
572C2#1059094811yescharacteristic
573C2#1059096011yescharacteristic
574C2#1059096611yescharacteristic
575C2#1059136311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1873
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
4. C2×C3×#816C2semidirect
5. C2×#63566C2semidirect
6. #10589417C2semidirect
7. #10589164C2semidirect
22. #63856C4semidirect
37. C2×#816D3semidirect
479. C32#1873semidirect
566. C3#69931semidirect
567. C3#70269semidirect

Maximal subgroups

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

subgroupindex
C2×#638562
C2×#638412
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635662
#105894172
#105891642
#702693
#699313