Finite Group Databasebeta

← #11870802

Subgroups — #11870802

Order 1152.

822 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2#10593859C211yesmaximal, characteristic
3#10592730C211yesmaximal, characteristic, complemented
4C3×#5021C211yesmaximal, characteristic, complemented
5#10591595C212yesmaximal
6#10591537C212yesmaximal, complemented
7#10590481C212yesmaximal, complemented
8#10590427C212yesmaximal
9#10590385C211yesmaximal, characteristic, complemented
10#10590310C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic
12#82447—31nomaximal
13#81092—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C2×#3756C2212yes—
17#64078C2211yescharacteristic
18C3×Q8×Dic3C2211yescharacteristic
19C3×D3×C4⋊C4—21no—
20C3×D3×C4⋊C4C2211yescharacteristic
21C3×#887—21no—
22C3×#887C2211yescharacteristic
23C3×C42×D3—21no—
24C3×C42×D3C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6—21no—
27C3×C4×Dic6C2211yescharacteristic
28#63869—21no—
29#63857C2212yes—
30#63856—21no—
31#63844C2212yes—
32Dic3×Dic6—21no—
33#63841—21no—
34C2×#3719C2212yes—
35#63637C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
37C3×#835C2212yes—
38C3×#807C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63576C2212yes—
41#63567C2212yes—
42#63565C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yes—
45C2×C3×C4×Q8—31no—
46#5728—31no—
47C4×D3×Q8D311yescharacteristic
48#5470—31no—
49C3×#477—31no—
50#5228—32no—
51#5091—31no—
52#5031—31no—
53#5031—31no—
54#5031—31no—
55#5031—61no—
56C4×#216—32no—
57C4×#216—32no—
58#5021—31no—
59#5021D311yescharacteristic, complemented
60#4970—32no—
61#4925—31no—
62#4884—32no—
63#4873—32no—
64#4849—31no—
65#4833—31no—
66#4809—32no—
67#4790—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634C2312yes—
70C3×D3×Q8—22no—
71C3×D3×Q8—22no—
72C2×C3×C4×D3—21no—
73C2×C3×C4×D3—21no—
74C2×C3×C4×D3D411yescharacteristic
75C2×C3×C4×D3D411yescharacteristic
76C2×C3×C4×D3C2311yescharacteristic
77C2×C3×Dic6—21no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84#3756—24no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)—21no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×Dic3⋊C4—21no—
95C3×C4×Dic3—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—21no—
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3724—22no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105Dic32—22no—
106#3719—24no—
107#3104—91noSylow
108C22×C3×Q8—31no—
109C2×D3×Q8C2×D311yescharacteristic
110C3×C4⋊Q8—31no—
111C3×C4×Q8—21no—
112C3×C4×Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115C3×C4×Q8—61no—
116C3×C4×Q8—61no—
117C3×C4×Q8C2×D311yescharacteristic
118C3×C4×Q8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—61no—
121C2×C3×C42—31no—
122C2×C3×C42—61no—
123#946—61no—
124Q8×Dic3—61no—
125Q8×Dic3C2×D311yescharacteristic
126C2×#216—32no—
127C2×#216—32no—
128C2×#216—32no—
129C2×#216—62no—
130#926—61no—
131#924—32no—
132#924—61no—
133C2×Dic12—32no—
134#897—32no—
135#892—61no—
136D3×C4⋊C4—21no—
137D3×C4⋊C4C2×D311yescharacteristic
138#890—61no—
139#887—21no—
140#887—32no—
141#887C2×D311yescharacteristic
142C42×D3—21no—
143C42×D3C2×D311yescharacteristic
144#870—61no—
145#869—31no—
146#869—31no—
147#869—61no—
148#869C2×D311yescharacteristic
149C4×Dic6—21no—
150C4×Dic6—32no—
151C4×Dic6—61no—
152C4×Dic6C2×D311yescharacteristic
153C3×#107—32no—
154C3×C4⋊C8—31no—
155C3×#103—32no—
156#835—32no—
157#835C2×D312yes—
158#830—32no—
159(C2×D3)⋊C8—32no—
160#816—32no—
161C8×Dic3—32no—
162#810—32no—
163#810—32no—
164#810—32no—
165#810—32no—
166#810—62no—
167#807—32no—
168#807—32no—
169#807C2×D312yes—
170C4⋊(C3⋊C8)—31no—
171C4⋊(C3⋊C8)—31no—
172C4⋊(C3⋊C8)—61no—
173C4⋊(C3⋊C8)C2×D311yescharacteristic
174C4×C3⋊C8—32no—
175C22×C3×D3C2×D411yescharacteristic
176C32×Q8—21no—
177C32×Q8#4112yes—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184#634—22no—
185#634—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C2×C3×Dic3C2×D411yescharacteristic
192C3×C4×D3—24no—
193C3×C4×D3—21no—
194C3×C4×D3—21no—
195C3×C4×D3—41no—
196C3×C4×D3—42no—
197C3×C4×D3Q1614yescomplemented
198C3×Dic6—24no—
199C3×Dic6—21no—
200C3×Dic6—42no—
201C3×Dic6#4112yes—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204#533—91no—
205C2×C4×Q8—31no—
206#484—92no—
207#477—31no—
208#477—91no—
209#462—91no—
210#462—91no—
211#451—92no—
212C4×Q16—92no—
213C4×Q16—92no—
214#431—91no—
215C2×C3×Q8—21no—
216C2×C3×Q8—31no—
217C2×C3×Q8—61no—
218C2×C3×Q8—62no—
219C2×C3×Q8—62no—
220C2×C3×Q8—61no—
221C2×C3×Q8C22×D311yescharacteristic
222C2×C3×Q8C22×D311yescharacteristic
223C22×C3×C4—31no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—61no—
227C22×C3×C4—61no—
228D3×Q8—22no—
229D3×Q8—22no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×C4×D3#6711yescharacteristic
233C2×C4×D3#6711yescharacteristic
234C2×C4×D3C22×D311yescharacteristic
235C2×Dic6—21no—
236C2×Dic6—21no—
237C2×Dic6—32no—
238C2×Dic6—32no—
239C2×Dic6—62no—
240C2×Dic6C22×D311yescharacteristic
241C2×C3×C8—32no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—32no—
247C3×C4⋊C4—41no—
248C3×C4⋊C4—61no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4C22×D311yescharacteristic
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—31no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—41no—
262C3×C42—61no—
263C3×C42—61no—
264C3×C42—61no—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D311yescharacteristic
267#217—62no—
268#216—64no—
269#216—64no—
270#216—64no—
271#216—124no—
272(C2×D3)⋊C4—62no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—61no—
279C4⋊Dic3—62no—
280C4⋊Dic3—121no—
281C4⋊Dic3—121no—
282C4⋊Dic3C22×D311yescharacteristic
283C4⋊Dic3C22×D312yes—
284Dic3⋊C4—21no—
285Dic3⋊C4—21no—
286Dic3⋊C4—21no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—62no—
290C4×Dic3—21no—
291C4×Dic3—21no—
292C4×Dic3—21no—
293C4×Dic3—62no—
294C4×Dic3—62no—
295C4×Dic3#6711yescharacteristic
296C4×Dic3#6711yescharacteristic
297C4×Dic3C22×D311yescharacteristic
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8C22×D312yes—
302Dic12—64no—
303C22×C32C22×D411yescharacteristic
304C2×C3×D3—21no—
305C2×C3×D3—21no—
306C2×C3×D3C2×Q1612yes—
307C32×C4—22no—
308C32×C4—21no—
309C32×C4—41no—
310C32×C4C2×Q1612yes—
311C32×C4C2×#4111yescharacteristic
312C32×C4C2×#4111yescharacteristic
313C3⋊Dic3—42no—
314C3×Dic3—21no—
315C3×Dic3—22no—
316C3×Dic3—21no—
317C3×Dic3—42no—
318C3×Dic3—41no—
319C3×Dic3C2×Q1612yes—
320C22×Q8—31no—
321C2×Q16—92no—
322C2×Q16—92no—
323C4⋊Q8—31no—
324C4⋊Q8—91no—
325#125—181no—
326C22⋊Q8—92no—
327C22⋊Q8—181no—
328C4×Q8—31no—
329C4×Q8—31no—
330C4×Q8—31no—
331C4×Q8—61no—
332C4×Q8—61no—
333C4×Q8—92no—
334C4×Q8—181no—
335C4×Q8D3211yescharacteristic
336#117—181no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—61no—
339C2×C42—31no—
340C2×C42—61no—
341#107—32no—
342#107—92no—
343C4⋊C8—31no—
344C4⋊C8—91no—
345#103—32no—
346#103—92no—
347#103—92no—
348#103—92no—
349C22⋊C8—92no—
350C4×C8—92no—
351C23×C3—31no—
352C22×D3C2×#6711yescharacteristic
353C3×Q8—21no—
354C3×Q8—21no—
355C3×Q8—22no—
356C3×Q8—32no—
357C3×Q8—41no—
358C3×Q8—64no—
359C3×Q8—61no—
360C3×Q8—122no—
361C3×Q8#23512yes—
362C3×Q8#23912yes—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—31no—
371C2×C3×C4—34no—
372C2×C3×C4—31no—
373C2×C3×C4—31no—
374C2×C3×C4—41no—
375C2×C3×C4—41no—
376C2×C3×C4—64no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—121no—
383C2×C3×C4—122no—
384C2×C3×C4D3×D411yescharacteristic
385C2×C3×C4D3×D411yescharacteristic
386C2×C3×C4C2×#6711yescharacteristic
387C2×C3×C4C2×#6711yescharacteristic
388C2×C3×C4C23×D311yescharacteristic
389C2×C3×C4C23×D311yescharacteristic
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3C2×#6711yescharacteristic
397C2×Dic3C2×#6711yescharacteristic
398C2×Dic3C2×#6711yescharacteristic
399C4×D3—24no—
400C4×D3—21no—
401C4×D3—21no—
402C4×D3—41no—
403C4×D3—42no—
404C4×D3#21614yescomplemented
405Dic6—24no—
406Dic6—21no—
407Dic6—42no—
408Dic6—62no—
409Dic6—62no—
410Dic6—62no—
411Dic6—62no—
412Dic6—122no—
413Dic6—122no—
414Dic6#23512yes—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—62no—
418C3⋊C8—62no—
419C3⋊C8—122no—
420C2×C32#52511yescharacteristic
421C2×C32C22×Q1611yescharacteristic
422C2×C32#57511yescharacteristic
423C3×D3—22no—
424C2×Q8—31no—
425C2×Q8—61no—
426C2×Q8—62no—
427C2×Q8—62no—
428C2×Q8—61no—
429C2×Q8—92no—
430C2×Q8C2×D3211yescharacteristic
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—61no—
435C22×C4—61no—
436Q16—184no—
437Q16—184no—
438C2×C8—32no—
439C2×C8—92no—
440C4⋊C4—21no—
441C4⋊C4—32no—
442C4⋊C4—31no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4—182no—
449C4⋊C4—182no—
450C4⋊C4—181no—
451C4⋊C4—181no—
452C4⋊C4C2×D3211yescharacteristic
453C22⋊C4—182no—
454C42—21no—
455C42—31no—
456C42—31no—
457C42—31no—
458C42—61no—
459C42—61no—
460C42—61no—
461C42—182no—
462C42C2×D3211yescharacteristic
463C22×C3—21no—
464C22×C3—32no—
465C22×C3—61no—
466C22×C3—61no—
467C22×C3C2×D3×D411yescharacteristic
468C22×C3C22×#6711yescharacteristic
469C2×D3—21no—
470C2×D3—21no—
471C2×D3C2×#21612yes—
472C3×C4—21no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—22no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—32no—
480C3×C4—41no—
481C3×C4—42no—
482C3×C4—41no—
483C3×C4—41no—
484C3×C4—61no—
485C3×C4—61no—
486C3×C4—62no—
487C3×C4—81no—
488C3×C4—121no—
489C3×C4—122no—
490C3×C4D3×Q1612yes—
491C3×C4C2×#21612yes—
492C3×C4C2×#23511yescharacteristic
493C3×C4C2×#23511yescharacteristic
494C3×C4C2×#23911yescharacteristic
495C3×C4D3×#4111yescharacteristic
496Dic3—21no—
497Dic3—22no—
498Dic3—21no—
499Dic3—42no—
500Dic3—41no—
501Dic3—122no—
502Dic3—122no—
503Dic3—242no—
504Dic3C2×#21612yes—
505C32#310411yescharacteristic, complemented, Sylow
506C23—31no—
507Q8—21no—
508Q8—32no—
509Q8—64no—
510Q8—61no—
511Q8—122no—
512Q8—182no—
513Q8—182no—
514Q8#379912yes—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—31no—
518C2×C4—34no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—64no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—121no—
528C2×C4—122no—
529C2×C4—182no—
530C2×C4D3×#6711yescharacteristic
531C2×C4D3×#6711yescharacteristic
532C2×C4C22×D3211yescharacteristic
533C8—62no—
534C8—182no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—62no—
539C2×C3#562711yescharacteristic
540C2×C3C2×D3×Q1611yescharacteristic
541C2×C3#577311yescharacteristic
542C2×C3#579111yescharacteristic
543C2×C3C22×#21611yescharacteristic
544C2×C3#582211yescharacteristic
545D3—22no—
546C22—32no—
547C22—61no—
548C22—61no—
549C22C2×D3×#6711yescharacteristic
550C4—21no—
551C4—22no—
552C4—32no—
553C4—41no—
554C4—61no—
555C4—61no—
556C4—62no—
557C4—121no—
558C4—122no—
559C4—362no—
560C4D3×#21612yes—
561C4C2×#379911yescharacteristic
562C4D3×#23511yescharacteristic
563C3—21no—
564C3#8109211yescharacteristic, complemented
565C3#8244711yescharacteristic, complemented
566C2—62no—
567C2#1059500511yescharacteristic
568C2C2×D3×#21611yescharacteristic
569C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
hypercenterC4×Q8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592730C2semidirect
4. C3×#5021C2semidirect
6. #10591537C2semidirect
7. #10590481C2semidirect
9. #10590385C2semidirect
10. #10590310C2semidirect
59. #5021D3semidirect
197. C3×C4×D3Q16semidirect
404. C4×D3#216semidirect
505. C32#3104semidirect
564. C3#81092semidirect
565. C3#82447semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
#105938592
#105927302
C3×#50212
#105915952
#105915372
#105904812
#105904272
#105903852
#105903102
#105902482
#824473
#810923