Finite Group Databasebeta

← #11870804

Subgroups — #11870804

Order 1152.

816 conjugacy classes of subgroups.

The subgroup lattice has 569 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#10592720C211yesmaximal, characteristic, complemented
4C3×#5031C211yesmaximal, characteristic, complemented
5#10591594C212yesmaximal
6Dic3×#216C212yesmaximal, complemented
7#10590517C212yesmaximal
8#10590476C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10#10590283C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic
12#82447—31nomaximal
13#80456—31nomaximal
14C2×C3×D3×Q8C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16#64078C2211yescharacteristic
17C3×Q8×Dic3C2211yescharacteristic
18C2×C3×#216C2212yes—
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#63857—21no—
30#63856C2212yes—
31#63844—21no—
32Dic3×Dic6C2212yes—
33#63841—21no—
34C2×#3718C2212yes—
35#63662C2212yes—
36#63634C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#810C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63566C2212yes—
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×#462—31no—
50#5228—32no—
51#5186—32no—
52Dic3×Q16—32no—
53#5090—31no—
54#5031—31no—
55#5031D311yescharacteristic, complemented
56C4×#216—32no—
57C4×#216—32no—
58#5021—31no—
59#5021—31no—
60#5021—31no—
61#5021—61no—
62#4970—32no—
63#4925—31no—
64#4850—31no—
65#4833—31no—
66#4811—32no—
67#4790—32no—
68C2×C32×Q8C2311yescharacteristic
69C2×#634—21no—
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×Dic6C2312yes—
79C2×C3×Dic6C2311yescharacteristic
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2311yescharacteristic
82C32×C42—21no—
83C32×C42C2311yescharacteristic
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#216—24no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3C2311yescharacteristic
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#3718—24no—
107#3104—91noSylow
108C22×C3×Q8—31no—
109C2×D3×Q8C2×D311yescharacteristic
110C2×C3×Q16—32no—
111C3×C4⋊Q8—31no—
112C3×C4×Q8—21no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115C3×C4×Q8—31no—
116C3×C4×Q8—61no—
117C3×C4×Q8—61no—
118C3×C4×Q8C2×D311yescharacteristic
119C3×C4×Q8C2×D311yescharacteristic
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—61no—
122C2×C3×C42—31no—
123C2×C3×C42—61no—
124#946—32no—
125Q8×Dic3—32no—
126Q8×Dic3C2×D311yescharacteristic
127C2×#216—32no—
128C2×#216—32no—
129C2×#216C2×D312yes—
130#926—61no—
131#924—32no—
132#924—61no—
133#897—61no—
134#892—61no—
135D3×C4⋊C4—21no—
136D3×C4⋊C4C2×D311yescharacteristic
137#890—61no—
138#887—21no—
139#887—61no—
140#887C2×D311yescharacteristic
141C42×D3—21no—
142C42×D3C2×D311yescharacteristic
143#870—61no—
144#869—31no—
145#869—31no—
146#869—61no—
147#869C2×D311yescharacteristic
148C4×Dic6—21no—
149C4×Dic6—32no—
150C4×Dic6—61no—
151C4×Dic6C2×D311yescharacteristic
152C3×C4⋊C8—31no—
153C3×#103—32no—
154#835—32no—
155#835—32no—
156#835—32no—
157#835—32no—
158#835—62no—
159#830—32no—
160(C2×D3)⋊C8—32no—
161#818—32no—
162#816—32no—
163C8×Dic3—32no—
164#810—32no—
165#810C2×D312yes—
166#807—32no—
167#807—32no—
168#807—32no—
169#807—62no—
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—42no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×C4×D3—24no—
192C3×C4×D3—21no—
193C3×C4×D3—21no—
194C3×C4×D3—41no—
195C3×C4×D3—42no—
196C3×C4×D3Q1614yescomplemented
197C3×Dic6—24no—
198C3×Dic6—21no—
199C3×Dic6—22no—
200C3×Dic6—22no—
201C3×Dic6#4112yes—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204#533—91no—
205C2×C4×Q8—31no—
206#484—92no—
207#477—91no—
208#477—91no—
209#462—31no—
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—32no—
218C2×C3×Q8—61no—
219C2×C3×Q8—62no—
220C2×C3×Q8—62no—
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—61no—
237C2×Dic6—61no—
238C2×Dic6—121no—
239C2×Dic6C22×D312yes—
240C2×Dic6C22×D311yescharacteristic
241C3×Q16—64no—
242C2×C3×C8—32no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—31no—
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⋊C4—61no—
254C3×C4⋊C4C22×D311yescharacteristic
255C3×C4⋊C4C22×D311yescharacteristic
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—21no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42—41no—
263C3×C42—61no—
264C3×C42—61no—
265C3×C42—61no—
266C3×C42C22×D311yescharacteristic
267C3×C42C22×D311yescharacteristic
268#217—62no—
269#216—24no—
270#216—64no—
271#216—64no—
272(C2×D3)⋊C4—62no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—32no—
277C4⋊Dic3—32no—
278C4⋊Dic3—62no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281C4⋊Dic3—62no—
282C4⋊Dic3—121no—
283C4⋊Dic3C22×D311yescharacteristic
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—
302C22×C32C22×D411yescharacteristic
303C2×C3×D3—21no—
304C2×C3×D3—21no—
305C2×C3×D3C2×Q1612yes—
306C32×C4—22no—
307C32×C4—21no—
308C32×C4—41no—
309C32×C4C2×Q1612yes—
310C32×C4C2×#4111yescharacteristic
311C32×C4C2×#4111yescharacteristic
312C3⋊Dic3—42no—
313C3×Dic3—21no—
314C3×Dic3—22no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3C2×Q1612yes—
319C22×Q8—31no—
320C2×Q16—32no—
321C2×Q16—92no—
322C4⋊Q8—31no—
323C4⋊Q8—91no—
324#125—181no—
325C22⋊Q8—92no—
326C22⋊Q8—181no—
327C4×Q8—31no—
328C4×Q8—31no—
329C4×Q8—31no—
330C4×Q8—61no—
331C4×Q8—61no—
332C4×Q8—92no—
333C4×Q8—181no—
334C4×Q8D3211yescharacteristic
335#117—181no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—61no—
338C2×C42—31no—
339C2×C42—61no—
340#107—92no—
341#107—92no—
342C4⋊C8—31no—
343C4⋊C8—91no—
344#103—32no—
345#103—92no—
346#103—92no—
347#103—92no—
348C22⋊C8—92no—
349C4×C8—92no—
350C23×C3—31no—
351C22×D3C2×#6711yescharacteristic
352C3×Q8—21no—
353C3×Q8—21no—
354C3×Q8—22no—
355C3×Q8—32no—
356C3×Q8—41no—
357C3×Q8—64no—
358C3×Q8—61no—
359C3×Q8—62no—
360C3×Q8—62no—
361C3×Q8#23512yes—
362C3×Q8#23712yes—
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—22no—
408Dic6—22no—
409Dic6—122no—
410Dic6—122no—
411Dic6—242no—
412Dic6#23512yes—
413C3×C8—62no—
414C3⋊C8—22no—
415C3⋊C8—62no—
416C3⋊C8—62no—
417C3⋊C8—122no—
418C2×C32#52511yescharacteristic
419C2×C32C22×Q1611yescharacteristic
420C2×C32#57511yescharacteristic
421C3×D3—22no—
422C2×Q8—31no—
423C2×Q8—32no—
424C2×Q8—61no—
425C2×Q8—62no—
426C2×Q8—62no—
427C2×Q8—181no—
428C2×Q8C2×D3211yescharacteristic
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—61no—
433C22×C4—61no—
434Q16—64no—
435Q16—184no—
436C2×C8—32no—
437C2×C8—92no—
438C4⋊C4—21no—
439C4⋊C4—31no—
440C4⋊C4—61no—
441C4⋊C4—61no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C4⋊C4—92no—
447C4⋊C4—182no—
448C4⋊C4—182no—
449C4⋊C4—181no—
450C4⋊C4C2×D3211yescharacteristic
451C22⋊C4—182no—
452C42—21no—
453C42—31no—
454C42—31no—
455C42—31no—
456C42—61no—
457C42—61no—
458C42—61no—
459C42—182no—
460C42C2×D3211yescharacteristic
461C22×C3—21no—
462C22×C3—32no—
463C22×C3—61no—
464C22×C3—61no—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C22×#6711yescharacteristic
467C2×D3—21no—
468C2×D3—21no—
469C2×D3C2×#21612yes—
470C3×C4—21no—
471C3×C4—22no—
472C3×C4—21no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—32no—
478C3×C4—41no—
479C3×C4—42no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—61no—
483C3×C4—61no—
484C3×C4—62no—
485C3×C4—81no—
486C3×C4—121no—
487C3×C4—122no—
488C3×C4D3×Q1612yes—
489C3×C4C2×#21612yes—
490C3×C4C2×#23511yescharacteristic
491C3×C4C2×#23511yescharacteristic
492C3×C4C2×#23711yescharacteristic
493C3×C4D3×#4111yescharacteristic
494Dic3—21no—
495Dic3—22no—
496Dic3—21no—
497Dic3—41no—
498Dic3—42no—
499Dic3—122no—
500Dic3—122no—
501Dic3—242no—
502Dic3C2×#21612yes—
503C32#310411yescharacteristic, complemented, Sylow
504C23—31no—
505Q8—21no—
506Q8—32no—
507Q8—64no—
508Q8—61no—
509Q8—62no—
510Q8—62no—
511Q8—362no—
512Q8#379512yes—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—31no—
516C2×C4—34no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—64no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—62no—
525C2×C4—121no—
526C2×C4—122no—
527C2×C4—182no—
528C2×C4D3×#6711yescharacteristic
529C2×C4D3×#6711yescharacteristic
530C2×C4C22×D3211yescharacteristic
531C8—62no—
532C8—182no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—62no—
537C2×C3#560611yescharacteristic
538C2×C3C2×D3×Q1611yescharacteristic
539C2×C3#577711yescharacteristic
540C2×C3#579111yescharacteristic
541C2×C3C22×#21611yescharacteristic
542C2×C3#582211yescharacteristic
543D3—22no—
544C22—32no—
545C22—61no—
546C22—61no—
547C22C2×D3×#6711yescharacteristic
548C4—22no—
549C4—21no—
550C4—32no—
551C4—41no—
552C4—61no—
553C4—62no—
554C4—61no—
555C4—122no—
556C4—121no—
557C4—362no—
558C4D3×#21612yes—
559C4C2×#379511yescharacteristic
560C4D3×#23511yescharacteristic
561C3—21no—
562C3#8045611yescharacteristic, complemented
563C3#8244711yescharacteristic, complemented
564C2—62no—
565C2#1059489211yescharacteristic
566C2C2×D3×#21611yescharacteristic
567C2#1059547011yescharacteristic
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. #10592720C2semidirect
4. C3×#5031C2semidirect
6. Dic3×#216C2semidirect
8. #10590476C2semidirect
9. #10590384C2semidirect
10. #10590283C2semidirect
55. #5031D3semidirect
196. C3×C4×D3Q16semidirect
404. C4×D3#216semidirect
503. C32#3104semidirect
562. C3#80456semidirect
563. 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
#105927202
C3×#50312
#105915942
Dic3×#2162
#105905172
#105904762
#105903842
#105902832
#105902482
#824473
#804563