Finite Group Databasebeta

← #11870819

Subgroups — #11870819

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×#5728C211yesmaximal, characteristic
2C4×D3×Dic6C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic, complemented
4C3×#5091C211yesmaximal, characteristic, complemented
5#10590604C212yesmaximal
6#10590481C212yesmaximal, complemented
7#10590476C212yesmaximal, complemented
8#10590440C212yesmaximal
9#10590388C211yesmaximal, characteristic, complemented
10#10590384C211yesmaximal, characteristic, complemented
11#10590248C211yesmaximal, characteristic
12#83368—31nomaximal
13#81092—31nomaximal
14C2×D3×Dic6C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#946—21no—
18C3×Q8×Dic3—21no—
19C3×#897C2212yes—
20C3×#892—21no—
21C3×#890—21no—
22C3×#887C2212yes—
23C3×C42×D3C2211yescharacteristic
24C3×#869C2211yescharacteristic
25C3×C4×Dic6C2211yescharacteristic
26C4×#627—21no—
27D3×C4⋊Dic3C2211yescharacteristic
28D3×Dic3⋊C4—21no—
29C4×D3×Dic3—21no—
30#63844C2211yescharacteristic
31Dic3×Dic6C2211yescharacteristic
32#63837—21no—
33C2×#3719C2212yes—
34C2×#3718C2212yes—
35#63637C2212yes—
36#63634C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#810C2212yes—
39C3×#807C2212yes—
40C3×C4⋊(C3⋊C8)C2211yescharacteristic
41#63566C2212yes—
42#63565C2212yes—
43(C2×D3)⋊(C3⋊C8)C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#533—31no—
46#5728D311yescharacteristic
47C4×D3×Q8—31no—
48C2×C4×Dic6—31no—
49C3×#477—31no—
50#5091—31no—
51#5091—31no—
52#5091—61no—
53#5091D311yescharacteristic, complemented
54#5090—31no—
55#5090—31no—
56#5050—32no—
57#5044—32no—
58#5031—31no—
59C4×#216—32no—
60C4×#216—32no—
61#4925—31no—
62#4884—32no—
63#4873—32no—
64#4849—31no—
65#4833—31no—
66#4809—32no—
67#4790—32no—
68C2×C32×Q8—21no—
69C2×#634C2311yescharacteristic
70C2×C3×C4×D3D411yescharacteristic
71C2×C3×C4×D3D411yescharacteristic
72C2×C3×C4×D3C2311yescharacteristic
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×D3×Dic3—21no—
77C2×D3×Dic3—21no—
78D3×Dic6—22no—
79D3×Dic6—22no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3—21no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3—22no—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3D411yescharacteristic
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3C2311yescharacteristic
99C2×C3×C3⋊C8C2312yes—
100#3724—21no—
101Dic3⋊Dic3—21no—
102Dic3⋊Dic3—21no—
103Dic32—21no—
104Dic32—21no—
105#3719—24no—
106#3718—24no—
107#3104—91noSylow
108C2×D3×Q8—31no—
109C22×Dic6—31no—
110C3×C4⋊Q8—21no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8C2×D311yescharacteristic
113C3×C4⋊Q8C2×D311yescharacteristic
114C3×#125—61no—
115C3×C22⋊Q8—32no—
116C3×C22⋊Q8—61no—
117C3×C4×Q8—32no—
118C3×C4×Q8—31no—
119C3×C4×Q8—61no—
120C3×#117—61no—
121C2×C3×C42—31no—
122#946—21no—
123Q8×Dic3—21no—
124Q8×Dic3—31no—
125C2×#216—32no—
126C2×#216—32no—
127C2×#216—32no—
128C2×C4⋊Dic3—31no—
129C2×Dic3⋊C4—61no—
130C2×C4×Dic3—61no—
131C2×Dic12—32no—
132#897C2×D312yes—
133#892—21no—
134D3×C4⋊C4—31no—
135D3×C4⋊C4—61no—
136#890—21no—
137#887—31no—
138#887—61no—
139#887C2×D312yes—
140C42×D3—61no—
141C42×D3C2×D311yescharacteristic
142#869C2×D311yescharacteristic
143C4×Dic6—31no—
144C4×Dic6—31no—
145C4×Dic6—31no—
146C4×Dic6—31no—
147C4×Dic6—61no—
148C4×Dic6—61no—
149C4×Dic6—61no—
150C4×Dic6—61no—
151C4×Dic6C2×D311yescharacteristic
152C3×#107—32no—
153C3×C4⋊C8—31no—
154C3×#103—32no—
155#835—32no—
156#835—32no—
157#830—32no—
158(C2×D3)⋊C8—32no—
159#816—32no—
160C8×Dic3—32no—
161#810—32no—
162#810—32no—
163#810—32no—
164#810—62no—
165#810C2×D312yes—
166#807—32no—
167#807—32no—
168#807—62no—
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—42no—
177C2×C32×C4—22no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181C2×C3⋊Dic3—21no—
182C2×C3⋊Dic3—21no—
183#634—21no—
184#634#4112yes—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D411yescharacteristic
189C2×C3×Dic3C2×D411yescharacteristic
190C2×C3×Dic3C2×D411yescharacteristic
191C3×C4×D3—21no—
192C3×C4×D3—21no—
193C3×C4×D3—41no—
194C3×C4×D3Q1614yescomplemented
195C3×Dic6—21no—
196C3×Dic6—22no—
197C3×Dic6—22no—
198C3×Dic6#4112yes—
199#627—24no—
200D3×Dic3—24no—
201D3×Dic3—42no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204#533—31no—
205C2×C4×Q8—91no—
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—21no—
217C2×C3×Q8—31no—
218C2×C3×Q8—32no—
219C2×C3×Q8—41no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×Dic3—61no—
224C22×Dic3—61no—
225D3×Q8—62no—
226D3×Q8—62no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3#6711yescharacteristic
230C2×C4×D3#6711yescharacteristic
231C2×C4×D3C22×D311yescharacteristic
232C2×Dic6—31no—
233C2×Dic6—31no—
234C2×Dic6—61no—
235C2×Dic6—62no—
236C2×Dic6—61no—
237C2×Dic6—61no—
238C2×Dic6—62no—
239C2×Dic6C22×D312yes—
240C2×Dic6C22×D311yescharacteristic
241C2×C3×C8—32no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—41no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4C22×D312yes—
253C3×C4⋊C4C22×D312yes—
254C3×C22⋊C4—62no—
255C3×C42—21no—
256C3×C42—31no—
257C3×C42—31no—
258C3×C42—31no—
259C3×C42—62no—
260C3×C42—61no—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D311yescharacteristic
263#216—64no—
264#216—64no—
265#216—64no—
266(C2×D3)⋊C4—22no—
267C4⋊Dic3—21no—
268C4⋊Dic3—21no—
269C4⋊Dic3—22no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D311yescharacteristic
276Dic3⋊C4—21no—
277Dic3⋊C4—22no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280Dic3⋊C4—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—121no—
285C4×Dic3—21no—
286C4×Dic3—22no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—121no—
294C4×Dic3#6711yescharacteristic
295C4×Dic3#6711yescharacteristic
296C4×Dic3C22×D311yescharacteristic
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8C22×D312yes—
301Dic12—64no—
302C22×C32C22×D411yescharacteristic
303C2×C3×D3—21no—
304C2×C3×D3—21no—
305C2×C3×D3C2×Q1612yes—
306C32×C4—21no—
307C32×C4—42no—
308C32×C4C2×Q1612yes—
309C32×C4C2×#4111yescharacteristic
310C32×C4C2×#4111yescharacteristic
311C3⋊Dic3—22no—
312C3⋊Dic3—41no—
313C3×Dic3—22no—
314C3×Dic3—21no—
315C3×Dic3—21no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3C2×Q1612yes—
319C22×Q8—91no—
320C2×Q16—92no—
321C2×Q16—92no—
322C4⋊Q8—31no—
323C4⋊Q8D3211yescharacteristic
324#125—61no—
325C22⋊Q8—32no—
326C22⋊Q8—61no—
327C4×Q8—32no—
328C4×Q8—31no—
329C4×Q8—61no—
330C4×Q8—91no—
331C4×Q8—91no—
332C4×Q8—91no—
333C4×Q8—181no—
334C4×Q8—181no—
335#117—61no—
336C2×C4⋊C4—91no—
337C2×C4⋊C4—181no—
338C2×C42—31no—
339C2×C42—181no—
340#107—32no—
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—32no—
353C3×Q8—42no—
354C3×Q8—42no—
355C3×Q8—61no—
356C3×Q8—62no—
357C3×Q8—62no—
358C3×Q8—82no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—31no—
365C2×C3×C4—34no—
366C2×C3×C4—31no—
367C2×C3×C4—31no—
368C2×C3×C4—42no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—121no—
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4C2×#6711yescharacteristic
378C2×C3×C4C2×#6711yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380C2×C3×C4C23×D311yescharacteristic
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—64no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—122no—
392C2×Dic3C2×#6711yescharacteristic
393C2×Dic3C2×#6711yescharacteristic
394C2×Dic3C2×#6711yescharacteristic
395C4×D3—21no—
396C4×D3—21no—
397C4×D3—41no—
398C4×D3—64no—
399C4×D3—122no—
400C4×D3#21614yescomplemented
401Dic6—21no—
402Dic6—22no—
403Dic6—22no—
404Dic6—32no—
405Dic6—32no—
406Dic6—62no—
407Dic6—64no—
408Dic6—64no—
409Dic6—61no—
410Dic6—61no—
411Dic6—121no—
412Dic6#23912yes—
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—21no—
423C2×Q8—31no—
424C2×Q8—32no—
425C2×Q8—91no—
426C2×Q8—181no—
427C2×Q8—182no—
428C2×Q8—182no—
429C22×C4—31no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—181no—
433C22×C4—181no—
434Q16—184no—
435Q16—184no—
436C2×C8—32no—
437C2×C8—92no—
438C4⋊C4—21no—
439C4⋊C4—31no—
440C4⋊C4—62no—
441C4⋊C4—62no—
442C4⋊C4—61no—
443C4⋊C4—61no—
444C4⋊C4—61no—
445C4⋊C4—91no—
446C4⋊C4—181no—
447C4⋊C4—181no—
448C4⋊C4—181no—
449C4⋊C4—181no—
450C4⋊C4C2×D3212yes—
451C22⋊C4—62no—
452C42—31no—
453C42—31no—
454C42—31no—
455C42—62no—
456C42—61no—
457C42—181no—
458C42—181no—
459C42—181no—
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—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—32no—
476C3×C4—41no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—61no—
480C3×C4—62no—
481C3×C4—61no—
482C3×C4—82no—
483C3×C4—121no—
484C3×C4—122no—
485C3×C4D3×Q1612yes—
486C3×C4C2×#21612yes—
487C3×C4C2×#23911yescharacteristic
488C3×C4D3×#4111yescharacteristic
489C3×C4D3×#4111yescharacteristic
490C3×C4D3×#4111yescharacteristic
491Dic3—21no—
492Dic3—21no—
493Dic3—22no—
494Dic3—41no—
495Dic3—42no—
496Dic3—62no—
497Dic3—62no—
498Dic3—122no—
499Dic3—121no—
500Dic3—121no—
501Dic3—241no—
502Dic3C2×#21612yes—
503C32#310411yescharacteristic, complemented, Sylow
504C23—31no—
505Q8—32no—
506Q8—42no—
507Q8—61no—
508Q8—62no—
509Q8—62no—
510Q8—92no—
511Q8—184no—
512Q8—181no—
513C2×C4—22no—
514C2×C4—31no—
515C2×C4—34no—
516C2×C4—31no—
517C2×C4—31no—
518C2×C4—61no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—62no—
523C2×C4—121no—
524C2×C4—184no—
525C2×C4—181no—
526C2×C4—181no—
527C2×C4—362no—
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#562711yescharacteristic
538C2×C3C2×D3×Q1611yescharacteristic
539C2×C3#577311yescharacteristic
540C2×C3C22×#21611yescharacteristic
541C2×C3#582211yescharacteristic
542C2×C3#582811yescharacteristic
543D3—22no—
544C22—32no—
545C22—61no—
546C22—61no—
547C22C2×D3×#6711yescharacteristic
548C4—21no—
549C4—32no—
550C4—42no—
551C4—61no—
552C4—61no—
553C4—62no—
554C4—121no—
555C4—122no—
556C4—182no—
557C4—361no—
558C4D3×#21612yes—
559C4D3×#23911yescharacteristic
560C4#6431911yescharacteristic
561C3—21no—
562C3#8109211yescharacteristic, complemented
563C3#8336811yescharacteristic, complemented
564C2—62no—
565C2#1059509511yescharacteristic
566C2C2×D3×#21611yescharacteristic
567C2#1059542411yescharacteristic
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. #10592790C2semidirect
4. C3×#5091C2semidirect
6. #10590481C2semidirect
7. #10590476C2semidirect
9. #10590388C2semidirect
10. #10590384C2semidirect
53. #5091D3semidirect
194. C3×C4×D3Q16semidirect
400. C4×D3#216semidirect
503. C32#3104semidirect
562. C3#81092semidirect
563. C3#83368semidirect

Maximal subgroups

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

subgroupindex
C3×#57282
C4×D3×Dic62
#105927902
C3×#50912
#105906042
#105904812
#105904762
#105904402
#105903882
#105903842
#105902482
#833683
#810923