Finite Group Databasebeta

← #11870817

Subgroups — #11870817

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3797C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4C3×#4850C211yesmaximal, characteristic, complemented
5C3×#4849C211yesmaximal, characteristic, complemented
6#10590950C212yesmaximal
7#10590818C212yesmaximal, complemented
8#10590790C212yesmaximal, complemented
9#10590689C212yesmaximal
10#10590384C211yesmaximal, characteristic, complemented
11#10590310C211yesmaximal, characteristic, complemented
12#81092—31nomaximal
13#80456—31nomaximal
14C2×#3797C2211yescharacteristic
15C42×C3⋊D3C2211yescharacteristic
16C2×C3×Dic12C2212yes—
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21C4×#627—21no—
22#63900C2211yescharacteristic
23#63883—21no—
24C4×#624—21no—
25#63872—21no—
26#63871—21no—
27#63871C2212yes—
28#63849—21no—
29#63843—21no—
30#63843C2211yescharacteristic
31#63843C2212yes—
32#63843C2211yescharacteristic
33#63838—21no—
34C2×#3718C2212yes—
35C32×C4⋊C8C2211yescharacteristic
36#63647C2212yes—
37C8×C3⋊Dic3C2212yes—
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C3×#818C2212yes—
40C3×#816C2212yes—
41C3×#816C2212yes—
42#63576C2212yes—
43#63565C2212yes—
44#63565C2212yes—
45#5728—31no—
46#5728—31no—
47C4×D3×Q8—31no—
48C4×D3×Q8—31no—
49C3×#477—31no—
50C3×#462—31no—
51#5186—32no—
52Dic3×Q16—32no—
53#5091—31no—
54#5090—31no—
55#5031—31no—
56#5021—31no—
57#4884—32no—
58#4873—32no—
59#4850D311yescharacteristic, complemented
60#4849D311yescharacteristic, complemented
61#4833—31no—
62#4833—31no—
63#4833—61no—
64#4811—32no—
65#4809—32no—
66#4790—32no—
67#4790—32no—
68C2×C4×C3⋊D3D411yescharacteristic
69C2×C4×C3⋊D3D411yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C3×Dic6—21no—
72C2×C3×Dic6C2312yes—
73C2×C3×Dic6C2311yescharacteristic
74C2×C3×Dic6C2311yescharacteristic
75C2×#627—21no—
76C2×#624—21no—
77C2×#624—21no—
78#3797—22no—
79#3797—22no—
80C2×C32×C8C2312yes—
81C32×C42C2311yescharacteristic
82C4×C3⋊Dic3D411yescharacteristic
83C4×C3⋊Dic3D411yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3—21no—
96C3×Dic12—24no—
97#3724—21no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100Dic3⋊Dic3—21no—
101Dic3⋊Dic3—21no—
102#3722—22no—
103Dic32—21no—
104Dic32—21no—
105Dic32—22no—
106#3718—24no—
107#3104—91noSylow
108C2×D3×Q8—31no—
109C2×D3×Q8—31no—
110C2×C3×Q16—32no—
111C3×C4⋊Q8—31no—
112C3×C4⋊Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×Q8—31no—
115#946—32no—
116#946—61no—
117Q8×Dic3—31no—
118Q8×Dic3—32no—
119Q8×Dic3—31no—
120Q8×Dic3—61no—
121C2×#216—32no—
122C2×#216—32no—
123C2×Dic12C2×D312yes—
124#897—32no—
125#897—61no—
126#892—61no—
127#892—61no—
128D3×C4⋊C4—31no—
129D3×C4⋊C4—31no—
130D3×C4⋊C4—61no—
131D3×C4⋊C4—61no—
132#890—61no—
133#890—61no—
134#887—31no—
135#887—32no—
136#887—31no—
137#887—61no—
138#887—61no—
139#887—61no—
140C42×D3—31no—
141C42×D3—31no—
142C42×D3—61no—
143C42×D3—61no—
144C42×D3—61no—
145#869C2×D311yescharacteristic
146#869C2×D311yescharacteristic
147C4×Dic6—61no—
148C4×Dic6—61no—
149C4×Dic6C2×D311yescharacteristic
150C4×Dic6C2×D311yescharacteristic
151C3×#107—32no—
152C3×C4⋊C8—21no—
153C3×C4⋊C8C2×D311yescharacteristic
154C3×C4⋊C8C2×D311yescharacteristic
155C3×#103—32no—
156C3×#103—32no—
157#835—32no—
158#835—32no—
159(C2×D3)⋊C8—32no—
160(C2×D3)⋊C8—32no—
161(C2×D3)⋊C8—62no—
162#818C2×D312yes—
163#816C2×D312yes—
164#816C2×D312yes—
165C8×Dic3—32no—
166C8×Dic3—32no—
167C8×Dic3—62no—
168#810—32no—
169#810—32no—
170#807—32no—
171#807—32no—
172C4⋊(C3⋊C8)—31no—
173C4⋊(C3⋊C8)—31no—
174C4⋊(C3⋊C8)—61no—
175C22×C3⋊D3C2×D411yescharacteristic
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2411yescharacteristic
179C2×C3⋊Dic3C2×D411yescharacteristic
180C2×C3⋊Dic3C2×D411yescharacteristic
181C2×C3⋊Dic3C2×D411yescharacteristic
182C4×C3⋊D3—21no—
183C4×C3⋊D3—21no—
184C4×C3⋊D3—41no—
185C4×C3⋊D3Q1614yescomplemented
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C3×Dic6—21no—
193C3×Dic6—21no—
194C3×Dic6—22no—
195C3×Dic6—22no—
196C3×Dic6—42no—
197C3×Dic6#4112yes—
198C3×Dic6#4112yes—
199#627—24no—
200#624—24no—
201#624—42no—
202C32×C8—22no—
203C3⋊(C3⋊C8)—22no—
204#533—91no—
205C2×C4×Q8—91no—
206#484—92no—
207#477—31no—
208#477—91no—
209#462—31no—
210#462—91no—
211#451—92no—
212C4×Q16—92no—
213C4×Q16—92no—
214#431—91no—
215C2×C3×Q8—31no—
216C2×C3×Q8—31no—
217C2×C3×Q8—32no—
218C2×C3×Q8—61no—
219D3×Q8—62no—
220D3×Q8—62no—
221D3×Q8—62no—
222D3×Q8—62no—
223C2×C4×D3—31no—
224C2×C4×D3—31no—
225C2×C4×D3—31no—
226C2×C4×D3—31no—
227C2×C4×D3—31no—
228C2×C4×D3—31no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×Dic6—21no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6C22×D312yes—
240C2×Dic6C22×D311yescharacteristic
241C2×Dic6C22×D311yescharacteristic
242C3×Q16—64no—
243C2×C3×C8—22no—
244C2×C3×C8C22×D312yes—
245C2×C3×C8C22×D312yes—
246C3×C4⋊C4—31no—
247C3×C4⋊C4—32no—
248C3×C4⋊C4—31no—
249C3×C4⋊C4—61no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4—61no—
252C3×C4⋊C4—61no—
253C3×C4⋊C4—61no—
254C3×C42—21no—
255C3×C42—61no—
256C3×C42—61no—
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259#216—64no—
260#216—64no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3—21no—
264C4⋊Dic3—21no—
265C4⋊Dic3—21no—
266C4⋊Dic3—61no—
267C4⋊Dic3—61no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272C4⋊Dic3C22×D311yescharacteristic
273Dic3⋊C4—21no—
274Dic3⋊C4—21no—
275Dic3⋊C4—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281C4×Dic3—21no—
282C4×Dic3—21no—
283C4×Dic3—31no—
284C4×Dic3—31no—
285C4×Dic3—31no—
286C4×Dic3—31no—
287C4×Dic3—31no—
288C4×Dic3—31no—
289C4×Dic3—61no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—61no—
295C4×Dic3—61no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—32no—
300C2×C3⋊C8—62no—
301Dic12—24no—
302C22×C32C22×D411yescharacteristic
303C2×C3⋊D3—21no—
304C2×C3⋊D3—21no—
305C2×C3⋊D3C2×Q1612yes—
306C32×C4—21no—
307C32×C4C2×Q1612yes—
308C32×C4C2×#4111yescharacteristic
309C32×C4C2×#4111yescharacteristic
310C3⋊Dic3—21no—
311C3⋊Dic3—21no—
312C3⋊Dic3C2×Q1612yes—
313C3×Dic3—22no—
314C3×Dic3—22no—
315C3×Dic3—42no—
316C3×Dic3—41no—
317C3×Dic3—41no—
318C3×Dic3—42no—
319C22×Q8—91no—
320C2×Q16—32no—
321C2×Q16—92no—
322C4⋊Q8—31no—
323C4⋊Q8—31no—
324#125—181no—
325C22⋊Q8—92no—
326C22⋊Q8—181no—
327C4×Q8—31no—
328C4×Q8—31no—
329C4×Q8—91no—
330C4×Q8—91no—
331C4×Q8—92no—
332C4×Q8—181no—
333C4×Q8—181no—
334C4×Q8—181no—
335#117—181no—
336C2×C4⋊C4—91no—
337C2×C4⋊C4—181no—
338C2×C42—91no—
339C2×C42—181no—
340#107—32no—
341#107—92no—
342C4⋊C8—91no—
343C4⋊C8D3211yescharacteristic
344#103—32no—
345#103—32no—
346#103—92no—
347#103—92no—
348C22⋊C8—92no—
349C4×C8—92no—
350C22×D3—31no—
351C22×D3—31no—
352C22×D3—61no—
353C3×Q8—32no—
354C3×Q8—32no—
355C3×Q8—61no—
356C3×Q8—61no—
357C3×Q8—62no—
358C3×Q8—62no—
359C3×Q8—122no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D411yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D311yescharacteristic
375C2×Dic3—21no—
376C2×Dic3—21no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—31no—
384C2×Dic3—31no—
385C2×Dic3—31no—
386C2×Dic3—31no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C4×D3—34no—
391C4×D3—34no—
392C4×D3—64no—
393C4×D3—64no—
394C4×D3—64no—
395C4×D3—61no—
396C4×D3—61no—
397C4×D3—61no—
398C4×D3—61no—
399C4×D3—121no—
400C4×D3—121no—
401C4×D3—122no—
402C4×D3—122no—
403C4×D3—121no—
404C4×D3—121no—
405C4×D3—122no—
406Dic6—21no—
407Dic6—21no—
408Dic6—22no—
409Dic6—22no—
410Dic6—42no—
411Dic6—64no—
412Dic6—64no—
413Dic6#23712yes—
414Dic6#23912yes—
415C3×C8—22no—
416C3×C8—22no—
417C3×C8—42no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C3⋊C8—122no—
421C2×C32#52511yescharacteristic
422C2×C32C22×Q1611yescharacteristic
423C2×C32#57511yescharacteristic
424C3⋊D3—22no—
425C2×Q8—31no—
426C2×Q8—31no—
427C2×Q8—32no—
428C2×Q8—61no—
429C2×Q8—181no—
430C2×Q8—182no—
431C2×Q8—182no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—181no—
436C22×C4—181no—
437Q16—64no—
438Q16—184no—
439C2×C8—92no—
440C2×C8C2×D3212yes—
441C4⋊C4—31no—
442C4⋊C4—32no—
443C4⋊C4—31no—
444C4⋊C4—61no—
445C4⋊C4—61no—
446C4⋊C4—61no—
447C4⋊C4—61no—
448C4⋊C4—61no—
449C4⋊C4—181no—
450C4⋊C4—181no—
451C4⋊C4—181no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C22⋊C4—182no—
455C42—61no—
456C42—61no—
457C42—91no—
458C42—91no—
459C42—91no—
460C42—181no—
461C42—181no—
462C42—182no—
463C42C2×D3211yescharacteristic
464C22×C3—21no—
465C22×C3C2×D3×D411yescharacteristic
466C22×C3C2×D3×D411yescharacteristic
467C2×D3—32no—
468C2×D3—32no—
469C2×D3—62no—
470C2×D3—61no—
471C2×D3—61no—
472C2×D3—61no—
473C2×D3—61no—
474C2×D3—121no—
475C2×D3—121no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—21no—
479C3×C4—22no—
480C3×C4—21no—
481C3×C4—41no—
482C3×C4—62no—
483C3×C4—62no—
484C3×C4—121no—
485C3×C4—121no—
486C3×C4—122no—
487C3×C4—122no—
488C3×C4D3×Q1612yes—
489C3×C4D3×Q1612yes—
490C3×C4C2×#23711yescharacteristic
491C3×C4C2×#23911yescharacteristic
492C3×C4D3×#4111yescharacteristic
493C3×C4D3×#4111yescharacteristic
494Dic3—22no—
495Dic3—22no—
496Dic3—32no—
497Dic3—32no—
498Dic3—42no—
499Dic3—41no—
500Dic3—41no—
501Dic3—42no—
502Dic3—62no—
503Dic3—62no—
504Dic3—61no—
505Dic3—61no—
506Dic3—61no—
507Dic3—61no—
508Dic3—121no—
509C32#310411yescharacteristic, complemented, Sylow
510C23—91no—
511Q8—32no—
512Q8—32no—
513Q8—61no—
514Q8—61no—
515Q8—62no—
516Q8—62no—
517Q8—122no—
518Q8—184no—
519C2×C4—61no—
520C2×C4—61no—
521C2×C4—61no—
522C2×C4—61no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—91no—
526C2×C4—94no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—184no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—361no—
533C2×C4—362no—
534C2×C4#380211yescharacteristic
535C2×C4#380211yescharacteristic
536C2×C4C22×D3211yescharacteristic
537C8—22no—
538C8—182no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3#560611yescharacteristic
543C2×C3#562711yescharacteristic
544C2×C3C2×D3×Q1611yescharacteristic
545C2×C3C2×D3×Q1611yescharacteristic
546C2×C3#577311yescharacteristic
547C2×C3#577711yescharacteristic
548D3—62no—
549D3—62no—
550D3—122no—
551C22—92no—
552C22—181no—
553C22—181no—
554C22C2×#380211yescharacteristic
555C4—21no—
556C4—62no—
557C4—62no—
558C4—92no—
559C4—122no—
560C4—121no—
561C4—121no—
562C4—122no—
563C4—181no—
564C4—181no—
565C4#6380212yes—
566C4D3×#23711yescharacteristic
567C4D3×#23911yescharacteristic
568C3—21no—
569C3#8045611yescharacteristic, complemented
570C3#8109211yescharacteristic, complemented
571C2—182no—
572C2#1059463211yescharacteristic
573C2C2×#6380211yescharacteristic
574C2#1059471811yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C8D32
hypocenterC32#3104
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4850C2semidirect
5. C3×#4849C2semidirect
7. #10590818C2semidirect
8. #10590790C2semidirect
10. #10590384C2semidirect
11. #10590310C2semidirect
59. #4850D3semidirect
60. #4849D3semidirect
185. C4×C3⋊D3Q16semidirect
509. C32#3104semidirect
569. C3#80456semidirect
570. C3#81092semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
#105938662
#105925322
C3×#48502
C3×#48492
#105909502
#105908182
#105907902
#105906892
#105903842
#105903102
#810923
#804563