Finite Group Databasebeta

← #11786839

Subgroups — #11786839

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic3C211yesmaximal, characteristic
2C2×#63659C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591352C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6#10589163C211yesmaximal, characteristic, complemented
7#10589155C211yesmaximal, characteristic, complemented
8#71606—31nomaximal
9#70168—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3×Dic3—21no—
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#217—21no—
15C3×D4×Dic3—22no—
16C3×D4×Dic3—22no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22#63659—22no—
23C3×#832C414yescomplemented
24#63579—21no—
25#63575—22no—
26C2×C3×C4×D4—31no—
27C2×D4×Dic3D311yescharacteristic
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#832—31no—
31C2×#832—61no—
32C2×#832D311yescharacteristic
33C2×#818—31no—
34#4984—31no—
35C2×#807—31no—
36#4928—31no—
37#4550—31no—
38#4529—31no—
39#4529—31no—
40#4524—31no—
41C24×C32—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C412yes—
46C2×C32×D4D412yes—
47C2×C32×D4Q812yes—
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C22×C3×Dic3—24no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—42no—
54C22×C3×Dic3—42no—
55C22×C3×Dic3D411yescharacteristic
56C22×C3×Dic3D411yescharacteristic
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C3×#217—24no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yescomplemented
66C3×C4⋊Dic3D412yes—
67C3×C4×Dic3—21no—
68C3×C4×Dic3—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8C2×C412yescomplemented
72Dic3⋊Dic3—42no—
73#1862—91noSylow
74C22×C3×D4—21no—
75C22×C3×D4C2×D311yescharacteristic
76C22×C3×D4C2×D311yescharacteristic
77C23×C3×C4—61no—
78C23×Dic3—21no—
79C22×C3×C8—31no—
80C3×C4×D4—62no—
81C3×C4×D4—62no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C22⋊C4—61no—
85C2×C3×C42—31no—
86C2×#217—21no—
87D4×Dic3—22no—
88D4×Dic3—22no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—61no—
96C2×C4×Dic3C2×D311yescharacteristic
97C22×C3⋊C8—31no—
98C22×C3⋊C8—31no—
99C22×C3⋊C8—61no—
100C22×C3⋊C8C2×D311yescharacteristic
101C3×#102—34no—
102#832—64no—
103#832—62no—
104#832—62no—
105#832Dic314yescomplemented
106C3⋊#95—61no—
107C3⋊#95—61no—
108#818—62no—
109#807—62no—
110C23×C32—22no—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32—41no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32—41no—
117C23×C32C2×D411yescharacteristic
118C32×D4—22no—
119C32×D4—22no—
120C32×D4—22no—
121C32×D4C4⋊C414yescomplemented
122C2×C32×C4C22×C411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×Q811yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—41no—
130C2×C3⋊Dic3—41no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—22no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—48no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3D812yes—
144C3⋊(C3⋊C8)—41no—
145C3×C3⋊C8—22no—
146C2×C4×D4—31no—
147C2×#107—91no—
148C2×#102—31no—
149C2×#102—91no—
150#389—91no—
151#340—91no—
152#336—91no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—41no—
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×C3×D4—21no—
160C2×C3×D4—21no—
161C2×C3×D4—21no—
162C2×C3×D4—22no—
163C2×C3×D4—22no—
164C2×C3×D4—22no—
165C2×C3×D4—41no—
166C2×C3×D4—41no—
167C2×C3×D4—41no—
168C2×C3×D4Dic612yes—
169C2×C3×D4Dic612yes—
170C2×C3×D4C4×D312yes—
171C2×C3×D4D1212yes—
172C2×C3×D4C2×Dic312yes—
173C2×C3×D4#6712yes—
174C22×C3×C4—21no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—64no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4—122no—
181C22×C3×C4—122no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—24no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—42no—
188C22×Dic3—42no—
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—121no—
192C22×Dic3#6711yescharacteristic
193C22×Dic3#6711yescharacteristic
194C2×C3×C8—32no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C3×C4⋊C4—32no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C22⋊C4—64no—
202C3×C42—61no—
203C3×C42—61no—
204#217—24no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—62no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4⋊Dic3—122no—
214C4⋊Dic3C2×Dic312yescomplemented
215C4⋊Dic3#6712yes—
216Dic3⋊C4—122no—
217C4×Dic3—21no—
218C4×Dic3—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8C2×Dic312yescomplemented
231C22×C32—24no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—42no—
236C22×C32—42no—
237C22×C32—42no—
238C22×C32C4×D411yescharacteristic
239C22×C32#12011yescharacteristic
240C22×C32C22⋊Q811yescharacteristic
241C22×C32C2×D811yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C22×C32#13711yescharacteristic
245C32×C4C2×C4⋊C411yescharacteristic
246C32×C4C4×D411yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C32×C4#12311yescharacteristic
249C3⋊Dic3—81no—
250C3×Dic3—22no—
251C3×Dic3—42no—
252C3×Dic3—42no—
253C3×Dic3—41no—
254C22×D4D3211yescharacteristic
255C23×C4—61no—
256C22×C8—31no—
257C22×C8—91no—
258C4×D4—62no—
259C4×D4—62no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—181no—
264C2×C22⋊C4—61no—
265C2×C42—31no—
266#107—182no—
267#102—34no—
268#102—182no—
269#95—181no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—22no—
273C23×C3—22no—
274C23×C3—22no—
275C23×C3—22no—
276C23×C3—21no—
277C23×C3—42no—
278C23×C3—42no—
279C23×C3—42no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3—41no—
283C23×C3—41no—
284C23×C3—41no—
285C23×C3—41no—
286C23×C3—41no—
287C23×C3—41no—
288C23×C3—81no—
289C23×C3—81no—
290C23×C3—81no—
291C23×C3—81no—
292C23×C3D3×D411yescharacteristic
293C23×C3C2×#6711yescharacteristic
294C3×D4—22no—
295C3×D4—22no—
296C3×D4—22no—
297C3×D4—22no—
298C3×D4—22no—
299C3×D4—22no—
300C3×D4—24no—
301C3×D4—42no—
302C3×D4—42no—
303C3×D4—42no—
304C3×D4Dic3⋊C414yescomplemented
305C3×D4C4⋊Dic314yescomplemented
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—61no—
316C2×C3×C4—62no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—62no—
320C2×C3×C4—128no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4C2×Dic611yescharacteristic
326C2×C3×C4C2×Dic611yescharacteristic
327C2×C3×C4C2×C4×D311yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4C22×Dic311yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—22no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—48no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—41no—
348C2×Dic3—41no—
349C2×Dic3—122no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—241no—
357C2×Dic3—241no—
358C2×Dic3#21312yes—
359C3×C8—62no—
360C3⋊C8—22no—
361C3⋊C8—122no—
362C3⋊C8—121no—
363C3⋊C8—121no—
364C2×C32—44no—
365C2×C32#38511yescharacteristic
366C2×C32C4×D811yescharacteristic
367C2×C32#44011yescharacteristic
368C2×C32#44711yescharacteristic
369C2×C32#45211yescharacteristic
370C2×C32#47411yescharacteristic
371C2×C32#47811yescharacteristic
372C24—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4D3×Dic312yes—
377C2×D4#62612yes—
378C2×D4#62712yes—
379C22×C4—31no—
380C22×C4—31no—
381C22×C4—64no—
382C22×C4—61no—
383C22×C4—61no—
384C22×C4—122no—
385C22×C4—122no—
386C22×C4—181no—
387C22×C4C2×D3211yescharacteristic
388C2×C8—32no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—181no—
392C2×C8—181no—
393C2×C8—181no—
394C4⋊C4—32no—
395C4⋊C4—32no—
396C4⋊C4—61no—
397C4⋊C4—61no—
398C4⋊C4—181no—
399C4⋊C4—181no—
400C4⋊C4—362no—
401C22⋊C4—64no—
402C42—61no—
403C42—61no—
404C22×C3—24no—
405C22×C3—24no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—44no—
414C22×C3—42no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3—42no—
418C22×C3—42no—
419C22×C3—42no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—82no—
427C22×C3—82no—
428C22×C3—82no—
429C22×C3—82no—
430C22×C3—82no—
431C22×C3—82no—
432C22×C3#87811yescharacteristic
433C22×C3#88211yescharacteristic
434C22×C3D3×D811yescharacteristic
435C22×C3#91211yescharacteristic
436C22×C3#91411yescharacteristic
437C22×C3#91511yescharacteristic
438C22×C3#92411yescharacteristic
439C22×C3C4×#6711yescharacteristic
440C22×C3C2×#21311yescharacteristic
441C22×C3#93211yescharacteristic
442C22×C3D4×Dic311yescharacteristic
443C22×C3#95011yescharacteristic
444C22×C3#95111yescharacteristic
445C22×C3#95311yescharacteristic
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—62no—
451C3×C4—122no—
452C3×C4—122no—
453C3×C4—121no—
454C3×C4#87811yescharacteristic
455C3×C4#88611yescharacteristic
456C3×C4C2×Dic3⋊C411yescharacteristic
457C3×C4#92411yescharacteristic
458C3×C4C2×C4⋊Dic311yescharacteristic
459C3×C4C4×#6711yescharacteristic
460C3×C4#92911yescharacteristic
461C3×C4D4×Dic311yescharacteristic
462Dic3—22no—
463Dic3—42no—
464Dic3—42no—
465Dic3—41no—
466Dic3—242no—
467Dic3—241no—
468Dic3—241no—
469C32#186211yescharacteristic, complemented, Sylow
470C23—22no—
471C23—22no—
472C23—22no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23D3×#6711yescharacteristic
478D4—22no—
479D4—22no—
480D4—22no—
481D4Dic3⋊Dic314yescomplemented
482C2×C4—32no—
483C2×C4—61no—
484C2×C4—61no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—128no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—361no—
496C2×C4—361no—
497C2×C4—361no—
498C2×C4C2×D3×Dic311yescharacteristic
499C2×C4#380411yescharacteristic
500C2×C4#380411yescharacteristic
501C2×C4C2×#62611yescharacteristic
502C2×C4C2×#62711yescharacteristic
503C2×C4D3×#6711yescharacteristic
504C8—62no—
505C8—361no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—44no—
514C2×C3—44no—
515C2×C3—84no—
516C2×C3#475911yescharacteristic
517C2×C3#476611yescharacteristic
518C2×C3#477311yescharacteristic
519C2×C3#478311yescharacteristic
520C2×C3#495011yescharacteristic
521C2×C3#500711yescharacteristic
522C2×C3#500911yescharacteristic
523C2×C3C4×#21311yescharacteristic
524C2×C3#501811yescharacteristic
525C2×C3Dic3×D811yescharacteristic
526C2×C3#516411yescharacteristic
527C2×C3#521011yescharacteristic
528C2×C3#521711yescharacteristic
529C2×C3#523911yescharacteristic
530C22—24no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22D3×#21311yescharacteristic
538C22#6392911yescharacteristic
539C22#6393311yescharacteristic
540C22#6393411yescharacteristic
541C22#6396411yescharacteristic
542C22Dic3×#6711yescharacteristic
543C22#6397711yescharacteristic
544C4—62no—
545C4—122no—
546C4—122no—
547C4—121no—
548C4—721no—
549C4#6396411yescharacteristic
550C4C2×Dic3⋊Dic311yescharacteristic
551C4#6396611yescharacteristic
552C4Dic3×#6711yescharacteristic
553C3—21no—
554C3#7016811yescharacteristic, complemented
555C3#7160611yescharacteristic, complemented
556C2—44no—
557C2#1059141011yescharacteristic
558C2#1059141111yescharacteristic
559C2Dic3×#21311yescharacteristic
560C2#1059144011yescharacteristic
561C2#1059144811yescharacteristic
562C2#1059146311yescharacteristic
563C2#1059171811yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC22×C32×D4C22
socleC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1862
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #10591352C2semidirect
5. C2×#63575C2semidirect
6. #10589163C2semidirect
7. #10589155C2semidirect
23. C3×#832C4semidirect
65. C3×C4⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
105. #832Dic3semidirect
121. C32×D4C4⋊C4semidirect
214. C4⋊Dic3C2×Dic3semidirect
230. C2×C3⋊C8C2×Dic3semidirect
304. C3×D4Dic3⋊C4semidirect
305. C3×D4C4⋊Dic3semidirect
469. C32#1862semidirect
481. D4Dic3⋊Dic3semidirect
554. C3#70168semidirect
555. C3#71606semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic32
C2×#636592
C2×C3×#8322
#105913522
C2×#635752
#105891632
#105891552
#716063
#701683