Finite Group Databasebeta

← #11786840

Subgroups — #11786840

Order 1152.

937 conjugacy classes of subgroups.

The subgroup lattice has 581 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C3×#832C211yesmaximal, characteristic
3C2×C3×#832C211yesmaximal, characteristic
4#10591357C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70168—31nomaximal
9#70167—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3—21no—
12C2×#3757—21no—
13D4×C3⋊Dic3—22no—
14D4×C3⋊Dic3—22no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×Dic3⋊Dic3—21no—
22C3×#832—22no—
23C3×#832C414yescomplemented
24#63579—21no—
25#63575—22no—
26C2×D4×Dic3—31no—
27C2×D4×Dic3—31no—
28C2×D4×Dic3—61no—
29C2×C3×#102—31no—
30C2×C3×#102—31no—
31C2×#832D311yescharacteristic
32C2×#832D311yescharacteristic
33C2×#818—31no—
34#4984—31no—
35#4972—31no—
36C2×#807—31no—
37#4551—31no—
38#4550—31no—
39#4550—31no—
40#4529—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—24no—
50C22×C3⋊Dic3—21no—
51C22×C3⋊Dic3—42no—
52C22×C3⋊Dic3—42no—
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57#3757—24no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)D412yes—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yescomplemented
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—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×Dic3—61no—
78C23×Dic3—61no—
79C23×Dic3—62no—
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×#217—61no—
85C2×#217—61no—
86C2×#217—62no—
87D4×Dic3—62no—
88D4×Dic3—62no—
89D4×Dic3—64no—
90D4×Dic3—64no—
91D4×Dic3—62no—
92D4×Dic3—62no—
93C2×C4⋊Dic3—31no—
94C2×C4⋊Dic3—31no—
95C2×C4⋊Dic3—61no—
96C2×C4⋊Dic3—61no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×Dic3⋊C4—61no—
100C2×C4×Dic3—31no—
101C2×C4×Dic3—31no—
102C2×C4×Dic3—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104C22×C3⋊C8C2×D311yescharacteristic
105C3×#102—34no—
106C3×#102—62no—
107#832—22no—
108#832Dic314yescomplemented
109C3⋊#95—61no—
110C3⋊#95—61no—
111#818—62no—
112#807—62no—
113C23×C32—22no—
114C23×C32—22no—
115C23×C32—22no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32—41no—
119C23×C32—41no—
120C23×C32C2×D411yescharacteristic
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—22no—
124C32×D4C4⋊C414yescomplemented
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×Q811yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—48no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C2×C3⋊Dic3D812yes—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—41no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C3×C3⋊C8—22no—
148C3×C3⋊C8—41no—
149C2×C4×D4—91no—
150C2×#107—91no—
151C2×#102—31no—
152C2×#102—31no—
153#389—91no—
154#340—91no—
155#336—91no—
156C24×C3—22no—
157C24×C3—21no—
158C24×C3—21no—
159C2×C3×D4—22no—
160C2×C3×D4—22no—
161C2×C3×D4—22no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4—22no—
171C2×C3×D4Dic612yes—
172C2×C3×D4Dic612yes—
173C2×C3×D4C4×D312yes—
174C2×C3×D4D1212yes—
175C2×C3×D4C2×Dic312yes—
176C2×C3×D4#6712yes—
177C22×C3×C4—21no—
178C22×C3×C4—61no—
179C22×C3×C4—61no—
180C22×C3×C4C22×D311yescharacteristic
181C22×C3×C4C22×D311yescharacteristic
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—31no—
185C22×Dic3—31no—
186C22×Dic3—31no—
187C22×Dic3—31no—
188C22×Dic3—61no—
189C22×Dic3—61no—
190C22×Dic3—62no—
191C22×Dic3—68no—
192C22×Dic3—64no—
193C22×Dic3—64no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—122no—
197C22×Dic3—122no—
198C22×Dic3—124no—
199C22×Dic3—124no—
200C22×Dic3—122no—
201C22×Dic3—122no—
202C2×C3×C8—32no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C2×C3×C8—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212#217—68no—
213#217—64no—
214#217—64no—
215C4⋊Dic3—21no—
216C4⋊Dic3—21no—
217C4⋊Dic3—21no—
218C4⋊Dic3—32no—
219C4⋊Dic3—32no—
220C4⋊Dic3—62no—
221C4⋊Dic3—62no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—122no—
225C4⋊Dic3C2×Dic312yescomplemented
226Dic3⋊C4—122no—
227C4×Dic3—62no—
228C4×Dic3—62no—
229C4×Dic3—61no—
230C4×Dic3—61no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—21no—
238C2×C3⋊C8C2×Dic312yescomplemented
239C22×C32—24no—
240C22×C32—42no—
241C22×C32—42no—
242C22×C32—42no—
243C22×C32—42no—
244C22×C32—42no—
245C22×C32—42no—
246C22×C32C4×D411yescharacteristic
247C22×C32#12011yescharacteristic
248C22×C32C22⋊Q811yescharacteristic
249C22×C32C2×D811yescharacteristic
250C22×C32#13511yescharacteristic
251C22×C32AGL(1,ℤ/8)11yescharacteristic
252C22×C32#13711yescharacteristic
253C32×C4C2×C4⋊C411yescharacteristic
254C32×C4C4×D411yescharacteristic
255C32×C4C22⋊Q811yescharacteristic
256C32×C4#12311yescharacteristic
257C3⋊Dic3—22no—
258C3⋊Dic3—42no—
259C3⋊Dic3—41no—
260C3×Dic3—42no—
261C3×Dic3—81no—
262C22×D4D3211yescharacteristic
263C23×C4—181no—
264C22×C8—31no—
265C22×C8—31no—
266C4×D4—182no—
267C4×D4—182no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—91no—
271C2×C4⋊C4—181no—
272C2×C22⋊C4—181no—
273C2×C42—91no—
274#107—182no—
275#102—34no—
276#102—62no—
277#95—181no—
278C23×C3—24no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—22no—
287C23×C3—21no—
288C23×C3—42no—
289C23×C3—42no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3—41no—
295C23×C3—41no—
296C23×C3—41no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3D3×D411yescharacteristic
301C23×C3D3×D411yescharacteristic
302C3×D4—24no—
303C3×D4—24no—
304C3×D4—24no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—22no—
310C3×D4—22no—
311C3×D4—24no—
312C3×D4Dic3⋊C414yescomplemented
313C3×D4C4⋊Dic314yescomplemented
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—21no—
320C2×C3×C4—62no—
321C2×C3×C4—121no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—121no—
325C2×C3×C4—121no—
326C2×C3×C4C2×Dic611yescharacteristic
327C2×C3×C4C2×Dic611yescharacteristic
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4#23711yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4C22×Dic311yescharacteristic
337C2×C3×C4C2×#6711yescharacteristic
338C2×Dic3—22no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—41no—
342C2×Dic3—41no—
343C2×Dic3—41no—
344C2×Dic3—41no—
345C2×Dic3—41no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—62no—
354C2×Dic3—64no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362C2×Dic3—62no—
363C2×Dic3—121no—
364C2×Dic3—121no—
365C2×Dic3—1216no—
366C2×Dic3—128no—
367C2×Dic3—128no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C3×C8—62no—
375C3×C8—121no—
376C3⋊C8—22no—
377C3⋊C8—41no—
378C2×C32—44no—
379C2×C32#38511yescharacteristic
380C2×C32C4×D811yescharacteristic
381C2×C32#44011yescharacteristic
382C2×C32#44711yescharacteristic
383C2×C32#45211yescharacteristic
384C2×C32#47411yescharacteristic
385C2×C32#47811yescharacteristic
386C24—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4D3×Dic312yes—
391C2×D4#62612yes—
392C2×D4#62712yes—
393C22×C4—61no—
394C22×C4—61no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—184no—
398C22×C4—181no—
399C22×C4—362no—
400C22×C4—362no—
401C22×C4C2×D3211yescharacteristic
402C2×C8—32no—
403C2×C8—61no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C4⋊C4—32no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—92no—
413C4⋊C4—181no—
414C4⋊C4—362no—
415C22⋊C4—184no—
416C42—181no—
417C42—181no—
418C22×C3—28no—
419C22×C3—24no—
420C22×C3—24no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—44no—
429C22×C3—44no—
430C22×C3—44no—
431C22×C3—44no—
432C22×C3—44no—
433C22×C3—44no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—42no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3#87811yescharacteristic
447C22×C3#87811yescharacteristic
448C22×C3#67⋊C411yescharacteristic
449C22×C3#88211yescharacteristic
450C22×C3D3×D811yescharacteristic
451C22×C3D3×D811yescharacteristic
452C22×C3#91111yescharacteristic
453C22×C3#91211yescharacteristic
454C22×C3#91411yescharacteristic
455C22×C3#91511yescharacteristic
456C22×C3#91511yescharacteristic
457C22×C3#91611yescharacteristic
458C22×C3D4×Dic311yescharacteristic
459C22×C3#93711yescharacteristic
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—122no—
465C3×C4—241no—
466C3×C4#87811yescharacteristic
467C3×C4#87811yescharacteristic
468C3×C4#67⋊C411yescharacteristic
469C3×C4#88611yescharacteristic
470C3×C4C2×Dic3⋊C411yescharacteristic
471C3×C4C2×C4⋊Dic311yescharacteristic
472C3×C4D4×Dic311yescharacteristic
473C3×C4#93511yescharacteristic
474Dic3—42no—
475Dic3—64no—
476Dic3—62no—
477Dic3—62no—
478Dic3—81no—
479Dic3—124no—
480Dic3—122no—
481Dic3—122no—
482Dic3—121no—
483Dic3—122no—
484Dic3—121no—
485C32#186211yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—22no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23#381111yescharacteristic
494D4—22no—
495D4—22no—
496D4—22no—
497D4Dic3⋊Dic314yescomplemented
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—121no—
501C2×C4—121no—
502C2×C4—121no—
503C2×C4—121no—
504C2×C4—121no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—182no—
511C2×C4—368no—
512C2×C4—361no—
513C2×C4—361no—
514C2×C4C2×D3×Dic311yescharacteristic
515C2×C4#380511yescharacteristic
516C2×C4#380511yescharacteristic
517C2×C4C2×#62611yescharacteristic
518C2×C4C2×#62711yescharacteristic
519C2×C4#381111yescharacteristic
520C8—62no—
521C8—121no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—48no—
530C2×C3—44no—
531C2×C3—44no—
532C2×C3#475611yescharacteristic
533C2×C3#475711yescharacteristic
534C2×C3#475911yescharacteristic
535C2×C3#475911yescharacteristic
536C2×C3#476311yescharacteristic
537C2×C3#476611yescharacteristic
538C2×C3#477311yescharacteristic
539C2×C3#478311yescharacteristic
540C2×C3#494611yescharacteristic
541C2×C3#495011yescharacteristic
542C2×C3Dic3×D811yescharacteristic
543C2×C3#515611yescharacteristic
544C2×C3#516411yescharacteristic
545C2×C3#517311yescharacteristic
546C22—24no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22#6392611yescharacteristic
554C22#6393111yescharacteristic
555C22#6393611yescharacteristic
556C22#6393711yescharacteristic
557C22#67⋊Dic311yescharacteristic
558C22#6398111yescharacteristic
559C22#6398211yescharacteristic
560C4—122no—
561C4—182no—
562C4—241no—
563C4—362no—
564C4—361no—
565C4#6396211yescharacteristic
566C4C2×Dic3⋊Dic311yescharacteristic
567C4#67⋊Dic311yescharacteristic
568C4#6398211yescharacteristic
569C3—21no—
570C3#7016711yescharacteristic, complemented
571C3#7016811yescharacteristic, complemented
572C2—44no—
573C2#1059143511yescharacteristic
574C2#1059144611yescharacteristic
575C2#1059145611yescharacteristic
576C2#1059146611yescharacteristic
577C2#1059147911yescharacteristic
578C2#1059149411yescharacteristic
579C2#1059171911yescharacteristic
subgroupG/H
centerC23#3811
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. #10591357C2semidirect
5. C2×#63575C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
23. C3×#832C4semidirect
65. C3×C4⋊Dic3C2×C4semidirect
71. C2×C3×C3⋊C8C2×C4semidirect
108. #832Dic3semidirect
124. C32×D4C4⋊C4semidirect
225. C4⋊Dic3C2×Dic3semidirect
238. C2×C3⋊C8C2×Dic3semidirect
312. C3×D4Dic3⋊C4semidirect
313. C3×D4C4⋊Dic3semidirect
485. C32#1862semidirect
497. D4Dic3⋊Dic3semidirect
570. C3#70167semidirect
571. C3#70168semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#8322
#105913572
C2×#635752
#105891642
#105891562
#701683
#701673