Finite Group Databasebeta

← #11859120

Subgroups — #11859120

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Dic3×#41C211yesmaximal, characteristic
2#10592933C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic
4#10591115C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10591063C212yesmaximal, complemented
7#10591057C211yesmaximal, characteristic, complemented
8#10591056C212yesmaximal, complemented
9#10591056C212yesmaximal, complemented
10#10591055C211yesmaximal, characteristic, complemented
11#10591053C212yesmaximal, complemented
12#82515—31nomaximal
13#78650—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×Q8×Dic3C411yescharacteristic
18C3×Q8×Dic3C411yescharacteristic
19C3×D4×Dic3C412yes—
20C3×D4×Dic3C411yescharacteristic
21C3×D4×Dic3C412yes—
22C3×D4×Dic3C411yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#926C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63657C2212yes—
30#63657C2212yes—
31C3×#830C2212yes—
32C3×#830C2212yes—
33Dic3⋊(C3⋊C8)C2211yescharacteristic
34Dic3⋊(C3⋊C8)C2212yes—
35Dic3⋊(C3⋊C8)C2211yescharacteristic
36Dic3⋊(C3⋊C8)C2211yescharacteristic
37Dic3⋊(C3⋊C8)C2212yes—
38Dic3⋊(C3⋊C8)C2211yescharacteristic
39#63554C2212yes—
40#63554C2212yes—
41Dic3×C3⋊C8C2212yes—
42Dic3×C3⋊C8C2212yes—
43C3×C4×#41—31no—
44Dic3×#41D311yescharacteristic
45C3×#408—31no—
46#5234—31no—
47#5234—31no—
48#5234—61no—
49#5234D311yescharacteristic
50#5122—31no—
51#5118—31no—
52#5101—31no—
53C2×Dic3⋊C8—31no—
54#5000—32no—
55#5000—32no—
56#4997—31no—
57#4997—31no—
58#4926—32no—
59#4925—32no—
60#4924—31no—
61C2×C4⋊(C3⋊C8)—31no—
62#4720—32no—
63#4720—32no—
64#4719—32no—
65#4718—32no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8C2×C411yescharacteristic
69C2×C32×D4C2×C412yes—
70C2×C32×D4C2×C411yescharacteristic
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3×Dic3C2×C412yes—
74C22×C3×Dic3C2×C411yescharacteristic
75C22×C3×Dic3C2×C412yes—
76C22×C3×Dic3C2×C411yescharacteristic
77#3748—22no—
78C2×C3⋊(C3⋊C8)—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2312yes—
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C3×#217C2×C412yes—
83C3×#217C2×C412yes—
84C3×#217C2×C412yes—
85C3×C4⋊Dic3C2×C412yes—
86C3×C4⋊Dic3C2×C412yes—
87C3×C4⋊Dic3C2×C411yescharacteristic
88C3×C4⋊Dic3C2×C411yescharacteristic
89C3×C4×Dic3C2×C412yes—
90C3×C4×Dic3C2×C411yescharacteristic
91C3×C4×Dic3C2×C412yes—
92C3×C4×Dic3C2×C411yescharacteristic
93C3×C4×Dic3C2311yescharacteristic
94C3×C4×Dic3C2312yes—
95C3×C4×Dic3C2311yescharacteristic
96C3×#208—22no—
97C2×C3×C3⋊C8—22no—
98C2×C3×C3⋊C8C2311yescharacteristic
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2312yes—
101#2925—91noSylow
102C2×C3×#41—21no—
103C2×C3×#41C2×D311yescharacteristic
104C2×C3×#41C2×D311yescharacteristic
105C2×C3×M16—31no—
106C22×C3×C8—31no—
107C3×C4×Q8—31no—
108C3×C4×Q8—31no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4—32no—
112C3×C4×D4—31no—
113C3×#117—31no—
114C3×#117—32no—
115C2×C3×C42—31no—
116C2×C3×C42—32no—
117Q8×Dic3Dic311yescharacteristic
118Q8×Dic3Dic311yescharacteristic
119D4×Dic3Dic312yes—
120D4×Dic3Dic311yescharacteristic
121D4×Dic3Dic312yes—
122D4×Dic3Dic311yescharacteristic
123#926C2×D311yescharacteristic
124#926C2×D312yes—
125C2×C4×Dic3C2×D312yes—
126C2×C4×Dic3C2×D311yescharacteristic
127C2×#208—31no—
128C2×#208—31no—
129C2×#208—61no—
130C2×#208C2×D311yescharacteristic
131C22×C3⋊C8—31no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—61no—
134C22×C3⋊C8C2×D311yescharacteristic
135C3×C22⋊C8—32no—
136C3×C22⋊C8—32no—
137#830—32no—
138#830—32no—
139#830—32no—
140#830—32no—
141#830—62no—
142#830—62no—
143#830C2×D312yes—
144#830C2×D312yes—
145#815—32no—
146#815—32no—
147Dic3⋊C8—31no—
148Dic3⋊C8—32no—
149Dic3⋊C8—31no—
150Dic3⋊C8—31no—
151Dic3⋊C8—31no—
152Dic3⋊C8—32no—
153C8×Dic3—32no—
154C8×Dic3—32no—
155C4⋊(C3⋊C8)—31no—
156C4⋊(C3⋊C8)—31no—
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—32no—
161#803—32no—
162#803—32no—
163C4×C3⋊C8—32no—
164C4×C3⋊C8—32no—
165C23×C32C22×C412yes—
166C23×C32C22×C411yescharacteristic
167C32×Q8—22no—
168C32×D4—24no—
169C32×D4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—22no—
172C2×C32×C4C22×C412yes—
173C2×C32×C4C22×C411yescharacteristic
174C2×C32×C4#4112yes—
175C2×C32×C4#4112yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3×Dic3—22no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—41no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3C22×C411yescharacteristic
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C411yescharacteristic
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3C22×C411yescharacteristic
186C2×C3×Dic3C22×C411yescharacteristic
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C4×#41—31no—
194#433—92no—
195#433—92no—
196#432—92no—
197#431—92no—
198#423—91no—
199C2×C4⋊C8—91no—
200#408—31no—
201#408—91no—
202#405—91no—
203#405—91no—
204C3×#41—22no—
205C3×#41—22no—
206C3×#41—22no—
207C3×#41—22no—
208C3×#41—42no—
209C3×#41—42no—
210C2×C3×Q8—21no—
211C2×C3×Q8C4×D311yescharacteristic
212C2×C3×Q8C2×Dic311yescharacteristic
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4C4×D312yes—
216C2×C3×D4C4×D311yescharacteristic
217C2×C3×D4C2×Dic312yes—
218C2×C3×D4C2×Dic311yescharacteristic
219C22×C3×C4—21no—
220C22×C3×C4—22no—
221C22×C3×C4—32no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—31no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×Dic3C2×Dic312yes—
230C22×Dic3C2×Dic311yescharacteristic
231C22×Dic3C2×Dic312yes—
232C22×Dic3C2×Dic311yescharacteristic
233C3×M16—62no—
234C2×C3×C8—31no—
235C2×C3×C8—32no—
236C2×C3×C8—31no—
237C2×C3×C8—62no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C22⋊C4—32no—
243C3×C22⋊C4—32no—
244C3×C22⋊C4—32no—
245C3×C42—32no—
246C3×C42—31no—
247C3×C42—32no—
248C3×C42—31no—
249C3×C42—32no—
250C3×C42—31no—
251C3×C42—31no—
252#217C2×Dic312yes—
253#217C2×Dic312yes—
254#217C2×Dic312yes—
255C4⋊Dic3C2×Dic312yes—
256C4⋊Dic3C2×Dic312yes—
257C4⋊Dic3C2×Dic311yescharacteristic
258C4⋊Dic3C2×Dic311yescharacteristic
259C4×Dic3C2×Dic312yes—
260C4×Dic3C2×Dic311yescharacteristic
261C4×Dic3C2×Dic312yes—
262C4×Dic3C2×Dic311yescharacteristic
263C4×Dic3C22×D312yes—
264C4×Dic3C22×D311yescharacteristic
265C4×Dic3C22×D311yescharacteristic
266#208—22no—
267#208—62no—
268#208—62no—
269#208—122no—
270C2×C3⋊C8—22no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—31no—
277C2×C3⋊C8—61no—
278C2×C3⋊C8—61no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—122no—
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D312yes—
285C2×C3⋊C8C22×D311yescharacteristic
286C22×C32—21no—
287C22×C32—21no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—22no—
291C22×C32#11712yes—
292C22×C32C23×C411yescharacteristic
293C32×C4—22no—
294C32×C4#11712yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4C2×#4111yescharacteristic
297C3×Dic3—21no—
298C3×Dic3—22no—
299C3×Dic3—21no—
300C3×Dic3—21no—
301C3×Dic3—22no—
302C3×Dic3#13112yes—
303C2×#41D3211yescharacteristic
304C2×M16—31no—
305C2×M16—91no—
306C22×C8—31no—
307C22×C8—91no—
308C4×Q8—31no—
309C4×Q8—31no—
310C4×D4—32no—
311C4×D4—31no—
312C4×D4—32no—
313C4×D4—31no—
314#117—31no—
315#117—32no—
316C2×C42—31no—
317C2×C42—32no—
318C4⋊C8—91no—
319C4⋊C8—91no—
320C4⋊C8—91no—
321C4⋊C8—91no—
322C4⋊C8—92no—
323C4⋊C8—92no—
324C22⋊C8—32no—
325C22⋊C8—32no—
326C22⋊C8—92no—
327C22⋊C8—92no—
328#97—92no—
329#97—92no—
330C4×C8—92no—
331C4×C8—92no—
332C23×C3—21no—
333C23×C3—22no—
334C23×C3C2×C4×D312yes—
335C23×C3C2×C4×D311yescharacteristic
336C23×C3C22×Dic312yes—
337C23×C3C22×Dic311yescharacteristic
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—42no—
341C3×D4—24no—
342C3×D4—24no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—42no—
346C3×D4—44no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—31no—
357C2×C3×C4—31no—
358C2×C3×C4—32no—
359C2×C3×C4—31no—
360C2×C3×C4—32no—
361C2×C3×C4—31no—
362C2×C3×C4—42no—
363C2×C3×C4—42no—
364C2×C3×C4—62no—
365C2×C3×C4—64no—
366C2×C3×C4—121no—
367C2×C3×C4—122no—
368C2×C3×C4C2×C4×D312yes—
369C2×C3×C4C2×C4×D311yescharacteristic
370C2×C3×C4#23512yes—
371C2×C3×C4#23512yes—
372C2×C3×C4#23712yes—
373C2×C3×C4#23712yes—
374C2×C3×C4C22×Dic312yes—
375C2×C3×C4C22×Dic311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378C2×Dic3—22no—
379C2×Dic3—24no—
380C2×Dic3—41no—
381C2×Dic3—42no—
382C2×Dic3C22×Dic311yescharacteristic
383C2×Dic3C22×Dic312yes—
384C2×Dic3C22×Dic311yescharacteristic
385C2×Dic3C22×Dic312yes—
386C2×Dic3C22×Dic311yescharacteristic
387C2×Dic3C22×Dic311yescharacteristic
388C3×C8—61no—
389C3×C8—61no—
390C3×C8—62no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C3⋊C8—22no—
394C3⋊C8—61no—
395C3⋊C8—61no—
396C3⋊C8—62no—
397C3⋊C8—61no—
398C3⋊C8—61no—
399C3⋊C8—62no—
400C3⋊C8—121no—
401C3⋊C8—121no—
402C3⋊C8—122no—
403C2×C32—22no—
404C2×C32—42no—
405C2×C32C2×#11711yescharacteristic
406C2×C32C2×#13111yescharacteristic
407C2×C32#56811yescharacteristic
408#41—22no—
409#41—22no—
410C2×Q8D3×Dic311yescharacteristic
411C2×D4D3×Dic312yes—
412C2×D4D3×Dic311yescharacteristic
413C22×C4—32no—
414C22×C4—31no—
415C22×C4—32no—
416C22×C4—31no—
417C22×C4C2×D3212yes—
418C22×C4C2×D3211yescharacteristic
419M16—62no—
420M16—182no—
421C2×C8—31no—
422C2×C8—32no—
423C2×C8—31no—
424C2×C8—62no—
425C2×C8—91no—
426C2×C8—92no—
427C2×C8—91no—
428C2×C8—182no—
429C4⋊C4—32no—
430C4⋊C4—32no—
431C4⋊C4—31no—
432C4⋊C4—31no—
433C22⋊C4—32no—
434C22⋊C4—32no—
435C22⋊C4—32no—
436C42—32no—
437C42—31no—
438C42—31no—
439C42—32no—
440C42—31no—
441C42—32no—
442C42—31no—
443C22×C3—21no—
444C22×C3—21no—
445C22×C3—21no—
446C22×C3—21no—
447C22×C3—22no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—22no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—22no—
455C22×C3—41no—
456C22×C3—41no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3#87712yes—
461C22×C3#92612yes—
462C22×C3C22×C4×D311yescharacteristic
463C22×C3C23×Dic311yescharacteristic
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—32no—
470C3×C4—42no—
471C3×C4—62no—
472C3×C4—61no—
473C3×C4—61no—
474C3×C4—62no—
475C3×C4—61no—
476C3×C4#87712yes—
477C3×C4#92612yes—
478C3×C4C2×#23511yescharacteristic
479C3×C4C2×#23511yescharacteristic
480C3×C4C2×#23711yescharacteristic
481C3×C4C2×#23711yescharacteristic
482Dic3—21no—
483Dic3—22no—
484Dic3—21no—
485Dic3—21no—
486Dic3—22no—
487Dic3#94812yes—
488C32#292511yescharacteristic, complemented, Sylow
489C23C2×D3×Dic312yes—
490C23C2×D3×Dic311yescharacteristic
491Q8—22no—
492D4—24no—
493D4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—31no—
497C2×C4—31no—
498C2×C4—32no—
499C2×C4—31no—
500C2×C4—32no—
501C2×C4—31no—
502C2×C4—62no—
503C2×C4—64no—
504C2×C4—121no—
505C2×C4—122no—
506C2×C4C2×D3×Dic312yes—
507C2×C4C2×D3×Dic311yescharacteristic
508C2×C4#380412yes—
509C2×C4#380412yes—
510C2×C4C22×D3211yescharacteristic
511C8—61no—
512C8—61no—
513C8—62no—
514C8—181no—
515C8—181no—
516C8—182no—
517C2×C3—22no—
518C2×C3—22no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—42no—
523C2×C3—42no—
524C2×C3—42no—
525C2×C3—82no—
526C2×C3C2×#87711yescharacteristic
527C2×C3D3×#13111yescharacteristic
528C2×C3#575011yescharacteristic
529C2×C3C2×#92611yescharacteristic
530C2×C3C2×#94811yescharacteristic
531C2×C3#581911yescharacteristic
532C22—21no—
533C22—21no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22#6395512yes—
538C22C22×D3×Dic311yescharacteristic
539C4—22no—
540C4—32no—
541C4—62no—
542C4—61no—
543C4—61no—
544C4—62no—
545C4—61no—
546C4#6395512yes—
547C4C2×#380411yescharacteristic
548C4C2×#380411yescharacteristic
549C3—21no—
550C3#7865011yescharacteristic, complemented
551C3#8251511yescharacteristic, complemented
552C2—22no—
553C2—42no—
554C2D3×#94811yescharacteristic
555C2#1059544111yescharacteristic
556C2C2×#6395511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
Fitting, prime radicalC2×C32×#41C22
cosocleC2×C32×C4C24
hypercenterC2×#41D32
hypocenterC32#2925
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #10591115C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
6. #10591063C2semidirect
7. #10591057C2semidirect
8. #10591056C2semidirect
9. #10591056C2semidirect
10. #10591055C2semidirect
11. #10591053C2semidirect
488. C32#2925semidirect
550. C3#78650semidirect
551. C3#82515semidirect

Maximal subgroups

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

subgroupindex
C3×Dic3×#412
#105929332
C3×#52342
#105911152
C2×Dic3⋊(C3⋊C8)2
#105910632
#105910572
#105910562
#105910552
#105910532
#825153
#786503