Finite Group Databasebeta

← #11805927

Subgroups — #11805927

Order 1152.

1057 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63843C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic
5#10591359C211yesmaximal, characteristic
6#10591331C212yesmaximal
7#10591274C211yesmaximal, characteristic
8#10591250C212yesmaximal
9#10591247C212yesmaximal
10#10591243C212yesmaximal
11#10591221C211yesmaximal, characteristic
12#76489—31nomaximal
13#73641—31nomaximal
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3750C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2212yes—
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic32C2212yes—
28C2×Dic32C2212yes—
29#63843C418yescomplemented
30#63658C2211yescharacteristic
31#63658C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×Q8×Dic3—31no—
39C2×#887—31no—
40C3×#391—31no—
41C3×C4×C4⋊C4—31no—
42#5229—31no—
43#4975—31no—
44#4975—31no—
45Dic3×C4⋊C4—31no—
46Dic3×C4⋊C4—31no—
47#4973—31no—
48C4×C4⋊Dic3D311yescharacteristic
49#4933—32no—
50C4×Dic3⋊C4—31no—
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—32no—
53C4×Dic3⋊C4—61no—
54#4929D311yescharacteristic
55#4654—32no—
56#4653—32no—
57#4652—32no—
58#4650—32no—
59#4650—32no—
60#4649—32no—
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—22no—
74C2×C3×Dic6C2×C414yes—
75C32×C42—22no—
76#3750—22no—
77#3750Q814yescomplemented
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2×C414yes—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3—22no—
82C3×C4⋊Dic3C2×C414yes—
83C3×C4×Dic3—42no—
84#3724—24no—
85#3724—42no—
86Dic3⋊Dic3C2×C418yes—
87Dic32—42no—
88Dic32C2×C418yes—
89#2355—91noSylow
90C22×C3×Q8—31no—
91C22×Dic6C2×D311yescharacteristic
92C2×C3×C4⋊C4—31no—
93C2×C3×C4⋊C4—31no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C42—21no—
96C2×C3×C42—32no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99Q8×Dic3—38no—
100C2×C4⋊Dic3—32no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4⋊Dic3C2×D311yescharacteristic
104C2×Dic3⋊C4—31no—
105C2×Dic3⋊C4—31no—
106C2×Dic3⋊C4—32no—
107C2×Dic3⋊C4—31no—
108C2×Dic3⋊C4—31no—
109C2×Dic3⋊C4—32no—
110C2×Dic3⋊C4—32no—
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×Dic3⋊C4—61no—
114C2×Dic3⋊C4—61no—
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—31no—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3—61no—
125C2×C4×Dic3C2×D312yes—
126#887—38no—
127C3×#95—32no—
128C3×#95—32no—
129C3×#95—32no—
130C3⋊#95—31no—
131C3⋊#95—31no—
132C3⋊#95—31no—
133C3⋊#95—31no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—61no—
141C3⋊#95—61no—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D312yes—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C2×Q812yes—
153C2×C32×C4#4112yes—
154C2×C32×C4#4112yes—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3C22×C412yes—
163C2×C3⋊Dic3C22×C412yes—
164C2×C3⋊Dic3C2×Q812yes—
165C2×C3⋊Dic3C2×Q812yes—
166C2×C3⋊Dic3#4112yes—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3C22×C414yes—
178C2×C3×Dic3C22×C414yes—
179C3×Dic6—28no—
180C2×C4×Q8—91no—
181#391—31no—
182#391—91no—
183#387—92no—
184#387—92no—
185#384—91no—
186#382—92no—
187C4×C4⋊C4—31no—
188C4×C4⋊C4—92no—
189C4×C4⋊C4—91no—
190C4×C4⋊C4—91no—
191C2×C3×Q8—34no—
192C2×C3×Q8—62no—
193C2×C3×Q8—62no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C2×Dic6—22no—
224C2×Dic6—22no—
225C2×Dic6C4×D314yes—
226C3×C4⋊C4—34no—
227C3×C4⋊C4—62no—
228C3×C4⋊C4—62no—
229C3×C42—22no—
230C3×C42—22no—
231C3×C42—42no—
232C3×C42—122no—
233C4⋊Dic3—22no—
234C4⋊Dic3—22no—
235C4⋊Dic3—38no—
236C4⋊Dic3C4×D314yes—
237Dic3⋊C4—34no—
238Dic3⋊C4—34no—
239Dic3⋊C4—38no—
240Dic3⋊C4—64no—
241Dic3⋊C4—64no—
242Dic3⋊C4—64no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—64no—
246Dic3⋊C4—122no—
247Dic3⋊C4—122no—
248C4×Dic3—34no—
249C4×Dic3—34no—
250C4×Dic3—38no—
251C4×Dic3—38no—
252C4×Dic3—42no—
253C4×Dic3—64no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256C4×Dic3—122no—
257C4×Dic3—122no—
258C4×Dic3—122no—
259C22×C32C23×C411yescharacteristic
260C22×C32C22×Q811yescharacteristic
261C22×C32C2×#4111yescharacteristic
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32H(5,𝔽2)11yescharacteristic
265C22×C322−1+411yescharacteristic
266C32×C4—22no—
267C32×C4—41no—
268C32×C4#11714yes—
269C3⋊Dic3—22no—
270C3⋊Dic3—22no—
271C3⋊Dic3—41no—
272C3⋊Dic3C4×Q814yes—
273C3×Dic3—24no—
274C3×Dic3—24no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C22×Q8—31no—
278C4×Q8—98no—
279C2×C4⋊C4—31no—
280C2×C4⋊C4—31no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—92no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—92no—
285C2×C4⋊C4—91no—
286C2×C4⋊C4—92no—
287C2×C42—32no—
288C2×C42—92no—
289C2×C42—91no—
290C2×C42—91no—
291C2×C42—92no—
292C2×C42D3211yescharacteristic
293#95—32no—
294#95—32no—
295#95—32no—
296#95—92no—
297#95—92no—
298#95—92no—
299#95—91no—
300#95—91no—
301C23×C3—21no—
302C23×C3C23×D311yescharacteristic
303C23×C3C23×D311yescharacteristic
304C3×Q8—68no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—34no—
321C2×C3×C4—34no—
322C2×C3×C4—41no—
323C2×C3×C4—41no—
324C2×C3×C4—41no—
325C2×C3×C4—41no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4C2×C4×D312yes—
337C2×C3×C4C2×C4×D312yes—
338C2×C3×C4#23512yes—
339C2×C3×C4#23512yes—
340C2×C3×C4#23712yes—
341C2×C3×C4#23712yes—
342C2×C3×C4D3×Q812yes—
343C2×C3×C4D3×Q812yes—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—32no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—61no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—121no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3C2×C4×D314yes—
391C2×Dic3C2×C4×D314yes—
392Dic6—28no—
393C2×C32C2×#11711yescharacteristic
394C2×C32C2×C4×Q811yescharacteristic
395C2×C32#52011yescharacteristic
396C2×C32#55411yescharacteristic
397C2×C32#55611yescharacteristic
398C2×C32#55711yescharacteristic
399C2×C32#55911yescharacteristic
400C2×Q8—34no—
401C2×Q8—62no—
402C2×Q8—62no—
403C22×C4—32no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4C2×D3211yescharacteristic
412C22×C4C2×D3211yescharacteristic
413C22×C4C2×D3211yescharacteristic
414C4⋊C4—34no—
415C4⋊C4—62no—
416C4⋊C4—62no—
417C4⋊C4—98no—
418C4⋊C4—94no—
419C4⋊C4—182no—
420C4⋊C4—184no—
421C4⋊C4—362no—
422C42—22no—
423C42—98no—
424C42—94no—
425C42—122no—
426C42—182no—
427C42—362no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3C22×C4×D311yescharacteristic
436C22×C3C22×C4×D311yescharacteristic
437C22×C3C2×#23511yescharacteristic
438C22×C3C2×#23511yescharacteristic
439C22×C3C2×#23711yescharacteristic
440C22×C3C2×#23711yescharacteristic
441C22×C3#100411yescharacteristic
442C22×C3C2×D3×Q811yescharacteristic
443C22×C3C2×D3×Q811yescharacteristic
444C22×C3#100711yescharacteristic
445C22×C3D3×#4111yescharacteristic
446C22×C3D3×#4111yescharacteristic
447C22×C3#100911yescharacteristic
448C22×C3#101011yescharacteristic
449C3×C4—22no—
450C3×C4—22no—
451C3×C4—24no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—64no—
457C3×C4—64no—
458C3×C4—122no—
459C3×C4—122no—
460C3×C4#87214yes—
461C3×C4#87714yes—
462Dic3—24no—
463Dic3—24no—
464Dic3—34no—
465Dic3—34no—
466Dic3—42no—
467Dic3—42no—
468Dic3—64no—
469Dic3—62no—
470Dic3—62no—
471Dic3—62no—
472Dic3—62no—
473Dic3—122no—
474Dic3—122no—
475Dic3—122no—
476Dic3—121no—
477Dic3—121no—
478C32#235511yescharacteristic, complemented, Sylow
479C23C22×D3211yescharacteristic
480Q8—68no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—34no—
487C2×C4—34no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—92no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4#379512yes—
511C2×C4#379712yes—
512C2×C4C4×D3212yes—
513C2×C4#380412yes—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3C2×#87211yescharacteristic
522C2×C3C2×#87711yescharacteristic
523C2×C3#551111yescharacteristic
524C2×C3#553311yescharacteristic
525C2×C3#554611yescharacteristic
526C2×C3#555911yescharacteristic
527C2×C3#556711yescharacteristic
528C2×C3C4×D3×Q811yescharacteristic
529C2×C3C4×D3×Q811yescharacteristic
530C2×C3#557411yescharacteristic
531C2×C3#563511yescharacteristic
532C2×C3#564111yescharacteristic
533C2×C3#568111yescharacteristic
534C2×C3#572111yescharacteristic
535C22C2×#379511yescharacteristic
536C22#6429711yescharacteristic
537C22C2×#379711yescharacteristic
538C22C2×C4×D3211yescharacteristic
539C22#6430611yescharacteristic
540C22#6430711yescharacteristic
541C22C2×#380411yescharacteristic
542C4—22no—
543C4—41no—
544C4—64no—
545C4—64no—
546C4—94no—
547C4—122no—
548C4—122no—
549C4—182no—
550C4—182no—
551C4—361no—
552C4#6387714yes—
553C3—21no—
554C3#7364111yescharacteristic, complemented
555C3#7648911yescharacteristic, complemented
556C2#1059386411yescharacteristic
557C2#1059388911yescharacteristic
558C2C4×#379711yescharacteristic
559C2#1059398111yescharacteristic
560C2#1059480911yescharacteristic
561C2C2×#6387711yescharacteristic
562C2#1059499111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2355
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
29. #63843C4semidirect
77. #3750Q8semidirect
478. C32#2355semidirect
554. C3#73641semidirect
555. C3#76489semidirect

Maximal subgroups

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

subgroupindex
C2×#638432
C4×#37502
C3×C4×C4⋊Dic32
C3×#49292
#105913592
#105913312
#105912742
#105912502
#105912472
#105912432
#105912212
#764893
#736413