Finite Group Databasebeta

← #11808847

Subgroups — #11808847

Order 1152.

1157 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic
3C3×#4981C211yesmaximal, characteristic
4C3×#4979C211yesmaximal, characteristic
5#10591358C211yesmaximal, characteristic
6#10591354C212yesmaximal
7#10591346C211yesmaximal, characteristic
8#10591340C212yesmaximal
9#10591252C211yesmaximal, characteristic
10#10591241C212yesmaximal
11#10591241C212yesmaximal
12#77740—31nomaximal
13#77171—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3750C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64096—24no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63843—24no—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×#887—31no—
41C2×#887—31no—
42C2×#887—31no—
43C2×#887—61no—
44C3×#398—31no—
45C3×#395—31no—
46#5230—31no—
47#4983—31no—
48#4982—32no—
49#4981D311yescharacteristic
50#4979—32no—
51#4979D311yescharacteristic
52Dic3×C4⋊C4—32no—
53Dic3×C4⋊C4—32no—
54#4661—31no—
55#4657—32no—
56#4656—31no—
57#4656—32no—
58#4649—32no—
59#4649—32no—
60#4648—31no—
61#4648—31no—
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×#634—22no—
70C2×#634—22no—
71C2×#634—22no—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79#3750—22no—
80#3750—22no—
81C4×C3⋊Dic3—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3D414yes—
84C3×C4⋊Dic3—22no—
85C3×Dic3⋊C4—24no—
86C3×Dic3⋊C4—24no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—24no—
89Dic3⋊Dic3—24no—
90Dic32—24no—
91Dic32Q818yescomplemented
92#2399—91noSylow
93C22×C3×Q8—31no—
94C22×Dic6—31no—
95C22×Dic6—31no—
96C22×Dic6—61no—
97C22×Dic6C2×D311yescharacteristic
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—32no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104Q8×Dic3—64no—
105C2×C4⋊Dic3—32no—
106C2×C4⋊Dic3—32no—
107C2×C4⋊Dic3—32no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—31no—
110C2×Dic3⋊C4—31no—
111C2×Dic3⋊C4—31no—
112C2×Dic3⋊C4—31no—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—61no—
117C2×Dic3⋊C4—61no—
118C2×Dic3⋊C4C2×D312yes—
119C2×Dic3⋊C4C2×D312yes—
120C2×C4×Dic3—31no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3—32no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—61no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3—61no—
133#887—64no—
134#887—64no—
135#887—64no—
136#887—68no—
137C3×#95—31no—
138C3×#95—31no—
139C3×#95—32no—
140C3×#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C3⋊#95C2×D312yes—
151C23×C32C2411yescharacteristic
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4—21no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4#4112yes—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D412yes—
167C2×C3⋊Dic3C2×Q814yes—
168C2×C3⋊Dic3#4112yes—
169#634—28no—
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×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×Q814yes—
180C2×C3×Dic3C2×Q814yes—
181C2×C3×Dic3#4114yes—
182C3×Dic6—28no—
183C2×C4×Q8—91no—
184C2×C4×Q8—91no—
185#398—31no—
186#398—92no—
187#398—91no—
188#395—31no—
189#395—92no—
190#395—91no—
191C4×C4⋊C4—92no—
192C4×C4⋊C4—92no—
193#376—91no—
194C2×C3×Q8—64no—
195C2×C3×Q8—62no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—31no—
212C22×Dic3—31no—
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—61no—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C2×Dic6—22no—
226C2×Dic6—24no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×Dic6—64no—
232C2×Dic6—64no—
233C2×Dic6—64no—
234C2×Dic6—62no—
235C2×Dic6—62no—
236C3×C4⋊C4—24no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—64no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—64no—
242C4⋊Dic3—22no—
243C4⋊Dic3—64no—
244C4⋊Dic3—64no—
245C4⋊Dic3—64no—
246Dic3⋊C4—24no—
247Dic3⋊C4—24no—
248Dic3⋊C4—64no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—64no—
254Dic3⋊C4—64no—
255Dic3⋊C4—62no—
256Dic3⋊C4—62no—
257C4×Dic3—34no—
258C4×Dic3—34no—
259C4×Dic3—38no—
260C4×Dic3—38no—
261C4×Dic3—64no—
262C4×Dic3—64no—
263C4×Dic3—64no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C22×C32C22×D411yescharacteristic
271C22×C32C22×Q812yes—
272C22×C32C2×#4111yescharacteristic
273C22×C32C2×#4112yes—
274C22×C32C2×#4111yescharacteristic
275C32×C4—22no—
276C32×C4—22no—
277C32×C4—41no—
278C3⋊Dic3—22no—
279C3⋊Dic3—22no—
280C3⋊Dic3—41no—
281C3⋊Dic3C4⋊Q814yes—
282C3×Dic3—24no—
283C3×Dic3—24no—
284C3×Dic3—24no—
285C3×Dic3—42no—
286C22×Q8—31no—
287C22×Q8—91no—
288C4×Q8—184no—
289C4×Q8—184no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—92no—
294C2×C4⋊C4—92no—
295C2×C4⋊C4—92no—
296C2×C4⋊C4—91no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4D3211yescharacteristic
299C2×C42—92no—
300C2×C42—91no—
301C2×C42—92no—
302C2×C42—91no—
303C2×C42—91no—
304#95—31no—
305#95—31no—
306#95—32no—
307#95—32no—
308#95—92no—
309#95—92no—
310#95—92no—
311C23×C3—21no—
312C23×C3C23×D311yescharacteristic
313C23×C3C23×D311yescharacteristic
314C3×Q8—68no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—22no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—34no—
331C2×C3×C4—34no—
332C2×C3×C4—34no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4D3×D412yes—
345C2×C3×C4D3×D412yes—
346C2×C3×C4#23712yes—
347C2×C3×C4#23912yes—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—61no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—62no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—122no—
387C2×Dic3#23714yes—
388C2×Dic3D3×Q814yes—
389C2×Dic3D3×Q814yes—
390Dic6—28no—
391Dic6—616no—
392Dic6—68no—
393Dic6—68no—
394C2×C32#52511yescharacteristic
395C2×C32#52511yescharacteristic
396C2×C32C2×C4⋊Q811yescharacteristic
397C2×C32#53312yes—
398C2×C32#53312yes—
399C2×Q8—64no—
400C2×Q8—62no—
401C2×Q8—182no—
402C2×Q8—182no—
403C2×Q8—182no—
404C22×C4—32no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—91no—
412C22×C4C2×D3211yescharacteristic
413C22×C4C2×D3211yescharacteristic
414C22×C4C2×D3211yescharacteristic
415C4⋊C4—22no—
416C4⋊C4—64no—
417C4⋊C4—64no—
418C4⋊C4—62no—
419C4⋊C4—182no—
420C4⋊C4—184no—
421C4⋊C4—184no—
422C4⋊C4—184no—
423C4⋊C4—182no—
424C42—98no—
425C42—94no—
426C42—182no—
427C42—182no—
428C42—184no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—21no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×#23711yescharacteristic
437C22×C3C2×#23712yes—
438C22×C3C2×D3×Q812yes—
439C22×C3C2×D3×Q812yes—
440C22×C3C2×#23911yescharacteristic
441C22×C3D3×#4111yescharacteristic
442C22×C3D3×#4111yescharacteristic
443C22×C3D3×#4112yes—
444C3×C4—24no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—64no—
454C3×C4—64no—
455C3×C4—64no—
456C3×C4—122no—
457Dic3—24no—
458Dic3—24no—
459Dic3—24no—
460Dic3—34no—
461Dic3—34no—
462Dic3—42no—
463Dic3—64no—
464Dic3—64no—
465Dic3—64no—
466Dic3—62no—
467Dic3—62no—
468Dic3—62no—
469Dic3—62no—
470Dic3—122no—
471Dic3—121no—
472Dic3—121no—
473C32#239911yescharacteristic, complemented, Sylow
474C23C22×D3211yescharacteristic
475Q8—68no—
476Q8—188no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—34no—
483C2×C4—34no—
484C2×C4—34no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—94no—
495C2×C4—92no—
496C2×C4—92no—
497C2×C4—92no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—182no—
503C2×C4—181no—
504C2×C4#379612yes—
505C2×C4#381112yes—
506C2×C3—21no—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3#558611yescharacteristic
512C2×C3#560611yescharacteristic
513C2×C3#562212yes—
514C2×C3#562212yes—
515C2×C3#562711yescharacteristic
516C2×C3#565611yescharacteristic
517C2×C3#568812yes—
518C2×C3D3×C4⋊Q811yescharacteristic
519C2×C3D3×C4⋊Q811yescharacteristic
520C2×C3#572812yes—
521C22C2×#379611yescharacteristic
522C22#6430611yescharacteristic
523C22D3×#23712yes—
524C22D32×Q812yes—
525C22C2×#381111yescharacteristic
526C4—22no—
527C4—22no—
528C4—41no—
529C4—64no—
530C4—64no—
531C4—64no—
532C4—94no—
533C4—122no—
534C4—182no—
535C4—182no—
536C4—361no—
537C3—21no—
538C3#7717111yescharacteristic, complemented
539C3#7774011yescharacteristic, complemented
540C2#1059438712yes—
541C2#1059438812yes—
542C2#1059492211yescharacteristic
543C2#1059516011yescharacteristic
544C2#1059536511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, prime radical, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2399
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
91. Dic32Q8semidirect
473. C32#2399semidirect
538. C3#77171semidirect
539. C3#77740semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638432
C3×#49812
C3×#49792
#105913582
#105913542
#105913462
#105913402
#105912522
#105912412
#777403
#771713