Finite Group Databasebeta

← #11801960

Subgroups — #11801960

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63874C211yesmaximal, characteristic
2C4×#3752C211yesmaximal, characteristic
3C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C3×C42×Dic3C211yesmaximal, characteristic, complemented
5#10591333C212yesmaximal, complemented
6C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7#10591289C212yesmaximal
8C4×#3722C211yesmaximal, characteristic
9#10591222C211yesmaximal, characteristic, complemented
10#10591194C212yesmaximal
11#10591193C212yesmaximal, complemented
12#73620—31nomaximal
13#73301—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C2×#3752C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C2×C3×Dic3⋊C4C2212yes—
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×C4×Dic3C2212yes—
21C2×C3×C4×Dic3C2212yes—
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×#3724C2211yescharacteristic
26C2×#3724C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2211yescharacteristic
30C2×#3722C2211yescharacteristic
31#63874C418yescomplemented
32#63658C2212yes—
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×#872—31no—
39C2×#872—31no—
40C3×C4×C4⋊C4—31no—
41C3×C43—31no—
42#4990—32no—
43#4978—32no—
44#4940—32no—
45#4940—32no—
46C4×(C2×D3)⋊C4—31no—
47C4×(C2×D3)⋊C4—31no—
48C4×(C2×D3)⋊C4—31no—
49C4×(C2×D3)⋊C4—31no—
50C4×(C2×D3)⋊C4—61no—
51C4×C4⋊Dic3—31no—
52#4933—32no—
53#4933—32no—
54#4932—31no—
55#4932—31no—
56C4×Dic3⋊C4—31no—
57C4×Dic3⋊C4D311yescharacteristic, complemented
58C42×Dic3D311yescharacteristic, complemented
59#4670—32no—
60#4655—32no—
61C23×C3⋊D3C2311yescharacteristic
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3C2×C414yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C32×C42—22no—
76#3752—24no—
77C4×C3⋊Dic3—22no—
78C3×Dic3⋊C4—24no—
79C3×C4×Dic3—24no—
80C3×C4×Dic3—22no—
81C3×C4×Dic3—22no—
82C3×C4×Dic3—24no—
83C3×C4×Dic3C2×C414yes—
84C3×C4×Dic3C2×C414yes—
85#3724C2×C414yes—
86#3724C2×C414yes—
87Dic3⋊Dic3—24no—
88#3722—24no—
89#3722C2×C414yes—
90#3722C2×C414yes—
91#2298—91noSylow
92C22×C4×D3—31no—
93C22×C4×D3—31no—
94C22×C4×D3—61no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C42—21no—
97C2×C3×C42—31no—
98C2×C3×C42—31no—
99C2×C3×C42—31no—
100C2×C3×C42—31no—
101C2×C3×C42—32no—
102C2×C3×C42—32no—
103C2×C3×C42C2×D311yescharacteristic
104C2×C3×C42C2×D311yescharacteristic
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3—32no—
115C2×Dic3⋊C4—31no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4C2×D312yes—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—61no—
124C2×C4×Dic3C2×D312yes—
125C2×C4×Dic3C2×D312yes—
126C2×C4×Dic3C2×D311yescharacteristic
127C2×C4×Dic3C2×D311yescharacteristic
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130#872—38no—
131#872—38no—
132C3×#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—62no—
144C3⋊#95C2×D312yes—
145C23×C32C2411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—21no—
149C22×C3⋊D3—21no—
150C22×C3⋊D3C22×C412yes—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4#4114yes—
155C2×C32×C4#4112yes—
156C2×C32×C4#4112yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3C22×C412yes—
163C4×C3⋊D3—28no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
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×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3#4114yes—
178C2×#117—91no—
179#388—92no—
180#388—92no—
181#387—92no—
182#387—92no—
183C4×C4⋊C4—31no—
184C4×C4⋊C4—91no—
185C4×C22⋊C4—91no—
186C4×C22⋊C4—91no—
187#376—91no—
188C43—31no—
189C23×D3—31no—
190C23×D3—31no—
191C23×D3—61no—
192C22×C3×C4—22no—
193C22×C3×C4—21no—
194C22×C3×C4—31no—
195C22×C3×C4—31no—
196C22×C3×C4—32no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—31no—
205C22×Dic3—31no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—61no—
209C22×Dic3—62no—
210C22×Dic3C22×D312yes—
211C22×Dic3C22×D311yescharacteristic
212C22×Dic3C22×D311yescharacteristic
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C22×Dic3C22×D312yes—
216C2×C4×D3—34no—
217C2×C4×D3—34no—
218C2×C4×D3—64no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—122no—
224C2×C4×D3—122no—
225C3×C4⋊C4—64no—
226C3×C42—22no—
227C3×C42—22no—
228C3×C42—34no—
229C3×C42—34no—
230C3×C42—42no—
231C3×C42—64no—
232C3×C42—64no—
233C3×C42—62no—
234C3×C42—62no—
235(C2×D3)⋊C4—34no—
236(C2×D3)⋊C4—34no—
237(C2×D3)⋊C4—34no—
238(C2×D3)⋊C4—34no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—68no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—64no—
245Dic3⋊C4—24no—
246Dic3⋊C4—34no—
247Dic3⋊C4—34no—
248Dic3⋊C4—34no—
249Dic3⋊C4—34no—
250Dic3⋊C4—64no—
251C4×Dic3—24no—
252C4×Dic3—22no—
253C4×Dic3—22no—
254C4×Dic3—24no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—122no—
258C4×Dic3C4×D314yes—
259C4×Dic3C4×D314yes—
260C22×C32C23×C411yescharacteristic
261C22×C32C2×#4112yes—
262C22×C32C2×#4111yescharacteristic
263C22×C32C2×#4111yescharacteristic
264C22×C32C2×#4112yes—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—22no—
267C2×C3⋊D3—22no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C32×C4—24no—
271C32×C4#11714yes—
272C3⋊Dic3—22no—
273C3⋊Dic3—42no—
274C3×Dic3—22no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—22no—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C23×C4—91no—
281#117—98no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—91no—
285C2×C4⋊C4—92no—
286C2×C22⋊C4—91no—
287C2×C22⋊C4—91no—
288C2×C22⋊C4—92no—
289C2×C22⋊C4—92no—
290C2×C42—31no—
291C2×C42—31no—
292C2×C42—32no—
293C2×C42—32no—
294C2×C42—31no—
295C2×C42—31no—
296C2×C42—91no—
297C2×C42D3211yescharacteristic
298#95—32no—
299#95—92no—
300#95—92no—
301#95—92no—
302#95—92no—
303#95—92no—
304C23×C3—21no—
305C23×C3C23×D311yescharacteristic
306C23×C3C23×D311yescharacteristic
307C22×D3—32no—
308C22×D3—32no—
309C22×D3—62no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—61no—
315C22×D3—61no—
316C22×D3—61no—
317C22×D3—61no—
318C22×D3—62no—
319C22×D3—121no—
320C22×D3—121no—
321C22×D3—122no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—24no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—34no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
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×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4C2×C4×D312yes—
347C2×C3×C4C2×C4×D312yes—
348C2×C3×C4#23514yes—
349C2×C3×C4#23514yes—
350C2×C3×C4#23512yes—
351C2×C3×C4#23512yes—
352C2×C3×C4#23712yes—
353C2×C3×C4#23912yes—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370C2×Dic3—64no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—122no—
378C2×Dic3—121no—
379C2×Dic3—121no—
380C2×Dic3—122no—
381C2×Dic3C2×C4×D312yes—
382C2×Dic3C2×C4×D312yes—
383C2×Dic3C2×C4×D312yes—
384C2×Dic3C2×C4×D312yes—
385C2×Dic3#23514yes—
386C4×D3—68no—
387C4×D3—68no—
388C4×D3—128no—
389C2×C32C2×#11711yescharacteristic
390C2×C32C4×#4111yescharacteristic
391C2×C32C4×#4111yescharacteristic
392C2×C32#52912yes—
393C2×C32#52912yes—
394C3⋊D3—42no—
395C24—91no—
396C22×C4—31no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—32no—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—91no—
403C22×C4—94no—
404C22×C4—92no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4C2×D3212yes—
408C22×C4C2×D3211yescharacteristic
409C4⋊C4—64no—
410C4⋊C4—94no—
411C4⋊C4—94no—
412C4⋊C4—184no—
413C22⋊C4—94no—
414C22⋊C4—94no—
415C22⋊C4—184no—
416C22⋊C4—184no—
417C42—22no—
418C42—34no—
419C42—34no—
420C42—64no—
421C42—64no—
422C42—62no—
423C42—62no—
424C42—182no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3C22×C4×D311yescharacteristic
431C22×C3C22×C4×D311yescharacteristic
432C22×C3C2×#23512yes—
433C22×C3C2×#23512yes—
434C22×C3C2×#23511yescharacteristic
435C22×C3C2×#23512yes—
436C22×C3C2×#23511yescharacteristic
437C22×C3C2×#23711yescharacteristic
438C22×C3C2×#23911yescharacteristic
439C22×C3D3×#4112yes—
440C2×D3—64no—
441C2×D3—62no—
442C2×D3—62no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—122no—
455C3×C4—24no—
456C3×C4—24no—
457C3×C4—24no—
458C3×C4—44no—
459C3×C4—62no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—64no—
464C3×C4—122no—
465C3×C4#87214yes—
466C3×C4#89214yes—
467Dic3—22no—
468Dic3—22no—
469Dic3—22no—
470Dic3—24no—
471Dic3—22no—
472Dic3—42no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32#229811yescharacteristic, complemented, Sylow
480C23—92no—
481C23—182no—
482C23—181no—
483C23—182no—
484C23—181no—
485C23C22×D3211yescharacteristic
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—32no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—32no—
492C2×C4—34no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—92no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—188no—
506C2×C4—182no—
507C2×C4—182no—
508C2×C4—182no—
509C2×C4#379814yes—
510C2×C4#379912yes—
511C2×C4C4×D3212yes—
512C2×C4#380412yes—
513C2×C3—22no—
514C2×C3—22no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3C2×#87211yescharacteristic
519C2×C3C4×#23511yescharacteristic
520C2×C3C4×#23511yescharacteristic
521C2×C3C4×#23511yescharacteristic
522C2×C3#547912yes—
523C2×C3#547912yes—
524C2×C3C2×#89211yescharacteristic
525C2×C3#552211yescharacteristic
526C2×C3#553812yes—
527C2×C3#558012yes—
528D3—124no—
529D3—122no—
530D3—122no—
531C22—182no—
532C22—182no—
533C22—182no—
534C22—362no—
535C22—362no—
536C22C2×#379812yes—
537C22C2×#379911yescharacteristic
538C22C2×C4×D3211yescharacteristic
539C22D3×#23512yes—
540C22C2×#380411yescharacteristic
541C4—24no—
542C4—64no—
543C4—62no—
544C4—62no—
545C4—62no—
546C4—62no—
547C4—122no—
548C4—182no—
549C4—362no—
550C4#6383614yes—
551C3—21no—
552C3#7330111yescharacteristic, complemented
553C3#7362011yescharacteristic, complemented
554C2—362no—
555C2#1059387012yes—
556C2C4×#379811yescharacteristic
557C2#1059396511yescharacteristic
558C2C2×#6383611yescharacteristic
559C2#1059483912yes—
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×Dic3⋊C4C2semidirect
4. C3×C42×Dic3C2semidirect
5. #10591333C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
9. #10591222C2semidirect
11. #10591193C2semidirect
31. #63874C4semidirect
57. C4×Dic3⋊C4D3semidirect
58. C42×Dic3D3semidirect
479. C32#2298semidirect
552. C3#73301semidirect
553. C3#73620semidirect

Maximal subgroups

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

subgroupindex
C2×#638742
C4×#37522
C3×C4×Dic3⋊C42
C3×C42×Dic32
#105913332
C4×Dic3⋊Dic32
#105912892
C4×#37222
#105912222
#105911942
#105911932
#736203
#733013