Finite Group Databasebeta

← #11802162

Subgroups — #11802162

Order 1152.

1519 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63966C211yesmaximal, characteristic
2C22×Dic32C211yesmaximal, characteristic, complemented
3C2×#63952C211yesmaximal, characteristic
4#10592657C211yesmaximal, characteristic
5C3×#4943C211yesmaximal, characteristic, complemented
6C3×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
7#10591719C211yesmaximal, characteristic, complemented
8#10591259C212yesmaximal, complemented
9#10591250C212yesmaximal, complemented
10#10591242C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12#74052—31nomaximal
13C4×#886—31nomaximal
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3752C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×#3724C2211yescharacteristic
25#63966C418yescomplemented
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2211yescharacteristic
29C2×#3722C2212yes—
30C2×Dic32—24no—
31C2×Dic32C2212yes—
32C2×Dic32C2211yescharacteristic
33C2×Dic32C2212yes—
34#63952—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#929—31no—
41C2×C4×#67—31no—
42C22×C4×Dic3—31no—
43C22×C4×Dic3—31no—
44C2×#886—31no—
45C2×#67⋊C4—31no—
46C3×#381—31no—
47C3×C4×C22⋊C4—31no—
48#4958—31no—
49#4958—31no—
50#4958—61no—
51#4950—31no—
52#4946—31no—
53#4943D311yescharacteristic, complemented
54Dic3×C22⋊C4D311yescharacteristic, complemented
55C4×(C2×D3)⋊C4—32no—
56C4×C4⋊Dic3—32no—
57#4670—32no—
58#4669—32no—
59#4666—32no—
60#4653—32no—
61#4652—32no—
62#4649—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C2×#638—22no—
67C2×#638—22no—
68C2×#638C2×C414yes—
69C22×C3⋊Dic3—22no—
70C22×C3⋊Dic3—24no—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2312yes—
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—24no—
76C22×C3×Dic3C2×C414yescomplemented
77C22×C3×Dic3D414yes—
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C2×#624—22no—
85C2×#624—24no—
86C32×C22⋊C4—22no—
87#3752—24no—
88C3×#217—22no—
89C3×#217C2×C414yescomplemented
90C3×C4×Dic3—24no—
91#3724—22no—
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3C2×C418yescomplemented
94#3722—22no—
95#3722C2×C418yescomplemented
96Dic32—22no—
97Dic32—24no—
98Dic32—24no—
99C4×#123—91noSylow
100C23×C3×C4—31no—
101C23×C3×C4—31no—
102C22×#67—31no—
103C22×#67—31no—
104C22×#67—61no—
105C23×Dic3—31no—
106C23×Dic3—31no—
107C23×Dic3—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C22⋊C4—31no—
115C2×C3×C22⋊C4C2×D311yescharacteristic
116C2×C3×C22⋊C4C2×D311yescharacteristic
117C2×C3×C42—32no—
118C2×#217C2×D311yescharacteristic
119C2×#217C2×D311yescharacteristic
120#929—38no—
121C4×#67—64no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—62no—
129C2×C4⋊Dic3—32no—
130C2×C4⋊Dic3—32no—
131C2×Dic3⋊C4—32no—
132C2×Dic3⋊C4—32no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×C4×Dic3—31no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—32no—
141C2×C4×Dic3—64no—
142C2×C4×Dic3—64no—
143C2×C4×Dic3C2×D312yes—
144#886—38no—
145#67⋊C4—64no—
146C3×#95—32no—
147C3×#95—32no—
148C3×#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—62no—
154C3⋊#95C2×D312yes—
155C3⋊#95C2×D312yes—
156C3⋊#95C2×D312yes—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32C22×C412yes—
160C23×C32C2×D412yes—
161C23×C32#4112yes—
162C23×C32C2411yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—21no—
167C22×C3⋊D3C22×C412yes—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171#638—28no—
172C2×C3⋊Dic3—28no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3C22×C412yes—
178C2×C3⋊Dic3#4114yes—
179C2×C3×Dic3—28no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—28no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C22×C414yes—
191C2×C3×Dic3C22×C414yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3#4114yes—
195#624—44no—
196C2×#123—91no—
197C2×C4×D4—91no—
198C22×C42—91no—
199#388—92no—
200#387—92no—
201#386—91no—
202#385—91no—
203#381—31no—
204C4×C4⋊C4—92no—
205C4×C22⋊C4—31no—
206C4×C22⋊C4—92no—
207C24×C3—21no—
208C24×C3C22×D311yescharacteristic
209C24×C3C22×D311yescharacteristic
210C23×D3—31no—
211C23×D3—31no—
212C23×D3—61no—
213C22×C3×C4—22no—
214C22×C3×C4—31no—
215C22×C3×C4—34no—
216C22×C3×C4—34no—
217C22×C3×C4—32no—
218C22×C3×C4—32no—
219C22×C3×C4—31no—
220C22×C3×C4—31no—
221C22×C3×C4—31no—
222C22×C3×C4—64no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D312yes—
226C22×C3×C4C22×D312yes—
227C2×#67—34no—
228C2×#67—34no—
229C2×#67—64no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—62no—
233C2×#67—62no—
234C2×#67—122no—
235C2×#67—122no—
236C22×Dic3—22no—
237C22×Dic3—22no—
238C22×Dic3—24no—
239C22×Dic3—32no—
240C22×Dic3—32no—
241C22×Dic3—31no—
242C22×Dic3—31no—
243C22×Dic3—61no—
244C22×Dic3—62no—
245C22×Dic3—64no—
246C22×Dic3—64no—
247C22×Dic3—62no—
248C22×Dic3—62no—
249C22×Dic3—124no—
250C22×Dic3—122no—
251C22×Dic3C4×D314yescomplemented
252C22×Dic3D1214yes—
253C22×Dic3C22×D311yescharacteristic
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D311yescharacteristic
258C22×Dic3C22×D311yescharacteristic
259C2×C4×D3—62no—
260C2×C4×D3—64no—
261C2×C4×D3—62no—
262C2×C4×D3—64no—
263C3×C22⋊C4—22no—
264C3×C22⋊C4—22no—
265C3×C22⋊C4—34no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—62no—
268C3×C42—64no—
269#217—22no—
270#217C4×D314yescomplemented
271(C2×D3)⋊C4—38no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—124no—
278C4⋊Dic3—38no—
279C4⋊Dic3—64no—
280Dic3⋊C4—38no—
281Dic3⋊C4—64no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284C4×Dic3—24no—
285C4×Dic3—64no—
286C4×Dic3—64no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—64no—
290C4×Dic3—64no—
291C22×C32—24no—
292C22×C32—22no—
293C22×C32—22no—
294C22×C32—24no—
295C22×C32C4×D414yes—
296C22×C32C23×C411yescharacteristic
297C22×C32C22×D411yescharacteristic
298C22×C32C2×#4111yescharacteristic
299C22×C32C2×#4112yes—
300C22×C32C2×#4112yes—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—24no—
303C2×C3⋊D3—41no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—42no—
306C32×C4—42no—
307C3⋊Dic3—22no—
308C3⋊Dic3—24no—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—41no—
313C3×Dic3—41no—
314C3×Dic3#12314yescomplemented
315C22×D4—91no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—91no—
319C23×C4—91no—
320#123—98no—
321C4×D4—184no—
322C2×C4⋊C4—92no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—92no—
325C2×C22⋊C4—31no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4D3211yescharacteristic
331C2×C42—32no—
332C2×C42—91no—
333C2×C42—92no—
334C2×C42—92no—
335C2×C42—184no—
336#95—32no—
337#95—32no—
338#95—32no—
339#95—92no—
340#95—92no—
341C23×C3—22no—
342C23×C3—22no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—21no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—42no—
350C23×C3—42no—
351C23×C3C2×C4×D312yes—
352C23×C3C2×C4×D312yes—
353C23×C3C2×D1212yes—
354C23×C3#23512yes—
355C23×C3D3×D412yes—
356C23×C3#23712yes—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D311yescharacteristic
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—62no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—122no—
371C22×D3—121no—
372C22×D3—121no—
373C22×D3—122no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—32no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—34no—
384C2×C3×C4—32no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—68no—
389C2×C3×C4—68no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399#67—68no—
400#67—68no—
401#67—128no—
402C2×Dic3—28no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—28no—
409C2×Dic3—21no—
410C2×Dic3—21no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—34no—
416C2×Dic3—34no—
417C2×Dic3—62no—
418C2×Dic3—64no—
419C2×Dic3—68no—
420C2×Dic3—68no—
421C2×Dic3—62no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—62no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—122no—
430C2×Dic3—122no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3—128no—
434C2×Dic3C2×C4×D314yes—
435C2×Dic3C2×C4×D314yes—
436C2×Dic3C2×D1212yes—
437C2×Dic3C2×D1212yes—
438C2×Dic3#23714yes—
439C4×D3—124no—
440C4×D3—124no—
441C2×C32—24no—
442C2×C32C2×C4×D411yescharacteristic
443C2×C32C4×#4112yes—
444C2×C32C2×#12311yescharacteristic
445C2×C32#52511yescharacteristic
446C2×C32#52912yes—
447C3⋊D3—42no—
448C24—91no—
449C24C2×D3211yescharacteristic
450C2×D4—94no—
451C2×D4—182no—
452C2×D4—182no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—31no—
456C22×C4—32no—
457C22×C4—34no—
458C22×C4—34no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—64no—
462C22×C4—62no—
463C22×C4—62no—
464C22×C4—92no—
465C22×C4—91no—
466C22×C4—182no—
467C22×C4—184no—
468C22×C4—184no—
469C22×C4—182no—
470C22×C4C2×D3212yes—
471C4⋊C4—98no—
472C4⋊C4—182no—
473C4⋊C4—184no—
474C22⋊C4—22no—
475C22⋊C4—34no—
476C22⋊C4—62no—
477C22⋊C4—98no—
478C22⋊C4—184no—
479C22⋊C4—182no—
480C42—64no—
481C42—184no—
482C42—184no—
483C42—182no—
484C22×C3—24no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—24no—
491C22×C3—24no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—24no—
498C22×C3—42no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—42no—
502C22×C3C4×D1214yes—
503C22×C3#67⋊C414yes—
504C22×C3C22×C4×D311yescharacteristic
505C22×C3C22×C4×D311yescharacteristic
506C22×C3C22×D1211yescharacteristic
507C22×C3C2×#23511yescharacteristic
508C22×C3C2×D3×D411yescharacteristic
509C22×C3C2×#23712yes—
510C22×C3C2×#23711yescharacteristic
511C22×C3D3×#4112yes—
512C22×C3D3×#4112yes—
513C22×C3D3×#4112yes—
514C2×D3—62no—
515C2×D3—62no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—122no—
519C2×D3—124no—
520C2×D3—122no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—122no—
526C2×D3—241no—
527C2×D3—242no—
528C2×D3—241no—
529C3×C4—34no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4—62no—
533C3×C4—64no—
534C3×C4—64no—
535C3×C4—82no—
536C3×C4—121no—
537C3×C4—121no—
538Dic3—24no—
539Dic3—22no—
540Dic3—24no—
541Dic3—41no—
542Dic3—41no—
543Dic3—64no—
544Dic3—62no—
545Dic3—62no—
546Dic3—64no—
547Dic3—124no—
548Dic3—122no—
549Dic3#88614yescomplemented
550C32C4×#12311yescharacteristic, complemented, Sylow
551C23—22no—
552C23—22no—
553C23—92no—
554C23—181no—
555C23—182no—
556C23—182no—
557C23—181no—
558C23C4×D3212yes—
559C23D3×D1212yes—
560C23#380412yes—
561C23C22×D3211yescharacteristic
562D4—188no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—32no—
567C2×C4—34no—
568C2×C4—34no—
569C2×C4—34no—
570C2×C4—32no—
571C2×C4—68no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—68no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—92no—
583C2×C4—94no—
584C2×C4—188no—
585C2×C4—182no—
586C2×C4—181no—
587C2×C4—182no—
588C2×C4—181no—
589C2×C4—364no—
590C2×C3—24no—
591C2×C3—24no—
592C2×C3—22no—
593C2×C3—21no—
594C2×C3—22no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—44no—
598C2×C3C2×C4×D1211yescharacteristic
599C2×C3C2×#67⋊C411yescharacteristic
600C2×C3C2×#88611yescharacteristic
601C2×C3#552212yes—
602C2×C3#552411yescharacteristic
603C2×C3C4×#23712yes—
604C2×C3#553812yes—
605C2×C3#564912yes—
606C2×C3D3×#12311yescharacteristic
607C2×C3#565611yescharacteristic
608D3—122no—
609D3—122no—
610D3—242no—
611C22—24no—
612C22—22no—
613C22—24no—
614C22—22no—
615C22—184no—
616C22—182no—
617C22—361no—
618C22—362no—
619C22—361no—
620C22#6388014yes—
621C22C2×C4×D3211yescharacteristic
622C22C2×D3×D1211yescharacteristic
623C22D3×#23712yes—
624C22#6431212yes—
625C22C2×#380411yescharacteristic
626C4—34no—
627C4—42no—
628C4—64no—
629C4—64no—
630C4—62no—
631C4—121no—
632C4—121no—
633C4—184no—
634C4—182no—
635C3—21no—
636C3C4×#88611yescharacteristic, complemented
637C3#7405211yescharacteristic, complemented
638C2—24no—
639C2—362no—
640C2#1059404812yes—
641C2#1059407911yescharacteristic
642C2D3×#88611yescharacteristic
643C2C2×#6388011yescharacteristic
644C2#1059511612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#123
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic32C2semidirect
5. C3×#4943C2semidirect
6. C3×Dic3×C22⋊C4C2semidirect
7. #10591719C2semidirect
8. #10591259C2semidirect
9. #10591250C2semidirect
10. #10591242C2semidirect
11. #10591233C2semidirect
25. #63966C4semidirect
53. #4943D3semidirect
54. Dic3×C22⋊C4D3semidirect
76. C22×C3×Dic3C2×C4semidirect
89. C3×#217C2×C4semidirect
93. Dic3⋊Dic3C2×C4semidirect
95. #3722C2×C4semidirect
251. C22×Dic3C4×D3semidirect
270. #217C4×D3semidirect
314. C3×Dic3#123semidirect
549. Dic3#886semidirect
550. C32C4×#123semidirect
636. C3C4×#886semidirect
637. C3#74052semidirect

Maximal subgroups

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

subgroupindex
C2×#639662
C22×Dic322
C2×#639522
#105926572
C3×#49432
C3×Dic3×C22⋊C42
#105917192
#105912592
#105912502
#105912422
#105912332
#740523
C4×#8863