Finite Group Databasebeta

← #11803408

Subgroups — #11803408

Order 1152.

1407 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
1C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
2C2×#63966C211yesmaximal, characteristic
3C2×#63952C211yesmaximal, characteristic
4#10592912C211yesmaximal, characteristic
5C3×#5210C211yesmaximal, characteristic, complemented
6Dic3×#217C211yesmaximal, characteristic, complemented
7#10591696C211yesmaximal, characteristic, complemented
8#10591374C212yesmaximal, complemented
9#10591258C212yesmaximal, complemented
10#10591254C212yesmaximal, complemented
11#10591246C212yesmaximal, complemented
12#82158—31nomaximal
13#74384—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C23×C3×Dic3C2211yescharacteristic
17C23×C3×Dic3C2211yescharacteristic
18C22×#624C2211yescharacteristic
19C2×#3757C2211yescharacteristic
20C2×#3752C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×Dic3⋊C4—24no—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×Dic3⋊C4C2212yes—
27C2×#3724C2211yescharacteristic
28#63966C418yescomplemented
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2211yescharacteristic
31C2×#3722C2212yes—
32C2×Dic32C2211yescharacteristic
33C2×Dic32C2212yes—
34#63952—24no—
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39#63579C2212yes—
40C22×C3×C4⋊C4—31no—
41C2×#929—31no—
42C2×C4×#67—31no—
43C22×Dic3⋊C4D311yescharacteristic, complemented
44C2×#886—31no—
45C2×#67⋊C4—31no—
46C3×#385—31no—
47#5213—31no—
48#5213—31no—
49#5213—61no—
50#5211—31no—
51#5210D311yescharacteristic, complemented
52C4×#217—31no—
53#4990—32no—
54#4989—32no—
55#4989—32no—
56#4978—32no—
57#4976—32no—
58#4972—32no—
59#4943—31no—
60Dic3×C22⋊C4—31no—
61#4669—32no—
62#4654—32no—
63C24×C32C2311yescharacteristic
64C23×C3⋊D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—42no—
67C22×C32×C4C2312yes—
68C2×#638—22no—
69C2×#638—22no—
70C2×#638C2×C414yes—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2311yescharacteristic
73C22×C3×Dic3—22no—
74C22×C3×Dic3—22no—
75C22×C3×Dic3—42no—
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—42no—
86#3757—22no—
87#3752—42no—
88C3×#217—22no—
89C3×#217C2×C414yescomplemented
90C3×Dic3⋊C4—24no—
91C3×Dic3⋊C4—24no—
92C3×Dic3⋊C4—42no—
93#3724—22no—
94Dic3⋊Dic3C2×C418yescomplemented
95#3722—22no—
96#3722C2×C418yescomplemented
97Dic32—22no—
98Dic32—42no—
99#2322—91noSylow
100C23×C3×C4—21no—
101C23×C3×C4—31no—
102C23×C3×C4—31no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—31no—
106C22×#67—31no—
107C22×#67—61no—
108C23×Dic3C2×D311yescharacteristic
109C23×Dic3C2×D311yescharacteristic
110C22×C4×D3—31no—
111C22×C4×D3—31no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—32no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C4⋊C4—64no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—31no—
118C2×#217—31no—
119C2×#217—31no—
120C2×#217—61no—
121C2×#217C2×D311yescharacteristic
122C2×#217C2×D311yescharacteristic
123#929—38no—
124C4×#67—64no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—62no—
132C2×C4⋊Dic3—32no—
133C2×Dic3⋊C4—24no—
134C2×Dic3⋊C4—32no—
135C2×Dic3⋊C4—31no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4C2×D312yes—
138C2×Dic3⋊C4C2×D312yes—
139C2×Dic3⋊C4C2×D312yes—
140C2×C4×Dic3—31no—
141C2×C4×Dic3—31no—
142C2×C4×Dic3—32no—
143C2×C4×Dic3—32no—
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—32no—
154C3⋊#95—32no—
155C3⋊#95—62no—
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—21no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3C22×C412yes—
168C2×C32×C4—22no—
169C2×C32×C4—22no—
170C2×C32×C4—22no—
171C2×C32×C4—44no—
172#638—28no—
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—22no—
178C2×C3⋊Dic3C22×C412yes—
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—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—44no—
191C2×C3×Dic3C22×C414yes—
192C2×C3×Dic3C22×C414yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195#624—44no—
196C2×#123—91no—
197C2×C4×D4—91no—
198C22×C4⋊C4—31no—
199#389—92no—
200#388—92no—
201#387—92no—
202#386—91no—
203#385—31no—
204#385—92no—
205#381—91no—
206C4×C22⋊C4—91no—
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—22no—
215C22×C3×C4—22no—
216C22×C3×C4—34no—
217C22×C3×C4—31no—
218C22×C3×C4—32no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4—34no—
222C22×C3×C4—31no—
223C22×C3×C4—31no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—44no—
228C22×C3×C4—62no—
229C22×C3×C4—62no—
230C22×C3×C4—122no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C2×#67—34no—
234C2×#67—34no—
235C2×#67—64no—
236C2×#67—62no—
237C2×#67—62no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67—122no—
241C2×#67—122no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—42no—
249C22×Dic3—61no—
250C22×Dic3—62no—
251C22×Dic3C4×D314yescomplemented
252C22×Dic3#6714yes—
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—62no—
261C2×C4×D3—122no—
262C2×C4×D3—122no—
263C3×C4⋊C4—64no—
264C3×C4⋊C4—64no—
265C3×C4⋊C4—122no—
266C3×C22⋊C4—34no—
267C3×C22⋊C4—62no—
268#217—22no—
269#217—62no—
270#217—62no—
271#217—122no—
272#217C4×D314yescomplemented
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—122no—
278(C2×D3)⋊C4—122no—
279(C2×D3)⋊C4—124no—
280C4⋊Dic3—38no—
281Dic3⋊C4—24no—
282Dic3⋊C4—24no—
283Dic3⋊C4—38no—
284Dic3⋊C4—42no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287C4×Dic3—62no—
288C4×Dic3—62no—
289C4×Dic3—122no—
290C4×Dic3—122no—
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×C32H(5,𝔽2)12yes—
300C22×C322−1+412yes—
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—42no—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—41no—
314C3×Dic3—41no—
315C22×D4—91no—
316C23×C4—31no—
317C23×C4—31no—
318C23×C4—91no—
319C23×C4D3211yescharacteristic
320#123—98no—
321C4×D4—184no—
322C2×C4⋊C4—32no—
323C2×C4⋊C4—32no—
324C2×C4⋊C4—32no—
325C2×C4⋊C4—64no—
326C2×C4⋊C4—92no—
327C2×C4⋊C4—91no—
328C2×C22⋊C4—31no—
329C2×C22⋊C4—31no—
330C2×C22⋊C4—92no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—92no—
334C2×C42—91no—
335C2×C42—92no—
336#95—32no—
337#95—92no—
338#95—92no—
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×C3#23512yes—
354C23×C3D3×D412yes—
355C23×C3#23912yes—
356C23×C3C2×#6712yes—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D311yescharacteristic
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—62no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—61no—
370C22×D3—122no—
371C22×D3—121no—
372C22×D3—121no—
373C22×D3—122no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—32no—
384C2×C3×C4—32no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—44no—
388C2×C3×C4—44no—
389C2×C3×C4—48no—
390C2×C3×C4—68no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—124no—
402#67—68no—
403#67—68no—
404#67—128no—
405C2×Dic3—28no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—44no—
419C2×Dic3—62no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—121no—
431C2×Dic3—121no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3—122no—
435C2×Dic3C2×C4×D314yes—
436C2×Dic3C2×C4×D314yes—
437C2×Dic3C2×#6712yes—
438C2×Dic3C2×#6712yes—
439C4×D3—124no—
440C4×D3—124no—
441C2×C32—24no—
442C2×C32C2×C4×D411yescharacteristic
443C2×C32#52012yes—
444C2×C32#53411yescharacteristic
445C2×C32#53611yescharacteristic
446C2×C32#53912yes—
447C3⋊D3—42no—
448C24—91no—
449C24C2×D3211yescharacteristic
450C2×D4—94no—
451C2×D4—182no—
452C2×D4—182no—
453C22×C4—22no—
454C22×C4—32no—
455C22×C4—31no—
456C22×C4—32no—
457C22×C4—31no—
458C22×C4—34no—
459C22×C4—34no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—42no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—91no—
466C22×C4—92no—
467C22×C4—122no—
468C22×C4—182no—
469C22×C4—362no—
470C22×C4C2×D3212yes—
471C4⋊C4—64no—
472C4⋊C4—64no—
473C4⋊C4—98no—
474C4⋊C4—122no—
475C4⋊C4—182no—
476C22⋊C4—34no—
477C22⋊C4—62no—
478C22⋊C4—98no—
479C22⋊C4—182no—
480C22⋊C4—182no—
481C22⋊C4—362no—
482C42—182no—
483C42—362no—
484C22×C3—24no—
485C22×C3—22no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—42no—
499C22×C3—44no—
500C22×C3—42no—
501C22×C3—44no—
502C22×C3#89314yes—
503C22×C3C4×#6714yes—
504C22×C3C22×C4×D311yescharacteristic
505C22×C3C22×C4×D311yescharacteristic
506C22×C3C2×#23511yescharacteristic
507C22×C3C2×D3×D411yescharacteristic
508C22×C3#100412yes—
509C22×C3#100412yes—
510C22×C3C2×#23911yescharacteristic
511C22×C3#100712yes—
512C22×C3#101012yes—
513C22×C3C22×#6711yescharacteristic
514C2×D3—62no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—64no—
518C2×D3—122no—
519C2×D3—124no—
520C2×D3—122no—
521C2×D3—121no—
522C2×D3—122no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—241no—
527C2×D3—242no—
528C2×D3—241no—
529C3×C4—44no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4—64no—
533C3×C4—64no—
534C3×C4—62no—
535C3×C4—62no—
536C3×C4—121no—
537C3×C4—121no—
538Dic3—24no—
539Dic3—24no—
540Dic3—22no—
541Dic3—22no—
542Dic3—41no—
543Dic3—41no—
544Dic3—62no—
545Dic3—62no—
546Dic3—122no—
547Dic3—122no—
548Dic3—122no—
549Dic3—242no—
550C32#232211yescharacteristic, complemented, Sylow
551C23—22no—
552C23—22no—
553C23—92no—
554C23—182no—
555C23—181no—
556C23—181no—
557C23—182no—
558C23#379912yes—
559C23C4×D3212yes—
560C23D3×#6712yes—
561C23C22×D3211yescharacteristic
562D4—188no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—34no—
567C2×C4—34no—
568C2×C4—32no—
569C2×C4—32no—
570C2×C4—44no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—68no—
578C2×C4—62no—
579C2×C4—61no—
580C2×C4—61no—
581C2×C4—62no—
582C2×C4—92no—
583C2×C4—124no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—182no—
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×#89311yescharacteristic
599C2×C3#550412yes—
600C2×C3#551512yes—
601C2×C3#554612yes—
602C2×C3#558911yescharacteristic
603C2×C3#564512yes—
604C2×C3#564811yescharacteristic
605C2×C3C2×C4×#6711yescharacteristic
606C2×C3#580411yescharacteristic
607C2×C3#581611yescharacteristic
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#6390414yes—
621C22#6429712yes—
622C22C2×#379911yescharacteristic
623C22C2×C4×D3211yescharacteristic
624C22C2×D3×#6711yescharacteristic
625C22#6433012yes—
626C4—42no—
627C4—64no—
628C4—64no—
629C4—62no—
630C4—62no—
631C4—121no—
632C4—121no—
633C4—182no—
634C4—362no—
635C3—21no—
636C3#7438411yescharacteristic, complemented
637C3#8215811yescharacteristic, complemented
638C2—24no—
639C2—362no—
640C2#1059487412yes—
641C2#1059489711yescharacteristic
642C2#1059498012yes—
643C2C2×#6390411yescharacteristic
644C2#1059552411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2322
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×Dic3⋊C4C2semidirect
5. C3×#5210C2semidirect
6. Dic3×#217C2semidirect
7. #10591696C2semidirect
8. #10591374C2semidirect
9. #10591258C2semidirect
10. #10591254C2semidirect
11. #10591246C2semidirect
28. #63966C4semidirect
43. C22×Dic3⋊C4D3semidirect
51. #5210D3semidirect
76. C22×C3×Dic3C2×C4semidirect
89. C3×#217C2×C4semidirect
94. Dic3⋊Dic3C2×C4semidirect
96. #3722C2×C4semidirect
251. C22×Dic3C4×D3semidirect
272. #217C4×D3semidirect
550. C32#2322semidirect
636. C3#74384semidirect
637. C3#82158semidirect

Maximal subgroups

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

subgroupindex
C22×C3×Dic3⋊C42
C2×#639662
C2×#639522
#105929122
C3×#52102
Dic3×#2172
#105916962
#105913742
#105912582
#105912542
#105912462
#821583
#743843