Finite Group Databasebeta

← #11819083

Subgroups — #11819083

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64078C211yesmaximal, characteristic, complemented
2C2×#63856C211yesmaximal, characteristic
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×#4929C211yesmaximal, characteristic, complemented
5#10591322C212yesmaximal
6#10591316C212yesmaximal
7#10591313C211yesmaximal, characteristic
8#10591273C212yesmaximal, complemented
9Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
10#10591220C211yesmaximal, characteristic, complemented
11#10591218C212yesmaximal, complemented
12#76633—31nomaximal
13#73508—31nomaximal
14C22×#634C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C2×C32×C42C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64078—24no—
22C2×C3×(C2×D3)⋊C4C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×#3724C2212yes—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×Dic32C2212yes—
30#63856—24no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×#946—31no—
40C2×#924—31no—
41C2×#869—31no—
42C2×#869—31no—
43C2×#869—61no—
44C3×#391—31no—
45C3×C4×C22⋊C4—31no—
46#5229—31no—
47#5212—31no—
48#4987—31no—
49Dic3×C4⋊C4—31no—
50#4951—32no—
51#4947—32no—
52C4×(C2×D3)⋊C4D311yescharacteristic
53C4×C4⋊Dic3—31no—
54#4929—31no—
55#4929D311yescharacteristic, complemented
56#4673—32no—
57#4670—32no—
58#4660—32no—
59#4660—32no—
60#4646—32no—
61#4646—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C2×#634—24no—
69C2×#634—24no—
70C2×#634—42no—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3—22no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6—22no—
82C32×C42—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4⋊(C3⋊Dic3)—24no—
85C4⋊(C3⋊Dic3)D414yes—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4Q814yescomplemented
88C3×C4⋊Dic3—22no—
89C3×C4×Dic3—22no—
90#3724—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—42no—
93Dic32—42no—
94#2492—91noSylow
95C22×C3×Q8—31no—
96C23×C3×C4—31no—
97C22×C4×D3C2×D311yescharacteristic
98C22×Dic6—32no—
99C22×Dic6—32no—
100C22×Dic6—62no—
101C22×Dic6C2×D311yescharacteristic
102C2×C3×C4⋊C4—31no—
103C2×C3×C22⋊C4—31no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C42—21no—
106C2×C3×C42—31no—
107C2×C3×C42C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109C2×#217—32no—
110C2×#217—32no—
111#946—64no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D311yescharacteristic
115C2×(C2×D3)⋊C4C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—31no—
122C2×C4⋊Dic3—61no—
123C2×C4⋊Dic3—61no—
124C2×C4⋊Dic3—62no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—64no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3C2×D311yescharacteristic
132#869—64no—
133#869—64no—
134#869—68no—
135C3×#95—31no—
136C3×#95—32no—
137C3×#95—31no—
138C3×#95—32no—
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×D312yes—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D312yes—
151C23×C32C2411yescharacteristic
152C22×C3×D3—21no—
153C22×C3×D3—21no—
154C22×C3×D3—21no—
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3C2×Q812yes—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×Q812yes—
165C2×C32×C4#4112yes—
166C2×C32×C4#4112yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×D414yes—
174#634—48no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3C2×Q812yes—
190C3×C4×D3—44no—
191C3×Dic6—44no—
192C2×C4⋊Q8—91no—
193C2×C22⋊Q8—91no—
194#400—92no—
195#393—92no—
196#391—31no—
197#391—92no—
198#391—91no—
199#388—92no—
200#380—91no—
201C4×C4⋊C4—91no—
202C4×C22⋊C4—31no—
203C24×C3—31no—
204C23×D3C22×D311yescharacteristic
205C2×C3×Q8—62no—
206C2×C3×Q8—62no—
207C2×C3×Q8—62no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—32no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4—62no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—32no—
226C22×Dic3—32no—
227C22×Dic3—32no—
228C22×Dic3—32no—
229C22×Dic3—62no—
230C22×Dic3—62no—
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D312yes—
235C22×Dic3C22×D311yescharacteristic
236C2×C4×D3—22no—
237C2×C4×D3—22no—
238C2×C4×D3—22no—
239C2×Dic6—22no—
240C2×Dic6—22no—
241C2×Dic6—22no—
242C2×Dic6—64no—
243C2×Dic6—64no—
244C2×Dic6—68no—
245C2×Dic6—64no—
246C2×Dic6—64no—
247C2×Dic6—124no—
248C2×Dic6—122no—
249C2×Dic6—122no—
250C2×Dic6—124no—
251C3×C4⋊C4—62no—
252C3×C22⋊C4—34no—
253C3×C22⋊C4—62no—
254C3×C42—24no—
255C3×C42—22no—
256C3×C42—22no—
257C3×C42—62no—
258#217—64no—
259#217—122no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—122no—
263(C2×D3)⋊C4Dic614yescomplemented
264C4⋊Dic3—22no—
265C4⋊Dic3—34no—
266C4⋊Dic3—34no—
267C4⋊Dic3—64no—
268C4⋊Dic3—64no—
269C4⋊Dic3—64no—
270C4⋊Dic3—68no—
271C4⋊Dic3—64no—
272C4⋊Dic3—62no—
273C4⋊Dic3—62no—
274Dic3⋊C4—64no—
275Dic3⋊C4—64no—
276C4×Dic3—22no—
277C4×Dic3—122no—
278C4×Dic3—122no—
279C22×C32C22×D411yescharacteristic
280C22×C32C22×Q811yescharacteristic
281C22×C32C2×#4111yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32H(5,𝔽2)11yescharacteristic
285C22×C322−1+411yescharacteristic
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—41no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4#12414yes—
296C3⋊Dic3—24no—
297C3⋊Dic3—42no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C3×Dic3—41no—
301C3×Dic3—42no—
302C3×Dic3—41no—
303C22×Q8—31no—
304C22×Q8—92no—
305C23×C4—31no—
306C4⋊Q8—184no—
307C22⋊Q8—184no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—92no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—92no—
313C2×C22⋊C4—31no—
314C2×C22⋊C4—31no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C42—31no—
318C2×C42—92no—
319C2×C42D3211yescharacteristic
320#95—31no—
321#95—31no—
322#95—32no—
323#95—32no—
324#95—92no—
325#95—92no—
326#95—92no—
327#95—92no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3C23×D311yescharacteristic
337C23×C3C23×D311yescharacteristic
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3C2×Dic612yes—
345C3×Q8—124no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—32no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—62no—
368C2×C3×C4—61no—
369C2×C3×C4—62no—
370C2×C3×C4—61no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—62no—
374C2×C3×C4—61no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—61no—
378C2×C3×C4—124no—
379C2×C3×C4C2×Dic612yes—
380C2×C3×C4#23512yes—
381C2×C3×C4#23512yes—
382C2×C3×C4#23512yes—
383C2×C3×C4D3×D412yes—
384C2×C3×C4D3×D412yes—
385C2×C3×C4#23712yes—
386C2×C3×C4#23712yes—
387C2×C3×C4D3×Q812yes—
388C2×C3×C4#23912yes—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—21no—
392C2×Dic3—22no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—34no—
404C2×Dic3—34no—
405C2×Dic3—64no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—122no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3—122no—
421C2×Dic3C2×Dic612yes—
422C4×D3—44no—
423Dic6—44no—
424Dic6—128no—
425Dic6—128no—
426Dic6—1216no—
427C2×C32C2×#12411yescharacteristic
428C2×C32#53311yescharacteristic
429C2×C32#54211yescharacteristic
430C2×C32#54611yescharacteristic
431C2×C32D4×Q811yescharacteristic
432C2×C32#55411yescharacteristic
433C2×C32#55611yescharacteristic
434C3×D3—42no—
435C24—31no—
436C2×Q8—62no—
437C2×Q8—62no—
438C2×Q8—62no—
439C2×Q8—184no—
440C2×Q8—184no—
441C2×Q8—362no—
442C22×C4—31no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—62no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—92no—
451C22×C4—92no—
452C22×C4C2×D3211yescharacteristic
453C22×C4C2×D3211yescharacteristic
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—62no—
456C4⋊C4—94no—
457C4⋊C4—184no—
458C4⋊C4—184no—
459C4⋊C4—182no—
460C22⋊C4—34no—
461C22⋊C4—62no—
462C22⋊C4—184no—
463C22⋊C4—362no—
464C42—22no—
465C42—62no—
466C42—362no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3—62no—
477C22×C3—121no—
478C22×C3—121no—
479C22×C3—121no—
480C22×C3—121no—
481C22×C3C22×Dic611yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×#23511yescharacteristic
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C2×D3×D411yescharacteristic
487C22×C3C2×#23711yescharacteristic
488C22×C3C2×#23711yescharacteristic
489C22×C3C2×D3×Q811yescharacteristic
490C22×C3C2×#23911yescharacteristic
491C22×C3#100911yescharacteristic
492C22×C3#100911yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3#101011yescharacteristic
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—22no—
498C2×D3—41no—
499C2×D3—41no—
500C2×D3—41no—
501C2×D3—41no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—24no—
509C3×C4—62no—
510C3×C4—121no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4—121no—
514C3×C4#88514yes—
515C3×C4#88514yes—
516Dic3—22no—
517Dic3—42no—
518Dic3—42no—
519Dic3—41no—
520Dic3—41no—
521Dic3—64no—
522Dic3—64no—
523Dic3—124no—
524Dic3—124no—
525Dic3—122no—
526Dic3—122no—
527C32#249211yescharacteristic, complemented, Sylow
528C23—32no—
529C23—61no—
530C23—61no—
531C23—61no—
532C23—61no—
533C23—61no—
534C23—61no—
535C23C22×D3211yescharacteristic
536Q8—124no—
537Q8—368no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—32no—
543C2×C4—61no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—62no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—61no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—61no—
557C2×C4—94no—
558C2×C4—124no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4D3×Dic612yes—
565C2×C4#379512yes—
566C2×C4#379512yes—
567C2×C4#379912yes—
568C2×C4#381112yes—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—122no—
577C2×C3#547011yescharacteristic
578C2×C3C2×#88511yescharacteristic
579C2×C3C2×#88511yescharacteristic
580C2×C3#553411yescharacteristic
581C2×C3D4×Dic611yescharacteristic
582C2×C3#554211yescharacteristic
583C2×C3#554311yescharacteristic
584C2×C3#555011yescharacteristic
585C2×C3#557911yescharacteristic
586C2×C3#558411yescharacteristic
587C2×C3#563011yescharacteristic
588C2×C3#563211yescharacteristic
589C2×C3#568211yescharacteristic
590C2×C3#572811yescharacteristic
591D3—42no—
592C22—62no—
593C22—62no—
594C22—62no—
595C22—121no—
596C22—121no—
597C22—121no—
598C22—121no—
599C22C2×D3×Dic611yescharacteristic
600C22C2×#379511yescharacteristic
601C22C2×#379511yescharacteristic
602C22#6429811yescharacteristic
603C22C2×#379911yescharacteristic
604C22#6430811yescharacteristic
605C22C2×#381111yescharacteristic
606C4—22no—
607C4—22no—
608C4—62no—
609C4—121no—
610C4—122no—
611C4—121no—
612C4—122no—
613C4—184no—
614C4—362no—
615C4#6391314yes—
616C3—21no—
617C3#7350811yescharacteristic, complemented
618C3#7663311yescharacteristic, complemented
619C2—122no—
620C2#1059385911yescharacteristic
621C2#1059387911yescharacteristic
622C2#1059396011yescharacteristic
623C2#1059396111yescharacteristic
624C2#1059491511yescharacteristic
625C2C2×#6391311yescharacteristic
626C2#1059501811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C42C22
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64078C2semidirect
4. C3×#4929C2semidirect
8. #10591273C2semidirect
9. Dic3×C4⋊Dic3C2semidirect
10. #10591220C2semidirect
11. #10591218C2semidirect
55. #4929D3semidirect
87. C3×(C2×D3)⋊C4Q8semidirect
263. (C2×D3)⋊C4Dic6semidirect
527. C32#2492semidirect
617. C3#73508semidirect
618. C3#76633semidirect

Maximal subgroups

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

subgroupindex
C2×#640782
C2×#638562
C3×C4×(C2×D3)⋊C42
C3×#49292
#105913222
#105913162
#105913132
#105912732
Dic3×C4⋊Dic32
#105912202
#105912182
#766333
#735083