Finite Group Databasebeta

← #11803067

Subgroups — #11803067

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C3×#4937C211yesmaximal, characteristic, complemented
3C3×#4936C211yesmaximal, characteristic, complemented
4#10591380C212yesmaximal
5#10591378C212yesmaximal, complemented
6#10591370C211yesmaximal, characteristic, complemented
7#10591355C211yesmaximal, characteristic, complemented
8#10591271C212yesmaximal, complemented
9#10591266C212yesmaximal, complemented
10#10591260C211yesmaximal, characteristic, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#74295—31nomaximal
13#74226—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C22×#624C2212yes—
18C2×C32×C42C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C4×C4⋊(C3⋊D3)C418yescomplemented
23C2×C3×C4⋊Dic3C2212yes—
24C2×#3724C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29C3×C3⋊#95C2211yescharacteristic
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×D12—31no—
39C2×C4×D12—31no—
40C2×C4×D12—61no—
41C3×#383—31no—
42C3×#382—31no—
43#4990—32no—
44#4989—32no—
45#4937D311yescharacteristic, complemented
46#4936D311yescharacteristic, complemented
47#4670—32no—
48#4668—32no—
49#4667—31no—
50#4667—31no—
51#4666—31no—
52#4666—31no—
53#4665—32no—
54#4665—32no—
55#4664—31no—
56#4664—31no—
57D3×#95—31no—
58D3×#95—31no—
59#4654—32no—
60#4653—32no—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—24no—
69C2×C4⋊(C3⋊D3)C2×C414yes—
70C2×C4×C3⋊D3—42no—
71C2×C4×C3⋊D3—42no—
72C2×C4×C3⋊D3C2×C414yes—
73C2×C4×C3⋊D3C2×C414yescomplemented
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×#624—24no—
79C2×#624—42no—
80C2×#624—42no—
81C32×C42C2×C414yescomplemented
82#3752C2×C414yes—
83#3752C2×C414yescomplemented
84C4⋊(C3⋊Dic3)C2×C414yescomplemented
85C3×C4⋊Dic3—42no—
86#3724—42no—
87#3722—24no—
88#3722—42no—
89#3722—42no—
90Dic32—42no—
91#2318—91noSylow
92C22×D12—31no—
93C22×D12—31no—
94C22×D12—61no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—31no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—61no—
102C22×C4×D3—61no—
103C2×C3×C4⋊C4—32no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—61no—
118C2×(C2×D3)⋊C4—61no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D312yes—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×C4×Dic3—32no—
126C2×C4×Dic3—32no—
127C4×D12—38no—
128C4×D12—38no—
129C4×D12—68no—
130C3×#95—32no—
131C3×#95—32no—
132C3×#95—31no—
133C3×#95—31no—
134C3×#95—31no—
135C3×#95—31no—
136C3×#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95C2×D312yes—
142C3⋊#95C2×D312yes—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D312yes—
148C23×C32C2411yescharacteristic
149C22×C3⋊D3—22no—
150C22×C3⋊D3—21no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3C22×C412yes—
157C22×C3⋊D3C22×C412yes—
158C22×C3⋊D3#4114yes—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C22×C412yes—
165C2×C32×C4C22×C412yes—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3C22×C412yes—
170C4⋊(C3⋊D3)—28no—
171C4×C3⋊D3—44no—
172C4×C3⋊D3—44no—
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×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185#624—48no—
186C2×C4×D4—91no—
187#388—92no—
188#387—92no—
189#386—92no—
190#385—92no—
191#383—31no—
192#382—31no—
193#381—91no—
194#380—91no—
195C4×C22⋊C4—91no—
196C2×#95—91no—
197C23×D3—31no—
198C23×D3—31no—
199C23×D3—31no—
200C23×D3—31no—
201C23×D3—61no—
202C23×D3—61no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C2×D12—34no—
227C2×D12—34no—
228C2×D12—64no—
229C2×D12—64no—
230C2×D12—64no—
231C2×D12—68no—
232C2×C4×D3—34no—
233C2×C4×D3—34no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×C4×D3—122no—
243C2×C4×D3—122no—
244C2×C4×D3—122no—
245C2×C4×D3—122no—
246C2×C4×D3—122no—
247C2×C4×D3—122no—
248C2×C4×D3—124no—
249C2×C4×D3—124no—
250C3×C4⋊C4—122no—
251C3×C42—24no—
252C3×C42C4×D314yescomplemented
253C3×C42C4×D314yescomplemented
254(C2×D3)⋊C4—34no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—122no—
263(C2×D3)⋊C4—122no—
264(C2×D3)⋊C4—122no—
265(C2×D3)⋊C4—122no—
266C4⋊Dic3—34no—
267C4⋊Dic3—34no—
268C4⋊Dic3—42no—
269C4⋊Dic3—64no—
270Dic3⋊C4—122no—
271Dic3⋊C4—122no—
272C4×Dic3—122no—
273C4×Dic3—122no—
274C22×C32C23×C411yescharacteristic
275C22×C32C2×#4112yes—
276C22×C32H(5,𝔽2)11yescharacteristic
277C22×C32H(5,𝔽2)12yes—
278C22×C322−1+411yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—22no—
281C2×C3⋊D3—22no—
282C2×C3⋊D3—24no—
283C2×C3⋊D3—24no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3#11714yes—
289C32×C4—22no—
290C32×C4—22no—
291C32×C4—22no—
292C3⋊Dic3—22no—
293C3⋊Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C22×D4—91no—
299C23×C4—92no—
300C23×C4—91no—
301C23×C4—91no—
302C4×D4—98no—
303C2×C4⋊C4—32no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—92no—
306C2×C22⋊C4—91no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—92no—
309C2×C22⋊C4—92no—
310C2×C22⋊C4—92no—
311C2×C42—92no—
312C2×C42D3211yescharacteristic
313#95—31no—
314#95—31no—
315#95—31no—
316#95—31no—
317#95—32no—
318#95—32no—
319#95—32no—
320#95—92no—
321#95—92no—
322C23×C3—21no—
323C23×C3C23×D311yescharacteristic
324C23×C3C23×D311yescharacteristic
325C22×D3—32no—
326C22×D3—32no—
327C22×D3—34no—
328C22×D3—34no—
329C22×D3—32no—
330C22×D3—32no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—64no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—61no—
340C22×D3—64no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—61no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—61no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4—62no—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4C2×C4×D312yes—
387C2×C3×C4C2×C4×D312yes—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412D12—68no—
413D12—68no—
414D12—616no—
415C4×D3—128no—
416C4×D3—128no—
417C4×D3—124no—
418C4×D3—124no—
419C4×D3—124no—
420C4×D3—124no—
421C4×D3—128no—
422C4×D3—128no—
423C2×C32C2×#11711yescharacteristic
424C2×C32#51811yescharacteristic
425C2×C32#52011yescharacteristic
426C2×C32#53812yes—
427C2×C32#53912yes—
428C3⋊D3—24no—
429C3⋊D3—42no—
430C24—91no—
431C24—91no—
432C2×D4—94no—
433C2×D4—184no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—94no—
441C22×C4—94no—
442C22×C4—184no—
443C22×C4—362no—
444C22×C4—362no—
445C22×C4—362no—
446C22×C4—362no—
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C4⋊C4—94no—
451C4⋊C4—122no—
452C4⋊C4—362no—
453C22⋊C4—94no—
454C22⋊C4—94no—
455C22⋊C4—184no—
456C22⋊C4—362no—
457C22⋊C4—362no—
458C42—362no—
459C42#62414yescomplemented
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—21no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3C22×C4×D311yescharacteristic
466C22×C3C22×C4×D311yescharacteristic
467C22×C3#100411yescharacteristic
468C22×C3#100711yescharacteristic
469C22×C3D3×#4112yes—
470C22×C3D3×#4112yes—
471C22×C3#100911yescharacteristic
472C22×C3#100912yes—
473C22×C3#100912yes—
474C22×C3#101011yescharacteristic
475C2×D3—34no—
476C2×D3—34no—
477C2×D3—64no—
478C2×D3—64no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—64no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—64no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—62no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—124no—
496C2×D3—122no—
497C2×D3—124no—
498C2×D3—122no—
499C2×D3—124no—
500C2×D3—124no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C3×C4—24no—
506C3×C4—24no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—22no—
513C3×C4—42no—
514C3×C4—122no—
515C3×C4—122no—
516C3×C4—122no—
517C3×C4—122no—
518Dic3—42no—
519Dic3—42no—
520Dic3—42no—
521Dic3—42no—
522Dic3—62no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—122no—
527Dic3—122no—
528C32#231811yescharacteristic, complemented, Sylow
529C23—94no—
530C23—92no—
531C23—92no—
532C23—181no—
533C23—181no—
534C23—182no—
535C23—181no—
536C23—182no—
537C23—181no—
538C23—182no—
539C23C22×D3211yescharacteristic
540D4—188no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—182no—
560C2×C4—182no—
561C2×C4—364no—
562C2×C4—364no—
563C2×C4—368no—
564C2×C4C2×#62412yes—
565C2×C4C2×#62412yes—
566C2×C4C2×#62412yes—
567C2×C3—21no—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3#550411yescharacteristic
573C2×C3D3×#11711yescharacteristic
574C2×C3D3×#11711yescharacteristic
575C2×C3#552111yescharacteristic
576C2×C3#552111yescharacteristic
577C2×C3#552311yescharacteristic
578C2×C3#567812yes—
579C2×C3#569212yes—
580C2×C3#570412yes—
581C2×C3#570712yes—
582D3—64no—
583D3—64no—
584D3—124no—
585D3—124no—
586D3—122no—
587D3—122no—
588C22—94no—
589C22—184no—
590C22—182no—
591C22—182no—
592C22—184no—
593C22—182no—
594C22—182no—
595C22—182no—
596C22—362no—
597C22—362no—
598C22#6429711yescharacteristic
599C22#6430612yes—
600C22#6430711yescharacteristic
601C22#6430812yes—
602C22C22×#62411yescharacteristic
603C4—22no—
604C4—22no—
605C4—22no—
606C4—122no—
607C4—122no—
608C4—122no—
609C4—122no—
610C4—182no—
611C4—182no—
612C3—21no—
613C3#7422611yescharacteristic, complemented
614C3#7429511yescharacteristic, complemented
615C2—184no—
616C2—362no—
617C2#1059394612yes—
618C2#1059401912yes—
619C2#1059496911yescharacteristic
620C2#1059499011yescharacteristic
621C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4937C2semidirect
3. C3×#4936C2semidirect
5. #10591378C2semidirect
6. #10591370C2semidirect
7. #10591355C2semidirect
8. #10591271C2semidirect
9. #10591266C2semidirect
10. #10591260C2semidirect
11. #10591219C2semidirect
22. C4×C4⋊(C3⋊D3)C4semidirect
45. #4937D3semidirect
46. #4936D3semidirect
73. C2×C4×C3⋊D3C2×C4semidirect
81. C32×C42C2×C4semidirect
83. #3752C2×C4semidirect
84. C4⋊(C3⋊Dic3)C2×C4semidirect
252. C3×C42C4×D3semidirect
253. C3×C42C4×D3semidirect
459. C42#624semidirect
528. C32#2318semidirect
613. C3#74226semidirect
614. C3#74295semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C3×#49372
C3×#49362
#105913802
#105913782
#105913702
#105913552
#105912712
#105912662
#105912602
#105912192
#742953
#742263