Finite Group Databasebeta

← #11806069

Subgroups — #11806069

Order 1152.

1249 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic
2#10592687C211yesmaximal, characteristic
3C3×#4977C211yesmaximal, characteristic, complemented
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5#10591371C212yesmaximal, complemented
6C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
7#10591320C211yesmaximal, characteristic
8#10591274C211yesmaximal, characteristic, complemented
9#10591259C212yesmaximal, complemented
10#10591233C212yesmaximal, complemented
11#10591194C212yesmaximal, complemented
12#74160—31nomaximal
13#73646—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3752C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×Dic3⋊Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×Dic32C2212yes—
31#63894C418yescomplemented
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2212yes—
35#63579C2211yescharacteristic
36#63579C2212yes—
37#63579C2211yescharacteristic
38C2×#893—31no—
39C2×C4×D12—31no—
40C3×#382—31no—
41C3×C4×C4⋊C4—31no—
42#4988—31no—
43#4988—31no—
44#4988—31no—
45#4988—61no—
46#4977D311yescharacteristic, complemented
47Dic3×C4⋊C4—31no—
48Dic3×C4⋊C4—31no—
49Dic3×C4⋊C4D311yescharacteristic, complemented
50#4940—32no—
51#4939—31no—
52C4×(C2×D3)⋊C4—32no—
53C4×C4⋊Dic3—31no—
54C4×Dic3⋊C4—31no—
55#4670—32no—
56#4670—32no—
57#4669—32no—
58#4666—32no—
59#4664—32no—
60#4664—32no—
61C23×C3⋊D3C2312yes—
62C22×C32×C4C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)C2×C414yes—
69C22×C3×Dic3C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C2×#624—42no—
76C2×#624—42no—
77C2×#624C2×C418yes—
78C32×C4⋊C4—22no—
79#3752—24no—
80#3752—42no—
81C4×C3⋊Dic3—22no—
82C3×C4⋊Dic3—22no—
83C3×C4⋊Dic3C2×C414yes—
84C3×C4×Dic3—22no—
85C3×C4×Dic3—42no—
86C3×C4×Dic3C2×C414yes—
87Dic3⋊Dic3—22no—
88Dic3⋊Dic3—22no—
89#3722—24no—
90#3722—42no—
91#3722C2×C418yes—
92Dic32—42no—
93#2357—91noSylow
94C22×D12—31no—
95C22×D12—31no—
96C22×D12—61no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104C2×C3×C42—31no—
105C2×C3×C42—31no—
106C2×C3×C42—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
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—62no—
118C2×(C2×D3)⋊C4—62no—
119C2×C4⋊Dic3—31no—
120C2×C4⋊Dic3—31no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×Dic3⋊C4—31no—
124C2×Dic3⋊C4—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—32no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3C2×D311yescharacteristic
131C2×C4×Dic3C2×D312yes—
132C2×C4×Dic3C2×D311yescharacteristic
133#893—38no—
134C4×D12—38no—
135C3×#95—32no—
136C3×#95—32no—
137C3×#95—32no—
138C3⋊#95—31no—
139C3⋊#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95C2×D312yes—
145C3⋊#95C2×D312yes—
146C3⋊#95C2×D312yes—
147C23×C32C2411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3C22×C414yes—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4—22no—
158C2×C32×C4C22×C412yes—
159C2×C32×C4#4112yes—
160C2×C32×C4#4112yes—
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
163C2×C3⋊Dic3—21no—
164C2×C3⋊Dic3—21no—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3#4112yes—
167C4⋊(C3⋊D3)—28no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—21no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C22×C412yes—
183C2×C3×Dic3C22×C414yes—
184C2×C3×Dic3C22×C412yes—
185C2×C3×Dic3#4112yes—
186#624—48no—
187C2×C4×D4—91no—
188#390—91no—
189#390—91no—
190#388—92no—
191#388—92no—
192#382—31no—
193#381—92no—
194C4×C4⋊C4—31no—
195C4×C4⋊C4—91no—
196C4×C4⋊C4—91no—
197C4×C22⋊C4—92no—
198C23×D3—32no—
199C23×D3—32no—
200C23×D3—62no—
201C22×C3×C4—21no—
202C22×C3×C4—22no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—32no—
208C22×C3×C4—31no—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—31no—
214C22×Dic3—31no—
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3C22×D312yes—
220C22×Dic3C22×D311yescharacteristic
221C22×Dic3C22×D311yescharacteristic
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C2×D12—34no—
226C2×D12—34no—
227C2×D12—64no—
228C2×D12—62no—
229C2×D12—62no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—122no—
233C2×D12—122no—
234C2×C4×D3—38no—
235C2×C4×D3—38no—
236C2×C4×D3—122no—
237C2×C4×D3—122no—
238C2×C4×D3—122no—
239C2×C4×D3—122no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—34no—
243C3×C4⋊C4—42no—
244C3×C4⋊C4—62no—
245C3×C42—34no—
246C3×C42—62no—
247C3×C42—122no—
248(C2×D3)⋊C4—38no—
249(C2×D3)⋊C4—38no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—124no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4—122no—
257(C2×D3)⋊C4—122no—
258(C2×D3)⋊C4—122no—
259(C2×D3)⋊C4—124no—
260C4⋊Dic3—22no—
261C4⋊Dic3—62no—
262C4⋊Dic3—62no—
263C4⋊Dic3C4×D314yes—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266C4×Dic3—22no—
267C4×Dic3—42no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3—122no—
271C4×Dic3—122no—
272C4×Dic3—122no—
273C4×Dic3C4×D314yes—
274C22×C32C23×C411yescharacteristic
275C22×C32C2×#4111yescharacteristic
276C22×C32C2×#4111yescharacteristic
277C22×C32C2×#4111yescharacteristic
278C22×C32C2×#4111yescharacteristic
279C22×C32H(5,𝔽2)11yescharacteristic
280C22×C32H(5,𝔽2)11yescharacteristic
281C2×C3⋊D3—24no—
282C2×C3⋊D3—24no—
283C2×C3⋊D3—24no—
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C32×C4—42no—
289C32×C4#11714yes—
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—24no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C22×D4—91no—
299C23×C4—92no—
300C4×D4—98no—
301C2×C4⋊C4—31no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4D3211yescharacteristic
306C2×C22⋊C4—92no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—92no—
309C2×C22⋊C4—92no—
310C2×C22⋊C4—92no—
311C2×C42—31no—
312C2×C42—31no—
313C2×C42—32no—
314C2×C42—91no—
315C2×C42—92no—
316#95—32no—
317#95—32no—
318#95—32no—
319#95—91no—
320#95—91no—
321#95—92no—
322C23×C3—21no—
323C23×C3C23×D311yescharacteristic
324C23×C3C23×D311yescharacteristic
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—64no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
339C22×D3—62no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—122no—
345C22×D3—122no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—32no—
356C2×C3×C4—34no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—42no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—61no—
365C2×C3×C4—61no—
366C2×C3×C4—62no—
367C2×C3×C4—61no—
368C2×C3×C4—62no—
369C2×C3×C4—61no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4C2×C4×D312yes—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4#23512yes—
379C2×C3×C4#23512yes—
380C2×C3×C4#23712yes—
381C2×C3×C4#23912yes—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—22no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—22no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—22no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—21no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—62no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—121no—
411C2×Dic3—121no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3C2×C4×D312yes—
415C2×Dic3C2×C4×D312yes—
416C2×Dic3C2×C4×D314yes—
417C2×Dic3#23912yes—
418D12—68no—
419D12—68no—
420D12—128no—
421C4×D3—128no—
422C4×D3—128no—
423C2×C32C2×#11711yescharacteristic
424C2×C32C4×#4111yescharacteristic
425C2×C32#51811yescharacteristic
426C2×C32#55311yescharacteristic
427C2×C32#55311yescharacteristic
428C2×C32#55911yescharacteristic
429C2×C32#55911yescharacteristic
430C3⋊D3—44no—
431C24—92no—
432C2×D4—94no—
433C2×D4—182no—
434C2×D4—182no—
435C22×C4—31no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—31no—
439C22×C4—31no—
440C22×C4—32no—
441C22×C4—98no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—362no—
445C22×C4—362no—
446C22×C4C2×D3212yes—
447C22×C4C2×D3211yescharacteristic
448C4⋊C4—22no—
449C4⋊C4—34no—
450C4⋊C4—62no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C22⋊C4—98no—
454C22⋊C4—184no—
455C22⋊C4—184no—
456C22⋊C4—362no—
457C22⋊C4—362no—
458C42—34no—
459C42—62no—
460C42—122no—
461C42—182no—
462C42—362no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3C22×C4×D311yescharacteristic
471C22×C3C22×C4×D311yescharacteristic
472C22×C3C2×#23511yescharacteristic
473C22×C3C2×#23511yescharacteristic
474C22×C3C2×#23711yescharacteristic
475C22×C3#100411yescharacteristic
476C22×C3C2×#23911yescharacteristic
477C22×C3C2×#23911yescharacteristic
478C22×C3D3×#4111yescharacteristic
479C22×C3D3×#4111yescharacteristic
480C22×C3D3×#4111yescharacteristic
481C22×C3#100911yescharacteristic
482C22×C3#100911yescharacteristic
483C22×C3#100911yescharacteristic
484C2×D3—64no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—64no—
488C2×D3—64no—
489C2×D3—64no—
490C2×D3—124no—
491C2×D3—124no—
492C2×D3—124no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—242no—
502C2×D3—242no—
503C2×D3—242no—
504C2×D3—242no—
505C3×C4—24no—
506C3×C4—42no—
507C3×C4—42no—
508C3×C4—62no—
509C3×C4—64no—
510C3×C4—62no—
511C3×C4—62no—
512C3×C4—82no—
513C3×C4—121no—
514C3×C4—122no—
515C3×C4#87214yes—
516C3×C4#89214yes—
517Dic3—22no—
518Dic3—22no—
519Dic3—22no—
520Dic3—24no—
521Dic3—42no—
522Dic3—41no—
523Dic3—62no—
524Dic3—62no—
525Dic3—122no—
526Dic3—122no—
527Dic3—121no—
528Dic3—121no—
529C32#235711yescharacteristic, complemented, Sylow
530C23—94no—
531C23—182no—
532C23—182no—
533C23—182no—
534C23—182no—
535C23—182no—
536C23—182no—
537C23C22×D3211yescharacteristic
538D4—188no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—32no—
543C2×C4—32no—
544C2×C4—34no—
545C2×C4—32no—
546C2×C4—61no—
547C2×C4—61no—
548C2×C4—61no—
549C2×C4—62no—
550C2×C4—61no—
551C2×C4—61no—
552C2×C4—62no—
553C2×C4—61no—
554C2×C4—61no—
555C2×C4—61no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—62no—
560C2×C4—92no—
561C2×C4—181no—
562C2×C4—181no—
563C2×C4—181no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—368no—
567C2×C4#379912yes—
568C2×C4C4×D3212yes—
569C2×C4#380412yes—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3C2×#87211yescharacteristic
578C2×C3C2×#89211yescharacteristic
579C2×C3#551411yescharacteristic
580C2×C3#552111yescharacteristic
581C2×C3#552211yescharacteristic
582C2×C3#553011yescharacteristic
583C2×C3#554511yescharacteristic
584C2×C3#555911yescharacteristic
585C2×C3C4×#23911yescharacteristic
586C2×C3#558511yescharacteristic
587C2×C3#568111yescharacteristic
588C2×C3#568111yescharacteristic
589C2×C3#569511yescharacteristic
590C2×C3#569511yescharacteristic
591D3—124no—
592D3—124no—
593D3—244no—
594C22—184no—
595C22—184no—
596C22—184no—
597C22—362no—
598C22—362no—
599C22—362no—
600C22—362no—
601C22C2×#379911yescharacteristic
602C22C2×C4×D3211yescharacteristic
603C22#6431211yescharacteristic
604C22#6431411yescharacteristic
605C22D3×#23911yescharacteristic
606C22#6432011yescharacteristic
607C22C2×#380411yescharacteristic
608C4—42no—
609C4—62no—
610C4—62no—
611C4—64no—
612C4—62no—
613C4—121no—
614C4—122no—
615C4—182no—
616C4—361no—
617C4#6383614yes—
618C3—21no—
619C3#7364611yescharacteristic, complemented
620C3#7416011yescharacteristic, complemented
621C2—364no—
622C2#1059436211yescharacteristic
623C2#1059456211yescharacteristic
624C2#1059457811yescharacteristic
625C2#1059460411yescharacteristic
626C2C2×#6383611yescharacteristic
627C2#1059521011yescharacteristic
628C2#1059538811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4977C2semidirect
4. C3×Dic3×C4⋊C4C2semidirect
5. #10591371C2semidirect
6. C4×Dic3⋊Dic3C2semidirect
8. #10591274C2semidirect
9. #10591259C2semidirect
10. #10591233C2semidirect
11. #10591194C2semidirect
31. #63894C4semidirect
46. #4977D3semidirect
49. Dic3×C4⋊C4D3semidirect
529. C32#2357semidirect
619. C3#73646semidirect
620. C3#74160semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
#105926872
C3×#49772
C3×Dic3×C4⋊C42
#105913712
C4×Dic3⋊Dic32
#105913202
#105912742
#105912592
#105912332
#105911942
#741603
#736463