Finite Group Databasebeta

← #11808237

Subgroups — #11808237

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 669 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C2×C4×#626C212yesmaximal, complemented
4C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
5#10591397C211yesmaximal, characteristic, complemented
6#10591395C212yesmaximal, complemented
7#10591394C211yesmaximal, characteristic, complemented
8#10591393C211yesmaximal, characteristic, complemented
9#10591312C212yesmaximal, complemented
10C4×#3722C211yesmaximal, characteristic, complemented
11#10591205C211yesmaximal, characteristic, complemented
12#73580—32nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×#627C2211yescharacteristic
18C22×#626C2212yes—
19C22×#626C2212yes—
20C22×#625C2211yescharacteristic
21C2×#3798—24no—
22C2×#3798—28no—
23C2×C32×C42C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C4×C4⋊(C3⋊D3)—24no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C4×#626—28no—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2211yescharacteristic
39#63579C2211yescharacteristic
40C22×#235—32no—
41C2×C4×#67—32no—
42C2×C4×D12—32no—
43C2×C4×D12—32no—
44C2×C4×D12—61no—
45C3×C4×C22⋊C4—32no—
46#4961—32no—
47#4961—32no—
48#4960—32no—
49#4960—32no—
50C4×(C2×D3)⋊C4—32no—
51C4×(C2×D3)⋊C4D312yescomplemented
52#4673—32no—
53#4672—32no—
54#4671—32no—
55#4656—32no—
56C23×C3⋊D3C2311yescharacteristic
57C23×C3⋊D3C2311yescharacteristic
58C23×C3×D3C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C32×C4C2311yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2311yescharacteristic
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4×C3⋊D3—24no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—24no—
70C2×C4×C3⋊D3D414yescomplemented
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C2×C3×C4×D3—24no—
75C2×C3×C4×D3—24no—
76C2×C3×C4×D3D418yescomplemented
77C2×#627—22no—
78C2×#627—24no—
79C2×#626—24no—
80C2×#626—24no—
81C2×#626—24no—
82C2×#626—24no—
83C2×#626—24no—
84C2×#626—24no—
85C2×#625—24no—
86C2×#625—22no—
87#3798—232no—
88C32×C42—22no—
89#3752—22no—
90#3752—22no—
91C4⋊(C3⋊Dic3)—22no—
92C3×(C2×D3)⋊C4—24no—
93C3×(C2×D3)⋊C4—24no—
94C3×C4×Dic3—24no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97#3722—24no—
98(C2×D3)⋊Dic3—24no—
99#2388—91noSylow
100C23×C3×C4—32no—
101C22×#67—32no—
102C22×#67—32no—
103C22×#67—32no—
104C2×#235—68no—
105C2×#235—68no—
106C2×#235—68no—
107C22×D12—32no—
108C22×D12—32no—
109C22×D12—32no—
110C22×D12—61no—
111C22×C4×D3—32no—
112C22×C4×D3—32no—
113C22×C4×D3—61no—
114C22×C4×D3—61no—
115C22×C4×D3C2×D312yes—
116C22×Dic6—32no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C42—21no—
120C2×C3×C42—32no—
121C2×C3×C42C2×D312yes—
122C2×#217—32no—
123C4×#67—68no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×C4⋊Dic3—32no—
137C2×C4⋊Dic3—61no—
138C2×Dic3⋊C4—32no—
139C2×C4×Dic3C2×D312yes—
140C4×D12—68no—
141C4×D12—68no—
142C4×D12—68no—
143C3×#95—32no—
144C3×#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95C2×D312yes—
148C3⋊#95C2×D312yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—21no—
151C22×C3⋊D3—21no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3C2×D412yes—
159C22×C3⋊D3#4112yescomplemented
160C22×C3×D3—22no—
161C22×C3×D3—22no—
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—22no—
165C22×C3×D3—22no—
166C22×C3×D3C2×D414yes—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D414yes—
172C2×C32×C4C2×D412yes—
173C2×C32×C4#4112yescomplemented
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3C2×D412yes—
178C4⋊(C3⋊D3)—28no—
179C4×C3⋊D3—28no—
180C4×C3⋊D3—44no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3C2×D414yes—
189C2×C3×Dic3#4114yescomplemented
190C3×C4×D3—216no—
191#627—28no—
192#626—216no—
193#626—216no—
194#625—28no—
195C22×#41—91no—
196C2×C4×D4—92no—
197C2×C4×D4—91no—
198#395—91no—
199#394—92no—
200#394—91no—
201#393—91no—
202#392—92no—
203#392—91no—
204C4×C22⋊C4—32no—
205C4×C22⋊C4—91no—
206C24×C3—32no—
207C23×D3—32no—
208C23×D3—32no—
209C23×D3—61no—
210C23×D3—61no—
211C23×D3C22×D312yes—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—21no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—38no—
218C22×C3×C4—32no—
219C22×C3×C4—64no—
220C22×C3×C4—64no—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D312yes—
224C2×#67—64no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C2×#67—64no—
231C2×#67—64no—
232C2×#67—64no—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240#235—664no—
241C2×D12—64no—
242C2×D12—64no—
243C2×D12—64no—
244C2×D12—64no—
245C2×D12—64no—
246C2×D12—64no—
247C2×D12—64no—
248C2×D12—64no—
249C2×D12—64no—
250C2×D12—64no—
251C2×D12—64no—
252C2×D12—64no—
253C2×C4×D3—24no—
254C2×C4×D3—24no—
255C2×C4×D3—38no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×C4×D3—124no—
264C2×C4×D3—124no—
265C2×C4×D3D1218yescomplemented
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6—64no—
269C3×C22⋊C4—64no—
270C3×C22⋊C4—64no—
271C3×C42—24no—
272C3×C42—24no—
273C3×C42—64no—
274#217—64no—
275(C2×D3)⋊C4—24no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285(C2×D3)⋊C4—64no—
286C4⋊Dic3—64no—
287C4⋊Dic3—64no—
288C4⋊Dic3—64no—
289Dic3⋊C4—64no—
290C4×Dic3—24no—
291C22×C32C22×D412yes—
292C22×C32C22×D411yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C22×C32C2×#4112yes—
295C22×C32C2×#4111yescharacteristic
296C2×C3⋊D3—22no—
297C2×C3⋊D3—22no—
298C2×C3⋊D3—22no—
299C2×C3⋊D3—24no—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—42no—
305C2×C3⋊D3—41no—
306C2×C3×D3—24no—
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—42no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C32×C4—22no—
314C32×C4—41no—
315C32×C4#12014yes—
316C3⋊Dic3—22no—
317C3⋊Dic3—41no—
318C3×Dic3—24no—
319C3×Dic3—24no—
320C3×Dic3—42no—
321C2×#41—188no—
322C2×#41—184no—
323C22×Q8—91no—
324C22×D4—92no—
325C22×D4—92no—
326C22×D4—91no—
327C22×D4—91no—
328C23×C4—32no—
329C23×C4—91no—
330C23×C4—91no—
331C4×D4—184no—
332C4×D4—188no—
333C2×C4⋊C4—92no—
334C2×C4⋊C4—91no—
335C2×C22⋊C4—32no—
336C2×C22⋊C4—32no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—92no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C42—32no—
343C2×C42D3211yescharacteristic
344#95—32no—
345#95—32no—
346#95—91no—
347#95—91no—
348C23×C3—21no—
349C23×C3—34no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—62no—
353C23×C3—62no—
354C23×C3—62no—
355C23×C3—62no—
356C23×C3C23×D312yes—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—22no—
361C22×D3—22no—
362C22×D3—22no—
363C22×D3—34no—
364C22×D3—34no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—122no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3C2×D1214yes—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—24no—
398C2×C3×C4—22no—
399C2×C3×C4—34no—
400C2×C3×C4—34no—
401C2×C3×C4—42no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—616no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4C2×D1214yes—
411C2×C3×C4#23514yescomplemented
412C2×C3×C4D3×D414yes—
413C2×C3×C4D3×D414yes—
414#67—616no—
415#67—616no—
416#67—616no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—34no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—122no—
433C2×Dic3—122no—
434C2×Dic3C2×D1214yes—
435C2×Dic3#23514yescomplemented
436D12—616no—
437D12—616no—
438D12—616no—
439D12—616no—
440C4×D3—216no—
441C4×D3—616no—
442C4×D3—128no—
443C4×D3—128no—
444C4×D3—128no—
445Dic6—616no—
446C2×C32C2×#12011yescharacteristic
447C2×C32#52512yes—
448C2×C32#52511yescharacteristic
449C2×C32#53212yes—
450C2×C32#53211yescharacteristic
451C3⋊D3—42no—
452C3⋊D3—42no—
453C3×D3—44no—
454C24—32no—
455C24—91no—
456C24—91no—
457#41—1832no—
458C2×Q8—184no—
459C2×Q8—182no—
460C2×D4—182no—
461C2×D4—182no—
462C2×D4—184no—
463C2×D4—184no—
464C2×D4—184no—
465C2×D4—184no—
466C2×D4—184no—
467C2×D4—184no—
468C2×D4—182no—
469C2×D4—184no—
470C2×D4—182no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—38no—
474C22×C4—32no—
475C22×C4—64no—
476C22×C4—64no—
477C22×C4—91no—
478C22×C4—94no—
479C22×C4—91no—
480C22×C4—184no—
481C22×C4—184no—
482C22×C4—182no—
483C22×C4C2×D3211yescharacteristic
484C22×C4C2×D3211yescharacteristic
485C22×C4C2×D3211yescharacteristic
486C4⋊C4—182no—
487C4⋊C4—184no—
488C22⋊C4—64no—
489C22⋊C4—64no—
490C22⋊C4—182no—
491C22⋊C4—182no—
492C22⋊C4—184no—
493C22⋊C4—184no—
494C22⋊C4—184no—
495C42—22no—
496C42—64no—
497C22×C3—21no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—64no—
503C22×C3—64no—
504C22×C3—64no—
505C22×C3—122no—
506C22×C3—122no—
507C22×C3—122no—
508C22×C3—122no—
509C22×C3C22×D1212yes—
510C22×C3C2×#23512yes—
511C22×C3C2×#23512yes—
512C22×C3C2×D3×D412yes—
513C22×C3C2×D3×D412yes—
514C22×C3D3×#4112yes—
515C22×C3D3×#4112yes—
516C2×D3—24no—
517C2×D3—24no—
518C2×D3—24no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—42no—
522C2×D3—42no—
523C2×D3—64no—
524C2×D3—64no—
525C2×D3—64no—
526C2×D3—64no—
527C2×D3—64no—
528C2×D3—64no—
529C2×D3—64no—
530C2×D3—64no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—124no—
534C2×D3—122no—
535C2×D3—124no—
536C2×D3—124no—
537C2×D3—122no—
538C2×D3—124no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—122no—
543C2×D3—122no—
544C2×D3—122no—
545C2×D3—122no—
546C2×D3—122no—
547C3×C4—24no—
548C3×C4—24no—
549C3×C4—24no—
550C3×C4—42no—
551C3×C4—42no—
552C3×C4—64no—
553C3×C4—64no—
554C3×C4—122no—
555C3×C4#88218yes—
556Dic3—24no—
557Dic3—24no—
558Dic3—42no—
559Dic3—64no—
560Dic3—122no—
561Dic3—122no—
562Dic3—122no—
563C32#238811yescharacteristic, complemented, Sylow
564C23—34no—
565C23—62no—
566C23—62no—
567C23—62no—
568C23—62no—
569C23—62no—
570C23—62no—
571C23—92no—
572C23—92no—
573C23—181no—
574C23—181no—
575C23—182no—
576C23—182no—
577C23—182no—
578C23—182no—
579C23—181no—
580C23—181no—
581C23C22×D3211yescharacteristic
582Q8—188no—
583D4—188no—
584D4—1816no—
585D4—1816no—
586D4—188no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—34no—
592C2×C4—34no—
593C2×C4—62no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—616no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—62no—
601C2×C4—92no—
602C2×C4—182no—
603C2×C4—188no—
604C2×C4—182no—
605C2×C4—181no—
606C2×C4—364no—
607C2×C4#379812yescomplemented
608C2×C4D3×D1214yes—
609C2×C4#381112yes—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—22no—
614C2×C3—21no—
615C2×C3—124no—
616C2×C3#547712yes—
617C2×C3C2×#88212yes—
618C2×C3#552412yes—
619C2×C3#554712yes—
620C2×C3#554712yes—
621C2×C3#554812yes—
622C2×C3#554812yes—
623D3—44no—
624D3—124no—
625D3—124no—
626D3—124no—
627D3—124no—
628C22—64no—
629C22—64no—
630C22—64no—
631C22—122no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—182no—
636C22—182no—
637C22—182no—
638C22—184no—
639C22—182no—
640C22—362no—
641C22—362no—
642C22—361no—
643C22—362no—
644C22—361no—
645C22C2×#379811yescharacteristic
646C22C2×D3×D1212yes—
647C22D3×#23512yes—
648C22#6430611yescharacteristic
649C22C2×#381111yescharacteristic
650C4—22no—
651C4—41no—
652C4—64no—
653C4—64no—
654C4—122no—
655C4—182no—
656C4—361no—
657C4#6392314yes—
658C3—21no—
659C3#7358012yescomplemented
660C2—124no—
661C2—362no—
662C2—362no—
663C2#1059396812yes—
664C2#1059399712yes—
665C2#1059501611yescharacteristic
666C2#1059501711yescharacteristic
667C2C2×#6392311yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×#3798C2semidirect
2. C2×C4×C4⋊(C3⋊D3)C2semidirect
3. C2×C4×#626C2semidirect
4. C3×C4×(C2×D3)⋊C4C2semidirect
5. #10591397C2semidirect
6. #10591395C2semidirect
7. #10591394C2semidirect
8. #10591393C2semidirect
9. #10591312C2semidirect
10. C4×#3722C2semidirect
11. #10591205C2semidirect
51. C4×(C2×D3)⋊C4D3semidirect
70. C2×C4×C3⋊D3D4semidirect
76. C2×C3×C4×D3D4semidirect
159. C22×C3⋊D3#41semidirect
173. C2×C32×C4#41semidirect
189. C2×C3×Dic3#41semidirect
265. C2×C4×D3D12semidirect
411. C2×C3×C4#235semidirect
435. C2×Dic3#235semidirect
563. C32#2388semidirect
607. C2×C4#3798semidirect
659. C3#73580semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×C4×C4⋊(C3⋊D3)2
C2×C4×#6262
C3×C4×(C2×D3)⋊C42
#105913972
#105913952
#105913942
#105913932
#105913122
C4×#37222
#105912052
#735803