Finite Group Databasebeta

← #11787352

Subgroups — #11787352

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×#63916C211yesmaximal, characteristic
3C2×C3×#809C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic, complemented
5C2×#63557C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70201—31nomaximal
9#68881—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4×C3⋊Dic3—21no—
17#64101—22no—
18#64101—22no—
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C2×(C2×D3)⋊Dic3—21no—
23#63916—22no—
24#63916C414yescomplemented
25C3×#809—22no—
26#63563—22no—
27#63557—22no—
28C2×#938—31no—
29C2×#895—31no—
30C2×#892—31no—
31C2×#892—31no—
32C2×#892—61no—
33C2×C3×#102—31no—
34C2×#832—31no—
35C2×#821—31no—
36C2×(C2×D3)⋊C8—31no—
37C2×(C2×D3)⋊C8—31no—
38C2×#809D311yescharacteristic, complemented
39C3×#340—31no—
40#4551—31no—
41#4529—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3D411yescharacteristic
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3C2×C412yes—
54C2×C4×C3⋊D3D412yes—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×#626—24no—
63C2×#626—42no—
64C2×#626—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yescomplemented
67#3752—24no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)D412yescomplemented
70C4×C3⋊Dic3—24no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2×C412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79(C2×D3)⋊Dic3—24no—
80#1875—91noSylow
81C22×C3×D4—31no—
82C22×#67—61no—
83C22×D12—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×#217—61no—
95#938—34no—
96#938—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—62no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3—61no—
106C2×C4×Dic3—61no—
107C2×C4×Dic3—62no—
108C22×C3⋊C8C2×D311yescharacteristic
109C22×C3⋊C8C2×D311yescharacteristic
110#895—34no—
111#895—62no—
112#892—62no—
113#892—62no—
114#892—64no—
115#892—64no—
116#892—62no—
117#892—62no—
118C3×#102—62no—
119#832—62no—
120#821—62no—
121(C2×D3)⋊C8—62no—
122(C2×D3)⋊C8—62no—
123#809—22no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—21no—
131C22×C3⋊D3C22⋊C412yes—
132C22×C3×D3—22no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C22×C3×D3—41no—
138C22×C3×D3—41no—
139C2×C32×C4—22no—
140C2×C32×C4—41no—
141C2×C32×C4—41no—
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147C2×C32×C4#4111yescharacteristic
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—41no—
153C2×C3⋊Dic3C22⋊C412yes—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—41no—
160C2×C3×Dic3—41no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—41no—
164C3×D12—41no—
165#626—48no—
166C3×C3⋊C8—41no—
167C3×C3⋊C8—41no—
168C2×#121—91no—
169C2×#117—91no—
170C2×#102—31no—
171C2×#102—91no—
172C2×C22⋊C8—91no—
173#340—31no—
174#340—91no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—31no—
178C23×D3—31no—
179C23×D3—61no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—22no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—21no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C2×#67—64no—
194C2×#67—122no—
195C2×#67—122no—
196C22×Dic3—21no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—61no—
200C22×Dic3—62no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—21no—
207C2×D12—21no—
208C2×D12—64no—
209C2×D12—122no—
210C2×D12—122no—
211C2×D12C4×D312yes—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—61no—
226C2×C4×D3—61no—
227C2×C4×D3—61no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—32no—
241C3×C4⋊C4—61no—
242C3×C4⋊C4D1212yescomplemented
243C3×C4⋊C4#6712yescomplemented
244#217—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—68no—
247(C2×D3)⋊C4—64no—
248(C2×D3)⋊C4—64no—
249C4⋊Dic3—21no—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3C4×D312yes—
257C4×Dic3—68no—
258C4×Dic3—64no—
259C4×Dic3—64no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—21no—
265C2×C3⋊C8—21no—
266C22×C32C2×C22⋊C411yescharacteristic
267C22×C32#12011yescharacteristic
268C22×C32#12311yescharacteristic
269C22×C32#13511yescharacteristic
270C22×C32#13511yescharacteristic
271C22×C32AGL(1,ℤ/8)11yescharacteristic
272C22×C32AGL(1,ℤ/8)11yescharacteristic
273C2×C3⋊D3—22no—
274C2×C3⋊D3—22no—
275C2×C3⋊D3—22no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3×D3—42no—
281C2×C3×D3—42no—
282C2×C3×D3—42no—
283C2×C3×D3—81no—
284C2×C3×D3—81no—
285C2×C3×D3—81no—
286C2×C3×D3—81no—
287C32×C4—42no—
288C32×C4C4×D411yescharacteristic
289C32×C4C4×D411yescharacteristic
290C32×C4#12111yescharacteristic
291C32×C4#12111yescharacteristic
292C3⋊Dic3—22no—
293C3⋊Dic3—42no—
294C3×Dic3—42no—
295C22×D4—31no—
296C22×D4—181no—
297C23×C4—91no—
298C22×C8—31no—
299C22×C8—31no—
300#121—94no—
301#121—182no—
302#117—182no—
303#117—182no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4D3211yescharacteristic
307C2×C22⋊C4—181no—
308C2×C22⋊C4—181no—
309C2×C42—181no—
310#102—62no—
311#102—182no—
312C22⋊C8—182no—
313C23×C3—21no—
314C23×C3—62no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3—121no—
319C23×C3—121no—
320C23×C3—121no—
321C23×C3D3×D411yescharacteristic
322C23×C3D3×D411yescharacteristic
323C22×D3—22no—
324C22×D3—32no—
325C22×D3—32no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—41no—
330C22×D3—41no—
331C22×D3—41no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—121no—
348C22×D3—121no—
349C22×D3—121no—
350C22×D3—121no—
351C3×D4—62no—
352C3×D4—62no—
353C3×D4—121no—
354C3×D4—121no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—42no—
365C2×C3×C4—42no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—62no—
371C2×C3×C4—121no—
372C2×C3×C4—121no—
373C2×C3×C4C2×C4×D311yescharacteristic
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4C2×D1211yescharacteristic
376C2×C3×C4#23511yescharacteristic
377C2×C3×C4#23511yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D411yescharacteristic
381C2×C3×C4D3×D411yescharacteristic
382C2×C3×C4#23711yescharacteristic
383C2×C3×C4#23911yescharacteristic
384C2×C3×C4C2×#6711yescharacteristic
385#67—128no—
386C2×Dic3—22no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—61no—
395C2×Dic3—61no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—64no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—122no—
403C2×Dic3—121no—
404C2×Dic3—121no—
405C2×Dic3—121no—
406C2×Dic3—121no—
407D12—22no—
408D12—22no—
409D12—41no—
410D12—41no—
411D12—128no—
412C4×D3—64no—
413C4×D3—64no—
414C4×D3—64no—
415C4×D3—64no—
416C4×D3—62no—
417C4×D3—62no—
418C4×D3—62no—
419C4×D3—62no—
420C4×D3—62no—
421C4×D3—62no—
422C4×D3—62no—
423C4×D3—62no—
424C3×C8—121no—
425C3×C8—121no—
426C3⋊C8—41no—
427C3⋊C8—41no—
428C2×C32#38611yescharacteristic
429C2×C32#41611yescharacteristic
430C2×C32#41811yescharacteristic
431C2×C32#44911yescharacteristic
432C2×C32#44911yescharacteristic
433C2×C32#48211yescharacteristic
434C2×C32#48211yescharacteristic
435C3⋊D3—42no—
436C3×D3—82no—
437C24—61no—
438C24—91no—
439C2×D4—32no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—61no—
443C2×D4—61no—
444C2×D4—61no—
445C2×D4—184no—
446C2×D4—362no—
447C2×D4—362no—
448C22×C4—21no—
449C22×C4—61no—
450C22×C4—91no—
451C22×C4—92no—
452C22×C4—92no—
453C22×C4—181no—
454C22×C4—181no—
455C22×C4—181no—
456C22×C4—181no—
457C22×C4—181no—
458C22×C4C2×D3211yescharacteristic
459C2×C8—61no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—61no—
463C2×C8—61no—
464C2×C8—61no—
465C4⋊C4—21no—
466C4⋊C4—32no—
467C4⋊C4—61no—
468C4⋊C4—92no—
469C4⋊C4—181no—
470C4⋊C4#62612yescomplemented
471C22⋊C4—184no—
472C22⋊C4—184no—
473C42—184no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—122no—
482C22×C3—122no—
483C22×C3—122no—
484C22×C3—241no—
485C22×C3—241no—
486C22×C3—241no—
487C22×C3—241no—
488C22×C3D3×C22⋊C411yescharacteristic
489C22×C3D3×C22⋊C411yescharacteristic
490C22×C3#88211yescharacteristic
491C22×C3#88311yescharacteristic
492C22×C3#89411yescharacteristic
493C22×C3#91111yescharacteristic
494C22×C3#91111yescharacteristic
495C22×C3#91211yescharacteristic
496C22×C3#91411yescharacteristic
497C22×C3#91411yescharacteristic
498C22×C3#91611yescharacteristic
499C22×C3#91611yescharacteristic
500C22×C3#91911yescharacteristic
501C22×C3#93711yescharacteristic
502C2×D3—42no—
503C2×D3—42no—
504C2×D3—42no—
505C2×D3—64no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—62no—
512C2×D3—81no—
513C2×D3—81no—
514C2×D3—81no—
515C2×D3—81no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—121no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—21no—
534C3×C4—44no—
535C3×C4—42no—
536C3×C4—42no—
537C3×C4—122no—
538C3×C4C4×D1211yescharacteristic
539C3×C4#67⋊C411yescharacteristic
540C3×C4#88411yescharacteristic
541C3×C4#88411yescharacteristic
542C3×C4#89311yescharacteristic
543C3×C4#89511yescharacteristic
544C3×C4C4×#6711yescharacteristic
545C3×C4#93811yescharacteristic
546Dic3—42no—
547Dic3—64no—
548Dic3—62no—
549Dic3—62no—
550Dic3—124no—
551Dic3—122no—
552Dic3—122no—
553C32#187511yescharacteristic, complemented, Sylow
554C23—62no—
555C23—92no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23—121no—
560C23—121no—
561C23—121no—
562C23—181no—
563C23—181no—
564C23—181no—
565C23—181no—
566C23—181no—
567C23—181no—
568C23#381111yescharacteristic
569D4—62no—
570D4—62no—
571D4—121no—
572D4—121no—
573D4—368no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—62no—
578C2×C4—92no—
579C2×C4—121no—
580C2×C4—121no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—182no—
584C2×C4—182no—
585C2×C4—182no—
586C2×C4—182no—
587C2×C4—182no—
588C2×C4—361no—
589C2×C4—361no—
590C2×C4#379611yescharacteristic
591C2×C4#379811yescharacteristic
592C2×C4C4×D3211yescharacteristic
593C2×C4#380211yescharacteristic
594C2×C4C2×#62611yescharacteristic
595C2×C4#381111yescharacteristic
596C8—121no—
597C8—121no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—242no—
606C2×C3#466511yescharacteristic
607C2×C3#477011yescharacteristic
608C2×C3#477011yescharacteristic
609C2×C3#477211yescharacteristic
610C2×C3#477911yescharacteristic
611C2×C3#478111yescharacteristic
612C2×C3#478411yescharacteristic
613C2×C3#480411yescharacteristic
614C2×C3#481011yescharacteristic
615C2×C3#486611yescharacteristic
616C2×C3#488511yescharacteristic
617C2×C3#495611yescharacteristic
618C2×C3#515811yescharacteristic
619C2×C3#517211yescharacteristic
620D3—82no—
621D3—124no—
622D3—122no—
623D3—122no—
624C22—122no—
625C22—122no—
626C22—122no—
627C22—182no—
628C22—182no—
629C22—182no—
630C22—241no—
631C22—241no—
632C22—241no—
633C22—241no—
634C22—361no—
635C22—361no—
636C22—361no—
637C22—361no—
638C22#6385311yescharacteristic
639C22#6392111yescharacteristic
640C22#6392711yescharacteristic
641C22#6393611yescharacteristic
642C22#6394111yescharacteristic
643C22#6395011yescharacteristic
644C22#6398111yescharacteristic
645C4—42no—
646C4—122no—
647C4—182no—
648C4—362no—
649C4#6388111yescharacteristic
650C4C4×#62611yescharacteristic
651C4#6391211yescharacteristic
652C4#6391611yescharacteristic
653C3—21no—
654C3#6888111yescharacteristic, complemented
655C3#7020111yescharacteristic, complemented
656C2—242no—
657C2—362no—
658C2#1059051211yescharacteristic
659C2#1059051311yescharacteristic
660C2#1059059411yescharacteristic
661C2#1059061111yescharacteristic
662C2#1059138711yescharacteristic
663C2#1059145711yescharacteristic
664C2#1059159311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1875
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64101C2semidirect
3. C2×C3×#809C2semidirect
4. C2×#63563C2semidirect
5. C2×#63557C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
24. #63916C4semidirect
38. C2×#809D3semidirect
42. #4529D3semidirect
66. C32×C4⋊C4D4semidirect
69. C4⋊(C3⋊Dic3)D4semidirect
242. C3×C4⋊C4D12semidirect
243. C3×C4⋊C4#67semidirect
470. C4⋊C4#626semidirect
553. C32#1875semidirect
654. C3#68881semidirect
655. C3#70201semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#639162
C2×C3×#8092
C2×#635632
C2×#635572
C3×#45292
#105891642
#702013
#688813