Finite Group Databasebeta

← #11787442

Subgroups — #11787442

Order 1152.

1017 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C22×#3717C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4#10591221C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70276—31nomaximal
9#68896—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C22×C3×Dic6C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16#64102—22no—
17#64102—22no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3717—22no—
22C2×#3717—22no—
23C2×#3717C414yescomplemented
24C3×#810—22no—
25#63579—21no—
26#63579—21no—
27#63564—22no—
28C22×#215—31no—
29C22×#204—31no—
30C2×#893—31no—
31C2×#893—31no—
32C2×#893—61no—
33C2×C3×#103—31no—
34#5229—31no—
35C2×#821—31no—
36#4973—31no—
37C2×#810D311yescharacteristic, complemented
38C2×#809—31no—
39C3×#340—31no—
40#4550—31no—
41#4550—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3—21no—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
47C22×C3⋊Dic3D411yescharacteristic
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)C2×C412yes—
52C2×C4⋊(C3⋊D3)D412yes—
53C2×C4⋊(C3⋊D3)D412yes—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—42no—
56C2×C4×C3⋊D3—42no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6—21no—
64C2×C3×Dic6C2×C412yescomplemented
65C32×C4⋊C4—21no—
66C32×C4⋊C4D412yes—
67#3752—24no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8C2×C412yescomplemented
78#3717—28no—
79#1877—91noSylow
80C22×C3×Q8—31no—
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×C4×D3—61no—
85C22×C4×D3—61no—
86C22×C4×D3—62no—
87C22×Dic6C2×D311yescharacteristic
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×#215—34no—
95C2×#215—62no—
96C2×#215—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—62no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4×Dic3—31no—
102C2×C4×Dic3—31no—
103C2×C4×Dic3—61no—
104C22×C3⋊C8C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C2×#204—34no—
107C2×#204—62no—
108C2×#204—62no—
109#893—62no—
110#893—62no—
111#893—64no—
112#893—64no—
113#893—62no—
114#893—62no—
115C3×#103—62no—
116C3⋊#95—61no—
117C3⋊#95—61no—
118C3⋊#95—61no—
119C3⋊#95—61no—
120#821—62no—
121#810—22no—
122#809—62no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3⋊D3—41no—
130C22×C3⋊D3—41no—
131C2×C32×C4—22no—
132C2×C32×C4—41no—
133C2×C32×C4—41no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—21no—
145C2×C3⋊Dic3SD1612yescomplemented
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—22no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)C22⋊C414yes—
150C4×C3⋊D3—48no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C3×Dic6—22no—
158C3×Dic6—22no—
159C3×Dic6—41no—
160C3×Dic6—41no—
161C3×C3⋊C8—22no—
162C3×C3⋊C8—41no—
163C22×SD16—91no—
164C2×C4×D4—91no—
165C2×#103—31no—
166C2×#102—91no—
167#391—91no—
168#340—31no—
169#336—91no—
170C23×D3—62no—
171C23×D3—61no—
172C23×D3—61no—
173C2×C3×Q8—32no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C22×C3×C4—22no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—31no—
190C22×Dic3—31no—
191C22×Dic3—31no—
192C22×Dic3—31no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—32no—
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—62no—
204C2×D12—62no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×C4×D3—68no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—122no—
217C2×C4×D3—122no—
218C2×C4×D3—124no—
219C2×C4×D3—124no—
220C2×C4×D3—122no—
221C2×C4×D3—122no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—21no—
225C2×Dic6—21no—
226C2×Dic6—21no—
227C2×Dic6C4×D312yescomplemented
228C2×C3×C8—32no—
229C2×C3×C8—61no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4D1212yes—
241C3×C4⋊C4#6712yes—
242#215—68no—
243(C2×D3)⋊C4—68no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—61no—
254C2×C3⋊C8—21no—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8C4×D312yescomplemented
260#204—68no—
261C22×C32C4×D411yescharacteristic
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32C2×SD1611yescharacteristic
265C22×C32#13511yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C22×C32#13711yescharacteristic
268C2×C3⋊D3—24no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—42no—
275C32×C4—42no—
276C32×C4C2×C22⋊C411yescharacteristic
277C32×C4C4×D411yescharacteristic
278C32×C4#12111yescharacteristic
279C32×C4#12311yescharacteristic
280C3⋊Dic3—22no—
281C3⋊Dic3—41no—
282C3×Dic3—42no—
283C3×Dic3—81no—
284C22×Q8—31no—
285C22×D4—91no—
286C23×C4—181no—
287C2×SD16—94no—
288C2×SD16—182no—
289C2×SD16—182no—
290C22×C8—31no—
291C22×C8—31no—
292C4×D4—182no—
293C4×D4—182no—
294C2×C4⋊C4—31no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—181no—
297C2×C42—91no—
298#103—62no—
299#102—182no—
300#95—181no—
301#95—181no—
302C23×C3—21no—
303C23×C3D3×D411yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—64no—
306C22×D3—64no—
307C22×D3—64no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—62no—
314C22×D3—122no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—121no—
319C22×D3—121no—
320C22×D3—121no—
321C22×D3—121no—
322C22×D3—121no—
323C22×D3—121no—
324C22×D3—121no—
325C22×D3—121no—
326C3×Q8—62no—
327C3×Q8—62no—
328C3×Q8—121no—
329C3×Q8—121no—
330C2×C3×C4—24no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—41no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—62no—
346C2×C3×C4—121no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—121no—
350C2×C3×C4—121no—
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×C4×D311yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4#23511yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23911yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×Dic3—22no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—41no—
367C2×Dic3—41no—
368C2×Dic3—41no—
369C2×Dic3—41no—
370C2×Dic3—41no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—61no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—121no—
386C2×Dic3—121no—
387D12—34no—
388D12—34no—
389D12—64no—
390D12—64no—
391D12—64no—
392D12—64no—
393D12—62no—
394D12—62no—
395D12—62no—
396D12—62no—
397D12—62no—
398D12—62no—
399C4×D3—1216no—
400C4×D3—128no—
401C4×D3—128no—
402Dic6—22no—
403Dic6—22no—
404Dic6—41no—
405Dic6—41no—
406C3×C8—62no—
407C3×C8—121no—
408C3⋊C8—22no—
409C3⋊C8—41no—
410C2×C32#38611yescharacteristic
411C2×C32C4×SD1611yescharacteristic
412C2×C32#44011yescharacteristic
413C2×C32#45011yescharacteristic
414C2×C32#45211yescharacteristic
415C2×C32#46111yescharacteristic
416C2×C32#46311yescharacteristic
417C3⋊D3—44no—
418C24—181no—
419C2×Q8—32no—
420C2×Q8—61no—
421C2×Q8—61no—
422C2×Q8—61no—
423C2×Q8—61no—
424C2×Q8—61no—
425C2×D4—92no—
426C2×D4—92no—
427C2×D4—92no—
428C2×D4—181no—
429C2×D4—181no—
430C2×D4—181no—
431C22×C4—21no—
432C22×C4—61no—
433C22×C4—61no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—184no—
437C22×C4—362no—
438C22×C4—362no—
439C22×C4C2×D3211yescharacteristic
440SD16—188no—
441C2×C8—32no—
442C2×C8—61no—
443C2×C8—61no—
444C2×C8—61no—
445C2×C8—61no—
446C2×C8—61no—
447C4⋊C4—21no—
448C4⋊C4—61no—
449C4⋊C4—61no—
450C4⋊C4#62612yes—
451C22⋊C4—184no—
452C42—181no—
453C42—181no—
454C22×C3—21no—
455C22×C3—21no—
456C22×C3—21no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3#67⋊C411yescharacteristic
462C22×C3#88211yescharacteristic
463C22×C3#88411yescharacteristic
464C22×C3#88411yescharacteristic
465C22×C3#89311yescharacteristic
466C22×C3#91111yescharacteristic
467C22×C3D3×SD1611yescharacteristic
468C22×C3D3×SD1611yescharacteristic
469C22×C3#91411yescharacteristic
470C22×C3#91611yescharacteristic
471C22×C3#91811yescharacteristic
472C22×C3#91811yescharacteristic
473C22×C3#91911yescharacteristic
474C22×C3#93711yescharacteristic
475C2×D3—68no—
476C2×D3—64no—
477C2×D3—64no—
478C2×D3—124no—
479C2×D3—124no—
480C2×D3—124no—
481C2×D3—124no—
482C2×D3—124no—
483C2×D3—124no—
484C2×D3—122no—
485C2×D3—122no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—122no—
490C2×D3—122no—
491C2×D3—122no—
492C2×D3—122no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C3×C4—21no—
497C3×C4—21no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—44no—
501C3×C4—42no—
502C3×C4—42no—
503C3×C4—122no—
504C3×C4—241no—
505C3×C4C4×D1211yescharacteristic
506C3×C4D3×C22⋊C411yescharacteristic
507C3×C4D3×C22⋊C411yescharacteristic
508C3×C4#88311yescharacteristic
509C3×C4#89411yescharacteristic
510C3×C4#89511yescharacteristic
511C3×C4C4×#6711yescharacteristic
512C3×C4#93811yescharacteristic
513Dic3—42no—
514Dic3—64no—
515Dic3—62no—
516Dic3—62no—
517Dic3—81no—
518Dic3—122no—
519Dic3—121no—
520Dic3—121no—
521C32#187711yescharacteristic, complemented, Sylow
522C23—182no—
523C23—182no—
524C23—182no—
525C23—361no—
526C23—361no—
527C23—361no—
528C23—361no—
529C23#381111yescharacteristic
530Q8—62no—
531Q8—62no—
532Q8—121no—
533Q8—121no—
534D4—94no—
535D4—182no—
536D4—182no—
537D4—182no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—62no—
542C2×C4—92no—
543C2×C4—121no—
544C2×C4—121no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—121no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—368no—
554C2×C4#379611yescharacteristic
555C2×C4#379811yescharacteristic
556C2×C4C4×D3211yescharacteristic
557C2×C4#380211yescharacteristic
558C2×C4C2×#62611yescharacteristic
559C2×C4#381111yescharacteristic
560C8—62no—
561C8—121no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3#466511yescharacteristic
570C2×C3#477611yescharacteristic
571C2×C3#478711yescharacteristic
572C2×C3#478811yescharacteristic
573C2×C3#480811yescharacteristic
574C2×C3#481711yescharacteristic
575C2×C3#481811yescharacteristic
576C2×C3#481811yescharacteristic
577C2×C3#481911yescharacteristic
578C2×C3#485211yescharacteristic
579C2×C3#488911yescharacteristic
580C2×C3#495611yescharacteristic
581C2×C3#516911yescharacteristic
582C2×C3#518711yescharacteristic
583D3—128no—
584D3—124no—
585D3—124no—
586C22—184no—
587C22—362no—
588C22—362no—
589C22—362no—
590C22—362no—
591C22—362no—
592C22—362no—
593C22#6388111yescharacteristic
594C22#6391211yescharacteristic
595C22#6393011yescharacteristic
596C22#6393711yescharacteristic
597C22#6394511yescharacteristic
598C22#6395011yescharacteristic
599C22#6398111yescharacteristic
600C4—42no—
601C4—122no—
602C4—182no—
603C4—241no—
604C4—361no—
605C4#6385311yescharacteristic
606C4C4×#62611yescharacteristic
607C4#6391611yescharacteristic
608C4#6392111yescharacteristic
609C3—21no—
610C3#6889611yescharacteristic, complemented
611C3#7027611yescharacteristic, complemented
612C2—364no—
613C2#1059048311yescharacteristic
614C2#1059048411yescharacteristic
615C2#1059054011yescharacteristic
616C2#1059056511yescharacteristic
617C2#1059138711yescharacteristic
618C2#1059146711yescharacteristic
619C2#1059160211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1877
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
3. C2×C3×#810C2semidirect
4. #10591221C2semidirect
6. C3×#4529C2semidirect
7. #10589156C2semidirect
23. C2×#3717C4semidirect
37. C2×#810D3semidirect
42. #4529D3semidirect
64. C2×C3×Dic6C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
145. C2×C3⋊Dic3SD16semidirect
227. C2×Dic6C4×D3semidirect
259. C2×C3⋊C8C4×D3semidirect
521. C32#1877semidirect
610. C3#68896semidirect
611. C3#70276semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C22×#37172
C2×C3×#8102
#105912212
C2×#635642
C3×#45292
#105891562
#702763
#688963