Finite Group Databasebeta

← #11792013

Subgroups — #11792013

Order 1152.

945 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×#64155C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C2×#63566C211yesmaximal, characteristic, complemented
6C2×#63557C211yesmaximal, characteristic
7#10589164C211yesmaximal, characteristic, complemented
8#72071—31nomaximal
9#70273—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×Dic6C2211yescharacteristic
13#64155—22no—
14#64155—22no—
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3750—21no—
18C2×C3×#216—22no—
19C2×C3×#216—22no—
20C2×C3×#216—22no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×#3722—21no—
26#63871—22no—
27#63871—22no—
28C3×#835—22no—
29#63566—22no—
30#63557—22no—
31C22×C3×Q16—31no—
32C2×#946—31no—
33C2×#946—31no—
34C2×#946—31no—
35C2×#946—61no—
36C22×#216D311yescharacteristic, complemented
37C2×#897—31no—
38C2×C3×#103—31no—
39C2×#835—31no—
40C2×#835D311yescharacteristic, complemented
41C2×(C2×D3)⋊C8—31no—
42C2×(C2×D3)⋊C8—31no—
43C2×#816—31no—
44#4551—31no—
45#4529—31no—
46C23×C3⋊D3D411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8D412yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3D411yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—21no—
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—21no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D412yes—
71#3752—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)D412yes—
74#3750—24no—
75C3×#216—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3D412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8D412yes—
84Dic3⋊Dic3—24no—
85#3722—24no—
86#2001—91noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8—31no—
89C22×C3×Q8C2×D311yescharacteristic
90C22×C3×Q8C2×D311yescharacteristic
91C22×C4×D3—31no—
92C22×C4×D3—31no—
93C22×C4×D3—61no—
94C22×Dic6C2×D311yescharacteristic
95C2×C3×Q16—62no—
96C2×C3×Q16—62no—
97C2×C3×Q16—62no—
98C22×C3×C8—31no—
99C22×C3×C8—31no—
100C2×C3×C4⋊C4—31no—
101#946—62no—
102#946—62no—
103#946—62no—
104#946—64no—
105#946—64no—
106#946—62no—
107#946—62no—
108#946—62no—
109C2×#216—22no—
110C2×#216—22no—
111C2×#216—22no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4—62no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3C2×D311yescharacteristic
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4—61no—
124C2×Dic3⋊C4—61no—
125C2×Dic3⋊C4—62no—
126C22×C3⋊C8C2×D311yescharacteristic
127C22×C3⋊C8C2×D311yescharacteristic
128#897—62no—
129#897—62no—
130C3×#103—62no—
131#835—22no—
132#835—62no—
133(C2×D3)⋊C8—62no—
134(C2×D3)⋊C8—62no—
135#816—62no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—21no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3—21no—
141C22×C3⋊D3—21no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3Q1612yescomplemented
144C32×Q8—22no—
145C32×Q8—22no—
146C32×Q8—41no—
147C32×Q8—41no—
148C2×C32×C4—22no—
149C2×C32×C4—41no—
150C2×C32×C4—41no—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4111yescharacteristic
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163C4×C3⋊D3—41no—
164C4×C3⋊D3—41no—
165C4×C3⋊D3—41no—
166C4×C3⋊D3—41no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C2×C3×Dic3—41no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—41no—
176C3×Dic6—41no—
177C3×C3⋊C8—22no—
178C3×C3⋊C8—41no—
179C22×Q16—31no—
180C2×C22⋊Q8—91no—
181C2×C22⋊Q8—91no—
182C2×#103—31no—
183C2×#103—91no—
184C2×C22⋊C8—91no—
185#340—91no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C2×C3×Q8—22no—
190C2×C3×Q8—21no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—22no—
201C2×C3×Q8—32no—
202C2×C3×Q8—41no—
203C2×C3×Q8—41no—
204C2×C3×Q8—41no—
205C2×C3×Q8—41no—
206C2×C3×Q8—61no—
207C2×C3×Q8—61no—
208C2×C3×Q8—61no—
209C2×C3×Q8—61no—
210C2×C3×Q8—61no—
211C2×C3×Q8D1212yes—
212C2×C3×Q8#6712yes—
213C22×C3×C4—22no—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—61no—
226C22×Dic3—62no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C2×C4×D3—62no—
230C2×C4×D3—62no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—61no—
240C2×C4×D3—61no—
241C2×C4×D3—61no—
242C2×C4×D3—61no—
243C2×C4×D3—121no—
244C2×C4×D3—121no—
245C2×C4×D3—121no—
246C2×C4×D3—121no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6#6712yes—
253C3×Q16—68no—
254C2×C3×C8—32no—
255C2×C3×C8—61no—
256C2×C3×C8—61no—
257C2×C3×C8—61no—
258C2×C3×C8—61no—
259C2×C3×C8—61no—
260C3×C4⋊C4—32no—
261C3×C4⋊C4—61no—
262#216—28no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—68no—
266(C2×D3)⋊C4—64no—
267(C2×D3)⋊C4—64no—
268C4⋊Dic3—21no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—64no—
273C4⋊Dic3—62no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3#6712yes—
277Dic3⋊C4—64no—
278Dic3⋊C4—68no—
279Dic3⋊C4—64no—
280Dic3⋊C4—64no—
281C2×C3⋊C8—21no—
282C2×C3⋊C8—21no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8#6712yes—
287C22×C32#12011yescharacteristic
288C22×C32#12011yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32C2×Q1611yescharacteristic
291C22×C32#13511yescharacteristic
292C22×C32#13711yescharacteristic
293C22×C32#13711yescharacteristic
294C2×C3⋊D3—22no—
295C2×C3⋊D3—22no—
296C2×C3⋊D3—22no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—41no—
299C2×C3⋊D3—41no—
300C2×C3⋊D3—41no—
301C32×C4—42no—
302C32×C4#12011yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4#12111yescharacteristic
305C32×C4#12711yescharacteristic
306C3⋊Dic3—41no—
307C3⋊Dic3—42no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C22×Q8—31no—
311C22×Q8D3211yescharacteristic
312C23×C4—91no—
313C2×Q16—62no—
314C2×Q16—62no—
315C2×Q16—62no—
316C22×C8—31no—
317C22×C8—31no—
318C22⋊Q8—182no—
319C22⋊Q8—182no—
320C22⋊Q8—182no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—181no—
325C2×C4⋊C4—181no—
326C2×C22⋊C4—181no—
327C2×C22⋊C4—181no—
328#103—62no—
329#103—182no—
330C22⋊C8—182no—
331C23×C3—21no—
332C23×C3D3×D411yescharacteristic
333C23×C3D3×D411yescharacteristic
334C22×D3—32no—
335C22×D3—32no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—62no—
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—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C3×Q8—22no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—22no—
359C3×Q8—42no—
360C3×Q8—42no—
361C3×Q8—42no—
362C3×Q8—42no—
363C3×Q8—41no—
364C3×Q8—41no—
365C3×Q8—41no—
366C3×Q8—41no—
367C3×Q8—62no—
368C3×Q8—62no—
369C3×Q8—121no—
370C3×Q8—121no—
371C2×C3×C4—24no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—121no—
389C2×C3×C4—121no—
390C2×C3×C4—121no—
391C2×C3×C4—121no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4#23511yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4#23711yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6711yescharacteristic
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—41no—
409C2×Dic3—41no—
410C2×Dic3—62no—
411C2×Dic3—64no—
412C2×Dic3—61no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—62no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—122no—
423C2×Dic3—122no—
424C2×Dic3—121no—
425C2×Dic3—121no—
426C2×Dic3—121no—
427C2×Dic3—121no—
428C4×D3—122no—
429C4×D3—122no—
430C4×D3—122no—
431C4×D3—122no—
432C4×D3—121no—
433C4×D3—121no—
434C4×D3—121no—
435C4×D3—121no—
436C4×D3—121no—
437C4×D3—121no—
438C4×D3—121no—
439C4×D3—121no—
440Dic6—22no—
441Dic6—22no—
442Dic6—41no—
443Dic6—41no—
444C3×C8—62no—
445C3×C8—121no—
446C3⋊C8—22no—
447C3⋊C8—41no—
448C2×C32#39211yescharacteristic
449C2×C32#45111yescharacteristic
450C2×C32#45111yescharacteristic
451C2×C32#45211yescharacteristic
452C2×C32#45211yescharacteristic
453C2×C32#46711yescharacteristic
454C2×C32#47011yescharacteristic
455C3⋊D3—42no—
456C24—91no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—32no—
463C2×Q8—61no—
464C2×Q8—61no—
465C2×Q8—61no—
466C2×Q8—61no—
467C2×Q8—61no—
468C2×Q8#62612yes—
469C22×C4—21no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—91no—
473C22×C4—181no—
474C22×C4—181no—
475C22×C4—181no—
476C22×C4—181no—
477C22×C4—181no—
478C22×C4—181no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481Q16—68no—
482C2×C8—32no—
483C2×C8—61no—
484C2×C8—61no—
485C2×C8—61no—
486C2×C8—61no—
487C2×C8—61no—
488C4⋊C4—32no—
489C4⋊C4—61no—
490C4⋊C4—92no—
491C4⋊C4—184no—
492C4⋊C4—184no—
493C4⋊C4—181no—
494C22⋊C4—184no—
495C22⋊C4—184no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3#88211yescharacteristic
504C22×C3#88411yescharacteristic
505C22×C3#91511yescharacteristic
506C22×C3#91611yescharacteristic
507C22×C3D3×Q1611yescharacteristic
508C22×C3D3×Q1611yescharacteristic
509C22×C3#91811yescharacteristic
510C22×C3#91811yescharacteristic
511C22×C3#91811yescharacteristic
512C22×C3#91911yescharacteristic
513C22×C3#93711yescharacteristic
514C22×C3#93711yescharacteristic
515C22×C3#93711yescharacteristic
516C22×C3#93811yescharacteristic
517C2×D3—64no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C2×D3—121no—
537C2×D3—121no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—44no—
543C3×C4—42no—
544C3×C4—42no—
545C3×C4—122no—
546C3×C4—122no—
547C3×C4#88211yescharacteristic
548C3×C4#88411yescharacteristic
549C3×C4#93011yescharacteristic
550C3×C4#93911yescharacteristic
551C3×C4#93911yescharacteristic
552C3×C4#94011yescharacteristic
553C3×C4#94011yescharacteristic
554C3×C4#95311yescharacteristic
555Dic3—42no—
556Dic3—42no—
557Dic3—122no—
558Dic3—124no—
559Dic3—122no—
560Dic3—121no—
561Dic3—121no—
562Dic3—122no—
563C32#200111yescharacteristic, complemented, Sylow
564C23—92no—
565C23—181no—
566C23—181no—
567C23—181no—
568C23—181no—
569C23—181no—
570C23—181no—
571C23#381111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—41no—
575Q8—41no—
576Q8—62no—
577Q8—62no—
578Q8—121no—
579Q8—121no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—121no—
586C2×C4—121no—
587C2×C4—121no—
588C2×C4—121no—
589C2×C4—181no—
590C2×C4—182no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—361no—
594C2×C4—361no—
595C2×C4—361no—
596C2×C4—361no—
597C2×C4—361no—
598C2×C4—361no—
599C2×C4#380411yescharacteristic
600C2×C4C2×#62611yescharacteristic
601C2×C4D3×#6711yescharacteristic
602C2×C4D3×#6711yescharacteristic
603C2×C4D3×#6711yescharacteristic
604C2×C4#381111yescharacteristic
605C8—62no—
606C8—121no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3#480811yescharacteristic
615C2×C3#480911yescharacteristic
616C2×C3#481311yescharacteristic
617C2×C3#481611yescharacteristic
618C2×C3#496011yescharacteristic
619C2×C3#517311yescharacteristic
620C2×C3#518611yescharacteristic
621C2×C3#518611yescharacteristic
622C2×C3#518611yescharacteristic
623C2×C3#518711yescharacteristic
624C2×C3#518711yescharacteristic
625C2×C3#518811yescharacteristic
626C2×C3#518911yescharacteristic
627C2×C3#522311yescharacteristic
628D3—124no—
629D3—122no—
630D3—122no—
631C22—182no—
632C22—182no—
633C22—182no—
634C22—361no—
635C22—361no—
636C22—361no—
637C22—361no—
638C22#6394411yescharacteristic
639C22#6394511yescharacteristic
640C22#6395011yescharacteristic
641C22#6395111yescharacteristic
642C22#6395811yescharacteristic
643C22#6398111yescharacteristic
644C22#6398311yescharacteristic
645C4—42no—
646C4—122no—
647C4—122no—
648C4—362no—
649C4—361no—
650C4#6397111yescharacteristic
651C4#6397711yescharacteristic
652C4#6397811yescharacteristic
653C4#6397911yescharacteristic
654C3—21no—
655C3#7027311yescharacteristic, complemented
656C3#7207111yescharacteristic, complemented
657C2—362no—
658C2#1059160011yescharacteristic
659C2#1059160111yescharacteristic
660C2#1059160211yescharacteristic
661C2#1059160311yescharacteristic
662C2#1059165411yescharacteristic
663C2#1059165611yescharacteristic
664C2#1059172411yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3⋊D3D4
hypercenterC22×Q8D32
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
4. C2×C3×#835C2semidirect
5. C2×#63566C2semidirect
7. #10589164C2semidirect
36. C22×#216D3semidirect
40. C2×#835D3semidirect
143. C22×C3⋊D3Q16semidirect
563. C32#2001semidirect
655. C3#70273semidirect
656. C3#72071semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C22×C3×#2162
C2×#638712
C2×C3×#8352
C2×#635662
C2×#635572
#105891642
#720713
#702733