Finite Group Databasebeta

← #11801220

Subgroups — #11801220

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C212yesmaximal
2C2×C4×D3×Dic3C211yesmaximal, characteristic
3C4⋊C4×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4987C211yesmaximal, characteristic
5C3×#4975C211yesmaximal, characteristic, complemented
6#10591366C212yesmaximal
7#10591349C211yesmaximal, characteristic, complemented
8#10591313C211yesmaximal, characteristic
9#10591274C211yesmaximal, characteristic, complemented
10#10591245C212yesmaximal, complemented
11#10591241C212yesmaximal, complemented
12#74318—31nomaximal
13#73864—31nomaximal
14C22×C3×C4×D3C2211yescharacteristic
15C22×D3×Dic3C2211yescharacteristic
16C22×D3×Dic3C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2212yes—
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×Dic3⋊C4C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×Dic3⋊Dic3C2212yes—
28C2×Dic3⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2211yescharacteristic
32C2×Dic32C2211yescharacteristic
33#63878—28no—
34C4×D3×Dic3C418yescomplemented
35#63658C2212yes—
36C3×C3⋊#95C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C22×C4×Dic3—31no—
40C2×#892—32no—
41C2×#877—32no—
42C2×C42×D3—31no—
43C3×#384—31no—
44C3×#380—31no—
45#5212—31no—
46#4987—31no—
47#4987—32no—
48#4987D311yescharacteristic
49#4977—32no—
50#4975—31no—
51#4975D311yescharacteristic, complemented
52Dic3×C4⋊C4—31no—
53Dic3×C4⋊C4—31no—
54Dic3×C4⋊C4—31no—
55Dic3×C4⋊C4—31no—
56Dic3×C4⋊C4—32no—
57Dic3×C4⋊C4—61no—
58#4942—32no—
59#4935—31no—
60#4650—32no—
61#4649—32no—
62C23×C3×D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2×C414yes—
76C2×D3×Dic3—22no—
77C2×D3×Dic3—22no—
78C2×D3×Dic3C2×C414yes—
79C2×D3×Dic3C2×C414yes—
80C2×D3×Dic3D414yes—
81C2×D3×Dic3Q814yes—
82C32×C4⋊C4—22no—
83C4⋊(C3⋊Dic3)—22no—
84C4×C3⋊Dic3—24no—
85C4×C3⋊Dic3C2×C414yes—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—22no—
89C3×Dic3⋊C4—24no—
90C3×Dic3⋊C4—24no—
91C3×C4×Dic3C2×C414yes—
92Dic3⋊Dic3—24no—
93Dic3⋊Dic3—24no—
94(C2×D3)⋊Dic3—24no—
95Dic32—24no—
96Dic32C2×C414yes—
97Dic32C2×C414yes—
98#2285—91noSylow
99C23×C3×C4—31no—
100C23×Dic3—31no—
101C23×Dic3—31no—
102C22×C4×D3—31no—
103C22×C4×D3—31no—
104C22×C4×D3C2×D311yescharacteristic
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—32no—
107C2×C3×C4⋊C4—32no—
108C2×C3×C4⋊C4—31no—
109C2×C3×C4⋊C4—31no—
110C2×C3×C4⋊C4C2×D311yescharacteristic
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—31no—
114C2×#217—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—31no—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3C2×D311yescharacteristic
123C2×C4⋊Dic3C2×D311yescharacteristic
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4C2×D312yes—
127C2×Dic3⋊C4C2×D312yes—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—38no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—32no—
139C2×C4×Dic3—61no—
140C2×C4×Dic3—62no—
141C2×C4×Dic3C2×D311yescharacteristic
142#892—68no—
143#877—68no—
144C42×D3—38no—
145C3×#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—62no—
153C3⋊#95C2×D312yes—
154C23×C32C2411yescharacteristic
155C22×C3×D3—21no—
156C22×C3×D3—21no—
157C22×C3×D3—21no—
158C22×C3×D3—21no—
159C22×C3×D3C22×C412yes—
160C22×C3×D3C2×D412yes—
161C22×C3×D3C2×Q812yes—
162C2×C32×C4—22no—
163C2×C32×C4—22no—
164C2×C32×C4—22no—
165C2×C32×C4C22×C412yes—
166C2×C32×C4#4112yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C22×C412yes—
174C2×C3⋊Dic3C22×C412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×Q812yes—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3C22×C412yes—
186C2×C3×Dic3C22×C412yes—
187C2×C3×Dic3C22×C412yes—
188C2×C3×Dic3C2×D412yes—
189C2×C3×Dic3C2×Q812yes—
190C2×C3×Dic3#4112yes—
191C2×C3×Dic3#4112yes—
192C3×C4×D3—28no—
193D3×Dic3—28no—
194D3×Dic3C4⋊C4116yescomplemented
195C2×#117—92no—
196C22×C42—91no—
197#384—31no—
198#384—91no—
199#382—92no—
200#380—31no—
201#380—92no—
202#380—91no—
203C4×C4⋊C4—92no—
204C4×C4⋊C4—91no—
205C4×C4⋊C4—91no—
206C24×C3—31no—
207C23×D3C22×D311yescharacteristic
208C22×C3×C4—21no—
209C22×C3×C4—22no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—34no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D312yes—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—34no—
225C22×Dic3—34no—
226C22×Dic3—34no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—34no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3—62no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D311yescharacteristic
241C22×Dic3C22×D311yescharacteristic
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3—34no—
245C2×C4×D3—34no—
246C2×C4×D3—34no—
247C2×C4×D3—34no—
248C2×C4×D3—62no—
249C2×C4×D3—62no—
250C2×C4×D3C4×D314yes—
251C3×C4⋊C4—24no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4—64no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C22⋊C4—64no—
259C3×C42—34no—
260#217—64no—
261(C2×D3)⋊C4—24no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3—64no—
266C4⋊Dic3—64no—
267C4⋊Dic3—64no—
268C4⋊Dic3—62no—
269C4⋊Dic3—62no—
270Dic3⋊C4—24no—
271Dic3⋊C4—24no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274C4×Dic3—34no—
275C4×Dic3—34no—
276C4×Dic3—34no—
277C4×Dic3—34no—
278C4×Dic3—34no—
279C4×Dic3—34no—
280C4×Dic3—64no—
281C4×Dic3—64no—
282C4×Dic3—64no—
283C4×Dic3—64no—
284C4×Dic3—64no—
285C4×Dic3—124no—
286C4×Dic3C4×D314yes—
287C22×C32C23×C411yescharacteristic
288C22×C32C22×D411yescharacteristic
289C22×C32C22×Q811yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32C2×#4111yescharacteristic
292C22×C32C2×#4111yescharacteristic
293C22×C32C2×#4111yescharacteristic
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—22no—
300C2×C3×D3C2×C4⋊C414yes—
301C32×C4—42no—
302C32×C4#11714yescomplemented
303C3⋊Dic3—22no—
304C3⋊Dic3—42no—
305C3⋊Dic3C2×C4⋊C414yes—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C3×Dic3—42no—
309C3×Dic3C2×C4⋊C414yes—
310C3×Dic3#11714yescomplemented
311C23×C4—31no—
312C23×C4—91no—
313C23×C4—91no—
314#117—188no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—31no—
317C2×C4⋊C4—32no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—92no—
320C2×C4⋊C4—92no—
321C2×C4⋊C4—91no—
322C2×C4⋊C4D3211yescharacteristic
323C2×C22⋊C4—32no—
324C2×C22⋊C4—92no—
325C2×C42—31no—
326C2×C42—98no—
327C2×C42—91no—
328C2×C42—91no—
329C2×C42—91no—
330C2×C42—92no—
331C2×C42—92no—
332#95—32no—
333#95—92no—
334#95—92no—
335#95—92no—
336C23×C3—21no—
337C23×C3—32no—
338C23×C3—32no—
339C23×C3—32no—
340C23×C3—61no—
341C23×C3—61no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3C23×D311yescharacteristic
345C23×C3C23×D311yescharacteristic
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—21no—
349C22×D3—21no—
350C22×D3C2×C4×D312yes—
351C22×D3D3×D412yes—
352C22×D3D3×Q812yes—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—32no—
367C2×C3×C4—32no—
368C2×C3×C4—32no—
369C2×C3×C4—32no—
370C2×C3×C4—42no—
371C2×C3×C4—42no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—68no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4#23712yes—
384C2×C3×C4#23712yes—
385C2×C3×C4#23712yes—
386C2×C3×C4#23912yes—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—32no—
396C2×Dic3—32no—
397C2×Dic3—32no—
398C2×Dic3—32no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—316no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—61no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—68no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C2×Dic3—62no—
420C2×Dic3—122no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3—122no—
424C2×Dic3C2×C4×D312yes—
425C2×Dic3C2×C4×D312yes—
426C2×Dic3C2×C4×D312yes—
427C2×Dic3D3×D412yes—
428C2×Dic3#23712yes—
429C2×Dic3D3×Q812yes—
430C2×Dic3#23912yes—
431C4×D3—28no—
432C4×D3—316no—
433C4×D3—68no—
434C2×C32C22×C4⋊C411yescharacteristic
435C2×C32C2×#11711yescharacteristic
436C2×C32C2×#11711yescharacteristic
437C2×C32#53211yescharacteristic
438C2×C32#53211yescharacteristic
439C2×C32#53311yescharacteristic
440C2×C32#53311yescharacteristic
441C3×D3—24no—
442C24—31no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—34no—
447C22×C4—32no—
448C22×C4—32no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—94no—
452C22×C4—94no—
453C22×C4—94no—
454C22×C4—94no—
455C22×C4—91no—
456C22×C4—91no—
457C22×C4—92no—
458C22×C4—182no—
459C22×C4—182no—
460C22×C4C2×D3212yes—
461C22×C4C2×D3211yescharacteristic
462C4⋊C4—22no—
463C4⋊C4—64no—
464C4⋊C4—64no—
465C4⋊C4—62no—
466C4⋊C4—62no—
467C4⋊C4—184no—
468C4⋊C4—184no—
469C4⋊C4—182no—
470C22⋊C4—64no—
471C22⋊C4—184no—
472C42—34no—
473C42—94no—
474C42—94no—
475C42—94no—
476C42—184no—
477C42—184no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—34no—
486C22×C3—62no—
487C22×C3—62no—
488C22×C3—62no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3C22×C4×D311yescharacteristic
493C22×C3C22×C4×D311yescharacteristic
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C22×C3C2×#23711yescharacteristic
497C22×C3C2×#23711yescharacteristic
498C22×C3C2×#23711yescharacteristic
499C22×C3C2×#23711yescharacteristic
500C22×C3C2×D3×Q811yescharacteristic
501C22×C3C2×D3×Q811yescharacteristic
502C22×C3C2×#23911yescharacteristic
503C22×C3C2×#23911yescharacteristic
504C22×C3D3×#4111yescharacteristic
505C22×C3D3×#4111yescharacteristic
506C2×D3—22no—
507C2×D3—22no—
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—22no—
512C2×D3D3×C4⋊C414yes—
513C3×C4—24no—
514C3×C4—34no—
515C3×C4—34no—
516C3×C4—44no—
517C3×C4—42no—
518C3×C4—42no—
519C3×C4—62no—
520C3×C4—122no—
521C3×C4—122no—
522C3×C4#87714yescomplemented
523C3×C4#89214yescomplemented
524Dic3—22no—
525Dic3—34no—
526Dic3—34no—
527Dic3—42no—
528Dic3—42no—
529Dic3—64no—
530Dic3—62no—
531Dic3—62no—
532Dic3—122no—
533Dic3—124no—
534Dic3—122no—
535Dic3—122no—
536Dic3D3×C4⋊C414yes—
537Dic3#89214yescomplemented
538C32#228511yescharacteristic, complemented, Sylow
539C23—32no—
540C23—32no—
541C23—32no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23—61no—
546C23C22×D3211yescharacteristic
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—32no—
551C2×C4—32no—
552C2×C4—32no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—32no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—68no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—916no—
567C2×C4—92no—
568C2×C4—92no—
569C2×C4—92no—
570C2×C4—92no—
571C2×C4—188no—
572C2×C4—181no—
573C2×C4—181no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4#379612yes—
578C2×C4C4×D3212yes—
579C2×C4#380512yes—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—64no—
588C2×C3C2×#87711yescharacteristic
589C2×C3C2×D3×C4⋊C411yescharacteristic
590C2×C3C2×D3×C4⋊C411yescharacteristic
591C2×C3C2×#89211yescharacteristic
592C2×C3C2×#89211yescharacteristic
593C2×C3D3×#11711yescharacteristic
594C2×C3#559611yescharacteristic
595C2×C3#559611yescharacteristic
596C2×C3#562211yescharacteristic
597C2×C3#562211yescharacteristic
598C2×C3#571611yescharacteristic
599C2×C3#572511yescharacteristic
600C2×C3#572811yescharacteristic
601C2×C3#572811yescharacteristic
602D3—24no—
603C22—34no—
604C22—62no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22C2×#379611yescharacteristic
611C22C2×C4×D3211yescharacteristic
612C22D32×D411yescharacteristic
613C22D3×#23711yescharacteristic
614C22D32×Q811yescharacteristic
615C22D3×#23911yescharacteristic
616C22C2×#380511yescharacteristic
617C4—34no—
618C4—34no—
619C4—42no—
620C4—62no—
621C4—94no—
622C4—122no—
623C4—122no—
624C4—182no—
625C4—362no—
626C4#6387814yescomplemented
627C3—21no—
628C3#7386411yescharacteristic, complemented
629C3#7431811yescharacteristic, complemented
630C2—64no—
631C2#1059436911yescharacteristic
632C2#1059438711yescharacteristic
633C2D32×C4⋊C411yescharacteristic
634C2D3×#89211yescharacteristic
635C2C2×#6387811yescharacteristic
636C2#1059513311yescharacteristic
637C2#1059536811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2285
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C4⋊C4×C3⋊Dic3C2semidirect
5. C3×#4975C2semidirect
7. #10591349C2semidirect
9. #10591274C2semidirect
10. #10591245C2semidirect
11. #10591241C2semidirect
34. C4×D3×Dic3C4semidirect
51. #4975D3semidirect
194. D3×Dic3C4⋊C4semidirect
302. C32×C4#117semidirect
310. C3×Dic3#117semidirect
522. C3×C4#877semidirect
523. C3×C4#892semidirect
537. Dic3#892semidirect
538. C32#2285semidirect
626. C4#63878semidirect
628. C3#73864semidirect
629. C3#74318semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C2×C4×D3×Dic32
C4⋊C4×C3⋊Dic32
C3×#49872
C3×#49752
#105913662
#105913492
#105913132
#105912742
#105912452
#105912412
#743183
#738643