Finite Group Databasebeta

← #11808439

Subgroups — #11808439

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C212yesmaximal, complemented
2C2×#63894C211yesmaximal, characteristic, complemented
3C2×#63836C211yesmaximal, characteristic, complemented
4#10592370C211yesmaximal, characteristic
5C3×#4661C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591326C211yesmaximal, characteristic, complemented
8#10591321C212yesmaximal, complemented
9#10591321C211yesmaximal, characteristic, complemented
10#10591311C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12#77737—31nomaximal
13#73776—31nomaximal
14C22×C4⋊(C3⋊D3)C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×#624C2212yes—
17C22×#624C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3752C2211yescharacteristic
20C2×C3×C4⋊Dic3C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4C2212yes—
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×C4×Dic3C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×Dic3⋊Dic3C2211yescharacteristic
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2211yescharacteristic
31C2×#3722C2212yes—
32C2×Dic32C2211yescharacteristic
33#63894—28no—
34#63894—24no—
35#63836—24no—
36C32×#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×#893—32no—
41C2×#893—31no—
42C2×#892—31no—
43C2×C4×D12—31no—
44C2×C4×D12—32no—
45C2×#872—31no—
46C3×#398—31no—
47C3×C4×C4⋊C4—31no—
48#4994—32no—
49#4994—32no—
50#4992—31no—
51#4991—32no—
52#4991—31no—
53C4×(C2×D3)⋊C4—32no—
54#4674—31no—
55#4672—31no—
56#4672—32no—
57#4671—31no—
58#4671—31no—
59#4671—61no—
60#4666—32no—
61#4661D311yescharacteristic, complemented
62#4649D311yescharacteristic, complemented
63C23×C3⋊D3C2311yescharacteristic
64C23×C3⋊D3C2312yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C3⋊Dic3C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—24no—
69C2×C4⋊(C3⋊D3)—24no—
70C2×C4⋊(C3⋊D3)—24no—
71C2×C4⋊(C3⋊D3)—22no—
72C2×C4⋊(C3⋊D3)—24no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×#624—22no—
80C2×#624—22no—
81C2×#624—24no—
82C2×#624—24no—
83C2×#624—24no—
84C2×#624D414yescomplemented
85#3752—22no—
86#3752—24no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3—24no—
89C3×Dic3⋊C4—22no—
90C3×Dic3⋊C4—24no—
91C3×C4×Dic3—24no—
92C3×C4×Dic3D414yescomplemented
93Dic3⋊Dic3—22no—
94#3722—24no—
95#3722—24no—
96#3722—22no—
97#3722—24no—
98#3722—24no—
99Dic32—22no—
100#2392—91noSylow
101C22×D12—31no—
102C22×D12—32no—
103C22×D12—32no—
104C22×D12—31no—
105C22×D12—62no—
106C22×D12—61no—
107C22×C4×D3—31no—
108C22×C4×D3—31no—
109C22×C4×D3—32no—
110C22×C4×D3—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C4⋊C4—32no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C42—31no—
116C2×C3×C42—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—32no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—61no—
132C2×(C2×D3)⋊C4—62no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×C4⋊Dic3C2×D312yes—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4C2×D312yes—
138C2×Dic3⋊C4C2×D311yescharacteristic
139C2×C4×Dic3—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3C2×D312yes—
142C2×C4×Dic3C2×D311yescharacteristic
143#893—68no—
144#893—64no—
145#892—64no—
146C4×D12—64no—
147C4×D12—68no—
148#872—64no—
149C3×#95—21no—
150C3×#95—32no—
151C3×#95—31no—
152C3×#95C2×D311yescharacteristic
153C3×#95C2×D311yescharacteristic
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D311yescharacteristic
157C3⋊#95C2×D312yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—21no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3—22no—
166C22×C3⋊D3—22no—
167C22×C3⋊D3—22no—
168C22×C3⋊D3—22no—
169C22×C3⋊D3C2×D412yes—
170C22×C3⋊D3#4114yes—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D412yes—
175C2×C32×C4#4114yes—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—22no—
178C4⋊(C3⋊D3)—28no—
179C4⋊(C3⋊D3)—216no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3—21no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3C2×D412yes—
194C2×C3×Dic3C2×D412yes—
195C2×C3×Dic3#4112yes—
196#624—28no—
197#624—48no—
198C2×C4×D4—91no—
199C2×C4×D4—92no—
200C2×#117—91no—
201#398—31no—
202#397—91no—
203#396—92no—
204#394—92no—
205#394—91no—
206#392—91no—
207C4×C4⋊C4—31no—
208C4×C22⋊C4—92no—
209C23×D3—31no—
210C23×D3—31no—
211C23×D3—32no—
212C23×D3—32no—
213C23×D3—61no—
214C23×D3—62no—
215C22×C3×C4—22no—
216C22×C3×C4—21no—
217C22×C3×C4—31no—
218C22×C3×C4—31no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—31no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D312yes—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D312yes—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—61no—
230C22×Dic3C22×D312yes—
231C22×Dic3C22×D312yes—
232C22×Dic3C22×D311yescharacteristic
233C22×Dic3C22×D311yescharacteristic
234C22×Dic3C22×D311yescharacteristic
235C22×Dic3C22×D311yescharacteristic
236C2×D12—64no—
237C2×D12—64no—
238C2×D12—64no—
239C2×D12—64no—
240C2×D12—64no—
241C2×D12—64no—
242C2×D12—62no—
243C2×D12—64no—
244C2×D12—62no—
245C2×D12—64no—
246C2×D12—124no—
247C2×D12—122no—
248C2×D12—124no—
249C2×D12—124no—
250C2×D12—124no—
251C2×C4×D3—34no—
252C2×C4×D3—34no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×C4×D3—64no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C3×C4⋊C4—64no—
264C3×C4⋊C4—62no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—64no—
267C3×C42—34no—
268C3×C42—64no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—64no—
271(C2×D3)⋊C4—64no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—64no—
274(C2×D3)⋊C4—64no—
275(C2×D3)⋊C4—64no—
276(C2×D3)⋊C4—62no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283(C2×D3)⋊C4—124no—
284(C2×D3)⋊C4—122no—
285C4⋊Dic3—22no—
286C4⋊Dic3—24no—
287C4⋊Dic3—62no—
288Dic3⋊C4—24no—
289Dic3⋊C4—22no—
290Dic3⋊C4—62no—
291C4×Dic3—24no—
292C4×Dic3—62no—
293C4×Dic3—62no—
294C4×Dic3D1214yescomplemented
295C22×C32C22×D411yescharacteristic
296C22×C32C22×D411yescharacteristic
297C22×C32C2×#4112yes—
298C22×C32C2×#4111yescharacteristic
299C22×C32C2×#4112yes—
300C2×C3⋊D3—22no—
301C2×C3⋊D3—24no—
302C2×C3⋊D3—24no—
303C2×C3⋊D3—24no—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—42no—
306C2×C3⋊D3—41no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3⋊D3—42no—
310C2×C3⋊D3—41no—
311C2×C3⋊D3—42no—
312C32×C4—22no—
313C32×C4—24no—
314C3⋊Dic3—41no—
315C3×Dic3—22no—
316C3×Dic3—22no—
317C3×Dic3—42no—
318C3×Dic3—41no—
319C3×Dic3—42no—
320C3×Dic3#12114yes—
321C22×D4—92no—
322C22×D4—91no—
323C23×C4—91no—
324C23×C4—92no—
325C4×D4—184no—
326C4×D4—188no—
327#117—184no—
328C2×C4⋊C4—31no—
329C2×C4⋊C4—32no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—32no—
332C2×C4⋊C4—91no—
333C2×C22⋊C4—91no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—92no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—92no—
340C2×C42—31no—
341C2×C42—32no—
342C2×C42—91no—
343#95—32no—
344#95—31no—
345#95—92no—
346#95D3211yescharacteristic
347C23×C3—21no—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—32no—
351C22×D3—32no—
352C22×D3—34no—
353C22×D3—34no—
354C22×D3—62no—
355C22×D3—64no—
356C22×D3—61no—
357C22×D3—62no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—61no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—61no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—122no—
377C22×D3—121no—
378C22×D3—122no—
379C22×D3—122no—
380C22×D3—122no—
381C22×D3—122no—
382C22×D3—122no—
383C22×D3—122no—
384C22×D3—121no—
385C22×D3—122no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—22no—
394C2×C3×C4—32no—
395C2×C3×C4—32no—
396C2×C3×C4—32no—
397C2×C3×C4—32no—
398C2×C3×C4—32no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—61no—
403C2×C3×C4—62no—
404C2×C3×C4—61no—
405C2×C3×C4—61no—
406C2×C3×C4—62no—
407C2×C3×C4—62no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4C2×D1212yes—
414C2×C3×C4#23514yes—
415C2×C3×C4D3×D412yes—
416C2×C3×C4#23914yes—
417C2×Dic3—22no—
418C2×Dic3—21no—
419C2×Dic3—21no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—21no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—61no—
429C2×Dic3—62no—
430C2×Dic3—61no—
431C2×Dic3—62no—
432C2×Dic3—122no—
433C2×Dic3—121no—
434C2×Dic3C2×D1212yes—
435C2×Dic3C2×D1212yes—
436C2×Dic3D3×D412yes—
437C2×Dic3D3×D412yes—
438C2×Dic3#23912yes—
439D12—68no—
440D12—68no—
441D12—616no—
442D12—616no—
443D12—1216no—
444D12—128no—
445C4×D3—68no—
446C4×D3—68no—
447C4×D3—128no—
448C4×D3—128no—
449C2×C32C2×#12111yescharacteristic
450C2×C32#52511yescharacteristic
451C2×C32#52512yes—
452C2×C32#52912yes—
453C2×C32#53211yescharacteristic
454C3⋊D3—42no—
455C3⋊D3—44no—
456C24—91no—
457C24—92no—
458C2×D4—184no—
459C2×D4—184no—
460C2×D4—184no—
461C2×D4—184no—
462C2×D4—182no—
463C22×C4—31no—
464C22×C4—31no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—94no—
470C22×C4—91no—
471C22×C4—182no—
472C22×C4—182no—
473C22×C4—184no—
474C22×C4—184no—
475C22×C4—184no—
476C22×C4C2×D3212yes—
477C22×C4C2×D3211yescharacteristic
478C4⋊C4—64no—
479C4⋊C4—64no—
480C4⋊C4—62no—
481C4⋊C4—62no—
482C4⋊C4—182no—
483C22⋊C4—182no—
484C22⋊C4—184no—
485C22⋊C4—184no—
486C22⋊C4—184no—
487C22⋊C4—184no—
488C22⋊C4—184no—
489C22⋊C4—182no—
490C42—34no—
491C42—64no—
492C42—182no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3C22×D1211yescharacteristic
499C22×C3C2×#23512yes—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C2×#23912yes—
504C22×C3C2×#23911yescharacteristic
505C22×C3D3×#4112yes—
506C22×C3D3×#4112yes—
507C22×C3D3×#4111yescharacteristic
508C2×D3—64no—
509C2×D3—64no—
510C2×D3—62no—
511C2×D3—64no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—62no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—122no—
522C2×D3—124no—
523C2×D3—121no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—121no—
527C2×D3—122no—
528C2×D3—121no—
529C2×D3—122no—
530C2×D3—122no—
531C2×D3—121no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—242no—
538C2×D3—241no—
539C2×D3—242no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—242no—
543C2×D3—241no—
544C3×C4—22no—
545C3×C4—22no—
546C3×C4—24no—
547C3×C4—24no—
548C3×C4—34no—
549C3×C4—44no—
550C3×C4—42no—
551C3×C4—62no—
552C3×C4—62no—
553C3×C4—122no—
554C3×C4—121no—
555C3×C4—122no—
556Dic3—22no—
557Dic3—22no—
558Dic3—41no—
559Dic3—42no—
560Dic3—42no—
561Dic3—121no—
562Dic3—121no—
563Dic3—241no—
564Dic3#89514yes—
565C32#239211yescharacteristic, complemented, Sylow
566C23—92no—
567C23—94no—
568C23—182no—
569C23—182no—
570C23—182no—
571C23—181no—
572C23—182no—
573C23—182no—
574C23—182no—
575C23—182no—
576C23—181no—
577C23—182no—
578C23C22×D3211yescharacteristic
579D4—1816no—
580D4—188no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—32no—
585C2×C4—32no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—32no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—61no—
594C2×C4—62no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—188no—
601C2×C4—182no—
602C2×C4—181no—
603C2×C4—368no—
604C2×C4#379914yes—
605C2×C4D3×D1212yes—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3#547711yescharacteristic
612C2×C3C2×#89511yescharacteristic
613C2×C3#552411yescharacteristic
614C2×C3#554712yes—
615C2×C3#558012yes—
616C2×C3D3×#12111yescharacteristic
617C2×C3#562712yes—
618C2×C3#565611yescharacteristic
619C2×C3#569112yes—
620C2×C3#572511yescharacteristic
621D3—122no—
622D3—124no—
623D3—124no—
624D3—122no—
625D3—242no—
626D3—244no—
627C22—184no—
628C22—184no—
629C22—184no—
630C22—182no—
631C22—184no—
632C22—362no—
633C22—361no—
634C22—362no—
635C22—362no—
636C22—362no—
637C22—362no—
638C22—361no—
639C22C2×#379912yes—
640C22C2×D3×D1211yescharacteristic
641C22D32×D411yescharacteristic
642C22#6431212yes—
643C22D3×#23911yescharacteristic
644C4—24no—
645C4—22no—
646C4—34no—
647C4—62no—
648C4—62no—
649C4—122no—
650C4—121no—
651C4—122no—
652C4—361no—
653C3—21no—
654C3#7377611yescharacteristic, complemented
655C3#7773711yescharacteristic, complemented
656C2—362no—
657C2—364no—
658C2#1059397011yescharacteristic
659C2#1059406612yes—
660C2#1059407911yescharacteristic
661C2#1059446412yes—
662C2D3×#89511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radical#10592370C2
hypercenter#95D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63894C2semidirect
2. C2×#63894C2semidirect
3. C2×#63836C2semidirect
5. C3×#4661C2semidirect
6. C3×#4649C2semidirect
7. #10591326C2semidirect
8. #10591321C2semidirect
9. #10591321C2semidirect
10. #10591311C2semidirect
11. #10591233C2semidirect
61. #4661D3semidirect
62. #4649D3semidirect
84. C2×#624D4semidirect
92. C3×C4×Dic3D4semidirect
294. C4×Dic3D12semidirect
565. C32#2392semidirect
654. C3#73776semidirect
655. C3#77737semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#638362
#105923702
C3×#46612
C3×#46492
#105913262
#105913212
#105913112
#105912332
#777373
#737763