Finite Group Databasebeta

← #11808462

Subgroups — #11808462

Order 1152.

1511 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63894C211yesmaximal, characteristic, complemented
2C2×#63880C212yesmaximal, complemented
3C2×#63877C211yesmaximal, characteristic, complemented
4#10592371C211yesmaximal, characteristic, complemented
5C3×#4674C211yesmaximal, characteristic, complemented
6C3×#4649C211yesmaximal, characteristic, complemented
7#10591395C211yesmaximal, characteristic
8#10591358C211yesmaximal, characteristic, complemented
9#10591347C212yesmaximal, complemented
10#10591291C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12#77457—31nomaximal
13#73776—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#626C2212yes—
16C22×#624C2212yes—
17C22×D3×Dic3C2211yescharacteristic
18C2×#3752C2212yes—
19C2×#3752C2212yes—
20C2×#3750C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×#3724C2211yescharacteristic
28C2×Dic3⋊Dic3C2212yes—
29C2×#3722C2212yes—
30C2×#3722C2212yes—
31C2×(C2×D3)⋊Dic3C2211yescharacteristic
32C2×Dic32C2211yescharacteristic
33#63894—24no—
34#63880—28no—
35#63877—24no—
36C32×#95C2211yescharacteristic
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2211yescharacteristic
39#63579C2212yes—
40C2×#893—31no—
41C2×#67⋊C4—32no—
42C2×#877—31no—
43C2×C4×D12—32no—
44C2×C4×D12—31no—
45C2×#872—31no—
46C3×#397—31no—
47C3×C4×C4⋊C4—31no—
48#4994—32no—
49#4991—32no—
50#4983—31no—
51#4960—31no—
52#4959—32no—
53C4×(C2×D3)⋊C4—32no—
54#4676—32no—
55#4674D311yescharacteristic, complemented
56#4672—31no—
57#4672—31no—
58#4672—61no—
59#4671—31no—
60#4666—32no—
61#4661—31no—
62#4649D311yescharacteristic, complemented
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—24no—
70C2×C4⋊(C3⋊D3)—22no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C2×#626—24no—
77C2×#626—24no—
78C2×#626—24no—
79C2×#624—24no—
80C2×#624—24no—
81C2×#624—24no—
82C2×D3×Dic3—22no—
83C2×D3×Dic3—22no—
84C2×D3×Dic3D414yescomplemented
85#3752—24no—
86#3752—24no—
87#3750—22no—
88C3×(C2×D3)⋊C4—24no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3—22no—
91C3×Dic3⋊C4—24no—
92C3×C4×Dic3—24no—
93C3×C4×Dic3D414yescomplemented
94#3724—22no—
95Dic3⋊Dic3—24no—
96#3722—24no—
97#3722—24no—
98(C2×D3)⋊Dic3—22no—
99Dic32—22no—
100#2392—91noSylow
101C22×#67—32no—
102C23×Dic3—31no—
103C22×D12—32no—
104C22×D12—31no—
105C22×D12—31no—
106C22×D12—61no—
107C22×C4×D3—31no—
108C22×C4×D3—32no—
109C22×C4×D3—32no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C22⋊C4—31no—
114C2×C3×C42—31no—
115C2×C3×C42—32no—
116C2×#217—31no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—62no—
127C2×(C2×D3)⋊C4—62no—
128C2×(C2×D3)⋊C4C2×D311yescharacteristic
129C2×(C2×D3)⋊C4C2×D312yes—
130C2×C4⋊Dic3—32no—
131C2×C4⋊Dic3C2×D311yescharacteristic
132C2×Dic3⋊C4—31no—
133C2×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—32no—
136C2×Dic3⋊C4—31no—
137C2×Dic3⋊C4—61no—
138C2×Dic3⋊C4C2×D312yes—
139C2×C4×Dic3—31no—
140C2×C4×Dic3—31no—
141C2×C4×Dic3C2×D312yes—
142C2×C4×Dic3C2×D311yescharacteristic
143#893—64no—
144#67⋊C4—68no—
145#877—64no—
146C4×D12—64no—
147C4×D12—68no—
148#872—64no—
149C3×#95—21no—
150C3×#95—31no—
151C3×#95—32no—
152C3×#95C2×D311yescharacteristic
153C3×#95C2×D311yescharacteristic
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95C2×D311yescharacteristic
157C3⋊#95C2×D312yes—
158C23×C32C2411yescharacteristic
159C22×C3⋊D3—22no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—22no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—22no—
165C22×C3⋊D3#4114yes—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3C2×D412yes—
171C2×C32×C4—22no—
172C2×C32×C4—22no—
173C2×C32×C4—22no—
174C2×C32×C4—22no—
175C2×C32×C4C2×D412yes—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3C2×D412yes—
181C4⋊(C3⋊D3)—28no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D412yes—
191C2×C3×Dic3C2×D412yes—
192C2×C3×Dic3C2×D412yes—
193C2×C3×Dic3#4114yes—
194C2×C3×Dic3#4112yes—
195#626—216no—
196#624—48no—
197D3×Dic3—28no—
198C2×C4×D4—92no—
199C2×C4×D4—91no—
200C2×#117—91no—
201#398—91no—
202#397—31no—
203#396—92no—
204#394—92no—
205#394—91no—
206#392—91no—
207C4×C4⋊C4—31no—
208C4×C22⋊C4—92no—
209C24×C3—31no—
210C23×D3—32no—
211C23×D3—32no—
212C23×D3—62no—
213C23×D3C22×D311yescharacteristic
214C22×C3×C4—21no—
215C22×C3×C4—22no—
216C22×C3×C4—31no—
217C22×C3×C4—32no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—31no—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—34no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—61no—
234C22×Dic3—61no—
235C22×Dic3—62no—
236C22×Dic3—62no—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D311yescharacteristic
239C22×Dic3C22×D311yescharacteristic
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D311yescharacteristic
242C2×D12—64no—
243C2×D12—64no—
244C2×D12—64no—
245C2×D12—64no—
246C2×D12—64no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—122no—
250C2×D12—124no—
251C2×C4×D3—34no—
252C2×C4×D3—62no—
253C2×C4×D3—62no—
254C2×C4×D3—64no—
255C2×C4×D3—64no—
256C2×C4×D3—64no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C3×C4⋊C4—64no—
261C3×C4⋊C4—62no—
262C3×C22⋊C4—64no—
263C3×C22⋊C4—62no—
264C3×C42—34no—
265C3×C42—64no—
266#217—62no—
267(C2×D3)⋊C4—24no—
268(C2×D3)⋊C4—22no—
269(C2×D3)⋊C4—64no—
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—62no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—64no—
278(C2×D3)⋊C4—124no—
279(C2×D3)⋊C4—124no—
280C4⋊Dic3—22no—
281C4⋊Dic3—64no—
282Dic3⋊C4—24no—
283Dic3⋊C4—64no—
284Dic3⋊C4—62no—
285Dic3⋊C4—62no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—122no—
289C4×Dic3—24no—
290C4×Dic3—62no—
291C4×Dic3—62no—
292C4×Dic3D1214yescomplemented
293C22×C32C22×D411yescharacteristic
294C22×C32C22×D411yescharacteristic
295C22×C32C2×#4112yes—
296C22×C32C2×#4111yescharacteristic
297C22×C32C2×#4112yes—
298C2×C3⋊D3—24no—
299C2×C3⋊D3—24no—
300C2×C3⋊D3—24no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—42no—
305C2×C3×D3—22no—
306C2×C3×D3—24no—
307C2×C3×D3—41no—
308C2×C3×D3—42no—
309C2×C3×D3—41no—
310C32×C4—22no—
311C32×C4—42no—
312C3⋊Dic3—22no—
313C3⋊Dic3—41no—
314C3×Dic3—24no—
315C3×Dic3—22no—
316C3×Dic3—42no—
317C3×Dic3—41no—
318C3×Dic3#12114yes—
319C22×D4—92no—
320C22×D4—91no—
321C23×C4—92no—
322C23×C4—91no—
323C4×D4—184no—
324C4×D4—188no—
325#117—184no—
326C2×C4⋊C4—31no—
327C2×C4⋊C4—32no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—92no—
330C2×C4⋊C4—91no—
331C2×C22⋊C4—31no—
332C2×C22⋊C4—32no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4—92no—
337C2×C22⋊C4—92no—
338C2×C42—31no—
339C2×C42—32no—
340C2×C42—91no—
341#95—32no—
342#95—31no—
343#95—92no—
344#95D3211yescharacteristic
345C23×C3—21no—
346C23×C3—32no—
347C23×C3—61no—
348C23×C3—62no—
349C23×C3—61no—
350C23×C3—62no—
351C23×C3C23×D311yescharacteristic
352C23×C3C23×D311yescharacteristic
353C22×D3—21no—
354C22×D3—21no—
355C22×D3—22no—
356C22×D3—22no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—64no—
360C22×D3—62no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—62no—
371C22×D3—62no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—122no—
378C22×D3D3×D412yes—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—32no—
389C2×C3×C4—32no—
390C2×C3×C4—32no—
391C2×C3×C4—32no—
392C2×C3×C4—34no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—42no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—62no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4C2×D1212yes—
406C2×C3×C4D3×D412yes—
407#67—616no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—21no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—62no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—68no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—62no—
427C2×Dic3—62no—
428C2×Dic3—121no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—122no—
432C2×Dic3C2×D1212yes—
433C2×Dic3C2×D1212yes—
434C2×Dic3#23514yes—
435C2×Dic3D3×D412yes—
436C2×Dic3#23912yes—
437D12—68no—
438D12—68no—
439D12—616no—
440D12—128no—
441C4×D3—68no—
442C4×D3—128no—
443C4×D3—128no—
444C2×C32C2×#12111yescharacteristic
445C2×C32#52511yescharacteristic
446C2×C32#52512yes—
447C2×C32#52912yes—
448C2×C32#53211yescharacteristic
449C3⋊D3—44no—
450C3×D3—42no—
451C24—31no—
452C24—92no—
453C2×D4—184no—
454C2×D4—184no—
455C2×D4—184no—
456C2×D4—184no—
457C2×D4—182no—
458C22×C4—31no—
459C22×C4—32no—
460C22×C4—31no—
461C22×C4—31no—
462C22×C4—32no—
463C22×C4—94no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—184no—
467C22×C4—184no—
468C22×C4—184no—
469C22×C4—182no—
470C22×C4—182no—
471C22×C4C2×D3212yes—
472C22×C4C2×D3211yescharacteristic
473C4⋊C4—64no—
474C4⋊C4—62no—
475C4⋊C4—182no—
476C4⋊C4—184no—
477C4⋊C4—182no—
478C22⋊C4—64no—
479C22⋊C4—62no—
480C22⋊C4—184no—
481C22⋊C4—184no—
482C22⋊C4—184no—
483C22⋊C4—184no—
484C22⋊C4—182no—
485C42—34no—
486C42—64no—
487C42—182no—
488C22×C3—21no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—22no—
492C22×C3—21no—
493C22×C3—62no—
494C22×C3—64no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—122no—
498C22×C3C22×D1211yescharacteristic
499C22×C3C2×#23512yes—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C2×#23911yescharacteristic
504C22×C3D3×#4112yes—
505C22×C3D3×#4112yes—
506C22×C3D3×#4112yes—
507C22×C3D3×#4111yescharacteristic
508C2×D3—24no—
509C2×D3—22no—
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—42no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—124no—
520C2×D3—124no—
521C2×D3—124no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—122no—
525C2×D3—122no—
526C2×D3—122no—
527C2×D3—122no—
528C2×D3—122no—
529C2×D3—122no—
530C2×D3—242no—
531C2×D3—242no—
532C2×D3—242no—
533C2×D3—242no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—34no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—42no—
540C3×C4—64no—
541C3×C4—62no—
542C3×C4—82no—
543C3×C4—121no—
544C3×C4—122no—
545Dic3—22no—
546Dic3—24no—
547Dic3—41no—
548Dic3—42no—
549Dic3—62no—
550Dic3—62no—
551Dic3—122no—
552Dic3—121no—
553Dic3—121no—
554Dic3—241no—
555Dic3#89514yes—
556C32#239211yescharacteristic, complemented, Sylow
557C23—32no—
558C23—61no—
559C23—62no—
560C23—62no—
561C23—61no—
562C23—94no—
563C23—182no—
564C23—182no—
565C23—182no—
566C23—182no—
567C23—182no—
568C23—182no—
569C23C22×D3211yescharacteristic
570D4—188no—
571D4—1816no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—34no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—61no—
585C2×C4—62no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—92no—
590C2×C4—188no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—182no—
595C2×C4—368no—
596C2×C4D3×D1212yes—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—22no—
600C2×C3—21no—
601C2×C3—22no—
602C2×C3—122no—
603C2×C3#547711yescharacteristic
604C2×C3C2×#89511yescharacteristic
605C2×C3#552411yescharacteristic
606C2×C3#554712yes—
607C2×C3#558012yes—
608C2×C3D3×#12111yescharacteristic
609C2×C3#565611yescharacteristic
610C2×C3#565612yes—
611C2×C3#566811yescharacteristic
612C2×C3#570612yes—
613D3—42no—
614D3—124no—
615D3—124no—
616D3—244no—
617C22—62no—
618C22—64no—
619C22—121no—
620C22—122no—
621C22—121no—
622C22—184no—
623C22—184no—
624C22—184no—
625C22—362no—
626C22—362no—
627C22—362no—
628C22—362no—
629C22C2×D3×D1211yescharacteristic
630C22D3×#23512yes—
631C22D32×D411yescharacteristic
632C22#6431212yes—
633C22D3×#23911yescharacteristic
634C4—22no—
635C4—34no—
636C4—42no—
637C4—62no—
638C4—64no—
639C4—122no—
640C4—121no—
641C4—182no—
642C4—361no—
643C3—21no—
644C3#7377611yescharacteristic, complemented
645C3#7745711yescharacteristic, complemented
646C2—122no—
647C2—364no—
648C2#1059396911yescharacteristic
649C2#1059407911yescharacteristic
650C2#1059426612yes—
651C2#1059442312yes—
652C2D3×#89511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radical#10591395C2
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×#63880C2semidirect
3. C2×#63877C2semidirect
4. #10592371C2semidirect
5. C3×#4674C2semidirect
6. C3×#4649C2semidirect
8. #10591358C2semidirect
9. #10591347C2semidirect
10. #10591291C2semidirect
11. #10591233C2semidirect
55. #4674D3semidirect
62. #4649D3semidirect
84. C2×D3×Dic3D4semidirect
93. C3×C4×Dic3D4semidirect
292. C4×Dic3D12semidirect
556. C32#2392semidirect
644. C3#73776semidirect
645. C3#77457semidirect

Maximal subgroups

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

subgroupindex
C2×#638942
C2×#638802
C2×#638772
#105923712
C3×#46742
C3×#46492
#105913952
#105913582
#105913472
#105912912
#105912332
#774573
#737763