Finite Group Databasebeta

← #11824571

Subgroups — #11824571

Order 1152.

1523 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63908C211yesmaximal, characteristic, complemented
2C2×#63908C212yesmaximal, complemented
3C2×#63879C211yesmaximal, characteristic, complemented
4#10592360C211yesmaximal, characteristic, complemented
5C3×#4671C211yesmaximal, characteristic, complemented
6C3×D3×#95C211yesmaximal, characteristic, complemented
7#10591381C212yesmaximal, complemented
8#10591376C212yesmaximal, complemented
9#10591316C212yesmaximal, complemented
10#10591315C211yesmaximal, characteristic, complemented
11#10591302C211yesmaximal, characteristic, complemented
12#76759—31nomaximal
13#73378—31nomaximal
14C22×C3×D12C2212yes—
15C22×C3×D12C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×#625C2212yes—
19C22×#625C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C2×#3750C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×(C2×D3)⋊Dic3C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31C2×Dic32C2211yescharacteristic
32#63908—24no—
33#63908—28no—
34#63879—24no—
35C32×#95C2211yescharacteristic
36#63658C2212yes—
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2212yes—
39#63579C2212yes—
40C2×#938—32no—
41C2×#938—31no—
42C2×#930—32no—
43C2×#930—31no—
44C2×C4×#67—31no—
45C2×#67⋊C4—31no—
46C3×#392—31no—
47C2×C3×#95—31no—
48#5222—31no—
49#5220—32no—
50#5213—32no—
51#4956—32no—
52#4953—31no—
53#4951—32no—
54#4674—31no—
55#4672—31no—
56#4671D311yescharacteristic, complemented
57#4670—32no—
58#4665—32no—
59D3×#95D311yescharacteristic, complemented
60#4661—31no—
61#4661—31no—
62#4661—61no—
63C23×C3×D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2312yes—
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C2×C3×D12—24no—
75C2×C3×D12—22no—
76C2×C3×D12—24no—
77C2×C3×D12—42no—
78C2×C3×D12—42no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3—24no—
81C2×C3×C4×D3—42no—
82C2×C3×C4×D3—42no—
83C2×C3×C4×D3D414yescomplemented
84C2×#625—22no—
85C2×#625—22no—
86C2×#625—24no—
87C2×#625—24no—
88C2×#625—24no—
89C2×#625D414yescomplemented
90C2×D3×Dic3—22no—
91C2×D3×Dic3—42no—
92C4⋊(C3⋊Dic3)—22no—
93C4⋊(C3⋊Dic3)—24no—
94#3750—22no—
95C3×(C2×D3)⋊C4—22no—
96C3×(C2×D3)⋊C4—24no—
97(C2×D3)⋊Dic3—22no—
98(C2×D3)⋊Dic3—24no—
99(C2×D3)⋊Dic3—24no—
100(C2×D3)⋊Dic3—24no—
101(C2×D3)⋊Dic3—42no—
102Dic32—22no—
103#2543—91noSylow
104C22×C3×D4—32no—
105C22×C3×D4—31no—
106C23×C3×C4—31no—
107C23×C3×C4—32no—
108C22×#67—31no—
109C22×#67—31no—
110C22×#67—32no—
111C22×#67—32no—
112C23×Dic3—31no—
113C22×D12C2×D312yes—
114C22×D12C2×D311yescharacteristic
115C22×C4×D3—31no—
116C22×C4×D3C2×D312yes—
117C22×C4×D3C2×D311yescharacteristic
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—31no—
120C2×#217—32no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—31no—
124C2×#217—32no—
125#938—68no—
126#938—64no—
127#930—68no—
128#930—64no—
129C4×#67—64no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×(C2×D3)⋊C4C2×D311yescharacteristic
137C2×C4⋊Dic3—32no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—32no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—62no—
142C2×C4⋊Dic3—61no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—61no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148#67⋊C4—64no—
149C3×#95—21no—
150C3×#95—32no—
151C3×#95—31no—
152C3×#95C2×D311yescharacteristic
153C3×#95C2×D311yescharacteristic
154C3⋊#95—32no—
155C3⋊#95—32no—
156C3⋊#95—32no—
157C3⋊#95—32no—
158C3⋊#95—62no—
159C3⋊#95C2×D312yes—
160C3⋊#95C2×D311yescharacteristic
161C23×C32C2411yescharacteristic
162C22×C3×D3—22no—
163C22×C3×D3—22no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—22no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—22no—
171C22×C3×D3—22no—
172C22×C3×D3—22no—
173C22×C3×D3—22no—
174C22×C3×D3—22no—
175C22×C3×D3C2×D412yes—
176C22×C3×D3C2×D412yes—
177C22×C3×D3C2×D412yes—
178C22×C3×D3#4112yes—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183C2×C32×C4#4114yes—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3C2×D412yes—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C2×D412yes—
199C3×D12—48no—
200C3×D12—44no—
201C3×C4×D3—44no—
202C3×C4×D3—48no—
203#625—28no—
204#625—48no—
205D3×Dic3—44no—
206C2×#121—91no—
207C2×#121—92no—
208C2×C4×D4—91no—
209#398—91no—
210#397—91no—
211#394—91no—
212#392—31no—
213#388—92no—
214#386—92no—
215#386—92no—
216C2×#95—31no—
217C24×C3—31no—
218C24×C3—31no—
219C24×C3—32no—
220C23×D3C22×D312yes—
221C23×D3C22×D311yescharacteristic
222C23×D3C22×D311yescharacteristic
223C2×C3×D4—64no—
224C2×C3×D4—62no—
225C2×C3×D4—64no—
226C2×C3×D4—122no—
227C2×C3×D4—122no—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—31no—
231C22×C3×C4—34no—
232C22×C3×C4—31no—
233C22×C3×C4—32no—
234C22×C3×C4—64no—
235C22×C3×C4—64no—
236C22×C3×C4—122no—
237C22×C3×C4—122no—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D312yes—
242C2×#67—34no—
243C2×#67—34no—
244C2×#67—62no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—62no—
248C2×#67—64no—
249C2×#67—64no—
250C2×#67—64no—
251C2×#67—64no—
252C2×#67—64no—
253C2×#67—64no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—32no—
259C22×Dic3—32no—
260C22×Dic3—61no—
261C22×Dic3—61no—
262C22×Dic3—62no—
263C22×Dic3—62no—
264C22×Dic3—122no—
265C22×Dic3C22×D311yescharacteristic
266C22×Dic3C22×D312yes—
267C22×Dic3C22×D311yescharacteristic
268C2×D12—24no—
269C2×D12—22no—
270C2×D12—24no—
271C2×D12—42no—
272C2×D12—42no—
273C2×C4×D3—24no—
274C2×C4×D3—24no—
275C2×C4×D3—42no—
276C2×C4×D3—42no—
277C2×C4×D3—62no—
278C2×C4×D3—122no—
279C2×C4×D3D1214yescomplemented
280C3×C22⋊C4—62no—
281C3×C22⋊C4—64no—
282#217—64no—
283#217—62no—
284#217—64no—
285#217—64no—
286#217—122no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—64no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—122no—
294C4⋊Dic3—64no—
295C4⋊Dic3—64no—
296C4⋊Dic3—62no—
297C4⋊Dic3—62no—
298C4⋊Dic3—124no—
299C4⋊Dic3—122no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302Dic3⋊C4—122no—
303C4×Dic3—62no—
304C4×Dic3—62no—
305C22×C32C22×D411yescharacteristic
306C22×C32C22×D411yescharacteristic
307C22×C32C2×#4112yes—
308C22×C32C2×#4111yescharacteristic
309C22×C32H(5,𝔽2)12yes—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—24no—
313C2×C3×D3—24no—
314C2×C3×D3—22no—
315C2×C3×D3—24no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C2×C3×D3—42no—
319C2×C3×D3—42no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—42no—
325C2×C3×D3—42no—
326C2×C3×D3#12114yes—
327C32×C4—22no—
328C32×C4—24no—
329C3⋊Dic3—22no—
330C3⋊Dic3—42no—
331C3⋊Dic3—41no—
332C3×Dic3—22no—
333C3×Dic3—41no—
334C3×Dic3—42no—
335C22×D4—32no—
336C22×D4—31no—
337C22×D4—91no—
338C22×D4—92no—
339C23×C4—31no—
340C23×C4—32no—
341C23×C4—91no—
342#121—184no—
343#121—188no—
344C4×D4—184no—
345C2×C4⋊C4—91no—
346C2×C4⋊C4—92no—
347C2×C4⋊C4—91no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—92no—
352C2×C22⋊C4—92no—
353C2×C22⋊C4—92no—
354C2×C22⋊C4—92no—
355C2×C42—91no—
356#95—32no—
357#95—31no—
358#95—92no—
359#95—92no—
360#95D3211yescharacteristic
361C23×C3—21no—
362C23×C3—32no—
363C23×C3—32no—
364C23×C3—32no—
365C23×C3—32no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—61no—
369C23×C3—62no—
370C23×C3—62no—
371C23×C3—61no—
372C23×C3—62no—
373C23×C3—62no—
374C23×C3—62no—
375C23×C3—62no—
376C23×C3—62no—
377C23×C3—62no—
378C23×C3—62no—
379C23×C3C23×D311yescharacteristic
380C23×C3C23×D311yescharacteristic
381C22×D3—22no—
382C22×D3—22no—
383C22×D3—21no—
384C22×D3—22no—
385C22×D3—22no—
386C22×D3—21no—
387C22×D3—22no—
388C22×D3—22no—
389C22×D3—22no—
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—22no—
394C22×D3C2×D1212yes—
395C22×D3D3×D412yes—
396C22×D3D3×D412yes—
397C22×D3#23912yes—
398C3×D4—128no—
399C3×D4—124no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—24no—
407C2×C3×C4—22no—
408C2×C3×C4—32no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—62no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—124no—
419C2×C3×C4—128no—
420C2×C3×C4C2×D1212yes—
421C2×C3×C4#23514yes—
422C2×C3×C4D3×D412yes—
423C2×C3×C4#23714yes—
424#67—68no—
425#67—68no—
426#67—128no—
427#67—128no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—32no—
435C2×Dic3—32no—
436C2×Dic3—62no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—62no—
443C2×Dic3—61no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—121no—
452C2×Dic3—121no—
453C2×Dic3—121no—
454C2×Dic3—122no—
455C2×Dic3—122no—
456C2×Dic3—122no—
457C2×Dic3—122no—
458C2×Dic3—124no—
459C2×Dic3C2×D1212yes—
460D12—48no—
461D12—44no—
462C4×D3—44no—
463C4×D3—48no—
464C4×D3—124no—
465C2×C32C2×#12111yescharacteristic
466C2×C32#53211yescharacteristic
467C2×C32#53411yescharacteristic
468C2×C32#54612yes—
469C2×C32#55312yes—
470C3×D3—24no—
471C3×D3—42no—
472C3×D3—82no—
473C24—31no—
474C24—31no—
475C24—32no—
476C2×D4—64no—
477C2×D4—64no—
478C2×D4—62no—
479C2×D4—94no—
480C2×D4—122no—
481C2×D4—122no—
482C2×D4—182no—
483C2×D4—182no—
484C2×D4—184no—
485C2×D4—184no—
486C2×D4—184no—
487C22×C4—31no—
488C22×C4—34no—
489C22×C4—32no—
490C22×C4—31no—
491C22×C4—64no—
492C22×C4—64no—
493C22×C4—91no—
494C22×C4—91no—
495C22×C4—92no—
496C22×C4—122no—
497C22×C4—122no—
498C22×C4—182no—
499C22×C4—362no—
500C22×C4C2×D3212yes—
501C22×C4C2×D3211yescharacteristic
502C4⋊C4—184no—
503C4⋊C4—182no—
504C4⋊C4—182no—
505C22⋊C4—64no—
506C22⋊C4—62no—
507C22⋊C4—184no—
508C22⋊C4—184no—
509C22⋊C4—182no—
510C22⋊C4—184no—
511C22⋊C4—362no—
512C42—182no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—22no—
517C22×C3—21no—
518C22×C3—34no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—64no—
522C22×C3—64no—
523C22×C3—64no—
524C22×C3—62no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—122no—
532C22×C3—122no—
533C22×C3—122no—
534C22×C3—122no—
535C22×C3C22×D1211yescharacteristic
536C22×C3C2×#23512yes—
537C22×C3C2×D3×D411yescharacteristic
538C22×C3C2×D3×D411yescharacteristic
539C22×C3C2×D3×D411yescharacteristic
540C22×C3C2×#23712yes—
541C22×C3#100412yes—
542C22×C3#100412yes—
543C22×C3C2×#23911yescharacteristic
544C22×C3D3×#4111yescharacteristic
545C2×D3—22no—
546C2×D3—24no—
547C2×D3—22no—
548C2×D3—24no—
549C2×D3—24no—
550C2×D3—22no—
551C2×D3—41no—
552C2×D3—41no—
553C2×D3—42no—
554C2×D3—42no—
555C2×D3—42no—
556C2×D3—42no—
557C2×D3—42no—
558C2×D3—42no—
559C2×D3—42no—
560C2×D3—42no—
561C2×D3#89514yes—
562C3×C4—24no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—24no—
566C3×C4—44no—
567C3×C4—42no—
568C3×C4—62no—
569C3×C4—121no—
570C3×C4—122no—
571Dic3—22no—
572Dic3—41no—
573Dic3—42no—
574Dic3—62no—
575Dic3—62no—
576Dic3—122no—
577Dic3—121no—
578Dic3—122no—
579Dic3—121no—
580Dic3—122no—
581Dic3—242no—
582Dic3—241no—
583C32#254311yescharacteristic, complemented, Sylow
584C23—32no—
585C23—32no—
586C23—32no—
587C23—32no—
588C23—62no—
589C23—62no—
590C23—62no—
591C23—61no—
592C23—62no—
593C23—61no—
594C23—62no—
595C23—62no—
596C23—62no—
597C23—62no—
598C23—62no—
599C23—62no—
600C23—62no—
601C23C22×D3211yescharacteristic
602D4—128no—
603D4—124no—
604D4—188no—
605D4—368no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—32no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—61no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—92no—
617C2×C4—124no—
618C2×C4—128no—
619C2×C4—181no—
620C2×C4—181no—
621C2×C4—181no—
622C2×C4—182no—
623C2×C4—182no—
624C2×C4—182no—
625C2×C4—182no—
626C2×C4—364no—
627C2×C4#379514yes—
628C2×C4D3×D1212yes—
629C2×C3—22no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—22no—
633C2×C3—21no—
634C2×C3—64no—
635C2×C3—122no—
636C2×C3—242no—
637C2×C3#547711yescharacteristic
638C2×C3#549012yes—
639C2×C3#549311yescharacteristic
640C2×C3C2×#89511yescharacteristic
641C2×C3#551412yes—
642C2×C3#558911yescharacteristic
643C2×C3#559112yes—
644C2×C3D3×#12111yescharacteristic
645C2×C3#561412yes—
646C2×C3#571611yescharacteristic
647D3—24no—
648D3—42no—
649D3—82no—
650C22—34no—
651C22—64no—
652C22—62no—
653C22—64no—
654C22—62no—
655C22—62no—
656C22—64no—
657C22—122no—
658C22—121no—
659C22—121no—
660C22—122no—
661C22—122no—
662C22—122no—
663C22—122no—
664C22—122no—
665C22—122no—
666C22—122no—
667C22C2×#379512yes—
668C22C2×D3×D1211yescharacteristic
669C22D32×D411yescharacteristic
670C22#6431312yes—
671C22D3×#23911yescharacteristic
672C4—24no—
673C4—22no—
674C4—62no—
675C4—121no—
676C4—122no—
677C4—182no—
678C4—362no—
679C4—361no—
680C3—21no—
681C3#7337811yescharacteristic, complemented
682C3#7675911yescharacteristic, complemented
683C2—64no—
684C2—122no—
685C2—242no—
686C2#1059389711yescharacteristic
687C2#1059418412yes—
688C2#1059429011yescharacteristic
689C2#1059456012yes—
690C2D3×#89511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
hypercenter#95D32
hypocenterC32#2543
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63908C2semidirect
2. C2×#63908C2semidirect
3. C2×#63879C2semidirect
4. #10592360C2semidirect
5. C3×#4671C2semidirect
6. C3×D3×#95C2semidirect
7. #10591381C2semidirect
8. #10591376C2semidirect
9. #10591316C2semidirect
10. #10591315C2semidirect
11. #10591302C2semidirect
56. #4671D3semidirect
59. D3×#95D3semidirect
83. C2×C3×C4×D3D4semidirect
89. C2×#625D4semidirect
279. C2×C4×D3D12semidirect
583. C32#2543semidirect
681. C3#73378semidirect
682. C3#76759semidirect

Maximal subgroups

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

subgroupindex
C2×#639082
C2×#638792
#105923602
C3×#46712
C3×D3×#952
#105913812
#105913762
#105913162
#105913152
#105913022
#767593
#733783