Finite Group Databasebeta

← #11803619

Subgroups — #11803619

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic, complemented
2C2×#63912C211yesmaximal, characteristic
3C2×#63902C211yesmaximal, characteristic, complemented
4C3×#4990C212yesmaximal, complemented
5#10591385C211yesmaximal, characteristic, complemented
6#10591383C212yesmaximal, complemented
7#10591379C212yesmaximal, complemented
8#10591364C212yesmaximal, complemented
9#10591355C211yesmaximal, characteristic, complemented
10C4×#3724C211yesmaximal, characteristic, complemented
11#10591328C211yesmaximal, characteristic, complemented
12#75461—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#626C2212yes—
15C22×#625C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64101—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×C4×Dic3C2212yes—
28C2×#3724C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2212yes—
32C2×#3722C2212yes—
33C2×(C2×D3)⋊Dic3C2212yes—
34#63912C418yescomplemented
35#63902—24no—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#892—32no—
40C2×#892—61no—
41C2×#884—32no—
42C2×#67⋊C4—32no—
43C3×#388—32no—
44#4990D312yescomplemented
45#4958—32no—
46#4957—32no—
47#4957—32no—
48#4950—32no—
49#4939—32no—
50C4×Dic3⋊C4—32no—
51#4668—32no—
52#4667—32no—
53#4665—32no—
54#4647—32no—
55C23×C3⋊D3C2311yescharacteristic
56C23×C3×D3C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C22×C3⋊Dic3C2311yescharacteristic
63C2×C4×C3⋊D3—22no—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3C2×C414yescomplemented
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×#626—42no—
70C2×#626—42no—
71C2×#626C2×C418yescomplemented
72C2×#625—22no—
73C2×#625—22no—
74C2×#625C2×C414yes—
75C2×D3×Dic3—24no—
76C2×D3×Dic3—42no—
77C2×D3×Dic3—42no—
78C32×C4⋊C4—22no—
79#3752—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3D414yescomplemented
84C3×(C2×D3)⋊C4—24no—
85C3×(C2×D3)⋊C4—42no—
86C3×(C2×D3)⋊C4C2×C418yescomplemented
87C3×C4×Dic3—42no—
88#3724—22no—
89#3724—22no—
90#3724C2×C414yescomplemented
91Dic3⋊Dic3—42no—
92#3722—42no—
93(C2×D3)⋊Dic3—42no—
94#2324—91noSylow
95C22×#67—32no—
96C22×#67—32no—
97C23×Dic3—32no—
98C22×D12—32no—
99C22×C4×D3—32no—
100C22×C4×D3—32no—
101C22×C4×D3—61no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4C2×D312yes—
104C2×C3×C22⋊C4—32no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C22⋊C4—32no—
107C2×C3×C42—32no—
108C2×#217—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×(C2×D3)⋊C4C2×D312yes—
118C2×(C2×D3)⋊C4C2×D312yes—
119C2×C4⋊Dic3—32no—
120C2×C4⋊Dic3—32no—
121C2×C4⋊Dic3—61no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×C4×Dic3—32no—
127C2×C4×Dic3—32no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3—61no—
130C2×C4×Dic3C2×D312yes—
131#892—68no—
132#892—68no—
133#884—316no—
134#67⋊C4—68no—
135C3×#95—32no—
136C3×#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D312yes—
140C3⋊#95C2×D312yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3—21no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—21no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3—21no—
147C22×C3⋊D3—21no—
148C22×C3⋊D3C22×C412yes—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3C22×C414yes—
156C2×C32×C4—21no—
157C2×C32×C4—21no—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C2×D412yes—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173C2×C3⋊Dic3#4112yes—
174C4×C3⋊D3—28no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3C22×C414yes—
184#626—48no—
185#625—28no—
186D3×Dic3—48no—
187C2×#121—91no—
188C2×C4×D4—91no—
189C2×#117—91no—
190#390—92no—
191#390—91no—
192#389—91no—
193#388—32no—
194#386—92no—
195#385—92no—
196#380—91no—
197C4×C4⋊C4—91no—
198C24×C3—32no—
199C23×D3—32no—
200C23×D3—61no—
201C23×D3C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4C22×D312yes—
209C22×C3×C4C22×D312yes—
210C22×C3×C4C22×D312yes—
211C2×#67—38no—
212C2×#67—38no—
213C2×#67—64no—
214C2×#67—64no—
215C2×#67—122no—
216C2×#67—122no—
217C22×Dic3—32no—
218C22×Dic3—32no—
219C22×Dic3—32no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—64no—
224C22×Dic3—122no—
225C22×Dic3—122no—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C22×Dic3C22×D312yes—
229C2×D12—38no—
230C2×D12—122no—
231C2×D12—122no—
232C2×C4×D3—38no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—122no—
240C2×C4×D3—122no—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—24no—
243C3×C22⋊C4—38no—
244C3×C22⋊C4—64no—
245C3×C22⋊C4—122no—
246C3×C42—122no—
247#217—122no—
248(C2×D3)⋊C4—24no—
249(C2×D3)⋊C4—42no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—122no—
255(C2×D3)⋊C4—122no—
256(C2×D3)⋊C4—122no—
257(C2×D3)⋊C4C4×D318yescomplemented
258C4⋊Dic3—64no—
259C4⋊Dic3—64no—
260C4⋊Dic3—122no—
261Dic3⋊C4—38no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—122no—
265C4×Dic3—38no—
266C4×Dic3—42no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C22×C32C23×C411yescharacteristic
271C22×C32C22×D411yescharacteristic
272C22×C32C2×#4111yescharacteristic
273C22×C32H(5,𝔽2)11yescharacteristic
274C22×C32H(5,𝔽2)11yescharacteristic
275C22×C32H(5,𝔽2)11yescharacteristic
276C22×C322−1+411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3×D3—24no—
285C2×C3×D3—24no—
286C2×C3×D3—24no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C32×C4—22no—
292C32×C4—22no—
293C32×C4—41no—
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3⋊Dic3C4×D414yes—
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C22×D4—92no—
301C22×D4—91no—
302C23×C4—92no—
303C23×C4—91no—
304#121—98no—
305C4×D4—184no—
306#117—184no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4—91no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—92no—
312C2×C4⋊C4D3211yescharacteristic
313C2×C22⋊C4—32no—
314C2×C22⋊C4—32no—
315C2×C22⋊C4—32no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—92no—
319C2×C22⋊C4—92no—
320C2×C42—32no—
321C2×C42—91no—
322C2×C42—91no—
323#95—32no—
324#95—32no—
325#95—92no—
326C23×C3—21no—
327C23×C3—34no—
328C23×C3—62no—
329C23×C3—62no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3C23×D312yes—
335C22×D3—22no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—34no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C22×D3—121no—
355C22×D3C2×C4×D314yes—
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—22no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—34no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—41no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
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×D314yes—
382C2×C3×C4D3×D414yes—
383#67—616no—
384#67—128no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—34no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—62no—
402C2×Dic3—62no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—121no—
408C2×Dic3—121no—
409C2×Dic3—121no—
410C2×Dic3—121no—
411C2×Dic3—128no—
412C2×Dic3C2×C4×D314yes—
413D12—128no—
414C4×D3—616no—
415C4×D3—616no—
416C4×D3—128no—
417C2×C32C2×C4×D411yescharacteristic
418C2×C32#51811yescharacteristic
419C2×C32#52011yescharacteristic
420C2×C32#53511yescharacteristic
421C2×C32#53711yescharacteristic
422C2×C32#54011yescharacteristic
423C2×C32#54211yescharacteristic
424C3⋊D3—42no—
425C3×D3—44no—
426C24—32no—
427C24—91no—
428C2×D4—98no—
429C2×D4—94no—
430C2×D4—182no—
431C2×D4—182no—
432C2×D4—362no—
433C2×D4—362no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—94no—
440C22×C4—91no—
441C22×C4—182no—
442C22×C4—182no—
443C22×C4—184no—
444C22×C4—362no—
445C22×C4—362no—
446C22×C4C2×D3211yescharacteristic
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C4⋊C4—22no—
450C4⋊C4—94no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C4⋊C4—362no—
455C22⋊C4—38no—
456C22⋊C4—64no—
457C22⋊C4—122no—
458C22⋊C4—182no—
459C22⋊C4—182no—
460C22⋊C4—362no—
461C22⋊C4—362no—
462C42—94no—
463C42—122no—
464C42—182no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—64no—
473C22×C3—64no—
474C22×C3—64no—
475C22×C3—122no—
476C22×C3—122no—
477C22×C3—122no—
478C22×C3—122no—
479C22×C3C22×C4×D312yes—
480C22×C3C2×D3×D412yes—
481C22×C3#100412yes—
482C22×C3D3×#4112yes—
483C22×C3#100912yes—
484C22×C3#100912yes—
485C22×C3#101012yes—
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—42no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—64no—
494C2×D3—64no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—42no—
511C3×C4—42no—
512C3×C4—42no—
513C3×C4—64no—
514C3×C4—122no—
515C3×C4—122no—
516Dic3—24no—
517Dic3—38no—
518Dic3—42no—
519Dic3—42no—
520Dic3—64no—
521Dic3—64no—
522Dic3—122no—
523Dic3—122no—
524Dic3—122no—
525C32#232411yescharacteristic, complemented, Sylow
526C23—34no—
527C23—62no—
528C23—62no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—62no—
533C23—92no—
534C23—181no—
535C23—181no—
536C23—181no—
537C23—181no—
538C23—181no—
539C23—181no—
540C23C22×D3211yescharacteristic
541D4—188no—
542D4—368no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—34no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—188no—
564C2×C4—181no—
565C2×C4—181no—
566C2×C4—181no—
567C2×C4—181no—
568C2×C4—181no—
569C2×C4—368no—
570C2×C4C4×D3212yes—
571C2×C4#381112yes—
572C2×C3—21no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—124no—
580C2×C3#552312yes—
581C2×C3C4×D3×D412yes—
582C2×C3#554512yes—
583C2×C3#559712yes—
584C2×C3#566312yes—
585C2×C3#567412yes—
586C2×C3#571012yes—
587D3—44no—
588D3—124no—
589D3—124no—
590C22—64no—
591C22—64no—
592C22—64no—
593C22—122no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—182no—
598C22—182no—
599C22—182no—
600C22—361no—
601C22—361no—
602C22—361no—
603C22—361no—
604C22C2×C4×D3211yescharacteristic
605C22#6430611yescharacteristic
606C22#6430911yescharacteristic
607C22#6431311yescharacteristic
608C22#6432011yescharacteristic
609C22#6432011yescharacteristic
610C22C2×#381111yescharacteristic
611C4—22no—
612C4—22no—
613C4—41no—
614C4—64no—
615C4—94no—
616C4—122no—
617C4—122no—
618C4—182no—
619C4—361no—
620C3—21no—
621C3#7546112yescomplemented
622C2—124no—
623C2—362no—
624C2#1059451111yescharacteristic
625C2#1059456811yescharacteristic
626C2#1059457111yescharacteristic
627C2#1059460611yescharacteristic
628C2C4×#381111yescharacteristic
629C2#1059516611yescharacteristic
630C2#1059543311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64101C2semidirect
3. C2×#63902C2semidirect
4. C3×#4990C2semidirect
5. #10591385C2semidirect
6. #10591383C2semidirect
7. #10591379C2semidirect
8. #10591364C2semidirect
9. #10591355C2semidirect
10. C4×#3724C2semidirect
11. #10591328C2semidirect
34. #63912C4semidirect
44. #4990D3semidirect
65. C2×C4×C3⋊D3C2×C4semidirect
71. C2×#626C2×C4semidirect
83. C4×C3⋊Dic3D4semidirect
86. C3×(C2×D3)⋊C4C2×C4semidirect
90. #3724C2×C4semidirect
257. (C2×D3)⋊C4C4×D3semidirect
525. C32#2324semidirect
621. C3#75461semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#639122
C2×#639022
C3×#49902
#105913852
#105913832
#105913792
#105913642
#105913552
C4×#37242
#105913282
#754613