Finite Group Databasebeta

← #11788138

Subgroups — #11788138

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63916C211yesmaximal, characteristic
2C22×#3712C211yesmaximal, characteristic, complemented
3#10592686C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70203—31nomaximal
9#68885—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C22×#626—21no—
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20#63916—22no—
21#63916C414yescomplemented
22C2×#3712—22no—
23C2×#3712—22no—
24C2×#3712—22no—
25#63658—21no—
26C3×#809—22no—
27#63563—22no—
28C2×#938—31no—
29C22×ΓL(1,𝔽25)—31no—
30C22×ΓL(1,𝔽25)—31no—
31C2×#895—31no—
32C2×C3×#102—31no—
33C2×#832—31no—
34C2×#821—31no—
35#4987—31no—
36#4987—31no—
37#4987—61no—
38C2×#809D311yescharacteristic, complemented
39C3×#340—31no—
40#4551—31no—
41#4529—31no—
42#4529D311yescharacteristic, complemented
43C23×C3⋊D3D411yescharacteristic
44C23×C3×D3—21no—
45C22×C32×C4—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3⋊Dic3D411yescharacteristic
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3C2×C412yes—
54C2×C4×C3⋊D3D412yes—
55C22×C3×Dic3—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C2×#626—24no—
63C2×#626—42no—
64C2×#626—42no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67#3752—42no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3C2×C412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77C2×C3×C3⋊C8D412yescomplemented
78(C2×D3)⋊Dic3—24no—
79#3712—28no—
80#1895—91noSylow
81C22×C3×D4—31no—
82C22×#67—61no—
83C22×D12—61no—
84C22×D12C2×D311yescharacteristic
85C22×C4×D3—31no—
86C22×C4×D3—31no—
87C22×C4×D3—61no—
88C22×C3×C8—31no—
89C22×C3×C8—31no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×#217—61no—
95#938—34no—
96#938—62no—
97C2×(C2×D3)⋊C4—61no—
98C2×(C2×D3)⋊C4—61no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—62no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C22×C3⋊C8C2×D311yescharacteristic
106C22×C3⋊C8C2×D311yescharacteristic
107C2×ΓL(1,𝔽25)—62no—
108C2×ΓL(1,𝔽25)—62no—
109C2×ΓL(1,𝔽25)—62no—
110C2×ΓL(1,𝔽25)—62no—
111C2×ΓL(1,𝔽25)—62no—
112C2×ΓL(1,𝔽25)—62no—
113#895—34no—
114#895—62no—
115C3×#102—62no—
116#832—62no—
117C3⋊#95—61no—
118C3⋊#95—61no—
119C3⋊#95—62no—
120#821—62no—
121#809—22no—
122C23×C32C2×D411yescharacteristic
123C22×C3⋊D3—21no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—21no—
126C22×C3⋊D3—21no—
127C22×C3⋊D3—21no—
128C22×C3⋊D3—21no—
129C22×C3⋊D3C22⋊C412yes—
130C22×C3×D3—22no—
131C22×C3×D3—41no—
132C22×C3×D3—41no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C22×C3×D3—41no—
136C22×C3×D3—41no—
137C2×C32×C4—41no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C2×C32×C4#4111yescharacteristic
146C2×C3⋊Dic3—21no—
147C2×C3⋊Dic3—21no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3—41no—
151C2×C3⋊Dic3C22⋊C412yes—
152C4×C3⋊D3—22no—
153C4×C3⋊D3—22no—
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—41no—
158C2×C3×Dic3—41no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—41no—
162C3×D12—41no—
163#626—48no—
164C3×C3⋊C8—22no—
165C3×C3⋊C8—22no—
166C22×M16—91no—
167C2×#121—91no—
168C2×#102—31no—
169C2×#102—91no—
170#380—91no—
171#340—31no—
172#340—91no—
173C24×C3—61no—
174C23×D3—21no—
175C23×D3—31no—
176C23×D3—31no—
177C23×D3—61no—
178C2×C3×D4—32no—
179C2×C3×D4—61no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C22×C3×C4—22no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—64no—
192C2×#67—122no—
193C2×#67—122no—
194C22×Dic3—21no—
195C22×Dic3—31no—
196C22×Dic3—31no—
197C22×Dic3—61no—
198C22×Dic3—62no—
199C22×Dic3—61no—
200C22×Dic3—61no—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12—64no—
207C2×D12—122no—
208C2×D12—122no—
209C2×D12C4×D312yes—
210C2×C4×D3—32no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—32no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—61no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—121no—
225C2×C4×D3—121no—
226C2×C4×D3—121no—
227C2×C4×D3—121no—
228C2×C3×C8—32no—
229C2×C3×C8—32no—
230C2×C3×C8—61no—
231C2×C3×C8—61no—
232C2×C3×C8—61no—
233C2×C3×C8—61no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—61no—
242#217—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—124no—
245(C2×D3)⋊C4—122no—
246(C2×D3)⋊C4—122no—
247C4⋊Dic3—21no—
248C4⋊Dic3—61no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—121no—
253C4⋊Dic3—121no—
254C4⋊Dic3C4×D312yes—
255C2×C3⋊C8—21no—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8—21no—
259C2×C3⋊C8D1212yescomplemented
260C2×C3⋊C8#6712yescomplemented
261ΓL(1,𝔽25)—68no—
262ΓL(1,𝔽25)—68no—
263C22×C32C2×C22⋊C411yescharacteristic
264C22×C32#12111yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32AGL(1,ℤ/8)11yescharacteristic
267C22×C32AGL(1,ℤ/8)11yescharacteristic
268C22×C32AGL(1,ℤ/8)11yescharacteristic
269C22×C32#13711yescharacteristic
270C2×C3⋊D3—22no—
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—41no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3×D3—42no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3—81no—
281C2×C3×D3—81no—
282C2×C3×D3—81no—
283C2×C3×D3—81no—
284C32×C4—81no—
285C32×C4C4×D411yescharacteristic
286C32×C4C4×D411yescharacteristic
287C32×C4#12011yescharacteristic
288C32×C4#12311yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—81no—
291C3×Dic3—42no—
292C22×D4—31no—
293C22×D4—181no—
294C23×C4—91no—
295C2×M16—182no—
296C2×M16—182no—
297C2×M16—182no—
298C22×C8—31no—
299C22×C8—31no—
300#121—94no—
301#121—182no—
302C2×C4⋊C4—31no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4D3211yescharacteristic
305C2×C22⋊C4—181no—
306C2×C22⋊C4—181no—
307#102—62no—
308#102—182no—
309#95—181no—
310C23×C3—21no—
311C23×C3—62no—
312C23×C3—121no—
313C23×C3—121no—
314C23×C3—121no—
315C23×C3—121no—
316C23×C3—121no—
317C23×C3—121no—
318C23×C3D3×D411yescharacteristic
319C23×C3D3×D411yescharacteristic
320C22×D3—22no—
321C22×D3—32no—
322C22×D3—32no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—61no—
337C22×D3—61no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—121no—
345C22×D3—121no—
346C22×D3—121no—
347C22×D3—121no—
348C3×D4—62no—
349C3×D4—62no—
350C3×D4—121no—
351C3×D4—121no—
352C2×C3×C4—21no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—42no—
359C2×C3×C4—42no—
360C2×C3×C4—42no—
361C2×C3×C4—41no—
362C2×C3×C4—41no—
363C2×C3×C4—41no—
364C2×C3×C4—41no—
365C2×C3×C4—41no—
366C2×C3×C4—41no—
367C2×C3×C4—62no—
368C2×C3×C4—121no—
369C2×C3×C4—121no—
370C2×C3×C4C2×C4×D311yescharacteristic
371C2×C3×C4C2×C4×D311yescharacteristic
372C2×C3×C4C2×D1211yescharacteristic
373C2×C3×C4#23511yescharacteristic
374C2×C3×C4#23511yescharacteristic
375C2×C3×C4D3×D411yescharacteristic
376C2×C3×C4D3×D411yescharacteristic
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D411yescharacteristic
379C2×C3×C4#23711yescharacteristic
380C2×C3×C4#23911yescharacteristic
381C2×C3×C4C2×#6711yescharacteristic
382#67—128no—
383C2×Dic3—22no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—62no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—121no—
394C2×Dic3—121no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—122no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—121no—
401C2×Dic3—121no—
402C2×Dic3—121no—
403C2×Dic3—121no—
404D12—22no—
405D12—22no—
406D12—41no—
407D12—41no—
408D12—128no—
409C4×D3—62no—
410C4×D3—62no—
411C4×D3—62no—
412C4×D3—62no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—62no—
416C4×D3—62no—
417C4×D3—122no—
418C4×D3—122no—
419C4×D3—122no—
420C4×D3—122no—
421C3×C8—62no—
422C3×C8—62no—
423C3⋊C8—22no—
424C3⋊C8—22no—
425C2×C32#38611yescharacteristic
426C2×C32#41711yescharacteristic
427C2×C32#41811yescharacteristic
428C2×C32#46811yescharacteristic
429C2×C32#46811yescharacteristic
430C2×C32#46911yescharacteristic
431C2×C32#46911yescharacteristic
432C3⋊D3—42no—
433C3×D3—82no—
434C24—61no—
435C24—91no—
436C2×D4—32no—
437C2×D4—61no—
438C2×D4—61no—
439C2×D4—61no—
440C2×D4—61no—
441C2×D4—61no—
442C2×D4—184no—
443C2×D4—362no—
444C2×D4—362no—
445C22×C4—21no—
446C22×C4—61no—
447C22×C4—91no—
448C22×C4—92no—
449C22×C4—92no—
450C22×C4—181no—
451C22×C4—181no—
452C22×C4—181no—
453C22×C4—181no—
454C22×C4—181no—
455C22×C4C2×D3211yescharacteristic
456M16—188no—
457C2×C8—32no—
458C2×C8—32no—
459C2×C8—61no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—61no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—32no—
466C4⋊C4—61no—
467C4⋊C4—181no—
468C4⋊C4—181no—
469C22⋊C4—184no—
470C22⋊C4—362no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—122no—
479C22×C3—122no—
480C22×C3—122no—
481C22×C3—241no—
482C22×C3—241no—
483C22×C3—241no—
484C22×C3—241no—
485C22×C3D3×C22⋊C411yescharacteristic
486C22×C3D3×C22⋊C411yescharacteristic
487C22×C3#88411yescharacteristic
488C22×C3#88411yescharacteristic
489C22×C3#89511yescharacteristic
490C22×C3#91111yescharacteristic
491C22×C3#91111yescharacteristic
492C22×C3#91111yescharacteristic
493C22×C3#91411yescharacteristic
494C22×C3#91411yescharacteristic
495C22×C3#91411yescharacteristic
496C22×C3#91511yescharacteristic
497C22×C3#91811yescharacteristic
498C22×C3#93811yescharacteristic
499C2×D3—42no—
500C2×D3—42no—
501C2×D3—42no—
502C2×D3—64no—
503C2×D3—62no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—81no—
510C2×D3—81no—
511C2×D3—81no—
512C2×D3—81no—
513C2×D3—122no—
514C2×D3—122no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—82no—
532C3×C4—81no—
533C3×C4—81no—
534C3×C4—122no—
535C3×C4C4×D1211yescharacteristic
536C3×C4#67⋊C411yescharacteristic
537C3×C4#88211yescharacteristic
538C3×C4#88311yescharacteristic
539C3×C4#89311yescharacteristic
540C3×C4#89411yescharacteristic
541C3×C4C4×#6711yescharacteristic
542C3×C4#93711yescharacteristic
543Dic3—42no—
544Dic3—62no—
545Dic3—62no—
546Dic3—122no—
547Dic3—242no—
548Dic3—241no—
549Dic3—241no—
550C32#189511yescharacteristic, complemented, Sylow
551C23—62no—
552C23—92no—
553C23—121no—
554C23—121no—
555C23—121no—
556C23—121no—
557C23—121no—
558C23—121no—
559C23—181no—
560C23—181no—
561C23—181no—
562C23—181no—
563C23—181no—
564C23—181no—
565C23#381111yescharacteristic
566D4—62no—
567D4—62no—
568D4—121no—
569D4—121no—
570D4—368no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—62no—
575C2×C4—92no—
576C2×C4—121no—
577C2×C4—121no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—182no—
581C2×C4—182no—
582C2×C4—182no—
583C2×C4—182no—
584C2×C4—361no—
585C2×C4—361no—
586C2×C4—361no—
587C2×C4#379911yescharacteristic
588C2×C4C4×D3211yescharacteristic
589C2×C4D3×D1211yescharacteristic
590C2×C4#380211yescharacteristic
591C2×C4#380411yescharacteristic
592C2×C4D3×#6711yescharacteristic
593C8—62no—
594C8—62no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—21no—
598C2×C3—21no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—242no—
603C2×C3#466511yescharacteristic
604C2×C3#477011yescharacteristic
605C2×C3#477011yescharacteristic
606C2×C3#477111yescharacteristic
607C2×C3#478011yescharacteristic
608C2×C3#478211yescharacteristic
609C2×C3#478211yescharacteristic
610C2×C3#480311yescharacteristic
611C2×C3#481211yescharacteristic
612C2×C3#486511yescharacteristic
613C2×C3#488611yescharacteristic
614C2×C3#495611yescharacteristic
615C2×C3#515911yescharacteristic
616C2×C3#517411yescharacteristic
617D3—82no—
618D3—124no—
619D3—122no—
620D3—122no—
621C22—122no—
622C22—122no—
623C22—122no—
624C22—182no—
625C22—182no—
626C22—182no—
627C22—241no—
628C22—241no—
629C22—241no—
630C22—241no—
631C22—361no—
632C22—361no—
633C22—361no—
634C22—361no—
635C22#6391011yescharacteristic
636C22#6392111yescharacteristic
637C22#6392711yescharacteristic
638C22#6393711yescharacteristic
639C22#6394111yescharacteristic
640C22#6395111yescharacteristic
641C22#6395811yescharacteristic
642C4—81no—
643C4—122no—
644C4—182no—
645C4—721no—
646C4#6385411yescharacteristic
647C4#6388011yescharacteristic
648C4#6390411yescharacteristic
649C4#6392211yescharacteristic
650C3—21no—
651C3#6888511yescharacteristic, complemented
652C3#7020311yescharacteristic, complemented
653C2—242no—
654C2—362no—
655C2#1059050611yescharacteristic
656C2#1059050811yescharacteristic
657C2#1059059411yescharacteristic
658C2#1059061211yescharacteristic
659C2#1059127511yescharacteristic
660C2#1059145411yescharacteristic
661C2#1059159011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63916C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1895
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#3712C2semidirect
3. #10592686C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63563C2semidirect
6. C3×#4529C2semidirect
7. #10589164C2semidirect
21. #63916C4semidirect
38. C2×#809D3semidirect
42. #4529D3semidirect
76. C2×C3×C3⋊C8D4semidirect
77. C2×C3×C3⋊C8D4semidirect
259. C2×C3⋊C8D12semidirect
260. C2×C3⋊C8#67semidirect
550. C32#1895semidirect
651. C3#68885semidirect
652. C3#70203semidirect

Maximal subgroups

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

subgroupindex
C2×#639162
C22×#37122
#105926862
C2×C3×#8092
C2×#635632
C3×#45292
#105891642
#702033
#688853