Finite Group Databasebeta

← #11788140

Subgroups — #11788140

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#71990—31nomaximal
9#68885—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C22×#626—21no—
13C22×C32×C8C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)—22no—
19C2×C3×ΓL(1,𝔽25)—22no—
20C2×C3×ΓL(1,𝔽25)—22no—
21C2×#3722—21no—
22C2×(C2×D3)⋊Dic3—21no—
23#63909—22no—
24#63909C414yescomplemented
25#63648—22no—
26#63579—21no—
27#63564—22no—
28C22×C3×M16—31no—
29C2×#930—31no—
30C22×ΓL(1,𝔽25)D311yescharacteristic, complemented
31C2×#895—31no—
32#5212—31no—
33C2×#821—31no—
34C2×#821—31no—
35C2×#821—31no—
36C2×#821—61no—
37#4987—31no—
38C2×#809—31no—
39C3×#340—31no—
40#4551—31no—
41#4551D311yescharacteristic, complemented
42#4529—31no—
43C23×C3⋊D3—21no—
44C23×C3×D3D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C22×C3×Dic3—21no—
54C22×C3×Dic3—21no—
55C22×C3×Dic3D411yescharacteristic
56C2×C3×C4×D3—21no—
57C2×C3×C4×D3—21no—
58C2×C3×C4×D3—21no—
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3C2×C412yes—
61C2×C3×C4×D3D412yes—
62C2×#626—24no—
63C2×#626—42no—
64C2×#626—42no—
65C2×C32×C8—21no—
66C2×C32×C8—21no—
67C2×C32×C8D412yescomplemented
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2×C412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8D412yescomplemented
77C3×ΓL(1,𝔽25)—28no—
78#3722—24no—
79(C2×D3)⋊Dic3—42no—
80#1895—91noSylow
81C23×C3×C4—31no—
82C22×#67—61no—
83C22×D12—31no—
84C22×D12—31no—
85C22×D12—61no—
86C22×D12—61no—
87C22×C4×D3C2×D311yescharacteristic
88C2×C3×M16—62no—
89C2×C3×M16—62no—
90C2×C3×M16—62no—
91C22×C3×C8—21no—
92C22×C3×C8—31no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×#217—61no—
98#930—34no—
99#930—62no—
100C2×(C2×D3)⋊C4—61no—
101C2×(C2×D3)⋊C4—61no—
102C2×(C2×D3)⋊C4—61no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4⋊Dic3C2×D311yescharacteristic
108C22×C3⋊C8C2×D311yescharacteristic
109C2×ΓL(1,𝔽25)—22no—
110C2×ΓL(1,𝔽25)—22no—
111C2×ΓL(1,𝔽25)—22no—
112#895—34no—
113#895—62no—
114C3⋊#95—61no—
115C3⋊#95—61no—
116#821—62no—
117#821—64no—
118#821—62no—
119#821—62no—
120#809—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—22no—
123C22×C3⋊D3—41no—
124C22×C3⋊D3—41no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—41no—
127C22×C3⋊D3—41no—
128C22×C3⋊D3—41no—
129C22×C3×D3—21no—
130C22×C3×D3—21no—
131C22×C3×D3—21no—
132C22×C3×D3—21no—
133C22×C3×D3—21no—
134C22×C3×D3—21no—
135C22×C3×D3C22⋊C412yes—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C3⋊Dic3—41no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—41no—
145C4⋊(C3⋊D3)—22no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)—41no—
148C4⋊(C3⋊D3)—41no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—21no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—41no—
153C2×C3×Dic3—41no—
154C2×C3×Dic3—41no—
155C2×C3×Dic3—41no—
156C2×C3×Dic3—41no—
157C2×C3×Dic3C22⋊C412yes—
158C3×C4×D3—22no—
159C3×C4×D3—22no—
160C3×C4×D3—22no—
161C3×C4×D3—22no—
162#626—48no—
163C32×C8—22no—
164C3×C3⋊C8—22no—
165C22×M16—31no—
166C2×#121—91no—
167C2×#102—91no—
168C2×#102—91no—
169#380—91no—
170#340—31no—
171#340—91no—
172C24×C3—31no—
173C23×D3—61no—
174C23×D3—61no—
175C23×D3—121no—
176C23×D3D1211yescharacteristic
177C22×C3×C4—21no—
178C22×C3×C4—31no—
179C22×C3×C4—32no—
180C22×C3×C4—32no—
181C22×C3×C4—61no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4—61no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C2×#67—64no—
190C2×#67—122no—
191C2×#67—122no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—121no—
197C22×Dic3D1211yescharacteristic
198C2×D12—32no—
199C2×D12—32no—
200C2×D12—62no—
201C2×D12—62no—
202C2×D12—62no—
203C2×D12—61no—
204C2×D12—61no—
205C2×D12—61no—
206C2×D12—61no—
207C2×D12—61no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—64no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—121no—
215C2×D12—121no—
216C2×D12—121no—
217C2×D12—122no—
218C2×D12—122no—
219C2×C4×D3—21no—
220C2×C4×D3—21no—
221C2×C4×D3—21no—
222C2×C4×D3—21no—
223C2×C4×D3C4×D312yes—
224C2×C4×D3#6712yes—
225C3×M16—68no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—22no—
231C2×C3×C8—32no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—61no—
235C2×C3×C8—61no—
236C2×C3×C8D1212yescomplemented
237C2×C3×C8#6712yescomplemented
238C3×C4⋊C4—32no—
239C3×C4⋊C4—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242#217—122no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—122no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248C4⋊Dic3—21no—
249C4⋊Dic3—62no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3—121no—
255C4⋊Dic3C4×D312yes—
256C2×C3⋊C8—21no—
257C2×C3⋊C8—21no—
258C2×C3⋊C8#6712yescomplemented
259ΓL(1,𝔽25)—28no—
260C22×C32C2×C22⋊C411yescharacteristic
261C22×C32#12111yescharacteristic
262C22×C32#12111yescharacteristic
263C22×C32AGL(1,ℤ/8)11yescharacteristic
264C22×C32AGL(1,ℤ/8)11yescharacteristic
265C22×C32AGL(1,ℤ/8)11yescharacteristic
266C22×C32#13711yescharacteristic
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C2×C3⋊D3—81no—
271C2×C3⋊D3—81no—
272C2×C3⋊D3—81no—
273C2×C3⋊D3—81no—
274C2×C3×D3—22no—
275C2×C3×D3—22no—
276C2×C3×D3—22no—
277C2×C3×D3—41no—
278C2×C3×D3—41no—
279C2×C3×D3—41no—
280C2×C3×D3—41no—
281C32×C4C4×D411yescharacteristic
282C32×C4C4×D411yescharacteristic
283C32×C4#12011yescharacteristic
284C32×C4#12311yescharacteristic
285C3⋊Dic3—81no—
286C3×Dic3—22no—
287C3×Dic3—42no—
288C3×Dic3—81no—
289C22×D4—91no—
290C22×D4—181no—
291C23×C4—31no—
292C2×M16—62no—
293C2×M16—62no—
294C2×M16—62no—
295C22×C8—31no—
296C22×C8D3211yescharacteristic
297#121—94no—
298#121—182no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—31no—
301C2×C4⋊C4—91no—
302C2×C22⋊C4—181no—
303C2×C22⋊C4—181no—
304#102—182no—
305#102—182no—
306#95—181no—
307C23×C3—21no—
308C23×C3—32no—
309C23×C3—61no—
310C23×C3—61no—
311C23×C3—61no—
312C23×C3—61no—
313C23×C3—61no—
314C23×C3—61no—
315C23×C3C2×D1211yescharacteristic
316C23×C3D3×D411yescharacteristic
317C22×D3—21no—
318C22×D3—21no—
319C22×D3—21no—
320C22×D3—21no—
321C22×D3—21no—
322C22×D3—21no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—121no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—121no—
336C22×D3—121no—
337C22×D3—121no—
338C22×D3—121no—
339C22×D3—121no—
340C22×D3—241no—
341C22×D3—241no—
342C22×D3—241no—
343C22×D3—241no—
344C22×D3(C2×D3)⋊C412yes—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—121no—
360C2×C3×C4—121no—
361C2×C3×C4—121no—
362C2×C3×C4—121no—
363C2×C3×C4—121no—
364C2×C3×C4C2×C4×D311yescharacteristic
365C2×C3×C4C2×C4×D311yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23511yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4#23511yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4#23911yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376#67—128no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—22no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—41no—
384C2×Dic3—41no—
385C2×Dic3—122no—
386C2×Dic3—121no—
387C2×Dic3—121no—
388C2×Dic3—121no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—241no—
393C2×Dic3—241no—
394C2×Dic3(C2×D3)⋊C412yes—
395D12—64no—
396D12—62no—
397D12—62no—
398D12—62no—
399D12—62no—
400D12—122no—
401D12—122no—
402D12—122no—
403D12—128no—
404D12—121no—
405D12—121no—
406D12—121no—
407D12—121no—
408C4×D3—22no—
409C4×D3—22no—
410C4×D3—22no—
411C4×D3—22no—
412C3×C8—22no—
413C3×C8—22no—
414C3×C8—42no—
415C3×C8—62no—
416C3⋊C8—22no—
417C2×C32#38611yescharacteristic
418C2×C32#41711yescharacteristic
419C2×C32#41811yescharacteristic
420C2×C32#46811yescharacteristic
421C2×C32#46811yescharacteristic
422C2×C32#46911yescharacteristic
423C2×C32#46911yescharacteristic
424C3⋊D3—82no—
425C3×D3—42no—
426C24—31no—
427C24—181no—
428C2×D4—92no—
429C2×D4—184no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—181no—
434C2×D4—181no—
435C2×D4—362no—
436C2×D4—362no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—61no—
444C22×C4—61no—
445C22×C4—61no—
446C22×C4—181no—
447C22×C4C2×D3211yescharacteristic
448M16—68no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—32no—
452C2×C8—61no—
453C2×C8—61no—
454C2×C8#62612yescomplemented
455C4⋊C4—32no—
456C4⋊C4—61no—
457C4⋊C4—61no—
458C4⋊C4—61no—
459C4⋊C4—181no—
460C4⋊C4—181no—
461C22⋊C4—184no—
462C22⋊C4—362no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—62no—
473C22×C3—121no—
474C22×C3—121no—
475C22×C3—121no—
476C22×C3—121no—
477C22×C3D3×C22⋊C411yescharacteristic
478C22×C3#88411yescharacteristic
479C22×C3#89511yescharacteristic
480C22×C3#90811yescharacteristic
481C22×C3#90811yescharacteristic
482C22×C3#90811yescharacteristic
483C22×C3#90911yescharacteristic
484C22×C3#91111yescharacteristic
485C22×C3#91411yescharacteristic
486C22×C3#91411yescharacteristic
487C22×C3#91811yescharacteristic
488C22×C3C2×(C2×D3)⋊C411yescharacteristic
489C22×C3#93011yescharacteristic
490C22×C3#93011yescharacteristic
491C2×D3—22no—
492C2×D3—22no—
493C2×D3—22no—
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—124no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—242no—
506C2×D3—242no—
507C2×D3—242no—
508C2×D3—242no—
509C2×D3—242no—
510C2×D3—242no—
511C2×D3—241no—
512C2×D3—241no—
513C2×D3—241no—
514C2×D3—241no—
515C2×D3—241no—
516C2×D3—241no—
517C2×D3—241no—
518C2×D3—241no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—62no—
524C3×C4—122no—
525C3×C4—241no—
526C3×C4C4×D1211yescharacteristic
527C3×C4#88211yescharacteristic
528C3×C4#89311yescharacteristic
529C3×C4#89411yescharacteristic
530C3×C4C4×#6711yescharacteristic
531C3×C4C4×#6711yescharacteristic
532C3×C4#92911yescharacteristic
533C3×C4#95311yescharacteristic
534Dic3—22no—
535Dic3—42no—
536Dic3—81no—
537Dic3—242no—
538Dic3—241no—
539Dic3—241no—
540C32#189511yescharacteristic, complemented, Sylow
541C23—32no—
542C23—61no—
543C23—61no—
544C23—61no—
545C23—61no—
546C23—61no—
547C23—61no—
548C23—182no—
549C23—361no—
550C23—361no—
551C23—361no—
552C23—361no—
553C23—361no—
554C23—361no—
555C23D3×D1211yescharacteristic
556D4—182no—
557D4—182no—
558D4—368no—
559D4—361no—
560D4—361no—
561C2×C4—32no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—361no—
575C2×C4—361no—
576C2×C4—361no—
577C2×C4#379811yescharacteristic
578C2×C4#379911yescharacteristic
579C2×C4C4×D3211yescharacteristic
580C2×C4C2×#62611yescharacteristic
581C2×C4D3×#6711yescharacteristic
582C2×C4D3×#6711yescharacteristic
583C8—22no—
584C8—62no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—122no—
593C2×C3#466511yescharacteristic
594C2×C3#477011yescharacteristic
595C2×C3#478211yescharacteristic
596C2×C3#480311yescharacteristic
597C2×C3#481211yescharacteristic
598C2×C3#486511yescharacteristic
599C2×C3#488611yescharacteristic
600C2×C3#513111yescharacteristic
601C2×C3#513311yescharacteristic
602C2×C3#513411yescharacteristic
603C2×C3#513411yescharacteristic
604C2×C3#513511yescharacteristic
605C2×C3#513511yescharacteristic
606C2×C3#521311yescharacteristic
607D3—42no—
608D3—244no—
609D3—242no—
610D3—242no—
611C22—62no—
612C22—62no—
613C22—62no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22—121no—
618C22—362no—
619C22—362no—
620C22—362no—
621C22—721no—
622C22—721no—
623C22—721no—
624C22—721no—
625C22#6379411yescharacteristic
626C22#6379411yescharacteristic
627C22#6379511yescharacteristic
628C22#6380111yescharacteristic
629C22#6390611yescharacteristic
630C22#6390911yescharacteristic
631C22D3×(C2×D3)⋊C411yescharacteristic
632C4—62no—
633C4—122no—
634C4—241no—
635C4—721no—
636C4#6385011yescharacteristic
637C4C4×#62611yescharacteristic
638C4#6390411yescharacteristic
639C4#6397711yescharacteristic
640C3—21no—
641C3#6888511yescharacteristic, complemented
642C3#7199011yescharacteristic, complemented
643C2—122no—
644C2—722no—
645C2#1059067111yescharacteristic
646C2#1059082711yescharacteristic
647C2#1059083511yescharacteristic
648C2#1059083811yescharacteristic
649C2#1059085011yescharacteristic
650C2#1059093911yescharacteristic
651C2#1059138211yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1895
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×ΓL(1,𝔽25)C2semidirect
3. C2×#63648C2semidirect
4. #10591313C2semidirect
5. C2×#63564C2semidirect
6. C3×#4551C2semidirect
7. #10589164C2semidirect
24. #63909C4semidirect
30. C22×ΓL(1,𝔽25)D3semidirect
41. #4551D3semidirect
67. C2×C32×C8D4semidirect
76. C2×C3×C3⋊C8D4semidirect
236. C2×C3×C8D12semidirect
237. C2×C3×C8#67semidirect
258. C2×C3⋊C8#67semidirect
454. C2×C8#626semidirect
540. C32#1895semidirect
641. C3#68885semidirect
642. C3#71990semidirect

Maximal subgroups

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

subgroupindex
C22×C3×ΓL(1,𝔽25)2
C2×#639092
C2×#636482
#105913132
C2×#635642
C3×#45512
#105891642
#719903
#688853