Finite Group Databasebeta

← #11787218

Subgroups — #11787218

Order 1152.

807 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic, complemented
2#10595022C211yesmaximal, characteristic
3C2×C3×#825C211yesmaximal, characteristic, complemented
4C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
5C2×#63568C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#71984—31nomaximal
9#70381—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×D3×M16—22no—
18C3×D3×M16—22no—
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21#63976—21no—
22#63961—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63908C411yescharacteristic, complemented
25#63908C411yescharacteristic, complemented
26C4×#625—21no—
27C4×#625—21no—
28#63856C411yescharacteristic, complemented
29#63856C411yescharacteristic, complemented
30C3×#825—22no—
31#63579—21no—
32#63568—22no—
33C22×C3×M16—31no—
34#5828—31no—
35#5791—31no—
36C2×D3×M16D311yescharacteristic, complemented
37C2×C3×#104—31no—
38C2×#837—31no—
39C4×#217—31no—
40C2×#825—31no—
41C2×#825D311yescharacteristic, complemented
42C4×(C2×D3)⋊C4—31no—
43#4555—31no—
44#4555—31no—
45#4555—31no—
46#4555—61no—
47#4523—31no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3—21no—
51C2×C3×#67—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3D411yescharacteristic
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12C2×C411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3C2×C411yescharacteristic
65C2×C3×C4×D3C2×C411yescharacteristic
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68C2×C3×Dic6C2×C411yescharacteristic
69C2×#625—21no—
70C2×#625—21no—
71C32×M16—21no—
72C32×M16D412yescomplemented
73C2×C32×C8—21no—
74#3757—21no—
75C4⋊(C3⋊Dic3)C2×C411yescharacteristic
76C4⋊(C3⋊Dic3)C2×C411yescharacteristic
77C4×C3⋊Dic3—21no—
78C4×C3⋊Dic3—21no—
79C4×C3⋊Dic3—21no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3—21no—
82C3×#208—21no—
83C3×#208D412yescomplemented
84C2×C3×C3⋊C8—21no—
85C3×ΓL(1,𝔽25)—24no—
86C3×D3×C8—24no—
87#3724—21no—
88#3724—21no—
89(C2×D3)⋊Dic3—24no—
90(C2×D3)⋊Dic3—21no—
91(C2×D3)⋊Dic3—21no—
92(C2×D3)⋊Dic3—21no—
93(C2×D3)⋊Dic3—21no—
94#1871—91noSylow
95C2×C3×#41—31no—
96C23×C3×C4—31no—
97C2×#235C2×D311yescharacteristic
98C22×C4×D3C2×D311yescharacteristic
99C2×C3×M16—21no—
100C2×C3×M16—31no—
101C2×C3×M16—61no—
102C2×C3×M16—62no—
103C2×C3×M16—62no—
104C2×C3×M16C2×D311yescharacteristic
105C2×C3×M16C2×D311yescharacteristic
106C22×C3×C8—61no—
107C2×C3×C42—31no—
108#953—61no—
109C2×#217—61no—
110#946—31no—
111#946—31no—
112#938—31no—
113#938—31no—
114#937—61no—
115#935—61no—
116#930—31no—
117#930—31no—
118#929—61no—
119C4×#67—61no—
120C4×#67—61no—
121C4×#67—61no—
122C4×#67—61no—
123C2×(C2×D3)⋊C4—61no—
124#926—31no—
125#926—31no—
126#926—61no—
127#924—31no—
128#924—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—61no—
132C2×C4×Dic3C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134D3×M16—22no—
135D3×M16—22no—
136C2×ΓL(1,𝔽25)—21no—
137C2×D3×C8—21no—
138C3×#104—62no—
139#837—62no—
140C3⋊#95—61no—
141C3⋊#95—61no—
142#825—22no—
143#825—62no—
144C23×C32C2×D411yescharacteristic
145C22×C3×D3—21no—
146C22×C3×D3—21no—
147C22×C3×D3—22no—
148C22×C3×D3—21no—
149C22×C3×D3—41no—
150C22×C3×D3C22⋊C411yescharacteristic
151C22×C3×D3C22⋊C411yescharacteristic
152C2×C32×C4C22×C411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4#4111yescharacteristic
157C2×C32×C4#4111yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—21no—
161C2×C3⋊Dic3—41no—
162C2×C3⋊Dic3—41no—
163C3×#67—41no—
164C3×#67—41no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3C22⋊C411yescharacteristic
172C2×C3×Dic3C22⋊C411yescharacteristic
173C3×D12—21no—
174C3×D12—21no—
175C3×C4×D3—21no—
176C3×C4×D3—21no—
177C3×C4×D3—21no—
178C3×C4×D3—21no—
179C3×C4×D3—21no—
180C3×C4×D3—21no—
181C3×C4×D3—21no—
182C3×C4×D3—21no—
183C3×C4×D3—41no—
184C3×C4×D3—41no—
185C3×Dic6—21no—
186C3×Dic6—21no—
187#625—42no—
188#625—42no—
189C32×C8—22no—
190C3×C3⋊C8—22no—
191C22×M16—31no—
192#525—91no—
193C2×#104—31no—
194C2×#104—91no—
195C4×C22⋊C4—91no—
196#339—91no—
197#339—91no—
198C24×C3—31no—
199C23×D3D1211yescharacteristic
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—61no—
203C3×#41—61no—
204C2×C3×Q8—31no—
205C2×C3×D4—31no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—21no—
222C2×#67—61no—
223C2×#67—61no—
224C2×#67—61no—
225C2×#67—61no—
226C22×Dic3—21no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—121no—
230C22×Dic3D1211yescharacteristic
231#235—21no—
232#235—21no—
233#235—21no—
234#235—21no—
235C2×D12C4×D311yescharacteristic
236C2×C4×D3—21no—
237C2×C4×D3—21no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3C4×D311yescharacteristic
242C2×C4×D3C4×D311yescharacteristic
243C2×C4×D3#6711yescharacteristic
244C2×C4×D3#6711yescharacteristic
245C2×Dic6C4×D311yescharacteristic
246C3×M16—21no—
247C3×M16—21no—
248C3×M16—22no—
249C3×M16—32no—
250C3×M16—41no—
251C3×M16—64no—
252C3×M16—61no—
253C3×M16#6712yescomplemented
254C3×M16#6712yescomplemented
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—41no—
258C2×C3×C8—64no—
259C2×C3×C8—61no—
260C3×C42—61no—
261C3×C42—61no—
262#217—61no—
263#217—61no—
264#217—64no—
265#217—61no—
266#217—61no—
267#217—61no—
268#217—61no—
269#217—121no—
270(C2×D3)⋊C4—61no—
271(C2×D3)⋊C4—61no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—61no—
275C4⋊Dic3—31no—
276C4⋊Dic3—31no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—61no—
280C4⋊Dic3—61no—
281Dic3⋊C4—61no—
282Dic3⋊C4—61no—
283Dic3⋊C4—61no—
284Dic3⋊C4—61no—
285C4×Dic3—21no—
286C4×Dic3—21no—
287C4×Dic3—61no—
288C4×Dic3—61no—
289C4×Dic3—62no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—61no—
293C4×Dic3—61no—
294C4×Dic3—121no—
295C4×Dic3—121no—
296#208—21no—
297#208#6712yescomplemented
298C2×C3⋊C8—21no—
299ΓL(1,𝔽25)—24no—
300D3×C8—24no—
301C22×C32—21no—
302C22×C32—21no—
303C22×C32C2×C22⋊C411yescharacteristic
304C22×C32#12111yescharacteristic
305C22×C32#12111yescharacteristic
306C2×C3×D3—21no—
307C2×C3×D3—21no—
308C2×C3×D3—21no—
309C2×C3×D3—21no—
310C2×C3×D3—21no—
311C2×C3×D3—42no—
312C2×C3×D3—42no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3#10412yescomplemented
317C32×C4C4×D411yescharacteristic
318C32×C4C4×D411yescharacteristic
319C32×C4#12011yescharacteristic
320C32×C4#12311yescharacteristic
321C3⋊Dic3—42no—
322C3⋊Dic3—41no—
323C3⋊Dic3—41no—
324C3×Dic3—21no—
325C3×Dic3—21no—
326C3×Dic3—42no—
327C3×Dic3—41no—
328C2×#41—31no—
329C23×C4—31no—
330C2×M16—31no—
331C2×M16—61no—
332C2×M16—62no—
333C2×M16—62no—
334C2×M16D3211yescharacteristic
335C22×C8—61no—
336#123—181no—
337C22⋊Q8—91no—
338C22⋊Q8—91no—
339#121—91no—
340#121—91no—
341#120—181no—
342C4×D4—181no—
343C4×D4—181no—
344#117—91no—
345C2×C22⋊C4—181no—
346C2×C42—31no—
347C2×C42—91no—
348#104—62no—
349#104—182no—
350#95—181no—
351C23×C3—21no—
352C23×C3—31no—
353C23×C3—31no—
354C23×C3—62no—
355C23×C3—61no—
356C23×C3—61no—
357C23×C3—61no—
358C23×C3—121no—
359C23×C3C2×D1211yescharacteristic
360C23×C3D3×D411yescharacteristic
361C22×D3—21no—
362C22×D3—21no—
363C22×D3—22no—
364C22×D3—21no—
365C22×D3—41no—
366C22×D3(C2×D3)⋊C411yescharacteristic
367C22×D3(C2×D3)⋊C411yescharacteristic
368C3×Q8—61no—
369C3×Q8—61no—
370C3×D4—61no—
371C3×D4—61no—
372C3×D4—121no—
373C3×D4—121no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—31no—
381C2×C3×C4—31no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—61no—
385C2×C3×C4—61no—
386C2×C3×C4—61no—
387C2×C3×C4—61no—
388C2×C3×C4—61no—
389C2×C3×C4—61no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—121no—
395C2×C3×C4—121no—
396C2×C3×C4—121no—
397C2×C3×C4—121no—
398C2×C3×C4C2×C4×D311yescharacteristic
399C2×C3×C4C2×C4×D311yescharacteristic
400C2×C3×C4#23511yescharacteristic
401C2×C3×C4#23511yescharacteristic
402C2×C3×C4#23511yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4#23711yescharacteristic
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410#67—41no—
411#67—41no—
412#67—122no—
413#67—122no—
414#67—122no—
415#67—122no—
416C2×Dic3—21no—
417C2×Dic3—21no—
418C2×Dic3—22no—
419C2×Dic3—21no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—122no—
429C2×Dic3—121no—
430C2×Dic3—121no—
431C2×Dic3—122no—
432C2×Dic3—121no—
433C2×Dic3—121no—
434C2×Dic3—122no—
435C2×Dic3—121no—
436C2×Dic3—121no—
437C2×Dic3(C2×D3)⋊C411yescharacteristic
438C2×Dic3(C2×D3)⋊C411yescharacteristic
439D12—21no—
440D12—21no—
441C4×D3—21no—
442C4×D3—21no—
443C4×D3—21no—
444C4×D3—21no—
445C4×D3—21no—
446C4×D3—21no—
447C4×D3—21no—
448C4×D3—21no—
449C4×D3—41no—
450C4×D3—41no—
451Dic6—21no—
452Dic6—21no—
453C3×C8—22no—
454C3×C8—22no—
455C3×C8—42no—
456C3×C8—62no—
457C3⋊C8—22no—
458C2×C32—21no—
459C2×C32—21no—
460C2×C32#38611yescharacteristic
461C2×C32C2×#10411yescharacteristic
462C2×C32#42111yescharacteristic
463C3×D3—22no—
464C3×D3—41no—
465C3×D3—81no—
466C24—31no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471C2×Q8—31no—
472C2×D4—31no—
473C2×D4—61no—
474C2×D4—181no—
475C2×D4—181no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—181no—
488C22×C4C2×D3211yescharacteristic
489M16—21no—
490M16—32no—
491M16—64no—
492M16—61no—
493M16#62512yescomplemented
494C2×C8—21no—
495C2×C8—64no—
496C2×C8—61no—
497C4⋊C4—91no—
498C4⋊C4—91no—
499C4⋊C4—181no—
500C4⋊C4—181no—
501C22⋊C4—181no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—184no—
506C22⋊C4—181no—
507C42—61no—
508C42—61no—
509C42—181no—
510C42—181no—
511C42—181no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—32no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—61no—
523C22×C3—61no—
524C22×C3—61no—
525C22×C3—61no—
526C22×C3—61no—
527C22×C3—122no—
528C22×C3—122no—
529C22×C3—121no—
530C22×C3—121no—
531C22×C3—121no—
532C22×C3D3×C22⋊C411yescharacteristic
533C22×C3#88411yescharacteristic
534C22×C3C2×(C2×D3)⋊C411yescharacteristic
535C22×C3#93011yescharacteristic
536C22×C3#93011yescharacteristic
537C22×C3#93811yescharacteristic
538C2×D3—21no—
539C2×D3—21no—
540C2×D3—21no—
541C2×D3—21no—
542C2×D3—21no—
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—41no—
546C2×D3—41no—
547C2×D3—41no—
548C2×D3#82512yescomplemented
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—61no—
554C3×C4—61no—
555C3×C4—122no—
556C3×C4—121no—
557C3×C4#67⋊C411yescharacteristic
558C3×C4#88311yescharacteristic
559C3×C4C4×#6711yescharacteristic
560C3×C4C4×#6711yescharacteristic
561C3×C4C4×#6711yescharacteristic
562C3×C4#92911yescharacteristic
563C3×C4#93711yescharacteristic
564C3×C4#95311yescharacteristic
565Dic3—21no—
566Dic3—21no—
567Dic3—42no—
568Dic3—41no—
569Dic3—122no—
570Dic3—122no—
571Dic3—124no—
572Dic3—121no—
573Dic3—121no—
574Dic3—121no—
575Dic3—121no—
576Dic3—241no—
577Dic3—241no—
578C32#187111yescharacteristic, complemented, Sylow
579C23—31no—
580C23—31no—
581C23—62no—
582C23—61no—
583C23—61no—
584C23—61no—
585C23—121no—
586C23D3×D1211yescharacteristic
587Q8—61no—
588Q8—61no—
589D4—61no—
590D4—61no—
591D4—121no—
592D4—121no—
593D4—362no—
594D4—362no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—61no—
598C2×C4—61no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—62no—
608C2×C4—61no—
609C2×C4—121no—
610C2×C4—121no—
611C2×C4—121no—
612C2×C4—121no—
613C2×C4—182no—
614C2×C4—181no—
615C2×C4—181no—
616C2×C4—361no—
617C2×C4—361no—
618C2×C4#379511yescharacteristic
619C2×C4#379811yescharacteristic
620C2×C4C4×D3211yescharacteristic
621C2×C4C2×#62511yescharacteristic
622C2×C4D3×#6711yescharacteristic
623C2×C4D3×#6711yescharacteristic
624C8—22no—
625C8—62no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—41no—
634C2×C3—41no—
635C2×C3—62no—
636C2×C3—121no—
637C2×C3—241no—
638C2×C3D3×#10411yescharacteristic
639C2×C3#482111yescharacteristic
640C2×C3#495611yescharacteristic
641C2×C3C2×#82511yescharacteristic
642C2×C3#513911yescharacteristic
643C2×C3#521311yescharacteristic
644D3—22no—
645D3—41no—
646D3—81no—
647C22—21no—
648C22—21no—
649C22—32no—
650C22—61no—
651C22—61no—
652C22—61no—
653C22—61no—
654C22—61no—
655C22—122no—
656C22—122no—
657C22—121no—
658C22—121no—
659C22—121no—
660C22#6390611yescharacteristic
661C22#6390811yescharacteristic
662C22D3×(C2×D3)⋊C411yescharacteristic
663C4—61no—
664C4—61no—
665C4—122no—
666C4—121no—
667C4—362no—
668C4—361no—
669C4—361no—
670C4#6387911yescharacteristic
671C4C4×#62511yescharacteristic
672C4#6390511yescharacteristic
673C4#6397611yescharacteristic
674C3—21no—
675C3#7038111yescharacteristic, complemented
676C3#7198411yescharacteristic, complemented
677C2—21no—
678C2—21no—
679C2—62no—
680C2—121no—
681C2—241no—
682C2D3×#82511yescharacteristic
683C2#1059100511yescharacteristic
684C2#1059138111yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radical#10595022C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1871
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×M16C2semidirect
3. C2×C3×#825C2semidirect
4. C4×(C2×D3)⋊Dic3C2semidirect
5. C2×#63568C2semidirect
6. #10589421C2semidirect
7. #10589162C2semidirect
24. #63908C4semidirect
25. #63908C4semidirect
28. #63856C4semidirect
29. #63856C4semidirect
36. C2×D3×M16D3semidirect
41. C2×#825D3semidirect
72. C32×M16D4semidirect
83. C3×#208D4semidirect
253. C3×M16#67semidirect
254. C3×M16#67semidirect
297. #208#67semidirect
316. C2×C3×D3#104semidirect
493. M16#625semidirect
548. C2×D3#825semidirect
578. C32#1871semidirect
675. C3#70381semidirect
676. C3#71984semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
#105950222
C2×C3×#8252
C4×(C2×D3)⋊Dic32
C2×#635682
#105894212
#105891622
#719843
#703813