Finite Group Databasebeta

← #11787215

Subgroups — #11787215

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
1#10595022C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#805C211yesmaximal, characteristic, complemented
5C2×#63569C211yesmaximal, characteristic, complemented
6#10589389C211yesmaximal, characteristic, complemented
7#10589162C211yesmaximal, characteristic, complemented
8#70381—31nomaximal
9#69453—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×C4×D3C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×C4×Dic3C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18#63976—21no—
19#63961—21no—
20#63908C411yescharacteristic, complemented
21#63908C411yescharacteristic, complemented
22C4×#625—21no—
23C4×#625—21no—
24#63856C411yescharacteristic, complemented
25#63856C411yescharacteristic, complemented
26C2×#3711—21no—
27D3×#208—22no—
28D3×#208—22no—
29C2×D3×C3⋊C8—21no—
30C3×C3⋊#95—21no—
31C3×#805—22no—
32#63569—22no—
33#5828—31no—
34#5791—31no—
35C22×#208—31no—
36C2×D3×M16—31no—
37C2×C3×#104—31no—
38C3×C4×C22⋊C4—31no—
39C2×#837—31no—
40C4×(C2×D3)⋊C4D311yescharacteristic, complemented
41C2×#805—31no—
42C2×#805D311yescharacteristic, complemented
43#4555—31no—
44#4523—31no—
45#4523—31no—
46#4523—31no—
47#4523—61no—
48C23×C3×D3D411yescharacteristic
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
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×C42—21no—
72C32×C42—21no—
73#3757—21no—
74C4⋊(C3⋊Dic3)C2×C411yescharacteristic
75C4⋊(C3⋊Dic3)C2×C411yescharacteristic
76C4×C3⋊Dic3—21no—
77#3748—21no—
78#3748D412yescomplemented
79C2×C3⋊(C3⋊C8)—21no—
80C3×(C2×D3)⋊C4—24no—
81C3×C4×Dic3—21no—
82C3×C4×Dic3—21no—
83C3×#208—21no—
84C3×#208D412yescomplemented
85C2×C3×C3⋊C8—21no—
86#3724—21no—
87#3724—21no—
88(C2×D3)⋊Dic3—21no—
89(C2×D3)⋊Dic3—21no—
90(C2×D3)⋊Dic3—21no—
91(C2×D3)⋊Dic3—21no—
92#3711—24no—
93D3×C3⋊C8—24no—
94#1871—91noSylow
95C2×C3×#41—31no—
96C23×C3×C4—31no—
97C2×#235C2×D311yescharacteristic
98C22×C4×D3C2×D311yescharacteristic
99C2×C3×M16—31no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—21no—
102C2×C3×C42—31no—
103C2×C3×C42C2×D311yescharacteristic
104C2×C3×C42C2×D311yescharacteristic
105#953—61no—
106#946—31no—
107#946—31no—
108#938—31no—
109#938—31no—
110#937—61no—
111#935—61no—
112#930—31no—
113#930—31no—
114#929—61no—
115C4×#67—61no—
116C4×#67—61no—
117C4×#67—61no—
118C4×#67—61no—
119C2×(C2×D3)⋊C4—21no—
120#926—31no—
121#926—31no—
122#926—61no—
123#924—31no—
124#924—31no—
125C2×C4×Dic3C2×D311yescharacteristic
126C2×#208—31no—
127C2×#208—31no—
128C2×#208—61no—
129C2×#208—61no—
130C2×#208—62no—
131C2×#208—62no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8—61no—
134D3×M16—62no—
135D3×M16—62no—
136C2×ΓL(1,𝔽25)—61no—
137C2×D3×C8—61no—
138C3×#104—62no—
139C3×#95—61no—
140#837—62no—
141C3⋊#95—21no—
142#805—22no—
143#805—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×C4—22no—
153C2×C32×C4—41no—
154C2×C32×C4—41no—
155C2×C32×C4C22×C411yescharacteristic
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4#4111yescharacteristic
160C2×C32×C4#4111yescharacteristic
161C2×C3⋊Dic3—21no—
162C2×C3⋊Dic3—21no—
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—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—22no—
191C22×M16—91no—
192#525—91no—
193C2×#104—31no—
194C2×#104—91no—
195C4×C22⋊C4—31no—
196#339—91no—
197#339—91no—
198C24×C3—31no—
199C23×D3#6711yescharacteristic
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—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—41no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4—61no—
221C22×C3×C4—61no—
222C22×C3×C4C22×D311yescharacteristic
223C22×C3×C4C22×D311yescharacteristic
224C2×#67—21no—
225C2×#67—61no—
226C2×#67—61no—
227C2×#67—61no—
228C2×#67—61no—
229C22×Dic3—21no—
230C22×Dic3#6711yescharacteristic
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×D3D1211yescharacteristic
244C2×C4×D3D1211yescharacteristic
245C2×Dic6C4×D311yescharacteristic
246C3×M16—32no—
247C3×M16—61no—
248C2×C3×C8—61no—
249C3×C22⋊C4—64no—
250C3×C42—22no—
251C3×C42—21no—
252C3×C42—21no—
253C3×C42—21no—
254C3×C42—21no—
255C3×C42—41no—
256C3×C42—61no—
257C3×C42—61no—
258#217—61no—
259#217—61no—
260#217—61no—
261#217—61no—
262#217—61no—
263#217—61no—
264#217—121no—
265(C2×D3)⋊C4—24no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—61no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—61no—
270C4⋊Dic3—31no—
271C4⋊Dic3—31no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276Dic3⋊C4—61no—
277Dic3⋊C4—61no—
278Dic3⋊C4—61no—
279Dic3⋊C4—61no—
280C4×Dic3—21no—
281C4×Dic3—21no—
282C4×Dic3—61no—
283C4×Dic3—61no—
284C4×Dic3—121no—
285#208—21no—
286#208—32no—
287#208—32no—
288#208—62no—
289#208—64no—
290#208—61no—
291#208—61no—
292#208—121no—
293#208#6712yescomplemented
294C2×C3⋊C8—21no—
295C2×C3⋊C8—64no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—61no—
298C2×C3⋊C8—121no—
299ΓL(1,𝔽25)—64no—
300D3×C8—64no—
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×C4—42no—
318C32×C4C4×D411yescharacteristic
319C32×C4C4×D411yescharacteristic
320C32×C4#12011yescharacteristic
321C32×C4#12311yescharacteristic
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—91no—
332C2×M16—181no—
333C2×M16—182no—
334C2×M16—182no—
335C22×C8—181no—
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—61no—
346C2×C42—31no—
347C2×C42D3211yescharacteristic
348#104—62no—
349#104—182no—
350#95—61no—
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×C3D3×D411yescharacteristic
360C23×C3C2×#6711yescharacteristic
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—22no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—31no—
383C2×C3×C4—31no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—61no—
396C2×C3×C4—61no—
397C2×C3×C4—61no—
398C2×C3×C4—61no—
399C2×C3×C4—61no—
400C2×C3×C4—61no—
401C2×C3×C4—62no—
402C2×C3×C4—61no—
403C2×C3×C4—121no—
404C2×C3×C4—121no—
405C2×C3×C4—121no—
406C2×C3×C4—121no—
407C2×C3×C4C2×C4×D311yescharacteristic
408C2×C3×C4C2×C4×D311yescharacteristic
409C2×C3×C4C2×D1211yescharacteristic
410C2×C3×C4#23511yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D411yescharacteristic
414C2×C3×C4D3×D411yescharacteristic
415C2×C3×C4#23711yescharacteristic
416C2×C3×C4#23711yescharacteristic
417C2×C3×C4#23711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419#67—41no—
420#67—41no—
421#67—122no—
422#67—122no—
423#67—122no—
424#67—122no—
425C2×Dic3—21no—
426C2×Dic3—21no—
427C2×Dic3—22no—
428C2×Dic3—21no—
429C2×Dic3—41no—
430C2×Dic3—41no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
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—62no—
454C3⋊C8—22no—
455C3⋊C8—62no—
456C3⋊C8—62no—
457C3⋊C8—122no—
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—21no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4C2×D3211yescharacteristic
489M16—32no—
490M16—61no—
491M16—92no—
492M16—184no—
493M16—181no—
494C2×C8—61no—
495C2×C8—184no—
496C2×C8—181no—
497C4⋊C4—91no—
498C4⋊C4—91no—
499C4⋊C4—181no—
500C4⋊C4—181no—
501C22⋊C4—64no—
502C22⋊C4—181no—
503C22⋊C4—181no—
504C22⋊C4—181no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C42—21no—
508C42—21no—
509C42—61no—
510C42—61no—
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#93811yescharacteristic
536C22×C3#93911yescharacteristic
537C22×C3#93911yescharacteristic
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#80512yescomplemented
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—42no—
554C3×C4—42no—
555C3×C4—44no—
556C3×C4—61no—
557C3×C4—61no—
558C3×C4—122no—
559C3×C4—121no—
560C3×C4#67⋊C411yescharacteristic
561C3×C4#67⋊C411yescharacteristic
562C3×C4#67⋊C411yescharacteristic
563C3×C4#88211yescharacteristic
564C3×C4#88311yescharacteristic
565C3×C4#88611yescharacteristic
566C3×C4C4×#6711yescharacteristic
567C3×C4#93711yescharacteristic
568Dic3—21no—
569Dic3—21no—
570Dic3—42no—
571Dic3—41no—
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×#6711yescharacteristic
587Q8—61no—
588Q8—61no—
589D4—61no—
590D4—61no—
591D4—121no—
592D4—121no—
593D4—362no—
594D4—362no—
595C2×C4—22no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—61no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—61no—
604C2×C4—61no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—61no—
610C2×C4—62no—
611C2×C4—61no—
612C2×C4—121no—
613C2×C4—121no—
614C2×C4—121no—
615C2×C4—121no—
616C2×C4—181no—
617C2×C4—181no—
618C2×C4#379511yescharacteristic
619C2×C4C4×D3211yescharacteristic
620C2×C4D3×D1211yescharacteristic
621C2×C4#380211yescharacteristic
622C2×C4#380511yescharacteristic
623C2×C4D3×#6711yescharacteristic
624C8—62no—
625C8—182no—
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×C3C2×#80511yescharacteristic
641C2×C3#495611yescharacteristic
642C2×C3#495811yescharacteristic
643C2×C3#500511yescharacteristic
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#6388511yescharacteristic
661C22D3×(C2×D3)⋊C411yescharacteristic
662C22#6397011yescharacteristic
663C4—42no—
664C4—61no—
665C4—61no—
666C4—122no—
667C4—121no—
668C4—361no—
669C4—361no—
670C4#6387911yescharacteristic
671C4#6389111yescharacteristic
672C4#6390211yescharacteristic
673C4#6392211yescharacteristic
674C3—21no—
675C3#6945311yescharacteristic, complemented
676C3#7038111yescharacteristic, complemented
677C2—21no—
678C2—21no—
679C2—62no—
680C2—121no—
681C2—241no—
682C2D3×#80511yescharacteristic
683C2#1059039211yescharacteristic
684C2#1059136311yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595022C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1871
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D3×#208C2semidirect
3. C3×C4×(C2×D3)⋊C4C2semidirect
4. C2×C3×#805C2semidirect
5. C2×#63569C2semidirect
6. #10589389C2semidirect
7. #10589162C2semidirect
20. #63908C4semidirect
21. #63908C4semidirect
24. #63856C4semidirect
25. #63856C4semidirect
40. C4×(C2×D3)⋊C4D3semidirect
42. C2×#805D3semidirect
78. #3748D4semidirect
84. C3×#208D4semidirect
293. #208#67semidirect
316. C2×C3×D3#104semidirect
548. C2×D3#805semidirect
578. C32#1871semidirect
675. C3#69453semidirect
676. C3#70381semidirect

Maximal subgroups

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

subgroupindex
#105950222
C2×D3×#2082
C3×C4×(C2×D3)⋊C42
C2×C3×#8052
C2×#635692
#105893892
#105891622
#703813
#694533