Finite Group Databasebeta

← #11788316

Subgroups — #11788316

Order 1152.

873 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#938C211yesmaximal, characteristic
2C2×D3×#208C211yesmaximal, characteristic, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4C2×C3×#833C211yesmaximal, characteristic, complemented
5#10591069C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71683—31nomaximal
9#70081—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67C412yes—
12C22×C3×C4×D3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#217C412yes—
16C3×#938—21no—
17C3×#938—21no—
18C3×#938—21no—
19C3×#938—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23C2×#3711—21no—
24D3×#208—22no—
25D3×#208—22no—
26C2×D3×C3⋊C8—21no—
27#63660—22no—
28C3×#833—22no—
29(C2×D3)⋊(C3⋊C8)—21no—
30(C2×D3)⋊(C3⋊C8)—21no—
31C2×C3×#121—31no—
32C2×#938D311yescharacteristic
33C22×#208—31no—
34C2×D3×M16—31no—
35C2×C3×#100—31no—
36C2×#833—31no—
37C2×#833—31no—
38C2×#833—61no—
39C2×#833D311yescharacteristic, complemented
40#5207—31no—
41#5126—31no—
42#4554—31no—
43#4554—31no—
44#4530—31no—
45#4530—31no—
46C24×C32C2×C412yes—
47C23×C3×D3C2×C411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C2×C32×D4—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C3×#67—22no—
56C2×C3×#67—22no—
57C2×C3×#67—44no—
58C22×C3×Dic3C2×C411yescharacteristic
59C22×C3×Dic3C2×C412yes—
60C2×C3×C4×D3—21no—
61C2×C3×C4×D3—21no—
62C2×C3×C4×D3—21no—
63C2×C3×C4×D3—21no—
64C2×C3×C4×D3D411yescharacteristic
65C2×C3×C4×D3D411yescharacteristic
66C2×C3×C4×D3D411yescharacteristic
67C2×C3×C4×D3D411yescharacteristic
68#3748—21no—
69#3748—21no—
70#3748—21no—
71#3748D412yescomplemented
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C3×#217—22no—
75C3×#217—22no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×#208—21no—
79C3×#208—21no—
80C3×#208—21no—
81C3×#208D412yescomplemented
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84#3711—24no—
85D3×C3⋊C8—24no—
86#1900—91noSylow
87C22×C3×D4—21no—
88C22×C3×D4—32no—
89C22×C3×D4C2×D311yescharacteristic
90C22×C3×D4C2×D311yescharacteristic
91C23×C3×C4—31no—
92C22×#67Dic312yes—
93C22×C4×D3C2×D311yescharacteristic
94C2×C3×M16—31no—
95C2×C3×M16—31no—
96C3×#121—61no—
97C3×#121—61no—
98C3×#121—61no—
99C3×#121—61no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—32no—
102C2×#217Dic312yes—
103#938—21no—
104#938—21no—
105#938—21no—
106#938—21no—
107C2×C4⋊Dic3C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208—61no—
114C2×#208—61no—
115C2×#208—62no—
116C2×#208—62no—
117C2×#208C2×D311yescharacteristic
118C2×#208C2×D311yescharacteristic
119C22×C3⋊C8—61no—
120D3×M16—62no—
121D3×M16—62no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—61no—
124C3×#100—62no—
125#833—22no—
126#833—62no—
127#833—62no—
128#833—64no—
129#830—61no—
130#830—61no—
131(C2×D3)⋊C8—61no—
132(C2×D3)⋊C8—61no—
133C23×C32—22no—
134C23×C32—22no—
135C23×C32—22no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C22×C411yescharacteristic
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—22no—
142C22×C3×D3—41no—
143C22×C3×D3C22⋊C411yescharacteristic
144C22×C3×D3C22⋊C411yescharacteristic
145C32×D4—41no—
146C32×D4—41no—
147C32×D4—41no—
148C32×D4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4#4111yescharacteristic
154C2×C32×C4#4111yescharacteristic
155C3×#67—44no—
156C3×#67—44no—
157C2×C3×Dic3—21no—
158C2×C3×Dic3—21no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C22⋊C411yescharacteristic
162C2×C3×Dic3C22⋊C411yescharacteristic
163C3×C4×D3—21no—
164C3×C4×D3—21no—
165C3×C4×D3—21no—
166C3×C4×D3—21no—
167C3×C4×D3—21no—
168C3×C4×D3—21no—
169C3×C4×D3—21no—
170C3×C4×D3—21no—
171C3⋊(C3⋊C8)—22no—
172C3⋊(C3⋊C8)—41no—
173C3×C3⋊C8—22no—
174C3×C3⋊C8—41no—
175C22×M16—91no—
176C2×#121—31no—
177C2×#100—31no—
178C2×#100—91no—
179#407—91no—
180#343—91no—
181#343—91no—
182C24×C3—22no—
183C24×C3—31no—
184C24×C3C4×D312yes—
185C24×C3C2×Dic312yes—
186C23×D3C2×Dic311yescharacteristic
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—21no—
199C2×C3×D4—21no—
200C2×C3×D4—21no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4—41no—
205C2×C3×D4—62no—
206C2×C3×D4—62no—
207C2×C3×D4—124no—
208C22×C3×C4—21no—
209C22×C3×C4—31no—
210C22×C3×C4—31no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—32no—
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—22no—
222C2×#67—22no—
223C2×#67—44no—
224C22×Dic3C2×Dic311yescharacteristic
225C22×Dic3C2×Dic312yes—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3#6711yescharacteristic
231C2×C4×D3#6711yescharacteristic
232C2×C4×D3#6711yescharacteristic
233C2×C4×D3#6711yescharacteristic
234C3×M16—32no—
235C3×M16—61no—
236C3×M16—61no—
237C3×M16—61no—
238C2×C3×C8—61no—
239C2×C3×C8—61no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4—61no—
242C3×C22⋊C4—62no—
243C3×C22⋊C4—62no—
244#217—22no—
245#217—22no—
246C4⋊Dic3—21no—
247C4⋊Dic3—21no—
248#208—21no—
249#208—21no—
250#208—21no—
251#208—32no—
252#208—32no—
253#208—62no—
254#208—64no—
255#208—61no—
256#208—61no—
257#208—62no—
258#208—61no—
259#208—61no—
260#208—61no—
261#208—61no—
262#208—121no—
263#208—121no—
264#208#6712yescomplemented
265C2×C3⋊C8—21no—
266C2×C3⋊C8—21no—
267C2×C3⋊C8—64no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8—61no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—121no—
273C2×C3⋊C8—121no—
274ΓL(1,𝔽25)—64no—
275D3×C8—64no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—42no—
279C22×C32—42no—
280C22×C32—42no—
281C22×C32—82no—
282C22×C32—82no—
283C22×C32C2×C22⋊C411yescharacteristic
284C22×C32C4×D411yescharacteristic
285C22×C32C4×D411yescharacteristic
286C2×C3×D3—21no—
287C2×C3×D3—21no—
288C2×C3×D3—21no—
289C2×C3×D3—21no—
290C2×C3×D3—21no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3#10012yescomplemented
294C32×C4#12011yescharacteristic
295C32×C4#12111yescharacteristic
296C32×C4#12111yescharacteristic
297C32×C4#12311yescharacteristic
298C3×Dic3—21no—
299C3×Dic3—21no—
300C3×Dic3—42no—
301C22×D4—32no—
302C22×D4D3211yescharacteristic
303C23×C4—31no—
304C2×M16—31no—
305C2×M16—31no—
306C2×M16—91no—
307C2×M16—91no—
308C2×M16—181no—
309C2×M16—182no—
310C2×M16—182no—
311C22×C8—181no—
312#121—61no—
313#121—61no—
314#121—61no—
315#121—61no—
316C2×C4⋊C4—31no—
317C2×C22⋊C4—32no—
318#100—62no—
319#100—182no—
320C22⋊C8—181no—
321C22⋊C8—181no—
322C23×C3—24no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—31no—
331C23×C3—31no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—62no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—82no—
342C23×C3—82no—
343C23×C3—121no—
344C23×C3C2×C4×D311yescharacteristic
345C23×C3C22×Dic311yescharacteristic
346C22×D3—21no—
347C22×D3—21no—
348C22×D3—22no—
349C22×D3—41no—
350C22×D3#21711yescharacteristic
351C22×D3#21711yescharacteristic
352C3×D4—42no—
353C3×D4—42no—
354C3×D4—42no—
355C3×D4—42no—
356C3×D4—41no—
357C3×D4—41no—
358C3×D4—41no—
359C3×D4—41no—
360C3×D4—41no—
361C3×D4—41no—
362C3×D4—41no—
363C3×D4—41no—
364C3×D4—124no—
365C3×D4—124no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—31no—
373C2×C3×C4—31no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—61no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—61no—
380C2×C3×C4—61no—
381C2×C3×C4—61no—
382C2×C3×C4—61no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—122no—
386C2×C3×C4#23511yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4#23711yescharacteristic
393C2×C3×C4#23711yescharacteristic
394C2×C3×C4#23711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398#67—44no—
399#67—44no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—22no—
403C2×Dic3—42no—
404C2×Dic3#21711yescharacteristic
405C2×Dic3#21711yescharacteristic
406C4×D3—21no—
407C4×D3—21no—
408C4×D3—21no—
409C4×D3—21no—
410C4×D3—21no—
411C4×D3—21no—
412C4×D3—21no—
413C4×D3—21no—
414C3×C8—62no—
415C3×C8—121no—
416C3⋊C8—22no—
417C3⋊C8—41no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C3⋊C8—122no—
421C3⋊C8—122no—
422C3⋊C8—121no—
423C3⋊C8—121no—
424C2×C32—21no—
425C2×C32—21no—
426C2×C32—82no—
427C2×C32#38611yescharacteristic
428C2×C32C2×#10011yescharacteristic
429C2×C32#41311yescharacteristic
430C3×D3—22no—
431C3×D3—41no—
432C24—31no—
433C24D3×Dic312yes—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—62no—
441C2×D4—62no—
442C2×D4—124no—
443C22×C4—31no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—32no—
449C22×C4—61no—
450C22×C4—61no—
451C22×C4—61no—
452C22×C4—61no—
453C22×C4C2×D3211yescharacteristic
454M16—32no—
455M16—61no—
456M16—61no—
457M16—61no—
458M16—92no—
459M16—184no—
460M16—181no—
461M16—181no—
462M16—181no—
463C2×C8—61no—
464C2×C8—61no—
465C2×C8—184no—
466C2×C8—181no—
467C2×C8—181no—
468C4⋊C4—61no—
469C4⋊C4—61no—
470C22⋊C4—62no—
471C22⋊C4—62no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—32no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—44no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—61no—
490C22×C3—61no—
491C22×C3—61no—
492C22×C3—61no—
493C22×C3—61no—
494C22×C3—82no—
495C22×C3—82no—
496C22×C3—82no—
497C22×C3—82no—
498C22×C3—82no—
499C22×C3—82no—
500C22×C3—84no—
501C22×C3—84no—
502C22×C3—122no—
503C22×C3—122no—
504C22×C3D3×C22⋊C411yescharacteristic
505C22×C3#67⋊C411yescharacteristic
506C22×C3C4×#6711yescharacteristic
507C22×C3D4×Dic311yescharacteristic
508C22×C3D4×Dic311yescharacteristic
509C22×C3C2×#21711yescharacteristic
510C2×D3—21no—
511C2×D3—21no—
512C2×D3—21no—
513C2×D3—21no—
514C2×D3—21no—
515C2×D3—42no—
516C2×D3—42no—
517C2×D3#83312yescomplemented
518C3×C4—21no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—61no—
523C3×C4—61no—
524C3×C4—122no—
525C3×C4#88311yescharacteristic
526C3×C4#88411yescharacteristic
527C3×C4#93511yescharacteristic
528C3×C4#93711yescharacteristic
529C3×C4#93711yescharacteristic
530C3×C4#93811yescharacteristic
531C3×C4#93911yescharacteristic
532C3×C4#93911yescharacteristic
533Dic3—21no—
534Dic3—21no—
535Dic3—42no—
536C32#190011yescharacteristic, complemented, Sylow
537C23—22no—
538C23—22no—
539C23—22no—
540C23—31no—
541C23—31no—
542C23—42no—
543C23—42no—
544C23—62no—
545C23—61no—
546C23—61no—
547C23—121no—
548C23C2×D3×Dic311yescharacteristic
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—124no—
554D4—124no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—122no—
569C2×C4#380411yescharacteristic
570C2×C4#380511yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4#381111yescharacteristic
575C8—62no—
576C8—121no—
577C8—182no—
578C8—361no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—41no—
587C2×C3—41no—
588C2×C3—62no—
589C2×C3—84no—
590C2×C3—82no—
591C2×C3—82no—
592C2×C3—121no—
593C2×C3D3×#10011yescharacteristic
594C2×C3#474511yescharacteristic
595C2×C3#495611yescharacteristic
596C2×C3C2×#83311yescharacteristic
597C2×C3#522011yescharacteristic
598C2×C3#523711yescharacteristic
599D3—22no—
600D3—41no—
601C22—21no—
602C22—21no—
603C22—32no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—61no—
608C22—61no—
609C22—61no—
610C22—61no—
611C22—61no—
612C22—82no—
613C22—82no—
614C22—122no—
615C22—122no—
616C22D3×#21711yescharacteristic
617C22Dic3×#6711yescharacteristic
618C22#67⋊Dic311yescharacteristic
619C4—61no—
620C4—61no—
621C4—122no—
622C4#6396911yescharacteristic
623C4#6397011yescharacteristic
624C4#6397111yescharacteristic
625C4#6398311yescharacteristic
626C3—21no—
627C3#7008111yescharacteristic, complemented
628C3#7168311yescharacteristic, complemented
629C2—21no—
630C2—21no—
631C2—62no—
632C2—82no—
633C2—121no—
634C2D3×#83311yescharacteristic
635C2#1059150111yescharacteristic
636C2#1059172111yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#938C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1900
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×#208C2semidirect
3. C2×#63660C2semidirect
4. C2×C3×#833C2semidirect
5. #10591069C2semidirect
6. #10589167C2semidirect
7. #10589167C2semidirect
39. C2×#833D3semidirect
71. #3748D4semidirect
81. C3×#208D4semidirect
264. #208#67semidirect
293. C2×C3×D3#100semidirect
517. C2×D3#833semidirect
536. C32#1900semidirect
627. C3#70081semidirect
628. C3#71683semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9382
C2×D3×#2082
C2×#636602
C2×C3×#8332
#105910692
#105891672
#716833
#700813